Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022: EASEC-17, Singapore 981197330X, 9789811973307

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Lecture Notes in Civil Engineering

Guoqing Geng Xudong Qian Leong Hien Poh Sze Dai Pang   Editors

Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022 EASEC-17, Singapore

Lecture Notes in Civil Engineering Volume 302

Series Editors Marco di Prisco, Politecnico di Milano, Milano, Italy Sheng-Hong Chen, School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China Ioannis Vayas, Institute of Steel Structures, National Technical University of Athens, Athens, Greece Sanjay Kumar Shukla, School of Engineering, Edith Cowan University, Joondalup, WA, Australia Anuj Sharma, Iowa State University, Ames, IA, USA Nagesh Kumar, Department of Civil Engineering, Indian Institute of Science Bangalore, Bengaluru, Karnataka, India Chien Ming Wang, School of Civil Engineering, The University of Queensland, Brisbane, QLD, Australia

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Guoqing Geng · Xudong Qian · Leong Hien Poh · Sze Dai Pang Editors

Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022 EASEC-17, Singapore

Editors Guoqing Geng Department of Civil and Environmental Engineering National University of Singapore Singapore, Singapore

Xudong Qian Department of Civil and Environmental Engineering National University of Singapore Singapore, Singapore

Leong Hien Poh Department of Civil and Environmental Engineering National University of Singapore Singapore, Singapore

Sze Dai Pang Department of Civil and Environmental Engineering National University of Singapore Singapore, Singapore

ISSN 2366-2557 ISSN 2366-2565 (electronic) Lecture Notes in Civil Engineering ISBN 978-981-19-7330-7 ISBN 978-981-19-7331-4 (eBook) https://doi.org/10.1007/978-981-19-7331-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Local Organizing Committee

Professor Liew Jat Yuen Richard (Advisor), National University of Singapore Associate Professor Qian Xudong (Chair), National University of Singapore Associate Professor Pang Sze Dai (Co-chair), National University of Singapore Associate Professor Poh Leong Hien (Secretary), National University of Singapore Assistant Professor Geng Guoqing (Conference Program Chair), National University of Singapore Dr Du Hongjian (Treasurer), National University of Singapore Dr Justin Yeoh Ker-Wei, National University of Singapore Assistant Professor He Xiaogang, National University of Singapore Assistant Professor Pearl Li Yuzhu, National University of Singapore Assistant Professor Gary Lei Jiarui, National University of Singapore Professor Tan Kiang Hwee, National University of Singapore Associate Professor Vincent Tan, National University of Singapore Dr Kevin Kuang Sze Chiang, National University of Singapore Dr Kong Kian Hau, National University of Singapore Professor Tan Kang Hai, Nanyang Technological University

v

Scientific Committee

Ippei Maruyama, Professor, Tokyo University Hongyu Nick Zhou, Assistant Professor, The University of Tennessee, Knoxville Zuhua Zhang, Professor, Hunan University Kemal Celik, Assistant Professor, NYU Abu Dhabi Enhua Yang, Associate Professor, Nanyang Technological University Jinyang Jiang, Professor, Southeast University Xin Nie, Associate Professor, Tsinghua University Juhyuk Moon, Associate Professor, Seoul National University Wenhui Duan, Professor, Monash University Manu Santhanam, Professor, Indian Institute of Technology Madras Zhang Dongming, Professor, Tongji University Xiao Jianzhuang, Professor, Tongji University Zhang Yunsheng, Professor, Lanzhou University of Technology Wang Qiang, Associate Professor, Tsinghua University Jay Sanjayan, Professor, Swinburne University of Technology Zhang Yamei, Professor, Southeast University Yang Jian, Professor, Shanghai Jiao Tong University Giang Nguyen, Associate Professor, The University of Adelaide Indra Vir Singh, Professor, Indian Institute of Technology Roorkee Tak Ming Chan, Associate Professor, The Hongkong Polytechnic University Vinh Dao, Lecturer, University of Queensland Lihai Zhang, Associate Professor, University of Melbourne Johnny Ho, Professor, Guangzhou University Gang Shi, Professor, Tsinghua University Wei Wang, Professor, Tongji University Yuanfeng Duan, Professor, Zhejiang University Justin Yeoh, Lecturer, National University of Singapore Shunzhi Qian, Associate Professor, Nanyang Technological University Yan Jiabao, Professor, Tianjin University Huang Zhenyu, Associate Professor, Shenzhen University Cao Hongyou, Professor, Wuhan University of Technology vii

viii

Scientific Committee

Fang Yihai, Assistant Professor, Monash University Benny Raphael, Professor, Indian Institute of Technology Madras Lu Yujie, Professor, Tongji University Alexander Lin, Lecturer, National University of Singapore Wang Qian, Assistant Professor, National University of Singapore Vincent Gan, Assistant Professor, National University of Singapore Adrian Chong, Assistant Professor, National University of Singapore Mark Gan, Associate Director of CDTL, National University of Singapore

EASEC International Steering Committee

Prof. S. Kitipornchai, Chairman Emeritus, University of Queensland, Australia Prof. Y. Fujino, Chairman Emeritus, Japan Prof. Y. B. Yang, Chairman Emeritus, Taiwan Prof. W. Kanok-Nukulchai, Chairman Emeritus, Thailand Prof. T. Ueda, Chairman, Hokkaido University, Japan Prof. C. M. Wang, Deputy Chairman, University of Queensland, Australia Prof. L. J. Leu, Deputy Chairman, National Taiwan University, Taiwan Dr. H. F. Lam, Secretary General, City University of Hong Kong, Hong Kong Prof. Hong Hao, Member, Curtin University, Australia Prof. Y. C. Loo, Member, School of Engineering and Built Environment, Griffith University, Australia Dr. Vinh Dao, Member, University of Queensland, Australia Prof. Hong Guan, Member, Griffith University, Australia Prof. S. O. Cheung, Member, City University of Hong Kong, Hong Kong Dr. D. Hoedajanto, Member, Indonesian Society of Civil and Structural Engineers (HAKI), Indonesia Prof. K. Maekawa, Member, Japan Prof. T. Matsumoto, Member, Hokkaido University, Japan Prof. Y. Okui, Member, Saitama University, Japan Prof. J. Niwa, Member, Tokyo Institute of Technology, Japan Prof. Wan Hamidon, Member, Universiti Kebangsaan Malaysia, Malaysia Prof. Y. Y. Chen, Member, Tongji University, P. R. China Prof. L. M. Sun, Member, Tongji University, P. R. China Prof. L. P. Yeh, Member, Tsinghua University, P. R. China Prof. L. H. Han, Member, Tsinghua University, P. R. China Prof. Jiping Hao, Member, Xi’an University of Architecture and Technology, P. R. China Prof. Johnny Ho, Member, Guangzhou University, P. R. China Prof. T. C. Pan, Member, Nanyang Technological University, Singapore Prof. Ser Tong QUEK, Member, Head of CEE Department at NUS, Singapore Prof. Jung Sik Kong, Member, Korea University, South Korea ix

x

EASEC International Steering Committee

Prof. Jae-Yeol Cho, Member, Seoul National University, South Korea Prof. C. S. Chen, Member, National Taiwan University, Taiwan Prof. P. Warnitchai, Member, Thailand Prof. Pruettha Nanakorn, Member, Sirindhorn International Institute of Technology, Thailand Prof. José L. Torero, Member, University of College London, UK Dr. G. Chiu, Member, USA Mr Steve Baldridge, Member, Baldridge & Associates Structural Engineering, Inc., USA Prof. N. Hoang, Member, Ho Chi Minh City University of Technology, Vietnam

Contents

Sustainable Binding Materials Study of Methods for Improving Strength and Durability of Low-Quality Recycled Aggregate Concrete . . . . . . . . . . . . . . . . . . . . . . . R. Yuya, N. Matsuda, M. Kojima, and T. Iyoda A Study on Strength and Durability of Mortar Using Low-quality Recycled Fine Aggregate with Accelerated Carbonation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y. Inoue, N. Matsuda, Y. Nishioka, and T. Iyoda Experimental Study to Improve Performance of Two-Stage Concrete Without Injection Focusing on the Interfacial Transition Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Karen Midori Masunaga, Tomoki Nagoya, and Takeshi Iyoda Application of Granite Fines to Substitute Sand in Concrete Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shunzhi Qian, Kang Hai Tan, Ziyang Li, Namyo Salim Lim, Lu Jinping, and Wong Sook Fun Effects of Various Ions in Seawater on Chloride Ion Behavior in Mortar Using Ground Granulated Blast-Furnace Slag . . . . . . . . . . . . . Takuma Nakada, Yuko Ogawa, Kenji Kawai, and Riya Catherine George

3

16

24

36

46

Advanced and Sustainable Concrete Materials Carbonation of Granite Fines Concrete in the Tropical Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ni Zhen and Xudong Qian

55

xi

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Contents

Carbonation Resistance of Portland Blast Furnace Slag Cement Type B Concrete Internally Cured by Using Roof-Tile Waste Aggregate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yusuke Inoue, Yuko Ogawa, Kenji Kawai, and Riya Catherine George

68

Strength Characteristics of Blast-Furnace Cement Mortar with Silicate-Type Surface Penetrants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kei Futagami, Takuya Kondo, and Katsunori Yokoi

77

Three-Dimensional Mesoscopic Modelling of Concrete Confined by FRP Under Static and Dynamic Loading . . . . . . . . . . . . . . . . . . . . . . . . . Nyembo Ya Lumbu Lars and Jinhua Zhang

87

Seismic Resilient Structures Development of Energy Dissipation Walls with Oil Dampers and Totally Reinforced Support Members Using Pre-stress . . . . . . . . . . . R. Sakamoto, K. Matsuda, and S. Hanai

101

Comparative Numerical Study on Efficiency of Various Energy Dissipating Devices Used in Hybrid Post-tensioned Shear Wall . . . . . . . . Shubham Tiwari, S. R. Dash, and G. Mondal

116

Three-Dimensional FEM Simulation of Hysteretic Performance of Traditional Chinese Dou-Gong Connections . . . . . . . . . . . . . . . . . . . . . . Xiaogang Zhang, Xiaobin Song, and Jingliang Dong

133

Research on Seismic Behavior of CFT-Frame-Buckling Restrained Steel Plate Shear Wall Structures Using Recycled Aggregate Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Amer Mohammed, Yansheng Du, Zhihua Chen, and Jin Huang Seismic Response Mitigation of Atrium Buildings with Truss-IMD System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Siyuan Li and Yung-Tsang Chen Seismic Performance of Isolated Liquid Storage Tanks Supplemented with Negative Stiffness and Inerter Based Dampers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Naqeeb Ul Islam and R. S. Jangid Experimental Study on Seismic Behavior of Liquid Storage Tanks Subjected to Vertical Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Y. Wu, Q. Q. Yu, and X. L. Gu

140

152

169

187

Resilience of Steel and Composite Structures Axial Behavior and Design of High-Strength Rectangular Concrete-Filled Steel Tube Long Columns . . . . . . . . . . . . . . . . . . . . . . . . . . Zhichao Lai, Jie Yan, and Dong Li

199

Contents

xiii

On the Accurate Strain Measurement in Split Hopkinson Tensile Bar Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cheng Chen and Xudong Qian

215

Adaptive Fatigue Assessment of Welded Plate Joints Based on Crack Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liuyang Feng, Xudong Qian, and Wei Zhang

223

Experimental Study on a Novel Sandwich Panel Under Repeated Impact Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wei Zhang and Zhenyu Huang

236

Smart Construction and Management Readiness and Potential Application of Smart Contracts in the Indonesian Construction Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kartika Wulandary, Kriengsak Panuwatwanich, and Michael Henry Construction Process Simulation Facing Digital Twin . . . . . . . . . . . . . . . . M. S. Dong, B. Yang, Y. L. Han, S. S. Jiang, and B. D. Liu Establishment and Application of Multi-agent Simulation System Based on On-Site Construction Performers . . . . . . . . . . . . . . . . . . B. D. Liu, B. Yang, Yilong Han, J. Z. Xiao, and M. S. Dong Digital Fabrication for DfMA of a Prefabricated Bridge Pier . . . . . . . . . T. K. Kim, D. C. Nguyen, and C. S. Shim Study on the Open Data System for Infrastructure Maintenance and Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Junha Hwang, Kei Kawamura, and Shuji Sawamura Road Development Risks and Challenges in the Philippines . . . . . . . . . . Kenneth Edward Torrella Fernando and Michael Henry

249 264

284 305

311 326

Teaching and Learning During and After Pandemic Understanding Sustainability Practices Through Sustainability Reports and Its Impact on Organizational Financial Performance . . . . . Mavian Xin Yi Tay and Stephen En Rong Tay Broadening the Perspective of the Roles of Civil Engineers – A Freshmen Module on How Engineers Solve Real-World Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kevin Sze Chiang Kuang and Weng Tat Chan SafeSim Design: A Digital Game-Based Learning Approach to Address Design for Safety (DfS) Competency . . . . . . . . . . . . . . . . . . . . . Sufiana Safiena, Juliana Tay, Yang Miang Goh, and Michelle Lim

343

353

360

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Contents

Identification of Critical Factors Influencing Students’ Engagement and Satisfaction of Online Live Learning in Higher Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lei Zhu, Lina Zhang, and Guifeng Zhu Preliminary Implementation of Adaptive Learning for Teaching Structural Systems to Non-engineering Students . . . . . . . . . . . . . . . . . . . . Xinping Hu, Yang Miang Goh, Alexander Lin, and Qizhang Liu

373

388

Resilient Infrastructural Solutions Analysis of the Clearance Time of Roadblock Events Caused by Geohazards in Bhutan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dhan Raj Chhetri and Michael Henry

403

Research on Cumulative Plastic Deformation of the Soft Clay Under Cyclic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xubing Xu, Zhendong Cui, and Yonglai Zheng

416

Improved Vehicle Scanning Method for Bridge Damage Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. S. Yang, C. M. Wang, and W. H. Duan

426

Positioning Accuracy Comparison of RTK Receivers Used for Disaster Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Toru Yamano, Kai Kiriyama, Osamu Okamoto, and Kei Kawamura

437

Corrosive Behavior of Structural Steel and Hot Dipped Galvanized Steel in the Central Part of Thailand by Atmospheric Exposure Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bunya Chea, Taweep Chaisomphob, and Takashi Matsumoto

448

High Performance Materials and Structures Experimental Investigation of Circular Reinforced Concrete Columns Exposed to Elevated Temperatures . . . . . . . . . . . . . . . . . . . . . . . . Jia Xu and Riyad Aboutaha

461

Mechanical Model for Parallel-to-Grain Withdrawal Failure of Self-tapping Screws in Glulam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lijing Fang, Wenjun Qu, and Shengdong Zhang

469

Behaviors of Steel-Concrete Composite Structures at Cold-Region Low Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jia-Bao Yan and Jian Xie

482

Development of Novel Sigma-shaped Self-locking Inter-modular Joints for Robust Modular Steel Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . Kashan Khan, Zhihua Chen, Xingwang Liu, Jia-Bao Yan, and Jiadi Liu

491

Contents

Shear Performance of Interface Between Normal Concrete and Ultra-high Performance Concrete in Cryogenic Circumstance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yujie Chen, Jian Xie, Ercong Kang, and Chenglong Tong

xv

506

Effects of Arctic Low Temperatures and Freeze-Thaw Cycles on Mechanical Properties of Ultra-high Performance Concrete . . . . . . . Ercong Kang, Jian Xie, Jiabao Yan, and Jing Tang

515

Compressive Behavior of High Strength Steel Wire-Mesh Reinforced Concrete Filled Steel Tubular Columns . . . . . . . . . . . . . . . . . . Fangyuan Gao, Mingxiang Xiong, and Fengming Ren

525

Prefabricated Construction and Composite Structures Numerical Study on Out-of-Plane Mechanical Performance of New Type Precast Shear Wall with Unspliced Vertical Distribution Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qiang Fu, Zhiwei Cao, and Heng Dong

533

Lightweight and Advance Precast Concrete System for Modular Building Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Junxuan Wang, Kian Hau Kong, and J. Y. Richard Liew

545

Study of Initial Imperfection of Concrete-Filled Square Steel Tube Columns for Direct Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zijuan Zhang, Jiale Xing, Yao-Peng Liu, and Guochang Li

565

Nonlinear Coupled Thermal-Structural Analysis of Monolithic and Precast Concrete Corbel Beam-to-Column Connection . . . . . . . . . . . Noor Azim Mohd. Radzi, Shanmugam Muniandy, Fadlin Sakina Ismasafie, and Roszilah Hamid Mechanical Performance of Novel UHPFRC Grouted SHS Tube-Sleeve Connection: Experiments, Numerical Simulation and Analytical Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhenyu Huang and Weixiong Deng

581

597

Effects of Gap Arrangement on the Compression Behavior of Square Tubed Steel Reinforced-Concrete Columns . . . . . . . . . . . . . . . . Biao Yan, Quanlin Zhou, and Dan Gan

614

A Modified Beam-to-Column Connection for Steel Modular Structures with Enhanced Repairability . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiajia Xu, Xudong Qian, Chengguang Xu, and Ran Tao

625

Numerical Analysis of Precast Shear Wall with Opening and Unspliced Vertical Distribution Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . Qi Cai, Xiaobin Song, and Xuwen Xiao

635

xvi

Contents

Structural Health Monitoring and Sensor Technologies for Civil Infrastructure Evaluation of the Application of Unmanned Aerial Vehicle Technology on Damage Inspection of Reinforced Concrete Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jiehui Wang and Tamon Ueda

651

Capture of Crack Evolution for Evaluation of Concrete Properties Using Dynamic Mode Decomposition . . . . . . . . . . . . . . . . . . . . . Jixing Cao, Ser-Tong Quek, and Yao Zhang

667

Model Updating with Neural Network Based on Component Model Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zihan Cao and Tao Yin

677

Crack Assessment of Beam Using Machine Learning with Augmented Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. H. Hwang and H. W. Park

685

Structural Health Monitoring of Steel-Concrete Composite Beams Using Acoustic Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dan Li, Jia-Hao Nie, Jia-Bao Yan, Chen-Xun Hu, and Peng Shen

691

Predicting the Modal Frequencies of a Cracked Beam Considering Crack Modes I and II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Taejeong Lim and Hyun Woo Park

702

Deep Learning-Based Crack Detection and Classification for Concrete Structures Inspection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. K. Nguyen, K. Kawamura, and H. Nakamura

710

Bayesian System Identification of Civil Engineering Structures: Development and Application Finite Element Model Updating Based on Neural Network Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuxuan He and Tao Yin

721

Damage Statistics and Integrity Assessment of Brick Masonry Structures in Historic Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haiyang Qin, Yongjing Tang, Jiao He, and Zhiwang Gu

730

Multi-view Target-Free Video Structural Motion Estimation: A Self-adaptive Co-calibration Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yi Zhang and Enjian Cai

739

Contents

A Robust Bayesian Sensor Placement Scheme with Enhanced Sparsity and Useful Information for Structural Health Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mujib Olamide Adeagbo and Heung-Fai Lam Investigation of the Performance of a Bioinspired Two-Fold Blades Wind Turbine with Airfoil Blade Sections by Using QBlade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yung-Jeh Chu, Heung-Fai Lam, and Hua-Yi Peng A Bayesian Adaptive Resize-Residual Deep Learning Network for Fault Diagnosis of Rotating Machinery . . . . . . . . . . . . . . . . . . . . . . . . . . L. Zou, K. J. Zhuang, and J. Hu

xvii

758

771

783

Mechanics of Materials and Structures with Generalized Continua: Flexible Structures, Composite Materials, Optimizations, and Applications Nonlinear Vibrations of Deepwater Catenary Riser Subjected to Wave Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nutwadee Lertchanchaikun, Karun Klaycham, Chainarong Athisakul, and Somchai Chucheepsakul Effects of High Turbulence Intensity on Dynamic Characteristics of Membrane Structure in Typhoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dong Li, Yiteng Lin, and Hongwei Huang Effects of Discretization Schemes on Free Vibration Analysis of Planar Beam Structures Using Isogeometric Timoshenko-Ehrenfest Beam Formulations . . . . . . . . . . . . . . . . . . . . . . . . . Duc Van Nguyen, Duy Vo, and Pruettha Nanakorn

805

819

829

Geometrically Nonlinear Behavior of L-Shaped Frames Under Forces Applied at Different Positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nghi Huu Duong, Duy Vo, and Pruettha Nanakorn

837

Interfacial Displacement Discontinuity in Coated Substrate with Couple-Stress Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W. Wongviboonsin, P. A. Gourgiotis, and J. Rungamornrat

843

Mechanical Properties of Lattice Specimens Having a Triangular Pattern with Different Relative Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . Itthidet Thawon, Pana Suttakul, Thongchai Fongsamootr, and Yuttana Mona Analytical Solution for Circular Microbeams with Strain Gradient Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zwe Yan Aung, Duy Vo, Toan Minh Le, and Jaroon Rungamornrat

852

860

xviii

Contents

Free Vibration Analysis of Toroidal Shell Segments with Novel Four-Unknown Refined Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Van-Loi Nguyen, Suchart Limkatanyu, and Jaroon Rungamornrat

873

Linear Analysis of Planar Curved Bi-directional Functionally Graded Microbeams Using the Modified Couple Stress Theory . . . . . . . Duy Vo, Pana Suttakul, Jaroon Rungamornrat, and Pruettha Nanakorn

884

Steel Braces Optimization Design of Steel Tall Building Based on Stiffness Performance Sensitivity Data . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuzhou Hou and Xin Zhao

894

Sensitivity Data Driven Composite Floor Structural Optimization for Tall Office Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Morn Chornay and Xin Zhao

905

Load-Resistant Mechanism and Failure Behaviour of RC Flat Plate Slab-Column Joints Under Concentric and Eccentric Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mengzhu Diao, Hong Guan, Huizhong Xue, Yi Li, and Xinzheng Lu Numerical Simulation for Parallel-To-Grain Withdrawal Failure of Self-tapping Screws in Glulam . . . . . . . . . . . . . . . . . . . . . . . . . . . Lijing Fang, Wenjun Qu, and Shengdong Zhang

917

929

Advances in Design and Intelligent Optimization of Large-Span Bridge A Study on Time Synchronization Method for Creating a Cable Surface Image of Cable-Stayed Bridge Using Image Processing . . . . . . . Z. Wei, K. Kawamura, T. Nakamura, and M. Shiozaki

943

Assembly Fault-Tolerant Interval Inversion Method for Cable-Stayed Bridge Based on Bilayer Surrogate Model . . . . . . . . . . Fan Wang, Jianling Zhao, Xiaoming Wang, Pengfei Li, and Pei Tao

959

Dimensionless Continuum Model of Vertical Free Vibration of Spatial Self-anchored Suspension Bridge . . . . . . . . . . . . . . . . . . . . . . . . . Jianling Zhao, Fan Wang, Xiaoming Wang, Pei Tao, and Pengfei Li

975

Dynamic Modal Parameters of an Extremely Lightweight Structure Using a Gyroid Core for Bridge Bearings . . . . . . . . . . . . . . . . . . P. Sengsri and S. Kaewunruen

992

Exploring Patterns in Municipal Bridge Management Issues and Their Relationship with Municipal Conditions in Hokkaido, Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1001 Michael Henry

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Mechanical Model for Parallel-to-Grain Withdrawal Failure of Self-tapping Screws in Glulam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015 Lijing Fang, Wenjun Qu, and Shengdong Zhang Practice of Sustainable Urban Development A Study on Estimation Method of Curing Influence Area for Prediction of Remaining Life on Real Concrete Structures . . . . . . . . 1031 T. Iyoda, A. Sugiyama, and M. Miyawaki Design Method on Flexural Behaviour of Singly-Reinforced PVA-ECC Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1040 Dan-Dan Wang, Shao-Bo Kang, Xiao-Fan Yu, Kun Liu, and Xun-Tian Tan Earthquakes, Reinforced Concrete Structures, and Circular Economy: A Systematic Review of Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 1050 Teklewoin Haile Fitwi Influence Mechanism of Farmers’ Sense of Gain in Tourism-Oriented Rural Infrastructure Construction and Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1070 Hongtao Jia, Lei Zhu, and Jing Du Numerical Analysis of Reinforced Concrete Composite Wall Under Concentric Axial Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1087 S. S. Yee, K. H. Kong, and R. J. Y. Liew Patterns in the Social Perspectives of Concrete Industry Stakeholders and Their Impact on the Sustainability Evaluation of Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1101 Ludmila Soares Carneiro and Michael Henry Research on the Industry Acceptance and Promotion Path of Interim Payment in Civil Engineering Projects . . . . . . . . . . . . . . . . . . . . 1116 Lei Zhu and Hui Xiong Advances in Vibration Mitigation of Long-Span Bridges and High-Rise Structures Damping Effects of Cable Dampers on Girder Vibrations of Cable-Stayed Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1135 P. Sae-ma, L. Sun, L. Chen, and Z. Liu Design and Optimization of Viscous Damping Outrigger Vibration Reduction for Ultra-high Structures . . . . . . . . . . . . . . . . . . . . . . 1146 Jie Yao and Xin Zhao

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Double-Track Nonlinear Energy Sink for Dynamic Response Control in Wind Turbine Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1159 Dong Li, Zheng Yu Zhang, and Xuhui Zhang Multi-stage Objective Algorithm for Accelerating the Structural Optimization of Tall Building Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1169 Xin Zhao, Gang Wang, and Jie Yao Optimal Design of Energy-Dissipated Substructure with Viscous Damper for High-Rise Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1182 Daohang Hu and Xin Zhao Optimization of Damped Outriggers for Maximizing Multimode Damping of Long-span Bridges for Vibration Suppression . . . . . . . . . . . . 1193 Zhanhang Liu, Lin Chen, and Limin Sun Intelligent Shield Tunnelling A Preliminary Review of Digital and Intelligent Cutterhead Management and the Enabling Technologies in Shield Tunnelling . . . . . 1211 Ziwei Yin, Gang Li, Hanbin Luo, and Zhengjun You Data-Driven Safety Assessment for Shield Tunnel Excavation: Interoperability Between Parametric Modeling and Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225 Ping Xie, Gang Li, Hanbin Luo, and Xiao Yang A Dynamic Model of Machine Learning and Deep Learning in Shield Tunneling Parameters Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . 1241 Ruohan Wang, Guan Chen, and Yong Liu Hybrid Model for Predicting Average Cutter Wear in TBM Excavation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255 A. Li, G. LI, C. Wang, and W.-L. Liu Optimal Control of Operation Parameters During EPB Shield Tunnelling Based on Artificial Neural Network Model . . . . . . . . . . . . . . . 1265 Xuejian Chen, Qing Kang, and Yong Liu Intelligent Decision Framework of Shield Attitude Correction Based on Deep Reinforcement Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1273 J. Xu, J. F. Bu, L. G. Zhang, J. Zhang, K. F. Li, and S. M. Liu Composite Materials and Structures Behavior of Bamboo Scrimber Beam-Column Joints with Bolted Steel Angles and T-Stubs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1291 Jun Xiong, Shu-Rong Zhou, and Shao-Bo Kang

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Experimental Study on the Behaviour of CFST Columns with Steel Slag Concrete Under Axial Compression . . . . . . . . . . . . . . . . . . 1304 Y. H. Lin, Y. Y. Jin, J. C. M. Ho, and M. H. Lai Experimental Study on the Post-fracture Property of Laminated Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316 Zhifei Chen, Suwen Chen, and Xing Chen Experimental Study on the Uni-axial Behaviour of MSCFST Columns Considering Concrete’s Wet Packing Density . . . . . . . . . . . . . . . 1327 J. H. Mo, M. R. Zeng, S. J. Yang, J. C. M. Ho, and M. H. Lai Load-Carrying Capacity of CFST Columns: Current Design Rules Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1339 X. L. Ou, J. C. M. Ho, and M. H. Lai Study on Mechanism of Pore Modification by Polymer Particles . . . . . . 1358 R. Yahiro, T. Kanda, K. Nishimura, and T. Iyoda Progressive Collapse and Ultimate Structural Resistance Effects of Modeling Methods of RC Diaphragm on the Behavior of Steel Staggered Truss Framing Structures . . . . . . . . . . . . . . . . . . . . . . . . 1369 Zexiang Li, Dan Gan, and Xuhong Zhou Finite Element Analysis of Bonded-PT Slab Column Connections Under Lateral Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1382 K. Kingkokgruad and U. Prawatwong Numerical Study of Prestressed Concrete Girder-Deck System with Variable Reinforcement and Span-depth Ratios . . . . . . . . . . . . . . . . . 1387 H. Ni and R. S. Aboutaha Disaster Mitigation Flexural Performance of Mill Cut Steel Fiber Reinforced Concrete Beam Degraded by Mild Corrosion . . . . . . . . . . . . . . . . . . . . . . . . 1403 Khanh Minh Vo, Withit Pansuk, Thi Nguyen Cao, and Hai Yen Thi Nguyen Structures Under Blast Loads from Academic Research into Engineering Applications: Advances and Limitations . . . . . . . . . . . . 1413 Tin V. Do and Asher Gehl Free and Forced Vibration Characteristics of Functionally Graded Sandwich Beam with GPL-Reinforced Porous Core . . . . . . . . . . 1432 Tran Quang Hung, Do Minh Duc, and Tran Minh Tu

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Engineering Design and Dynamics Structural Response Ballastless Track Support Deterioration Evaluation Using Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1455 Jessada Sresakoolchai, Ting Li, and Sakdirat Kaewunruen Bursting Effects in Prestressed Concrete Sleepers at Different Prestressed Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1464 Dan Li, Sakdirat Kaewunruen, and Ruilin You Plate Thickness Distribution Estimation of a Belt Conveyor Support Structure Member Based on Cross-Sectional Vibration Modes Using Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1471 Daichi Ogawa, Yaohua Yang, Tomonori Nagayama, Sou Kato, Kazumasa Hisazumi, and Tomonori Tominaga Simulation and Simplified Method Study on Seismic Collapse of Core-outrigger Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1481 Y. Liu, J. Huang, F. F. Sun, and G. Y. Chen Advanced Transportation Infrastructure and System Application of Ai-based Deformation Extract Function from a Road Surface Video to a Road Pavement Condition Assessment System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1503 Hisao Emoto, Miori Numata, and Atsuki Shiga Assessing the Sustainability Characteristics of Modified Asphalt Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1515 G. Muna and M. Henry Factors Affecting the Deterioration of Bituminous Pavements in Khyber Pakhtunkhwa Province, Pakistan . . . . . . . . . . . . . . . . . . . . . . . . 1528 Azam Amir and Michael Henry Investigation on Recycling Application of Waste Rubber Tyres in Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1539 Shengtian Zhai, Yunsheng Zhang, and Laibao Liu Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1553

Sustainable Binding Materials

Study of Methods for Improving Strength and Durability of Low-Quality Recycled Aggregate Concrete R. Yuya1(B) , N. Matsuda1 , M. Kojima2 , and T. Iyoda1 1 Shibaura Institute of Technology, 3-7-5, Toyosu, Koto-Ku, Tokyo 135-8548, Japan

{mh21024,na21107,iyoda}@shibaura-it.ac.jp 2 Takenaka Corporation, 1-5-1, Otsuka, Inzai City, Chiba 270-1395, Japan

[email protected]

Abstract. In recent years, the amount of concrete waste is increasing every year by demolishing and renewing of concrete structures in Japan. In addition, it is expected to continue to increase in the future. In addition, there is a concern about the decrease of disposal sites, so it is necessary to have an effective method to use concrete waste. As an effective method of using concrete waste, the use of recycled aggregate can be considered. In order to promote the use of recycled aggregate, it is necessary to promote the use of low-quality recycled aggregate that can be produced with low energy and low cost. However, the strength and durability of concrete using low-quality recycled aggregate are significantly lower than those using normal aggregate. In previous studies, we examined the improving methods of mortar using low-quality recycled fine aggregate and concrete using low-quality recycled coarse aggregate. It was found that accelerated carbonation of recycled aggregate was optimal for mortar using low-quality recycled fine aggregate, and addition of C–S–H type accelerator was optimal for concrete using low-quality recycled coarse aggregate. Therefore, in this study, we aimed to improve the strength and durability of concrete using both low-quality recycled fine and coarse aggregate, so we examined the improving methods and its mechanism. There are two methods to improve the strength and durability of concrete using low-quality recycled aggregate: accelerated carbonation of recycled aggregate and addition of C–S–H type accelerator. As a result, it was found that the combinations of accelerated carbonation of recycled fine aggregate and addition of C–S–H type accelerator had a high improving effect in concrete using both low-quality recycled fine and coarse aggregate. Keywords: Recycled fine aggregate · Recycled coarse aggregate · Accelerated carbonation of recycled aggregate · C–S–H type accelerator

1 Introduction In order to prevent global warming, it is effective to reduce the emission of greenhouse gases, especially carbon dioxide (CO2 ). Also in Japan, the government has stated “Carbon Neutral by 2050” to reduce the emissions of greenhouse gases to zero by 2050, and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 3–15, 2023. https://doi.org/10.1007/978-981-19-7331-4_1

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has made efforts in various fields to contribute to creating decarbonized society. Also in concrete field, various technologies have been considered to create a decarbonized society, such as reducing the use of Ordinary Portland cement by using admixtures of blast furnace slag powder and fly ash to significantly reduce CO2 emissions from concrete materials, and developing carbon-recycled concrete using calcium carbonate produced from collected CO2 . In addition, in “Carbon Dioxide Utilization (CO2U)ICEF ROADMAP1.0” presented at the ICEF international conference held in 2016, it was shown that CO2 capture and storage in concrete and concrete aggregates has a great potential for effective utilization of CO2 on a global scale in the near future. By taking strategic actions, there is a potential to reduce 3.6 billion tons of CO2 on a global scale by 2030 through CO2 capture and storage in concrete aggregate. On the other hand, in recent years, the amount of concrete waste is increasing every year by demolishing and renewing of concrete structures in Japan. In addition it is expected to continue to increase in the future. In addition, there is a concern about the decrease of disposal sites, so it is considered necessary to have an effective method to use concrete waste. As an effective method of using concrete waste, the use of recycled aggregate can be considered. In order to promote the use of recycled aggregate, it is necessary to promote the use of low-quality recycled aggregate that can be produced with low energy and low cost. However, the strength and durability of concrete using low-quality recycled aggregate are significantly lower than those using normal aggregate. In previous studies, we examined the improving methods of mortar using low-quality recycled fine aggregate and concrete using low-quality recycled coarse aggregate. It was found that accelerated carbonation of recycled aggregate was optimal for mortar using low-quality recycled fine aggregate, and addition of C–S–H type accelerator was optimal for concrete using low-quality recycled coarse aggregate. Therefore, in this study, we aimed to improve the strength and durability of concrete using both low-quality recycled fine and coarse aggregate, so we examined the improving methods and its mechanism. Two methods were used to improve the strength and durability of low-quality recycled aggregate concrete: accelerated carbonization of recycled aggregate and addition of C–S–H type accelerator.

2 Location of the Porosity and Improving Methods for Recycled Aggregate Concrete 2.1 Location of the Porosity in Recycled Aggregate Concrete It is thought that the cause of the decrease in strength and durability of low quality recycled aggregate concrete is the large amount of porosity. In previous studies, it has been reported that there are many porosity in attached mortar and interfacial transition zone (ITZ) of the recycled aggregate concrete. Figure 1 shows location of porosity in recycled aggregate concrete. There are five locations of porosity in recycled aggregate concrete: (1) cement paste, (2) attached paste of recycled fine aggregate, (3) ITZ of recycled fine aggregate, (4) attached mortar of recycled coarse aggregate, and (5) ITZ of recycled coarse aggregate. It is thought that the strength and durability of low-quality recycled aggregate concrete will be improved by improving these porosities. In fact, it is thought that porosity also exists in the old ITZ between the attached mortar and the aggregate. This porosity was difficult to study and was not indicated.

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Fig. 1. Location of the porosity in recycled aggregate concrete

2.2 Improving Methods of Recycled Aggregate Concrete 2.2.1 Accelerated Carbonation of Recycled Aggregate Carbonation of concrete is considered to cause corrosion of the reinforcing bars in reinforced concrete. But focusing only on concrete, it is known that calcium hydroxide changes to calcium carbonate, and strength of concrete increases as porosity is densified by carbonation. Therefore, if the attached mortar of recycled aggregate can be densified by carbonated, recycled aggregate can be improved, and the strength and durability of concrete can be improved. In this study, recycled aggregate was carbonated for 1 week in accelerated carbonation chamber at a temperature of 20 °C, a relative humidity of 60% and a carbon dioxide concentration of 5%. 2.2.2 Addition of C–S–H Type Accelerator C–S–H type accelerator is an admixture based on Calcium Silicate Hydrate (C–S–H). It has been explained that C–S–H nanoparticles works as seed of crystal growth in cement hydration process, then setting and strength development in early age are enhanced by

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this nanoparticles in this accelerator. In this study, the addition rate was set at 10% of the unit water content.

3 Outline of Experiment Table 1 shows the physical properties of fine and coarse aggregate used in this study. In this study, Class L recycled fine and coarse aggregate were used, also normal fine and coarse aggregate were used. Figures 2 and 3 show the improving effect on dry density and water absorption rate of recycled aggregate by accelerated carbonation. Before mixing concrete, both recycled fine and coarse aggregate were pre-wetted for 24 h before mixing to be used in the surface dry state. In addition, in this study, Ordinary Portland cement was used in all mix propotions. Table 2 shows the mix proportion of concrete. The mix proportion was set at a constant water-cement ratio of 50% and s/a of 48%. The mix proportions were as follows: one with no accelerated carbonation of both fine and coarse aggregate, one with accelerated carbonation of only fine aggregate, one with accelerated carbonation of both fine and coarse aggregate, and C–S–H type accelerator added at 10% of unit water content. In this study, the names of mix proprtion are indicated by fine aggregate type and coarse aggregate type, and those with C–S–H type accelerator are indicated by fine aggregate type and coarse aggregate type-ACX. Table 1. Physical properties of fine and coarse aggregate Sample name

Surface dry density (g/cm3 )

Absolute dry density (g/cm3 )

Water absorption rate (%)

Amount of fine particles (%)

NS

2.60

2.55

1.92

2.00

LS

2.24

2.00

12.01

8.60

LSC

2.31

2.13

8.47

NG

2.70

2.69

0.32

0.80

LG

2.51

2.37

5.90

1.00

LGC

2.55

2.45

4.35

NS is normal fine aggregate, LS is recycled fine aggregate and LSC is carbonated of LS. NG is normal coarse aggregate, LG is recycled coarse aggregate and LGC is carbonated of LG

3.1 Compressive Strength Test Compressive strength test was carried out in 28days, according to JIS A 1108. All specimens were cured in 20 °C tap water. 3.2 Air Permeability Test The specimens were dried at 40 °C in a drying oven until the weight loss became constant. Measurement was carried out in an air permeability testing equipment. The

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Fig. 2. Improving effect on dry density and water absorption rate of recycled fine aggregate

Fig. 3. Improving effect on dry density and water absorption rate of recycled aggregate Table 2. Mix proportion of concrete Symbol name

Improving method

Aggregate

Carbonated

ACX

Fine

Coarse

NSNG

–

–

NS

NG

LSLG

–

–

LS

LG

LSLG-ACX

–

O LSC

LG

LSC

LGC

LSCLG

S carbon ate d

–

LSCLG-ACX

S carbon ate d

O

LSCLGC

S,G carbonated

–

LSCLGC-ACX

S,G carbonated

O

W/C (%)

s/a (%)

Air (%)

50

48

4.5

air permeability coefficient was calculated using Eq. (1). All specimens were cured for 28 days in 20 °C tap water. Q 2LP1 · K=  2 2 P1 − P2 A

(1)

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K: Air permeability coefficient (cm4 /(N × s)), L: Specimen thickness (cm), P1 : Loading pressure (N/mm2 ), P2 : Outflow side pressure (N/cm2 ), Q: Amount of permeated air (cm3 /s), A: permeable area (cm2 ). 3.3 Drying Shrinkage Test Drying shrinkage test was carried out, 1, 2, 4, 8, 13 weeks after cured period according to JIS A 1129-3. All specimens were cured for 28days in 20 °C tap water. 3.4 Porosity Test The porosity was calculated by Archimedes method. After 28 days of curing, the specimens for the air permeability test were immediately saturated in a vaccuum state, and the saturated mass and the mass in water were measured. After that, It was the specimens were dried at 40 °C in a drying oven until the weight loss became constant and measured the mass in an absolutely dry state. The porosity was calculated by the Archimedes method using these values.

4 Results and Discussion 4.1 Compressive Strength Test Figure 4 shows compressive strength. Compressive strength of LSLG was about 50% of compressive strength of NSNG. Comparing compressive strength of LSLG with that of LSCLG and LSCLGC, it can be seen that compressive strength was improved by accelerated carbonation of recycled aggregate. On the other hand, in the previous studies, compressive strength was not improved by accelerated carbonation of only recycled coarse aggregate. Therefore, compressive strength is most improved by accelerated carbonation of both recycled fine and coarse aggregate, but the improving effect of accelerated carbonation of recycled fine aggregate was higher than that of accelerated carbonation of recycled coarse aggregate. In addition, compressive strength of LSLG-ACX, LSCLG-ACX, and LSCLGC-ACX was also greatly improved compared to no addition of C–S–H type accelerator (LSLG, LSCLG, and LSCLGC). Also, compressive strength of LSCLGC-ACX was improved to 90% of compressive strength of NSNG, while compressive strength of LSCLG-ACX was also greatly improved to 85% of compressive strength of NSNG. 4.2 Air Permeability Test Figure 5 shows air permeability coefficient. Air permeability coefficient of LSLG is significantly larger than that of NSNG. Comparing air permeability coefficient of LSLG with that of LSCLG and LSCLGC, it can be seen that air permeability coefficient was improved by accelerated carbonation of recycled aggregate. On the other hand, in the previous studies, air permeability coefficient was not improved by accelerated carbonation of only recycled coarse aggregate. Therefore, as in the case of compressive strength, air

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Fig. 4. Compressive strength

permeability coefficient was most improved by accelerated carbonation of both recycled fine and coarse aggregate, but the improving effect of accelerated carbonation of recycled fine aggregate was higher than that of accelerated carbonation of recycled coarse aggregate. In addition, air permeability coefficient of LSLG-ACX, LSCLG-ACX, and LSCLGC-ACX was also greatly improved compared to that of no addition of C–S–H type accelerator (LSLG, LSCLG, and LSCLGC). Also, the air permeability coefficient of LSCLGC-ACX was the most improved, while the air permeability coefficient of LSCLG-ACX was also greatly improved.

Fig. 5. Air permeability coefficient

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4.3 Drying Shrinkage Test Figure 6 shows length change rate and Fig. 7 shows mass change rate. The length change rate at the 13th week after the end of curing was about −1100 × 10−6 in case of LSLG while it was about −500 × 10−6 in case of NSNG. Drying shrinkage of concrete can be suppressed if the water content of concrete at the end of curing is reduced. In other words, if the porosity can be made dense, the amount of excess water at the end of curing is reduced and drying shrinkage can be suppressed. In the case of the accelerated carbonation of aggregate, the water absorption rate of the aggregate was reduced, therefore, the porosity of the adhered mortar was made dense, and the water content of the aggregate was reduced by pre-wetting, thus, the drying shrinkage was suppressed. Comparing drying shrinkage of LSLG, LSCLG, and LSCLGC, it can be seen that drying shrinkage of LSCLGC was most suppressed, but the gap between LSLG and LSCLG was larger than that between LSCLG and LSCLGC. This may be due to the fact that the water absorption rate of recycled fine aggregate is higher than that of recycled coarse aggregate, and the improving effect of water absorption rate by accelerated carbonation is greater. In addition, drying shrinkage of LSLG-ACX, LSCLGACX, and LSCLGC-ACX was also suppressed compared to that of LSLG, LSCLG, and LSCLGC. It is thought that porosity of cement paste and ITZ of coarse aggregate was densified by addition of C–S–H type accelerator and reduced the amount of excess water at the end of curing, thus drying shrinkage was suppressed. In addition, from Fig. 7, it can be seen that mass change rate is smaller for mix proportions in which drying shrinkage is suppressed. Thus, it is considered to be important to reduce the amount of excess water, in other words, porosity of concrete at the end of curing.

Fig. 6. Length change rate

4.4 Relationship Between Porosity and Each Physical Property Figure 8 shows the relationship between porosity and compressive strength and Fig. 9 shows the relationship between porosity and air permeability coefficient. It can be seen that compressive strength and air permeability coefficient improved as porosity decreased. In addition, improving effect of LSLG-ACX and LSCLG was small. On the

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Fig. 7. Mass change rate

other hand, it can be seen that LSCLGC-ACX which carried out three improving methods was the most efficient, but LSCLG-ACX, which carried out two improving methods, was also greatly improved. In addition, porosity of atached mortar, in (2) and (4) in Fig. 1, is considered to be improved by accelerated carbonation of recycled aggregate. However, in porosity test by Archimedes method, porosity is calculated by summing up porosity of the five pores which are shown in Fig. 1. Therefore, it is difficult to specify the degree of improving each porosity other than (2) and (4). Since both strength and air permeability coefficient of concrete are greatly affected by ITZ, so investigated to what degree porosity at ITZ of recycled coarse aggregate, was improved by each improving method. In this study, in order to investigate the mechanism of porosity improvement by each improvement method, Vickers hardness was mesured.

Fig. 8. Relationship between porosity and compressive strength

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R. Yuya et al.

Fig. 9. Relationship between porosity and air permeability coefficient

5 Investigation of the Porosity Improving Mechanism by Each Improving Method 5.1 Method of Vickers Hardness Test Vickers hardness test was carried out by making 30 mm × 30 mm × 10 mm specimens from the specimens after air permeability test, and the specimen surfaces were mirrorfinished on a turntable using abrasive paper #120-15000. Vickers hardness was measured using a micro hardness tester (load: 0.9807 N, test force: 10 µm/s). Two points were measured at 20 µm intervals from the edge of the coarse aggregate to 200 µm on a line orthogonal to the edge of the coarse aggregate, and the average value was calculated. 5.2 Vickers Hardness Figure 10 shows the Vickers hardness and Table 3 shows the thickness of ITZ. In all mix proportions, there is ITZ with low Vickers hardness a few tens µm from the edge of the aggregate. At a distance from the edge of the aggregate, there is a bulk area with the same degree of Vickers hardness that is not affected by aggregate. Since Vickers hardness of the bulk part is about 80–120 N/mm2 , if ITZ is defined as the part where Vickers hardness is less than 80 N/mm2 , the thickness of ITZ is about 40 µm in NSNG while it is about 120 µm in LSLG. This is because of the high water absorption rate of recycled aggregate, and the water inside recycled aggregate exuded to the aggregate interface when the hardening process was completed, resulting in the thickness of ITZ being expanded. On the other hand, it was found that the thickness of ITZ was reduced by accelerated carbonation of recycled aggregate and addition of C–S–H type accelerator. Comparing each improving method, the thickness of ITZ of LSLG-ACX is smaller than that of LSCLG and LSCLGC, it is considered that addition of C–S–H type accelerator has a greater effect on densifying porosity in ITZ than accelerated carbonation of recycled aggregate. In addition, Vickers hardness of the bulk part of LSLG-ACX, LSCLG-ACX and LSCLGC-ACX was slightly larger than that of LSLG, LSCLG and LSCLGC. Thus, it is considered that the addition of the C–S–H type accelerator may also improve the porosity of the cement paste (1). In addition, the thickness of ITZ of LSCLGC-ACX

Study of Methods for Improving Strength

13

and LSCLG-ACX, which showed significant improving in strength and durability, was about 60 µm. It is considered that this is because densification of porosity of ITZ by addition of C–S–H type accelerator and reduction of water absorption rate and water exudation after hardening process by accelerated carbonation of recycled aggregate.

Fig. 10. Vickers hardness

Table 3. Thickness of ITZ Symbol name

Thickness of ITZ (µm)

NSNG

40

LSLG

120

LSLG-ACX

80

LSCLG

100

LSCLG-ACX

60

LSCLGC

80

LSCLGC-ACX

60

5.3 Investigation of the Location of Porosity Improved by Each Improving Method Table 4 shows location of porosity improved by each improving method. Based on the test results in this study, it is discussed which porosity shown in Fig. 1 was improved by the accelerated carbonation of aggregate and addition of C–S–H type accelerator. First, the addition of C–S–H type accelerator (LSLG-ACX) had little effect on the compressive strength and air permeability coefficient, but the thickness of ITZ was greatly reduced and Vickers hardness of the bulk part was slightly increased. This suggests that there is an effect on the porosity of (1) cement paste and (5) ITZ of coarse aggregate. Accelerated

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R. Yuya et al.

carbonation of recycled fine aggregate (LSCLG) had little effect on compressive strength, air permeability coefficient, and the thickness of ITZ. This is because the water absorption rate of the aggregate is greatly improved, and the water exuded to the fine aggregate interface is considered to be reduced. This suggests that there are effects on the porosity of (2) attached paste of recycled fine aggregate and (3) ITZ of recycled fine aggregate. In the case of accelerated carbonation of fine and coarse aggregate (LSCLGC), the results are similar, so it is considered that there are effects on the porosity of (2), (4) attached mortar of fine and coarse aggregate and (3), (5) ITZ of fine and coarse aggregate. The combination of accelerated carbonation of fine aggregate and addition of C–S– H type accelerator (LSCLG-ACX) had significant effect on compressive strength, air permeability coefficient and the thickness of ITZ. This suggests that there are effects on the porosity of (1) cement paste, (2) attached paste of fine aggregate, and (3), (5) ITZ of fine and coarse aggregate. In the case of the combination of accelerated carbonation of fine and coarse aggregate and addition of C–S–H type accelerator (LSCLGC-ACX), the results are similar, so the effects are considered to be on the porosity of (1) cement paste, and (2), (4) attached mortar of fine and coarse aggregate, and (3), (5) ITZ of fine and coarse aggregate. Therefore, it is important to improve the porosity of (5) ITZ of coarse aggregate. Table 4. Location of porosity improved by each improving method Sample name

(1) cement paste

LSLG-ACX

o

LSCLG LSCLG-ACX

o

LSCLGC LSCLGC-ACX

o

(2) attached paste of recycled fine aggregate

(3) ITZ of recycled fine aggregate

(4) attached mortar of recycled coarse aggregate

(5) ITZ of recycled coarse aggregate ◎ ◎

o

o

o

o

o

o

o

o

o

o

o

◎

6 Conclusion The following was concluded about the improving effects on strength and durability of low quality recycled aggregate concrete caused by each improving methods. 1. Accelerated carbonation of aggregate improves the porosity of attached mortar and ITZ of aggregate, and, thus, improves compressive strength, air permeability coefficient and drying shrinkage. 2. Addition of C–S–H type accelerator improves the porosity of cement paste and ITZ of coarse aggregate, but improving effects on compressive strength, air permeability coefficient and drying shrinkage is small.

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3. The combination of accelerated carbonation of aggregate and addition of C–S–H type accelerator greatly improves the porosity of cement paste and attached mortar of aggregate, especially ITZ of coarse aggregate, as well as compressive strength, air permeability coefficient, and drying shrinkage. In particular, looking at strength, the strength of recycled aggregate concrete (LSLG) was 50% of that of normal concrete (NSNG), but the combination of accelerated carbonation of aggregate and addition of C–S–H type accelerator (LSCLGC-ACX) improved the strength to about 90%.

Acknowledgements. This result was obtained as a result of the work (JPNP16002) commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

References Matsuda, N., Kameyama, T., Matsuda, M., Iyoda, T.: Study on the production method of lowenergy recycled aggregate by forced adsorption of CO2 gas. Proc. Jpn Concr. Inst. 36, 1732– 1737 (2014) Imoto, H., Koizumi, S., Hanabusa, K., Baba, Y.: Initial hardening properties and bleeding suppression effect of concrete using C–S–H type accelerator. Proc. Jpn Concr. Inst. 36, 2248–2253 (2014) Poon, C.S., Shui, Z.H., Lam, L.: Effect of microstructure of ITZ on compressive strength of concrete prepared with recycled aggregates. Constr. Build. Mater. 18, 461–468 (2004) Sakai, K., Matsuda, N., Sugiyama, T., Iyoda, T.: Study of improving harden property of recycled coarse aggregate concrete by several methods for pore structure modified. Proc. Jpn Concr. Inst. 43, 959–964 (2019) Yuya, R., Matsuda, N., Sugiyama, T., Iyoda, T.: investigation of method for improving strength and durability of mortar using low-quality recycled fine aggregate. Proc. Jpn Concr. Inst. 43, 965–970 (2019)

A Study on Strength and Durability of Mortar Using Low-quality Recycled Fine Aggregate with Accelerated Carbonation Y. Inoue1(B) , N. Matsuda1 , Y. Nishioka2 , and T. Iyoda1 1 Shibaura Institute of Technology, 37-5 Koto-Ku, Toyosu 135-8548, Japan

[email protected] 2 Takenaka Corporation, 1-5-1, Otsuka, Inzai City, Chiba 270-1395, Japan

Abstract. Recycled aggregate produced from demolished concrete and waste fresh concrete are classified into three types of quality using the density in oven-dry condition and water absorption ratio in Japan. Among the three types, compared to medium and high quality recycled aggregate (M and H), low quality recycled aggregate (L) can be produced with less energy and cost, and reduces the generation of fine powder by-product. However, concrete made from L have problems are it has lower strength and greater length change due to drying shrinkage. When considering the widespread use of L, these must be improved with less cost. For these modifications, we have been investigating the use of CO2 gas for accelerated carbonation technology. This technology focuses on the carbonation mechanism of concrete and blows CO2 gas on recycled aggregate to carbonate the cement paste that are attached mortar. It has been found that the physical properties of recycled fine aggregate are greatly improved using this technology. Therefore, to investigate the effect of recycled fine aggregate with accelerated carbonation on the hardened samples, we conducted tests on mortars made from that fine aggregate. It has shown that mortar has improved strength and durability due to the reduction of mortar voids attached on recycled fine aggregate. Especially, we reported that there was a large improvement in the out of specification of L (outside of L). There is a difference in amount of fine powder. L contains 3% fine powder, while outside of L contains 12%. We considered that the fine powder influenced the hardened samples. Therefore, in this study we focused on the granularity, such as fine powder of low quality recycled fine aggregate and conducted tests on mortar to compare the difference in the effect of accelerated carbonation modification technology. Keywords: Recycled fine aggregate · Accelerated carbonation technology · Fine powder · Granularity

1 Introduction Carbon neutrality, which aims to reduce greenhouse gas emissions to zero as a whole, is being promoted on a global scale. In Japan, various efforts are being made to achieve carbon neutrality by 2050. In the concrete field, studies are being conducted to reduce © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 16–23, 2023. https://doi.org/10.1007/978-981-19-7331-4_2

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17

the use of cement, which emits a large amount of CO2 during production, and to fix CO2 using carbonation mechanisms in concrete and aggregates. On the other hand, the use of recycled aggregate produced from dismantled concrete masses is also important for a recycling-oriented society such as carbon neutral. Recycled aggregate is classified into three types, H, M, and L, in descending order of quality. The classification method is based on differences in quality resulting from the condition of the original concrete demolition material and the processing method. It is also known that low-quality recycled aggregates have low strength and durability when used in concrete, although energy and cost during production are low. The carbonation of such low-quality recycled aggregate can adsorb and fix CO2 , which may help to achieve carbon neutrality. Furthermore, the density increases and the water absorption rate decreases. In addition, it has been found that the strength of cured bodies using these materials is greatly improved when low-quality recycled fine aggregate or recycled fine aggregate of poorer quality is used, and the air permeability coefficient is improved for recycled fine aggregate of poorer quality. Each of these aggregates has a different particle size distribution, and among them, the poor quality fine aggregate has a large amount of fine particles, which suggests that the difference in particle size is the key to the improvement effect of carbonation. Therefore, in order to compare which particle size should be carbonated to obtain a greater improvement to the hardened samples, this study examined the effect of different particle sizes of aggregate on the strength and permeability of mortar.

2 Outline of Experiment 2.1 Materials Used and Mix Proportions In this study, mortar was made to study the effect of carbonating the fine aggregate. The mortar was formulated with a water cement ratio 50% and a constant cement: fine aggregate ratio 3.0. The cement used was Ordinary Portland Cement. The physical properties of the recycled fine aggregate used in this study are shown in Table 1. In this study, L-class recycled fine aggregate(LS) and it was carbonated(LSC) were used. The carbonated fine aggregate was placed in an accelerated carbonation system for one week at a temperature of 20 °C, relative humidity of 60% and CO2 concentration of 5%. Figure 1 show the improving effect of dry density and water absorption rate of recycled fine aggregate by accelerated carbonation. A treatment of fine aggregate used in the mortar is shown in Fig. 2. The recycled fine aggregate was sieved into five particle sizes. Then, in order to reduce the difference in the effect of the mass of each particle size, mass ratio equalized by 20%. In (1) to (5), each particle size range was partially carbonated and the effects of different fine aggregate particle sizes on the strength and permeability of the mortar were investigated. Then, the transition zone thickness, which is known to affect strength and permeability, was examined. The whole grain unmodified and the whole grain carbonated were also prepared at the same time to compare the different effects on the mortar (Table 1).

18

Y. Inoue et al. Table 1. Physical properties of recycled fine aggregate

Sample name

Surface dry density (g/cm3 )

Absolute dry density (g/cm3 )

Water absorption rate (%)

Amount of fine particles (%) 8.60

LS

2.24

2.00

12.01

LSC

2.31

2.13

8.47

Fig. 1. Improving effect of dry density and water absorption rate of recycled fine aggregate

2.2 Test Items and Test Methods 2.2.1 Compressive Strength Test Mortar bars of 40 × 40 × 160 mm were used, and the test was conducted in accordance with JIS R 5201 at 28 days curing in top water. 2.2.2 Air Permeability Test A cylindrical specimen of ϕ100 × 25mm cured in water for 28 days was placed in a drying oven at 40 °C until its mass became constant, and the test was conducted. Air was allowed to permeate through the material at a pressure of 0.1 MPa in an air permeability testing chamber. The amount of air permeation was measured by the water displacement method using a measuring cylinder, and the permeability coefficient was calculated from the following Eq. (1). 2LP1 Q · K=  2 P1 − P22 A

(1)

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19

Fig. 2. Mixture name and Fine aggregate used in mortar

K: Air permeability coefficient (cm4 /Ns), L: Specimen thickness (cm), P1: Loading pressure(N/mm2 ), P2: Outflow side pressure (N/cm2 ), Q: Amount of air permeability (cm3 /s), A: permeable area (cm2 ). 2.2.3 Vickers Hardness Test The test was conducted using pieces of the specimen after the compression test. The piece surface was finished on a turntable using abrasive paper #120~1200, and the Vickers hardness of the fine aggregate interface was measured with a vickers hardness tester (load: 0.9807 N, test force: 10 μm/s). From 3 to 4 mm size aggregate easily recognized as aggregate ten points were measured at 20 μm intervals from the edge of the fine aggregate, and the approximate interfacial transition zone thickness was calculated from the Vickers hardness measurements.

3 Results and Discussion 3.1 Compressive Strength Test Figure 3 shows the results of compressive strength test. No significant change in compressive strength was observed in the cases (1) to (5) where the particle size of fine aggregate was partially carbonated. On the other hand, there was a significant improvement in all CO2 . The reason may be that the partial carbonation is only 20% by mass of the total aggregate, and the remaining unmodified parts are more affected by porosity and brittleness.

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Y. Inoue et al.

Fig. 3. Compressive strength

3.2 Air Permeability Test Figure 4 shows the results of air permeability test. Air permeability tends to be improved when carbonating the fine grain range as in (1) and (2). However, compared to the improvement effect of all CO2 , it is found to be small. This suggests that partial carbonation of aggregate particle size improves the air permeability of mortar in the smaller diameter particle size range, but the improvement is smaller than that of forced carbonation of the entire particle size. By the way, since the air permeability of the hardened material depends on the structure of the interfacial transition zone, we think that the improvement mechanism of the interfacial transition zone may be different for each grain size. 3.3 Vickers Hardness Test 3.3.1 Test Results Figure 5 shows the results of Vickers hardness test. Based on the discussion in the air permeability test, the interfacial transition zone thickness was calculated from the vickers hardness test. In this section, the results for the carbonated particle sizes of (2), (3), and (4) had similar slopes, so only the results for the particle size of (3) are shown. All proportions are higher than 80 N/mm2 up to around 40 μm, suggesting that it is not the interfacial transition zone, but the aggregate or adhesion paste. In the case of the finer grain size (1), the interfacial transition zone was improved at a distance from the aggregate. In the case of coarse grain size (5), the interfacial transition zone was improved near the aggregate compared to the others. These results suggest that the mechanism of improvement of the interfacial transition zone varies depending on the particle size of carbonation. By the way, we consider that the reason why there was almost no improvement in (2), (3), and (4) was because the aggregate particle size measured

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21

Fig. 4. Air permeability

for the interfacial transition zone thickness was about 3~4 mm, which was not modified in (2), (3), and (4).

Fig. 5. Vickers hardness

3.3.2 Discussion Figure 6 shows the images of transition zone improvement mechanism. In the case of carbonation of fine-grained (1), we believe that the fine-grained content is converted to almost pure CaCO3 by carbonation, which improves the interfacial transition zone by promoting hydration at the cement paste interface. On the other hand, we consider that

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Y. Inoue et al.

carbonation of coarse-grained (5) improves the transition zone by modifying the adherent paste around the aggregate and reducing the amount of water that exudes due to lower water absorption. In short, although the measured interfacial transition zone thickness of the all CO2 was thicker than (5), the actual interfacial transition zone thickness is expected to be more improved because both of the above improvement effects occur. Therefore, permeability is more improved.

Particle size

Before reformulation

After reformulation

(1) 0.15mm under

(5) 2.364.75mm

allCO2

Fig. 6. Images of transition zone improvement mechanism

4 Conclusions (1) In the case of accelerated carbonation of a partial grain size range, there was little improvement in compressive strength under any condition. There was no significant

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23

effect of any of the particle size ranges (1) to (5). On the other hand, the smaller the particle size, the better the improvement of air permeability was observed. (2) Although the smaller the particle size range, the better the air permeability of the mortar, carbonation of all particles has the greatest improvement in both strength and air permeability. (3) The improvement mechanism of the transition zone depends on the grain size. The finer particles are themselves converted to CaCO3 by carbonation. to CaCO3 , which improves the transition zone. The coarser grains are considered to have modified the adhesion paste by carbonation and to have improved the transition zone.

Acknowledgements. This result was obtained as a result of the work (JPNP16002) commissioned by the New Energy and Industrial Technology Development Organization (NEDO).

References Matsuda, N., Kameyama, T., Matsuda, M., Iyoda, T.: Study on the production method of lowenergy recycled aggregate by forced adsorption of CO2 gas. Proc. Jpn. Concr. Inst. 36, 1732– 1737 (2014) Yuya, R., Matsuda, N., Sugiyama, T., Matsuda, M., Iyoda, T.: Study of method for improving strength and durability of mortar using low-quality recycled fine aggregate. Proc. Jpn. Concr. Inst. 43, 965–970 (2021)

Experimental Study to Improve Performance of Two-Stage Concrete Without Injection Focusing on the Interfacial Transition Zone Karen Midori Masunaga1(B) , Tomoki Nagoya1 , and Takeshi Iyoda2 1 Graduate School of Engineering and Science, Shibaura Institute of Technology, 3-7-5 Toyosu,

Koto-ku, Tokyo 135-8548, Japan [email protected] 2 Department of Civil Engineering, Shibaura Institute of Technology, 3-7-5 Toyosu, Koto-ku, Tokyo 135-8548, Japan

Abstract. Two-stage concrete (TSC), also known as preplaced aggregate concrete, prepacked concrete, and rock-filled concrete, is a non-conventional concrete with an unusual construction method. It is produced by firstly placing the coarse aggregate into the formwork and after that, the voids are filled with a high-flow mortar mixture. This type of concrete has been applied in mass concrete, underwater concrete, and repair and strengthening of existing structures with economical and technical benefits. Previous studies showed that the interfacial transition zone between the coarse aggregate and the cementitious material has a primary influence on TSC, affecting the performance of hardened concrete. Also, more than the mechanical resistance of the coarse aggregate, other factors such as shape, good particle size distribution, combined with a mortar with non-shrinkage, nonsegregation characteristics, and good flowability are important to achieve satisfactory performance of TSC. In this experimental study, several types of admixtures (C–S–H type hardening accelerator and three types of expansive mineral admixtures) were added to a premixed high flow mortar to improve the interfacial transition zone between aggregate and mortar of TSC blocks without injection. Measurements of porosity, air permeability coefficient, and compressive strength were conducted for TSC cores and conventional concrete specimens. Experimental results showed that the use of Calcium Oxide (CaO) expansive admixture was the most effective method evaluated and that there is a high potential to expand applications of the TSC produced without injection, as it was possible to improve significantly both mechanical performance and mass transfer resistance, reaching similar values when compared to conventional concrete. Keywords: Two-stage concrete (TSC) · Special concrete · Interfacial transition zone · Expansive admixtures

1 Introduction 1.1 Two-Stage Concrete Two-stage concrete (TSC), also known by other denominations such as preplaced aggregate concrete, prepacked concrete, and rock-filled concrete, is a special type of concrete © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 24–35, 2023. https://doi.org/10.1007/978-981-19-7331-4_3

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characterized by an unconventional construction method: initially the coarse aggregates are inserted into the formwork, and then the remaining voids are filled with grout or high flow mortar. In this second stage of casting, pressurized injection method may be used but grout gravity pouring method without injection is more convenient and has economic benefits (Li et al. 2019).

Fig. 1. Direct contact of aggregates, absent in conventional concrete, significantly influences the stress transfer mechanism in two-stage concrete.

TSC has a higher volumetric aggregate ratio than conventional concrete and, thus, presents a peculiar mechanism of stress transfer, which occurs through the direct contact points of the aggregates (Fig. 1). While the structural performance of conventional concrete depends on the properties of the coarse aggregate, it has been reported that the mechanical strength of the aggregate has little influence in TSC, while the texture, particle size distribution, and void ratio have a dominant effect (Najjar et al. 2014). Moreover, to achieve superior performance for this type of concrete, a good adhesion at the interface of the aggregate with the cementitious material, also called interfacial transition zone (ITZ), is essential, since the stresses are transferred first through the coarse aggregate and later to the cementitious material. Thus, the amount and distribution of coarse aggregate, as well as the ITZ, significantly affect the axial compressive strength and mass transfer properties of TSC (An et al. 2014). 1.2 Advantages and Disadvantages of TSC The initial insertion of coarse aggregates into the formwork can make TSC an economic and sustainable concreting method because it allows the use of high quantities of coarse aggregate (cheaper) and, consequently, the reduction of cementitious material (more expensive). To achieve it, it is necessary an appropriate definition of the aggregate particle size distribution, which will reduce the void ratio. This feature results TSC having a higher modulus of elasticity when compared to conventional concrete, even for similar compressive strength values, since the modulus of the coarse aggregate is generally higher than that of the cement paste (Najjar et al. 2014). Another positive aspect of TSC is that it only requires the transportation of coarse aggregates and grout preparation and pouring, and do not require vibration. So, the production costs related to these steps can be reduced compared to the costs of obtaining a conventional ready-mix concrete at a

26

K. M. Masunaga et al.

construction site. In addition, this construction method makes possible to reduce the heat of hydration and segregation for mass concrete. On the other hand, to produce a good TSC a high-performance grout is essential. This means a binder material with good fluidity to fill the voids, that does not segregate and has small autogenous shrinkage – which can have an excessive cost. Otherwise, it will cause a reduction in mechanical strength and durability. It is also necessary to prepare leak-proof formworks for the flowable grout, which can also increase production costs. Due to the challenges to balance technical and economic performance, the use of TSC is still limited, having been used mostly with injection method in large concrete structures specially in China, in underwater concreting, and in repairs and strengthening of structures where transport and concreting with conventional concrete would not be feasible (Abdelgader et al. 2015). 1.3 Enhancing TSC Performance A lot of research has been developed to improve the performance of TSC, but the attention to TSC has increased with the increasing interest in reducing cement consumption for sustainable issues and with the development of new chemical admixtures for ultra-high performance concrete (UHPC). This is because UHPC can be combined with TSC to develop a material with excellent mechanical properties, high volume of coarse aggregate and low binder consumption, especially when supplementary cementitious material are used (Li et al. 2019). The following items were compiled by Najjar et al. (2014, 2016) to improve TSC’s performance. For example, it is indicated that the size of the coarse aggregate should be at least 4 times the largest size of the fine aggregate. Also, to obtain a void ratio between 25 and 50%, it is recommended to adopt a combination of aggregates with different particle size distribution and geometries (for example, crushed material which is more rectangular combined with natural aggregate which is rounder). This will reduce the voids and increase stress transfer points. Additionally, it was verified that the use of fly ash has positive effects as a supplementary cementitious material and can reduce bleeding and that silica fume and metakaolin has a microfiller effect and pozzolanic activity, improving mechanical properties, but it reduces the fluidity. Also, it was reported that expansive admixtures, despite may reduce the strength of grout by producing voids in the cementitious material, in TSC they result in a confining effect, reducing voids that are formed mainly under the coarse aggregate (cumulated water pockets), which usually has large dimensions. Li et al. (2019) also evaluated the effect of supplementary cementitious materials, like fly ash, metakaolin and silica fume, on the fresh and hardened mechanical properties of TSC, as well as the possibility of correlating the grout mechanical strength to the TSC mechanical strength. And to expand the applications of TSC, Yoon et al. (2015) studied the possibility of producing lightweight concrete using TSC, because with TSC pouring method a larger amount of lightweight aggregate could be preplaced without segregation. As an existing structure strengthening approach, Lee et al. (2018) and Esmaeili and Amiri (2022) recently investigated the use of TSC to transform ballasted railway tracks into slab tracks, by just pouring the cementitious grout to improve the transport capacity in a rapid and convenient way.

Experimental Study to Improve Performance

27

Considering economical and sustainable aspects, the unavoidable aging and deterioration of infrastructures and the increasing necessity of repairing and strengthening, as well as the continued use of concrete as a construction material, TSC may be a promising sustainable alternative option to conventional concrete, using large amounts of aggregates, saving cement and innovating construction methods. A previous study showed that the ITZ between the coarse aggregate and the cementitious material exerts significant influence on the TSC, resulting in low mechanical and mass transport resistance, regardless of the type of coarse aggregate used (Shibuya and Iyoda 2019). Also, experimental tests conducted by An et al. (2014) and Abdelgader et al. (2015) showed that the permeate paths were along the edges and that failures occurred by cracking forming around the coarse aggregate. Thus, this experimental program was conducted to improve performance of TSC without injection focusing on the treatment of ITZ. Compressive strength and mass transference properties of TSC produced using different types of admixtures were compared and analyzed.

2 Materials and Methods 2.1 Mix Design Core samples extracted from TSC blocks were compared with conventional concrete specimens, using porosity, air permeability, and axial compressive strength tests. In conventional concrete mix design, it was used Ordinary Portland Cement (OPC) with 40% of ground granulated blast furnace slag (GGBFS) replacement; and TSC was produced using industrialized pre-mixture high flow grout which contains about 40% of GGBFS replacement. The water binder ratio (W/B) was set at 0.45. To improve the performance of TSC without injection, Calcium silicate hydrate (C– S–H) type hardening accelerator admixture and three types of expansive admixtures were used to compensate for the adoption of concreting without injection method (Tables 1 and 2). The C–S–H type hardening accelerator chemical admixture (ACX) is a liquid product and was added replacing 5% of the water mass in the mix design. The expansive mineral admixtures EX1, EX2, and EX3 are solid material (powder) and were added 20 kg/m3 , only for TSC. Generally, they are added in replacement of cement, but as industrialized grout was used in the mix design of TSC, to compare the expansive admixtures effect, an extra mix design of TSC was produced by adding 20 kg/m3 of slag cement to the industrialized grout (BB). The mix design as well as the fresh state characteristics are shown in Table 3. The addition of the expansive materials reduced the fluidity of the mortar but did not compromise the workability to fill the TSC blocks. The coarse aggregate type used was common gravel with a maximum size of 20 mm for all mix designs, but for TSC particles smaller than 10 mm were also removed. 2.2 Casting Procedures and Experimental Tests for Concrete 2.2.1 Axial Compressive Strength After 3 days of sealed curing, from the rectangular concrete blocks of TSC and of conventional concrete 0.30 × 0.50 × 0.20 m, cylindrical cores were cut, with diameter

28

K. M. Masunaga et al. Table 1. Admixtures description

Name

Component

Information

ACX

C–S–H (calcium silicate hydrate)

Hardening accelerator admixture with C–S–H nanoparticles that meets the JIS A 6204:2021

EX1

Ettringite

EX2

Mixed compound (CaSO4 + CaO + 3CaO : 3Al2 O3 : CaSO4 )

EX3

Calcium oxide (CaO)

Expansive admixtures that react with water and are used to compensate for cement autogenous shrinkage and to prevent cracks. All admixtures agree with the JIS A 6202:2017

BB

Slag cement (ordinary portland cement with 40% GGBFS replacement)

Table 2. Expansive admixtures chemical composition Expansive Admixture

Ig loss (%)

SiO2 (%)

Al2O3 (%)

Fe2O3 (%)

MgO (%)

SO3 (%)

CaO (%)

F-CaO (%)

EX1

< 3.0

1.0–2.0

12.5–15.0

0.3–0.8

0.4–2.3

27–31

50–53.6

17.5–22

EX2

–

1.0

7.2

0.8

–

18.5

70.6

49.8

EX3

1.0

4.8

1.4

1.0

0.6

15.8

76.2

–

D = 0.1 m and height H = 0.2 m. After that, the concrete cores were cured in water for 28 days for the axial compressive strength test (Fig. 2). The mechanical performance evaluation was conducted following the JIS A 1108:2018: Method of test for compressive strength of concrete. 2.2.2 Air Permeability The cylindrical cores D = 0.1 m obtained according to item 2.2.1 were sectioned into 4 cylinders with height h = 0.05 m and dried in a chamber at 40 °C temperature until stabilization of mass for the air permeability test (Fig. 2). The test was conducted adapting the RILEM recommendations TC 116-PCD: ‘Permeability of concrete as a criterion of its durability’. It is measured the volume of air that permeates the cylindrical specimen in a period, under a fixed pressure. The inlet pressure was set at 0.1 MPa and the air permeability coefficient was obtained according to Eq. (1). K=

Q 2LP1 × A P21 − P22

K = Air permeability coefficient (cm4 /N・s) L = Thickness of specimen in airflow direction (cm) P1 = Inlet pressure (N/cm2 ) P2 = Outlet pressure - atmospheric pressure (N/cm2 )

(1)

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29

Table 3. Mix design of conventional concrete and TSC with admixtures Concrete type

Admixture

W/B

Type

Amount

–

–

ACX

5% of water mass

–

–

4

ACX

5

1

Conventional

2 3

TSC

0.45

OPC with 40% replacement of GGBFS

Fresh properties Slump

Flow

11.5 cm

–

–

–

Industrialized – grout (about 40% replacement of GGBFS)

312 mm

5% of water mass

–

282 mm

EX1

20 kg/m3

–

299 mm

EX2

20 kg/m3

–

293 mm

7

EX3

20 kg/m3

–

288 mm

8

BB

20 kg/m3

–

292 mm

6

0.45

Binder type

Q = Volume of permeated air (cm3 /s) A = Permeated area (cm2 ) 2.2.3 Porosity The cylindrical specimens D = 0.1 m and h = 0.05 m used in the air permeability test were used for the determination of porosity. After o mass stabilization in a chamber at 40 °C, the dry mass was obtained. After that, the specimens were saturated with water in a vacuum chamber at 0.1 MPa until complete water saturation. The saturated and submerged masses were then measured. The porosity was calculated according to the Eq. (2). Porosity =

masssaturated − massdry masssaturated − masssubmerged

(2)

2.3 Casting Procedures and Experimental Tests for Mortar To verify if the improving methods were acting on the cement matrix or on the ITZ of TSC, mortar specimens were also produced, with the same composition of the mixtures in Table 3, but without coarse aggregate. It should be noted that the identification “TSC” for mortar test results refers to the industrialized grout, used as a binder in the TSC, while the identification “CONV” relates to mortar produced with OPC with 40% GGBFS replacement.

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Fig. 2. Flow chart of the procedure to obtain specimens for the experimental tests for TSC and conventional concrete.

The mortar cylindrical specimens with diameter D = 0.05 m and height h = 0.1 m were cured in water for 28 days. Axial compressive test was performed adapting JIS A 1108:2018 for the specimens’ size, and the porosity was determined according the procedures described in 2.2.3, but using the fragments obtained from the compressive test.

3 Results and Discussions The compressive strength test results for concrete (TSC and conventional) and mortar are shown in Fig. 3. The use of ACX in the concrete mixtures improved the mechanical resistance of TSC (TSC + ACX) and conventional concrete (CONV + ACX). However, the strength’s increase for TSC was higher (+29%), compared to the increase occurred in conventional concrete (+6%). This is caused by the action of the C–S–H nanoparticles in ACX, which can not only reduce the setting time but also fill the voids in the mortar and the ITZ of TSC, improving adhesion between coarse aggregate and cementitious material (Sakai et al. 2021). When comparing the effect of adding the expansive admixtures EX1, EX2, EX3, and the cement slag BB in concrete, it was observed that, in all cases, there was an increase of the compressive strength, but the CaO admixture (EX3) resulted in the most significant improvement (+59%) and even exceeded the strength of conventional concrete (CONV). A different pattern can be seen in the mortar compressive strength results. It can be observed that there was no significant increase in the mechanical performance of mortars with the use of improving agents. This indicates that the admixtures acted in the ITZ of TSC and not only in the cement matrix of the mortar. Although mortars showed good mechanical strength, around 60 MPa, when they were used to produce TSC, it was not possible to reach similar values of strength for TSC, because the adhesion of the mortar to the coarse aggregate was the limiting factor, reducing the mechanical performance of TSC. It can be noted that EX3, despite resulting in lower compressive strength for mortar, resulted in the highest values for the TSC. As explained by Najjar et al. (2014), this is caused by the confinement effect induced by the interlocked aggregate particles in TSC, which limit the expansion of the mortar.

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31

Fig. 3. Compressive strength results for concrete (TSC and conventional) and mortar.

Figure 4 presents the results of concrete porosity and air permeability tests, and there is a linear relationship between these parameters for TSC. Also, the use of the improvement methods resulted in a reduction of the porosity to lower values, and of the air permeability coefficient to similar values compared to conventional concrete. However, for conventional concrete, there was no notable change in these parameters with the use of the ACX admixture. The reduction in the porosity and air permeability with the use of ACX for TSC confirms the effectiveness of ACX in reducing the ITZ, the weak point of TSC. In the case of conventional concrete there was no substantial improvement in these parameters because, although ITZ exists, its influence on concrete’s performance is less significant than in TSC.

Fig. 4. Relationship between porosity and air permeability coefficient for TSC and conventional concrete.

Figure 5 relates porosity and air permeability to the compressive strength results. Using different types of admixtures improved mass transfer properties of TSC to similar values, so the porosity and air permeability coefficient of TSC were similar for all improving methods. But the Figure shows that compressive strength was not the same, as previously shown in Fig. 3, and only EX3 resulted in a significant increase in mechanical performance, to a value higher than conventional concrete. This confirms that the compressive strength of TSC is influenced, not only by the total porosity itself, but also

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Fig. 5. Relationship between porosity and compressive strength and air permeability coefficient and compressive strength for TSC and conventional concrete.

by other parameters that affects the confinement caused by the expansive admixtures, such as compactness, position, and geometry of coarse aggregate. To analyze which type of porosity was being improved, the porosity results of concrete and mortar were compared. In the Fig. 6, it is possible to observe that all improving methods reduced the porosity of TSC, but for mortar, only EX3 and BB resulted in a significant reduction in the porosity of the cementitious matrix. Relating it to the compressive strength results (Fig. 3), it is possible to affirm that the increase in mechanical strength of TSC with the use of EX3, BB and ACX, the last ones in a smaller rate, is also related to the reduction of cement matrix porosity, a result that was not obtained with the other admixtures (EX1, and EX2).

Fig. 6. Porosity changes for TSC and mortar caused by the improvement methods.

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33

The admixtures acted in different ways when improving the TSC performance, as summarized in the Table 4. Experimental results indicated that the use of CaO expansive admixture (EX3) acted in reducing the voids both in the cement matrix and in the ITZ and it was more effective than the addition of slag cement (BB). Table 4. Effect of the adopted improvement methods for TSC Admixture

Cement matrix

ITZ

1

ACX



◯

2

EX1

✕

◯

3

EX2

✕

◯

4

EX3

◯

◎

5

BB

◯

◯

Figure 7 illustrates the stress transfer and rupture models of TSC, elaborated after this experimental investigation. To achieve maximum performance, three main aspects need to be evaluated: (i) ITZ, (ii) strength and good particle size distribution of the aggregate and (iii) strength of the cementitious matrix itself. The last one usually is not the limiting factor for mechanical performance, as it is easier to ensure superior quality. If all these aspects are not secured, the rupture will occur (a) on ITZ or (b) on the aggregate, with lower resistance and without reaching the full capacity resistance of the cement matrix. If all factors are evaluated and combined, TSC can achieve its full performance and stress transfer will occur uniformly through cement matrix and aggregates (c). Since the geometric factor and good particle size combination for coarse aggregate were not evaluated in this study, it is believed that it is possible to achieve even better performance for TSC.

Fig. 7. Rupture models for TSC: (a) on interfacial transition zone; (b) in the coarse aggregate; (b) in both cement matrix and coarse aggregate uniformly.

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4 Conclusion Two-Stage Concrete (TSC) has a peculiar mechanism of stress transfer, which may result in lower performance than conventional concrete, especially when high flow mortar is poured without injection. However, with the use of appropriate materials and good execution, the TSC without injection can achieve performance equal to or even better than conventional concrete, both in mechanical strength and mass transfer resistance, which is related to the durability of the hardened concrete. To improve the performance of TSC without injection, several methods were evaluated in this research. The improvement methods contributed significantly to reduce the negative effect of the interfacial transition zone, which is one of the weak points of TSC. The use of C–S–H type hardening accelerator admixture (ACX) contributed to increase the compressive strength and air permeability resistance. Depending on the type of expansive material, the effect on the final properties of the TSC was different. While the addition of slag cement (BB) and CaO type expansive admixture (EX3) showed a positive influence on both mechanical and durability properties, ettringite (EX1) and mixed compound (EX2) based expansive admixtures reduced only the porosity and air permeability coefficient of the TSC, but did not improve compressive strength to the same extent. Better performance and the consequent feasibility of TSC without injection for structural applications can be achieved with appropriate aggregate volume, geometrical shape and grading combination. Therefore, further research about these topics should be developed.

References Abdelgader, H.S., et al.: Self-compacting grout to produce two-stage concrete. In: ISBS: 2nd International Sustainable Buildings Symposium. Ankara, Turkey, 28–30 May 2015 (2015) An, X., et al.: Rock-filled concrete, the new norm of SCC in hydraulic engineering in China. Cement Concr. Compos. 54, 89–99 (2014) Esmaeili, M., Amiri, H.: Laboratory investigation into the flexural behavior of embedded concrete sleepers in two-stage concrete with preplaced ballast aggregate. Int. J. Conc. Struct. Mater. 16(12) (2022) JIS: JIS A 1108:2018: Method of test for compressive strength of concrete (2018) JIS: JIS A 6202:2017: Expansive additive for concrete (2017) JIS: JIS A 6204:2021: Chemical admixtures for concrete (2021) Lee, S., et al.: Effects of redispersible polymer powder on mechanical and durability properties of preplaced aggregate concrete with recycled railway ballast. Int. J. Concr. Struct. Mater. 12(1), 1–17 (2018). https://doi.org/10.1186/s40069-018-0304-1 Li, P.P., et al.: Conceptual design and performance evaluation of two-stage ultra-low binder ultrahigh performance concrete. Cement Conc. Res. 125 (2019) Najjar, M.F., Soliman, A.M., Nehdi, M.L.: Critical overview of two-stage concrete: properties and applications. Constr. Build. Mater. 62, 47–58 (2014) Najjar, M.F., Soliman, A.M., Nehdi, M.L.: Two-stage concrete made with single, binary and ternary binders. Mater. Struct. 49(1–2), 317–327 (2016). https://doi.org/10.1617/s11527-0140499-9

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RILEM: TC 116-PCD: permeability of concrete as a criterion of its durability. Mater. Struct. 32, 163–173 (1999) Sakai, K. et al.: Study of improving performance of recycled coarse aggregate concrete by several methods for pore structure modification. In: The 9th International Conference of Asian Concrete Federation (ACF2020/2021): Advanced and Innovative Concrete Technology, pp. 115–121. Thailand, 26–27 Nov (2021) Shibuya, A., Iyoda T.: A review of preplaced-aggregate concrete using recycled aggregate and railway wasted ballast. In: 16th East Asia-Pacific Conference on Structural Engineering and Construction (EASEC16). Australia, 3–6 Dec (2019) Yoon, J.Y., et al.: Lightweight concrete produced using two-stage casting process. Materials 2015(8), 1384–1397 (2015)

Application of Granite Fines to Substitute Sand in Concrete Production Shunzhi Qian1(B) , Kang Hai Tan1(B) , Ziyang Li1 , Namyo Salim Lim1 , Lu Jinping2 , and Wong Sook Fun3 1 School of Civil and Environmental Engineering, Nanyang Technological University, 50

Nanyang Avenue, Singapore 639798, Singapore {szqian,ckhtan,alex.li,namyolim}@ntu.edu.sg 2 American Concrete Institute-Singapore Chapter, 58 Sungei Kadut Loop, Singapore 729501, Singapore [email protected] 3 Centre for Urban Sustainability (CUS)-Temasek Polytechnic, 21 Tampines Ave 1, Singapore 529757, Singapore [email protected]

Abstract. Nowadays, sustainable construction by using alternative concrete materials has been advocated around the globe due to the exhaustion of major sources of natural sand (NS), compounded with environmental and ecological considerations. In the meantime, a huge amount of granite fines (GF) as a by-product of crushing and sizing of granite in production of building stone for masonry industry, tile, coarse aggregate for the concrete industry, etc. are produced every year which generally treated as waste. And the landfilling of them causes serious environmental problems. Considering the stable source and sand-like physical properties of GF, it can serve as an ideal alternative material to substitute sand as the fine aggregate component in the production of concrete, which not only minimizes environmental issues but also provides economic benefits, especially in small countries such as Singapore with limited or almost zero sources of sand. The technical feasibility is conducted for three classes of concrete, i.e., C32/40, C40/50, and C50/60 produced with GF with varying fines content which is defined as the percentage of particle size finer than 62.5 µm (10%, 16%, and 22%) and percentage substitution (0%, 30%, 50%, 75%, and 100%). The technical feasibility of producing concrete with GF substitution is then evaluated based on performance comparisons between specimens with GF and NS (0% substitution) with regards to fresh concrete properties (workability through slump test, and setting time) and durability of hardened concrete properties (water absorption, water penetration, and rapid chlorine penetration). Keywords: Recycled granite fine · Durability · Sustainable concrete

1 Introduction The exhaustion of major sources of natural sand (NS) around the globe, compounded with environmental and ecological considerations, has motivated the use of alternative © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 36–45, 2023. https://doi.org/10.1007/978-981-19-7331-4_4

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materials for sustainable concrete construction (Xiao et al. 2012; Thomas et al. 2013; Guo et al. 2018; Strukar et al. 2019). At the same time, a huge amount of granite fines (GF) as a by-product of crushing and sizing of granite in the production of building stone, tile, coarse aggregate, etc. for the masonry and the concrete industry are generally treated as waste and landfilled, causing serious environmental problems (Almeida et al. 2007; Sobreiro and Teresa 2001; Medina et al. 2018; Febin et al. 2019). Hence, GF serves as an ideal alternative material to substitute sand as a fine aggregate component in the production of concrete, not only minimizing environmental issues but also providing economic benefits, especially in a small country like Singapore with limited or almost zero sources of sand. The usage of GF substituting NS has been encouraged in many countries, especially in some regions where NS has become a scarce resource (Meng et al. 2018; Bravard et al. 2013). While in fact, the application of GF in the local and global concrete production is limited due to a lack of clear guidance and speculation on the long-term durability of concrete produced with GF, partly owing to the unfamiliarity of dealing with GF and inconsistent research findings and understanding of GF substitutional concrete. In Singapore, although Singapore Standard SS-EN 206:2013 “Concrete. Specification, performance, production and conformity” (Committee 2014) does not limit the percentage of GF substituting NS in concrete production, there is no industrial application of GF due to the aforementioned consideration. Therefore, to address the durability concern and boost the confidence of the Singapore concrete industry in the adoption of higher GF substitution, it is imperative to demonstrate the technical feasibility of producing GF concrete with equivalent performance to that of conventional concrete with NS. In this paper, the technical feasibility of GF concrete (up to standard) is mainly focused instead on the effect of GF incorporation (fines content and percentage substitution) on the performance of concrete. The rationale is focusing on the latter may not facilitate confidence towards immediate application as it may possibly lead to inconsistency and contradicting results as extracted from numerous publications (Singh et al. 2016b). This is because concrete is generally sensitive to numerous factors which are not easily controlled such as the source of GF and other constituents, mixed design, mixing quality, etc. In addition, theoretically, higher fines content (generally observed in GF) would improve the strength and durability as it would fill the void, making a compact structure with low permeability (Jain et al. 2019, 2020; Ghannam et al. 2016; Chen et al. 2020). The inferior performance with increasing fines content reported in some publications was generally associated with poor mixing (due to an increase in w/c ratio demand) (Singh et al. 2016a, c; Cheah et al. 2019). Hence, it can be implied that higher fines content and percentage substitution of GF could give a comparable or superior concrete performance (strength and durability) but under conditions of proper or good quality mixing. This further emphasized the more practical or effective approach of focusing on the technical feasibility (overall aspect) rather than only on certain aspects as it may not represent the universal conclusion. The technical feasibility is conducted for three classes of concrete, i.e., C32/40, C40/50, and C50/60 produced with GF with varying fines content (10%, 16%, and 22%) and percentage substitution (0%, 30%, 50%, 75%, and 100%). Then it is evaluated based

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on performance comparisons between specimens with GF and NS (0% substitution) with regards to fresh concrete properties (workability through slump test and setting time) and durability of hardened concrete properties (water absorption, water penetration and rapid chloride penetration). Industry recommendations on the specification of GF for concrete production would be established based on the tests.

2 Experimental Program To demonstrate the technical feasibility and translate it into the actual application of GF in the production of concrete in Singapore, the baseline conditions are established as follows: 1. All the concrete constituents, including GF, used in the research should comply with the existing code in Singapore SS EN 12620 (EN) for aggregate and SS EN 206 (Committee 2014) for other constituents. 2. The concrete mixes for GF with varying fines content and percentage substitution must satisfy two basic conditions which are of utmost interest in practice, i.e., first, the strength must be kept within 3 MPa from the targeted strength, and second, the workability should be of slump class S3. 3. Concrete mixes with 100% percentage substitution of GF containing 22% fines contents (f 22 ) represented the upper limit of the feasibility studies, while the ranges below are devised to investigate the implication or trend in concrete performance with the varying parameters. As the main industry concern hindering adoption of higher percentage substitution is the high fines content which may lead to inferior performance, in particular durability, it could be implied that if GF with higher fines content and substitution demonstrated comparable concrete performances to that of NS, there would be no issue for GF with lower fines content and substitution. 2.1 Material Preparation To produce samples with 10%, 16%, and 22% fines content, granite fines sample was dried naturally once received from the supplier. In the next stage, the sample was sieved through 8 mm, 4 mm, 2 mm, 1 mm, 0.5 mm, 0.25 mm, 0.125 mm, and 0.063 mm. After each size fraction has been separated, the composition of GF was reconstructed following the gradation of natural sand and adding extra fine GF powders to achieve the fines content of 10%, 16%, and 22%, respectively as illustrated in Fig. 1. The details of aggregate testing of GF complying with SS EN 12620 (EN) are summarized in Table 1. 2.2 Mix Design The attainment of targeted strength within 3 MPa tolerance in each concrete class is realized through adjustment of w/c ratio, in which the cement content is kept constant with variation in the water content, while the workability of class S3 (slump 100 mm

Application of Granite Fines to Substitute Sand in Concrete

39

100.0 Percentage passing (%)

90.0 80.0 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0.0625

0.125

0.25

Natural Sand

10% fines

16% fines

22% fines

0.5 1 Sieve size (mm)

2

4

8

Fig. 1. Gradation of granite fines with varying fines content and referenced natural sand

Table 1. Properties of granite fines Requirement

Properties

Value

Geometrical

Grading

GF85

% Passing 0.5 mm sieve

28% (CP)

Fines content

8%

MBV value

0.3 g/kg

Physical

Density

2630 kg/m3

Chemical

Water soluble chloride

< 0.01%

Acid-soluble sulphate

< 0.8%

Organic substance (in presence of humus)

Negative (lighter than organic plate no. 3)

Note: MBV-Methylene blue value

to 150 mm ± 10) is fulfilled by incorporating an adequate amount of superplasticizer. It is worth highlighting that while strength is mainly affected by the w/c ratio, the workability is highly sensitive to both the w/c ratio and amount of superplasticizer, in which the increase in w/c ratio and/ or superplasticizer led to a higher slump. Thus, the two varying parameters must be simultaneously considered in the mix design. In general, a lower w/c ratio may require a higher amount of SP for the mix design composition. In this paper, concrete classes C32/40, C40/50, C50/60 is termed as G40, G50, and G60, respectively. In SS EN 206 (Committee 2014), the amount of superplasticizer (SP) was recommended to be kept below 50 g per kg cement usage (5%). The SP used in this research is “MasterRheobuild” RH1000 with a density of 1.2 g/cm3 , which means the mass of

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1L SP equals 1200 g. The range of SP for G40, G50, and G60 are 1.8–4.1%, 1.9–2.7%, and 1.5–6%. It should be noted that the usage of 6% SP is for G60 with GF fines content of 22% and 100% substitution representing the ultimate upper bound in this study. Moreover, this concrete mix resulted in a slump value of 160 mm, implying the possible reduction of SP to 5%, while still satisfying the class S3 workability. It should be noted although the fresh properties are tested immediately upon mixing, the value could only be qualified if the 28-day strength of concrete could be satisfied (represented by 3 cube samples for each mix).

3 Test Results and Discussion 3.1 Fresh Concrete Properties Fresh properties of concrete are tested as summarized in Table 2. Table 2. Test standards and specifications for fresh concrete Properties

Standards/Specification

Slump

SS EN 206 (EN 12350-2:2019 2019)

Testing fresh concrete. Part 2: Slump test

Setting time

ASTM C 403 (Concrete and Aggregates 2008)

Admixtures for concrete, mortar and grout—test methods—Part 2: Determination of setting time

3.1.1 Slump Test The slump value for the three concrete classes plotted in Fig. 2 shows that all concrete mixes satisfy the class S3 slump requirement (100 mm to 150 mm ± 10 mm). To accommodate the event of a long delivery time from the concrete plant to construction site, a 2-h slump retention test is performed on G40 with 100% substitution of GF containing 16% fines content. G40 is selected as the most common use concrete class, while 16% represents a reasonable limit of fines content generally found in most of GF supplied, and ideally, it is aimed to achieve 100% GF substitution. To 2-h slump retention with a requirement of (50 mm to 90 mm ± 10 mm) is successfully achieved by incorporating set retarder RH168 which would generally have little effect on concrete properties other than delaying the setting of cement. Note that the concrete composition is slightly adjusted to meet the two basic conditions, i.e. strength and workability, with water, cement, 20 mm coarse aggregate, GF, RH1000, RH168 as 210 kg, 330 kg, 900 kg, 890 kg, 3.3 L, and 1 L. 3.1.2 Setting Time In general, as GF may facilitate the initial hydration, especially in G40 and G50, the setting time may be shortened (Jain et al. 2019, 2020; Ghannam et al. 2016). At the same

Application of Granite Fines to Substitute Sand in Concrete

41

Fig. 2. Slump value with varying replacement level of GF

time, the setting time may also be lengthened (as observed in some batches) owing to the usage of a higher dosage of superplasticizer (RH1000) which may delay the hydration and extended slump retention, leading to an overall increase in setting time (Chen et al. 2020; Cheah et al. 2019). Despite the variation in the trend of setting time as shown in Figs. 3 and 4, all the mixes had an initial setting time of more than 4 h, and most of the samples with GF up to 100% could complete the final setting between 8 and 20 h, which is generally acceptable for industry practice, as it allowed concrete delivery time as well as demoulding after 24 h. For industrial practice, a longer initial setting time of concrete may be beneficial and required: 1) When the concrete temperature is high, causing the concrete loses its slump too rapidly if its setting time is not delayed; 2) When concrete delivery takes more than 1.5 h; 3) When cold joints have to be avoided in massive concrete construction; 4) When concrete is slip formed at a very slow rate.

Fig. 3. Initial setting time with varying replacement levels of GF

Fig. 4. Final setting time with varying replacement levels of GF

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3.2 Durability Water absorption, water penetration, and rapid chloride penetration tests were performed to characterize the durability of hardened concrete as summarised in Table 3. These three indices are mainly determined by the porosity of the concrete, in which a more compact concrete will be beneficial towards concrete durability property, especially for those with reinforced structure. Table 3. Test standards and specifications for the durability of hardened concrete Properties

Standards/Specification

Description

Water absorption

BS 1881-122-2011

Testing fresh concrete. Part 2: Slump test

After 28 day’s curing, coring 75 mm ± 3 mm diameter core with 150 mm thickness, test and get the absorption value

Water penetration

BS EN 12309-8 2019

Testing fresh concrete. Part 7: Air content pressure methods

After 28 day’s curing, treat one surface of the 150 mm cube with 500 ± 50 kPa water pressure for 72 ± 2 h

Rapid chloride penetration

ASTM C1202-19

Admixtures for concrete, mortar and grout - test methods Part 4: Determination of bleeding of concrete

Monitor the current passing 50 mm slice of 100 mm diameter cores or cylinders in 6 h with 60 V DC

3.2.1 Water Absorption As could be seen in Fig. 5, most of the samples have water absorption ratios between 1% and 2%. Concrete incorporating GF shows either improved or comparable performance as compared to concrete with NS. Technically, the fines would fill up the pores, thereby reducing the porosity and resulting in the reduction of water absorption, which is beneficial for concrete durability (Prokopski et al. 2020; Jain et al. 2019, 2020). On the other hand, a higher w/c ratio (lower concrete strength class) will increase the water absorption of concrete due to the increment of porosity (Chen et al. 2020). In addition, the relatively higher water absorption of 2.5–3.5% exhibited in the reference batch of G40 and the corresponding batches containing 10% fines content was probably due to less ideal mixing or slight measurement inaccuracy. Notwithstanding, it is still below the industry practice limit of 4–5% for normal concrete. 3.2.2 Water Penetration Figure 6 shows that the water penetration of reference batches (0% GF substitution) of G40 and G50 is significantly higher than the reference batch of G60. This is because

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Fig. 5. Water absorption with varying replacement levels of GF

the higher w/c ratio in G40 and G50 has a significant influence in increasing the water penetration (Singh et al. 2016c). It could be seen that the use of GF can significantly reduce the water penetration for concrete classes below G60 owing to the filling up of fines into the pores and thus reducing the permeability (Jain et al. 2019, 2020). This influence is also identified to be more significant for concrete with a higher w/c ratio (Prokopski et al. 2020).

Fig. 6. Water penetration with varying replacement levels of GF

3.2.3 Rapid Chloride Penetration It is observed in Fig. 7 that for most of the samples, the charges of ion passing are below 4200 coulombs denoting moderate permeability. Generally, concrete mixes incorporating GF have comparable or slightly more adverse RCPT results compared to NS concrete, possibly due to the angular shape of GF making the pore structure link each other for easy transport of solution. Nevertheless, when durability against chloride is of concern, e.g. structure near to coastal area with high potential of airborne chloride, the resistance could be improved by the addition of waterproofing admixture, such as GGBS and silica fume which can reduce the permeability.

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Fig. 7. Rapid chlorine penetration with varying replacement levels of GF

4 Conclusion Testing on fresh and hardened concrete properties has been exhaustively performed on concrete mixes incorporating GF (satisfying the requirement in SS EN206:2008 (Committee 2014)) with varying fines content (10, 16, and 22%) and substitution level (30, 50, 75, and 100%) covering concrete classes C32/40, C40/50, and C50/60. Satisfactory performances were observed in all concrete mixes, signifying the technical feasibility in the application of GF in the production of concrete. With proper mixing and upon satisfying the basic requirement for strength and slump, the performance (fresh and hardened concrete properties) of GF concrete should not be of much concern as theoretically, the presence of higher fines content, as well as rough and angular shape of GF would produce a more compact concrete with better strength and durability (lower porosity). From the two above points and most importantly to drive towards a sustainable concrete production (minimize the exhaustion of sand and waste of GF), it is strongly encouraged to adopt a higher substitution rate of GF (even 100% for practicability).

References EN 12350-2: Testing fresh concrete. Slump test. BSI (2019) Almeida, N., Branco, F., de Brito, J., Santos, J.R.: High-performance concrete with recycled stone slurry. Cem. Concr. Res. 37, 210–220 (2007) Bravard, J.-P., Goichot, M., Gaillot, S.: Geography of sand and gravel mining in the Lower Mekong River. First survey and impact assessment. EchoGéo (2013) Cheah, C.B., Lim, J.S., Ramli, M.B.: The mechanical strength and durability properties of ternary blended cementitious composites containing granite quarry dust (GQD) as natural sand replacement. Constr. Build. Mater. 197, 291–306 (2019) Chen, J., Li, B., Ng, P., Kwan, A.: Adding granite polishing waste as sand replacement to improve packing density, rheology, strength and impermeability of mortar. Powder Technol. 364, 404– 415 (2020) Committee, B. A. C. S. 2014. SS EN 206: Concrete. Specification, performance, production and conformity (2014) Concrete, A. C. C.-O. & Aggregates, C.: Standard test method for time of setting of concrete mixtures by penetration resistance. ASTM International (2008) EN, S. 12620: 2008–Specification for aggregates for concrete. Spring, Singapore Febin, G.K., et al.: Strength and durability properties of quarry dust powder incorporated concrete blocks. Constr. Build. Mater. 228, 116793 (2019)

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Ghannam, S., Najm, H., Vasconez, R.: Experimental study of concrete made with granite and iron powders as partial replacement of sand. Sustain. Mater. Technol. 9, 1–9 (2016) Guo, H., et al.: Durability of recycled aggregate concrete—a review. Cement Concr. Compos. 89, 251–259 (2018) Jain, A., Gupta, R., Chaudhary, S.: Performance of self-compacting concrete comprising granite cutting waste as fine aggregate. Constr. Build. Mater. 221, 539–552 (2019) Jain, K.L., Sancheti, G., Gupta, L.K.: Durability performance of waste granite and glass powder added concrete. Constr. Build. Mater. 252, 119075 (2020) Medina, G., Del Bosque, I.S., Frías, M., De Rojas, M.S., Medina, C.: Durability of new recycled granite quarry dust-bearing cements. Constr. Build. Mater. 187, 414–425 (2018) Meng, X., Jiang, X., Li, Z., Wang, J., Cooper, K.M., Xie, Z.: Responses of macroinvertebrates and local environment to short-term commercial sand dredging practices in a flood-plain lake. Sci. Total Environ. 631, 1350–1359 (2018) Prokopski, G., Marchuk, V., Huts, A.: The effect of using granite dust as a component of concrete mixture. Case Stud. Constr. Mater. 13, e00349 (2020) Singh, S., Khan, S., Khandelwal, R., Chugh, A., Nagar, R.: Performance of sustainable concrete containing granite cutting waste. J. Clean. Prod. 119, 86–98 (2016) Singh, S., Nagar, R., Agrawal, V.: A review on properties of sustainable concrete using granite dust as replacement for river sand. J. Clean. Prod. 126, 74–87 (2016) Singh, S., Nagar, R., Agrawal, V., Rana, A., Tiwari, A.: Sustainable utilization of granite cutting waste in high strength concrete. J. Clean. Prod. 116, 223–235 (2016) Sobreiro, M., Teresa, V.: World performance of dimension stone industry in 2000. Mines Bulletin (2001) Strukar, K., Šipoš, T.K., Miliˇcevi´c, I., Buši´c, R.: Potential use of rubber as aggregate in structural reinforced concrete element—a review. Eng. Struct. 188, 452–468 (2019) Thomas, C., Setién, J., Polanco, J., Alaejos, P., De Juan, M.S.: Durability of recycled aggregate concrete. Constr. Build. Mater. 40, 1054–1065 (2013) Xiao, J., Li, W., Fan, Y., Huang, X.: An overview of study on recycled aggregate concrete in China (1996–2011). Constr. Build. Mater. 31, 364–383 (2012)

Effects of Various Ions in Seawater on Chloride Ion Behavior in Mortar Using Ground Granulated Blast-Furnace Slag Takuma Nakada, Yuko Ogawa, Kenji Kawai(B) , and Riya Catherine George Civil and Environmental Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashihiroshima City, Japan {ogaway,kkawai,riya}@hiroshima-u.ac.jp

Abstract. Concrete using ground granulated blast-furnace slag (GGBS) is said to have a greater effect on suppressing chloride penetration than concrete using only ordinary Portland cement (OPC). However, the chloride behavior and change of the pore structures in concrete using GGBS in the presence of various ions such as magnesium ions or sulfate ions in seawater have not been well investigated. This study aims to clarify the effects of various ions in seawater on chloride behavior in the mortar using GGBS. Two types of mortar were prepared with a water to binder ratio of 0.50. Only OPC and a mix of OPC and GGBS with a replacement ratio of 50% were used as binders. Crushed sand and tap water were used as fine aggregate and mixing water, respectively. After water curing of specimens at 20 °C for 28 days, an immersion test was conducted with four types of solutions for 28 or 56 days. The parameters for investigations in the immersion test were the total chloride content, the amount of Friedel’s salt measured with powder Xray diffraction analysis, the porosity, and the pore size distribution. The results showed that the effect of various ions in seawater on the penetration of chloride ions was smaller for the mortar blended with GGBS than for the mortar using only OPC. In the chloride binding ability tests, regardless of the presence of various ions, the mortar blended with GGBS produced more Friedel’s salt than the mortar using only OPC. In addition, it was confirmed that the amount of Friedel’s salt in mortars using only OPC was reduced due to the influence of sulfate ions. Also, for the mortar using only OPC, the filling of hydrates into pores was observed after immersion in the solution with various ions, but only slightly for the mortar blended with GGBS. Keywords: Ground granulated blast-furnace slag · Chloride ion · Friedel’s salt · Artificial seawater · Pore structure

1 Introduction Reinforced concrete structures in marine environments are affected by external seawater, which may cause deterioration of concrete and corrosion of bars. Corrosion of steel is caused by chloride ions entering from the outside, which prevent or destroy the passivation of iron. On the other hand, chloride ions in hardened cement paste are classified © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 46–51, 2023. https://doi.org/10.1007/978-981-19-7331-4_5

Effects of Various Ions in Seawater

47

into free chloride ions, which move freely in the pore solution, and binding chloride ions, which do not move in a normal concentration gradient or advection environment. Therefore, it is important to understand the behavior of chloride ions in hardened cement in detail in order to establish a method for predicting the deterioration and maintenance of marine structures. In a previous study, it was reported that magnesium ions (Mg2+ ) and sulfate ions (SO4 2− ) in seawater affected the chloride ion penetration and binding ratio in hardened cement paste using ordinary Portland cement (OPC) (De Weerdt 2014) (Naomachi 2017). Concrete using ground granulated blast-furnace slag (GGBS) is said to have a greater effect on suppressing chloride penetration than concrete using only OPC, and its application to marine structures is being promoted (Luo 2003). However, there are few studies on the effects of various ions in seawater on the behavior of chloride ions in the hardened cement paste using GGBS. This study aims to clarify the effects of various ions in seawater on chloride behavior in the mortar using GGBS.

2 Experiment 2.1 Mixture Proportions and Specimens In this study, immersion tests were conducted to investigate the effects of various ions on the behavior of chloride ions and the change in pore structure in mortar. Table 1 shows the physical properties of the materials used and Table 2 shows the chemical composition of OPC and GGBS. Table 3 shows the mixture proportions of mortar. Two types of mortars were prepared with a water to binder ratio of 0.50. Only OPC and a mix of OPC and GGBS with a replacement ratio of 50% were used as binders. Crushed sand and tap water were used as fine aggregate and mixing water, respectively. The fine aggregate volume ratio was 0.46. The specimens (50×100 mm) were demolded at the age of 1 day and cured in water at 20 °C until the age of 28 days. After curing, 10 mm thick sections were cut off from the top and bottom of the specimens, and the specimens were coated with epoxy resin except for the section used as the exposed surface. After confirming the hardening of the epoxy resin, the specimens were stored in water for 24 h. Table 1. Physical properties of materials Materials

Name

Notation

Physical properties

Cement

Ordinary portland cement

OPC

Density 3.16 g/cm3 Blaine fineness 3380 cm2 /g

Admixture

Ground granulated blast-furnace slag

GGBS

Density 2.91 g/cm3 Blaine fineness 4170 cm2 /g

Fine aggregate

Crushed sand

S

Density 2.59 g/cm3 Water absorption 1.21%

Water

Tap water

W

48

T. Nakada et al. Table 2. Chemical composition of binders Chemical composition (%) LOI SiO2

OPC

Al2 O3 Fe2 O3 CaO

1.97 20.24

K2 O TiO2 MgO Na2 O S

SO3 Cl−

5.12

3.07

65.58 0.32 –

1.22

0.23

–

GGBS 0.05 35.45 14.06

0.27

43.78 0.23 0.56

5.84

0.24

0.62 –

2.00 0.008 –

Table 3. Mixture proportions Notation

W/B

Unit (kg/m3 )

Fine aggregate volume ratio

W

OPC

GGBS

S

O

0.50

0.46

281

562

0

1411

OB

0.50

0.46

276

276

276

1411

2.2 Immersion Test The specimens were immersed in four different solutions: artificial seawater (SW), NaCl solution (NC), NaCl+MgCl2 solution (MC), and NaCl+Na2 SO4 solution (NS) for periods of 28 and 56 days. Table 4 shows the composition of the solution. The composition of each solution was determined based on the ionic concentration of artificial seawater prepared in accordance with Japanese industrial standard JIS A 6205 (Corrosion inhibitor for reinforcing steel in concrete). Table 4. Composition of the solution Concentration (mmol/L)

Cl−

Mg2+

SO4 2−

Na+

K+

Ca2+

Artificial seawater (SW)

560

55

29

477

9

11

NaCl (NC)

560

0

0

560

0

0

NaCl+MgCl2 (MC)

560

55

0

450

0

0

NaCl+Na2 SO4 (NS)

560

0

29

617

0

0

After immersion, the specimens were cut at 7 mm from the surface and the following measurements were carried out. The total and soluble chloride ion contents, Friedel’s salt content, and pore size distribution were quantified. The total and soluble chloride ion contents were measured in accordance with JIS A 1154, and Friedel’s salt content was determined by powder X-ray diffraction analysis. The pore size distribution was measured using a mercury intrusion porosimeter.

Effects of Various Ions in Seawater

49

3 Results and Discussions 3.1 Chloride Ion Contents and Pore Structure

2.0

(a)O Series 56d

1.5

NC

SW

MC

NS

1.0 0.5 0.0 0

7 14 21 Distanse from the surface (mm)

28

The amount of Soluble Chloride ion(%)

The amount of Soluble Chloride ion(%)

The soluble chloride ion contents (Clsol) after 56 days of immersion are shown in Fig. 1, and the penetration of chloride ion is suppressed in the OB series (Fig. 1b) mixed with GGBS compared with the O series (Fig. 1a). Regardless of whether GGBS was used or not, immersion in a solution with Mg2+ increased the number of soluble chloride ions. This may be due to an increase in the amount of chloride ions, which are anions, due to an increase in cations in the pore solution as magnesium ions increase. The pore size distribution of the OB series after 56 days of immersion (Fig. 2) showed a decrease in the total pore volume and an increase in the percentage of micropores smaller than 50 nm compared to that of the O series, regardless of the immersion solution type. This difference suggests that the densification of the pore structure by using GGBS is a factor in the suppression of chloride ion penetration. In the O-series, the total pore volume increased when immersed in SW and MC due to the presence of Mg2+ (Fig. 2). The reason for this increase was the change of calcium hydroxide (CH) into magnesium hydroxide (Brucite) in the presence of Mg2+ . The decrease in CH content led to an increase in the pores with the diameter of approximately 1 µm (Sudo et al. 2004). In addition, the volume of pores with the diameter below 0.01 µm is large compared to those from samples immersed in a solution without Mg2+ . This increase may be due to the conversion of some of the calcium silicate hydrate (C–S–H) to Magnesium silicate hydrate (M–S–H) and the decrease in the Ca/Si ratio. M–S–H is reported to be more weak than C–S–H and to affect durability loss (Yi 2020). On the other hand, there was little difference among the pore structures of the mortars using GGBS depending on the type of solution (Fig. 3b). This indicates that the presence of various ions in seawater has little effect on the pore structure of the mortar using GGBS. 2.0

(b)OB Series 56d

1.5

NC

SW

MC

NS

1.0 0.5 0.0 0

7 14 21 Distanse from the surface (mm)

Fig. 1. Amount of soluble chloride ion (immersion period: 56 days)

28

(a) 28 days

O OB NC

O OB

O OB

Total pore volume (cc/g)

T. Nakada et al. Total pore volume (cc/g)

50

(b) 56 days

O OB

O OB

NC

SW MC NS Pores more than 50 nm in diameter Pores less than 50 nm in diameter

O OB

O OB

O OB

SW MC NS Pores more than 50 nm in diameter Pores less than 50 nm in diameter

Fig. 2. Total pore volume 0.025

0.025

(b)OB Series 56d

0.020 0.015

NC

SW

MC

NS

Pore Volume(cc/g)

Pore Volume(cc/g)

(a)O Series 56d

0.010 0.005 0.000 0.001 0.01

0.1 1 10 Pore Size(μm)

100

1000

0.020 0.015

NC

SW

MC

NS

0.010 0.005 0.000 0.001 0.01

0.1 1 10 Pore Size(μm)

100

1000

Fig. 3. Pore size distribution (immersion period: 56 days)

3.2 FRiedel’s Salt Figure 4 shows the amount of Friedel’s salt after 56 days of immersion. The Friedel’s salt formation increased in the OB series except for immersion in NC. In the OB series, the amount of Friedel’s salt increased in the presence of various ions. The increase in the amount of Friedel’s salt produced by immersion in SW and MC was attributed to the higher concentration of chloride ions in the surface layer than in NC as Fig. 1. However, the effect of Mg2+ on the increase in Friedel’s salt production could not be clarified. In the O series, C3A, which is necessary for Friedel’s salt formation, is partially used for ettringite formation due to the presence of, which is thought to reduce the amount of Friedel’s salt formation compared to NC. The reason for the increase in Friedel’s salt production in the presence of SO4 2− in the OB series is thought to be due to the conversion of monosulfate hydrate to Friedel’s salt. GGBS is rich-Al2 O3 , so OB series contents many C3 A than O series. This is thought to produce larger amounts of ettringite and Friedel’s salt than the O series, even in the presence of SO4 2− .

4 Conclusions It was found that the penetration of chloride ions in the mortars using GGBS was suppressed more than that in the mortars without GGBS, regardless of the presence of

Amount of Friedel's Salt(g/sample-1g)

Effects of Various Ions in Seawater

0.12

NC

SW

MC

51

NS

0.10 0.08

0.06 0.04 0.02 0.00

O series

OB series

Fig. 4. Amount of Friedel’s salt (Immersion period: 56 days)

various ions in seawater. This is due to the densification of the pore structure caused by the replacement of cement with GGBS. The results suggest that the various ions in the seawater have little effect on the change in the pore structure of the mortar with GGBS. In addition, the amount of Friedel’s salt increased when cement was replaced with GGBS, compared to no GGBS replacement. Furthermore, the amount of Friedel’s salt in the mortar using GGBS increased during immersion in solutions containing various ions compared to immersion in NaCl solution.

References De Weerdt, K., Orsáková, D., Geiker, M.R.: The impact of sulphate and magnesium on chloride binding in Portland cement paste. Cem. Concr. Res. 65, 30–40 (2014) Luo, R., Cai, Y., Wang, C., Huang, X.: Study of chloride binding and diffusion in GGBS concrete. Cem. Concr. Res. 33(1), 1–7 (2003) Naomachi, S., Kato, K., Hashimoto, N., Kato, E.: Experimental study on effects of various ions and pH toward development of highly accurate prediction method for chloride induced deterioration of concrete superstructure of piled pier. J. Jpn Soc. Civ. Eng. 73(2), 438–443 (2017) Sudo, S., Haga, K., Hironaga, M., Tanaka, T., Nagasaki, S.: Modelling the leaching behaviour of Ca and the dependence of porosity on the diffusion coefficient. J. Jpn Soc. Civ. Eng. 753, 13–22 (2004) Yi, Y., Zhu, D., Guo, S., Zhang, Z., Shi, C.: A review on the deterioration and approaches to enhance the durability of concrete in the marine environment. Cem. Concr. Compos. 113, 103695 (2020)

Advanced and Sustainable Concrete Materials

Carbonation of Granite Fines Concrete in the Tropical Environment Ni Zhen(B) and Xudong Qian Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Queenstown S117576, Singapore {zhenni,qianxudong}@nus.edu.sg

Abstract. The exhaustion of major sources of natural sand in the region has provoked the use of alternative materials for sustainable concrete construction. Granite fines (GF) has been encouraged in many countries, including Singapore, to replace natural sand in concrete mixing. Carbonation is one of the most detrimental durability problems that cause the deterioration of reinforced concrete in the tropical countries like Singapore. However, the effect of GF replacement on the carbonation resistance of concrete is not well understood at present. The objective of the current work is to understand the effect of substituting natural sand with GF on the carbonation resistance of concrete in both accelerated and natural exposure condition. This study conducted a series of carbonation tests in both accelerated testing condition and natural exposure condition, on concrete produced with 0, 50, and 100% of granite fines substitution. The test results demonstrated that the replacement of natural sand with GF can enhance the carbonation resistance of the concrete. This study also established a correlation between the accelerated testing condition and natural exposure condition. The findings of this research provide recommendations on the service life design for industrial projects and may be further incorporated in design codes of the region. Keywords: Granite fines concrete · Carbonation · Service life design · Sustainability · Durability

1 Introduction In the recent years, the major sources of natural sand in the region has been depleted due to either environmental or ecological reasons. There is an urgent need to replace the use of natural sand with alternative materials in concrete production, especially for countries like Singapore where the construction materials are largely dependent on importing from the neighboring countries in the region. The Singapore Standard SS EN 12620: 2008 (2008) encourages the utilization of Granite fines (GF) to substitute natural sand in concrete production. GF is a by-product from the manufacture of granite aggregates. Unprocessed GF is flaky and irregular in shape, and generally contain a large amount of fine content whose particle sizes are smaller than 0.063 mm. Usually GF is not utilized and will be stored in waste

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 55–67, 2023. https://doi.org/10.1007/978-981-19-7331-4_6

56

N. Zhen and X. Qian

dumps, which could cause pollution to the environment. Adopting GF in concrete production could not only provide alternative sources of fine aggregates but also benefit the sustainability of the environment. However, the effect of GF replacement on the long-term durability performance, particularly carbonation, of concrete is not well understood at present. As the atmospheric concentration of carbon dioxide (CO2 ) is increasing throughout the years due to industrialization and rise in population, carbonation has become the main deterioration problem of steel-reinforced concrete structures, especially in tropical countries like Singapore. The objective of this study is to determine the effect of GF, which replaces the use of natural sand, on the carbonation resistance of concrete at the same grade. Besides, this study also aims to determine the correlation between the accelerated testing condition and the natural exposure condition, so that recommendations can be made for the future tests. In order to achieve such objectives, this study conducted a series of carbonation tests in both accelerated testing condition and natural exposure condition, on concrete produced with 0, 50, and 100% of GF substitution. The rate of carbonation for different replacement percentages of GF are compared. This study also established a correlation between the accelerated testing condition and the natural exposure condition. The service life design will also be recommended for industrial projects.

2 Review of the Previous Researches on Concrete Carbonation Being surrounded by the highly alkaline environment of concrete, a thin and non-porous passive protective oxide layer film could form on the surface of the steel reinforcement, protecting it from potential corrosion. When the environmental CO2 diffuses into concrete, it will react with both calcium hydroxide (Ca(OH)2 ) and calcium silicate hydrates (C–S–H) in the presence of moisture, producing calcium carbonates (CaCO3 ) as illustrated in Eqs. (1) and (2), Ca(OH)2 + CO2 → CaCO3

(1)

xCaO.ySiO2 .zH2 O + xCO2 → xCaCO3 + y(SiO2 .tH2 O) + (z − yt)H2 O

(2)

Such reactions can lower the pH value of the pore solution in concrete. If the environmental pH value drops below 9, the protective oxide layer will be destroyed, leading to the corrosion of the steel reinforcement. As steel corrodes, its volume expands, which results in the spalling of the concrete cover and loss of structural integrity. The carbonation process can be considered as a diffusion process. Papadakis et al. (1989) proposed the concept of “carbonation front” to describe the boundary that separates the fully carbonated areas from those that CO2 has yet to diffuse to. The depth of the carbonation front measured from the exposure surface is derived to be proportional to the square root of exposure time t √ d =k t (3) based on the diffusivity model (Currie 1986; Papadakis et al. 1989), where d represents the depth of carbonation and k stands for the rate of carbonation. The value of k can be

Carbonation of Granite Fines Concrete in the Tropical Environment

57

determined from the plot of the carbonation depth against the square root of exposure time. It can also be used to predict the carbonation depth after certain service life of a building. For example, from the measurement of the carbonation depth of several buildings aged 7 to 59 years √ in Singapore, Roy et al. (1996) determined the rate of carbonation to be 7 mm/ year. This √ indicates that in 100 years’ time, the average carbonation depth will achieve 7 × 100 = 70 mm. From the Fick’s Law (1855), the rate of carbonation can also be derived as follows (Rezagholilou et al. 2017),  2DC (4) k= M where C is the concentration of CO2 , D stands for the diffusion rate of CO2 into the concrete and M is the amount of the alkaline content in a unit volume of concrete. Assuming both D and M are independent of the CO2 concentration, one can obtain the correlation between the rate of carbonation under different CO2 concentration. This provides the theoretical basis for the adoption of the accelerated testing condition with higher CO2 concertation as an alternative for carbonation under natural exposure condition.

3 Material and Specimen Preparation In the current research, a normal concrete grade G40 with three replacement percentages of GF, namely 0, 50 and 100%, is investigated. Table 1 presents the material proportions for the three mixes, where the cement was ordinary Portland cement (OPC). The maximum size of the coarse aggregates was 20 mm. The particle size distribution of the natural sand and GF used in the specimen preparation are illustrated in Fig. 1, where the GF has a fine content of 16%. In order to achieve similar compressive strength, the water to cement (w/c) ratio for the reference mix G40 needs to be slightly lower than the other two GF mixes. The concrete specimens for both the compressive test and carbonation test were 100 × 100 × 100 mm cubes. Table 2 summarizes the compressive strengths for the different mixes. Two batches of specimens for the natural-sand mix G40 were prepared. The mean compressive strength for the first batch of the G40 mix (G40-1) was much lower, and the standard deviation (St. Dev) was higher than the other mixes. The poor and varying quality of the reference natural-sand concrete could affect the comparability of different mixes. In this regard, the natural sand mix G40 was then re-cast to achieve the desirable strength grade. The second batch of the natural-sand mix, G40-2, developed a mean compressive strength of 43 MPa at 31 days’ age and is considered acceptable for the subsequent carbonation tests. In the meantime, the carbonation test of G40-1 was continued to provide supplementary data on the comparison between the accelerated testing condition and the natural exposure condition.

4 Testing Conditions The carbonation tests under accelerated testing condition and natural exposure condition were performed in accordance to the British Standards BS 1881-210:2013 (2013) and

58

N. Zhen and X. Qian Table 1. Mix proportions for the test specimens (kg per m3 of concrete) w/c

Water

Cement

Coarse aggregates

Natural sand

Granite fines

RH1000

G40-NS

0.630

159.1

267.2

1064.0

856.0

0.0

9.2

G40-GF50

0.652

168.4

267.2

968.0

475.0

475.0

5.6

G40-GF100

0.652

165.0

267.2

968.0

0.0

950.0

9.0

Fig. 1. Particle size distribution for the natural sand and GF used in the specimen preparation

BS EN 12390-10: 2018 (2018) respectively. The detailed testing conditions are summarized in Table 3. For the accelerated testing condition, the ambient temperature adopted 27 °C for a closer temperature to the natural environment, and the relative humidity (RH) adopted 65% as specified by the RILEM Recommendation (1988). The actual environmental condition at the natural exposure site were continuously monitored for a period of 4 months. The average CO2 concentration was 3.93%, the average temperature was 28 °C and the average RH was 74.8%. Figures 2 and 3 illustrate the placement of the specimens inside the carbonation chamber for the accelerated testing condition, and at the site for the natural exposure condition. The carbonation depth of concrete specimens was determined by the color indication of 1% phenolphthalein ethanol solution. In the presence of non-carbonated concrete where it is still highly alkaline, the solution will turn pink. When the concrete is fully

Carbonation of Granite Fines Concrete in the Tropical Environment

59

Table 2. Compressive strengths of the test specimens Compressive strength (MPa) Specimen number

G40-1

G40-2

G40-GF50

G40-GF100

Testing age

31 days

31 days

34-day

32-day

1

33.38

45.53

47.84

43.76

2

44.06

38.43

44.36

43.87

3

29.3

45.32

46.34

44.69

4

34.84

43.08

–

–

5

43.4

–

–

–

Mean

37

43

46

44

St. Dev.

5.8

3.3

1.4

0.4

carbonated, the alkalinity of the concrete will be reduced and the solution will remain colorless. Table 3. Testing conditions for the two types of carbonation test Accelerated testing condition Natural exposure condition Standards

BS 1881-210:2013 [1]

BS EN 12390-10: 2018 [2]

Temperature

27 °C

25–32 °C

CO2 concentration

4%

~ 0.04%

Relative humidity (RH)

65%

60–90%

Conditioning

In the laboratory air for 14 days after curing

Nil

Sealing

Top, bottom and two side surfaces with paraffin wax

Nil

Exposure period

7, 14, 28, 42 56, 63, 70 and 84 days

3, 6, 9 months, 1 year…, up to 2 years

5 Results and Analysis 5.1 Accelerated Testing Condition The carbonation depths under the accelerated testing condition are presented in Table 4. The two natural-sand mixes were measured up to 84 days and the two GF mixes were measured up to 109 days. The carbonation depths are also plotted against the square root of the exposure time in Fig. 4. In general, as the replacement percentage of GF

60

N. Zhen and X. Qian

Fig. 2. Specimens being placed in the carbonation chamber

Fig. 3. Specimens in the natural exposure condition.

increases, the rate of carbonation becomes smaller. The rate of carbonation for G40-2 is lower than G40-1, which is consistent with their compressive strengths. Among all the mixes, G40-GF100 has the best resistance to carbonation, indicating an excellent long-term durability performance. Such beneficial performance of GF concrete could be attributed to the larger fine content of the GF particles, where they fill in the pores of the concrete. As a result, the diffusion of the CO2 slows down the diffusion, so does the carbonation process. The overall carbonation rate of G40-2 is only slightly higher than the G40-GF50 mix. However, the standard deviation of the measured carbonation depth for the naturalsand mixes are much larger than the GF mixes, suggesting a wider spread of data of the measured carbonation depth. This can also be observed from the carbonation patterns at the 84-day measurement in Fig. 5.

Carbonation of Granite Fines Concrete in the Tropical Environment

61

Table 4. Carbonation depth under the accelerated carbonation condition Carbonation depth (mm) Duration (days)

G40-1

G40-2

G40-GF50

G40-GF100

Mean

St. Dev.

Mean

St. Dev.

2.76

0.50

1.94

0.54

4.09

0.62

2.57

0.68

1.10

5.30

0.42

4.37

0.53

1.35

7.40

0.64

5.12

0.87

2.78

8.58

0.77

5.49

0.69

10.25

2.70

8.57

0.80

5.81

0.82

9.84

4.07

8.81

0.81

5.91

0.69

10.89

3.59

10.69

1.37

7.40

0.97

Mean

St. Dev.

Mean

St. Dev.

7

3.66

0.55

2.16

0.64

15

5.58

0.77

3.54

0.98

28

7.49

0.89

5.43

42

11.03

1.61

6.99

56

18.18

1.63

8.78

63

20.43

1.78

70

14.64

2.55

84

17.62

2.06

98

–

–

–

–

11.76

1.01

7.16

1.67

109

–

–

–

–

11.10

1.12

9.04

1.27

Carbonation Depth in the Accelerated Testing Condition 20 G40-1 18

G40-2

y = 33.11x R² = 0.97

16

G40-GF50

Carbonation Depth (mm)

G40-GF100 14

y = 22.13x R² = 0.97

12

y = 21.22x R² = 0.99

10 8

y = 14.73x R² = 0.97

6 4 2 0 0.0

0.1

0.2 0.3 0.4 0.5 Square Root of Exposure Time (√years)

0.6

Fig. 4. Carbonation depths against the square root of time in the accelerated testing condition

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N. Zhen and X. Qian

Fig. 5. Illustration of the carbonation depth after 84 days’ exposure to the accelerated testing condition for (a) G40-1, (b) G40-2, (c) G40-GF50 and (d) G40-GF100

5.2 Natural Exposure Condition The carbonation depths under natural exposure condition are presented in Table 5 as well as plotted against the square root of exposure time in Fig. 6. The trend in the rate of carbonation is consistent with the accelerated testing condition. It is also worth noting that the carbonation depth for G40-GF100 was still very small even after 20 months’ exposure, as illustrated in Fig. 7. Such small carbonation depth cannot be measured accurately and the results for G40-GF100 presented in Table 5 and Fig. 6 are only indicative. Despite that, G40-GF100 still have the best carbonation resistance among all the mixes studied, implying a superior resistance to carbonation of the 100% replacement of GF.

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Table 5. Carbonation depth under natural exposure condition Carbonation depth (mm) Duration (months)

G40-1

G40-GF50

G40-GF100

Mean

St. Dev

G40-2 Mean

St. Dev

Mean

St. Dev

Mean

St. Dev

3

1.79

0.84

0.99

0.51

0.81

0.40

~ 0^

–

6.5

2.73

1.00

1.94

0.48

1.69

0.43

–

–

9

3.47

1.16

2.29

0.66

2.20

0.57

–

–

12

4.68

0.89

–

–

2.41

0.56

–

–

13

–

–

2.79

0.83

–

–

–

–

16

5.15

1.17

–

–

2.58

0.98

–

–

20

6.85

1.2

–

–

2.93

0.68

~ 1.00^

–

Note ^The carbonation depth for G40-GF100 is only indicative Carbonation Depth in the Natrual Exposure Condition

Carbonation Depth (mm)

10

G40-1

9

G40-2

8

G40-GF50 G40-GF100^

7

y = 4.58x R² = 0.94

6 5 4

y = 2.60x R² = 0.98

3

y = 2.30x R² = 0.97

2 1 0 0.00

0.20

0.40 0.60 0.80 1.00 1.20 Square Root of Exposure Time (√years)

1.40

1.60

Fig. 6. Carbonation depth in the natural exposure condition Note ^The carbonation depth for G40-GF100 is only indicative

5.3 Design Recommendations A general development of the steel reinforcement corrosion is reproduced in Fig. 8. According to fib Model Code (2006), there is no model that is broadly accepted to predict the length of the corrosion period till cracking, spalling or collapse of the structure

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Fig. 7. Carbonation depth of G40-GF100 after 20 months’ exposure in the natural condition

occurs. For this reason, the service life is normally predicted by assuming the limit state, i.e. failure criterion, of reinforcement de-passivation. The propagation period of the corrosion until cracking then serves as the safety margin. In the case of carbonation, this corresponds to the point when the concrete cover is fully carbonated, or when the carbonation front reaches the surface of the steel reinforcement. Hence, the design thickness of the concrete cover td can then be calculated as √ td = k × SL (5) where SL is the design service life. The rate of carbonation is preferably the value directly measured from the natural exposure condition. However, if such data is not available due to the longer testing duration, it can be estimated from the accelerated carbonation test instead. As indicated by Eq. (4), if one assumes that the diffusion rate of CO2 and the alkaline content in a unit volume of concrete are independent of the CO2 concentration and the concrete composition, the theoretical ratio between the rate of carbonation for the accelerated testing condition and the natural exposure condition should be √ √ Ca 4% ka = √ =√ ≈ 10 (6) kn Cn 0.0393% where ka and kn are the rates of carbonation under accelerated testing and natural exposure conditions, Ca and Cc stand for the corresponding CO2 concentration. Table 6 summarizes the measured rate of carbonation for the two types of carbonation test, the corresponding ratio of k, as well as the minimum design thickness of the concrete cover for a 100 years’ service life. The actual ratio of k is not a constant, rather, it ranges from 7.23 to 9.22 for the concrete mixes studied in the current research. Such deviation indicates that the previous assumption made may not be correct. The diffusion rate of CO2 should be dependent on the CO2 concentration and the composition of the concrete.

Carbonation of Granite Fines Concrete in the Tropical Environment

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Fig. 8. Typical deterioration levels for a steel reinforced concrete structure suffering from reinforcement steel corrosion (fib 2006)

Table 6. Summary of the rate of carbonation and the ratio between the accelerated testing condition and the natural exposure condition Exposure condition

G40-1 k

R2

G40-2 k

R2

G40-GF50 k

R2

G40-GF100 k

R2

Accelerated testing

33.11

0.97

22.13

0.97

21.22

0.99

14.73

0.97

Natural exposure

4.58

0.94

2.60

0.98

2.30

0.97

1.47^

–

Ratio of k

7.23

8.51

9.22

10^

Design thickness of concrete cover* (mm)

46

26

23

15^

Note ^Estimated from the theoretical ratio of k, i.e., 10; * Assumed a 100 years’ service life

In the absence of accurate measurement for G40-GF100 under the natural exposure condition, the ratio of k is assumed to be 10. This is conservative because the actual carbonation depth after 20 months’ exposure is smaller than 1 mm as indicated in Fig. 7. The rate of √carbonation under the natural exposure condition is hence estimated to be 1.47 mm/ year, which results in a design cover thickness of 15 mm. However, if in any future study that the carbonation test under the natural exposure condition is totally

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unavailable, the ratio of k should conservatively adopt the minimum value determined in the current study, which is 7.23, for the design and evaluation of the concrete cover thickness.

6 Conclusions This study has investigated the effect of replacing natural sand with GF at different percentages on the resistance to carbonation for grade G40 concrete. Carbonation tests under both the accelerated testing condition and natural exposure condition demonstrated that the adoption of GF in concrete production can enhance the concrete’s resistance to carbonation. As the replacement level increases, the carbonation of concrete becomes slower. The design concrete cover thickness for the G40 concrete with 50 and 100% GF replacement are 23 mm and 15 mm respectively, which are much less than the normal range of concrete cover thickness. Hence, the adoption of GF in concrete production can also provide additional safety margin against carbonation induced reinforcement corrosion in addition to the benefits of sustainability. This study also determined the correlation between the rate of carbonation, k, under the accelerated testing condition and the natural exposure condition. It is recommended to conservatively adopt 7.23 as the ratio of k based on the minimum value determined in the current study, instead of the theoretical ratio of 10. Acknowledgement. The authors would like to thank Building and Construction Authority (BCA) Singapore for their financial support of the research project. The authors would also like to extend their gratitude to American Concrete Institute Singapore Chapter (ACI-SC) for preparing the specimens for the carbonation test.

References BS 1881-210: 2013: Determination of the potential carbonation resistance of concrete – Accelerated carbonation method. The British Standard Institution, London, UK (2013) BS EN 12390-10: 2018: Determination of the carbonation resistance of concrete at atmospheric levels of carbon dioxide. The British Standard Institution, London, UK (2018) Currie, R.J.: Carbonation depth in structural-quality concrete: an assessment of evidence from investigations of structures and from other sources. Building Research Establishment (UK) Report (1986) Fick, A.: On liquid diffusion. London Edinburgh, Dublin Philosophical Mag. J. Sci. 10(63), 30–39 (1855) International Federation for Structural Concrete (fib): Model code for service life design. fib Bulletin, vol. 34. Lausanne, Switzerland Papadakis, V.G., Vayenas, C.G., Fardis, M.N.: A reaction engineering approach to the problem of concrete carbonation. Am. Inst. Chem. Eng. J. 35, 1639–1650 (1989) Rezagholilou, A., Papadakis, V.G., Nikraz, H.: Rate of carbonation in cement modified base course material. Constr. Build. Mater. 150, 646–652 (2017) RILEM CPC-18 Measurement of hardened concrete carbonation depth. In: RILEM Recommendations for the Testing and Use of Constructions Materials, pp. 56–58 (1988)

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Roy, S.K., Beng, P.K., Northwood, D.O.: The carbonation of concrete structures in the tropical environment of Singapore and a comparison with published data for temperate climates. Mag. Concr. Res. 48(177), 293–300 (1996) SS EN 12620:2008: Specification for aggregates for concrete. In: Building and Construction Standards Committee, Singapore

Carbonation Resistance of Portland Blast Furnace Slag Cement Type B Concrete Internally Cured by Using Roof-Tile Waste Aggregate Yusuke Inoue, Yuko Ogawa, Kenji Kawai(B) , and Riya Catherine George Civil and Environmental Program, Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashihiroshima City, Japan {m211385,ogaway,kkawai,riya}@hiroshima-u.ac.jp

Abstract. Internal curing is a method in which a portion of the aggregate is replaced by a porous material having a high water absorption to supply curing water inside the concrete. The use of roof-tile waste aggregate as an internal curing material has been investigated, and its effect on reducing the autogenous shrinkage and increasing the compressive strength of ultra-high strength concrete has been reported. The purpose of this study was to evaluate the effects of roof-tile waste aggregate on the carbonation resistance of Portland blast furnace slag cement type B concrete. Six types of concrete with water-to-cement ratios of 0.50 and 0.35 were prepared with different replacement ratios of roof-tile waste coarse aggregates and fine aggregates. Concrete specimens were cured under sealed condition at 20 °C for 7 days before exposing to the air (20 °C, 60%R.H.). The accelerated carbonation resistance, air permeability, and pore structure of concrete near the exposed surface were investigated. From the investigations, no densification of the pore structure by roof-tile waste aggregate was observed. It was found that roof-tile waste aggregate did not improve the carbonation resistance with a waterto-cement ratio of 0.50. When the water-to-cement ratio was 0.35, carbonation did not proceed enough to measure the carbonation depth and no difference was observed in the use of roof-tile waste aggregate. On the other hand, the use of rooftile waste aggregate reduced permeability, regardless of the water-to-cement ratio. Therefore, the relationship between carbonation resistance and air permeability was different depending on the presence or absence of roof-tile waste aggregate. It is because the surface water content of concrete with roof-tile waste aggregate is higher than that without roof-tile waste aggregate, allowing more water to be stored inside the concrete and consequently increasing its impermeability. Keywords: Blast furnace slag · Roof-tile waste aggregate · Carbonation · Air permeability · Pore structure

1 Introduction Since the hydration reaction of Portland blast furnace slag cement type B occurs more slowly than that of ordinary Portland cement, long wet curing is required for concrete © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 68–76, 2023. https://doi.org/10.1007/978-981-19-7331-4_7

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made with Portland blast-furnace slag cement type B at early ages. In contrast, several studies have investigated the application of internal curing using roof-tile waste aggregate with moderate water absorption and crushing value to blast furnace slag cement concrete, and it has been confirmed that the pore structure is densified, and strength is improved by the internal curing. On the other hand, there are few reports on the effect of internal curing of roof-tile waste aggregate on durability, such as resistance to carbonation and chloride ion penetration. In particular, in reinforced concrete structures, carbonation as well as chloride ion penetration of the concrete cover causes internal steel corrosion, so a more detailed study on the relationship between internal curing and carbonation is necessary for the practical application of concrete using roof-tile waste aggregate. The present study aims to investigate carbonation resistance of Portland blast furnace slag cement type B concrete internally cured by using roof-tile waste aggregate.

2 Experiment 2.1 Materials Portland blast-furnace slag cement type B (BB) was used in this study. It conforms to JIS R 5211 and contains 30–60% blast furnace slag. The density of the cement was 3.04 g/cm3 while the Blaine fineness was 3860 cm2 /g. Crushed quartz-porphyry was used as the conventional fine and coarse aggregates in the concrete. Roof-tile waste coarse aggregate (RWCA) and roof-tile waste fine aggregate (RWFA) were used as internal curing materials in a saturated surface-dry condition after 7-day water immersion. The physical properties of these aggregates are listed in Table 1 and the particle size distributions are shown in Fig. 1. Images of roof-tile waste aggregates are shown in Fig. 2. G2010 and G1505 were mixed in a volume ratio of 55:45, and the roof-tile waste coarse aggregates were replaced by G1505 for considering particle size distribution. 2.2 Mixture Proportions and Specimens The unit water content was 170 kg/m3 , the water-to-cement ratios (W/C) were 0.35 and 0.50, and the fine aggregate ratio were 41.6% and 44.6%, respectively. The target slump value was 10.0 ± 2.0 cm and the target air content was 4.5 ± 0.5%, which were adjusted by using chemical admixtures. Six types of concrete were prepared with various amounts of roof-tile aggregate replacement: no replacement of roof-tile waste aggregate (50BBC, 35BBC), 30vol% replacement of roof-tile waste coarse aggregate (50G30, 35G30), 40vol% and 45vol% replacement of roof-tile waste fine aggregate (50S40, 35S45). The replacement ratio of roof-tile waste fine aggregate was adjusted so that the water absorption was the same as that of roof-tile waste coarse aggregate at each water-cement ratio (Table 2). Prism specimens with dimensions of 100 × 100 × 400 mm were prepared. After casting, the specimens were sealed and cured at 20 °C. The specimens were demolded at the age of 7 days, and one side was exposed to the air, and the other five sides were covered with aluminum adhesive tape. Then, they were placed in a chamber at 20 °C and 60%RH.

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Y. Inoue et al. Table 1. Physical properties of aggregates Crushed quartz-porphyry

Roof-tile waste

fine aggregate

coarse aggregate

fine aggregate

coarse aggregate

Notation

S

G (2010)

G (1505)

RWFA

RWCA

Density in saturated surface-dry condition (g/cm3 )

2.61

2.61

2.61

2.24

2.25

Water absorption (%)

1.07

0.68

0.66

9.34

10.02

Aggregate size (mm)

0–5

10–20

5–15

1–5

5–13

Fraction passing (%)

100 90

S

80

G

70

RWFA

60

RWCA

50 40 30 20 10 0 0.075

0.15

0.3

0.6

1.2

2.4

5 4.8

10 9.6

20 19.2

40 38.4

Sieve size (mm)

Fig. 1. Particle size distributions of aggregates

(a) RWFA

(b) RWCA

Fig. 2. Images of roof-tile waste aggregates

Carbonation Resistance of Portland Blast Furnace Slag Cement

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Table 2. Mixture proportions and properties of fresh concrete Unit content (kg/m3 ) W

BB S

AE WR Properties of (BB × (BB × fresh concrete %) RWFA G G RWCA %) Slump Air (2010) (1505) (cm) content (%)

35-BBC 170 486 679 –

525

428

–

0.0040 0.0040

9.0

4.8

35-G30

679 –

525

141

246

0.0040 0.0040

9.0

4.0

35-S45

373 263

525

428

–

0.0020 0.0035 12.0

4.0

535

438

–

0.0030 0.0025

8.5

4.0

50-BBC

340 783 –

50-G30

783 –

535

146

251

0.0030 0.0020

8.0

4.2

50-S40

472 268

535

438

–

0.0030 0.0020

8.0

4.2

2.3 Testing Procedure The accelerated carbonation rate coefficient, air permeability, and pore size distribution were examined. The accelerated carbonation rate coefficient was calculated by conducting accelerated carbonation tests in accordance with JIS A 1153. The specimens were placed in an accelerated carbonation chamber (20 °C, 60%RH, 5.0%CO2 ) after the age of 35 days, and the carbonation depth was measured just before the start of accelerated carbonation, and at the accelerated carbonation periods of 1 week, 4 weeks and 9 weeks. The carbonation depth was assumed to be proportional to the square root of time, and the slope of the regression line between the square root of the carbonation period and the accelerated carbonation depth was calculated as the accelerated carbonation rate coefficient. The pore size distribution test was performed by the mercury intrusion method. From the specimen after the carbonation depth measurement, 0–5 mm and 5–10 mm from the exposed surface were cut out with an oil cutter and crushed to less than 5 mm. In the cases of 35S40 and 50S45, the roof-tile waste fine aggregates were removed from the sample. The air permeability of the surface layer was measured by the Torrent method, using the same specimen placed in the accelerated carbonation chamber at the same age as the accelerated carbonation depth measurement. It is reported that the reliability of air permeability by the Torrent method can be ensured when the surface moisture content is less than 5.5% [Torrent 2014], so it was measured at the same ages as the air permeability test.

3 Result and Discussions 3.1 Accelerated Carbonation Test The accelerated carbonation depths are shown in Fig. 3, and the accelerated carbonation rate coefficient and its determination coefficient are shown in Table 3. At the water-tocement ratio of 0.50, the carbonation progressed at the same level regardless of whether

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roof-tile waste aggregate was replaced or not although it has been reported that internal curing with roof-tile waste aggregate densifies the pore structure of concrete, which was expected to improve the carbonation resistance [Sato 2011]. On the other hand, in the case of the water-to-cement ratio of 0.35, the depth of 35G30 is slightly smaller than that of the other mixtures. However, the progress of carbonation at 9 weeks of the accelerated carbonation period was hardly observed, and it is difficult to indicate that the effect of roof-tile waste aggregate replacement was fully recognized. Therefore, it is necessary to study the effect with the water-to-cement ratio of 0.35 on carbonation for a longer time. 0.80

12.00 10.00 8.00 6.00 4.00 2.00 0.00 0.00

50BBC 1.00

50G30 2.00

50S40

Accelerated carbonation depth(mm)

Accelerated carbonation depth(mm)

14.00

0.60 0.40 0.20 35BBC

0.00

3.00

0.00

1.00

35G30

35S45

2.00

3.00

Square root of accelerated carbonation period(√week)

Square root of accelerated carbonation period(√week)

Fig. 3. Accelerated carbonation depth (left: W/C 0.50, right: W/C 0.35)

Table 3. Accelerated carbonation rate coefficient and determination coefficient 50BBC 50G30 50S40 35BBC 35G30 35S45 Accelerated carbonation rate coefficient 3.98 √ (mm/ week)

3.91

4.20

0.14

0.098

0.13

Determination coefficient

0.986

0.979

0.947

0.828

0.944

0.998

3.2 Air Permeability The air permeability kT and surface moisture content are shown in Fig. 4. For 35BBC, the air permeability kT was almost constant regardless of the decrease in the surface moisture content, whereas the kT increased with the decrease in the surface moisture content for the other mixtures. This trend was more significant for mixtures with higher water-to-cement ratios and mixtures using roof-tile waste aggregate. In the case of the water-to-cement ratio of 0.50, the water evaporation was large, and the inhibition of the cement hydration due to the drying surface layer caused coarsening of the pore structure, resulting in the sharp increase in the air permeability with the decrease in the surface moisture content. On the other hand, the pore structure with a water-to-cement ratio of 0.35 is denser than that with a water-to-cement ratio of 0.50, which caused the low water evaporation and the low air permeability. It is known that the air permeability is affected by the moisture content of concrete, and it is correlated with the amount of water

Carbonation Resistance of Portland Blast Furnace Slag Cement

73

evaporation at the same W/C as well as the surface moisture content [Hayakawa 2012]. In this study, when roof-tile waste aggregate was used in mixtures with a low water-tocement ratio, the air permeability was lower in the early ages because the water in the concrete surface was retained by the internal curing water. However, when the water-tocement ratio was higher, the air permeability was also affected by the greater moisture evaporation, especially near the exposed surface. While the progress of carbonation was similar for mixtures with the same water-to-cement ratio, the air permeability showed a different trend depending on whether roof-tile waste aggregate was used or not. 10

10

kT(10-16m2)

1 0.1 0.01

0.001

35BBC 35G30 35S45

1

kT(10-16m2)

50BBC 50G30 50S40

0.1 0.01 0.001

3.5

4.0 4.5 5.0 5.5 Surface moisture content(%)

3.5

4.0 4.5 5.0 5.5 Surface moisture content(%)

Fig. 4. Air permeability kT and surface moisture content (left: W/C 0.50, right: W/C 0.35)

3.3 Pore Structure The pore size distributions at the depths of 0–5 mm and 5–10 mm from the exposed surface are shown in Figs. 5, 6, 7, 8, 9 and 10. In the case of the water-to-cement ratio of 0.50, the area from the exposed surface to 10 mm is sufficiently carbonated at the accelerated carbonation period of 9 weeks, whereas the area for the water-to-cement ratio of 0.35 is hardly carbonated (see Fig. 3). At the water-to-cement ratio of 0.50, the volume of pore with a diameter of 0.1 µm or less is dominant before the start of accelerated carbonation (0 week) at 0–5 mm and 5–10 mm, and it decreases significantly with age. The pore volume of specimens 50G30 and 50S40 at 0–5 mm increased in the diameter range of 0.2–1 µm, which may be one of the reasons for the increase in the air permeability as described in Sect. 3.2. The reason for the increase in pore volume in the range of 0.2–1 µm could be the significant water evaporation due to drying, as shown in the previous section. It is also known that blast furnace slag cement tends to produce C-S-H with low C/S, which can be carbonated easily and increased the pore size [Uehara 2011]. However, in the 5–10 mm area, there was no difference in the volumes of pores larger than 0.1 µm between the mixtures. It suggests that the pore structure was affected by carbonation and drying only near the surface. There was little difference in the pore size distribution among the mixtures with the water-to-cement ratio of 0.35. On the other hand, as shown in Sect. 3.2, the air permeability kT appeared to be smaller in the mixtures with the replacement of roof-tile waste aggregate, suggesting that the presence of internal curing water suppressed the

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0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

1

10

100

Pore volume(cm3/g)

Pore volume(cm3/g)

permeability in addition to the difficulty of water evaporation due to dense pore structure. It should also be noted that the pore volumes in 50S40 and 35S45 are large because the roof-tile waste fine aggregate was not fully removed from the test samples.

1000

0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

Pore size(μm)

1

10

100

1000

Pore size(μm)

0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

1

10

100

Pore volume(cm3/g)

Pore volume(cm3/g)

Fig. 5. Pore size distribution of 50BBC (left: 0–5 mm, right: 5–10 mm)

1000

0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

Pore size(μm)

0.1

1

10

100

1000

Pore size(μm)

0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

1

10

Pore size(μm)

100

1000

Pore volume(cm3/g)

Pore volume(cm3/g)

Fig. 6. Pore size distribution of 50G30. (left: 0–5 mm, right: 5–10 mm) 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

1

10

100

1000

Pore size(μm)

Fig. 7. Pore size distribution of 50S40 (left: 0–5 mm, right: 5–10 mm)

4 Conclusions 1) Improvement of carbonation resistance could not be confirmed in the mixture using roof-tile waste aggregate within the 9-week accelerated carbonation. 2) It was confirmed that the mixture using roof-tile waste aggregate suppressed air permeability at the early age. However, the air permeability increased with the ages. This could be attributed to the presence of internal curing water and the increase in water evaporation due to drying.

0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

1

10

100

Pore volume(cm3/g)

Pore volume(cm3/g)

Carbonation Resistance of Portland Blast Furnace Slag Cement

1000

0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

75

0week 4week 9week

0.01

0.1

Pore size(μm)

1

10

100

1000

Pore size(μm)

0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

1

10

100

Pore volume(cm3/g)

Pore volume(cm3/g)

Fig. 8. Pore size distribution of 35BBC (left: 0–5 mm, right: 5–10 mm)

1000

0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

Pore size(μm)

1

10

100

1000

Pore size(μm)

0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

1

10

Pore size(μm)

100

1000

Pore volume(cm3/g)

Pore volume(cm3/g)

Fig. 9. Pore size distribution of 35G30 (left: 0-5mm, right: 5-10mm) 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.000 0.001

0week 4week 9week

0.01

0.1

1

10

100

1000

Pore size(μm)

Fig. 10. Pore size distribution of 35S45. (left: 0-5mm, right: 5-10mm)

3) In the case of a water-to-cement ratio of 0.50, a coarsening of the pore structure near the exposed surface was observed due to the replacement of roof-tile waste aggregate.

References Hayakawa, K., Mizukami, S., Kato, Y.: A fundamental study for quality evaluation of structural cover-concrete by surface air permeability. J. Japan Soc. Civil Eng. Ser. E2 (Mater. Concrete Struct.) 68(4), 385–398 (2012) Iron and Steel Slag Association: Utilization of Steel Slag for Blast Furnace Cement (2020) Japanese Standards Association: JIS R 5211 Portland blast-furnace slag cement (2009) Japanese Standards Association: JIS A 1153 Method of accelerated carbonation test for concrete (2012)

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Sato, R., Shigematsu, A., Nukushina, T., Kimura, M.: Improvement of properties of portland blast furnace cement type B concrete by internal curing using ceramic roof material waste. J. Mater. Civ. Eng. 23(6), 777–782 (2011) Torrent, R., Moro, F., Jornet, A.: Coping with the effect of moisture on air permeability measurements, International workshop on performance-based specification and control of concrete durability. Zagreb, Croatia, pp. 11–13 (2014) Uehara, J., Li, C.H., Nakarai, K., Ishii, Y.: Influence of CO2 concentration on micro-pore structure and oxygen diffusion coefficient of carbonated cement paste at early age. Cement Sci. Concrete Technol. 64(1), 111–118 (2011)

Strength Characteristics of Blast-Furnace Cement Mortar with Silicate-Type Surface Penetrants Kei Futagami(B) , Takuya Kondo, and Katsunori Yokoi National Institute of Technology, Kochi College, 200-1, Otsu, Monobe, Nankoku City 7838508, Japan [email protected], {tkondou,yokoi}@ce.kochi-ct.ac.jp

Abstract. Concrete-using blast-furnace cement is more effective in increasing long-term strength, suppressing chloride-ion permeation, and alkali-silica reaction than ordinary cement. However, its strength development takes time, and it requires proper curing. In Japan, surface penetrants are used to maintain existing structures. In addition, the latent hydraulic property is promoted because the silicate-type surface penetrants are alkaline. The cover concrete becomes dense by reacting with the unreacted slag in the blast-furnace cement. The curing period can be shortened, and the quality of the cover concrete can be improved using this mechanism, leading to a new curing method. Therefore, in this study, we prepared a specimen in which 28 days old blast-furnace mortar was supplied with the amount of silicatetype surface penetrants used and an aqueous solution of calcium hydroxide as a reaction aid. We investigated its effect on strength characteristics. Keywords: Blast-furnace cement · Silicate-type surface penetrants · Vickers hardness · Compressive strength

1 Introduction Recently, the use of surface penetrants for maintaining existing structures has been increasing in Japan. Among them, the silicate-type surface penetrants (abbreviated as “surface penetrants”) react with Ca(OH)2 and water in concrete to produce C-S-H gel and densify the concrete surface. Therefore, the reaction with the surface penetrants is reduced in the carbonated ordinary Portland cement mortar, with low Ca(OH)2 content (abbreviated as “Ordinary mortar”). This tended to reduce the Vickers hardness compared to ordinary mortar (Takahashi et al. 2020). In blast-furnace cement mortar (abbreviated as “blast-furnace mortar”), in which cement is replaced by blast-furnace slag fine powder, less Ca(OH)2 is produced as the cement content reduces. Therefore, we are conceivable that Vickers hardness will reduce as in ordinary mortar with accelerated carbonation. However, blast-furnace slag fine powder demonstrates latent hydraulic properties. This latent hydraulic conductivity means that under an alkaline condition, with a pH of 12 or higher, the bonds of SiO2 are broken, and CaO, MgO, Al2 O3 , etc. are leached out. This property causes the formation of an insoluble hydrate, similar to cement, which hardens. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 77–86, 2023. https://doi.org/10.1007/978-981-19-7331-4_8

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In the case of blast-furnace cement, the microstructure of concrete, after hardening, becomes denser than that of latent hydraulic conductivity (Iyoda 2014). This increased density increases compressive strength and inhibits the penetration of Cl− . However, not all of the blast-furnace slag powder in the concrete reacts; many of them remain (Imoto 2015). Therefore, to improve the reforming effect of the surface penetrants, the alkali supplied from the outside reacts with the remaining unreacted blast-furnace slag fine powder. In this study, the effects of the surface penetrants and supplement of calcium hydroxide solution, used as a reaction aid on the strength and shrinkage characteristics of blast-furnace mortar after 28 days, were investigated to accelerate the age of the application.

2 Outline of Specimen 2.1 Mortar Formulation and Application Volume Test factors and levels of this test are shown in Table 1. To examine the effect of alkali supply on the strength and shrinkage characteristics of blast-furnace mortar, the surface penetrants and calcium hydroxide solution were used as test factors. In addition, the type of cement and curing conditions were used as test factors for comparison. Table 1. Test factors and levels Test case

Level

Types of cement

Blast-furnace cement (Blast-furnace mortar) Ordinary cement (Ordinary mortar)

Amount of silicate type surface penetrants used 0.2 L/m2 , 0.8 L/m2 Ca supplementary material

Used/Unused

In this test, the mortar was used as the specimen. The mortar mixture is shown in Table 2. Blast-furnace cement type B (density: 3.04 g/cm3 ) and ordinary Portland cement (density: 3.15 g/cm3 ) were used. Crushed sandstone (density: 2.58 g/cm3 , water absorption: 1.29%) was used as fine aggregate. AE agent was used as the admixture. The surface penetrants were sodium silicate (pH = 11.46), and the dry solid content was adjusted to achieve a density of 1.2 g/cm3 . In the compressive strength test, the specimens were cylindrical specimens of 50 mm × 100 mm in diameter. The Vickers hardness test was performed on prismatic specimens of 40 mm × 40 mm × 160 mm. The mortar was demolded a day after casting. The specimens were wet-cured for 7 days, and then, the mortar was kept at 20 °C and 60% R.H. for 28 days. The surface penetrants were applied after 28 days. Water was sprayed to increase the surface moisture content of the mortar to about 7% before the penetrant application. The sentence needs to be restructured to enhanced clarity. Could it be that 0.2 L/m2 was applied 4 times to form 0.8 L/m2A saturated calcium hydroxide

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Table 2. Specimen Types of Cement

W/C (%)

unit amount (kg/m3 ) W

C

S

Ad

Blast-furnace cement

55

263

478

1433

0.5

Ordinary cement

55

264

480

1440

0.5

solution (pH = 12.45) was used as a Ca supplementary material. The Ca supplementary material was supplied in the same amount as the surface penetrants immediately after the surface penetrants were applied. This was based on the literature by Someya and Keto (2014). The specimens in the air condition, including the specimens with surface penetrants applied after installation, were kept at 20 °C and 60% R.H. until before each test. The specimens without the application of surface penetrants were considered blank specimens. Among the blank specimens, the specimens that were cured in the air after 28 days were called airblank specimens. The specimens that were cured in water at 20 °C were called water-blank specimens. 2.2 Outline of Specimen and Test Method 2.2.1 Vickers Hardness Test The Vickers hardness-test specimens were coated with epoxy resin on five sides, including the casting surface, one day before the application of the surface penetrants. Surface penetrants were applied on the remaining one side (40 mm × 160 mm). After 56 days, the specimens were cut into 40 mm × 40 mm × 20 mm pieces using a table cutter. Due to the cutting, it was inspected virtually to determine whether cracks were on the measured surface. For the Vickers hardness test, the surface hardness of the mortar-cut surface was measured using a microhardness tester and electron microscope according to JIS Z 2244. The surface hardness of the mortar-cut surface was measured. Five measurements were taken per point, and the average of the values within the range of ±1 Hv was adopted. The electron microscope was used to select the striking points while avoiding the visible points as aggregate. 2.2.2 Compressive Strength Test The surface penetrants were applied to the entire surface of the cylindrical specimen. Compressive strength tests were conducted according to JIS R 5201. Blanks were tested by polishing one side of the hammering surface. For the specimens with surface penetrants, the test was conducted with both ends polished. Tests were conducted after 28, 42, 56, 84, and 201 days. Five specimens per factor were tested, and the average value was used.

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3 Results and Discussion 3.1 Vickers Hardness Test Figure 1 compares the Vickers hardness distribution from the mortar surface according to the quantity of surface penetrants used in the blast-furnace mortar. The Vickers hardness increases as the quantity of surface penetrants in the mortar increases, in the range of 9 mm from the mortar surface. This range is considered the modified range of the blastfurnace mortar. The Vickers hardness at a depth of 1 mm was about 30 Hv for 0.2 L/m2 and 39 Hv for 0.8 L/m2 . The modified area of 0.2 L/m2 was about 6 mm from the mortar surface, whereas that of 0.8L/m2 was about 9 mm. This is because the surface penetrants penetrated the interior due to the increase in the quantity of surface penetrants applied, which caused the reaction at a deeper location. Figure 2 compares the amount of surface penetrants used in ordinary mortar. For the ordinary mortar, the depth of modification increased with the amount of surface penetrants used. However, no difference was found in hardness. In this test, the measurement error of Vickers hardness was set at ±1 Hv; thus, the difference between 1 and 3 mm of the surface was not significant. Researchers confirmed in the previous study that varying the amount of surface penetrants used in the ordinary mortar does not increase the hardness (Kondo et al. 2020). Therefore, the promotion of latent hydraulic conductivity by the alkali contained in the surface penetrants and the reaction between the silicate and Ca (OH)2 is the reason for the increase in Vickers hardness when the surface penetrants are applied to the blast-furnace mortar.

Vickers Hardness (Hv)

60 50

Air Blank 0.2L/m² Ca× 0.8L/m² Ca×

40 30 20 0 3 6 9 Depth from mortar surface (mm)

12

Fig. 1. Vickers hardness distribution. (Blast-furnace mortar, comparison by the amount used)

Figure 3 compares the results for the 0.2 L/m2 application rate, with and without Ca supplementary material in the blast-furnace mortar. The Vickers hardness and reforming depth increased when Ca supplementary was used at 0.2 L/m2 because the alkali supply promoted the latent hydraulic hardness, and the alkali component penetrated the mortar by supplying the aqueous solution.

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Vickers Hardness (Hv)

60 50 40 30

Air Blank 0.8L/m² Ca×

20

0.2L/m² Ca×

0 3 6 9 Depth from mortar surface (mm)

12

Fig. 2. Vickers hardness distribution. (Ordinary mortar, comparison by the amount used)

comparison by the Vickers Hardness (Hv)

60 50

Air Blank 0.2L/m² Ca× 0.2L/m² Ca

40 30 20

Fig. 3. Vickers hardness distribution (0.2 L/m2 ). (Blast-furnace mortar, with and without Ca supplementary material)

Figure 4 compares the results for the 0.8 L/m2 application rate, with and without Ca supplementary material in the blast-furnace mortar. At the application rate of 0.8 L/m2 , no difference was found in Vickers hardness depending on whether Ca supplementary material was used. This may be because the amount of alkali supplied to promote latent hydraulic hardness was already exceeded when the surface penetrants were supplied. Figure 5 compares the Vickers hardness distributions of specimens with 0.2 and 0.8 L/m2 of Ca supplementary material in the blast-furnace mortar. Figure 5, with the Ca supplementary material, shows an increase in Vickers hardness due to the difference in the amount of surface penetrants used. This difference is because the supplied Ca supplementary material, with higher pH, provided more alkali components to the specimen during the 0.2 L/m2 application, promoting latent hydraulic hardness.

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Vickers Hardness (Hv)

60

Air Blank 0.8L/m² Ca× 0.8L/m² Ca

50 40 30 20

0 3 6 9 Depth from mortar surface (mm)

12

Fig. 4. Vickers hardness distribution (0.8 L/m2 ). (Blast-furnace mortar, with and without Ca supplementary material)

Vickers Hardness (Hv)

60

Air Blank 0.2L/m² Ca 0.8L/m² Ca

50 40 30 20

0 3 6 9 Depth from mortar surface (mm)

12

Fig. 5. Vickers hardness distribution. (Blast-furnace mortar, comparison by amount used)

3.2 Compressive Strength Test Figure 6 shows the change in compressive strength of specimens with different amounts of surface penetrants. The compressive strength of the water-blank specimens increased with time. However, no increase occurred in compressive strength of the air-blank specimens after 28 days. This may be because the specimens were left without moisture, which decreased the reaction and prevented the strength from increasing. The compressive strength of the specimens with surface penetrants increased after 42 days. The compressive strength of the 0.8 L/m2 specimens increased compared to the 0.2 L/m2 specimens. This showed a similar trend to the Vickers hardness test results in 3.1. Therefore, we considered that the supply of surface penetrants contributed to the increase in compressive strength of mortar specimens. However, no significant increase in strength was observed after 56 days because the latent hydraulic reaction occurred immediately

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Compressive strength (N/mm²)

after the supply of the surface penetrants; the long-term strength did not increase because it did not lead to a subsequent reaction.

80 70 60 50 40 30 20

70 120 170 220 270 Material age (day) Air Blank Water Blank 0.2L/m² Ca× 0.8L/m² Ca×

Compressive strength (N/mm²)

Fig. 6. Compressive strength test results. (Comparison by the amount used)

80 70 60 50 40 30 20

70 120 170 220 270 Material age (day) Air Blank Water Blank 0.2L/m² Ca× 0.2L/m² Ca

Fig. 7. Compressive strength test results. (With and without Ca supplementary material: 0.2 L/m2 )

Figure 7 shows the variation of compressive strength with time for 0.2 L/m2 , with and without Ca supplement. Figure 8 shows the variation of compressive strength with time for 0.8 L/m2 , with and without Ca supplement. The compressive strength tended to increase with the supply of Ca supplementary material in the amounts used because the supply of Ca supplementary material, with high alkalinity, accelerated the reaction due

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Compressive strength (N/mm²)

84

80 70 60 50 40 30 20

70 120 170 220 270 Material age (day) Air Blank Water Blank

Fig. 8. Compressive strength test results. (With and without Ca supplementary material: 0.8 L/m2 )

Compressive strength ratio (Penetrant/Blank)

1.4 1.3 1.2 1.1 1 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Vickers hardness ratio (Penetrant/Blank) Fig. 9. Relationship between Vickers hardness ratio and compressive strength ratio. (…Regression line of measured values, −1:1 line)

to the latent hydraulic properties. The alkaline component penetrated the mortar because of the water supplied. Figure 9 relates the Vickers hardness ratio from the surface penetrants to 3.1 and the compressive strength ratio to 3.2. The Vickers hardness ratio is the ratio of the average Vickers hardness of the blank specimen, up to a depth of 10 mm, to the average Vickers hardness of the specimen within a few millimeters, where the modification was observed in the Vickers hardness test conducted after 56 days. The compressive strength ratio was the ratio of the compressive strength of the air-blank specimen to the compressive strength of the specimen with the surface penetrants applied after 56 days. Figures 1, 2, 3, 4 and 5 show that the reformed zone of the surface penetrants in this test is

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about 6–10 mm. The compressive strength increased as the Vickers hardness increased in the reformed zone. In addition, the correlation coefficient is large. However, the Vickers hardness and compressive strength show a proportional relationship, as shown in the paper by Feldman et al. (Feldman and Huang 1985). The Vickers hardness ratio increased more than the compressive strength ratio; it showed such a tendency in this study. This is because the diameter of the compressive strength specimen is 50 mm, whereas the modified area is only about 10 mm at both ends. Since the modified area is small throughout the specimen, the effect of increasing the compressive strength of the whole specimen is limited. These investigations showed that the application of the surface penetrants to mortarcontaining blast-furnace slag powder after 28 days could increase the strength of the specimens. However, the effects on shrinkage properties and durability need to be investigated. Therefore, clarifying the reaction mechanism of the surface penetrants and alkaline solution is necessary by conducting more experiments.

4 Conclusions In this study, 28 days old blast-furnace mortar was applied with different amounts of silicate-type surface penetrants and Ca supplementary materials. Then, the specimens were subjected to Vickers-hardness and compressive-strength tests to compare their properties. The results are shown below. 1. The Vickers hardness of the impregnated area increased with the application of the silicate-type surface penetrants. The hardness increases with the amount of penetrant used and by supplying a saturated calcium hydroxide solution. 2. The compressive strength test increased with an increase in the amount of silicatetype surface penetrants and with the supply of saturated calcium hydroxide solution. 3. A positive correlation was observed between Vickers hardness and compressive strength in the modified zone.

Acknowledgements. We thank Professor Shinichi Miyazato of Kanazawa Institute of Technology for his useful advice on Vickers hardness testing. And we would like to express our gratitude to Mr. Hideki Nishino of Fuji Chemical for his valuable comments in preparing the test plan. We would like to express our gratitude to Mr. Hideki Nishino of Fuji Chemical Co.

References Takahashi, Y., Kondo, T., Miyazato, S., Kuroiwa, D., Yokoi, K.: Relationship between Clpermeation inhibition and modification effect of silicate type surface penetrants. Proc. Concr, Struct, Scenarios, JSMS 20, 423–428 (2020) Iyoda, T.: Concrete made with a large amount of blast-furnace slag fine powder. Concr. Inst. 52(5), 409–414 (2014) Imoto, H.: Effect of C–H–S accelerating strengthener on strength development of blast-furnace cement concrete. In: Proceedings of the 24th Symposium Japan Prestressed Concrete Institute, pp. 327–330 (2015)

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Someya, N., Kato, Y.: Basic study on the penetration mechanism and modification effect of silicate type surface penetrants. Concr. Res. Technol. 25, 181–189 (2014) Kondo, T., Miyazato, S., Nishino, H., Yokoi, K.: A Study on the Vickers hardness distribution of mortar coated with silicate type surface penetrants. Cem. Sci. Concr. Technol. 73, 333–339 (2020) Feldman, R.F., Huang, C.Y.: Properties of portland cement-silica fume pastes II. Mechanical properties. Cem. Concr. Res. 15(6), 943–952 (1985)

Three-Dimensional Mesoscopic Modelling of Concrete Confined by FRP Under Static and Dynamic Loading Nyembo Ya Lumbu Lars and Jinhua Zhang(B) School of Civil Engineering, Southeast University, Nanjing 210096, China {larslumbu,zhangjh}@seu.edu.cn

Abstract. The strengthening of concrete materials has become one of the most important aspects in the design of any civil engineering structure, leading to a number of research to investigate and improve its mechanical behavior. The purpose of this study is to investigate the mechanical behavior of concrete confined with fiber reinforced polymer (FRP) under static and dynamic loading using a simple and thorough method. Two identical mesoscale concrete specimens and one FRP layer were created (concrete cylinder with a diameter of 50 mm, a depth of 100 mm, and the FRP layers with 1.27 mm of thickness) to compare the Finite element results to those of an existing experiment and a similar study previously conducted. The mechanical behavior of the simulated confined and unconfined concrete was compared to the mechanical behavior of an experiment with the same specimen size ratio. The localized phenomena in each element were considered in order to investigate the overall reaction of the created specimens, driven by the fact that concrete is a heterogeneous material made up of coarse particles, ITZ (Interfacial Transition Zone), and mortar. The parameters such as unconfined strength of concrete, maximum tensile, and maximum confinement stress are determined utilizing the confining pressure generated by the wrapped Fiber Reinforced Polymer on the three-dimensional mesoscopic concrete model based on the concrete-to-FRP confinement mechanism. From the findings of the investigation carried in this work, it is demonstrated that this study provides substantial insights into the question of strengthening and improving the mechanical behavior of concrete specimens subjected to static and dynamic loading. Keywords: EASEC-17 · Singapore · Mesoscopic modelling · Concrete · Confining pressure · Mechanical property · Fiber reinforced polymer

1 Introduction 1.1 Mesoscale Modelling of Concrete Confined by FRP With the fast growth of civil engineering infrastructure and military facilities, the requirement for improved engineering structure performance has constantly increased. As one of the most frequently and widely used building materials, concrete’s mechanical qualities have garnered widespread interest from experts worldwide. Apart from the static © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 87–97, 2023. https://doi.org/10.1007/978-981-19-7331-4_9

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stresses that must be considered during structural design, the majority of structures are susceptible to strong dynamic loads such as collision, explosion, and penetration. As a result, a thorough examination of the static and dynamic behavior of concrete is critical (Wu et al. 2021a). Concrete is a composite material that requires an explicit representation of its heterogeneous composition to understand the initiation and evolution of localized phenomena like damage and fracture (Wang et al. 2019). Coarse aggregates, mortar (cement with sand and fine aggregates embedded), and ITZ (Interfacial Transition zone) are the ingredients of concrete at the longest length scale with observable heterogeneities, referred to as the meso-scale (Wang et al. 2019). Based on a mesoscale understanding of the heterogeneous structure of concrete, a micromechanical model capable of predicting the fracture process of concrete is proposed and used to investigate the fracture parameters of concrete under uniaxial or biaxial loading (Wu et al. 2021a). As a result, many additional materials have been investigated to enhance and increase the concrete’s resistance to dynamic and static loads. One of the approaches demonstrated in this article is the confinement of FRP materials using a cylindrical concrete specimen. Fiber reinforced polymer (FRP) composite materials have been used to strengthen concrete structures since the early 1990s, and the technique is now widely used around the world (Wang et al. 2019). Fiber Reinforced Polymer composites have a wide range of applications as a concrete confining material, including seismic retrofitting of existing reinforced concrete columns and the construction of concrete-filled Fiber Reinforced Polymer tubes as earthquake-resistant columns in new construction (Li et al. 2011).This article also looks at the use of Glass Fiber Reinforced Polymer material. 1.1.1 Material and Finite Element Modeling The mesoscale concrete specimen (Mortar, Aggregate, and ITZ) was modeled and created in Ansys using the mesoscopic modeling approach as shown in Fig. 1. An additional material known as Glass Fiber Reinforced Polymer is modeled in LS DYNA in order to further investigate and strengthen the behavior of mesoscale concrete. Glass fiber reinforced polymer composites are manufactured in a variety of ways and are widely employed in a wide variety of applications. Initially, the ancient Egyptians utilized glass fibers extracted from heat softened glass to create vessels (Sathishkumar et al. 2014). The GFRP layer wrapped around the mesoscopic concrete is modeled as a shell element with a thickness to the scale of 1 mm and the height of 100 mm to match that of the mortar matrix.LS DYNA is one of the most sophisticated finite element software packages available, and it comes with a wide library of composite materials to use in your simulations. In this study, the orthotropic materials behavior of unidirectional layers in composite shell constructions, which can be characterized by MAT054/055, is studied, as well as other related topics. Chang-Chang matrix failure criterion is used as the failure type in this simulation. The FRP-Concrete bond behavior was investigated using the *TIED_NODE_TO_SURFACE_OFFSET key card. Coarse Aggregate Material Model The behavior of concrete aggregate stress–strain and damage function have been studied extensively in recent years (Wu et al. 2021a). For the concretes simulated in this study, coarse aggregate is considered more elastic

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than mortar (Forti et al. 2020). Various studies have used elastic modulus and Poisson’s ratio to simulate aggregate mechanical properties under quasistatic loads (Wu et al. 2021a). While creating materials models for mesoscale modelling, various mechanical and physical properties of concrete were taken into account (Wu et al. 2021a). This is because aggregates are not elastic under high strain rates (Wu et al. 2021a).

Fig. 1. Mesoscopic specimen and FRP layer

Ciment Mortar Material Model A common elastoplastic substance is mortar. Both compression and tension depict softening behavior in distinct ways. Compression is done through a damage. Tension may be relieved by the usage of cohesive cracks (Wu et al. 2021a). When it comes to simulating mortar matrix using the K&C model is an excellent choice to examine the tensile, shear, and compressive behavior of the material. Several researchers have used it. ITZ Material Model The weakest connection between the aggregate and the mortar matrix is the Interfacial Transition Zone (ITZ). ITZ’s properties are not entirely known, however its significant heterogeneity and high porosity and lower strength than mortar are well-accepted characteristics (Zhou and Hao 2008). ITZ has an elastic modulus of 50–70% of that of mortar (Shuguang and Qingbin 2015). As a conclusion, the comparable ITZ strength may be reduced to 75% of mortar, which has been identified and utilized in mesoscale models to capture the mechanical features of the ITZ phase (Wu et al. 2021a). K&C model was used for static compression stress-strain relationship and failure behavior of concrete. A 3D random mesoscale model and the K&C material model have been used to simulate and study ITZ failure patterns as well as their effects on the dynamic characteristics of concrete in previous research by Zhang et al. (Wu et al. 2021a). 1.2 Static Test 1.2.1 Load and Boundary Conditions Numerical simulation relies heavily on the use of load and boundary conditions. LS Dyna’s compression test machine simulates a realistic environment by applying BOUNDARY SPC on the specimen’s top and bottom, representing the platens along

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the compression axis. Using the Boundary Prescribed Motion Key Card, a compression Load was generated as a displacement on the specimen’s top, while the specimen’s bottom and FRP are constrained in all directions. Static compression is performed on both confined and unconfined mesoscopic concrete specimens in LS Dyna. First, the mechanical behavior of an unconfined cylindrical concrete specimen with a diameter of 50 mm and a height of 100 mm as shown in Fig. 1 is analyzed and compared to that of a confined cylindrical concrete specimen in the following section. 1.3 SHPB Simulation Test To assess the dynamic compressive strength of (FFRP) Flax Riber Reinforced Polymer confined concrete, a split Hopkinson pressure bar system with a diameter of 106 mm was generated in Ls dyna. As shown in Fig. 3, this setup consists of an 848 mm long projectile, a 7060 mm long incident bar, and a 4240 mm long transmission bar. The mesoscopic concrete specimen used in this simulation has a diameter of 100 mm and a height of 54 mm, while the wrapped FRP jacket has a thickness of 0.135 and 0.405 mm and an elastic modulus of 788 MPa Fig. 2(c). Both the incident and transmitted bars were modelled with elastic properties, with densities and elasticity modulus of 7800 kg/m3 and 210 GPa, respectively, to facilitate the propagation of the stress wave effect from the projectile impact to the specimen. Because the coast of the simulation was enormous when using the wave velocity used in the experiment conducted by (Bai et al. 2021), lowering the wave velocity and increasing the modulus of elasticity of the bars led to a significant shorter simulation run time. The strain rates investigated during the SHPB experiments were used to calculate the wave velocities used in this simulation (Bai et al. 2021).The mesoscale concrete specimen was inserted in between transmission and incident bars Fig. 2(a), and the contact nodes-segments between the specimen and the bars were also defined to simulate the stress wave from the incident bar to the transmission bar through the specimen. Two sensors were installed on the incident and transmission bars, respectively, at 3300 and 2800 mm from the specimen’s ends as shown in Fig. 3.

Fig. 2. Mesoscopic concrete specimen for dynamic analysis; (a) confined by FRP in the SHPB system (b) Unconfined specimen (c) confined specimen

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2 Numerical Simulation Results As we all know, the mechanical behavior of composite materials is significantly controlled by the unique qualities of their basic components, as well as the bonding strength of their transition zone (Wu et al. 2021b). The primary goal of this research is to determine the mechanical characteristics and failure factors of different kinds of composite materials. This article compares the findings of two kinds of mesoscale concrete models, confined and unconfined, investigated using uniaxial static and SHPB Dynamic compression tests. The type of FRPs used are GFRP for static compression analysis and flax FRP for dynamic analysis. In Table 1, L and D, are in mm, D/L is the ratio of the used bars.

Fig. 3. SHPB setup for numerical simulation (mm)

Table 1. Size ratio of SHPB set up for numerical simulation Experiment setup L mm

D D/L mm

Striker

600

75

Incident bar

FEM setup Sensor location L mm mm

0.125 –

848

D D/L mm

Sensor location mm

106 0.125 –

5000 75

0.015 2340

7060 106 0.015 3300

Transmitted bar 3000 75

0.025 2000

4240 106 0.025 2800

Specimen

1.85

54

38

70

–

100 1.85

–

2.1 Concrete’s Mechanical Reaction to Static Loading The concrete models explored in this study have equivalent material properties and are subjected to the same loading situation for better simulation results observation and validation. In addition to the peak stress modelling and observation, an identical element is selected to study the optimal mechanical behavior of the constituent materials in both confined and unconfined specimens. Figure 4 shows the stress propagation in the unconfined concrete specimens. As noted above that concrete’s ingredients have an influence on the simulated results. Each constituents have their mechanical property. Since the ITZ is the weakest part of a concrete specimen, after loading the stress propagation and fractures patterns are noticed along the ITZ and aggregates as indicated in Figs. 4 and 5.

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In the case of the confined concrete, the contact between the external part of the concrete specimen with wrapped FRP layer jacket create a passive pressure that is perpendicular to the compression axis. Considering the mechanical properties of Glass fiber reinforced polymer. The binding strength provided by the tight connection between concrete and FRP produces a strengthening mechanism (Eqs. 1–3) that improve the ultimate strength of the analyzed concrete specimen. The failure patterns observed under compression loading of confined and unconfined mesoscopic concrete specimens leads to a complete failure that agrees with the experimental result results (Fig. 6). 2.1.1 Confinement Mechanism The lateral confinement pressure is typically passive in the case of a FRP jacket on concrete. When an axial compression force is applied to FRP confined concrete cylinders, the concrete matrix expands laterally, and the FRP material acts as a barrier, preventing this expansion (Touhari and Mitiche-Kettab 2016).

Fig. 4. Unconfined concrete failure patterns

Fig. 5. Confined concrete failure patterns

Confined concrete’s mechanical behavior are summarized into two parts: first, it is elastic, which corresponds to low strain levels (Berthet et al. 2006). The elasticity and strain compatibility of the concrete core and composite jacket are the essential components for the relationships that describe the first branch (Berthet et al. 2006). The plastic branch is the second part of this phenomenon. At this point, increased levels of stress are observed (Berthet et al. 2006). Figure 6 plot the maximum effective stress

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Fig. 6. Static stress-strain curve and failure patterns comparison to the experiment by (Touhari and Mitiche-Kettab 2016)

strain curve of mortar matrix. Firstly, the unconfined stress strain is plotted. Based on the compressive strength of the simulated concrete, the peak value is determined. The plotted curve looks similar to that of the conventional concrete subjected to uniaxial compression test see Fig. 6. Due to the confinement mechanism, the predicted stressstrain curve is in accordance with the experimental results of most confined concrete specimens. fl = ρk ρε fco =

2Ef εh,rup t D

2Ef t  ρε =   fco εco D εh,rup ρε = εco

(1) (2) (3)

Assuming that the unconfined concrete strength is equal to fco , and that the axial strain is equal to fco Ef , the elastic modulus of the FRP wrap is equal to keh,rup . The actual rupture strain of the FRP wrap and D is the concrete core diameter. The maximum confinement stress is determined as fl (Ahmad et al. 2020; Sadeghian and Fam 2015). ρk and ρε relationship is governed by Eqs. (1–3) presented by Teng et al. (Lim et al. 2016). 2.2 Concrete’s Mechanical Reaction to Dynamic Loading 2.2.1 Stress Wave Figure 4(a) shows the comparison of the shaped pulse wave deduced from the SHPB simulation to the experimental test. On the basis of the one-dimensional elastic wave concept Eq. (4), a stress pulse balance is achieved when the sum of the transmitted and reflected waves equals the transmitted wave (Bai et al. 2021; Yang et al. 2015). σi + σr = σt

(4)

where σi , σr andσt are the dynamic stress of the incident, reflected and transmitted wave as can be seen in Fig. 10.The stress equilibrium is achieved by comparing the two waves.

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2.2.2 Dynamic Compressive Strength The peak stress of the stress strain curve (Fig. 8) represents the dynamic compressive strength predicted through numerical simulation and compared to the dynamic compressive strength obtained during the experiment. Following several simulations, it was discovered that the dynamic compressive strength obtained during simulation also increases with increasing strain rate, which is consistent with the experiment (Bai et al. 2021). With an increase in the strain rate, the dynamic compressive strength of the concrete specimen confined with different layers of FFRP jackets also increases. 2.2.3 Definition of Strain Rate for SHPB Simulation It is well proven that concrete behaves differently under various strain rates (Yang et al. 2015). Because the velocity used in the experiment (Bai et al. 2021) is too high for numerical analysis and results in a significant increase in simulation errors. Therefore, the strain rates obtained during the experiment were divided by the height of the numerical specimen to obtain similar deformation in simulation at identical strain rates. The figure illustrates the comparison of the stress train generated by the numerical simulation and the experiment test following a single impact at 157 and 149 s−1 (Fig. 8). The failure modes of the confined specimen with two, four, and six layers of FRP at various strain rates are depicted in (Figs. 7, 8, 9 and 10).

(a)

(b)

Fig. 7. Typical failure mode of Concrete confined with by FFRP jackets; (a) 2 layers at 101s-1, (b) 4 layers at 182s (c) 6 layers at 153s-1(Bai et al. 2021)

3 Conclusions For the purpose of investigating the mesoscale behavior of concrete confined by fiber reinforced polymer under static and impact loading, Ls’s dyna, which is one of the most

Three-Dimensional Mesoscopic Modelling of Concrete Confined 140 120

Stress (MPa)

100 80 60

EXP confined 157S-1 Bai et al. 2021 FEM Confined 157s-1 FEM Unconfined 157s-1 FEM confined 149s-1 EXP confined 149s-1 Bai et al. 2021

40 20 0

0

1

2

3

4

5

6

Strain (%) Fig. 8. Stress-strain curve of 6 layers FFRP-confined concrete after Impact.

Fig. 9. Typical SHPB waveforms

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Fig. 10. Incident + reflected wave

widely used finite element modelling software packages, was used in this research to investigate and verify the static and dynamic mechanical responses of confined mesoscale concrete models with glass fiber reinforced polymer for static analysis and flax fiber reinforced polymer for dynamic analysis. The failure mode of FRP-confined concrete as well as the dynamic compression stress-strain curve were investigated, discussed, and compared to experimental test results obtained using the SHPB method. To ensure that the simulation was accurate, other mechanical parameters were examined. These included dynamic compressive strength, strain rate, and the stress wave balance, all of which were used to verify the accuracy of the simulation. As a result, the main conclusion of this work can be briefly summarized as follows: 1. A significant improvement in the strength and toughness of the structure was observed in both dynamic and static tests when the confinement mechanism of glass fiber reinforced polymer and flax fiber reinforced polymer was used on a mesoscale concrete model. 2. Changes in the thickness of the wrapped FRP layer jacket have a significant impact on the confined concrete specimen. 3. Increased strain rate causes a high-velocity wave impact in simulations, resulting in significant concrete damage; the dynamic compressive strength of concrete is defined in accordance with these findings. 4. At remarkably high strain rates simulation, confined concrete performed similarly to unconfined concrete.

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References Ahmad, A., Plevris, V., Khan, Q.-U.-Z.J.C.: Prediction of properties of FRP-confined concrete cylinders based on artificial neural networks. 10, 811 (2020) Bai, Y.-L., Yan, Z.-W., Jia, J.-F., Ozbakkaloglu, T., Liu, Y.: Dynamic compressive behavior of concrete confined with unidirectional natural flax FRP based on SHPB tests. Compos. Struct. 259, 113233 (2021) Berthet, J.F., Ferrier, E., Hamelin, P.: Compressive behavior of concrete externally confined by composite jackets: Part B: Modeling. Constr. Build. Mater. 20, 338–347 (2006) Forti, T., Batistela, G., Forti, N., Vianna, N.: 3D mesoscale finite element modelling of concrete under uniaxial loadings. Materials (Basel), 13 (2020) Li, X.Q., Chen, J.F., Lu, Y.: Meso-scale modelling of FRP-to-concrete bond behaviour using LSDYNA. In: Ye, L., Feng, P., Yue, Q. (eds.), Advances in FRP Composites in Civil Engineering, pp. 494–498. Berlin, Heidelberg. Springer Berlin Heidelberg (2011) Lim, J.C., Karakus, M., Ozbakkaloglu, T.: Evaluation of ultimate conditions of FRP-confined concrete columns using genetic programming. Comput. Struct. 162, 28–37 (2016) Sadeghian, P., Fam, A.J.E.S.: Improved design-oriented confinement models for FRP-wrapped concrete cylinders based on statistical analyses. 87, 162–182 (2015) Shuguang, L., Qingbin, L.: Method of meshing ITZ structure in 3D meso-level finite element analysis for concrete. Finite Elem. Anal. Des. 93, 96–106 (2015) Sathishkumar, T.P., Satheeshkumar, S., Naveen, J.: Glass fiber-reinforced polymer composites—A review. J. Reinforced Plastics Composites 33, 1258–1275 (2014) Touhari, M., Mitiche-Kettab, R.: Behaviour of FRP confined concrete cylinders: Experimental investigation and strength model. Periodica Polytechnica Civil Eng. 60, 647–660 (2016) Wang, J., Jivkov, A.P., Engelberg, D.L., Li, Q.M.: Parametric study of cohesive ITZ in meso-scale concrete model. Proc. Struct. Integrity 23, 167–172 (2019) Wu, Z., Zhang, J., Fang, Q., Yu, H., Haiyan, M.: Mesoscopic modelling of concrete material under static and dynamic loadings: A review. Constr. Build. Mater. 278, 122419 (2021) Wu, Z., Zhang, J., Yu, H., Ma, H., Fang, Q.: 3D mesoscopic analysis on the compressive behavior of coral aggregate concrete accounting for coarse aggregate volume and maximum aggregate size. Compos. Struct. 273, 114271 (2021) Yang, H., Song, H., Zhang, S.: Experimental investigation of the behavior of aramid fiber reinforced polymer confined concrete subjected to high strain-rate compression. Constr. Build. Mater. 95, 143–151 (2015) Zhou, X.Q., Hao, H.: Modelling of compressive behaviour of concrete-like materials at high strain rate. Int. J. Solids Struct. 45, 4648–4661 (2008)

Seismic Resilient Structures

Development of Energy Dissipation Walls with Oil Dampers and Totally Reinforced Support Members Using Pre-stress R. Sakamoto1(B) , K. Matsuda1 , and S. Hanai2 1 Department of Architecture, Meijo University, Nagoya 4688052, Japan

[email protected] 2 Quake Damping System Division, Chihiro Sangyo Co., Ltd, Shinshiro 4338118, Japan

Abstract. Many studies have been conducted on energy dissipation walls for small houses to improve the earthquake resistance of structures in Japan. Oil dampers, a main damper, is installed in studs to increase their strength. However, this method tends to deform each member and joint—“support members”— owing to tensile force, and therefore, the energy absorption performance of the damper tends to decrease. In this study, we propose an energy-dissipation wall that increases the overall stiffness by prestressing the support members to prevent tensile deformation. From 2020 to 2021, two types of specimens using laminated veneer lumber (LVL) as supporting members—Type 1 and Type 2—were tested to understand the mechanical behavior of the wall. Both types were subjected to static loading tests. Additionally, dynamic loading tests were applied to Type 2. Moreover, the dynamic behavior of the one-story wooden structure installed on the Type 1 wall was investigated by subjecting it to artificial earthquake waves. In state R which the damper part of the energy dissipation wall is restrained the load-deformation relationships obtained from the static loading tests for the two types of specimens using LVL as support members showed almost linear behavior up to the assumed damper load level for both specimens. In the dynamic loading test on Type 2, a stable load-deformation history with almost no slip was obtained. In shaking table test on Type 1, it was found that the energy dissipation wall incorporated into the wooden structure absorbed the energy of the artificial earthquake shaking and prevented the deterioration of its bearing capacity. Keywords: Timber structure · Energy dissipation wall · Oil damper · Post-tension · Shaking table tests

1 Introduction One way to efficiently improve the earthquake resistance of wooden structures is to install an energy-dissipation wall inside the wall. Oil dampers, which exhibit stable performance with little temperature dependence, have been used as the damping mechanism of an energy dissipation wall. However, small oil dampers, which can be easily accommodated in the wall of a house, bear some drawbacks, such as a relatively low load level and low © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 101–115, 2023. https://doi.org/10.1007/978-981-19-7331-4_10

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energy absorption efficiency, when the drift deformation is small. In addition, increasing the number of members to deal with such shortcomings often causes problems in terms of cost and construction complexity. For this reason, oil dampers are widely used for vibration control in high-rise buildings, but not very often in small-scale houses, although some examples have been developed (Satsuya and Yuji 2011; Atsufumi et al. 2010). To improve the design flexibility of small houses, it is important to study an efficient method of oil damper installation in small houses. In this study, we propose a new passive control system for wooden houses that uses oil dampers. To take advantage of the high energy-absorbing performance of oil dampers, even in the case of small deformations, this system is designed to prevent the loss of damper deformation due to slippage of joints and bending deformation of horizontal members, which is characteristic of wooden structures. This study discusses the results of static and dynamic loading tests conducted to understand their mechanical behavior.

2 Concept The concept of an energy-dissipating wall is described below. In a series of studies, oil dampers, one of the main types of dampers commonly used as response-control systems, are subjected to load levels of 4–8 kN, which can be easily accommodated in the wall of a house. When the damper load is converted into a horizontal resistance force energy dissipation wall, the ratio varies depending on the installation of the damper. For example, as shown in Fig. 1, if dampers are installed in the general brace type, the horizontal resistance force will be approximately 1/3 because of the aspect ratio of the wall, which is low for the structural element of a wooden house. On the other hand, if dampers are installed horizontally in the form of a stud-type damper, as shown in Fig. 2, the damper load is almost equal to the horizontal resistance force of the energy dissipation wall, thus increasing the strength of the energy dissipation wall. However, the members and joints around the damper (“support members”) are easily deformed by tensile forces; therefore, it is difficult to improve the stiffness of the support members, which reduces the amount of damper deformation in response to wall deformation, specifically, the amount of energy absorption of the damper. In addition, when enhancing the stiffness of the support members by constraint, this would result in a design that is unreasonable in terms of cost and construction. In addition, to accommodate various wall heights and pillar spans with the same product, it is common to add a length-adjustment mechanism to the support members of energy dissipation walls for wooden houses, but this also causes slippage in the support members, making the design of passive control systems even more difficult. In this study, we propose a stud-type passive control system consisting of an oil damper and entirely post-tensioned support members (Fig. 3). Entirely post-tensioned support members were extremely strong before the separation of the crimped surfaces from the girders. The tension force required to keep the crimped surface from separating can be easily evaluated from the strength of the damper used. In this case, two M12 full-thread bolts were sufficient for the tension members. As the crimped surface is always in a state of compressive stress, the design of the joint

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F Fd/3

Support members

Deform

Oil damper Fig. 1. Brace-type energy dissipation wall

Support members

F Fd Slippage Lengthadjustment

Deform

Pin

End joint

Oil damper

Bending deformation

Fig. 2. Stud-type energy dissipation wall

Tension member Pin (connect the damper Oil damper

Post tension Compressive force

Fig. 3. Concept of the post-tensioning energy dissipation wall

connections of the crimped surfaces, such as the number of screws, can be simplified. The end of the tension members on the damper side should be the same as the pin of the

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910

910 LVL

joiner metal Stiffness lateral

steel plate Receiving

2812.5

restraint

member

(E-160) Receiving

nut Steel plate

member

Tension member insert

LVL

drift pin Anchor bolt

(E-140)

Between

Biss

Brace and sill

(a) Type 1

(cannot been (b) Type 2

Fig. 4. Two type specimens (“state R”)

Pantographs

Oil jack

Specimen

Fig. 5. Setup (Type 2)

oil damper and support members to prevent the bending deformation of each member. The end of the lower tensioner was fixed to the hardware anchored to the foundation to reduce the loss of damper deformation owing to the bending of the foundation. It was confirmed that the bending deformation and bending stress of the beam-side end of the upper tensioning material do not pose a problem if the beam length is approximately 180 mm. As for the length adjustment mechanism to fit various house sizes, the entire system is tensioned after adjustment to prevent rattling at the relevant part.

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Table 1. The loading schedule Slope by drift-deformation(rad.) 1/900

Drift-deformation(mm) 3.13

1/600

4.69

1/450−(1)

6.25

1/300

9.38

1/200−(1) 1/450−(2) (*1, 2) 1/150

14.06 6.25 18.75

1/100−(1)

28.13

1/200−(2) (*2)

14.06

1/75

37.50

1/50 (*1)

56.25

1/100−(2) (*2)

28.13

3 Static Loading Tests 3.1 Overview of the Specimens Figure 4 shows the two types of specimens, LVL Type 1 and LVL Type 2 (hereinafter referred to as “Type 1” and “Type 2”). In these studies, the test specimens are the “state N” in which the damper part of the energy dissipation wall is unrestrained (No-damper) and the “state R” in which the damper part is restrained (Rigid-Damper) (Kazuhiko and Keisuke 2006; Kazuhiko et al. 2011). However, state N is considered to be the same for both types, and the experiments were conducted only for Type 2. States N and R were simulated by removing the damper and attaching a sufficiently rigid steel plate to the damper section, respectively. Both specimens were 1P wood frames with a height of 2812.5 mm and column span of 910 mm. The beams were made of glued laminated timber of different grades of cedar (strength grade E65-F225), and the foundation and columns were made of glued laminated timber of the same grade (strength grade E65-F255). M12 full-thread bolts were used as tensioners, and 15 kN of tension was applied to each tensioner by tightening the nuts that connected the tensioners to the pins of the dampers after assembling the structure. When the tensioners were left for approximately two days after post-tensioning was introduced in the tension materials in Type 1, the axial force decreased by up to 9% from the initial value, although the amount of change in axial force decreased with time. Therefore, it was necessary to introduce a post-tension slightly higher than the target value. Structural LVLs (E-140 for Type 1 and E-160 for Type 2) with a width of 89 mm and thickness of 38 mm were used as support materials. The LVLs and cross members were connected by screwing to the L-shaped hardware, and a steel plate (PL-3.2 for Type 1, PL-4.5 for Type 2, Fig. 4) was placed between them to prevent localized sinking. In

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addition, an out-of-plane restraint was installed near the damper of the support material to prevent its out-of-plane deformation of the support material. In Type 1, the support members and damper are connected by inserting a steel plate (hereafter referred to as “receiving-member”) into the slit in the LVLs and driving a drift pin into it. In contrast, in Type 2, the support members and damper are connected by screws between the LVL cross section and the receiving member, increasing the contact area between the two. 3.2 Outline of Experiments Figure 5 shows the setup. The beam was loaded by applying a horizontal forced displacement using an oil jack. The hold-down joiner metals at the pillar head and pillar foot were subjected to a bolt axial force of 3 kN before loading. In “state R,” the axial force of the tension members and LVL braces is determined by the axial force and strain relationship obtained from each separate calibration. To prevent deformation in the lateral direction, a roller-type lateral restraint was attached to the side of the beam of the Type 1 specimen, and a pantograph was attached to the top of the beam for Type 2. In Table 1, the loading schedule consists of three repetitions of positive and negative alternating loading from the slope by drift deformation. However, for Type 1, the second load of 1/450 rad. is not conducted. For “state N,” the load at the top of the beam F N , the drift deformation uN , and the deformation ud of the part with the damper are mainly measured; for “state R,” the load at the top of the beam F R , the drift deformation uR , the lifting of the pillar foot and the deformation of the sill, among others, as well as the axial force of the support members and the horizontal displacement and lifting of the joint members are measured. 3.3 Experimental Result The load-deformation relationship for state N is shown in Fig. 6. It can be observed that the stiffness of the girders in state N is approximately 1/20 of that of the specimen in state R because the only resistance element to the load at the top of the beam is the shaft assembly. Figure 7 shows the load-deformation relationship for “state R” for Type 1 and Type 2 specimens. From Fig. 7, it can be observed that the beam load F R and drift deformation uR maintained a linear relationship within a range of 6 kN, which was within the assumed damper load level for both specimens. If the initial stiffness is defined as the stiffness evaluated based on the values at the maximum positive and negative loads in each cycle of 1/450 rad., the initial stiffness of Type 2 is 0.71 kN/mm, which is slightly higher than that of the Type 1 and close to the stiffness of the previous specimens using plywood or steel pipes as the support members. In the case of Type 2, separation between the receiving member and brace began to occur at 1/75 rad. And progressed with impact at 1/50 rad. Loading (Fig. 8).

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K=0.02(kN/mm) FN (kN)

2

0 -50

0

50

uN (mm) -2 Fig. 6. Load-deformation relationships (state N)

K=0.60(kN/mm) FR (kN)

K=0.71(kN/mm) FR (kN)

15

0 -50

15

0 0

50

-50

0

uR (mm) -15

(a) Type 1

50

uR (mm) -15

(b) Type 2

Fig. 7. Load-deformation relationships (state R)

4 Dynamic Loading Test 4.1 Outline of the Experiment A dynamic loading test was conducted on the Type 2 specimens. The details of the structure were almost the same as those in Sect. 3.1, except for the damper. An oil damper with a maximum load of approximately 6 kN was attached to the damper section. The setup is shown in Fig. 9. As in the static loading tests, pantographs were installed on top of the beam, and the beam was dynamically vibrated by an actuator. The holddown joiner metals of the pillar were controlled by center-hole load cells with a bolt axial force of 3 kN before loading.

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(a) 1/75 rad.

(b) 1/50 rad. (1 cyclic load on the way)

Fig. 8. The separation between the receiving-member and brace.

Pantographs

Actuator Specimen (Type 2)

Fig. 9. Setup

4.2 Outline of Experimental Design The load F and drift deformation u at the top of the energy-dissipation wall, load F d , and deformation ud of the damper were measured. In addition, to understand the balance of the axial force of the support members, the damper load and axial force of the LVL were measured using strain gauges attached to the surface and back of each member. However, owing to the poor measurement of the damper strain, the damper load is the average of the values obtained from the balance of the axial forces of the support members at nodal points P1 and P2 (Fig. 10) according to Eq. (1). N1 cos θ + N2 cos φ = −Fd ∴ Fd = −(N1 cos θ + N2 cos φ)

(1)

Table 2 shows the set of target slopes based on the drift deformations and frequencies for each excitation. The sample period was 102.4 Hz.

Development of Energy Dissipation Walls with Oil Dampers

φ

N3: brace-axal force

θ

FR: loading force

(top) N2: Tension-force

N1: brace-axal force

(top)

(top)

P1: nodal point

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P2: nodal point N2’: Tension-force

Damper force: Fd

(bottom) N1’: brace-axal force

N3’: brace-axal force

(bottom)

θ

φ

(bottom)

Fig. 10. Axial force on the support members

Table 2. Excitation schedule and frequency Slope by drift-deformation (rad.)

Drift-deformation (mm)

Frequency (Hz)

1/1000

3.2

2.06

1/500

5.6

2.06

1/400

6.6

2.06

1/240

11.7

2.04

1/200

14.5

1.70

1/120

24.8

1.02

1/100

30.0

0.85

1/67

43.3

0.57

1/60

48.6

0.51

1/45

63.6

0.38

4.3 Experimental Result In Figs. 11 and 12, the hysteretic curves of the system and dampers are shown at 1/400, 1/200, 1/120, 1/67, and 1/60 rad. The area of the curve is small at small deformations, and the dampers do not absorb much energy; however, after that, the history shape was almost rectangular, and little slip was observed. The equivalent stiffness K eq and equivalent damping ratio heq , evaluated based on the split-line stiffness at the maximum

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deformation at each deformation angle, were obtained. The equivalent stiffness K eq and equivalent damping ratio heq were obtained as follows:   1 W heq = (2) 4π W where ΔW is the energy consumption of one cycle and W is the strain energy at maximum deformation.

F (kN)

8

0 -60

0

60

u (mm) -8 Fig. 11. Hysteretic curves (energy dissipation wall)

Fd (kN) 8

0 -60

0

60

ud (mm) -8 Fig. 12. Hysteretic curves (damper)

Figure 13 shows the equivalent stiffness and damping ratio of the specimens under each load. As mentioned earlier, the dampers do not absorb much energy at small deformations, and deformations other than the dampers are dominant, but at 1/1000–1/400 rad. The equivalent damping ratio was approximately 0.1 at 1/1000–1/400 rad. When the load did not reach 6 kN and was approximately 0.5 after 1/120 rad. When the maximum load exceeded 6 kN. However, the equivalent stiffness gradually decreased. Figure 14 shows the energy absorbed by the frame and dampers in one cycle of each excitation, and the ratio of the maximum deformation of the dampers(ud,max ) to the maximum deformation of the energy dissipation wall(umax ) in that cycle, 1/400 rad. Thereafter, the energy absorption of both the energy dissipation wall and dampers increases at a constant rate with respect to deformation. After 1/400 rad., the energy absorption of both the damper and energy dissipation wall increased at a constant rate against the

Development of Energy Dissipation Walls with Oil Dampers

Keq(-)

heq(-)

0.8 0.6

111

0.6 0.4

0.4 0.2

0.2

u(mm)

0 0

20

40

60

u(mm)

0

80

0

(a) equivalent stiffness

20

40

60

80

(b) equivalent damping ratio

Fig. 13. Equivalent stiffness Keq and equivalent damping ratio heq

deformation, indicating that the dampers were responsible for more than 80% of the energy absorption of the structure. The ratio of ud,max to umax increased from 1/400 rad. Onward and exceeded 80% in the region of large deformation. W(kN m)1.4

1.0 ud,max /umax

Ratio of ud,max to umax

(mm/mm)

Energy absorption of Energy absorption

0.0

0.0 0

umax(mm) 80

Fig. 14. Absorption energy of girders and dampers in one cycle

5 Shaking Table Test of LVL Type 1 5.1 Outline of the Test Specimens The two types of specimens to be compared are shown in Fig. 15. Both are 3P wooden frames, and the outside of both are particle board bearing walls for earthquake resistance element (ERE). Up to four sheets can be stretched on both sides. The resisting-forceratio-of-various-wooden-wall was adjusted according to the number of nails, and for the bearing wall only, three walls had a resisting-force-ratio of various-wooden-wall equivalent to 2.9, and one wall had a resisting-force-ratio-of-various-wooden-wall equivalent to 2.5. For the bearing wall and energy dissipation wall, one wall equivalent to the resistingforce-ratio-of-various-wooden-wall of 2.9 and two walls equivalent to 2.5 were installed, considering the 6 kN strength of the energy dissipation wall placed in the center, so that the apparent strength of the two systems would be approximately 20 kN. That is, (2.9

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× 0.91 × 3 + 2.5 × 0.91 × 1) × 1.96 = 19.98 kN for the bearing wall only, and (2.9 × 0.91 × 1 + 2.5 × 0.91 × 2) × 1.96 + 6.0 = 20.09 kN for the bearing wall and the energy dissipation wall. 5.2 Outline of Experimental Design Figure 16 shows a single-layer wooden structure that was vibrated. The two specimens described above were built into a one-layer wooden frame with fixed inertia weights, and seismic motion was input to the shaking table. The seismic weight for the first floor in a two-story house of 99.3 m2 was set to 60 kN, and the mass of the weight was adjusted so that the value of the standard shear coefficient C0 of each specimen was 0.333. Forty-five percent and 91% of the Basic Safety Limit (BSL) waves were used as input earthquake-resisting elements: ERE and these were input alternatively. The structure with only earthquake resisting elements was vibrated once, and the structure with energy dissipation wall (EDW)—“passive control system” (PCS)—was vibrated three times alternatively, and then 45% was input.

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3000 2625

270

The resisting-force-ratio-of-various-wooden-wall energy

Bearing wall

dissipation wall

2.9

2.9

(2 9

(2 5

2.9

2.9

surface

()

(2 5

(back)

910 910 910

910 910 910

(a) Only ERE

(b)PCS (ERE+EDW)

Fig. 15. Specimens

weight Specimen Shaking direction

wooden structure

Fig. 16. The wooden structure

5.3 Experimental Results Figure 17 shows the relationship between story shear force Q and drift deformation u for each girder. The stiffness of the structure with only earthquake-resistant elements

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decreased when the structure was 91%, and then 45% again. However, although the stiffness of the present PCS gradually decreased as the excitation progressed, the relationship between story shear force and the drift deformation depicted a bilinear history when the wave at 45% BSL was input. From the above, it can be seen that the introduction of the present energy-dissipation wall into the wooden frame can reduce the deterioration of the strength and response. 1st time

ERE

(BSL45%) Q(kN) 40

0

-80

0

0

-40

-40

0

80 -80

u(mm)

0

0

-40

0

80 -80

u(mm)

-40

(BSL45%) Q(kN)40

Q(kN)40

80 -80

u(mm)

0

0

u(mm)

-40

-40

80

u(mm) -80

0

0

-40

(a) Up to 3 times excitation

0

80

u(mm)

-40

7 times

(BSL91%) 40 Q(kN)

0

0

80 -80

6 times

Q(kN)40

0

5 times

4 times (BSL91%)

(BSL45%) Q(kN)40

u(mm)

40

0

3 times

80 -80

Q(kN)

40

PCS

0

80 -80

Q(kN)

0

(BSL91%) Q(kN) 40

u(mm)

-40

-80

2nd times

(BSL45%) 40 Q(kN)

0

80 -80

u(mm)

-40

0

80

u(mm)

(b) 4 times to 7 times (PCS)

Fig. 17. Relationship between the story shear force Q and the drift deformation u

In Fig. 18, the load F d -deformation ud relationship of the damper attached to the vibration control wall is shown. 1st time (BSL45%) Fd(kN) 8

2nd times (BSL91%) Fd(kN) 8

0 -80

80 ud(mm)

-80

0 -8

0 0

80 -80

ud(mm)

80 ud(mm)

-80

80

ud(mm)

-80

0 0

-8

80 ud(mm)

7 times (BSL45%) 8 Fd(kN)

0 0

-8

0 -8

6 times (BSL91%) 5 times (BSL45%) 8 8 Fd(kN) Fd(kN)

0 -8

0

0 0

-8 4 times (BSL91%) 8 Fd(kN) -80

3 times (BSL45%) Fd(kN) 8

80

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0 0

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Even at a value of nearly 8 kN, which is beyond the assumed maximum value of 6 kN for the load of the present damper, the shape of the history does not collapse significantly, indicating that the damper maintains a certain degree of performance under loads above the maximum load. Figure 19 shows the time histories of the energy absorption of the structure and damper from the first to third excitation times. From Fig. 19, it can be observed that the energy absorption of the damper increases with each loading, and the ratio of the energy absorption of the structure gradually increases. This is because the dampers compensate for the loss of energy absorption owing to damage to the frame. In order to evaluate the damping with each specimen, we derived the averageequivalent-damping-ratio hs . If we assume that the total work done by the ground motion at the end of the earthquake is equal to the total work done by the equivalent viscous damping, the average-equivalent-damping-ratio hs can be obtained as follows: t hs =

t v2 dt

a0 v dt/2ωe 0

(3)

0

is obtained by where ωe =2π (k e /m)0.5 , k e : equivalent stiffness at maximum deformation In Fig. 20, the relationship between the average-equivalent-damping ratio hs and the maximum drift deformation umax obtained from Eq. (3) is shown. From Fig. 20, it can be seen that the maximum value of hs is approximately 0.15 for the structure with only earthquake resisting elements, but for the system, the value is around 0.14 after the first excitation, but thereafter it takes values between 0.25 and 0.45 and becomes larger as the excitation proceeds.

6 Conclusion The major findings of this study are as follows:

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hs(-) 0.5

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PCS 4 times (91%) 5 times(45%) 6 ti

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Fig. 20. Average-equivalent-damping-ratio and maximum drift deformation

• In static loading tests, the initial stiffnesses of the Type 1 and Type 2 were 0.60 and 0.71 kN/mm, respectively. In the case of Type 2, the joint between the brace and the receiving member separated simultaneously during 1/50 rad. Loading and the stiffness decreased significantly. • In the Type 2 dynamic loading test, the hysteretic curves of the dampers and the energy dissipation walls showed almost no slip, and the dampers absorbed approximately 85% of the energy of the wall. • As a result of alternating inputs of large and small artificial earthquake waves (91 and 45% of BSL waves) to a wooden frame incorporating Type 1, its shear force and drift deformation showed a stable history even after repeated exposure to large earthquakes.

References Atsufumi, I., Hiroshi, I., Masatoshi, S.: Analytical simulation of displacement responses for twostory wood frames with oil-dampers shear wall and design value for wood shear wall with damper. J. Struct. Constr. Eng. AIJ 660, 363–370 (2010) Kazuhiko, K., Keisuke, I.: Reduced expression for various passive control systems and conversion to shear spring model. J. Struct. Constr. Eng. AIJ 605, 37–46 (2006) Kazuhiko, K., Hiroyasu, S., Yoji, O., Yoshihiro, Y.: Dynamic behavior and simplified modeling method for a timber frame with Knee Brace dampers. J. Struct. Constr. Eng. AIJ 664, 1109–1118 (2011) Satsuya, S., Yuji, M.: Mechanical model of wooden frame with compressive Knee-Brace oil dampers. J. Struct. Constr. Eng. AIJ 648, 377–384 (2011)

Comparative Numerical Study on Efficiency of Various Energy Dissipating Devices Used in Hybrid Post-tensioned Shear Wall Shubham Tiwari(B) , S. R. Dash, and G. Mondal School of Infrastructure, Indian Institute of Technology Bhubaneswar, Argul, Odisha 752050, India [email protected], {srdash,gmondal}@iitbbs.ac.in

Abstract. Conventional shear walls as a lateral-load resisting system have the disadvantage of getting damaged during severe earthquake shaking and can only be used after repair. This violates the philosophy of sustainable development, which is a critical aspect of the modern socio-economic scenario. To overcome this problem, shear walls are integrated with the post-tensioned (PT) tendons and are referred to as “PT shear walls.” Since the PT tendons remain elastic, the PT shear walls undergo rocking motion over the base and regain the original position after the seismic event; thus, the wall posses self–centering behaviour. Thus, they are reusable even after such events, and the downtime of the structure is minimal, thereby fulfilling the goal of resilient and sustainable development. However, the problem with the PT shear walls is that they have low energy dissipation capacity, owing to their elastic rocking behaviour. For energy dissipation, PT shear walls are fitted with additional energy dissipating devices and are known as “hybrid PT shear walls.” Conventionally the dissipating devices are placed internally, which solves the issue of low energy dissipation; however, it makes the shear wall weaker after an earthquake, and the replacement of dissipating devices is not possible. Therefore, recently the hybrid walls are fitted with dissipating devices externally, which provides good energy dissipation and the benefit of ease of replacement. Although several dissipating devices have been used in the past in various civil engineering applications, their suitability in hybrid PT shear walls is not available in the literature. Therefore, the present study aims at assessing the comparative response of these dissipating devices subjected to axial monotonic and cyclic loading through finite element (FE) analyses. Keywords: Hybrid post-tensioned shear wall · Energy dissipating devices · External energy dissipating devices · Self-centering shear wall

1 Introduction PT shear walls fitted with energy dissipating devices are termed as “Hybrid PT shear walls” (Fig. 1). Mainly two types of dissipating devices, namely mild steel dampers and viscous dampers, have been used in the past in hybrid PT shear walls. Out of these two,

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 116–132, 2023. https://doi.org/10.1007/978-981-19-7331-4_11

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predominantly mild steel dampers have been used in the past. Though a wide variety of these energy dissipating devices are available, their choice is not well defined. At present, their choice depends upon the site, techniques used in the installation, and mainly upon the designer. So, if we either have to choose an energy dissipating device, no comprehensive comparative data is available. Thus, there is a need for comparative studies to eliminate the dilemma while choosing a particular dissipator for hybrid PT shear walls. In this paper, a comparative study among different configurations of mild steel is presented in terms of load-carrying capability, energy dissipation capacity, ductility, and overstrength ratio.

Fig. 1. Hybrid PT shear wall (Taori 2019)

2 Use of Dissipating Devices in Hybrid Shear Wall Mild steel (Fig. 2a, c–e) and viscous dampers (Fig. 2b) have been extensively used in hybrid PT shear walls for energy dissipation. Marriott et al. 2008 and Marriott 2009 carried out experimental studies to check the best combination of steel and viscous dampers (Fig. 2b). They concluded that the viscous dampers are less effective than the steel dampers. Many researchers used mild steel in energy dissipating devices as it is widely available and it has good energy dissipation (Holden et al. 2003; Restrepo and Rahman 2007; Rivera 2013; Smith et al. 2013; Tuna et al. 2014; Teruna et al. 2015; Yooprasertchai et al. 2016; Obara et al. 2018; Gu et al. 2019; Wu et al. 2020, 2021; Taori et al. 2020; Bedriñana et al. 2021; Moghaddam and Shooshtari 2021). Teruna et al. (2015)

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compared different types of hysteretic steel dampers used in various civil engineering applications. They found that the convex-shaped side specimen showed stable hysteretic behavior, energy dissipation capabilities, and ductility factor. Yooprasertchai et al. (2016) fitted the buckling-restrained braces in PT shear wall and demonstrated their applicability and suitability in the wall (Fig. 2e). Obara et al. (2018) concluded that hybrid PT shear walls having steel dampers showed a stable energy dissipation up to a drift of 2.0%. Taori et al. (2020) performed a comparative numerical study on the hybrid PT shear walls fitted with internal Energy Dissipating Reinforcements (EDRs) and external EDRs, and with PT shear walls without EDRs. They concluded that the hybrid PT wall with external EDR dissipated more energy than that with internal EDR (Fig. 2a). Smith et al. (2013) and Taori (2019) found that the internally fitted mild steel bars are not readily replaceable after an earthquake. Notch plates (Fig. 2c) used by Guha (2020) had better energy dissipation capacity than steel bars. Wu et al. (2020) found that the energy dissipation capacity increased while the self-centering capacity decreased with an increase in the number of mild steel dissipators or the number of limbs in a dissipator (Fig. 2d). Moghaddam and Shooshtari (2021) performed a comparative study among PT shear walls without energy dissipating devices, with the multi-slit device, and with the energy dissipating bars. They found that the PT shear wall with multi-slit devices has high energy dissipation capacity, ductility, and deformability, but low-stress concentration and strength drop.

Fig. 2. Different energy dissipating devices: (a) mild steel bar (Taori et al. 2020), (b) viscous damper (Marriott 2009), (c) notch plates (Guha 2020), (d) mild steel dissipator (Wu et al. 2020), (e) buckling restrained braces (Yooprasertchai et al. 2016).

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3 Numerical Model Development for Dissipating Devices Under Investigation The different dissipating devices used for the comparative study are (a) stepped bar, (b) notch plate, (c) cut plate, and (d) X-shaped (Fig. 3). These dissipating devices have to be used in the hybrid PT shear walls designed by Taori (2019) according to ACI-ITG 5.2. Two hybrid PT shear walls are lateral load resisting systems in a three-bay threestory prototype building 8.5m high. Each hybrid PT shear wall requires four dissipating devices. According to the design, each dissipating device in the hybrid PT shear walls requires a minimum area of 80 mm2 and the unbonded length of dissipating devices of 200 mm. Therefore, in this study, different configurations having a minimum area of 80 mm2 and a length of 200 mm are considered. The minimum area is kept at the center of the specimen to avoid slippage or failure at the connection. The material used for the dissipating devices is mild steel with a yield stress of 385 MPa and ultimate stress of 542 MPa. The modulus of elasticity and Poisson’s ratio of the material are 175 GPa and 0.3, respectively. The engineering stress-strain curve is shown in Fig. 4. The numerical model is developed in ABAQUS (Hibbit 2002). The boundary condition (BC) considered for the models is similar to that taken in UTM. It is fixed in all directions at the bottom and free in the axial direction of the specimen at the top. BC for the X-shaped specimen is shown in Fig. 5 and similar BC is used for other specimens. The meshing is done using linear hexahedral elements of type C3D8R and the meshing of the region of expected failure is finer as compared to the other regions. Uniaxial monotonic and cyclic loadings were applied separately in the axial direction of the specimens to study their behavior (Fig. 5). For monotonic loading, positive displacement in the axial direction is applied, increasing the magnitude up to 30 mm. The displacement controlled cyclic loading in both positive and negative directions having a period of 100 s is applied, as shown in Fig. 6. The results obtained from monotonic loading are used to calculate the ductility and overstrength ratios of the specimens. In contrast, the result obtained from cyclic loading is used to calculate the hysteresis behavior and energy dissipation capacity of the specimens.

4 Validation of Numerical Model The model is validated with the experimental data obtained by carrying out the forcebased monotonic loading on the specimen (Fig. 7a). The modulus of elasticity (E) of the material is 1736 MPa and the Poisson’s ratio (ν) is 0.35. The load applied is 2777 N. The boundary conditions and the loading are shown in Fig. 7b. Figure 7c shows that the stress-strain curve obtained from the experimental data and the ABAQUS model is the perfect match. The force-displacement data obtained from the experimental test and ABAQUS is shown in Fig. 7d. This shows that the model developed can be used for the comparative analysis of the dissipating devices.

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Fig. 3. Different configurations of dissipators: (a) stepped bar, (b) notch plate, (c) cut plate, (d) X-shaped

Fig. 4. Engineering stress and strain curve for mild steel

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Fig. 5. Boundary conditions and the direction of load application

5 Results and Discussion 5.1 Force-Displacement Behaviour Under Monotonic Loading The force-displacement behaviour obtained from monotonic loading is shown in Fig. 8. The X-shaped dissipating device has the highest load-carrying capacity (45.3 kN), followed by the notch plate (44.8 kN), cut plate (43.8 kN), and stepped bar (38.4 kN) dissipating devices. Also, the displacement at the ultimate force is the highest in the stepped bar (9.6 mm) among all the dissipating devices, followed by X-shaped (5.6 mm), cut plate (4.9 mm), and notch plate (1.7 mm) dissipating devices. The notch plate reached its maximum force at very low displacement, the lowest among all dissipating devices. 5.2 Force-Displacement Behaviour Under Cyclic Loading The behaviour of the dissipating devices under cyclic loading is shown in Fig. 9. Also, from Fig. 9 we can see that the stepped bar, notch plate, and X-shaped dissipating devices show stable hysteresis behavior under the applied load. But, the cut plate dissipating device shows unstable hysteresis behaviour in negative cycles. The reason for the same is that the depth of the cut is small (2.5 mm), due to which both faces of the cut collide

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3 2.5 2 1.5 1 0.5 0 -0.5 0 -1 -1.5 -2 -2.5 -3

50 100 150 200 250 300 350 400 450 500 550

Time (sec) Fig. 6. Displacement controlled cyclic loading

Fig. 7. Validation of the numerical model

with each other during the negative cycle, and there is instability in its behaviour. Also, we can see that for the stepped bar, notch plate, and X-shaped plate, the area under the hysteresis loop increases in initial cycles (upto 3 cycles) due to strain hardening. After 4 cycles, the downward trend is observed due to strain softening in the dissipating devices.

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Fig. 8. Force-displacement behaviour of specimens under monotonic loading

5.3 Energy Dissipation The area under the hysteresis curve is the energy dissipation capacity of the different dissipating devices. The calculated energy dissipation capacity for each dissipating device in different cycles is shown in Table 1. It can be seen that the notch plate dissipates the maximum energy (1076.80 Nm) in comparison to the other dissipating devices (Fig. 10). It is followed by X-shaped, stepped bar and cut plate dissipating devices. The energy dissipated by the cut plate is far less than the other three dissipating devices. It is due to the collision of the opposite faces of the cut plate during negative cycles which is more prominent in higher cycles. 5.4 Ductility The calculation of the yield point and the ultimate point is taken from FEMA (2009). The effective yield displacement (y ) is taken as the intersection of the extension of a line drawn from origin and 0.6 of maximum force to the horizontal maximum force line. The yield point is the intersection between the vertical yield displacement line and the curve. The ultimate point is taken as the point of 0.8 of the maximum load on the curve. The yield point and ultimate point are shown in Fig. 11. The ductility (μ) is defined as the ratio of ultimate displacement (u ) and the effective yield displacement (y ) and is calculated from Eq. 1, μ=

u y

(1)

From Fig. 12 we can see that the X-shaped dissipating device has the maximum ductility of 20.6 among all the dissipating devices, followed by the cut plate (15.7), notch plate (11.3), and stepped bar (4.0). This shows that the X-shaped dissipating device can

Fig. 9. Behavior of the dissipating devices under cyclic loading

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Table 1. Energy dissipation of dissipating devices in different cycles Dissipator Type

Cycle 1

Cycle 2

Cycle 3

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Cycle 4

Cycle 5

20.14

82.63

23.26

112.50

(c) cut plate

5.39

(d) X-shaped

17.85

Total energy dissipated (Nm)

171.21

261.05

344.63

879.66

220.53

316.53

403.98

1076.80

9.98

43.68

45.71

52.64

157.40

89.44

190.18

297.45

389.61

984.53

Fig. 10. Comparison of total energy dissipation

undergo large plastic deformation under cyclic loading. Thus, it should perform better when the number of cycles in the loading is increased and, in turn, should also increase the energy dissipation capacity of the wall. 5.5 Overstrength Ratio () The overstrength ratio (Ω) is defined as the ratio of maximum force (Vmax ) to the design force (V), as shown in Eq. 2. As in this study design of the system is not being carried out so the design force is taken equal to the yield force (Vy ) for the calculation of Ω. =

Vmax   V = Vy

(2)

From Fig. 13 we can see that the Ω of the stepped bar is the highest among all dissipating devices. The value of Ω for the stepped bar, X-shaped, and the cut plate is 1.51, 1.46, and 1.44. They are comparable with no such major difference. But the value of Ω for the notch plate is 1.13, which is the smallest among all the dissipating devices. This means that the notch plate reaches its maximum force earliest after reaching the yield point.

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Fig. 11. Yield point and ultimate point (FEMA 2009)

Fig. 12. Ductility of different dissipating devices

5.6 Equivalent Viscous Damping (ξ) The damping potential of the various energy dissipating devices is calculated using equivalent viscous damping (ξ) given by Eq. 3 and it is estimated as defined in Fig. 14. ξ=

ED 4π ESo

(3)

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Fig. 13. Overstrength ratio () of different dissipating devices

where, ED is the area enclosed by the hysteresis loop, and ESo is the maximum strain energy corresponding to the shaded area.

Fig. 14. Estimation of equivalent damping ratio (Kim and Kim 2020)

The ξ calculated for each cycle is shown in Fig. 15 and the trend of ξ is shown in Fig. 16. From Figs. 15 and 16, the observation that can be drawn is that for the first two cycles the stepped bar has the highest equivalent viscous damping then for cycles 3,4, and 5 the notch plate had the highest equivalent viscous damping. Initially, the X-shaped

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plate had the lesser equivalent viscous damping than the stepped bar but later in cycles 4 and 5 it’s equivalent viscous damping is more than the stepped bar because the X-shaped had better ductility. So, as the number of cycles will increase the damping potential of X-shaped is going to increase. It can also be seen from the trend (Fig. 16) that the average percentage increase of the X-shaped over 5 cycles is the highest at 39.5%. Also, it can be observed from Figs. 15 and 16, that the cut plate had the least equivalent damping ratio, and also it has an unstable trend (from Fig. 16). 80

Equivalent viscous damping (ξ)

stepped bar

notch plate

cut plate

X-shaped

70

50.92 47.07

50

42.83 38.18 37.73

40

20

59.53

59.51

60

30

68.22

24.75 20.61 18.09 16.63

51.36 44.48

15.41 9.53

10

51.73

54.75

10.96

9.54

Cycle 4

Cycle 5

0 Cycle 1

Cycle 2

Cycle 3

Different cycles Fig. 15. Equivalent viscous damping of dissipating devices in different cycles

5.7 Stress Distribution in Dissipating Devices The von Mises stress distribution in considered energy dissipating devices is tabulated in Table 2 in the 4th positive and negative cycle at the displacement of 2 mm. From Table 2, it can be observed that most of the elements in the designated failure zone of X-shaped and notch plate energy dissipating devices are stressed to a maximum value in both the positive and negative cycles. On the other hand, the elements reaching maximum stress value are different in the positive and negative cycles of the stepped bar and cut plate. Thus, the elemental participation in energy dissipation is more in the X-shaped and notch plate and lesser in the stepped bar and cut plate in each cycle. Therefore, the notch plate and X-shaped dissipate more energy than the stepped bar and cut plate energy dissipating devices.

6 Summary and Conclusions This numerical study aimed at carrying out a comparative study among the stepped bar, notch plate, cut plate, and X-shaped dissipating devices under monotonic and

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Equivalent viscous damping (ξ)

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70 60 50 40 30 20 10 0 1

1.5

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3 3.5 Different cycles

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4.5

5

Fig. 16. Overall trend of equivalent viscous damping of different energy dissipating devices

displacement-based cyclic loading. The parameters considered for the comparative study are, namely, load-carrying capacity, energy dissipation capacity, ductility, and overstrength ratio. Under monotonic loading, the X-shaped dissipating device has the highest load-carrying capacity followed by the notch plate, cut plate, and stepped bar. Under the cyclic loading, the notch plate dissipated the highest energy followed by X-shaped, stepped bar, and cut plate dissipating devices. In terms of ductility, the X-shaped dissipating device has the highest ductility followed by the cut plate, notch plate, and stepped bar dissipating devices. The overstrength ratio of the stepped bar is highest followed by X-shaped, cut plate, and the notch plate. Apart from this, the damping potential is calculated using the equivalent viscous damping for the considered energy dissipating devices and the notch plate has the highest equivalent viscous damping and the X-shaped has the highest percentage increase in the damping potential. The conclusion drawn from the present study is as follows: • From the numerical study carried out, considering all the parameters like load-carrying capability, energy dissipation capacity, ductility, overstrength ratio, and equivalent viscous damping the X-shaped dissipating device performed satisfactorily in every parameter. Thus, it is the most suitable choice as the energy dissipating device for the hybrid PT shear walls. • Under cyclic loading, the X-shaped, cut-plate, and notch plate have stable hysteresis behaviour. Whereas the cut plate has unstable hysteresis behavior because of the collision of the inner faces of the cut during the negative cycles. So size optimization of the cut needs to be carried out to get stable hysteresis behaviour.

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Posive cycle (Displacement 2.0 mm)

Negave cycle (Displacement 2.0 mm)

Different energy dissipators

Acknowledgements. The authors want to thank the Indian Institute of Technology Bhubaneswar, India, for providing the necessary resources to carry out this research work.

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References ACI-ITG-5.2-09: Requirements for Design of a Special Unbonded Post-tensioned Precast Shear Wall Satisfying ACI-ITG-5.1 and Commentary Bedriñana, L.A., Tani, M., Nishiyama, M.: Deformation and cyclic buckling capacity of external replaceable hysteretic dampers for unbonded post-tensioned precast concrete walls. Eng. Struct. 235 (2021). https://doi.org/10.1016/j.engstruct.2021.112045 FEMA: Quantification of Building Seismic Performance Factors, US Department of Homeland Security, Applied Technology Council (2009) Gu, A., Zhou, Y., Xiao, Y., Li, Q., Qu, G.: Experimental study and parameter analysis on the seismic performance of self-centering hybrid reinforced concrete shear walls. Soil Dyn. Earthq. Eng. 116, 409–420 (2019). https://doi.org/10.1016/j.soildyn.2018.10.003 Guha, A.: Seismic response of post-tensioned hybrid shear walls with external energy dissipating reinforcement. Master’s Thesis, Indian Institute of Technology Bhubaneswar, India (2020) Hibbit, K.: Sorensen Inc. ABAQUS/ Standard User’s Manual, Version, 5 (2002) Holden, T., Restrepo, J., Mander, J.B.: Seismic performance of precast reinforced and prestressed concrete walls. J. Struct. Eng. 129(3), 286–296 (2003). https://doi.org/10.1061/(ASCE)07339445(2003)129:3(286) Kim, S.W., Kim, K.H.: Evaluation of structural behavior of hysteretic steel dampers under cyclic loading. Appl. Sci. 10(22), 8264 (2020) Moghaddam, S.H., Shooshtari, A.: Nonlinear static and dynamic behaviours assessment of selfcentering post-tensioned concrete wall with multiple-slit device. J. Build. Eng. 43, 102999 (2021) (Elsevier Ltd). https://doi.org/10.1016/j.jobe.2021.102999 Obara, T., Watanabe, H., Kuwabara, T., Kono, S.: Quantification of damage of rocking concrete walls with energy dissipating elements. In: 16th European Conference on Earthquake Engineering, 18–21 June, Thessaloniki, Greece (2018) Restrepo, J.I., Rahman, A.: Seismic performance of self-centering structural walls incorporating energy dissipators. J. Struct. Eng. 133(11), 1560–1570 (2007). https://doi.org/10.1061/(ASC E)0733-9445(2007)133:11(1560) Rivera, M.: Experimental laboratory procedures for the construction and testing of seismic resistant unbonded post-tensioned special reinforced concrete walls. Master’s Thesis, Lehigh University, USA (2013) Smith, B.J., Kurama, Y.C., McGinnis, M.J.: Behaviour of precast concrete shear walls for seismic regions: comparison of hybrid and emulative specimens. J. Struct. Eng. 139(11), 1917–1927 (2013). https://doi.org/10.1061/(ASCE)st.1943-541x.0000755 Taori, P.: Seismic response of post-tensioned hybrid shear walls with external energy dissipating reinforcement. Master’s Thesis, Indian Institute of Technology Bhubaneswar, India (2019) Taori, P., Dash, S.R., Mondal, G.: Seismic response of post tensioned hybrid shear walls with External Energy Dissipating Reinforcement (EEDR). J. Earthq. Eng. 1–16 (2020). https://doi. org/10.1080/13632469.2020.1778587 Teruna, D.R., Majid, T.A., Budiono, B.: Experimental study of hysteretic steel damper for energy dissipation capacity. Adv. Civil Eng. (2015). https://doi.org/10.1155/2015/631726 Tuna, Z., Gavridou, S., Wallace, J.W., Nagae, T., Matsumori, T.: 2010 E-defense four-story reinforced concrete and post-tensioned buildings—preliminary comparative study of experimental and analytical results. In: 15th World Conference on Earthquake Engineering, 24–28 Sept, Lisbon, Portugal (2014) Wu, H., Sui, L., Zhou, T., Huang, B., Li, X.: A novel self-centering energy-dissipating wall panel with framed beams as boundaries. Eng. Struct. 232, 111864 (2021). https://doi.org/10.1016/j. engstruct.2021.111864

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Wu, H., Wang, J., Sui, L., Zhou, T., Bai, Y.: Experimental investigation of self-centering steel reinforced concrete coupled wall panels with replaceable energy dissipaters. Eng. Struct. 212, 110473 (2020) (Elsevier). https://doi.org/10.1016/j.engstruct.2020.110473 Yooprasertchai, E., Hadiwijaya, I.J., Warnitchai, P.: Seismic performance of precast concrete rocking walls with buckling restrained braces. Mag. Concr. Res. 68(9), 462–476 (2016). https:// doi.org/10.1680/jmacr.15.00237

Three-Dimensional FEM Simulation of Hysteretic Performance of Traditional Chinese Dou-Gong Connections Xiaogang Zhang(B) , Xiaobin Song, and Jingliang Dong Department of Structural Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China [email protected]

Abstract. Dou-gong connection (complex bracket) is one of the typical woodwood connections commonly used in traditional Chinese timber structures. The hysteretic performance of dou-gong connections is pertinent to the seismic performance of the traditional timber structures. Compared with experimental research, numerical simulation is more cost effective and not limited experimental techniques and thus is more versatile in study of hysteretic performance of dou-gong connections. In this paper, a three-dimensional finite element method(FEM) based analysis on hysteretic performance of single and double dou-gong connections was presented considering three dimensional elastic-plastic and damage constitutive model of wood. The results showed that the model prediction of the initial stiffness and lateral resistance of the connections agreed well with the test results in literature. Keywords: Dou-gong connection · Elastic-plastic damage model · Hysteretic performance

1 Introduction Wood is one of the oldest construction materials in the history of human architecture. Traditional timber buildings are a type of architectural form with typical characteristics formed in the long history. In China, such heritage is diverse and of extremely high historical and humanistic value. Wood-wood connections play an important role of the traditional timber structure. Study of the mechanical properties of the wood-wood connection is critical to the safety of the traditional timber structure. Dou-gong connection is a kind of unique connection widely used in traditional Chinese timber structures. Such connection has significant hysteretic energy dissipation capacity under earthquakes. Experimental studies on the mechanical properties of dou-gong connection found that compressive performance was mainly depended on the effective bearing [1–3] area. And the supporting block and vertical loads had a great influence on the lateral resistance performance of dou-gong connection [4, 5].

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 133–139, 2023. https://doi.org/10.1007/978-981-19-7331-4_12

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Numerical simulation studies found that the FEM could reasonably represent the nonlinear mechanical behavior of wood under tension and compression [6]. And the finite element model introduced with the elastic-plastic damage model can represent the strength softening and stiffness degradation behavior of the single dou-gong connection well [7]. It can be found from the existing research that the simulation accuracy of dougong connection FEM still require improvement. And there is no finite element analysis research on the hysteretic performance of double dou-gong connections. In this paper, refined finite element models of single and double dou-gong connections were established based on the elastic-plastic damage model. And the rationality of model parameter selection was verified by the existing mechanical performance experiment results of dou-gong connections.

2 Finite Element Analysis of Dou-Gong Connections 2.1 Model Introduction The models of dou-gong connections were based on the scaled lateral cyclic loading test [8]. The models of dou-gong connections were based on the scaled mechanical performance experiment by Wu et al. The material of wood was African rosewood. The connection formation and configuration are shown in Figs. 1 and 2. The nominal dimension of the components is listed in Table 1.

Fig. 1. Formation of a single dou-gong connection.

The lateral cyclic loading test was carried out according to the CUREE loading system [9]. Three dou-gong connections were loaded in the test, numbered in Table 2.

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Table 1. Nominal cross-sectional dimension of the dou-gong connection components. Component

Cross section/thickness(mm)

Bottom beam (Pupai-fang)

245 × 80

Cap block (Ludou)

175 × 175

Short beam (Nidao-gong)

55 × 114

Small blocks (Sandou)

93 × 93

Overhanging beams (Hua-gongs)

55 × 100

Straight beams (Fangs)

55 × 80

Column

165

Wood shear key

10 × 20

Hidden tenon

30 × 30

(a) Double dou-gong connection

(b) Single dou-gong connection

Fig. 2. Dimensions of the dou-gong connections. Table 2. Specimen of the dou-gong connections. Model type

Model number

Vertical load (kN per column)

Single dou-gong connection

S1

45

Double dou-gong connection

D1

45

D2

18

2.2 Establishment of the Finite Element Models The finite element software ABAQUS as used to establish the refined finite element model according to the geometric dimension in the test, including the single and double dou-gong connections. To improve the convergence of the calculation, the material constitutive of components was defined differently according to the importance. The short

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beam and the cap block (the green components in Fig. 3) were defined by the elasticplastic damage model, and the other components (the white components in Fig. 3) were defined by the orthotropic ideal elastic-plastic model. The material properties are shown in Table 3. Table 3. Test results of mechanical properties of African rosewood small clear specimens. Mechanical property

ER

ET

EL

GRT

GRL

GTL

μRT

μRL

μTL

Mean values

1977

1450

15207

274

1141

912

0.373

0.047

0.033

Mechanical property

f tR

f tT

f tL

f cR

f cT

f cL

f νRT

f νTL

f νRL

Mean values

3.53

2.83

101.99

9.35

8.96

50.44

2.00

10.32

11.71

Note 1. Except for Poisson’s ratio, which is dimensionless, all other parameters are in MPa 2. f t , f c , and f ν represent the tensile, compressive and shear strength of the material respectively, and the following subscripts R, T, and L represent the radial, tangent, and longitudinal directions of the material respectively

The loading method of finite element simulation is also shown in Fig. 3. The analysis step was divided into two steps: the first step was to apply a vertical load to the top surface of each column, and the second step was to apply the horizontal displacement referring to the CUREE loading system. The control displacement of the lateral cyclic loading was taken as 40 mm.

Fig. 3. Finite element model of the double dou-gong connection

The calculation element adopted C3D8R (three-dimensional eight-node hexahedron linear reduced-integration element). Each component was divided into several regions for mesh division (Fig. 4). Interactions between the overhanging beams and between the straight beams were defined by the Tie constraints. The interactions between the other components were simulated by contact. The normal interactions were defined by the Hard contact, and the tangential interactions were described by the Coulomb friction model. The friction coefficient is taken as 0.4, referring to the existing research results [2].

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(a)Column

(b)Cap block

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(c)Short beam

Fig. 4. Meshing of the components.

Three boundary constraints were set in the finite element model: The fixed constraints at the bottom of the bottom beam, the horizontal displacement constraint at the top of the column, and the displacement constraints at the end of the overhanging beams.

3 Model Verification The Hysteresis loops of single and double dou-gong connections are shown in Fig. 5. It can be seen that the finite element models can reasonably reflect the nonlinear force behavior of the dou-gong connections under cyclic loading, and the numerical simulation curve is very close to the experimental results. And the pinching effect, strength softening and stiffness degradation of the hysteresis loop were represented well. The initial stiffness k and horizontal bearing capacity P of the connections were calculated as shown in Table 4. It can be seen that the finite element models have good prediction accuracy. The initial stiffness errors of the three models were all within 6%, and the error of the ultimate bearing capacity of the double dou-gong connection model D1 was within 4%.

4 Conclusions This paper provided with a three-dimensional finite element method based analysis on hysteretic performance of dou-gong connections considering three dimensional elasticplastic and damage constitutive model of wood. The hysteresis curves including single dou-gong connection and double dou-gong connection were presented. The following conclusions are drawn based on the simulation and comparison results: (1) The finite element models established in this paper can reasonably represent the initial stiffness, ultimate bearing capacity and pinching effect of the dou-gong connections under cyclic loading. (2) Compared with the experimental results, the model prediction accuracy was good. The initial stiffness error was within 6%, and the error of the bearing capacity of the double dou-gong connections was within 4%.

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(a) Hysteresis loops of model S1

(b) Hysteresis loops of model D1

(c) Hysteresis loops of model D2 Fig. 5. Hysteresis loops of models S1, D1 and D2.

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Table 4. Numerical simulation calculation error Initial stiffness k/(kN/mm)

Error δ k

Ultimate bearing capacity P/kN

Error δ m

Single dou-gong connection S1 Experimental results

0.88

–

7.70

Numerical simulation results

0.80

9.1%

9.50

– 23.4%

Double dou-gong connection D1 Experimental results

1.27

–

37.84

Numerical simulation results

1.34

5.5%

36.37

– −3.9%

Double dou-gong connection D2 Experimental results

0.66

–

21.39

–

Numerical simulation results

0.67

1.5%

17.80

−16.8%

References 1. Chen, et al.: Structural performance of Dou-Gong brackets of Yingxian Wood Pagoda under vertical load—an experimental study. Eng. Struct. (2014) 2. Xie, et al.: Experimental study and finite element analysis of Dou Gong joints built with fork column under vertical loading. J. Build. Struct. 39(09), 66–74 (2018) 3. Cheng, et al.: Experimental study on mechanical properties of Song-style Dougong joints with Ang. J. Build. Struct. 40(04), 133–142 (2019) 4. Yuan, et al.: Experimental research on bracket set models of Yingxian Timber Pagoda. J. Build. Struct. 32(07), 66–72 (2011) 5. Yuan, et al.: Finite element model of Dou-Gong based on energy dissipation by friction-shear. J. Build. Struct. 33(06), 151–157 (2012) 6. Chen, et al.: Numerical simulation of mechanical behaviour of wood under complex stress. Chin. J. Comput. Mech. 28(04), 629–634+640 (2011) 7. Wang, et al.: Analysis on hysteretic performance of Dou-gong connection based on three dimensional elastic-plastic damage evolution. Build. Struct. 51(09), 103–108+113 (2021) 8. Wu, Y., Song, X., Li, K.: Compressive and racking performance of eccentrically aligned Dougong connections. Eng. Struct. 175, 743–752 (2018) 9. Krawinkler, H., Parisi, F., Ibarra, L.F., Ayoub, A., Medina, R.A.: Development of a testing protocol for wood frame structures (2001)

Research on Seismic Behavior of CFT-Frame-Buckling Restrained Steel Plate Shear Wall Structures Using Recycled Aggregate Concrete Amer Mohammed2 , Yansheng Du1,2(B) , Zhihua Chen1,2 , and Jin Huang2 1 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin 300072, China

[email protected] 2 School of Civil Engineering, Tianjin University, Tianjin 300072, China

Abstract. Several studies on steel plate shear walls (SPSWs) systems have revealed that the seismic demand on the vertical boundary elements (VBEs) is relatively high for ordinary structures. To resolve this problem and boost the application of concrete-filled steel tubes, two types of concrete-filled steel tubes (CFT) columns (square and L-shaped sections) for SPSWs, consisting of one span and two stories, were designed and tested under quasi-static load. Four corner and double sides connections welding form between frame elements and the shear wall were used to enhance the bearing capacity and stiffness. On the other hand, four corner and double sides fish plates were connected to the steel plate using high-strength bolts to improve the ductility and reduce the local buckling of the steel plate. In terms of buckling restrained, recycled aggregate concrete (RAC) and autoclaved lightweight concrete (ALC) were used as panels to minimize the buckling of steel plates. RAC was also used as a concrete infill. The specimens were evaluated based on hysteretic and skeleton curves. The bearing capacity and stiffness of both types VBEs using four-corner connections were enhanced while the double-sides connections improved the ductility of the SPSWs. Furthermore, connecting the frame elements by high-strength bolts improves the ductility but reduces the bearing capacity and stiffness compared with the welding ones. Finally, both RAC and ALC contributed almost the same buckling restraint in this study. Keywords: Buckling-restrained steel plate shear walls (SPSWs) · Seismic behavior · Type of columns (square and L-shaped) · Connections forms (four-corner · Double-sides) · Type concrete panels · Recycled aggregate concrete (RAC) · Autoclaved lightweight concrete (ALC)

1 Introduction For several decades, reinforced concrete (RC) shear walls have been widely used as lateral load resistance in high-rise buildings. Due to continuous increasing the height of high-rise buildings, the shear force, bending moment, and self-weight of the top structures affecting on lower stories that lead to increase the cross-sectional size of RC © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 140–151, 2023. https://doi.org/10.1007/978-981-19-7331-4_13

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core shear walls while the axial compression ratio of these kinds of shear walls was restricted to obviate cause damage during earthquakes [1, 2]. Therefore, this increased cross-sectional area of RC shear walls would reduce the amount of leasable space in structures while also increasing the mass of the shear walls, which would amplify the horizontal base shear force under earthquake loads. Additionally, increasing the ductility of the RC shear wall requires raising the amount of steel reinforcement that increases the reinforcement details. Prefabricated Steel plate shear walls SPSW could exceed all these drawbacks of RC shear wall structures and provide practical solutions to raise ductility, minimize structural self-weight, and increase deformation ability. Furthermore, SPSW can be easier and more expeditious in construction and repair. Consequently, SPSW has been used in the last 30-years in high rise-building to bear the lateral load, such as earthquake and wind load [3]. Prefabricated SPSW system comprises infill steel plates surrounded by boundary elements, as shown in Fig. 1 [4–10]. Some researchers have been conducted on the traditional SPSW. Astaneh et al. [3, 11] proposed and studied SPSW composing precast concrete panels embedded with thin steel plates connected with shear bolts. The precast concrete panel aims to restrain the buckling of the thin steel plates, thereby improving the bearing capacity and energy dissipation capacity of the structure. Nevertheless, the concrete panel edge gets deformed frequently once the panel touches the boundary frame due to the deformation. Thus, the restraint impact of the concrete panel on the steel plate turns to be very weak. Based on this, Astaneh et al. [12]. Suggested an innovative steel plate shear wall that separates the concrete panel from the frame, in which the concrete panel is only connected with the steel plate by shear bolts. In this way, the concrete panel will not contribute to the role of external restraint on the steel plates but also effectively constrain the buckling of steel plates and avoid the lateral deformation concrete panel caused by the frame.

A

A

A-A Fig. 1. Steel plate shear wall [10]

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2 Influence of Using Different Types of Columns Concrete-filled steel tube (CFT) structures have the advantages of both steel and concrete structures. These structures can effectively minimize the cost of construction, enhance the fire resistance behavior, enhance building comfort and construction speed. However, the common CFT column’s sections columns may decrease the available space of the buildings, so recently, some innovative special-shaped columns such as L-shaped, Tshaped and cross-shaped were proposed and investigated by Chen et al. (see Fig. 2) [13– 16]. Several experimental research was conducted on the seismic behavior of specialshaped CFT columns. Zhuo et al. experimentally carried out that the L-shaped column has an excellent bearing capacity ductility under axial load, bending load and cyclic load [14–17]. Besides, the research indicated that within increasing the length-width ratio, the ductility and energy dissipation capacity are increased, but the bearing capacity and stiffness are decreased. In terms of using the special-shaped column in frame systems, a quasi-static test on a special-shaped column-frame system has been carried out by Zhuo el at. the results showed that the system has a stable behavior, good bearing capacity, and ductility. Additionally, Zhoa et al. investigated the seismic performance of a braced-frame using a special-shaped CFT column, and the results revealed a significant enhancement in bearing capacity and energy dissipation compared with an unbraced-frame. Accordingly, a combined special-shaped CFT column-frame buckling restrained steel plate shear wall was proposed and studied. This system’s bearing capacity and stiffness are significantly improved compared to a braced frame [18–20]. Based on all of the above, and due high demand for seismic behavior of steel plate shear wall, two sets of 1:2 scaled specimens were designed to study seismic performance and mechanical properties of frame shear walls using two types of columns, including square and L-shaped CFT columns. Four gusset corner welding connections were used to connect the steel plate to the boundary frame, as shown in Fig. 2. The design approach and geometrical details of these specimens were derived from actual Engineering projects in China. Both specimens were named SPSW-1 and SPSW-2 corresponding square and L-shaped CFT columns. An H-section beam is used to fabricate the boundary beams. Besides, this design provides a fixability for applying steel plate shear walls on-site engineering.

3 Influence Connection Forms On the other hand, it was found that the seismic performance of SPSW is affected by connections between the boundary elements (beam and columns) and the frame’s stiffness. In spite of all of the data supplied by researchers that it is appropriate and ductile against lateral loads, it is not widely used [21–26]. It is well known among scholars that the main reason for the shortage application of this system is the abnormal size of the columns [27]. Consequently, many scholars proposed different connection forms such as perforated SPSW panels [28], low yield point and light-gauge SPSW [26, 29], steel plate shear with slits SPSW [30], partially connected to horizontal members SPSW [31], bound-columns with buckling-restrained SPSW [32], buckling-restrained steel SPSW

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Steel plate Steel plate

L-shaped column-to shear wall

Square column-to shear wall

(a) Top-view of different types of columns 40 100 150

H-section beam

Four-corner connections

3200

1350

Vertical stiffener connection

150

Square CFT columns

1350

L-shaped CFT columns

60

Unit: mm

SPSW with square columns

SPSW with L-shaped columns

(b) Elevation view of SPSW different VBEs and four corner connection

Fig. 2. Details of SPSW with different types of CFT-columns

with inclined-slots [33] and partially connected bucking SPSW [34]. However, these connections have complicated fabrication and construction processes, resulting in poorer materials and economic efficiency. Additionally, some scholars recently suggested a novel partially connected inner buckling-restrained SPSW to create an unbreakable system that can resist lateral load with low stiffness requirements for columns [35–38]. Furthermore, it was found that the steel plate is more likely to buckle diagonally at an early stage. To prevent the local buckling, innovative precast concrete panels were proposed by Astaneh el at [11]; however, when this precast concrete touched the boundary frame, it early cracked. Thus, later on it was suggested to separate the concrete panels from boundary beam because it did contribute on the bearing capacity and stiffness of the structure. Steel plate shear walls structural system with L-shaped column required an extensive study, so double-side connection form with and without concrete panels.

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Then compared with four corner connections forms, as shown in Fig. 3. The aim of this using double-side connection forms with and without concrete is to improve the ductility, energy dissipation and restrained the buckling waves. 40 100 150

H-section beam

Four-corner connections

1350

3200

Double-side connection

Vertical stiffener connection

150

L-shaped CFT columns

1350

60

Unit: mm SPSW with double-sides and four-corner connection forms without panels

40 100 150

H-section beam

Four-corner connections RC panels

RC panels

1350

1350

Double-side connection Vertical stiffener connection

150

1350

Shear bolts L-shaped CFT columns Unit: mm

60 SPSW with double-sides and four-corner connection forms with RC-panels

Fig. 3. Details of SPSW with different connections forms

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4 Influence of Types of Concrete Panels The dimensions of the inner steel plate play a significant factor in local buckling and the overall seismic performance of SPSWs. There are two  types of SPSWs (thick and thin) categorized based on the height-to-thickness (Hp ts ) of inner steel plates. The thick steel plate yield before buckling when the ratio of height-to-thickness is small, and the steel plate fully uses lateral stiffness. In contrast, the thinner steel plate has a larger height-to-thickness ratio, so the steel plate expedites buckling before it reaches its yield. Based on JGJ/J 380-2015 [39],  the height-to-thickness ratio of SPSW must be in the following range 100 < Hp /ts 235/fy < 600. In addition, Du al el. carried out experimental and numerical research on buckling column frame-buckling restrained SPSW welding connection forms [38]. The results revealed that the connection forms greatly influence failure modes, bearing capacity, stiffness, and buckling behavior. Accordingly, to overcome the buckling the early buckling of the steel plate and enhance the ductility of the structures, two specimens were designed with four corner gusset connection forms. The gusset plates were connected to the steel plate using high-strength bolts. Besides, two types of concrete panels were used to restrain the buckling of steel plate, including recycled aggregate concrete (RAC) panels and autoclaved lightweight concrete (ALC), as shown in Fig. 4. 40 100 150

H-section beam

Shear bolts Four-corner connections

1350

1350

Vertical stiffener connection

150

RC panel 1350

ALC panel Square-CFT columns

Welded Plates

high-strength bolts Unit: mm 60

Fig. 4. Details of steel plate shear wall with different types concrete panels

5 Influence of Types of Restrained Steel Plate As mentioned above, the steel plate is sandwiched by two precast concrete and connected by shear bolts, and the main purpose of the precast concrete is to groove the local buckling

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with any contribution on bearing capacity and stiffness. Besides, the precast concrete was cracked in the early stage when it touched with the boundary elements. Later on, scholars conducted that the concrete panel gets partially damaged due to shear deformation caused by shear bolts. As a result, Guo et al. [10]. Designed the buckling restrained shear wall based on Astaneh’ model that provides slippage space for shear bolts, placing ellipse holes on the concrete panel in order to avoid excessive local deformation on the concrete panel around bolts. The concrete panel prevents the steel plate from out-plan large deformations. The obtainable study illustrated that the buckling restrained steel plate shear wall has excellent static lateral and seismic performance due to its rotationally of structures [40]. Accordingly, to provide an economical, structural and architectural panel, autoclaved lightweight concrete (ALC) was used as panels in this structural system, as shown in Fig. 5. In addition, double-side guests’ plates were connected to the steel plate using welding and bolts to improve the stiffness and ductility of SPSWs.

6 The Innovation and Aims of SPSWs Polite research on L-shaped CFT column frame-buckling steel plate shear wall with different connection forms, including four-side, four-corner and groove connections, was carried out by Du el at [38]. It was found that concrete crackling on the corner of concrete panels and column fracture and damage finally appeared using four-side connections. It is also noticed that the using four-sides connection dropped quickly to lower than 85% of the lateral resistance, and the boundary columns were totally damaged in the bottom because of the full connection between frame and shear wall, which is not favorable in buckling restrained SPSW system, as shown in Fig. 6(a). Local buckling of the inner steel plate and concrete cracking in the corner of concrete panels were captured with concrete separation between the inner steel plate and concrete panels when fourcorner connections were used, as seen in Fig. 6(b). However, there was no damage to the boundary columns due to reducing the connections between the shear wall and boundary frame. It can be seen that there are several failures of using groove connections, such as local buckling of steel plate, cracking of concrete panels, and fracture and tearing on inner steel plate and boundary columns, as seen in Fig. 6(c). Furthermore, the results revealed that the frame shear wall system has excellent seismic behavior, bearing capacity and stiffness. Additionally, due to local buckling of the steel plate, the pinch behavior appeared on the hysteretic curves affected by connection forms. In other words, BRSW-1 was the fullest among all specimens due full connection with the frame element, while BRSW-3 was the clearest one among all due less connection with frame elements and high-buckling of the steel plate, as seen in Fig. 7(a). Furthermore, the connection forms greatly influenced the bearing capacity and stiffness. They were reduced with reduced the connection between the frame elements, as shown in Fig. 7(b). Consequently, the CFT L-shaped columns framebuckling SPSW reflects a goof seismic behavior, but it observed damage and failure on the frame elements, increasing the connection with them, which is not favorable in seismic design even though the bearing capacity and stiffness were increased. Accordingly, to exceed all damage and failure on the frame element and enhance seismic behavior of frame-buckling restrained SPSW, this paper explores the overall

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H-section beam

Double-side connections

1350

1350

147

150

Vertical stiffener connection

1350

Square-CFT columns

ALC panel ALC panel

Welded Plates

High-strenght bolts

Unit: mm 60 SPSW with double side-bolt/welding connection forms 40 100 150

H-section beam

Double-side connections

1350

1350

Vertical stiffener connection

150

Square-CFT columns

1350 high-strength bolts

Unit: mm 60 SPSW with double side-bolt connection forms without ALC

Fig. 5. Details of steel plate shear wall with different types of restrained connections

performance of CFT-column Frame buckling restrained steel plate shear wall. It has several features, including assembling on-site, easy to fabricate, increased useable space, and improved overall structural performance compared to reinforced concrete structures. The main objective and aims of this paper can be listed as follows; 1. To investigate the CFT-column frame-buckling restrained steel plate shear wall based on column section types, including L-section and square-section.

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Broken of the column Concrete cracking

Fracture on the mano column

(a) Deformation and damage of the BRSW-1

Concrete cracking

Separation

Local buckling

(b) Deformation and damage of the BRSW-2

Tearing Concrete cracking

Local buckling

Concrete damage

(c) Deformation and damage of the BRSW-3

Fig. 6. Samples of failure modes

2. To investigate the most effective connections forms in order to enhance the bearing capacity and stiffness of the CFT-frame buckling restrained steel plate shear wall. 3. Study the buckling restrained of steel plates by providing two types of panels, including RAC and ALC concrete panels, with innovative connection forms for steel plates. 4. Compare the connection forms between the gusset and steel plates in terms of welding and bolts. 5. To provide a cleaner production, eco-friendly and sustainable application of material, iron ore tailings sand (IOTs) and recycled coarse aggregate (RCA) are adopted to manufacture concrete in this study.

1250

1250

1000

1000

750

750

500

500

250

250

F (kN)

F (kN)

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BRSW-1 BRSW-2 BRSW-3

-1000 -1250 -80

0 -250 Yield Peak

-500

-500

-60

-40

-20

0

20

40

60

80

149

-750

BRSW-1 BRSW-2 BRSW-3

-1000 -1250 -80

-60

-40

-20

0

Δ (mm)

Δ (mm)

a

b

20

40

60

80

Fig. 7. Load displacement curves

7 Conclusion Steel plate shear wall has been recently used in a high-rise building, which comprises from infill steel plate surrounded by frame elements (beam and columns). To extend the application of CFT-columns, including square and L-shaped, ten sets 1:2 scale structural model specimens with a single span and two stories were designed to study the cyclic behavior of frame-buckling steel plate shear wall (SPSW). Several parameters were covered in this design to understand this structural system’s features and drawbacks, including types of boundary columns, connection forms, types of concrete panels, and types of steel plates restrained. An eco-friendly and sustainable recycled concrete (RC) was adopted in this research to manufacture the concrete infill and concrete panels. 1. Investigate the seismic performance of SPSW using two types of CFT columns, including square and L-shaped, that would extend their application in the high-rise building in different positions. This structural system reduces the useable space and increases stiffness and bearing capacity. 2. The connections forms between the shear wall and boundary frame, including double-sides and four-corner connections, were designed to improve the seismic behavior and mechanical properties of the SPSWs. On the other hand, with and without concrete panels were covered in these specimens using the connections forms to analyze the welding connections’ buckling behavior. 3. Previous research showed that the concrete panels do not contribute to the seismic performance of frame-buckling SPSW, and the main aims of the concrete panels are to restrain the steel plate. Therefore, RAC and ALC concrete panels were adopted in this study to delay the local buckling of the steel plate and increase the ductility. 4. The connection forms between the steel plate and gusset plates significantly influence the ductility, stiffness, and buckling behavior. Therefore, welded and bolts connections were used. In addition, using normal precast concrete panels to sandwich the steel plate does not meet economical and architectural requirements, so ALC panels were designed and compared with none panels in order to study their structural effect.

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Acknowledgments. This work is sponsored by the National Key Research and Development Program of China (Grant No. 2019YFD1101005).

References 1. Nie, J.-G., Hu, H.-S., Fan, J.-S., Tao, M.-X., Li, S.-Y., Liu, F.-J.: Experimental study on seismic behavior of high-strength concrete filled double-steel-plate composite walls. J. Constr. Steel Res. 88, 206–219 (2013) 2. Hu, H.-S., Nie, J.-G., Eatherton, M.R.: Deformation capacity of concrete-filled steel plate composite shear walls. J. Constr. Steel Res. 103, 148–158 (2014) 3. Astaneh-Asl, A.: Seismic Behavior and Design of Composite Steel Plate Shear Walls. Structural Steel Educational Council Moraga, CA (2002) 4. Takahashi, Y., Takemoto, Y., Takeda, T., Takagi, M.: Experimental study on thin steel shear walls and particular bracings under alternative horizontal load. In: Preliminary Report, IABSE, Symp. On Resistance and Ultimate Deformability of Tsructures Acted on by Well-defined Repeated Loads, Lisbon, Portugal, 1973 5. Thorburn, L., Kulak, G., Montgomery, C.: Analysis of steel plate shear walls, Structural Engineering Report No. 107. University of Alberta, Department of Civil Engineering, Edmonton, Alberta (1983) 6. Tromposch, E.W., Kulak, G.L.: Cyclic and static behaviour of thin panel steel plate shear walls (1987) 7. Caccese, V., Elgaaly, M., Chen, R.: Experimental study of thin steel-plate shear walls under cyclic load. J. Struct. Eng. 119(2), 573–587 (1993) 8. Driver, R.: Seismic behavior of steel plate shear walls [Dissertation of Ph. d.]. University of Alberta, Alberta, Canada, D. Department of Civil and Environmental engineering (1997) 9. Park, H.-G., Kwack, J.-H., Jeon, S.-W., Kim, W.-K., Choi, I.-R.: Framed steel plate wall behavior under cyclic lateral loading. J. Struct. Eng. 133(3), 378–388 (2007) 10. Guo, Y., Dong, Q., Zhou, M.: Tests and analysis on hysteretic behavior of buckling-restrained steel plate shear wall. J. Build. Struct. 30(1), 31–39 (2009) 11. Astaneh-Asl, A.: Seismic Behavior and Design of Steel Shear Walls. Structural Steel Educational Council Moraga, CA (2001) 12. Zhao, Q., Astaneh-Asl, A.: Cyclic behavior of traditional and innovative composite shear walls. J. Struct. Eng. 130(2), 271–284 (2004) 13. Zhihua, C.: New-Type special-shaped column by steel structure and composite. Steel Constr. 2, 27–29 (2006) 14. Zhou, T., Chen, Z., Liu, H.: Seismic behavior of special shaped column composed of concrete filled steel tubes. J. Constr. Steel Res. 75, 131–141 (2012) 15. Du, Y., Chen, Z., Xiong, M.-X.: Experimental behavior and design method of rectangular concrete-filled tubular columns using Q460 high-strength steel. Constr. Build. Mater. 125, 856–872 (2016) 16. Du, Y., Chen, Z., Yu, Y.: Behavior of rectangular concrete-filled high-strength steel tubular columns with different aspect ratio. Thin-Walled Struct. 109, 304–318 (2016) 17. Zhou, T., Jia, Y., Xu, M., Wang, X., Chen, Z.: Experimental study on the seismic performance of L-shaped column composed of concrete-filled steel tubes frame structures. J. Constr. Steel Res. 114, 77–88 (2015) 18. Zhao, B.: Mechanical behavior of the special-shaped column composed of concrete-filled square steel tube braced frame system. PhD Thesis, Tianjin University, Tianjin, China (2017) 19. Zhao, B., et al.: Experimental seismic behavior of SCFRT column chevron concentrically braced frames. J. Constr. Steel Res. 133, 141–155 (2017)

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20. Chen, Z., Xu, H., Zhao, Z., Yan, X., Zhao, B.: Investigations on the mechanical behavior of suspend-dome with semirigid joints. J. Constr. Steel Res. 122, 14–24 (2016) 21. Shekastehband, B., Azaraxsh, A., Showkati, H., Pavir, A.: Behavior of semi-supported steel shear walls: Experimental and numerical simulations. Eng. Struct. 135, 161–176 (2017) 22. Hajimirsadeghi, M., Mirtaheri, M., Zandi, A., Hariri-Ardebili, M.: Experimental cyclic test and failure modes of a full scale enhanced modular steel plate shear wall. Eng. Fail. Anal. 95, 283–288 (2019) 23. Yu, J.-G., Yu, H.-S., Feng, X.-T., Dang, C., Hou, T.-F., Shen, J.: Behaviour of steel plate shear walls with different types of partially-encased H-section columns. J. Constr. Steel Res. 170, 106123 (2020) 24. Paslar, N., Farzampour, A., Hatami, F.: Investigation of the infill plate boundary condition effects on the overall performance of the steel plate shear walls with circular openings. Structures Elsevier 27, 824–836 (2020) 25. Cui, J.-C., Xu, J.-D., Xu, Z.-R., Huo, T.: Cyclic behavior study of high load-bearing capacity steel plate shear wall. J. Constr. Steel Res. 172, 106178 (2020) 26. Berman, J.W., Bruneau, M.: Experimental investigation of light-gauge steel plate shear walls. J. Struct. Eng. 131(2), 259–267 (2005) 27. Berman, J.W., et al.: Research needs and future directions for steel plate shear walls. In: Structures Congress 2008: Crossing Borders, pp. 1–10 (2008) 28. Roberts, T.M., Sabouri-Ghomi, S.: Hysteretic characteristics of unstiffened perforated steel plate shear panels. Thin-Walled Struct. 14(2), 139–151 (1992) 29. Chen, S.-J., Jhang, C.: Cyclic behavior of low yield point steel shear walls. Thin-Walled Struct. 44(7), 730–738 (2006) 30. Hitaka, T., Matsui, C., Sakai, J.I.: Cyclic tests on steel and concrete-filled tube frames with Slit Walls. Earthq. Eng. Struct. Dyn. 36(6), 707–727 (2007) 31. Choi, I.-R., Park, H.-G.: Steel plate shear walls with various infill plate designs. J. Struct. Eng. 135(7), 785–796 (2009) 32. Liu, Q., Li, G., Lu, Y.: Experimental and theoretical study on the steel bound-columns with buckling restrained steel plate shear wall. In: Proceedings of the EUROSTEEL, 7th European Conference on Steel and Composite Structures, Italy (2014) 33. Jin, S., Ou, J., Liew, J.R.: Stability of buckling-restrained steel plate shear walls with inclinedslots: Theoretical analysis and design recommendations. J. Constr. Steel Res. 117, 13–23 (2016) 34. Wei, M.-W., Liew, J.R., Du, Y., Fu, X.-Y.: Seismic behavior of novel partially connected buckling-restrained steel plate shear walls. Soil Dyn. Earthq. Eng. 103, 64–75 (2017) 35. Wei, M.-W., Liew, J.R., Xiong, M.-X., Fu, X.-Y.: Hysteresis model of a novel partially connected buckling-restrained steel plate shear wall. J. Constr. Steel Res. 125, 74–87 (2016) 36. Wei, M.-W., Liew, J.R., Fu, X.-Y.: Panel action of novel partially connected bucklingrestrained steel plate shear walls. J. Constr. Steel Res. 128, 483–497 (2017) 37. Wei, M.-W., Liew, J.R., Yong, D., Fu, X.-Y.: Experimental and numerical investigation of novel partially connected steel plate shear walls. J. Constr. Steel Res. 132, 1–15 (2017) 38. Du, Y., Zhang, Y., Zhou, T., Chen, Z., Zheng, Z., Wang, X.: Experimental and numerical study on seismic behavior of SCFRT column frame-buckling restrained steel plate shear wall structure with different connection forms. Eng. Struct. 239, 112355 (2021) 39. JGJ/T 380: Technical specification for steel plate shear walls (2015) (in Chinese) 40. Ye, L., Guoqiang, L., Feifei, S.: Experimental study on buckling-restrained composite steel plate shear wall with large aspect ratio. Progress Steel Build. Struct. 11(2), 18–27 (2009)

Seismic Response Mitigation of Atrium Buildings with Truss-IMD System Siyuan Li and Yung-Tsang Chen(B) Department of Civil Engineering, University of Nottingham, Ningbo 315100, China {Siyuan.Li,Yung-Tsang.Chen}@nottingham.edu.cn

Abstract. In this paper, a novel truss-inertial mass damper (IMD) system is developed for seismic response mitigation of atrium buildings with an internal structure. An IMD with nonlinear damping characteristic is introduced to provide passive vibration control, and the unsynchronized dynamic response between the tops of the building and the structure inside the atrium is utilized to activate the IMD for energy dissipation purpose. Parametric studies are conducted to evaluate the effectiveness of the truss-IMD system on suppressing structural responses under earthquakes, with two performance indices set to reflect the response intensities in interstory drift and story absolute acceleration. Results indicate that for a preset IMD nonlinearity, there exists an optimal combination of inertance and damping coefficient to maximize a building performance for a given equivalent stiffness of the truss and internal structure. Results also show that the maximum achievable structural performance and the corresponding optimal IMD design parameters generally increase with increasing effective stiffness for a given velocity exponent. Multi-objective optimizations are also performed to further evaluate the capacity of the proposed system in reducing the interstory drift and story acceleration simultaneously using a 6-story building. Keywords: Inertial mass damper · Atrium building · Passive vibration control

1 Introduction Excessive dynamic response induced by earthquakes and other external disturbances could cause damage to non-structural components, fatigue and/or immediate collapse of structures. To suppress undesirable dynamic response and enhance structural safety during earthquakes, various types of control systems have been developed for building structures, among which passive energy dissipation system is most widely used due to its high stability, low cost, and independence of additional energy supply (Lazar et al. 2014; Ma et al. 2021b). Conventional types of passive control devices, such as viscous dampers, viscoelastic dampers, and friction dampers, are generally recognized as effective means to dissipate earthquake energy (Symans et al. 2008). Previous studies have revealed that the energy dissipation devices with negative stiffness characteristics are more effective than conventional ones (Høgsberg 2011), as the negative stiffness, which means a force is introduced to assists motion, can amplify the relative displacements between the two © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 152–168, 2023. https://doi.org/10.1007/978-981-19-7331-4_14

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ends of the devices and thus increase their energy dissipation capacity. Some negative stiffness devices have been developed in the past decade to improve performance of dampers (Walsh et al. 2021; Zhou et al. 2020). In addition to these devices, inerter also exhibits negative stiffness behavior (Ma et al. 2021a) and can thus be used to upgrade conventional energy dissipators such as fluid viscous dampers. The concept of the inerter was first proposed by Smith (2002). An ideal inerter is a linear massless two-terminal mechanical element, producing a force proportional to the relative acceleration between its two ends with a constant proportionality termed “inertance” and measured in the unit of mass (kg). The physical realization of inerter can be achieved by different mechanisms, e.g., ball screw (Li et al. 2012), rack-and-pinion (Papageorgiou et al. 2008), hydraulic (Wang et al. 2011) and living-hinge (John and Wagg 2019). The inerter provides additional mass to a connected system, thus many inerterbased vibration absorbers have been developed in the past two decades for upgrading the convention tuned mass dampers, such as tuned mass damper inerter (TMDI) (Marian and Giaralis 2014) and tuned inerter damper (TID) (Lazar et al. 2014). Other types of inerter-based passive control systems like base isolation systems (Ma et al. 2020) and some hybrid systems (Cao and Li 2022; Li et al. 2021) have also been proposed and investigated. Inertial mass damper (IMD) is another type of passive control device that takes advantage of the negative stiffness effect of the inerter to increase damping capacity. An ideal IMD can be represented by an inerter in parallel with a viscous damper (Ma et al. 2021a), which could be physically realized by different mechanisms. For example, Hwang et al. (2007) proposed a rotational inertia-viscous damper that uses a ball screw to transform the interstory drift of a structure to rotation movement of a flywheel, which is immersed in viscous fluid to dissipate input energy. Ikago et al. (2012) developed a tuned viscous mass damper (TVMD) that consists of an IMD with ball screw mechanism and a spring that connects a damper to the structure. Nakamura et al. (2014) presented an electromagnetic inertial mass damper (EIMD) that combines an IMD with an electromagnetic damper. Recently, Ali Sadeghian et al. (2021) proposed an adaptive tuned viscous inertance damper (ATVID) for vibration control of structures based on continuously variable transmissions; the damper can be mathematically modeled as an IMD and a spring connected in series. These studies generally suggested superior performance of IMDs in response control of building structures compared with conventional types of dampers. The aforementioned studies generally used linear dashpots to represent the damping characteristic of IMDs. In this paper, a nonlinear IMD consisting of a nonlinear dashpot and an inerter is introduced to consider its damping behavior. Based on this type of IMD, a novel truss- IMD system is developed for seismic response mitigation of a specific type of building, namely, building with atria. The atrium building typology has apparent advantages in functioning, natural lighting, heating, and self-ventilation; thus, it has been widely used in many commercial buildings like hotels and shopping malls (Hung 2003; Hussain and Oosthuizen 2012). The proposed configuration contains a truss extending from the roof of the building towards the top of an internal structure, e.g., an elevator tower or a purpose-built structure inside the atrium, as shown in Fig. 1a, and an IMD placed between the tip of the cantilever truss and the internal structure, as shown in Fig. 1b. The unsynchronized dynamic response between the tops of the building and the

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internal structure can thus be utilized to activate the IMD. Unlike conventional damper placement strategy that installed dampers between stories, such a system takes advantage of the large hollow space inside the structure and thus avoiding imposed changes in usable area and aesthetic appearance of the building. In the present work, the effectiveness of the truss-IMD system on enhancing different structural seismic performances was first investigated numerically using a single-degree-of-freedom (SDOF) structure. Multiobjective optimizations were then performed using a non-dominated sorting genetic algorithm (NSGA-II) developed by Deb et al. (2002) to assess the performance of the proposed system in mitigating interstory drift and story acceleration of a multi-story building simultaneous when subjected to several different earthquakes.

Fig. 1. (a) Atrium building with an internal structure (b) truss-IMD system for the building.

2 An Atrium Building with a Truss-IMD System 2.1 Analytic Model of the Building-Truss-IMD System The proposed truss-IMD system incorporates an internal structure into the seismic control system for the atrium building. The internal structure can be an elevator or a purposebuilt structure, as shown in Fig. 1, of which the structural mass and damping are relatively small compared to the main building. In this study, the internal structure is idealized as a stiffness element with a lateral stiffness coefficient k c , with the mass and damping been neglected for simplification. The structural system shown in Fig. 2a is thus be adopted as the analytic model of a N-story atrium building equipped with a truss-IMD system, where mi , ci and k i (i = 1, 2, …, N) denote the story mass, damping coefficient and stiffness of the building, respectively, b, cd and ν are the inertance, damping coefficient and velocity exponent of the IMD, respectively, and k t is the stiffness of the truss in the horizontal direction. The relative displacement between the atrium building and the internal structure will transmit to the IMD through the truss. It can be seen from Fig. 2a that, since the internal

Seismic Response Mitigation of Atrium Buildings xN (t)

mN cd ,v kc

cN

kt

mN-1

b

m2

kN xN-1(t)

cN

cd ,v

m1 c1

mN-1

kN xN-1(t)

m2

x2 (t)

b

x2 (t) c2

xN (t)

mN ke

c2

k2 x1 (t)

m1 c1

k1

xg (t)

xg (t)

(a)

(b)

155

k2 x1 (t) k1

Fig. 2. (a) Analytic model of an atrium building with a simplified truss-IMD-internal structure system and (b) an equivalent model.

structure has been idealized into a pure stiffness element and it is in series with the trussIMD system, the internal structure and the truss can be represented by an equivalent spring with a stiffness coefficient of k e , as shown in Fig. 2b, where 1 1 1 = + ke kc kt

(1)

The effect of the lateral stiffness of the truss and internal structure can thus be investigated through evaluations of the equivalent stiffness of the spring. Importantly, as the IMD and the equivalent spring are arranged in series, the following kinematic condition must be satisfied: (t) = d (t) + e (t)

(2)

where (t) is the total deformation of the equivalent spring and IMD, d (t) and e (t) are the deformations of the IMD and the spring, respectively. 2.2 Dynamic Response of the Atrium Building 2.2.1 Equations of Motion The equation of motion of the atrium building shown in Fig. 2b under earthquake excitation can be represented by a second-order differential equation: M¨x(t) + C˙x(t) + Kx(t) + Fd (t) = −M1¨xg (t)

(3)

where M, C and K are the N×N mass, inherent damping, and stiffness matrices of the atrium building, respectively, x(t) is the N×1 response vector of the building, 1 is a N×1 influence vector with each element equal to unity, and x¨ g (t) is the horizontal

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ground acceleration. The damper force vector, Fd (t), is a N×1 vector with the following expression:   0(N−1)×1 (4) Fd (t) = fd (t) where f d (t) is the force in the IMD. The equation of motion in Eq. (3) can be solved numerically with different approaches; this paper adopts the state-space technique (Meirovitch 1990) to calculate the dynamic response of the building during an earthquake input x¨ g (t). The response- history can be computed once the damper force f d (t) is calculated at each computational instant. 2.2.2 Force in the Truss-IMD System The damper force in the IMD f d (t) can be expressed as:   ˙ d (t)v sgn( ˙ d (t))b ¨ d (t) = ke e (t) fd (t) = cd 

(5)

where d (t) is the deformation of the IMD, and e (t) is the deformation of the equivalent spring, i.e., the total deformation of the truss and the internal structure. To calculate the damper force at each time step, Eq. (5) is first rewritten as: ¨ d (t) + 

 cd  k ˙ d (t)v sgn( ˙ d (t)) = e e (t)  b b

(6)

The substitution of Eq. (2) into Eq. (6) yields: ¨ d (t) + 

 cd  k k ˙ d (t)v sgn( ˙ d (t)) + e d (t) = e (t)  b b b

(7)

The total deformation of the spring and IMD, (t), is equal to the roof displacement of the atrium building x N (t). It can be seen from Eq. (7) that the damper deformation d (t) can be calculated from an input (t) (or x N (t)). In this paper, it is assumed that the roof displacement changes linearly between two consecutive sampling instants, thus Eq. (7) becomes an initial value problem:  c  k ˙ d (t)v sgn( ¨ d (t) + d  ˙ d (t)) + e d (t)  b b 1 − 0 ke t), = (0 + for t0 ≤ t ≤ t0 + t b t ˙ ˙ d (0) = d ,0 , d (t0 ) = d ,0 , (t0 ) = 0 , (t + t) = 1

(8)

The roof displacement of the building at two adjacent time instants kt and (k+1)t can be computed from Eq. (3), Eq. (8) can thus be expressed as:  c  k ¨ d (t) + d  ˙ d (t)v sgn( ˙ d (t)) + e d (t)  b b [k + 1] − [k] ke for kt ≤ t ≤ (k + 1)t t), = ([k]) + b t ˙ d (0) =  ˙ d [k] d (0) = d [k], 

(9)

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ode45 based on the explicit Runge-Kutta (4, 5) pair of Dormand and Prince (1980) is adopted to solve Eq. (8) between two adjacent computational instants. The next step damper deformation, d [k+1], can be calculated by extracting the numerical solution at t = (k+1)t. Noting that the substitution of d [k+1] into Eq. (2) gives the spring deformation e [k+1]. Therefore, the next step damper force f d [k+1] can be calculated from either the IMD deformation or the spring deformation using Eq. (5).

3 Performance Assessment of a SDOF Atrium Building with a Truss-IMD System The effectiveness of the proposed truss-IMD system will be evaluated based on the structural performance of the atrium building. Different performance indices will be defined to quantify the structural response intensities during an earthquake. Response reductions can thus be calculated from the performance indices to reflect the improve structural performance after the installation of a truss-IMD system. The performance assessment will be conducted in the next two sections using a SDOF atrium building. 3.1 Minimization of Story Drift The performance of a building under seismic excitation may be assess based on structural interstory drifts. An interstory drift index, which is defined as the mean value of root-mean- square (rms) of the interstory drift time-history, is adopted to be the first performance index: 1 rms(δi ) for n - story building n n

PID =

(10)

i=1

where δi = x i − x i−1 is the interstory drift time-history of the i-th floor of the building, and δ 1 = x 1 for the first floor. Notably, the performance index of a building without a supplemental control system under a given earthquake is a constant, and it is denoted as PI D,org . To calculate the response reduction in interstory drift after the installation of a trussIMD system, a response reduction ratio RRD is used with the following expression: RRD (%) =

PID,org − PID × 100 PID,org

(11)

The equivalent model in Fig. 2b will be adopted to assess the effectiveness of a truss-IMD system when it is installed on top of an internal structure. The model has four design parameters, namely k e , b, cd and ν, indicating the stiffness, inertance, damping and nonlinearity of the truss-IMD-internal structure system, respectively. The first three design parameters are related to the building properties with three new parameters: η≡

ke b cd ,λ ≡ ,β ≡ k1 M1 2M1 ω1

(12)

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where η is the stiffness ratio of the equivalent spring, λ and β are the inertial mass ratio and damping ratio of the IMD, respectively, k 1 is the first story stiffness of the building, M 1 and ω1 are the modal mass and natural circular frequency of the first vibration mode of the building, respectively. Notably, η and λ are dimensionless parameters, while β has a unit of (s/m)ν −1 . A SDOF structural model is first considered to assess the effectiveness of the trussIMD system. The investigated model has the following properties: structural mass m = 2533 kg, structural lateral stiffness k = 100 kN/m and inherent damping ratio ξ = 2%. Noting that the natural period of the structure is set to 1 second. A white-noise acceleration time-history with a zero-mean is adopted to be the ground excitation input of the building model.

Fig. 3. 3-dimensional mesh plots and contour plots of story drift response reduction versus equivalent stiffness ratio and IMD damping ratio (λ = 0.02).

Figure 3 shows the variations of the story drift response reduction of the atrium building with the stiffness ratio of the equivalent spring and the damping ratio of the IMD for different velocity exponents. From the mesh plots it can be seen that, for a given inertial mass ratio of the IMD, the response reduction generally increases with increasing equivalent stiffness ratio and damping ratio. However, it can also be seen that using a larger damping ratio may not result in a greater response reduction, and there exists an optimal damping ratio to maximize the story drift performance for a given equivalent stiffness k e . The red dot in the contour plots indicate the minimum equivalent stiffness ratio from the truss and internal structure ηmin , and the corresponding “optimal”

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damping ratio from the IMD, required to achieve a target response reduction. As the target RRD increases, the required minimum stiffness ratio and “optimal” damping ratio also increase.

Fig. 4. Mesh and contour plots of story drift response reduction versus inertial mass ratio and damping ratio of the IMD for different equivalent stiffness ratios (ν = 0.4).

Figure 4 shows the variations of response reduction in story drift with inertial mass ratio and damping ratio of the IMD for equivalent stiffness ratios of 0.1, 0.2 and 0.5. It can be seen from the figure that, for a given equivalent stiffness of the truss and internal structure, there is an optimal combination of inertial mass ratio and damping ratio for the atrium building to achieve a global maximum response reduction. Here, the optimal combination is defined as the optimal design parameters of the IMD for a given stiffness ratio. It can be observed from Fig. 4d–f that, the maximum achievable response reduction of the building increases with increasing equivalent stiffness of the truss and internal structure, so do the optimal inertial mass ratio and damping ratio of the IMD.

Fig. 5. (a) Maximum response reductions in story drift (b) optimal inertial mass ratios and (c) optimal damping ratios for the atrium building under white-noise.

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The maximum story drift response reductions of the atrium building, and the corresponding optimal design parameters for different velocity exponents are plotted in Fig. 5. It can be seen from Fig. 5a that the maximum response reduction increases rapidly with increasing equivalent stiffness when η is small; when η > 0.1, the increasing rate of RRD,max reduces significantly. This growth pattern of RRD,max is noted regardless of the velocity exponent, indicating the nonlinearity of IMD has no significant impact on the optimal performance of the truss-IMD system. From Fig. 5b, c it can be seen that, the optimal inertance and damping of the IMD also increase with the equivalent stiffness; however, for a given stiffness ratio, the optimal inertial mass ratios are similar for different velocity exponents, while a greater amount of optimal damping will be required when using a larger velocity exponent. 3.2 Minimization of Story Acceleration In addition to the performance index in interstory drift, a story acceleration index is also defined to assess the performance of the atrium building: 1 rms(ai ) for n - story building n n

PIA =

(13)

i=1

where ai is the absolute acceleration-history of i-th floor. A response reduction ratio RRA is also defined to evaluate the improved structural performance after the installation of a truss-IMD system: RRA (%) =

PIA,org − PIA × 100 PIA,org

(14)

where PI A,org is the constant story acceleration index of the atrium building without an additional truss-IMD system. Based on the response reduction in story acceleration, the effectiveness of the IMD system on enhancing acceleration-related performance of the building is assessed using the same structural model in Sect. 3.1. Figure 6 shows the 3-dimensional mesh plots and contour plots of RRA against the equivalent stiffness ratio and the damping ratio of the IMD for velocity exponent equals 0.6 and 0.8. Similar to RRD , the response reduction in story acceleration also increases with increasing equivalent stiffness ratio. However, it can be seen from the mesh plot in Fig. 6a that, as both η and β become larger, RRA does not necessarily increase, indicating an excessively large damping will deteriorate acceleration performance of the atrium building. A minimum equivalent stiffness will also be required to achieve a target story acceleration response reduction, as shown in the contour plots, and this minimum stiffness and the corresponding “optimal” damping are also noted to increase with the response reduction desired. An optimal combination of the inertance and damping of the IMD also exists for a given equivalent stiffness to achieve a maximum response reduction in story acceleration, as shown in Fig. 7. The optimal inertial mass ratio and damping ratio are also noted to increase with the equivalent stiffness; however, it can be seen from Fig. 7d–f that, the optimal IMD design variables required to achieve a RRA,max are generally smaller than

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Fig. 6. Mesh and contour plots of story acceleration response reduction versus equivalent stiffness ratio and IMD damping ratio (λ = 0.02).

those required to achieve a RRD,max , which indicates that the optimal IMD parameters for the story drift performance may be overlarge for the story acceleration performance of the atrium building, namely, optimize one performance may deteriorate the other. Figure 8 shows the achievable maximum story acceleration response reductions of the atrium building, and the corresponding optimal inertial mass ratios and damping ratios, against the equivalent stiffness ratio. Similar to the maximum story drift response reduction, RRA,max increases sharply when η < 0.1 and tends towards a diminishing return, as can be seen from Fig. 8a. However, in terms of the optimal IMD inertance, for the examined range of η, unlike λD,opt that increases continuously with η, λA,opt stops growing when η > 0.5. Moreover, it can be observed from Fig. 8a, b that the optimal inertance and damping for story acceleration are generally smaller than those for maximizing the story drift performance.

4 Numerical Example: Multi-objective Optimal Design of a Truss-IMD System To further assess the effectiveness of the proposed truss-IMD system on mitigating seismic response of atrium buildings, a six-story shear-type building is considered with the following properties: the story mass and stiffness of the building are identical for all floors, namely, m1 = m2 = … = m6 = 50 tons and k 1 = k 2 = … = k 6 = 40 MN/m;

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Fig. 7. Mesh and contour plots of story acceleration response reduction versus inertial mass ratio and damping ratio of the IMD for different equivalent stiffness ratios (ν = 0.4).

Fig. 8. (a) Maximum response reductions in story acceleration (b) optimal inertial mass ratios and (c) optimal damping ratios for the atrium building under white-noise.

the resulting fundamental period of the structure T 1 is 0.92 s. A 3% inherent damping is assigned to the building, and a truss-IMD system is used to connect the roof with an internal structure. The building is designated occupancy category II based on ASCE 7-05 (2005), and it is assumed to be located in downtown Los Angeles, on stiff soil that is classified as site class D. The seismic design parameters considered are summarized in Table 1. The multi-objective optimization algorithm NSGA-II proposed by Deb et al. (2002) will be used to minimize structural interstory drift and story acceleration responses simultaneously. 4.1 Optimization Problem Formulation In a multi-objective optimization problem, the objectives are usually in conflict with each other, i.e., the improvement of one may lead to degrading of the others. To solve the problem, multi-objective optimizations, which output a set of non-inferior solutions,

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Table 1. Seismic design parameters for ASCE 7-05. Parameters

Value

Importance factor

1

Seismic design category

D

Site class

D

Spectral response acceleration parameter at short periods S DS (g)

1.298

Spectral response acceleration parameter at period 1 s-period S D1 (g)

0.733

Long-period transition period T L (s)

8

also known as Pareto front or Pareto optimal solutions (Deb et al. 2002), can be used. Notably, any solution lies on the Pareto front is deemed an acceptable solution to the problem, as none of the solutions can be identified as the “best” one, i.e., none of the solutions dominate the others. In this paper, an improved version of non-dominated sorting genetic algorithm (NSGA-II) (Deb et al. 2002) is adopted to solve the multiobjective optimization problems, which can detect Pareto optimal solutions at even a single simulation run. The optimal design present here aimed at finding the combinations of IMD inertance and damping coefficient to minimize structural responses in interstory drift as well as story absolute acceleration under multiple earthquake inputs, for a given equivalent stiffness of the truss and internal structure. The optimization problem is formulated as: Find : λopt and βopt   PID (j) Minimize : f1 = max PID,org (j)   PIA (j) f2 = max PIA,org (j) j = 1, 2, . . . , m

(15)

where λopt and β opt are the optimal solutions (design parameters) of the formulated problem, f 1 and f 2 are the fitness functions for interstory drift and story acceleration of the building, respectively, and m is the total number of earthquakes considered. Noting that a larger ratio of PI D (j) to PI D,org (j) (or PI A (j) to PI A,org (j)) represents a larger structural response under j-th earthquake. Five earthquake ground motion records were selected for design and analysis of the example building. These ground motions were scaled to have a mean response spectrum that approximately matches the design response spectrum of the construction site, especially between periods of 0.2T 1 and 1.5T 1 , as illustrated in Fig. 9. The design spectrum is computed based on the parameters listed in Table 1 per ASCE 7-05. The selected earthquake events are summarized in Table 2.

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Fig. 9. Design response spectrum at downtown Los Angeles (based on parameters in Table 1) and acceleration response spectrums of the selected earthquakes.

Table 2. Selected ground motions used in the numerical example. Code

Earthquake event

Year

Station

EQ1

Imperial Valley-02

1940

EQ2

Managua, Nicaragua-01

EQ3

Magni-tude

PGA (g)

Scale factor

El Centro Array #9 6.95

0.48

1.8313

1972

Managua_ ESSO

6.24

0.60

1.7874

Coyote Lake

1979

Gilroy Array #4

5.74

0.53

2.2894

EQ4

Imperial Valley-06

1979

EC County Center FF

6.53

0.47

2.2124

EQ5

Corinth, Greece

1981

Corinth

6.60

0.53

2.3292

4.2 Numerical Analyses and Discussion The IMD installed in between the building roof and the internal structure has been optimally designed through solving the multi-objective problem formulated in Eq. (15) using NSGA-II algorithm. In this paper, the size of population and the maximum number of generations of the genetic algorithm are set to 60 and 50, respectively, and a constant mutation probability of 0.02 is used. For a given equivalent stiffness, all the parameter combinations lie on the Pareto front are deemed optimal solutions, denoted as λopt and β opt . To increase the convergence rate of the algorithm, the upper and lower bounds of both the inertial mass ratio and damping ratio have been set to 0.1 (for β the unit is (s/m)−0.5 ) and 0, respectively, for η equals 0.5 and ν equals 0.5. These bounds were decided through trial and error to ensure the inclusion of optimal solutions; as can be seen from Table 3, the optimal design variables are within the bounds set.

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Table 3. Optimal design parameters of the IMD (η = 0.5, ν = 0.5). Optimal parameter combinations of IMD

λopt

β opt ((s/m)−0.5 )

Combo 1

0.0473

0.0471

Combo 2

0.0398

0.0397

Combo 3

0.0381

0.0342

Figure 10 shows the Pareto optimal solutions computed from three different runs of the algorithm for η equals 0.5 and ν equals 0.5. It can be seen from the figure that the 3 Pareto fronts generally match with each other, and there exist multiple combinations of ratios of the performance indices in interstory drift and story acceleration that can be achieved by the truss- IMD system. All these combinations are optimal solutions to design the IMD, one can select desired combinations according to the design requirements. Here, the performances of a combination that minimizes the interstory drift, denoted as “Combo 1”, a combination minimizing the story acceleration, denoted as “Combo 2”, and a “Combo 3”, lies between these two combinations, are compared in this study. The location of Combo 2 is determined from a perpendicular extending from the midpoint of a line that connects Combo 1 and Combo 3, as shown in Fig. 10. Table 4 summarizes the mean structural responses and average base shear force of the building under the 5 earthquakes. It can be seen from the table that all of the 3 optimal parameter combinations can significantly alleviate the structural responses. When equipped with the truss-IMD systems, the mean values of interstory drift, story displacement, story acceleration and base shear force have been reduced by around 45%, 35%, 27% and 36%, respectively. It can also be observed from Table 4 that the IMD system with parameter Combo 1 mitigates more structural interstory drift and story displacement among the three combinations, while Combo 3 performs better in reducing base shear force. Figure 11 shows the maximum roof displacement and base shear force of the atrium building with the optimal truss-IMD systems and the uncontrolled structure under the five earthquakes. From the figure it can be observed that the maximum roof displacements of the controlled building with parameter Combo 1 are generally smaller than those with the other two parameter combinations, and the IMD system with parameter Combo 3 outperformed those with Combo 1 and Combo 2. However, as root-mean-square of the responses are used as the performance indices, and five earthquakes have been considered in the optimizations, not all of the optimal combinations can reduce the maximum roof displacement and base shear, e.g., the maximum base shear force under EQ1 excitation has been amplified with the optimal IMD systems. To further illustrate the seismic behavior of the atrium building with an optimal IMD, the story displacement and absolute acceleration time-histories of the first, fourth and sixth floors with parameter Combo 2 are plotted, as shown in Fig. 12. As can be seen, the truss-IMD system can effectively mitigate the overall responses of the building during an earthquake.

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Fig. 10. Pareto fronts of the multi-objective optimization problem for the atrium building under selected earthquakes (η = 0.5, ν = 0.5). Table 4. Mean responses of the atrium building with different parameter combinations under selected ground motions (η = 0.5, ν = 0.5). Parameter combinations

Interstory drift (mm)

Story displ. (mm)

Story accel. (m/s2 )

Base shear (kN)

Uncontrolled

1.04

3.51

0.44

55.52

Combo 1

0.55

2.17

0.32

36.47

Combo 2

0.57

2.29

0.32

35.31

Combo 3

0.59

2.40

0.32

34.88

Fig. 11. Maximum roof displacements and base shear forces of the atrium building under different earthquakes.

5 Conclusions This paper evaluates the performance of a proposed truss-IMD system in mitigating seismic response of atrium buildings with an internal structure. Two response reduction

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Fig. 12. Story displacement and acceleration time-histories of the uncontrolled building and with parameter Combo 2 IMD system under EQ5 earthquake.

ratios have been defined to reflect the effectiveness of the proposed system on suppressing interstory drift and story absolute acceleration of the building. Results from the parametric studies on a simple system revealed that a minimum equivalent stiffness of the truss and internal structure will be required to achieve a target response reduction of the building, and for a preset damper nonlinearity, there exists an optimal combination of inertance and damping coefficient of the IMD to maximize the response reduction for a given equivalent stiffness. The maximum response reductions and the corresponding optimal IMD design variables generally increase with increasing equivalent stiffness, and the velocity exponent has no significant influence on the maximum structural performance and optimal IMD inertance. A 6-story building example is investigated to further assess the performance of the truss-IMD system on mitigating structural interstory drift and story acceleration responses simultaneously subjected to multiple earthquake inputs. Results from the 6-story building also suggest good performance of the truss- IMD system, e.g., the mean responses in interstory drift and base shear force have been reduced by around 45% and 36% respectively when equipped with the proposed systems, and the maximum roof displacement and base shear force have also been alleviated. Acknowledgements. This work is supported by the Short-Term RKE Project Funding Scheme from University of Nottingham Ningbo China.

References Ali Sadeghian, M., Yang, J., Wang, X.-E., Wang, F.: Novel adaptive tuned viscous inertance damper (ATVID) with adjustable inertance and damping for structural vibration control. Structures 29, 814–822 (2021) ASCE: Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, Washington, DC (2005)

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Cao, L., Li, C.: A high performance hybrid passive base-isolated system. Struct. Control. Health Monit. 29(3), e2887 (2022) Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002) Dormand, J.R., Prince, P.J.: A family of embedded Runge-Kutta formulae. J. Comput. Appl. Math. 6(1), 19–26 (1980) Høgsberg, J.: The role of negative stiffness in semi-active control of magneto- rheological dampers. Struct. Control. Health Monit. 18(3), 289–304 (2011) Hung, W.: Architectural aspects of atrium. Int. J. Eng. Performance-Based Fire Codes 5(4), 131– 137 (2003) Hussain, S., Oosthuizen, P.H.: Numerical investigations of buoyancy-driven natural ventilation in a simple atrium building and its effect on the thermal comfort conditions. Appl. Therm. Eng. 40, 358–372 (2012) Hwang, J.-S., Kim, J., Kim, Y.-M.: Rotational inertia dampers with toggle bracing for vibration control of a building structure. Eng. Struct. 29(6), 1201–1208 (2007) Ikago, K., Saito, K., Inoue, N.: Seismic control of single-degree-of-freedom structure using tuned viscous mass damper. Struct. Control. Health Monit. 41(3), 453–474 (2012) John, E.D.A., Wagg, D.J.: Design and testing of a frictionless mechanical inerter device using living-hinges. J. Franklin Inst. 356(14), 7650–7668 (2019) Lazar, I.F., Neild, S.A., Wagg, D.J.: Using an inerter-based device for structural vibration suppression. Earthq. Eng. Struct. Dyn. 43(8), 1129–1147 (2014) Li, C., Chang, K., Cao, L., Huang, Y.: Performance of a nonlinear hybrid base isolation system under the ground motions. Soil Dyn. Earthq. Eng. 143, 106589 (2021) Li, C., Liang, M., Wang, Y., Dong, Y.: Vibration suppression using two-terminal flywheel Part I: modeling and characterization. J. Vib. Control 18(8), 1096–1105 (2012) Ma, R., Bi, K., Hao, H.: Heave motion mitigation of semi-submersible platform using inerter-based vibration isolation system (IVIS). Eng. Struct. 219, 110833 (2020) Ma, R., Bi, K., Hao, H.: Inerter-based structural vibration control: a state-of-the-art review. Eng. Struct. 243, 112655 (2021) Ma, R., Bi, K., Hao, H.: A novel rotational inertia damper for amplifying fluid resistance: experiment and mechanical model. Mech. Syst. Signal Process. 149, 107313 (2021) Marian, L., Giaralis, A.: Optimal design of a novel tuned mass-damper–inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems. Probab. Eng. Mech. 38, 156–164 (2014) Meirovitch, L.: Dynamics and Control of Structures, 1st edn. Wiley, Hoboken (1990) Nakamura, Y., et al.: Seismic response control using electromagnetic inertial mass dampers. Earthq. Eng. Struct. Dyn. 43(4), 507–527 (2014) Papageorgiou, C., Houghton, N.E., Smith, M.C.: Experimental testing and analysis of inerter devices. J. Dyn. Syst. Meas. Contr. 131(1), 011001 (2008) Smith, M.C.: Synthesis of mechanical networks: the inerter. IEEE Trans. Autom. Control 47(10), 1648–1662 (2002) Symans, M.D., et al.: Energy dissipation systems for seismic applications: current practice and recent developments. J. Struct. Eng. ASCE 134(1), 3–21 (2008) Walsh, K.K., Sallar, G., Haftman, J.T., Steinberg, E.P.: Resetting passive stiffness damper with passive negative stiffness device for seismic protection of structures. Struct. Control. Health Monit. 28(8), e2774 (2021) Wang, F.-C., Hong, M.-F., Lin, T.-C.: Designing and testing a hydraulic inerter. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 225(1), 66–72 (2011) Zhou, P., Liu, M., Li, H.: A passive negative stiffness damper in series with a flexible support: theoretical and experimental study. Struct. Control. Health Monit. 27(9), e2594 (2020)

Seismic Performance of Isolated Liquid Storage Tanks Supplemented with Negative Stiffness and Inerter Based Dampers Naqeeb Ul Islam(B) and R. S. Jangid Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India [email protected], [email protected]

Abstract. Liquid storage tanks (LSTs) are lifeline structures that must stay operational during and after earthquakes. Their ability to withstand large earthquakes is a major worry. Although base-isolation protects LSTs from far-fault earthquakes, large-amplitude and long-period velocity pulses seen in near-fault earthquakes can generate substantial isolator and sloshing displacements, posing a problem. Supplemental damping in the isolation system may reduce isolator displacements, but the superstructure response may be hampered. To remove the drawback, this study presents novel combinations of negative stiffness dampers (NSDs) and inerter based dampers that utilise minimal dashpot co-efficient as supplemental dampers to base-isolated LSTs. The continuous liquid mass of the tank is modelled as lumped masses known as sloshing mass, impulsive mass and rigid mass. Based on the tank wall and liquid mass parameters, the stiffness constants associated with these lumped masses are calculated. The governing equations for isolated LSTs with proposed supplemental dampers are derived and represented in state-space form. Numerical studies show that combinations of optimally designed NSDs and inerter based dampers improve the performance of base-isolated LSTs in terms of isolator displacement, sloshing displacement and sloshing height under both near-fault and far-field ground motion. Keywords: Base-Isolation · Inerters · Liquid storage tanks · Negative stiffness dampers · Supplemental dampers

1 Introduction Liquid storage tanks (LST) are lifeline structures that must stay operational for public serviceability during and after the earthquakes. LSTs are used in water distribution systems, chemical industries, and nuclear reactors. These facilities are prone to earthquake damage, and the results can be catastrophic in terms of both life and money. A number of disasters to such lifeline structures have been reported (Steinbrugge and Flores 1963; Niwa and Clough 1982; Manos and Clough 1985; Krausmann and Cruz 2013). For LST protection against earthquakes, several researchers have successfully implemented passive base isolation techniques both experimentally and theoretically (Jadhav and Jangid © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 169–186, 2023. https://doi.org/10.1007/978-981-19-7331-4_15

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2004a; Shekari et al. 2010; Panchal and Jangid 2011; Kalantari 2017). Base isolation mainly works by enlarging the fundamental period of the main structure and isolating the structure from dominant components of ground motion. Several researchers have studied the dynamic response of LST due to ground shaking, which is different from the dynamic behaviour of buildings and bridges. LSTs are subjected to hydrodynamic forces and inertial loads due to interactions of sloshing fluid with the walls of the tank. Simplified lumped models for hydrodynamic modelling of LSTs have been proposed in the literature (Housner 1963; Haroun and Housner 1981; Haroun 1983; Veletsos and Tang 1987; Malhotra 1997; Malhotra et al. 2000). Assuming that the tank walls are rigid, the storage liquid in the tank is divided into two lumped mass components: one component moves synchronously with the tank wall, known as a rigid component, while the other component experiences sloshing motion, known as the convective component (or sloshing component). However, considering the flexibility of tanks walls such as steel LST, storage liquid can be modelled into three lumped mass components: convective or sloshing component (i.e., the top liquid mass associated with the surface movement), impulsive component (i.e., the middle liquid mass vibrating due to the flexible tank wall), and rigid component (i.e., the bottom liquid mass moving rigidly with the tank bottom part). Although the base isolation has been successfully implemented in buildings and tanks, the isolation system may come to critical working conditions under near-fault pulse type excitations. There is a significant increase in the sloshing displacement of the tank liquid and base displacement due to isolation under near-fault motion (Shekari et al. 2010; Mehrparvar and Khoshnoudian 2012; Panchal and Jangid 2012; Luo et al. 2016; Uckan et al. 2018; Akhavan Hejazi and Khan Mohammadi 2019; Tsipianitis and Tsompanakis 2022). One possible solution to contain high displacement demand is the design of larger isolators, but this will lead to an uneconomic design. Another approach is to use supplemental passive energy dissipation systems such as viscous fluid dampers, viscous elastic dampers, frictional dampers etc. (Shekari et al. 2010; Güler and Alhan 2021; Tsipianitis and Tsompanakis 2022). Although supplemental dissipation devices effectively control the base displacement demand, they may cause amplification of superstructure responses such as sloshing displacements (Jadhav and Jangid 2006; Drosos et al. 2019; Tsipianitis and Tsompanakis 2022). Recently inerter and negative stiffness based supplemental dampers have been proposed. An inerter is a device that produces force in the proportion of relative acceleration across its two ends (Smith 2002). The constant proportionality is called inertance and is measured in mass units. Inerter based vibrations absorbers or dampers (IVAs) have been categorised as inerter based energy dissipators, inerter based dynamic vibration absorbers and inerter based vibration isolators in literature (Chen and Hu 2019). The primary advantage of inerters lies in the mass amplification effect. The use of different types of IVAs and optimal design for various civil engineering structures can be referred to here (Tsai and Lin 1993; Takewaki et al. 2012; Murakami et al. 2013; Marian and Giaralis 2014; De Domenico and Ricciardi 2018; Taflanidis et al. 2019; Jiang et al. 2020; Gao et al. 2021; Talley et al. 2021; Jangid 2021; Li et al. 2021; Nyangi and Ye 2021; Pietrosanti et al. 2021). Not many studies concerning seismic control of base-isolated LSTs with IVAs have been reported. Jiang et al. (2020) proposed an optimal design

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method based on an analytical solution for a storage tank with an inerter isolation system. A novel strategy for controlling the sloshing response of seismically excited LSTs with rigid walls based on an inerter-based isolation system has been developed (Labaf et al. 2020). Another type of passive control device called a negative stiffness damper (NSD) is gaining popularity. The force produced by the negative stiffness (NS) spring is proportional to relative displacement across its ends, but the force deformation slope is negative (Li et al. 2008). NSD is a combination of viscous damper and NS, which works on the principle of force assisting motion (Nagarajaiah et al. 2010; Pasala et al. 2013). Several analytical and experimental studies with NSD as a supplemental energy dissipation device have shown promising results (Sarlis et al. 2013, 2016; Wang et al. 2019a, b). Though the inerter and NSD are different devices, both devices show a phase delay of π when subjected to harmonic excitations (Wang et al. 2022), resulting in similar dynamic characteristics. A concurrent combination of inerters and NSDs, aiming to club the advantages of the two mechanical devices as a supplemental damper to base-isolated structure and fixed base benchmark model, has shown promising results as a control device (Islam and Jangid 2021, 2022a, b). This study adopts the combinations of the NSD and inerter mechanisms called NSIDs as supplemental damping devices for isolated LSTs. The specific objectives of the study are: (i) presenting the NSIDs as supplemental damping devices for flexible isolated LST (ii) investigating the effectiveness of NSIDS under near-fault (NF) and far-field (FF) ground excitations seismic control of base-isolated LSTs, and (iii) presenting the optimal parameters of NSIDs for effective control of sloshing and base displacement.

2 Mechanical Modelling of Storage Tanks The model considered for the base-isolated cylindrical LST with a supplemental damper is shown in Fig. 1. The storage liquid considered in this study is incompressible, inviscid and has irrotational motion. The LST geometry is characterised by the height of tank H and the radius of tank R. During the horizontal base excitation, the entire liquid mass in the tank vibrates in three lumped mass models (Kim and Lee 1995; Jadhav and Jangid 2004; Jiang et al. 2020): (1) sloshing or convective mass mc (the top liquid mass associated with free surface movement) (2) impulsive mass mi (the middle portion of the liquid mass vibrating due to flexible tank wall) (3) rigid mass mr (i.e., the lower liquid mass which rigidly moves with the tank wall). The complete dynamic response of LST can be accurately predicted by considering only the first modes of convective and impulsive masses (Kim and Lee 1995; Malhotra 1997). Thus, three degrees of freedom are defined as x c , x i and x b, which represent sloshing mass displacement, impulsive mass displacement and rigid mass displacement, respectively. The three lumped mass components can be expressed as a fraction of total liquid mass m = ρπ R2 H , (where ρ is the unit weight of liquid and H is the height of liquid) as mc = γc m; mi = γi m; and mr = γr m

(1)

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Fig. 1. Structural model of base-isolated storage tanks with supplemental damper

where γc , γi and mr are the mass ratios defined in terms of tank aspect ratio S = H /R (R is the radius of the cylindrical tank). The interaction between the convective and impulsive lumped masses with LST walls is modelled by equivalent spring and dashpot connected in parallel. The equivalent stiffness ratio and dashpot coefficient is represented  by kc , cc  and ki , ci , respectively. The circular frequency of vibration for convective (ωc = kc mc )   and impulsive masses (ωi = ki mi ) are given by (Haroun 1983)     H g γP E and ωi = (2) ωc = 1.84 tanh 1.84 R R H ρt where g is the acceleration due to gravity, E is the modulus of elasticity of tank wall, ρt is the density of tank wall and γP is the dimensionless ratio, which depends on aspect ratio S. The dimensionless ratios are determined using the aspect ratio S of the tank using the following expression (Haroun 1983; Panchal and Jangid 2011; Jiang et al. 2020) ⎧ ⎫ ⎫ ⎡ ⎧ ⎤⎪ 1⎪ ⎪ ⎪ ⎪ 1.01327 −0.87578 0.35708 −0.06692 0.00439 ⎪ γc ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ S ⎬ ⎬ ⎢ ⎨ ⎨ ⎥ −0.15467 1.21716 −0.62839 0.14434 −0.0125 γi ⎥ S2 (3) =⎢ ⎣ −0.01599 0.86356 −0.30941 0.04083 ⎦⎪ ⎪ ⎪ 0 ⎪ ⎪ ⎪ S3 ⎪ ⎪ γr0 ⎪ ⎭ ⎪ ⎩ ⎪ ⎪ γP 0.037085 0.0384302 −0.05088 0.012523 −0.0012 ⎪ ⎭ ⎩ S4 ⎪ where γr0 represents the nominal mass ratio of mr and γr = γr0 − γi . The isolation bearings are assumed to have linear stiffness and linear viscous damping represented by stiffness constant kd and damping √ coefficient cd , respectively. The expression for the isolation period is given by T = kd /M where M = mi + mc + mr .

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3 Modelling of Supplemental Dampers The schematic representation and geometry of supplemental dampers are shown in Fig. 2. For all the supplemental dampers considered in Fig. 2, terminal 1 is connected to the isolator base mass while terminal 2 is connected to the ground. Let kns , kp , cd and b represent negative stiffness, positive stiffness, dashpot damping and inertance of supplemental dampers, respectively. Figure 2a represents passive devices named negative stiffness dampers (NSDs) that utilise compressed spring and damper configuration (Wang et al. 2019a, b). Geometrically, NSD consists of a negative stiffness spring in parallel combination with a viscous damper (VD), a series connected with a positive spring. The following expression gives the damping force generated by NSD fd = kns y + cd y˙ = kp (xb − y)

(4)

where y is the displacement between the terminals 3 and 2 of NSD and xb is base isolator displacement. Figure 2b shows a schematic representation of negative stiffness inerter damper (NSID)-1. The proposed NSID-1 consists of an inerter parallel to a positive spring in an otherwise NSD configuration. The damping force developed across NSID-1 can be given as fd = kns y + cd y˙ = b(¨xb − y¨ ) + kp (xb − y)

(5)

Figure 2c shows the schematic representation of NSID-2. Here, the role of the inerter is reversed with the dashpot element in the otherwise NSID-1 configuration. Control force developed across ends of NSID-2 is given by fd = kns y + b¨y = kp (x − y) + cd (˙x − y˙ )

(6)

A schematic representation of NSID-3 is given in Fig. 2d. The NSID-3 setup is the modification of NSD where dashpot and inerter are placed parallel to the negative spring. The corresponding control force is by  fd = kns y + b¨z = kp (x − y) (7) b¨z = cd (˙y − z˙ ) where y is the relative displacement across terminals 3–2; and z is the displacement across terminals 4–2 of NSID-3.

4 Optimisation Classical H∞ optimisation is followed to obtain the best possible response with the four supplemental dampers. H∞ optimisations aim to reduce the structure’s maximum response (resonant amplitude). This optimisation criterion is used for obtaining the optimally tuned mass damper (TMD) parameters (Den Hartog 1985). It has been observed that for an undamped single degree of freedom system (SDOF) with supplemental NSD

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Fig. 2. Schematic representation of supplemental dampers (a) NSD (b) NSID-1 (c) NSID-2 (d) NSID-3

and NSIDs, there exist points in the frequency response function (FRF) curves that are independent of damper damping (Islam and Jangid 2022b). These points are called fixed points or invariant points. The objective of the optimisation is to find an optimal curve such that a horizontal tangent passes through the highest of fixed points. For the isolated LST with supplemental NSD and NSIDs under consideration following dimensionless parameters are defined α=

kp cd cb cd b kns ;β = ;γ = ;ξ = ; ξd = and μ = kp kb cb 2M ωb 2M ωb M

(8)

where α, β and γ are the negative stiffness ratio, positive stiffness ratio, inertance to mass ratio, respectively; and ξ and ξd are the isolation damping ratio and supplemental damping ratio, respectively. Assuming a harmonic earthquake excitation as x¨ g = X¨ g eiωt , √ where ω is circular forcing frequency and i = −1. Considering the first mode as dominant in base-isolated LST, the steady-state response for the first mode, i.e. the base displacement response, can be represented as xb = H (iω)eiωt

(9)

where H (iω) is the frequency response function or transfer function for base displacement xb . Defining the frequency ratio as λ = ωωb , the magnitude of complex FRF for LST be expressed as    A2 + B2  2 |Ri (λ)| = H (iω)ωn  = (10) C 2 + D2 where i = 1, 2, 3 or 4 corresponds to LST with NSD, NSID-1, NSID-2 or NSID3, respectively. Corresponding to the value of i, Table 1 provides the FRF parameters A, B, C and D.

4

3

−



+β

αβ



μλ2

β − μλ2



  (2ξd λ) αβ + β − μλ2

2ξd λ

2ξd λ

  αβ + β − μλ2

2

αβ+

2ξd λ

β + αβ

1



B

A

i

C D       2 2 2 1 − λ (β + αβ)−4ξ ξd λ +αβ 2λ ξd 1 − λ2 + ξ (α + αβ) + βξd ⎧ ⎫   ⎨ ⎬    ξ αβ + β − μλ2 2 2     1−λ αβ + β − μλ − (2λ) ⎩ +ξd 1 − λ2 + ξd β − μλ2 ⎭   4ξ ξd λ2 + αβ −μλ2 ⎧ ⎫   ⎨ ⎬    ξ αβ + β − μλ2     1 − λ2 αβ + β − μλ2 − (2λ) ⎩ +ξd 1 − λ2 + ξd αβ − μλ2 ⎭   αβ 4ξ ξd λ2 + αβ −μλ2         1 − λ2 −(αβ + β) μλ2 + (2λ) 1 − λ2 + βλ2 α + αβ − μλ2 ξd − β 2 ξd − (αβ + β) μλ2 ξ +βλ2   αβ 2 2 4ξ ξd λ + β 2 μλ2 +β − μλ2

Table 1. Frequency response function parameters for LSTs with supplemental dampers

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The plots of FRF (Ri (λ)) for the four supplemental dampers given in Fig. 3 shows the presence of fixed points or invariants (P, Q and R). For the optimisation, there exist four parameters (α, β, μ, ξd ) for NSIDs and three for NSD (α, β, ξd ). The objective of optimal design is to find the optimal curve of the transfer function for which the horizontal tangent passes through the highest of fixed points. The parameters of the optimal curve of the transfer function will define optimal parameters for various supplemental dampers. For the optimisation process, inherent damping ξb of the isolation system is neglected for simplicity.

Fig. 3. FRF curves for the four supplemental dampers showing the presence of fixed points (a) NSD (b) NSID-1 (c) NSID-2 (d) NSID-3

The detailed optimisation process for the NSD and NSIDs has been presented in a study by Islam and Jangid (2022). The optimal parameters for each of the supplemental dampers are tabulated in Table 2. For NSD and NSID-3, given a value of β optimal optimal parameters are derived while for NSID-1 and NSID-2, given a value of μ optimal parameters are derived.To arrive at the optimal value of ξd , fixed points are made maxima   ∂R2  i   for a FRF by ensuring  ∂λ2  = 0. at fixed points

β−2 2(β+1)

2 3 3β 4 2(1+β)3

√

+α + 1

αμ2 + 2αμ

μ

βopt

αopt

ξd ,opt

NSID-1

NSD

4(μ+1)

⎫ ⎧ ⎬ ⎨ 2μ + 3− −  ⎩ 4μ2 + 12μ + 1 ⎭

αopt

2μ

+μ2 + αμ + 2

2α + 3μ + αμ2

βopt

NSID-2

μ − 4(μ+2)

αopt

Table 2. Optimal expressions for four supplemental devices

2α−3β+2

(α + 1)2

2β(1 − β)

μopt

NSID-3



 1 3 β − 1 2 2

αopt

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5 Numerical Study The dynamic equation of motion for LST with supplemental dampers can be written in the following matrix form ⎤⎧ ⎫ ⎤⎧ ⎫ ⎡ ⎡ cc 0 0 ⎨ u˙ c ⎬ mc 0 mc ⎨ u¨ c ⎬ ⎣ 0 mi mi ⎦ u¨ i + ⎣ 0 ci 0 ⎦ u˙ i ⎩ ⎭ ⎩ ⎭ mc mi M u¨ b u˙ b 0 0 cb ⎡ ⎤⎧ ⎫ ⎧ ⎫ kc 0 0 ⎨ uc ⎬ ⎨ 0 ⎬ ⎣ + 0 ki 0 ⎦ ui + 0 fd ⎩ ⎭ ⎩ ⎭ ub 0 0 kb 1 ⎤⎧ ⎫ ⎡ mc 0 mc ⎨ 0 ⎬ = −⎣ 0 mi mi ⎦ 0 u¨ g (11) ⎩ ⎭ mc mi M 1 where ub = xb , ui = xi − xb and uc = xb − xc are the relative displacements w.r.t base isolator and u¨ g is the acceleration of ground motion. The various supplemental damping parameters are defined in Table 3. In this study, a storage tank with S = 1.5, R = 7.32 considered, where tank walls are made up of steel with the modulus of elasticity E = 200 GPa and density ρt = 7900 kg/m3 . The damping ratios of the convective mass ξc and impulsive mass ξi are assumed as 0.005 and 0.02. The liquid contained in the storage tank is assumed to be water (ρ = 1000 kg/m3 ). The isolation bearing are assumed to be linear with Tb = 2 s and damping ratio of ξb = 0.1. Once the dynamic response of the three lumped masses are determined, the liquid sloshing height can be expressed as (Haroun 1983) uh =

 R 2 u¨ c + u¨ b + u¨ g 2 1.84 − 1 g

(12)

In this study, both near-fault (NF) and far-field (FF) real earthquake records are used to evaluate the effectiveness of proposed supplemental damper systems. The earthquake records are tabulated in Table 4. Table 3. Optimal parameters for supplemental dampers used in the study S. No

Supplemental dampers

μopt

βopt

αopt

ξd ,opt

1

NSD

–

0.25

−0.7

0.0392

2

NSID-1

0.1344

0.25

−0.3593

0.0203

3

NSID-2

0.4120

0.25

−0.0427

0.0314

4

NSID-3

0.2836

0.25

−0.3125

0.1024

The time history analysis results are given in Figs. 4, 5 and 6. The general observation from Fig. 4 is that the base displacement under FF ground motion is far lesser

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Table 4. Earthquake ground motions used in this study S. No

Earthquake name

Station

Year

Type

1

Kobe Japan

Takarazuka

1995

NF

2

Northridge-01

Sylmar- onverter Sta East

1994

NF

3

Northridge-01

Sylmar Olive

1994

NF

4

Gazli USSR

Karakyr

1976

NF

5

Loma Prieta

Saratoga W Valley Coll

1989

NF

6

Imperial Valley 02

El Centro Array #9

1940

FF

7

Coalinga-01

Parkfield - Fault Zone 14

1983

FF

than NF ground motions. Thus, supplemental dampers are not deemed to be required for the FF excitations, although there is some reduction due to proposed supplemental damping devices. However, very high base displacement is observed under the NF motion, which requires effective control. All four damping devices effectively control the base displacement effectively. In particular, NSD appears to be the superior device for base displacement control but requires higher negative stiffness. NSID-1 and NSID-2 are somewhat equivalent in base response control, followed by NSID-3. The effectiveness of a supplemental damper depends on simultaneously controlling other response parameters, i.e. sloshing height and sloshing displacement. The advantage of using NSD or NSIDs lies in the fact it doesn’t amplify other responses for LSTs. In fact, proposed supplemental dampers show control of sloshing displacement to a great extent and control of sloshing height to some extent when compared to uncontrolled isolated LST. This can be inferred from the time histories of sloshing displacement and height given in Figs. 5 and 6. Among the four supplemental dampers, NSD and NSID-2 are very efficient in simultaneous control of base displacement as well as sloshing height. Figure 7 shows the peak response of LST with proposed supplemental dampers. From Table 3, it can be deduced that the negative stiffness requirement is higher for NSD than NSIDs. This is an advantage for NSIDs as the minimum payload is required to maintain the spring’s negative stiffness. However, it slightly increases the dynamic response of the system.

6 Conclusions This study presents the analytical study of supplemental dampers in the form of NSD and NSID for base-isolated LSTs. NSIDs are novel combinations of inerter and negative stiffness mechanisms along with viscous damping elements. LSTs are modelled as three lumped mass systems with a linear isolator. Optimal expressions that reduce the H∞ norm are also proposed for optimal NSID and NSD parameters. The important findings are summarised as. 1. There is a high displacement demand for a base-isolated LST under NF motions. This also results in increasing sloshing displacements. Under the influence of FF

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Fig. 4. Time history for base displacement (a) Coalinga (FF) (b) Kobe (NF)

motions, base displacement demand is lesser and may not require additional damping mechanism 2. The proposed optimisation method based on reducing the H∞ norm works efficiently for controlling the base displacement demand of isolated LSTs while simultaneously reducing the sloshing response. 3. Combinations of the inerter and negative mechanisms enhance the dashpot energy dissipation capacity. As a result, a minimal dashpot coefficient is required for effective response control. 4. Among the four proposed supplemental dampers, NSD and NSID-2 are very efficient in simultaneous reduction of base displacement and sloshing demand.

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Fig. 5. Time history for sloshing displacement (a) Coalinga (FF) (b) Kobe (NF)

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Fig. 6. Time history for sloshing height (a) Coalinga (FF) (b) Kobe (NF)

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Fig. 7. Peak response of LST with proposed supplemental dampers (a) Base Displacement (b) Sloshing Displacement (c) Sloshing height

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Experimental Study on Seismic Behavior of Liquid Storage Tanks Subjected to Vertical Earthquakes J. Y. Wu1,2 , Q. Q. Yu1,2 , and X. L. Gu1,2(B) 1 Key Laboratory of Performance Evolution and Control for Engineering Structures (Ministry of

Education), Tongji University, 1239 Siping Road, Shanghai 200092, China [email protected] 2 Department of Structural Engineering, College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China

Abstract. Previous studies on seismic performance of large-scale liquefied natural gas (LNG) storage tanks mainly focused on the horizontal earthquake excitations. However, vertical earthquake actions may lead to structural damage, overturning and even failure of a liquid storage tank, especially under near-fault earthquakes. In this study, aiming to investigate seismic behavior of the inner tank of a large-scale LNG storage tank subjected to vertical earthquakes, a shaking table test of a 1:25 scaled steel tank with full-filled liquid was carried out. Vertical components of El Centro waves, Chi-Chi 1529 waves and Chi-Chi 1505 waves were selected as input, representing near-field earthquakes, near-fault earthquakes without and with vertical velocity pulse, respectively. Seismic responses, including the sloshing wave height, hydrodynamic pressure and stress on the tank wall were obtained and analyzed. Results showed that the sloshing wave height under Chi-Chi waves was 1.2 ~ 2.5 times larger than that under El Centro waves. In comparison with El Centro waves with the peak ground acceleration (PGA) of 0.26 g, the peak hydrodynamic pressure increased by 10 and 36% under Chi-Chi 1529 waves and Chi-Chi 1505 waves, respectively. In addition, the vertical velocity pulse contained in near-fault earthquakes significantly amplified the stress on tank wall. For instance, the hoop and axial stress were increased by 269.12 and 63.50% at most under the excitations of Chi-Chi 1529 waves, respectively. Dynamic responses of liquid under vertical near-fault earthquakes were greater than that under near-field earthquakes, especially under the near-fault earthquakes with vertical velocity pulse. Keywords: Liquid storage tank · Near-fault earthquake · Seismic response · Vertical earthquake

1 Introduction Liquefied natural gas (LNG) tanks as part of the lifeline facilities occupy an important role in modern urban cities (Rotzer 2019). Since damages to LNG storage tanks would lead to

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 187–196, 2023. https://doi.org/10.1007/978-981-19-7331-4_16

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serious economic losses and casualties, safety of LNG storage tanks under earthquakes has attracted much attention (Hamdan 2000). Liquid storage tanks mainly exhibit in shapes of the beam vibration mode under earthquakes (Shih 1981; Park et al. 2016; Virella et al. 2006), whereas the elliptical vibration mode of tanks would be excited when the frequency of seismic waves is approximate to the natural frequency of the tanks (Etsuo et al. 1983). The elliptical vibration mode affects distribution of hydrodynamic pressure on the tank, leading to more vulnerable inelastic buckling on the tank wall (Maekawa et al. 2004), i.e., elephant foot buckling. To assure safety of LNG storage tanks, seismic responses of tanks have been extensively studied, and variables including liquid level (Burkacki and Jankowski 2014; Bae and Park 2018), foundation stiffness (Ormeño et al. 2019; Kianoush and Ghaemmaghami 2011), floating roof (Fang et al. 2013), the type of earthquakes (Li et al. 2018; Chiba et al. 1986) and so on. It was implied that the floating roof could be used to reduce the sloshing height of liquid. In comparison with rigid foundations, liquid storage tanks equipped with flexible foundations were witnessed a decline in axial compressive stress on the tank, but increased in displacements and accelerations of the tank. In addition, accelerations and stress of tanks under three-dimensional excitations were significantly amplified compared with horizontal unidirectional loading. However, the aforementioned studies were focused on responses of liquid storage tanks under horizontal earthquakes, and the effect of vertical component of earthquakes on dynamic analysis of liquid storage tanks has not been fully understood. Vertical acceleration is transmitted to the liquid storage tank in the forms of horizontal hydrodynamic pressure, which mainly results in amplified hoop stress of the tank wall. The combined effect of vertical and horizontal excitations would increase the possibility of inelastic buckling of the tank wall. Haroun and Tayel proposed a finite element method for analyzing seismic responses of cylindrical liquid storage tanks under vertical earthquakes. Results showed that vertical earthquakes could cause a substantial increase in hoop stress of the tank wall (Haroun and Tayel 1985). Seismic responses of vertically excited liquid storage tanks considering both the rigid and flexible foundations were further investigated (Veletsos and Yu 1986; Haroun and Abdel-Hafiz 1986). A comprehensive study was carried out by Haroun and Abou-Izzeddine, it was shown that the interaction between the tank and the foundation reduced tank responses, and the magnitude of this reduction was related to the geometries of the tank (Haroun and Abou-Izzeddine 1992a, 1992b). Kianoush and Chen investigated seismic responses of concrete rectangular liquid storage tanks subjected to vertical ground motions, and it was found that the base shear due to vertical acceleration reached 45% of that due to horizontal acceleration (Kianoush and Chen 2006). To the best of the authors’ knowledge, dynamic behavior of LNG storage tanks subjected to vertical earthquakes are less reported. In this study, a shaking table test on a 1:25 scaled steel inner tank model of a 160,000 m3 LNG storage tank under vertical earthquakes was carried out. Vertical components of three seismic waves were selected, representing near-field earthquakes, near-fault earthquakes without and with vertical velocity pulse. The sloshing wave height, hydrodynamic pressure and stress on the tank wall were recorded and analyzed.

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2 Specimens and Materials The prototype structure, i.e., a 160,000 m3 LNG storage tank, is consisted of a prestressed concrete outer tank and a 9% Ni steel inner tank. The diameter and height of the inner tank are 80.00 m and 35.43 m, respectively. Considering the limitation of the shaking table, a reduced-scale model of the inner tank was designed (Lu and Lu 2001) and the detailed dimensions are listed in Table 1. Due to processing difficulties, thicknesses of both the tank wall and the bottom plate were taken as 5.00 mm. LNG and 9%Ni steel in the prototype structure were simulated by water and Q345 steel (GB/T 709-2006), respectively. Inner tanks of large-scale LNG storage tanks are generally unanchored, i.e., located on a ring beam which is infilled with thermal insulation materials. Therefore, a scaled reinforced concrete ring beam infilled with sand was manufactured as the bearing platform in this test. In order to prevent liquid leakage to the shaking table during the test, a thin steel plate was set around the bearing platform (Fig. 1). Cubic compressive strength and elastic modulus of the concrete were 50.51 MPa and 4.12 × 104 MPa, respectively (GB/T 50081-2002). Mechanical properties of the Q345 steel were determined according to tensile coupon tests (GB/T 228.1-2010). The average elastic modulus, yield strength and tensile strength were 2.12 × 105 MPa, 413.33 MPa and 502.33 MPa, respectively. Table 1. Geometries of the scaled model Parameter

Dimension

Diameter (m)

3.20

Height (m)

1.42

Liquid level height (m)

1.00

Thickness of the tank wall (mm)

5.00

Thickness of the bottom plate (mm)

5.00

3 Shaking Table Test The shaking table test was carried out in State Key Laboratory for Disaster Reduction in College of Civil Engineering, Tongji University, China. 3.1 Selection of Seismic Waves Vertical components of El Centro waves, Chi-Chi 1529 waves and Chi-Chi 1505 waves were selected (from the database of Pacific Earthquake Engineering Research Centre), representing near-field earthquakes, near-fault earthquakes without and with vertical velocity pulse, respectively (Figs. 2, 3 and 4). The seismic waves were compressed in

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Tank model

Thin steel plate Shaking table

Bearing platform

Fig. 1. Test set-up

time by 1/5 factor in consideration with the reduced length scale of the model. The peak ground acceleration (PGA) of seismic waves in the Z direction was set as 0.13 g and 0.26 g, as listed in Table 2. 10 Velocity (cm/s2)

Acceleration (g)

0.2 0.1 0.0 -0.1

5 0 -5

-10

-0.2 0

20

Time (s)

40

60

0

20

(a) Acceleration

Time (s)

40

60

(b) Velocity

Fig. 2. Time history of original El Centro waves

80 Velocity (cm/s2)

Acceleration (g)

0.2 0.1 0.0

-0.1 -0.2 0

20

40 60 Time (s)

(a) Acceleration

80

100

40 0 -40 -80 0

20

40 60 Time (s) (b) Velocity

Fig. 3. Time history of original Chi-Chi 1529 waves

80

100

Experimental Study on Seismic Behavior of Liquid Storage 300 Velocity (cm/s2)

Acceleration (g)

0.6

191

0.4 0.2 0.0

-0.2

200 100 0 -100 -200

-0.4 0

20

40 60 Time (s)

80

100

0

(a) Acceleration

20

40 60 Time (s)

80

100

(b) Velocity

Fig. 4. Time history of original Chi-Chi 1505 waves Table 2. Summary of the test program. Scenario

Seismic waves

Target input PGA (g)

Actual input PGA (g)

1

El Centro

0.130

0.124

2

Chi-Chi 1529

0.130

0.130

3

Chi-Chi 1505

0.130

0.123

4

El Centro

0.260

0.277

5

Chi-Chi 1529

0.260

0.272

6

Chi-Chi 1505

0.260

0.255

3.2 Instruments Figure 5 shows layout of the instruments. Pressure transducers were arranged inside the tank wall along height to record hydrodynamic pressure in the X direction. In order to obtain the hoop and axial strain of the tank wall, strain gauges were installed along the circumferential and vertical directions. A three-dimensional dynamic displacement measurement system, consisted of a charge-coupled device (CCD) lens, markers and an acquisition system, was applied to measure the sloshing height of the liquid. Markers were attached to a buoy, and spatial coordinates of markers could be recorded by CCD lens.

4 Experimental Results 4.1 Sloshing Wave Height Figure 6 displays time history of the sloshing wave height under vertical excitations. Significant sloshing was observed during the excitation of vertical seismic waves, and the convective period of liquid was about 2 s. The amplitude of liquid sloshing increased with the seismic intensity increment, with a maximum value up to 40 mm (Chi-Chi 1505 waves with PGA = 0.26 g). In comparison with El Centro waves, the liquid sloshing amplitude under Chi-Chi waves was obviously larger. The peak sloshing height under

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150

Pressure transducers

920

100 Strain gauges

420 170 180

Marker

400 300 300 400

1420

420

CCD lens

350

3200

350

3900

Fig. 5. Layout of the instruments (unit in mm, not to scale)

El Centro waves, Chi-Chi 1529 waves and Chi-Chi 1505 waves (PGA = 0.13 g) were 6 mm, 15 mm and 16 mm, respectively. Generally, the sloshing wave height under Chi-Chi waves was 1.2 ~ 2.5 times larger than that under El Centro waves. Due to the velocity pulse, the liquid sloshing heights under Chi-Chi 1505 waves were slightly larger than that under Chi-Chi 1529 waves. 4.2 Hydrodynamic Pressure The peak hydrodynamic pressure along the height of the tank is shown in Fig. 7, and the vertical axis represents the ratio of the measuring point elevation h to the tank height H. The hydrodynamic pressure decreased along the height, and the maximum pressure appeared at the bottom of the tank wall. In addition, the peak hydrodynamic pressure monitored at the top measuring point (h/H = 0.77) was approximate to zero, indicating the impact of liquid sloshing on the tank wall was limited under the excitation of vertical earthquakes. Vertical excitations had a significant effect on the impulsive motion of liquid, and the maximum hydrodynamic pressure reached to 2.65 kPa (Chi-Chi 1505 waves with PGA = 0.26 g). The hydrodynamic pressure at the lower part of the tank wall under Chi-Chi 1505 waves was obviously larger than that under El Centro waves and Chi-Chi 1529 waves. For example, the maximum hydrodynamic pressure under Chi-Chi 1505 with PGA = 0.26 g was about 1.36 and 1.23 times that under El Centro waves and Chi-Chi 1529 waves, respectively. It was demonstrated that the impulsive motion of liquid was more severe under near-fault earthquakes, especially under vertical components with velocity pulse. 4.3 Stress on the Tank Wall According to the detected strain value and elastic modulus of the steel, the hoop and axial stress on the tank wall was extracted and are listed in Tables 3 and 4. The maximum

Sloshing wave height (mm)

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30

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El Centro Chi-Chi 1529 Chi-Chi 1505

20 10 0 -10 -20 -30 0

2

4

6

8

10 12 Time (s)

14

16

18

20

Sloshing wave height (mm)

(a) PGA = 0.13 g 100

El Centro Chi-Chi 1529 Chi-Chi 1505

50 0 -50 -100 0

2

4

6

8

10 12 Time (s)

14

16

18

20

(b) PGA = 0.26 g Fig. 6. Time history of the sloshing wave height

hoop stress generally appeared at the tank bottom, and the peak hoop stress at the tank bottom reached to 12.55 MPa under the Chi-Chi 1529 waves with PGA = 0.26 g. In comparison with El Centro waves (PGA = 0.26 g), the hoop stress at the tank bottom under Chi-Chi 1529 waves and Chi-Chi 1505 waves increased by 269.12 and 13.53% at most, respectively. It was because the vertical component of near-fault earthquakes resulted in larger hydrodynamic pressure, and consequently larger hoop stress on the tank wall. In terms of axial stress on the tank wall, the maximum value was witnessed at the top of the tank. Under the excitation with PGA = 0.26 g, the maximum axial stress at the top of the tank reached to 9.06 MPa, slightly smaller than the maximum value of hoop stress. The axial stress of tank wall under Chi-Chi waves were larger than that under El Centro waves. For example, the axial stress at the top of the tank under Chi-Chi 1529 waves and Chi-Chi 1505 waves increased by 63.50 and 4.00% at most, respectively, in comparison with that subjected to El Centro waves (PGA = 0.26 g). In addition, the

194

J. Y. Wu et al. 1.0

0.6 0.4

El Centro Chi-Chi 1529 Chi-Chi 1505

0.8 h/H

h/H

0.8

0.6 0.4 0.2

0.2 0

1.0

El Centro Chi-Chi 1529 Chi-Chi 1505

0 0 1 2 3 Peak hydrodynamic pressure (kPa)

0 1 2 3 Peak hydrodynamic pressure (kPa)

(b) PGA = 0.26 g

(a) PGA = 0.13 g

Fig. 7. Peak hydrodynamic pressure along the height of the tank

influence of near-fault earthquakes on hoop stress on the tank wall was greater than that on axial stress. Table 3. Peak hoop stress of tank wall (MPa) PGA (g)

Waves

h/H 0

0.13

0.26

0.2

0.4

0.7

1.0

El Centro

0.26

0.58

0.31

0.17

0.75

Chi-Chi 1529

0.14

1.06

0.45

0.24

1.41

Chi-Chi 1505

0.16

0.66

0.36

0.20

0.92

El Centro

3.40

1.17

0.72

0.22

2.33

Chi-Chi 1529

12.55

1.28

0.91

0.49

3.33

Chi-Chi 1505

3.86

1.09

0.72

0.28

2.09

5 Conclusions In this paper, a shaking table test was carried out to analyze dynamic behavior of the steel inner tank of LNG storage tanks subjected to vertical earthquakes. A sequence of base excitations with PGAs of 0.13 and 0.26 g were applied, including near-field earthquakes and near-fault earthquakes without and with velocity pulse. The following observations and conclusions were drawn: (1) The liquid sloshing amplitude under Chi-Chi waves was obviously larger than that under El Centro waves. For example, the sloshing wave height under Chi-Chi waves was 1.2 ~ 2.5 times larger than that under El Centro waves.

Experimental Study on Seismic Behavior of Liquid Storage

195

Table 4. Peak axial stress of tank wall (MPa) PGA (g) 0.13

0.26

Waves

h/H 0

0.2

0.4

0.7

1.0

El Centro

0.85

0.29

0.36

0.75

2.77

Chi-Chi 1529

1.27

0.40

0.21

0.65

8.06

Chi-Chi 1505

0.81

0.25

0.32

0.40

4.51

El Centro

1.59

0.53

0.72

1.40

5.54

Chi-Chi 1529

5.32

1.59

0.47

1.33

9.06

Chi-Chi 1505

3.89

1.16

0.65

0.35

5.76

(2) Vertical excitations had a significant effect on the impulsive motion of liquid rather than convective motion. In addition, the impulsive motion of liquid was more severe under near-fault earthquakes, especially under vertical components with velocity pulse. For instance, the maximum hydrodynamic pressure under Chi-Chi 1505 with PGA = 0.26 g was about 1.36 and 1.23 times that under El Centro waves and Chi-Chi 1529 waves, respectively. (3) Near-fault earthquakes amplified the hoop and axial stress of the tank wall. The maximum hoop and axial stress under Chi-Chi 1529 waves with PGA = 0.26 g increased by 269.12% and 63.50% in comparison with El Centro waves, respectively.

Acknowledgements. This research work was supported by the National Key R&D Program of China (2017YFC1500700).

References Bae, D., Park, J.H.: Shaking table test of steel cylindrical liquid storage tank considering the roof characteristics. Int. J. Steel Struct. 18(4), 1167–1176 (2018) Burkacki, D., Jankowski, R.: Experimental study on steel tank model using shaking table. Civil Environ. Eng. Rep. 14(3), 37–47 (2014) Chiba, M., Tani, J., Hashimoto, H., Sudo, S.: Dynamic stability of liquid-filled cylindrical shells under horizontal excitation, Part I: experiment. J. Sound Vibr. 104(2), 301–319 (1986) Etsuo, S., Masaaki, N., Kouji, Y.: Experimental study on the steady response of the large thinwalled cylindrical liquid storage tank model excited by the sinusoidal wave. J. High-Pressure Inst. Japan 21(1), 39–47 (1983) Fang, Z., Chen, Z., Yan, S., Cao, G., Wang, J.: Dynamic experimental investigation on the uplift response of liquid storage tanks under seismic excitations with different characteristics. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 227(7), 1525–1534 (2013) Hamdan, F.H.: Seismic behaviour of cylindrical steel liquid storage tanks. J. Constr. Steel Res. 53(3), 307–333 (2000) Haroun, M.A., Tayel, M.A.: Response of tanks to vertical seismic excitations. Earthq. Eng. Struct. Dyn. 13(5), 583–595 (1985)

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Haroun, M.A., Abdel-Hafiz, E.A.: A simplified seismic analysis of rigid base liquid storage tanks under vertical excitation with soil-structure interaction. Soil Dyn. Earthq. Eng. 5(4), 217–225 (1986) Haroun, M.A., Abou-Izzeddine, W.: Parametric study of seismic soil-tank interaction. I: Horizontal excitation. J. Struct. Eng. 118(3), 783–797 (1992a) Haroun, M. A. & Abou-Izzeddine, W., (1992b), Parametric Study of Seismic Soil-Tank Interaction. II: Vertical Excitation, Journal of Structural Engineering, 118 (3), 798 – 811 Kianoush, M.R., Chen, J.Z.: Effect of vertical acceleration on response of concrete rectangular liquid storage tanks. Eng. Struct. 28(5), 704–715 (2006) Kianoush, M.R., Ghaemmaghami, A.R.: The effect of earthquake frequency content on the seismic behavior of concrete rectangular liquid tanks using the finite element method incorporating soil-structure interaction. Eng. Struct. 33(7), 2186–2200 (2011) Li, H.H., Zhao, W., Wang, W.: Dynamic response of a 100,000 m3 cylindrical oil-storage tank under seismic excitations: experimental tests and numerical simulations. Shock Vibr. 8, 2074946.1– 2074946.19 (2018) Lu, L., Lu, X.: Study of dynamic similitude law for the shaking table test to cancel the gravity distortion effect. Struct. Eng. 4(008), 45–48 (2001). (in Chinese) Maekawa, A., Shimizu, Y., Suzuki, M., Fujita, K.: Vibration test of a 1/10 reduced scale model of cylindrical water storage tank. J. Pressure Vessel Technol. 132(5), 051–801 (2004) Ministry of Housing and Urban-Rural Development of the People’s Republic of China: Standard for Test Method of Mechanical Properties on Ordinary Concrete, GBT 500081-2002. Architecture & Building Press, Beijing (China) (2003) Ministry of Housing and Urban-Rural Development of the People’s Republic of China: Dimension, Shape, Weight and Tolerances for Hot-Rolled Steel Plates and Sheets, GB/T 709-2006. Architecture & Building Press, Beijing (China) (2006) Ministry of Housing and Urban-Rural Development of the People’s Republic of China: Metallic Materials–Tensile Testing–Part 1: Method of Test at Room Temperature, GB/T 228.1-2010. Architecture & Building Press, Beijing (China) (2010) Ormeño, M., Larkin, T., Chouw, N.: Experimental study of the effect of a flexible base on the seismic response of a liquid storage tank. Thin-Walled Struct. 139, 334–346 (2019) Park, J.H., Bae, D., Oh, C.K.: Experimental study on the dynamic behavior of a cylindrical liquid storage tank subjected to seismic excitation. Int. J. Steel Struct. 16(3), 935–945 (2016). https:// doi.org/10.1007/s13296-016-0172-y Rötzer, J.: Design and Construction of LNG Storage Tanks. Wiley, New York, USA (2019) Shih, C.: Failure of liquid storage tanks due to earthquake excitation. California Institute of Technology (1981) Veletsos, A.S., Yu, T.: Dynamics of vertically excited liquid storage tanks. J. Struct. Eng. 112(6), 1228–1246 (1986) Virella, J.C., Godoy, L.A., Suarez, L.E.: Fundamental models of tank-liquid systems under horizontal motions. Eng. Struct. 28(10), 1450–1461 (2006)

Resilience of Steel and Composite Structures

Axial Behavior and Design of High-Strength Rectangular Concrete-Filled Steel Tube Long Columns Zhichao Lai, Jie Yan, and Dong Li(B) Department of Civil Engineering, Fuzhou University, College Road 2, Fuzhou 350108, China {laiz,dongli}@fzu.edu.cn, [email protected]

Abstract. Due to the lack of adequate research and deep understanding of highstrength concrete-filled steel tube (CFST) long columns, the current specifications cannot provide the available guidelines and design equations. To address the gap, this paper investigates the axial behavior of high-strength rectangular CFST long columns by experimental database, finite element analysis, and theoretical modeling. Firstly, the experimental database including 74 specimens for high-strength rectangular CFST long columns was compiled. Then, the detailed 3D non-linear finite element method (FEM) models were developed and verified for parametric studies. The effects of steel yield stress, concrete strength, section slenderness ratio and slenderness ratio on the ultimate strength and slenderness reduction factor were investigated. Finally, the possibility of extending the current design equations in different specifications was evaluated. Keywords: CFST · High-strength material · Long column · Axial behaviour · Database

1 Introduction Concrete-filled steel tube (CFST) members have gained extensive attention because of their outstanding advantages such as high load-bearing capacity and satisfactory ductility on various building projects viable globally. When CFST members are under axial compression, the lateral expansion of core concrete is restrained due to the confinement and the concrete infilled delays local buckling of steel tube, consequently the compressive strength and ductility can be improved obviously (Lai et al. 2014). CFST members have been used as piles in bridge engineering or columns in tall buildings extensively in the past few decades. However, with the trend of buildings and bridges towards higher and longer, the demand of compressive forces increases greatly and should be met sufficiently. The application of high-strength material makes it possible in large-span structures. By using high-strength material in CFST columns, the section strength can be improved significantly without additional size thus the construction time and cost could be reduced obviously. Columns are typically categorized as short columns (KL/H ≤ 6.0) and long columns (KL/H > 6.0) based on the slenderness ratio (Lai and Varma 2018). Large numbers © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 199–214, 2023. https://doi.org/10.1007/978-981-19-7331-4_17

200

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of studies have been undertaken to evaluate the behavior of high-strength rectangular CFST short columns (Uy and Patil 1996; Liu et al. 2003; Sakino et al. 2004; Mursi and Uy 2004; Liu 2005; Zhang et al. 2005; Young and Ellobody 2005; Yu et al. 2006; Thai et al. 2014; Aslani et al. 2015; Xiong et al. 2017; Lee et al. 2019). Parameters mainly consisted of steel yield stress (f y ), concrete strength (fc ), and section slenderness ratio (b/t). The effect of initial imperfection is usually ignored when designing rectangular CFST short columns. However, for high-strength rectangular CFST long columns, it results in a slight reduction of column strengths and ductility, even leading to the occurrence of flexural buckling. Several researchers have conducted tests or theoretical analysis on the behavior of high-strength rectangular CFST long columns (Cederwall et al. 1990; Chung et al. 2001; Dung et al. 2007; Wu 2008; Perea et al. 2013; Dundu 2016; Khan 2017; Li et al. 2021). Parameters mainly consisted of steel yield stress (f y ), concrete strength (fc ), section slenderness ratio (b/t) and slenderness ratio (KL/H). Current code provisions such as AISC 360-16, GB 50936-2014 and Eurocode 4 are all limited for designing high-strength rectangular CFST long columns due to the lack of database compilation and design equations. This paper tries to evaluate the possibility of current code provisions for designing high-strength rectangular CFST long columns and find the relationship of the main parameters based on parametric analysis. The outline of this paper is shown as following: firstly, compiled results of high-strength rectangular CFST long columns were presented and main gaps of current code provisions were found. Then nonlinear finite element method (FEM) models were developed for detailed parameter discussion. Finally, the feasibility of current design provisions was evaluated based on experimental database and extended FEM results.

2 Experimental Database The test database of high-strength rectangular CFST long columns was established by reviewing the previous results. This paper focused on high-strength CFST long columns consisting of high-strength steel (f y > 525 MPa) or high-strength concrete (fc > 70 MPa). The slenderness ratio (KL/H) should be more than 6. The database was compiled with 74 specimens and categorized into Type HS-HC, Type HS-CC and Type CS-HC based on the material strength (Lai and Varma 2018). Type HS-HC means high-strength steel tube (f y > 525 MPa) filled with high-strength concrete (fc > 70 MPa). Type HS-CC means highstrength steel tube (f y > 525 MPa) and conventional-strength concrete fc < 70 MPa). Type CS-HC means conventional-strength steel tubes (f y < 525 MPa) combined with high-strength concrete (fc > 70 MPa). Results show that most researchers focused on the investigation of Type HS-HC (63.5% of all) and Type CS-HC (32.4%) while fewer columns with Type HS-CC (4.1% of all) were investigated as shown in Fig. 1(a) and Table 1. Figure 1(b) shows the distribution of columns categorized by section slenderness coefficient (λcoeff ) according to AISC 360-16 (2016). It indicates that quantities of tests have been carried out for compact and noncompact columns, however there are less tests with regard to slender columns. This study aims to address gaps by conducting extensive 3D finite element analysis, especially for Type HS-CC long columns.

Axial Behavior and Design of High-Strength Rectangular …

30

24

20

3

15 12 9 6

HS-CC

CS-HC

HS-HC

(a)

Slender

3 0

0

Compact

Noncompact

40

10

18

47

Number of tests

Number of tests

50

201

0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 λcoeff

(b)

Fig. 1. Distribution of test data for high-strength rectangular CFST long columns with respect to (a) material strength; (b) slenderness coefficient (λcoeff ).

3 Finite-Element Method Analysis 3.1 3D FEM Model Details This part presents the modelling, validation and modification of the 3D finite element models for high-strength rectangular CFST long columns. This analysis was conducted by using Abaqus (SIMULIA 2016) to investigate its fundamental behaviour. Most modelling technics are based on the paper proposed by the authors before (Lai et al. 2014; Lai and Varma 2018) However, initial imperfections such as residual stress and loading eccentricity are not considered in these papers. But they should not be neglected for long column. According to AISC360-16, the allowable value of the normalized initial out-of-straightness (δ o /L) is no more than 0.1%. It is taken 0.1% in this paper. Local imperfection was obtained by conducting eigenvalue buckling analysis and the first buckling mode was selected with an amplitude equal to 0.1 times thickness of steel tube (Varma 2000). For steel tube fabricated from four steel plates by welding, residual stress existed and could not be neglect in the welding and fabrication process. Compressive residual stress of 0.1 f y and tensile residual stress of f y were assumed in this paper (Thai et al. 2014). 3.2 Benchmarking To validate the FEM model, the FEM results were compared with the experimental results (Khan et al. 2017). Typical failure modes were compared between the FEM model and experimental results as shown in Fig. 2 where both of them existed overall buckling in the middle height of columns. Figure 3 shows several comparisons of the axial load-displacement between FEM modelling and experimental results which show a good agreement in terms of stiffness, peak loads and descending behaviour of columns. The average PFEM /Pexp is 1.01, and the coefficient of variation is 0.08. Based on the above discussion, it can be found that the FEM modelling and analysis can predict the load bearing capacity and failure mode of high-strength rectangular CFST long columns with reasonable accuracy.

1500 2250 3000 3750

C12-0

C18-0

C24-0

C30-0

Zhang et al. (2007)

Liu et al. (2005)

Liu et al. (2003)

1000

C8-0

Chung (2001)

1110.0 2200.0 3101.0 1085.0 2201.0 3100.0 993.0 1980.0 921.0

SA1

SA2

SA3

SA4

SA5

SA6

RA1

RA2

RA3

480.0

600.0

C12-2 480.0

600

C11-2

R9-2

480

C10-2

R9-1

480

C9-2

3000

14

Cederwall (1990)

KL (mm)

Specimen identifier

Reference

199.3

176.5

175.7

150.7

150.0

151.4

148.6

149.5

150.2

160.0

160.0

199.8

200.2

160.6

160.7

125.0

125.0

125.0

125.0

125.0

120.0

B (mm)

2.92

2.91

2.91

4.89

4.90

4.77

2.93

2.89

2.91

4.00

4.00

4.18

4.18

4.18

4.18

3.20

3.20

3.20

3.20

3.20

8.00

t (mm)

319.3

319.3

319.3

316.6

316.6

316.6

319.3

319.3

319.3

495.0

495.0

550.0

550.0

550.0

550.0

360.0

360.0

360.0

360.0

360.0

379.0

f y (MPa)

78.5

78.5

78.5

78.5

78.5

78.5

78.5

78.5

78.5

89.0

89.0

72.1

60.8

72.1

60.8

94.0

94.0

94.0

94.0

94.0

80.0

f’c (MPa)

Table 1. Database of high-strength rectangular CFST long columns

2636.0

2283.0

2401.0

1627.0

2381.0

2597.0

1558.0

2077.0

2352.0

1858.0

1878.0

2800.0

2380.0

2100.0

1820.0

762.3

1082.0

1614.8

1836.8

1877.5

1610.0

Pexp (kN)

(continued)

2272.4

2170.4

2202.8

1807.8

2315.0

2413.6

1708.8

1985.0

2116.5

1800.2

1800.2

2451.1

2249.0

1728.5

1712.2

847.0

1078.0

1578.1

1748.6

1830.2

1786.6

PFEM (kN)

202 Z. Lai et al.

1512.0 1512.0 1512.0 1512.0 1512.0 1512.0 1512.0 2512.0 2512.0 2512.0

CB15-SL1(B)

CB15-SL1(C)

CB20-SL1(A)

CB20-SL1(B)

CB20-SL1(C)

CB25-SL1(A)

CB25-SL1(B)

CB15-SL2(A)

CB15-SL2(C)

CB20-SL2(A)

3000.0

S300-2 1512.0

3000.0

S300-1

CB15-SL1(A)

1500.0

S150-2

Khan et al. (2017)

1500.0

S150-1

2700.0

900.0

S2-2

900.0

S90-2

1829.0

RA4

S90-1

KL (mm)

Specimen identifier

Dundu (2016)

Yu et al. (2008)

Reference

109.8

84.9

84.2

134.2

134.0

109.1

108.7

108.7

83.5

83.6

83.7

60.0

100.0

100.0

100.0

100.0

100.0

100.0

199.9

B (mm)

4.90

4.92

4.90

4.89

4.93

4.89

4.92

4.93

4.96

4.89

4.89

4.00

1.90

1.90

1.90

1.90

1.90

1.90

2.90

t (mm)

Table 1. (continued)

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

528.6

404.0

404.0

404.0

404.0

404.0

404.0

319.3

f y (MPa)

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

19.7

110.6

110.6

110.6

110.6

110.6

110.6

78.5

f’c (MPa)

1377.0

594.0

583.0

3560.0

3748.0

2374.0

2109.0

2087.0

1572.0

1362.0

1732.0

127.7

466.0

474.0

945.0

915.0

1010.0

1013.0

2303.0

Pexp (kN)

(continued)

1478.0

645.0

530.0

3423.1

3407.3

2017.9

2014.0

2139.2

1517.5

1521.9

1516.6

129.8

513.2

513.2

970.1

970.1

1074.5

1077.7

2171.6

PFEM (kN)

Axial Behavior and Design of High-Strength Rectangular … 203

Reference

KL (mm) 2512.0 2512.0 2512.0 2512.0 2512.0 2512.0 2512.0 2512.0 2512.0 2512.0 3512.0 3512.0 3512.0 3512.0 3512.0 3512.0 3512.0 3512.0

Specimen identifier

CB20-SL2(B)

CB20-SL2(C)

CB25-SL2(A)

CB25-SL2(B)

CB25-SL2(C)

CB30-SL2(A)

CB30-SL2(B)

CB40-SL2(A)

CB40-SL2(B)

CB40-SL2(C)

CB15-SL3(A)

CB15-SL3(C)

CB20-SL3(A)

CB20-SL3(B)

CB20-SL3(C)

CB25-SL3(A)

CB25-SL3(C)

CB30-SL3(B)

158.7

134.3

134.3

109.4

109.2

108.9

83.9

84.3

209.6

209.3

209.5

159.8

159.6

134.4

134.9

134.5

109.2

109.9

B (mm)

4.93

4.95

4.92

4.92

4.92

4.95

4.89

4.95

4.92

4.92

4.95

4.91

4.94

4.92

4.89

4.93

4.91

4.93

t (mm)

Table 1. (continued)

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

f y (MPa)

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

f’c (MPa)

2303.0

1539.0

1535.0

761.0

851.0

810.0

410.0

469.0

6329.0

6004.0

6141.0

3739.0

3938.0

2522.0

2546.0

2823.0

1235.0

1049.0

Pexp (kN)

(continued)

2503.3

1479.8

1461.9

875.0

869.7

860.0

398.6

430.3

6574.7

6558.8

6579.2

3831.9

3843.9

3838.2

2410.4

2594.9

2689.7

1386.5

PFEM (kN)

204 Z. Lai et al.

Reference

KL (mm) 3512.0 3512.0 3512.0 3512.0 1514.0 1514.0 1514.0 1514.0 1514.0 1514.0

Specimen identifier

CB30-SL3(C)

CB40-SL3(A)

CB40-SL3(B)

CB40-SL3(C)

CB30-SL1(A)

CB30-SL1(B)

CB30-SL1(C)

CB40-SL1(A)

CB40-SL1(B)

CB40-SL1(C)

208.8

208.8

208.7

159.5

159.3

159.6

210.5

209.4

209.7

159.8

B (mm)

4.94

4.92

4.91

4.95

4.94

4.93

4.93

4.92

4.93

4.93

t (mm)

Table 1. (continued)

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

762.0

f y (MPa)

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

113.0

f’c (MPa)

6460.0

7506.0

7478.0

5085.0

4833.0

5164.0

5052.0

5896.0

5002.0

2556.0

Pexp (kN)

6929.2

6910.7

6910.5

4540.2

4550.8

4569.9

5769.9

5696.4

5711.0

2550.3

PFEM (kN)

Axial Behavior and Design of High-Strength Rectangular … 205

206

Z. Lai et al.

Fig. 2. Typical failure modes between FEM and experimental results (Khan et al. 2017). 2400

2400 EXP-CB20-SL1(A) FEM-CB20-SL1(A)

2100 1800

1800

P (kN)

P (kN)

1500 1200 900

1500 1200 900

600

600

300

300

0

0

2

4

6

8 10 12 14 16 18 20 U (mm)

(a) CB20-SL1(A)

EXP- CB20-SL1(B) FEM-CB20-SL1(B)

2100

0

0

2

4

6

8 10 12 14 16 18 20 U (mm)

(b) CB20-SL3(B)

Fig. 3. Typical load-displacement comparisons between experimental and FEM results.

3.3 Parameter Analysis This part aims to carry out parametric analysis to: (1) address the above gaps and (2) identify the relationship of four main parameters and their effects on the behaviour of high-strength rectangular CFST long columns. The FEM modelling has provided comprehensive addition to address the database gaps as shown in Fig. 4. 3.3.1 Steel Yield Stress (fy ) Figure 5 shows the impact of steel yield stress (f y ) on the load-bearing capacity of columns. The increase in steel yield stress enhanced the load-bearing capacity of columns when slenderness ratio (KL/H) is less than 30. However, this increase tendency was indistinguishable for columns with larger slenderness ratio (KL/H > 30). The slenderness reduction factor (ϕ) was the ratio of nominal compressive strength of columns considering length effects (Pn ) to nominal section strength (Pno ). In the

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8 6 4 2 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 λcoeff

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following part, the axial load-bearing capacity of long columns obtained by FEM analysis was divided by that of corresponding short columns (KL/H = 3) to obtain the slenderness reduction factor (ϕ). The impact of steel yield stress (f y ) on the slenderness reduction factor (ϕ) differed regarding on the section types as shown in Fig. 6. For columns with compact sections, the slenderness reduction factor (ϕ) increased with increasing steel yield stress (f y ) when slenderness ratio (KL/H) did not exceed 20. However, when slenderness ratio (KL/H) was more than 20, the slenderness reduction factor (ϕ) decreased with increasing steel yield stress (f y ). For columns with noncompact or slender sections, the contribution of steel yield stress on the ultimate strengths was so limited that the effect was insignificant. 3.3.2 Compressive Strength of Concrete (fc ) As is shown in Fig. 7, the load-bearing capacity of columns increased almost linearly with an increase in fc . However, this increase tendency was less significant for columns with larger slenderness ratios (KL/H). Figure 8 presents the effect of concrete compressive strength (fc ) on the slenderness reduction factor (ϕ). As is shown, the slenderness reduction factor (ϕ) decreased with an increase of concrete strength (fc ). For columns with compact sections, concrete compressive strength (fc ) had no evident effect on the slenderness reduction factor (ϕ). However, for columns with slender sections, the slenderness reduction factor (ϕ) was

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was due to the less effective confinement provided by the steel tube with larger section slenderness ratio (b/t). The impact of section slenderness ratio (b/t) on ultimate strengths was significantly related to yield stress of steel (f y ): the steel contribution ratio was larger with the increasing of steel yield stress (f y ). Thus, the effect of section slenderness ratio (b/t) on ultimate strengths was more remarkable with increasing of steel yield stress as shown in Fig. 9. Further results could be obtained that with the increase of slenderness ratio (KL/H), the effect of slenderness ratio (b/t) was less significant. This was because columns with larger slenderness ratio (KL/H) failed more easily due to overall buckling and the effect of section slenderness ratio (b/t) on columns strengths was less significant. 15000

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Figure 10 is the slenderness reduction factor (ϕ) versus slenderness ratio (KL/H) curve. Figure 10(a) shows ϕ—KL/H curve for Type CS-HC columns. The concrete predominantly contributed to the load bearing capacity thus the section slenderness ratio (b/t) had no evident impact on the slenderness reduction factor (ϕ). Figure (b) and (c) shows ϕ—KL/H curve of Type HS-CC and Type HS-HC. Slenderness reduction factor (ϕ) decreased with increasing of section slenderness ratio (b/t) before KL/H exceeded

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3.3.4 Column Slenderness Ratio (KL/H) Figure 11 presents load-bearing capacity with different column slenderness ratios (KL/H). The ultimate strength of long columns was shown to decrease as the slenderness ratio (KL/H) increased. Furthermore, it seems that for columns with KL/H more than 30, increasing the material strength is not a superior choice for enhancing the column strengths. Figure 10 indicated that the slenderness reduction factor (ϕ) decreased as the slenderness ratio (KL/H) increased. And the decreasing tendency of slenderness reduction factor (ϕ) was more significant with increasing of material strengths. From the above discussion, it can be found that: (1) though the ultimate strengths of columns could be increased by increasing material strengths (fc and f y ), this increasing tendency is closely related with section slenderness ratio (b/t) and slenderness ratio

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(KL/H). (2) the ultimate strength of columns could be increasing by decreasing section slenderness ratio (b/t) and slenderness ratio (KL/H). However, this increasing tendency is closely related with material strengths (fc and f y ).

4 Evaluation of Current Design Provisions Many international design specifications provide design methods for estimating the loadbearing capacity of CFST long columns such as GB 50936-2014 (China Architecture and Building Press 2014), Eurocode 4 (CEN2004) and AISC 360-16 (AISC 2016). Table 2 gives detail information of strength limits in three different code provisions. Comparisons demonstrate that the three design provisions are all limited to conventionalstrength columns, and the columns strength (including steel yield strength and concrete compressive strength) of collected database or FEM results are all out of the limitations of these codes. Therefore, the purpose of this part is to evaluate the feasibility of three different codes for high-strength CFST long columns. Table 2. Strength limits for the three country code provisions. Design codes

Concrete strength permitted

Steel yield strength permitted

GB50936-2014

30 MPa ≤ fcu ≤ 80 MPa

235 MPa ≤ fy ≤ 460 MPa

Eurocode 4

20 MPa ≤ fc ≤ 60 MPa

235 MPa ≤ fy ≤ 460 Mpa

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AISC 360-16

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λcoeff ≤ λlimit

y

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Table 3. Comparison of mean and variance of load-bearing capacity for three provisions. Type

Index

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As shown in Table 3, GB 50936-2014 gives a mean of 0.98 and a standard deviation of 0.21. From Fig. 12(a), it can be found that (i) GB 50936-2014 conservatively estimates the load-bearing capacity of high-strength rectangular CFST long columns when section slenderness coefficient (λcoeff ) is less than 1.5. However, it overestimates the strength

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with large errors when section slenderness coefficient (λcoeff ) exceeds 1.5. (ii) Eurocode 4 (CEN 2004) conservatively estimates the strength of most columns with compact sections, while it has an overestimating prediction for columns with noncompact and slender sections. The mean and standard deviation value of Pue /Puc in Eurocode 4 (CEN 2004) are 1.14 and 0.19 respectively. (iii) AISC 360-16 (AISC 2016) conservatively estimates the load-bearing capacity of high-strength rectangular CFST long columns. There are only 9 specimens which are all compact sections with Pue /Puc ratio less than 1. The mean and standard deviation value of Pue /Puc are 1.25 and 0.18 respectively. In summary, the estimation of AISC 360-16 (AISC 2016) is conservative and safe especially for noncompact and long columns, and its prediction is more reliable.

5 Conclusions This paper investigated the availability of current design provisions based on the compiled experimental and additional FEM database. The compiling database showed that fewer columns with Type HS-CC and slender sections were investigated. These gaps were addressed by performing parametric analysis. Results from parametric analysis shows that: (1) The ultimate strength increased with increasing of steel yielding stress and concrete strength but decreased with increasing of section slenderness ratio (b/t) and slenderness ratio (KL/H); (2) The increasing tendency of column strength by increasing material strength is closely affected by b/t and KL/H; (3) Ultimate strength of columns with slender sections could not be improved significantly by using high-strength steel. Results from compiled database and FEM results were compared with ultimate strengths calculated by using code provisions. The evaluation indicated that GB 509362014 overestimates the strength with large errors when section slenderness coefficient (λcoeff ) exceeds 1.5; Eurocode 4 (CEN 2004) overestimates ultimate strengths of slender columns; AISC 360-16 (AISC 2016) conservatively estimates the load-bearing capacity of high-strength rectangular CFST long columns in general. The modified equations would be proposed in our future work to estimate the load-bearing capacity of high-strength rectangular CFST long columns more accurately.

References Aslani, F., Uy, B., Tao, Z., Mashiri, F.: Behaviour and design of composite columns incorporating compact high-strength steel plates. J. Constr. Steel Res. 107, 94–110 (2015) Cederwall, K., Engstrom, B., Grauers, M.: High-strength Concrete Used in Composite Columns. ACI Special Publication, SP-121-11, pp. 195–214 (1990) Chung, J., Matsui, C., Tsuda, K.: Simplified design formula of slender concrete filled steel tubular beam-columns. Struct. Eng. Mech. 12(1), 141–146 (2001) Dundu, M.: Column buckling tests of hot-rolled concrete filled square hollow sections of mild to high strength steel. Eng. Struct. 127, 73–85 (2016) Khan, M., Uy, B., Tao, Z., Mashiri, F.: Behaviour and design of short high-strength steel welded box and concrete-filled tube (CFT) sections. Eng. Struct. 147, 458–472 (2017) Lai, Z.C., Varma, A.H., Zhang, K.: Noncompact and slender rectangular CFT members: experimental database, analysis, and design. J. Constr. Steel Res. 101, 455–468 (2014)

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Lai, Z.C., Varma, A.H.: High-strength rectangular CFT members: database, modeling, and design of short columns. J. Struct. Eng. 144(5), 04018036 (2018) Lee, H.J., Park, H.G., Choi, I.R.: Compression loading test for concrete-filled tubular columns with high-strength steel slender section. J. Constr. Steel Res. 159, 507–520 (2019) Li, G.C., Chen, B.W., Yang, Z.J., Liu, Y.P., Feng, Y.H.: Experimental and numerical behavior of eccentrically loaded square concrete-filled steel tubular long columns made of high-strength steel and concrete. Thin-Walled Struct. 159(2), 107289 (2021) Liu, D., Gho, W.M., Yuan, J.: Ultimate capacity of high-strength rectangular concrete-filled steel hollow section stub columns. J. Constr. Steel Res. 59(12), 1499–1515 (2003) Liu, D.: Tests on high-strength rectangular concrete-filled steel hollow section stub columns. J. Constr. Steel Res. 61(7), 902–911 (2005) Lue, D.M., Liu, J.L., Yen, T.: Experimental study on rectangular CFT columns with high-strength concrete. J. Constr. Steel Res. 63(1), 37–44 (2007) Mansur, M.A., Asce, M., Islam, M.M.: Interpretation of concrete strength for nonstandard specimens. J. Mater. Civ. Eng. 14(2), 151–155 (2002) Mursi, M., Uy, B.: Strength of slender concrete filled high strength steel box columns. J. Constr. Steel Res. 60(12), 1825–1848 (2004) Perea, T., Leon, R.T., Hajjar, J.F., Denavit, M.D.: Full-scale tests of slender concrete-filled tubes: axial behavior. J. Struct. Eng. 139(7), 1249–1262 (2013) Sakino, K., Nakahara, H., Morino, S., Nishiyama, I.: Behavior of centrally loaded concrete-filled steel-tube short columns. J. Struct. Eng. 130(2), 180–188 (2004) SIMULIA: ABAQUS version 6.16 analysis user’s manuals. Dassault Systemes Simulia Corporation, Providence, RI (2016) Thai, H.T., Uy, B., Khan, M., Tao, Z., Mashiri, F.: Numerical modelling of concrete-filled steel box columns incorporating high strength materials. J. Constr. Steel Res. 102(2014), 256–265 (2014) Varma, A.H.: Seismic behavior, analysis, and design of high strength square concrete filled steel tube (CFT) columns. Lehigh University (2000) Xiong, M.X., Xiong, D.X., Liew, J.: Axial performance of short concrete filled steel tubes with high- and ultra-high-strength materials. Eng. Struct. 136, 494–510 (2017) Young, B., Ellobody, E.: Experimental investigation of concrete-filled cold-formed high strength stainless steel tube columns. J. Constr. Steel Res. 62(5), 482–492 (2005) Yu, Q., Tao, Z., Wu, Y.X.: Experimental behaviour of high-performance concrete-filled steel tubular columns. Thin-Walled Struct. 46(4), 362–370 (2008) Yu, Z.W., Ding, F.X., Cai, C.S.: Experimental behavior of circular concrete-filled steel tube stub columns. J. Constr. Steel Res. 63(2), 165–174 (2006) Zhang, S., Guo, L., Ye, Z., Wang, Y.: Behavior of steel tube and confined high strength concrete for concrete-filled RHS tubes. Adv. Struct. Eng. 8(2), 101–116 (2005)

On the Accurate Strain Measurement in Split Hopkinson Tensile Bar Tests Cheng Chen(B) and Xudong Qian Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576, Singapore [email protected]

Abstract. The Split Hopkinson Tensile Bars (SHTB) are utilized to evaluate the dynamic material property under high strain rates. The one dimensional (1D) wave theory applies to determine the stress and strain of the test specimen. This study adopts the digital image correlation (DIC) technique to measure the fullfield deformation along the specimen and compare the strain results with those collected from the strain gauges. The DIC-based strain results reveal nonhomogeneous specimen deformation under the dynamic conditions, and thus provide more accurate strain measurement to establish the stress-strain curve in the SHTB tests. Keywords: SHTB · 1D wave · DIC · Strain measurement

1 Introduction The split Hopkinson bar system is the most widely used technique to measure the material property under high strain rates. The experimental work of Hopkinson bar is first investigated by Hopkinson (1872). The Hopkinson bar methods, including tension, pressure, shear, torsion, bending and combined load conditions (Jiang and Vecchio 2009), have been developed in recent decades. The split Hopkinson bar system usually consists of the incident and the transmitter bars, with the specimen sandwiched in between. Although there is no international standard of the split Hopkinson bar tests, several guidelines are summarized by Gray (2012) and Gama et al. (2004), recommending general setup such as the bar configuration and the strain gauge position. Under their recommendations, common issues such as the oscillation and dispersion (Gu et al. 2016) are alleviated in the impact tests, which facilitates the application of classical 1D wave theory (Kolsky 1949) and enhances the accuracy of the stress-strain results. Recent development on digital image correlation (DIC) techniques (Pan 2011) has provided an alternative method for the non-contact strain measurement. DIC is a computer-vision based technique which allows full-field deformation tracing. Pierron et al. (2011) utilize the high-speed camera to examine the bending wave under a threepoint-bending split Hopkinson bar test and discuss the inertial effects during the impact. Gilat et al. (2009) adopt the 3D-DIC technique to analyze the full-field strain under different strain rates. The DIC results reveal the deformation difference of the copper © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 215–222, 2023. https://doi.org/10.1007/978-981-19-7331-4_18

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specimens in compressive and tensile split Hopkinson bar tests. Verleysen et al. (2008) investigate the geometry effects on the strain accuracy by changing the gauge area and the transition zone size in the dog-bone specimens. An optical measurement is utilized to compare with the results collected by the strain gauges. Their experimental results indicate that specimens with higher effective length-to-width ratio (≥ 1) yield better strains consistency between the optical and traditional measurement. Rusinek et al. (2008) optimize the specimen dimension through numerical analysis. The authors also demonstrate the importance of the transition zone size to the accuracy of the stress-strain curves. This paper aims to establish the stress-strain curve data of the aluminum materials under different strain rates and investigate the strain accuracy through the non-contact DIC method. The servo-hydraulic machine is utilized for the quasi-static test while the split Hopkinson tensile bar (SHTB) is used for the high-strain-rate tests. The high-speed camera records the images during the impact tests and enables the full-field deformation measurement on the specimen gauge area. Strain results from the strain gauge method are compared with the DIC measurement to investigate the dynamic effects on the strain measurement.

2 Methodology The split Hopkinson tensile bar consists of the striking bar, gas gun, the incident and the transmitter bars. Figure 1 shows the SHTB system used in the current study. The specimen is placed between the incident and the transmit bars. Strain gauges are mounted in the bars to collect the strain values during the impact tests.

Fig. 1. SHTB system

The 1D wave theory applies to determine the specimen stress and strain from the bar data (Kolsky 1949). The 1D wave theory assumes that the bars are linear and dispersionfree, while the specimen experiences negligible inertial effects (Gray 2000). The 1D wave propagation follows the fundamental equations, ∂ 2u 1 ∂ 2u = ∂x2 c2 ∂t 2

(1)

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(2)

u˙ T = −cεT

(3)

where u is the displacement, u˙ is the displacement rate, x denotes the wave propagation direction, c represents the wave propagation velocity, t refers to the time and ε is the

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strain. The subscript I , R, T denotes the incident, reflect and transmit waves. Based on the stress equilibrium between the incident and the transmitter bars, the strain and stress of the specimen derive as, ε˙ = 2cεR /Ls  ε = 2c/Ls

t

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0

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where ε˙ is the strain rate, Ls and AS are the specimen gauge length and cross-section area. E and A are the elastic modulus and the cross-section area of the Hopkinson bars. σ indicates the specimen stress. The classical 1D wave theory measures the specimen stress and strain from the strain gauge data, and is widely adopted for the SHTB tests (Huh et al. 2002; Tucker et al. 2010).

3 Experimental Tests 3.1 Quasi-static Test The quasi-static tests are conducted under a servo-hydraulic machine in the Structural Engineering Laboratory at National University of Singapore. The specimens are made of aluminium 5083. Figure 2a shows the configuration of the aluminium specimen. The specimen has a total length of 56mm and an effective gauge length of 4 mm. The width in the gauge area is 4 mm while the transition zone has a radius of 7.5 mm. The specimen thickness is 1mm. The quasi-static test shows a yielding stress of 258 MPa and an elastic modulus of 70 GPa for the aluminium 5083 material. The engineering stress-strain curve from the quasi-static tests is plotted in Fig. 2b.

Fig. 2. (a) Specimen configuration; (b) Quasi-static stress-strain curve

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3.2 SHTB Test Figure 3 presents the experimental setup for the SHTB tests. The tests are carried out in the Impact Laboratory of National University of Singapore. The high-speed camera is utilized to record the specimen deformation during the impact tests. The image plane is parallel placed with the specimen to reduce the correlation error. The camera has a resolution of 128 × 64 pixels with a frame rate of 300000 frames per second. The actual length to pixel ratio is 0.08 mm/pixel for the current specimen, which is similar to the dynamic DIC resolution in Reu and Miller (2008) and Pop et al. (2011). The illumination creates the contrast for the image correlation. The specimen has the same dimension as the quasi-static coupon specimen (Fig. 2) to ensure the direct comparison of the material response under different loading conditions. The specimen surface is covered with speckles for the image correlation. Two additional bolts are fabricated at the grip end of the specimen to connect with the Hopkinson bars. The strain rates range from 500/s to 3000/s for the SHTB tests in the current study.

Fig. 3. SHTB test setup

Figure 4a illustrates the strain results from the incident and transmitter bars at the strain rate of 2000/s. Figure 4b calculates the stress-strain curve under impact load following Eqs. (1–6) and the results are compared with the quasi-static results. Although the material indicates clear signs of yielding, hardening and necking stages during the impact test, the strain results are not reliable considering the critical discrepancy between the impact and the static test results. In contrast to the material response under quasistatic condition, the impact test shows a severely deviated initial slope, which leads to an underestimated elastic modulus at high strain rates. The elastic modulus is only around 3 GPa compared with the 70 GPa in the quasi-static test. Several researchers have also reported similar phenomenon and attributed the underestimation of the elastic modulus to the transition zone size (Verleysen et al. 2008) and the grip effect (Huh et al. 2002). In light of the inaccuracy of strain from the traditional strain gauge measurement, the DIC method is further applied to evaluate the strain abnormality in the SHTB tests. To investigate the strain variation along the specimen, three virtual extensometers (VE) are defined in the gauge area, with 1–3 mm length respectively. Furthermore, the middle point is also selected to extract the pointwise strain values (Fig. 5a). Figure 5b presents the horizontal displacement at 150 µs after the impact. x denotes the elongation

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Fig. 4. (a) Strain gauge results; (b) Stress-strain curves comparison

direction. The horizontal displacement indicates non-uniform distribution within the gauge area, as the deformation gradients varies along the x direction.

Fig. 5. (a) Definition of virtual extensometer; (b) DIC-measured displacement

Figure 6a summarizes the elongation measured by different virtual extensometers (Fig. 5a) using the DIC method. The bar results are also included as a comparison. Apparently a critical difference exists between the displacement from the bar end and the specimen. This reveals the overestimation of the specimen displacement using the bar data. The discrepancy originates from the grip connection between the bar and the specimen. Figure 6b further calculates the strain results from the bar data and the DIC measurement. The DIC results demonstrate the over-prediction of the strain values from the bar ends, especially at the start of the impact. This explains the underestimation of the elastic modulus in Fig. 4b. On the other hand, the strain results based on different VE lengths are also different inside the gauge area. Figure 6b shows that the strains decrease with the VE length in the initial 150 µs time after the impact, which reflects the nonhomogeneous deformation along the gauge area in Fig. 5b. This non-homogeneity marks the critical characteristic of the specimen deformation under impact loads. Unlike the quasi-static condition where the gauge area observes similar strain patterns, the location of the VE affects the dynamic strain results. A local 1 mm VE yields similar strain results compared with the pointwise strain measurement from the DIC field. Since the fracture occurs in the middle of the

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specimen, the strain results closer to the middle of the gauge region represent more accurate material strains for the impact tests. The pointwise strains increase dramatically after 150 µs due to the localized necking before the fracture occurs. This study focus on the material response before the necking and exclude the strain data after 150 µs.

Fig. 6. (a) Comparison of the elongations; (b) Comparison of the strains

Since the strain results from the bar measurement is not able to represent the actual specimen strain accurately, the DIC-based strain results are utilized as the actual strain of the specimen. Figure 7a replace the strains in Fig. 4b with the DIC-based pointwise strain results while retaining the stress values. The modified strain-stress curve coincides with the quasi-static test in the initial elastic stage. The elastic modulus is close to 70 GPa in the DIC-modified curve. The modified results demonstrate the accuracy of the DIC strain measurement. The aluminium material shows slightly increased strength under impact loading, although only a 5% difference is observed compared to the quasi-static results.

Fig. 7. (a) DIC-modified stress-strain curve; (b) True stress-strain curves

Following the same procedures, Fig. 7b summarizes the DIC-modified true stress– strain results under various strain rates from 500 to 3000/s. The stress-strain data are fitted using the Ramberg-Osgood expression (Ramberg and Osgood 1943). The Aluminium 5083 show relatively low rate-dependence under high strain rates. Although the material demonstrates slightly enhanced strength under impact conditions, the difference

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under strain rates of 500/s and 3000/s is not distinguishable. The rate-insensitivity of Aluminium materials are also reported by (Chen et al. 2009). The strain modification by the DIC method effectively correct the strain overestimation from the bar results. The full-field DIC results demonstrate the nonhomogeneous deformation and the pointwise strain results represents the accurate specimen strain during the impact tests.

4 Conclusions This paper investigates the strain discrepancy between the bar results and the specimen using the DIC method and discusses the strain rate effects on the Aluminum 5083 material. The DIC results reveal the non-homogeneity of deformation in the gauge area and provide more accurate strain measurement for the split Hopkinson tensile bar tests. The strain results measured by the strain gauges on the bars significantly overestimate the specimen strain and lead to critically biased elastic modulus. The DIC-modified strain results achieve better agreement with the quasi-static results at the elastic stage. Therefore, the DIC method is a preferred approach to obtain the accurate strain results for impact tests. The DIC-modified stress-strain curves show that the Aluminum 5083 material is insensitive to the strain rate. The material strength under 3000/s strain rate is similar to that under 500/s strain rate, and both results only have a 5% increase compare to the quasi-static material property. Acknowledgements. The research scholarship provided by the National University of Singapore to the first author is gratefully appreciated.

References Chen, Y., et al.: Stress-strain behaviour of aluminium alloys at a wide range of strain rates. Int. J. Solids Struct. 46(21), 3825–3835 (2009). https://doi.org/10.1016/j.ijsolstr.2009.07.013 Gama, B.A., Lopatnikov, S.L., Gillespie, J.W.: Hopkinson bar experimental technique: a critical review. Appl. Mech. Rev. 57(1–6), 223–250 (2004). https://doi.org/10.1115/1.1704626 Gilat, A., Schmidt, T.E., Walker, A.L.: Full field strain measurement in compression and tensile split Hopkinson bar experiments. Exp. Mech. 49(2), 291–302 (2009). https://doi.org/10.1007/ s11340-008-9157-x Gray, G.T. (Rusty): High-strain-rate testing of materials: the Split-Hopkinson pressure bar. Characterization Mater. (2012). https://doi.org/10.1002/0471266965.com023.pub2 Gray III, G.T.: Classic split Hopkinson pressure bar testing. ASM handbook. Mech. Test. Eval. 8, 462–476 (2000) Gu, X., et al.: Wave dispersion analysis and simulation method for concrete SHPB test in peridynamics. Eng. Fracture Mech. 160, 124–137 (2016) Hopkinson, J.: On the rupture of iron wire by a blow. Proc. Literary Philos. Soc. Manchester 1, 40–45 (1872) Huh, H., Kang, W.J., Han, S.S.: A tension split Hopkinson bar for investigating the dynamic behavior of sheet metals. Exp. Mech. 42(1), 8–17 (2002). https://doi.org/10.1177/001851200 2042001784

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Jiang, F., Vecchio, K.S.: Hopkinson bar loaded fracture experimental technique: a critical review of dynamic fracture toughness tests. Appl. Mech. Rev. 62(6), 1–39 (2009). https://doi.org/10. 1115/1.3124647 Kolsky, H.: An investigation of the mechanical properties of materials at very high rates of loading. In: Proceedings of the Physical Society. Section B, vol. 62, issue 11, p. 676. IOP Publishing (1949) Pan, B.: Recent progress in digital image correlation. Exp. Mech. 51(7), 1223–1235 (2011) Pierron, F., Sutton, M.A., Tiwari, V.: Ultra high speed DIC and virtual fields method analysis of a three point bending impact test on an aluminium bar. Exp. Mech. 51(4), 537–563 (2011). https://doi.org/10.1007/s11340-010-9402-y Pop, O., et al.: Identification algorithm for fracture parameters by combining DIC and FEM approaches. Int. J. Fract. 170(2), 101–114 (2011). https://doi.org/10.1007/s10704-011-9605-y Ramberg, W., Osgood, W.R.: Description of Stress-Strain Curves by Three Parameters (1943) Reu, P.L., Miller, T.J.: The application of high-speed digital image correlation. J. Strain Anal. Eng. Des. 43(8), 673–688 (2008). https://doi.org/10.1243/03093247JSA414 Rusinek, A., et al.: Dynamic behaviour of high-strength sheet steel in dynamic tension: experimental and numerical analyses. J. Strain Anal. Eng. Des. 43(1), 37–53 (2008). https://doi.org/ 10.1243/03093247JSA320 Tucker, M.T., et al.: The effect of varying strain rates and stress states on the plasticity, damage, and fracture of aluminum alloys. Mech. Mater. 42(10), 895–907 (2010). https://doi.org/10.1016/j. mechmat.2010.07.003 Verleysen, P., et al.: Influence of specimen geometry on split hopkinson tensile bar tests on sheet materials. Exp. Mech. 48(5), 587–598 (2008). https://doi.org/10.1007/s11340-008-9149-x

Adaptive Fatigue Assessment of Welded Plate Joints Based on Crack Measurements Liuyang Feng1(B) , Xudong Qian1 , and Wei Zhang2 1 Department of Civil and Environmental Engineering, National University of Singapore, 1

Engineering Drive 2, Singapore 117576, Singapore {ceefeng,qianxudong}@nus.edu.sg 2 Shenzhen Urban Public Safety and Technology Institute, Shenzhen 518046, Guangdong, China

Abstract. Accurate fatigue assessment of welded plate joints remains critical for bridges, ships, offshore platforms, and steel structures subjected to cyclic environmental actions. Adaptive fatigue assessment of the structures incorporating with the crack measurement is essential for the digitalization process in civil engineering. This study conducts high-cycle fatigue tests of welded plate joints and proposes a new and enhanced constitutive damage model to simulate the fatigue damage. The constitutive damage model successfully predicts the fatigue life of welded plate joints under different levels of cyclic loadings. The remaining fatigue life of welded plate joints is updated through adsorbing periodic crack measurement information and achieves good agreement with the experimental results. The framework of this study lays the foundation in the digital twin of the local welded plate joints in offshore structures. Keywords: Fatigue assessment · Crack measurement · Continuum damage mechanics · Welded plate joints

1 Introduction As the critical structural components in engineering structures, welded plate joints (Chang and Yeh 2019; Radaj et al. 2006) tend to fail due to the stress concentration under cyclic environmental loadings. Various environmental scenarios generate high- and lowcycle fatigue cracks in welded connections, furthermore, lead to the fatigue-induced fracture failure of structural components. Therefore, the accurate fatigue assessment of the welded plate joints is essential for the safety of large-scale engineering structures. Traditional fatigue assessment approaches without updating strategy rely on the stress, strain and energy density to evaluate the total fatigue life of welded plate joints. To zoom into the detailed fatigue crack initiation and propagation, methods dealing with low and high-cycle fatigue assessment tend to be different. Linear fracture mechanics (Pugno et al. 2006) quantifies the high-cycle fatigue crack propagation utilizing the stress intensity factor, while elastic-plastic fracture mechanics (Anderson 2017) quantifies the low-cycle fatigue crack propagation utilizing the J integral. Continuum damage mechanics as the alternative approach deal with high- and low-cycle fatigue by incorporating © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 223–235, 2023. https://doi.org/10.1007/978-981-19-7331-4_19

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the damage index with stress, strain and energy. Lemaitre and Chaboche (Lemaitre and Desmorat 2006) incorporate the stress-related parameters into the damage evolution for high-cycle fatigue assessment. Remes et al. (2012) utilize the damage parameters by Socie and Marquis (Socie and Marquis 2000) to quantify every crack growth in a characteristic material length under high-cycle fatigue actions. Strain-based damage indicators are widely used for low-cycle fatigue evaluation. Lemaitre and Plumtree (1979) suggest that the plastic strain is the leading indicator of fatigue life. Pandey et al. (2021) combine the maximum equivalent strain and stress triaxiality function to simulate the low-cycle fatigue crack propagation utilizing the extended finite element method (XFEM). Feng and Qian (2019) demonstrate the potential of the strain energy density-based damage indicators in the rapid determination of the S-N curve for low-cycle fatigue. The nonuniform damage indicators for high and low-cycle fatigue impose challenges in the quick assessment of welded plate joints under various environmental loads. Feng et al. (2020) recently present a uniform fatigue driving force for the high and low-cycle fatigue of smooth and notched specimens based on plastic energy, positive elastic energy and maximum stress. Applications of the proposed approach to the wide range of welded connections used in engineering structures require further validations. Updating strategy is vital for the digital twinning of steel structures. Different fatigue assessments based on the S-N curve or traditional fracture mechanics have emerged considering the uncertainties in material parameters, loading information, assessment parameters. Fang et al. (2022) propose the GP-based finite element surrogate model approach for SIF and evaluate the fatigue life based on linear fracture mechanics. Soliman et al. (2015) conduct the fatigue reliability assessment of aluminium high-speed naval vessels with respect to an individual measured operational condition (sea state, heading angle, and speed). Ling and Mahadevan (2012) classify the uncertainty sources in fatigue assessment and developed the stress intensity factor-based fatigue remaining life strategy. VanDerHon et al. (2022) consider the publicly available vessel-specific operations data and build the digital twin of fatigue damage monitoring and prognosis framework. However, the commonly used fatigue life evaluation relying on the S-N curves and fracture mechanics tends to either neglect the detailed crack profiles or introduce lots of arbitrarily defined parameters. The continuum damage mechanics-based fatigue analysis provides an alternative strategy for adaptive fatigue assessment. Currently, structural health monitoring techniques (strain data and crack size) provide additional useful information on the remaining fatigue life. However, the adaptive fatigue assessment based on continuum damage mechanics and periodical crack measurement is critical for digital twinning in civil structures, yet limited. This study presents the framework of the proposed damage-based indicator in assessing the high- and low-cycle fatigue, and verifies the accuracy through experimental investigations. Thereafter, this study improves the fatigue assessment by incorporating the crack measurement into the fatigue assessment of one specific welded plate joint. This paper is organized as follows. Section 2 presents the experimental setup and details. Section 3 elaborates the proposed framework of the continuum damage model. Section 4 conduct the fatigue assessment based on the proposed damage-based numerical strategy. Section 5 examines the crack measurement information in enhancing the

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fatigue life assessment of one specific welded joint. Finally, Sect. 6 summarizes the main conclusions and future work.

2 Experimental Setup and Details Figure 1a, b present the geometry details and experimental setup of the welded plate joints tested in this study. The welded plate joint is under three-point bending, with the main plate simply supported at the ends, as shown in Fig. 1. The welded plate joints are made of S550 is a high strength steel with good weldability, ductility and enhanced toughness and is thus widely used in ships, marine and offshore structures and bridges. The supported span of the welded plate joint is 300 mm. The geometry details of the welded plate joints include two main plate thicknesses (t = 20 mm and 40 mm) with the same width of 40 mm. The full penetration welds for all the welded plate joints entail a weld leg size of 10 mm. The total height of the specimen is 400 mm, with the thickness of the vertical attachment equal to 20 mm. The downward loading P creates tensile bending stresses at the bottom of the welded plate joints. Therefore, fatigue-induced cracks tend to occur in these two weld toes (yellow block in Fig. 1a). The experimental tests of the welded plate joints are subjected to load-controlled cyclic loadings. The load-controlled cyclic loadings stop when the generated crack reaches 50% of the main plate thickness or the welded plate joints lose the stiffness to withstand the cyclic loads. Table 1 lists the fatigue loading information for all the welded plate joints.

BT40

20

Units: mm

(b)

(a)

P

320- t 10 10 t 20

80 340 Site 1

Site 2

Fatigue crack initiation locations

Fig. 1. (a) Geometry configuration of welded plate joints; (b) experimental setup of welded plate joints

This study adopts the low cycle fatigue test results and cyclic elastic-plastic material properties of the standard coupon S550 specimens from the previous study (Feng and Qian 2018a).

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Specimens Main plate thickness Maximum load Pmax (kN) t (mm)

Load ratio R Loading Frequency (Hz)

BT20_1

20

25

0.1

1

BT20_3

20

30

0.1

1

BT20_4

20

30

0.1

1

BT40_1

40

50

0.1

5

BT40_2

40

50

0.1

5

BT40_3

40

50

0.1

5

BT40_4

40

60

0.1

5

BT40_5

40

80

0.1

1

BT40_6

40

100

0.1

1

3 New Continuum Damage Model Compared with conventional fracture mechanics, which requires a prior defined crack shape or growth path, continuum damage mechanics is a tractable numerical approach to simulate the crack initiation and propagation (damage indicator reaching threshold value (Lemaitre 2012)) under fatigue cyclic loadings. The common challenges and controversies in different continuum damage mechanics theories exist due to different levels of material plasticity caused by the fatigue loading (Anderson 2017; Lemaitre and Desmorat 2006) (e.g., high-cycle fatigue versus low-cycle fatigue), fatigue driving forces (Lazzarin and Zambardi 2002, Dong 2001; Lim et al. 2013) (stress, strain and strain energy density), the distinction between fatigue crack initiation and propagation (de Jesus et al. 2012; Feng and Qian 2018b). To alleviate the above challenges and controversies, our previous study (Feng et al. 2020) proposed a fatigue life estimation strategy based on the uniform fatigue driving force for the crack initiation and propagation in notched specimens under high- and low-cycle fatigue loadings. Inspired by the weakest link theory (Wallin 1991), as shown in Fig. 2a, the fracture process zone comprises of a large number of random cleavage initiation sites (microcracks), the fatigue crack propagation in the homogeneous material is a consequence of a series of microscopic fatigue crack growth, namely, the fatigue crack “initiation” ahead of a growing tip (Remes et al. 2012). The energy-based fatigue driving force provides a uniform treatment of the high- and low-cycle fatigue. Based on the previous study (Feng et al. 2020), a new fatigue indicator involving the plastic strain energy density, positive elastic strain energy density and mean stress effect follows the expression in Eq. (1), as also shown in Fig. 2b   σmax α × W e+ W t = W p + σref (1)   t B A · W =N

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(a)

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(b)

σ

ΔW

p

σ max ΔW e +

ε Fig. 2. (a) Concept of the weakest link theory; (b) definition of total strain energy density.

where W p represents the range of the plastic hysteresis energy; W e+ denotes the positive elastic strain energy range; σmax is the maximum stress; and σref is the reference stress to normalize the effect of the maximum stress. The reasonability of Eq. (1) is validated in detail in our previous paper (Feng et al. 2020). Therefore, this study utilizes the total energy W t to quantify the fatigue driving force and damage indicator. Figure 3 presents the damage evaluation and updating scheme in the numerical simulation. At the end of each cycle (each cycle with a period of T ), the numerical procedure calculates the fatigue damage, the plastic strain energy density, positive strain energy density and positive maximum principal stress. Following Eq. (1), the corresponding fatigue life Ni derives from 1 B  Wit / Ni = (2) A and the damage accumulated in one cycle is

 Di = 1 Ni

(3)

This study adopts the threshold value of the damage indicator (Dthre ) as 0.98 to examine the condition of the damage indicator Di after each calculation. If the damage indicator is less than 0.98, the damage will accumulate. To reduce the computational cost, the numerical simulation employs the cycle jump strategy (Abdul-Latif et al. 2019; Moslemian et al. 2010). Therefore, the updated value of the damage indicator follows Di+1 = Di + D × N

(4)

where N denotes the jumped cycles in the finite element analysis. Aftereach step, the   elements with a damage value equal to 0.98: Edamage or less than 0.98: Enon−damage can be determined. Finally, the nodes along the boundary between the damaged elements and undamaged elements define the crack front profile.

4 Fatigue Assessment of Welded Plate Joints The damage simulation of welded plate joints requires the calibration of cyclic material properties and damage related material parameters from the S550 smooth coupon specimen. This study adopts the cyclic elastic-plastic material parameters of the S550 from

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i = i +1

ti → t i + T Wi p ,Wi e + ,σ imax

{E {E

damage

N i = f (Wi p ,Wi e + ,σ imax )

NO

thre

i +1

thre

{node} = {Edamage } I {Enon − damage } Crack Front Profile

Di ≤ Dthre Yes

i +1

non − damage

ΔDi = 1 N i

Di +1 = Dthre

} = Elements [ D = D ] } = Elements [ D < D ]

Cycle jump Δ N

Di +1 = Di + ΔD × ΔN

Fig. 3. Framework of the damage evaluation and updating in the developed algorithm.

(Feng and Qian, 2018a). According to the experiment results in (Feng and Qian 2018a), the plastic strain energy density, positive strain energy density and maximum positive stress correspond to the values at half of the fatigue life. Based on Eq. (1), this study calibrates the parameters between the total energy density and fatigue life, as shown in Table 2. Figure 4a compares the predicted fatigue life with the experimental fatigue life, which indicates a good agreement based on the total strain density indicators. This study developed the UMAT subroutine in ABAQUS (Abaqus 2011) to verify the calibrated damage-related material properties, incorporating the damage assessment and updating scheme in Fig. 4b. Table 2. Damage-related material parameters in Eq. (1) of S550 steel

S550

σ ref (MPa)

α

A

B

250

2.5

104363.489

−1.9484

The calibrated damage-related material parameters based on the smooth specimen lay the foundation to evaluate more complex structural joints such as welded plate joints under different levels of fatigue loadings. Based on the experimental tests of the welded plate joints under three-point bending in Fig. 1, the crack can initiate in the bottom tension zone on both sides of the joints. However, crack propagation takes place predominantly only on one side. Figure 5a, b present the nondestructive crack measurement by the ACPD at seven points along the width of welded plate joints with the main plate thickness of 40 mm under the maximum load of 50 kN. The fatigue crack initiates around 4000 cycles

Adaptive Fatigue Assessment of Welded Plate Joints

10000

N pre

(a)

2.5 ⎛ ⎞ ⎛σ ⎞ 104363.489 × ⎜ W p + ⎜ max ⎟ × We ⎟ ⎜ ⎟ ⎝ 250 ⎠ ⎝ ⎠

10000

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(b)

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=N

1000

1000

100 100

1000

10000

100 100

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N exp

10000

N Exp f

Fig. 4. (a) Comparison between the predicted fatigue life and experimental results based on Eq. (1). (b) comparison between the numerical fatigue life in ABAQUS and experimental results

at both Site 1 and Site 2 (Site 1 locates on the left side of the specimen, while Site 2 on the right, as shown in Fig. 1). The fatigue crack thereafter grows fast at Site 1 to almost half of the main plate thickness, while the initiated fatigue crack at Site 2 remains small till the end of the fatigue life.

(a)

c(mm) 25

2 mm 9 mm 15 mm 20 mm 25 mm 30 mm 38 mm

20 15

1 mm 7 mm 16 mm 21 mm 29 mm 35 mm 39 mm

12

Site 2

8 4

5 0

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80000

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N

80000

120000

Fig. 5. The propagation of the crack depths in seven measurements along the width of welded plate joints for Site 1 and Site 2.

This study constructs the full finite element model of welded plate joints, using the continuous elements C3D8 in ABAQUS (Abaqus 2011), with a total of 47292 nodes and 38190 elements, as shown in Fig. 6. The mesh near the weld toe has the smallest element size of 0.4 mm. To replicate the crack propagation only on one side of the welded joint observed in the experiment, Fig. 7a presents a modelling approach by assigning the damage material models only to the elements on one side of the joint, which corresponds to the blue color zone in Fig. 7a. Consequently, the fatigue crack emerges and propagations only on one side of the welded plate joint. Due to the consistent local geometry along the weld toe, the numerical analysis predicts an approximately uniform crack depth (a) along the width of welded plate joints under different fatigue cycles, as shown in Fig. 7b. In the following numerical

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Node No.: 47292 Element No.: 38190

Y Z X

Fig. 6. The full finite element model of welded plate joints under three-point bending.

(a)

15

(b)

a (mm)

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5

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25

30

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Z (mm) Fig. 7. (a) The local mesh model of the welded plate joints; (b) the crack evolution in the numerical simulation.

simulation of the welded plate joints under three-point bending, this study adopts the same methodology and simulation strategy for the BT specimens under three-point bending. To validate the proposed damage methodology and assessment scheme, this study combines the experiments presented in this study and other fatigue tests of cruciform welded plate joints made of S550 steel from literature (Feng and Qian 2018b; Zhiping 2015). Figure 8a presents the half finite element model of PT specimens under axial fatigue loadings. The half-finite element model entails the damage constitutive model. Figure 8b compares the experimental test results and numerical simulation results for all the BT and PT specimens. The numerical simulation based on the proposed damage indicator and evaluating scheme can achieve a good agreement with the experimental fatigue life of welded plate joints under high- and low-cycle fatigue loadings, which verifies the accuracy and efficiency of the proposed methodology.

Adaptive Fatigue Assessment of Welded Plate Joints Symmetry plane

N FEM (×1000 ) f

(a) 1000

Y

231

Z

(b)

BT specimens PT specimens

100

X

10 N FEM = 1.1967 N exp f f

δ

1 0.1 0.1

R 2 = 0.924

1

10

100

N exp f ( ×1000 )

1000

Fig. 8. (a) The finite element model of welded plate joints under axial loadings (b) the comparison between the numerically calculated fatigue life and experimental fatigue life.

5 Improved Fatigue Assessment Based on Crack Measurement The above sessions verify the accuracy of the calibrated damage-related material parameters and proposed framework. The fatigue life assessment unifies the treatment for the high- and low-cycle fatigue of welded plate connections. However, the scatter still exists in predicting the fatigue life (Fig. 8b). With increased accuracy requirement in the digital twin techniques, the adaptive fatigue assessment for one specific specimen is urgent with absorbing additional nondestructive measurement information. This session aims to examine the fatigue crack evolution and fatigue life assessment based on the proposed damage mechanics and crack measurement information under different cycles. The alternating current potential drop (ACPD) as the main non-destructive crack measurement technique can provide reasonable crack information under different fatigue cycles. This session takes the BT 40 specimens under cyclic loading with the maximum value of 50 kN. As shown in Fig. 9, this study adopts the three crack measurement information under 50000th , 80000th and 100000th cycle. Therefore, this study generates the pre-crack model in ABAQUS finite element model following the measured crack in Fig. 9. Figure 10a–d present the damage failure under non-existing crack model, and pre-existing cracked model under 50000th , 80000th and 100000th cycle, respectively. The final failure indicated by the damage distribution shows some difference along the side surface in the finite element model. Figure 11 presents the crack evolution under different fatigue cycles along the width direction based on different pre-existing crack profiles. The crack evolves differently with different preexisting crack profiles. Without any existing crack profile, the crack depth along the width of the welded plate joints is almost uniform. With pre-existing crack profile, the evolution of the crack maintains a similar shape of the pre-existing crack profile. Figure 12a compares the final crack profiles by the numerical simulation and silicon replica from the experimental tests. With the 3rd crack measurement information, the final crack profile reaches a great achievement with the experimental results, which validates that the crack information can significantly enhance the prediction of the fatigue crack propagation. Figure 12b summarizes the numerical simulation of the fatigue life for this BT40 specimen. Without any pre-existing crack, the predicted fatigue life is 90000, in

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a (mm) 6 50000th cycle 80000th cycle 100000th cycle

4

3rd crack measurement

2nd crack measurement

2

0

1st crack measurement

0

10

20

30

40

Z (mm) Fig. 9. The measured crack profile by the ACPD under 50000th , 80000th , and 100000th cycle

(a) No existing crack

(b) 1st crack measurement

(c) 2nd crack measurement

(d) 3rd crack measurement

Fig. 10. The final failure based on the damage model with different pre-existing measured crack.

comparison with the fatigue life value of 117500. In contrast, with any of the three crack measurements, the predicted fatigue life can be significantly enhanced, with a much smaller gap between the numerical simulation fatigue life and experimental fatigue life.

Adaptive Fatigue Assessment of Welded Plate Joints a (mm)

(a)

15

a (mm)

15

10

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5

5

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a (mm)

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Z (mm)

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Fig. 11. The crack evolution with different fatigue cycles under different pre-existing crack profiles. a (mm)

(a)

20

15

N f (×10000 )

(b) 126000

15

N exp = 11750 f

90000

No precrack 1st measurement 2nd measurement 3nd measurement Duplica of crack

5 0

112000

10

10

0

10

116000

20

Z (mm)

30

40

5 No crack measurem ent

1st crack measurem ent

2nd crack measurem ent

3rd crack measurem ent

Fig. 12. The final failure based on the damage model with different pre-existing measured cracks.

6 Conclusions The adaptive fatigue assessment is conducted by combing the proposed damage-based model and measured crack information. The detailed experimental investigation and numerical simulation in this study support the following conclusions.

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This study validates the proposed damage-based model in evaluating the fatigue of welded plate joints under different levels of loadings. Experimental fatigue life can be well predicted by the numerical simulation. The proposed damage-based model provides a straightforward method to determine the fatigue life, eliminating the tedious numerical crack modelling procedure to determine the stress intensity factors and J integral in linear fracture mechanics and nonlinear fracture mechanics, respectively. This study examines the effect of crack measurements in adaptive fatigue assessment based on the proposed damage-based model. The great improvement in remaining fatigue life overcomes the limitations of the traditional S-N curve method in absorbing the crack information. The adaptive fatigue assessment method lays the solid foundation of the digital twinning of steel structures. Acknowledgements. The authors would like to acknowledge the financial contribution provided by the ENSURE PROJECT (Grant no. A19F1a0104) under RIE2020 Advanced Manufacturing and Engineering (AME) Industry Alignment Fund-Pre-Positioning.

References Abaqus, G.: Abaqus 6.11. Dassault Systemes Simulia Corporation, Providence, RI, USA (2011) Abdul-Latif, A., Razafindramary, D., Rakotoarisoa, J.: New hybrid cycle jump approach for predicting low-cycle fatigue behavior by a micromechanical model with the damage induced anisotropy concept. Int. J. Mech. Sci. 160, 397–411 (2019) Anderson, T.L.: Fracture Mechanics: Fundamentals and Applications. CRC Press (2017) de Jesus, A.M., Matos, R., Fontoura, B.F., Rebelo, C., da Silva, L.S., Veljkovic, M.: A comparison of the fatigue behavior between S355 and S690 steel grades. J. Constr. Steel Res. 79, 140–150 (2012) Dong, P.: A structural stress definition and numerical implementation for fatigue analysis of welded joints. Int. J. Fatigue 23, 865–876 (2001) Fang, X., Wang, H., Li, W., Liu, G., Cai, B.: Fatigue crack growth prediction method for offshore platform based on digital twin. Ocean Eng. 244, 110320 (2022) Feng, L., Qian, X.: Low cycle fatigue test and enhanced lifetime estimation of high-strength steel S550 under different strain ratios. Mar. Struct. 61, 343–360 (2018) Feng, L., Qian, X.: Size effect and life estimation for welded plate joints under low cycle actions at room and low ambient temperatures. Thin-Walled Struct. 132, 195–207 (2018) Feng, L., Qian, X.: Rapid SN type life estimation for low cycle fatigue of high-strength steels at a low ambient temperature. Steel Compos. Struct. 33, 777–792 (2019) Feng, L., Qian, X., Jiang, R.: A uniform volume-based fatigue indicator for high-and low-cycle assessment of notched components. Int. J. Fatigue 144, 106048 (2020) Lazzarin, P., Zambardi, R.: The equivalent strain energy density approach re-formulated and applied to sharp V-shaped notches under localized and generalized plasticity. Fatigue Fract. Eng. Mater. Struct. 25, 917–928 (2002) Lemaitre, J.: A Course on Damage Mechanics. Springer Science & Business Media (2012) Lemaitre, J., Desmorat, R.: Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer Science & Business Media (2006) Lemaitre, J., Plumtree, A.: Application of Damage Concepts to Predict Creep-Fatigue Failures (1979)

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Lim, C., Choi, W., Sumner, E.A.: Parametric study using finite element simulation for low cycle fatigue behavior of end plate moment connection. Steel Compos. Struct. 14, 57–71 (2013) Ling, Y., Mahadevan, S.: Integration of structural health monitoring and fatigue damage prognosis. Mech. Syst. Signal Process. 28, 89–104 (2012) Moslemian, R., Karlsson, A.M., Berggreen, C.: Application of a cycle jump technique for acceleration of fatigue crack growth simulation. In: 9th International Conference on Sandwich Structures (2010) Pandey, V., Singh, I., Mishra, B.: A strain-based continuum damage model for low cycle fatigue under different strain ratios. Eng. Fract. Mech. 242, 107479 (2021) Pugno, N., Ciavarella, M., Cornetti, P., Carpinteri, A.: A generalized Paris’ law for fatigue crack growth. J. Mech. Phys. Solids 54, 1333–1349 (2006) Remes, H., Varsta, P., Romanoff, J.: Continuum approach to fatigue crack initiation and propagation in welded steel joints. Int. J. Fatigue 40, 16–26 (2012) Socie, D., Marquis, G.B.: Multiaxial Fatigue, Society of Automotive Engineers Warrendale, PA (2000) Soliman, M., Barone, G., Frangopol, D.M.: Fatigue reliability and service life prediction of aluminum naval ship details based on monitoring data. Struct. Health Monit. 14, 3–19 (2015) Vanderhorn, E., Wang, Z., Mahadevan, S.: Towards a digital twin approach for vessel-specific fatigue damage monitoring and prognosis. Reliab. Eng. Syst. Saf. 219, 108222 (2022) Wallin, K.: Statistical modeling of fracture in the ductile to brittle transition region. In: Defect Assessment in Components-Fundamentals and Applications, pp. 415–445 (1991) Zhiping, C.: Fatigue Initiation Life Assessment for Offshore Structural Details (2015)

Experimental Study on a Novel Sandwich Panel Under Repeated Impact Loads Wei Zhang1,2(B) and Zhenyu Huang2 1 Shenzhen Urban Public Safety and Technology Institute, Shenzhen 518046, Guangdong,

China [email protected] 2 College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, Guangdong, China [email protected]

Abstract. Engineering structures may suffer repeated impacts from vehicles or falling objects during service life. Compared to traditional reinforced concrete structures, Steel-concrete-steel (SCS) sandwich composite fully uses the excellent tensile property of steel and compressive property of concrete. When subjected to impact, the steel plate can effectively prevent the impactor penetration, and the concrete core works as the energy dissipation layer, leading to excellent impact resistance of the sandwich structure. To further improve the impact performance, on the material side, the study adds rubber powder into the UltraLightweight High-Ductility Cement Composite (ULHDCC) to develop the rubberized ULHDCC, i.e., RULHDCC; and on the structural side, the study utilizes hybrid shear connectors and double-layer sandwich. The study conducts an experimental program on the newly developed sandwich panels under repeated impact loads using the drop-hammer impact test machine. The failure modes, impact force responses, mid-span displacement responses, peak impact force, peak displacement and residual displacement are discussed in detail. The study also reveals the influences of the design parameters to the impact resistances of the sandwich panels, such as layer number, type of shear connector, spacing of shear connector, rubber content and impact number. Keywords: Sandwich panel · Double-layer · RULHDCC · Repeated impact

1 Introduction The steel-concrete-steel (SCS) sandwich composite structure is formed with steel plates as the shell and concrete as the core material. Compared with the traditional reinforced concrete (RC) structure, the SCS composite structure exhibits the advantages of tensile properties of steel and compressive properties of concrete. As it can effectively prevent the penetration of the impactor, the SCS composite structure shows higher ductility, integrity, bearing capacity and impact resistance (Leng et al. 2015; Liew et al. 2017). In view of these advantages, SCS composite structures are more and more applied to industrial and civil buildings such as nuclear power plants, offshore platforms, shear © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 236–246, 2023. https://doi.org/10.1007/978-981-19-7331-4_20

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walls, etc. These structures may be subjected to continuous impacts from ships, vehicles, or continuous falling of heavy objects. Therefore, it is of great significance to study the impact resistance of SCS composite structures under repeated impact loads and thereby to protect people’s lives and properties. Currently, some researches have been carried out on the dynamic response of SCS composite structures subjected to low-speed and high-speed impact. Remennikov et al. (2013) conducted a drop weight impact test on a SCS protective wall restrained at both ends. The results show that the restraint can fully exert the membrane effect of the steel plate and improve the energy dissipation capacity of the components. Liew et al. (2009) conducted a drop weight impact test on steel-lightweight concrete-steel composite beams and slabs using J hooks as shear connectors, and found that the J hooks can effectively reduce the separation of steel plates and concrete. Based on the energy principle, a calculation method for predicting the deformation of composite panels under impact load is proposed. Jung et al. (2019) conducted impact tests on SCS composite walls under high-speed impact (95.6–152.4 m/s) loads. The test is achieved by the impact of the compressed air projectile on the shear wall. Compared to the ordinary RC shear wall, the SCS composite shear wall can effectively reduce the splash of debris when subjected to the penetration of the projectile. Punching shear failure is a common failure mode of sandwich composite panels under local impact load. Lu et al. (2021) proposed a flat steel-concrete-corrugated steel sandwich panel and experimentally studied its dynamic response under impact loading. The impact energy was found mainly dissipated by the concrete core, then by the corrugated plate and the flat plate. Wang et al. (2021) improved the impact resistance of SCS beams by welding additional stiffeners on the tension plate. All the specimens in the experiment showed a flexural failure with a plastic hinge generated at the mid-span. Huang et al. (2021) proposed to improve the bearing and deformation capacity of the sandwich panel through both material and structural aspects. In terms of core material, rubber powder is added into the ULHDCC (UltraLightweight High-Ductility Cement Composite) to form the RULHDCC (rubberized ULHDCC). In terms of structure, the single-layer sandwich panel is optimized to a multi-layer sandwich panel. Through static and single impact loading tests, combined with numerical and theoretical methods, the force transfer mechanism and failure mode of the multi-layer composite structure were revealed, and it was confirmed that the multilayer SCS composite structure has higher ductility, ultimate bearing capacity and impact resistance. In this paper, a multi-layer steel-RULHDCC-steel sandwich composite structure is designed. Under the same steel content, the number of core layers is optimized from a single layer to a double layer, and the lightweight and high ductility RULHDCC is used as the core material. The study conducts an experimental program on the newly developed sandwich panels under repeated impact loads using the drop-hammer impact test machine. The failure modes, impact force responses, mid-span displacement responses, peak impact force, peak displacement and residual displacement are discussed in detail. The study also reveals the influences of the design parameters to the impact resistances of the sandwich panels, such as layer number, type of shear connector, spacing of shear connector, rubber content and impact number.

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2 Experiment 2.1 Specimens A total of seven composite panels were designed for the drop weight impact test (Table 1). The plane dimensions of all composite panels are 1200 mm * 1200 mm, and the section height is 158 mm. The main research parameters include the number of core layers, the space between shear connectors, the dosage of rubber powder, connector type and number of impacts. The number of core layers includes single-layer and double-layer. The thickness of the two steel plates of the single-layer composite panel is 9 mm, and the thickness of the three steel plates of the double-layer composite panel is 6 mm, and the total thickness of the core concrete is 140 mm. To study the influence of connector type on the impact resistance of the composite panel, two types of connectors are adopted, which are pure J-hooks and hybrid connectors with both J hooks and overlapped headed studs. The rubber powder content is also set as a variable in this experiment, and 5% and 10% volume proportion of rubber powder are added to ULHDCC by replacing the same volume of fine aggregates (fly ash cenospheres) in the mix. The name of each specimen consists of three parts. The first part, SULCS, SR5ULCS or SR10ULCS, indicates, respectively, that the material of the sandwich core is ULCC, ULCC with 5% rubber powder in volume or ULCC with 10% rubber powder in volume. The second part, 100, 150 or 200, indicates that the spacing between the shear connectors. The third part, 9(SH), 6(DH) or 6(DJ), indicates that the thickness of the steel plate is either 9mm or 6mm, where S and D are for Single and Double Layer, and H and J represent Hybrid or pure J-hooks. 2.2 Materials The study designs three mix proportions of lightweight high ductility concrete, namely the ULHDCC, the ULHDCC with 5% and 10% volume proportion of rubber powder (R5ULHDCC and R10ULHDCC). The rubber powder replaces the same volume of fine aggregates (fly ash cenospheres) in the mix. Table 2 lists the mix proportion of the ULHDCC and RULHDCC, each mix is added with 5.8 kg/m3 (0.6% volume proportion) PE fiber, the length of which is 12mm. High-water reducing agent is added to ensure the fluidity of the concrete that is 220-230mm, measured according to BS EN 1015-3 (1999). Three 100 mm × 100 mm × 100 mm cubes and three standard coupons have been casted for each mix of concrete, and tested according to GB/T50081 (2019) for compressive strength and JSCE (2008) for tensile strength, respectively, after 28 days’ curing. The compressive strengths of ULHDCC, R5ULHDCC and R10ULHDCC are tested as 49.2 MPa, 44.3 MPa and 40.2 MPa, respectively, and the tensile strengths are tested as 2.9 MPa, 3.1 MPa and 3.2 MPa, respectively, and the elastic moduli are tested as 11.8 GPa, 9.9 GPa and 8.5 GPa, respectively. Since all three concretes contain 0.6% PE fiber, they all show a multi-crack failure mode when they fail in the compressive test and tensile test. Due to the bridging effect of fibers, the integrity of the specimen is good at failure. In the concrete coupon tensile test, the maximum tensile strain of the specimen reaches about 3%, indicating that all three concretes have good ductility.

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Table 1. Geometric and material parameters of specimens Specimen

Layer number

hc (mm)

tp (mm)

ht (mm)

s (mm)

J-hook

Headed stud

SULCS-150-9(SH)

1

141

9.2

159.4

150

φ12@300

φ13@300

SULCS-100-6(DH)

2

70

5.8

157.4

100

φ12@200

φ13@200

SULCS-150-6(DH)

2

70

5.8

157.4

150

φ12@300

φ13@300

SULCS-200-6(DH)

2

70

5.8

157.4

200

φ12@400

φ13@400

SULCS-150-6(DJ)

2

70

5.8

157.4

150

φ12@150

/

SR5ULCS-150-6(DH)

2

70

5.8

157.4

150

φ12@300

φ13@300

SR10ULCS-150-6(DH)

2

157.4

150

φ12@300

φ13@300

70

5.8

Specimen

ρ (%)

ï

fc (MPa)

f ys (MPa)

f us (MPa)

f yJ (MPa)

f yH (MPa)

SULCS-150-9(SH)

11.5

0.43

49.2

292

460

463

772

SULCS-100-6(DH)

11.1

1.00

49.2

288

440

463

772

SULCS-150-6(DH)

11.1

0.64

49.2

288

440

463

772

SULCS-200-6(DH)

11.1

0.37

49.2

288

440

463

772

SULCS-150-6(DJ)

11.1

0.64

49.2

288

440

463

/

SR5ULCS-150-6(DH)

11.1

0.64

44.3

288

440

463

772

SR10ULCS-150-6(DH)

11.1

0.64

40.2

288

440

463

772

Notes: hc = height of one-layer concrete; t p = thickness of steel plate; ht = total height of SCS panel; s = spacing between shear connectors; J-hook ∅ 12@300 indicates the J-hook diameter is 12mm and the spacing between two J-hooks is 300 mm; Headed stud ∅ 13@300 indicates the headed stud diameter is 13mm and the spacing between two headed studs is 300mm; ρ = 2t p /ht for single-layer specimen, and 3t p /ht for double-layer specimen, indicating the steel contribution ratio; η is the degree of composite action; f c is the concrete compressive strength; f ys and f us are the yield strength and ultimate strength of steel plate, respectively; f yJ and f yH are the yield strength of the J-hook and headed stud, respectively

Table 2. Mix proportion of ULHDCC and RULHDCC (kg/m3 )

ULHDCC

W

OPC

SF

GGBFS

R

F

HWRA

SRA

259.0

702.0

78.0

339.9

/

5.8

12.0

9.0

R5ULHDCC

259.0

702.0

78.0

322.9

18.8

5.8

12.4

9.0

R10ULHDCC

259.0

702.0

78.0

305.9

37.7

5.8

12.8

9.0

Notes: W = water; OPC = ordinary Portland cement; SF = silica fume; GGBFS = mineral powder; R = rubber powder; F = steel fiber; HWRA = high Water reducing agent; SRA = shrinkage reducing agent

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The steel used in the test includes the Q235 steel plate, headed stud, and J-hook. The steel plate has two thicknesses of 6 mm and 9 mm, the J-hook connector is bent from HPB300 steel bar with a diameter of 12 mm, and the diameter of the headed stud is 13 mm and the length is 100mm. The material properties of the steel components are tested according to ASTM E8/E8M (2011). The yield strengths of the 6 mm steel plate, 9 mm steel plate, J hook and headed stud are tested as 288 MPa, 292 MPa, 463 MPa and 772 MPa, respectively, and the ultimate tensile strengths are tested as 440 MPa, 460 MPa, 640 MPa and 916 MPa, respectively, and the elastic moduli are tested as 202 MPa, 208 MPa, 202 MPa and 205 MPa, respectively.

Fig. 1. Double-layer sandwich panel and test set-up

2.3 Test Set-up The impact test is carried out on a drop-weight impact test machine (Fig. 1). The dropweight ranges from 512 kg to 1012 kg, with the maximum height of 5 m, and thereby the maximum impact energy can reach 50 kJ. The head of the drop hammer is round shaped with a diameter of 100 mm. In this test, the selected impact mass is 1012 kg, and each specimen is subjected to three times of impact loading. For the first two impact tests, the drop heights are both 5 m. Since the hammer has obviously penetrated into the composite panel after the second impact, the height of the third impact is reduced to 3 m to avoid damage to the force sensor which is located above the hammer head. Therefore, the energies of the three impact tests are 50 kJ, 50 kJ and 30 kJ, respectively.

3 Result and Discussion 3.1 Failure Mode The composite panels exhibit obvious punching failure mode under repeated impact loads, as shown in Fig. 2a. Similar to the force transfer mechanism under static load

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(Huang et al. 2021), the composite panel also forms a punching cone with the inclination angle of about 60° under the drop hammer, and the impact load is transmitted to the steel plate and concrete through the punching cone. As ULHDCC and RULHDCC are lightweight porous materials, the concrete inside the punching cone is compacted during impact. The upper steel plate suffers punching shear failure. Figure 2b shows the damage extent of the upper steel plate of the specimen SULCS-150-6 (DH) after 1st , 2nd , and 3rd impacts. After the first impact, the upper steel plate is partially indented, and the steel in the concave area yields; after the second impact, the upper steel plate is torn near the contact of the hammer head; after the third impact, the upper steel plate is torn more seriously and finally penetrated. Figure 2c, d show the overall front view, top view and partial view of the specimens SULCS-150-6(DH) and SULCS-200-6(DH) after 3rd impact, respectively, both of which exhibit overall flexural deformation and local punching failure. Compared to SULCS-150-6(DH), SULCS-200-6(DH) also exhibits local buckling on the top steel plate, which is due to the large spacing (200 mm) between shear connectors in this composite panel resulting in a low degree of composite action (ï = 0.37). Slippage occurs between the steel plate and concrete during the impact process, and the steel plate is prone to local buckling after being freed from the constraints of the concrete. The rest of the specimens exhibit similar failure modes to SULCS-150-6(DH).

Fig. 2. Failure mode

3.2 Response Curves The responses of impact force/mid-span displacement are important indexes to evaluate the impact resistance of the structure. Figure 3a–g plots the impact force-time curve and mid-span displacement-time curve of each specimen under repeated impact loads. The suffixes “1”, “2” and “3” in the figure represent the first, second and third impacts,

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respectively. By analyzing and comparing the results of the seven specimens, the following conclusions can be drawn: (1) The maximum impact force of the single-layer panel SULCS-150-9(SH) under the 2nd impact decreases by 5.6% compared to that under the 1st impact, while the maximum impact force of the other six double-layer panels under the 2nd impact increases with varying degrees compared to that under the 1st impact. This is because after the 1st impact, the top steel plate of the single-layer panel has begun to tear, resulting in the reduction of bearing capacity of the panel. But the double-layer panel still keeps good structural integrity after the 1st impact, and the steel plate is still in the plastic hardening stage, so that the double-layer panel can withstand greater force in the 2nd impact; (2) In the 3rd impact, the maximum impact force of the single-layer panel SULCS-150-9(SH) and the double-layer panel SULCS-100-6(DH) significantly decreases by 31.5% and 14.4%, respectively, compared to that under the 1st impact, due to the severe tear fracture of the top steel plate after the first two impacts. Compared with the other five double-layer panels, SULCS-100-6(DH) has the smallest spacing between shear connectors, indicating the highest degree of composite action and largest stiffness. Under the same impact energy, its deformation is the smallest, and the impact force is the largest; (3) the mid-span displacement of the seven specimens shows the similar trend under repeated impact loads, that is, the maximum mid-span displacement decreases with the number of impacts. The reasons are as follows: (a) The impact load causes plastic deformation of the steel plate, and an irreversible residual deformation is formed after impact. The plastic hardening increases the yield strength of the steel plate and decreases its deformation capacity; (b) After repeated impacts, the local deformation dominates, and the energy is mainly absorbed by the local deformation; (c) After repeated impacts, the equivalent mass of the members participating in the impact resistance may be different. The change of mass ratio (member/drop weight) may introduce changes in the distribution of momentum after impact, possibly reducing the total energy absorbed by the members. 3.3 Influence of Layer Number Figure 4A compares the residual deformation of the top and bottom steel plates between the single-layer specimen SULCS-150-9(SH) and SULCS-150-6(DH), the steel contribution ratio of which are very close (less than 5% difference). The two specimens have almost the same residual deformation on the bottom steel plate. Compared with the single-layer panel, the penetration depth of the top steel plate of the double-layer panel is 103.4 mm, which is 10.9% lower than that of the single-layer panel, 116.1 mm. After three impacts, the tearing area on the top steel plate of the single-layer panel is larger, almost the entire circumference, while the tearing area of the double-layer panel is relatively small, only half of the circumference. This is because after the first impact load, the top steel plate of the single-layer panel has already been torn, and the degree of tearing further increases under the following impact loads. According to the cutting profile, the punching cone of the single-layer panel is more obvious, the main crack in the concrete extends from the top steel plate to the bottom steel plate, and the concrete damage is more serious, while the main crack in the double-layer composite board is shorter, which is because the presence of the middle steel plate prevents the extension of cracks along the thickness of the concrete and avoids greater damage to the structure.

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Fig. 3. Impact force and mid-span displacement history curves

In short, with the same steel contribution ratio, the double-layer panel has better impact resistance than the single-layer panel under repeated impact loads. 3.4 Influence of Connector Type Figure 4B compares the residual deformation of the top and bottom steel plates between the specimen with pure J-hooks SULCS-150-6(DJ) and hybrid shear connectors SULCS150-6(DH), respectively. The penetration depth of the top plate and the residual deflection of the bottom plate for the specimen SULCS-150-6 (DH) are 103.4 mm and 57.0 mm, respectively, while those values for the specimen SULCS-150-6(DJ) are larger as 125.3 mm and 58.9 mm, respectively. The cutting profile shows that the tearing area of the top steel plate for SULCS-150-6(DJ) is larger. The reason is that the J hooks inside the punching zone are in the state of compression rather than tension, the “interlocking effect” of the J hooks does not work, while the J hooks outside the punching cone are stretched due to the membrane effect, producing the “interlocking effect” which prevents the separation of the steel plates. In contrast, the sandwich panel with hybrid shear connectors has less damage and better impact resistance.

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3.5 Influence of Connector Spacing Figure 4C compares the residual deformation of the top and bottom steel plates among the specimens with the spacing between shear connectors ranges from 200 mm, 150 mm and 100 mm, respectively. With the decrease of spacing, the penetration depth of the top steel plate reduces from 109.5 mm to 103.4 mm and 91.8 mm by 5.6% and 16.2%, respectively; and the residual deformation of the bottom steel plate decreases from 61.3 mm to 57.0 mm and 47.7 mm by 7.0% and 22.2, respectively. The smaller the spacing between the shear connectors, the larger the number of cracks in the concrete core. The cutting profile of SULCS-100-6(DH) clearly exhibits the entire punching cone, the internal main cracks and micro cracks. As SULCS-100-6 (DH) is a fully composite design, the shear connectors can effectively restrain the lateral movement of the concrete, and there is no obvious bond-slip between the steel plate and concrete. SULCS-1506 (DH) and SULCS-200-6 (DH) are both partially composite panels. As the spacing between the connectors increases, the bond-slip between the steel plate and concrete increases, and the number of internal vertical cracks decreases. Therefore, the partially composite sandwich panel has better toughness and deformation capacity than the fully composite sandwich panel, and can maintain better structural integrity under impact load. In addition, during the third impact, the two partially composite sandwich panels bear a greater impact force than the fully composite sandwich panel, indicating that appropriately reducing the degree of composite action is more conducive to improving the energy dissipation capacity of the structure. 3.6 Influence of Rubber Powder The waste rubber tires are ground into rubber powder and added to concrete to develop the rubberized concrete, which is not only beneficial for absorbing energy and preventing crack development, but also disposes most of the rubber waste. In order to analyze the role of rubber powder in ULHDCC under impact load, three variable parameters of equal volume of rubber powder, 0%, 5% and 10%, are set to replace the fine aggregates (fly ash cenospheres). According to Fig. 4d, although the addition of rubber powder has little effect on the penetration depth of the top plate and the residual deflection of the bottom plate of the sandwich panel, with the increase in the amount of rubber powder, the main cracks are reduced and the micro-cracks are increased. This is because the rubber powder with lower elastic modulus plays the role of energy absorption, buffering and crack resistance in the ULHDCC, reducing the damage to the concrete caused by the impact energy. 3.7 Influence of Impact Number A total of three specimens mixed with 10% rubber powder are designed in the test, and they are subjected to one time of impact of 50 kJ, two times of impact of 100 kJ (two 50 kJ) and three times of impact of 130 kJ (two 50 kJ, one 30 kJ). After the test, the three sandwich panels are cut respectively to observe the damage of the steel plate and the cracking of the concrete. The results show that with the increase of the number of impacts, the penetration depth of the top steel plate and the residual deflection of the

Experimental Study on a Novel Sandwich Panel

(a) layer number

(c) connector spacing

245

(b) Connector type

(d) rubber powder

(e) impact number

Fig. 4. Influences of design parameters

bottom steel plate gradually increase. The top steel plate is partially dented after the first impact, and torn after the second impact, and penetrated after the third impact. The internal concrete does not show obvious cracks after the first impact, a small number of micro-cracks appear after the second impact, and the number of micro-cracks further increases after the third impact. In the third impact, no major cracks are found in the concrete. This is because all three specimens are added with 10% rubber powder, which further verifies that the rubber powder plays an energy-absorbing and anti-cracking role in the ULHDCC.

4 Conclusions The following conclusions are achieved: 1) The sandwich composite panel shows obvious punching failure mode under repeated impacts. The impact load is transmitted to the steel plate and concrete core through the punching cone, resulting in the tearing or even penetration of the steel plate. The

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ULHDCC and RULHDCC developed in this paper are lightweight porous materials. The concrete inside the punching cone is compacted during the impact process, which plays a good role in buffering and absorbing energy and reduces the degree of cracking damage of the concrete. 2) Compared with the single-layer panel, the double-layer panel shows better impact resistance. On one hand, the double-layer panel can withstand greater impact force and has a stable residual bearing capacity. On the other hand, the presence of the middle steel plate prevents the extension of cracks along the thickness of the concrete, maintains the rigidity and toughness of the structure, and avoids greater damage to the structure. 3) The composite panel using hybrid connector has less damage and stronger protection ability than the panel using pure J hooks, and the production and installation of the hybrid connector are also simpler. The partially composite sandwich panel has better toughness and deformation capacity than the fully composite sandwich panel. 4) The addition of rubber powder plays a good role in energy-absorbing and anticracking, and is effective to reduce the damage caused by impact energy to the concrete core.

References ASTM E8/E8M: Standard Test Methods for Tension Testing of Metallic Materials. ASTM Standards, West Conshohocken, PA, USA (2011) BS EN 1015-3: Methods of Test for Mortar for Masonry–Determination of Consistence of Fresh Mortar (by flow table). British Standard Institution, UK (1999) GB/T50081: Standard for Test Methods of Concrete Physical and Mechanical Properties. China Architecture & Building Press, Beijing, China (2019) Huang, Z.Y., Zhao, X.L., Zhang, W., et al.: Load transfer mechanism of novel double-layer steelLHDCC-steel sandwich panels under punching loads. Eng. Struct. 226, 111427 (2021) JSCE: Recommendations for Design and Construction of High Performance Fiber Reinforced Cement Composites with Multiple Fine Cracks. High Performance Fiber Reinforced Cement Composites, Tokyo, Japan (2008) Jung, J.W., Yoon, Y.C., Jang, H.W., et al.: Investigation on the resistance of steel-plate concrete walls under high-velocity impact. J. Constr. Steel Res. 162, 105732 (2019) Leng, Y.B., Song, X.B., Wang, H.L.: Failure mechanism and shear strength of steel–concrete–steel sandwich deep beams. J. Constr. Steel Res. 106, 89–98 (2015) Liew, J.Y.R., Yan, J.B., Huang, Z.Y.: Steel-concrete-steel sandwich composite structures-recent innovations. J. Constr. Steel Res. 130, 202–221 (2017) Liew, J.Y.R., Sohel, K., Koh, C.G.: Impact tests on steel–concrete–steel sandwich beams with lightweight concrete core. Eng. Struct. 31(9), 2045–2059 (2009) Lu, J., Wang, Y., Zhai, X.: Response of flat steel-concrete-corrugated steel sandwich panel under drop-weight impact load by a hemi-spherical head. J. Build. Eng. 102890 (2021) Remennikov, A.M., Kong, S.Y., Uy, B.: The response of axially restrained non-composite steel– concrete–steel sandwich panels due to large impact loading. Eng. Struct. 49, 806–818 (2013) Wang, Y., Lu, J., Liu, S., et al.: Behaviour of a novel stiffener-enhanced steel–concrete–steel sandwich beam subjected to impact loading. Thin-Walled Structures 165, 107989 (2021)

Smart Construction and Management

Readiness and Potential Application of Smart Contracts in the Indonesian Construction Industry Kartika Wulandary1 , Kriengsak Panuwatwanich1(B) , and Michael Henry2 1 School of Civil Engineering and Technology, Sirindhorn International Institute of Technology,

Thammasat University, Pathum Thani 12121, Thailand [email protected], [email protected] 2 Department of Civil Engineering, Shibaura Institute of Technology, Tokyo 135-8548, Japan [email protected]

Abstract. A construction project requires a contract to run safely by minimizing costs, schedules and maintaining project quality. In traditional contracts, contractual transactions between trustless parties are generally conducted in a centralized form, requiring a trusted third party to act as witnesses and make them legally binding, enforceable, and trustworthy. However, involving third parties is associated with high costs and delays. In this case, Smart Contracts can be a solution. A smart contract is a code that contains rules that will execute a transaction itself according to the agreement of two parties. Smart Contracts contained in Blockchain Technology have received much attention globally, including in the construction industry. Smart Contracts can enable automatic payments without delays, hassles and without third parties (mediators) carried out in a decentralized network to ensure integrity and transparency by preventing the potential of record manipulation existed in traditional contracts. This paper presents an overview of the potential application of Smart Contracts in Indonesian construction industry. This paper was prepared based on a literature review of several existing studies to obtain data related to the current state of Blockchain Technology, technological readiness, and the potential areas that Smart Contracts can be applied. It is hoped that the findings from the literature review will explain various aspects of the potential for adopting Smart Contracts in the construction industry and can assist in the development of further research that will focus on the application of Smart Contracts in the Indonesian construction industry. Keywords: Smart Contracts · Blockchain · Construction industry · Readiness · Indonesia

1 Introduction The construction industry is one sector that is very influential on economic development, especially in developing countries (Pooworakulchai et al. 2017). Its value is arguably tremendous, and many parties are involved. Notably, projects in the construction sector

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 249–263, 2023. https://doi.org/10.1007/978-981-19-7331-4_21

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are generally considered the projects with the most significant risk compared to other sectors (Bahamid and Doh 2017). These risks include risks to time (occurring delays in work), costs (change of work to construction costs), and work performance (methods and materials that are not following several factors). Furthermore, the traditional contractual transactions between stakeholders are generally conducted in a centralized form. This requires a trusted third party to act as a witness and making them legally binding, enforceable, and trustworthy (Ashworth and Perera 2018; Roy et al. 2021; Singh et al. 2021). However, according to studies involving third parties could associate with high costs and delays in the construction process (Chaveesuk et al. 2020; Elghaish et al. 2021; Hamledari and Fischer 2021b). Thus, many construction project parties sometimes ignore contracts, which resulted in payments being delayed withheld or even rejected. Research found that late, withheld or declined payments were one of the leading causes of delays in the construction project process (Assaf and Al-Hejji 2006; Badi et al. 2021; Kim et al. 2009). On the other hand, Smart Contracts embodied in Blockchain Technology have received much attention globally, including in the construction industry. Smart Contracts can enable automatic payments without delays, hassles and without third parties (mediators) carried out in a decentralized network to ensure integrity and transparency by preventing potential manipulation of records contained in traditional contracts (Hamledari and Fischer 2021a; Yang et al. 2020). In this case, Smart Contracts can be the solution. Smart Contracts can be recommended to offer significant time and cost efficiencies (Dakhli et al. 2019; Wang et al. 2017). This study aimed to analyze the potential applications of Smart Contracts in the construction industry in Indonesia, which is experiencing a rapid increase in infrastructure development. This study also discusses the need to solve problems with regards to contracts that often occur in the Indonesian construction industry.

2 The Challenges of Contract Management in Construction Industry Indonesia, the world’s fourth most populous country, is in desperate need of improved infrastructure, as well as residential and commercial real estate. Indonesia’s construction sector, according to Kog (2019), will expand to become one of the largest in the world during the next few decades. Indonesian construction industry contributes significantly to the country’s economic growth. Indonesia is actively developing the infrastructure sector in order to promote a more prosperous economy. Chui and Moon (2021) state that the construction industry is based on orders, i.e. the construction process begins when the contracting party initiates the order by signing a contract that stipulates certain contract terms. At the moment, traditional contracts are frequently utilized in construction projects, and the Indonesian construction industry is no exception. Traditional contracts, also known as paper contracts, are the outcome of stakeholder negotiations, drafting phases, and legal contributions that used to present the obligations of parties required to perform certain activity. When the contract is signed, the parties are bound by the terms of the contract, then the parties form a temporary team

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with the common goal of completing the construction project. Therefore, the contract plays an important role in the success of the project. The owner’s responsibility for making progress payments and meeting technical requirements should also be reviewed during the construction process. In some cases, the owner must pay the contractor in installments for the work carried out according to schedule. Therefore, the terms of the contract for the construction project must be provided in writing at the beginning of the project. It must also meet the technical requirements for the specifications. The construction industry can be characterized as an industry with a complex product system that involves individuals or entities with a variety of expertise collaborating on a project that will cease after the project is completed (McMeel and Sims 2021; Pradeep et al. 2019). However, due to inefficient processes and poor levels of productivity, this relationship frequently results in hostility between individuals or entities, and even between industries (Fernandes et al. 2018; McNamara and Sepasgozar 2018; Rahmani et al. 2017; Shojaei 2019). Thus, this “winner and loser mentality” results in a lack of trust among stakeholders and frequent conflict. Therefore, the importance of a good contract agreement to achieve the desired agreement results without any party feeling aggrieved to reduce disputes. Traditionally, it is possible that the contracting parties will ignore the terms of the contract, leading to legal disputes. Lack of awareness about contract terms may be the main cause of construction claims (Chui and Moon 2021). Other problems that often occur in the construction industry, according to the current literature, can be described in Table 1. The issues outlined in Table 1 are also frequently encountered in the Indonesian construction industry. For instance, consider the issues of late payment and non-payment. Hansen et al. (2017) stated that late payments and non-payments are the primary risk Table 1. Summary of problems in construction projects related to construction contracts Problems

Descriptions

Sources

Trusted party/Trusted authorities

In traditional contracts, it is very necessary to bring trusted third parties such as banks and lawyers to act as witnesses and make them legally binding in the construction contract agreement

Ashworth and Perera (2018), Chaveesuk et al. (2020), Roy et al. (2021), Singh et al. (2021)

Using a trusted third-party, Chaveesuk et al. (2020), Perera costs extra which is sometimes et al. (2020), Elghaish et al. not necessary (2021) Using a trusted third party sometimes delays the construction process

Chaveesuk et al. (2020), Hamledari and Fischer 2021b (continued)

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Problems

Descriptions

Sources

Late payment

Project stakeholders usually experience delays or do not pay, even though the construction stage process has been completed

Alaghbari et al. (2007), Nanayakkara et al. (2019), Chia et al. (2020)

Late payment for one work can Sambasivan and Soon (2007) result in delaying the next work Construction process delay

Delays in the construction Abdellatif and Alshibani process are often caused by late (2019) procurement from the owner, supplying construction materials and equipment, and delivery Delays are also caused by poor Trigunarsyah (2004) constructor input timeliness; lack of documentation and lessons learned; and misguided design goals and performance measures of designers

Contracting with funds

Owner requires contractor to adopt a contracting with funds mode such as Finance, Engineering, Procurement and Construction

Liu et al. (2022)

Prepayment for construction

Contractor assumes project Liu et al. (2022) construction costs and does not receive payment until project construction reaches agreed conditions

Unstable construction funds Contractor faces unstable construction funding due to insufficient payments or payment delays

Liu et al. (2022)

Security against corruption and Bribery

Le et al. (2014), Shan et al. (2017), Ameyaw et al. (2017), Cheng and Darsa (2021), Wang et al. (2021), Liu et al. (2022)

The use of trusted authorities does not guarantee that one of the stakeholders commits fraud such as corruption/bribery, fraud, and collusion by cooperating with these authorities

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variables in the relationship between subcontractors and main contractors in the construction industry. In Indonesia, construction workers demonstrate over subcontractors almost every year whom the main contractor does not pay. For example, the problem with the Riau main stadium project for PON XVIII in 2012. Hansen et al. (2017) stated that 12 subcontractors were boycotted due to payment contract issues for the project. All subcontractor contracts have not been paid by the main contractor, a consortium of three major Indonesian construction companies. It includes contracts for the sound system and the scoreboard and flooring and athletics contracts. So, in this case, all the subcontractors involved suffered huge losses. To overcome the above issues, researchers provided some recommendations based on the following aspects that can be described in Table 2. Table 2. Researchers’ recommendations to overcome problems in construction projects related to construction contracts Aspects

Descriptions

Sources

Payment

Payments are better made automatically on the same day with the work that finished to assign

Li et al. (2019), Shojaei (2019), Chia et al. (2020), Badi et al. (2021)

Payments are better to be generated directly from owner to contractors and suppliers

Chia et al. (2020)

Transparent data

Data of project information and Li et al. (2005), Yu et al. funding must be transparent to all (2006), Thizy et al. (2019) stakeholders and teams in the construction project

Progress report

Work progress reports must be Perera et al. (2020), Jiang updated at real-time on the digital et al. (2021), Zhang et al. platform to avoid fraud in (2021) construction projects

Data access rights

All project information data must Chia et al. (2020) be accessible to all interested parties and teams in the construction project

Contract administration

It is necessary to provide reliable Hargaden et al. (2019) contract administration services through the implementation of a process by which construction contracts can be formed and monitored (continued)

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Aspects

Descriptions

Sources

A system is needed to automate Qian and Papadonikolaki the contract, make it seamlessly (2020) flawless and minimize people’s distrust of the other party signing the agreement, thereby increasing the efficiency and legal protection of the participants in signing the contract To increase trust between stakeholders, it is necessary to have a platform that can be accessed by all parties in the construction project, but the data inputted on the platform cannot be changed/deleted by anyone Trusted third party

Hargaden et al. (2019), Badi et al. (2021)

It is urgently needed something Turk and Klinc (2017), that can keep the project contract Chaveesuk et al. (2020) safe and can guarantee its validity but does not use a trusted third party to reduce unnecessary funds Trusted third parties sometimes Shojaei (2019), Chaveesuk cannot be fully trusted because it et al. (2020) is possible that these parties conspire with one of the parties in the project to embezzle funds

Information data tracking

Tracking historical information should be easy to do to improve project workflow

Zhang et al. (2021), Li et al. (2021), Taneja et al. (2011), Perera et al. (2020)

All construction information data Zheng et al. (2019), must be recorded and easily Hamma-adama et al. (2020) tracked, so that when an error occurs in the project, the audit will more easily find the cause of the error

3 Potential Application of Smart Contracts in Construction Management A smart contract is a computer program that automates the execution, control, and documentation of a transaction according to the terms of the parties’ contractual agreement (Mohanta et al. 2018; Wohrer and Zdun 2018). It is written in coding and executed on the blockchain network. The term “blockchain” refers to a technology that is used as

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a digital storage system that is connected via cryptography and ensures that all stored data is permanently recorded and cannot be altered. Blockchain Technology, as a decentralized system, can securely store data and has a very low risk of being hacked. The blockchain’s overall operation is depicted in Fig. 1, and it consists of the following steps: the transaction is requested, the block representing the transaction is created, the block is broadcast to the P2P network, the network validates the transaction, the verified block is added to the blockchain, and the transaction is completed (Shojaei et al. 2019). Blockchain can be divided into open (public or hybrid) or closed (private or consortium), as summarized in Table 3.

Fig. 1. Illustration of Blockchain Technology operation adopted from Shojaei et al. (2019)

With Blockchain Technology based on Smart Contracts, the recommendations to overcome the issues in construction contracts presented in the previous section can be realized. According to Chia et al. (2020), Smart Contracts are the key of Blockchain Technology because that can enable the expensive enforcement of agreements by controlling real-world valuable property via “digital means”. Thus, Smart Contracts can both compel the functional implementation of a requirement and provide evidence of whether certain conditions are met. While Smart Contracts are merely enabling technology, the consequences of their actions can be incorporated into a legal agreement. The outcomes of a smart contract can be used as an audit trail to demonstrate whether the terms of a legal agreement have been followed. Mougayar (2016) in Chia et al. (2020) state that Smart Contracts are well-suited to interacting with physical assets, intelligent properties, the Internet of Things (IoT), and financial service instruments. They are not restricted to the flow of money. They are applicable to almost anything that changes its state over time and can be assigned a monetary value.

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K. Wulandary et al. Table 3. Summary of blockchain types (Hamma-adama et al. 2020)

Types of blockchain

Read

Write

Commit

Example

Open

Public

Anyone

Anyone

Bitcoin, Ethereum

Hybrid

Authorized participants

All or subset of authorised participants

Sovrin

Consortium

Authorized participants

All or subset of authorised participants

Multiple banks operating a shared ledger

Private

Network operator only

Network operator only

Internal bank ledger shared between parent company and subsidiaries

Closed

3.1 Smart Contract for Contract Management Smart Contracts in the context of Blockchain Technology have been used in other industries and could be a game-changer for the construction industry’s digitization. A construction contract is a critical component of initiating construction work. As time passes, significant changes are required to digitalize construction management. Digital contracts like Smart Contracts in Blockchain Technology are an example of digitalization and how industry 4.0 technology is applied. It is an essential thing to simplify the work and reduce the time consuming, and therefore, it would be more costefficient. Nevertheless, the transition from the traditional to the more modern way is needed to apply this concept in construction contractor work. Blockchain Technology can resolve the issue of trust in construction contracts, particularly in terms of payments. Through the use of algorithms and rules in smart contract applications, blockchain applications automate construction contracts (San et al. 2019). Smart Contracts act as agents for auto-triggered transactions or events (de Leon et al. 2017), enabling digital contracts to run on a distributed ledger and be programmed to automate payment execution in the system after meeting predefined contract terms while securing payment credentials (Nawari and Ravindran 2019). This smart contract system enables individuals to create their own digital contracts by allowing terms to be agreed upon by individuals who are not physically present (Cong and He 2019). 3.2 Readiness for Smart Contracts in Indonesian Construction Industry The construction industry is notorious for payment disputes between clients, prime contractors, subcontractors, and material suppliers where according to (San et al. 2019), subcontractors are the worst victims of all the construction stakeholders listed. These types of issues frequently arise in Indonesia because of miscommunication between the

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project’s interested parties, resulting in non-payment and late payments, or sometimes payment disputes. In Indonesia, construction projects that frequently garner public attention are those that include the development of public facilities and are organized by the Ministry of State and State-Owned Enterprises (BUMN). Typically, these projects are completed by a third party hired as a construction service provider according to a construction contract (Iskandar et al., 2021). According to Trigunarsyah (2004), professional designers and constructors are involved in distinct contracts in Indonesian construction projects. Typically, the contractor is not involved until the design phase is complete which has been blamed for Indonesia’s lack of construction expertise, resulting in budget overrun and schedule slippage. Smart Contracts can be used to resolve non-payment and late payment issues in the construction industry, thereby reducing the number of payment disputes between clients and contractors. Smart Contracts running on an immutable distributed ledger can provide payment certainty, stabilizing smaller contractors (McNamara and Sepasgozar 2018). Smart Contracts can also increase the level of trust among construction businesses. Additionally, Smart Contracts can be used to automate the appointment process between the client and the project consultant (designer, cost engineer, or project management). As a result, the nature of legal contracting is likely to undergo significant change, and litigation may take a back seat to prevention (Diedrich 2016). In the construction industry, Smart Contracts have created numerous opportunities for completing the legal contract life cycle (Nawari and Ravindran 2019). Public blockchains are incompatible with platforms for legal construction contracts. Xu et al. (2016) stated that private blockchains, which enable developers to explicitly grant permission to participants, were found to be more suitable for safeguarding data privacy from the public. However, consortium blockchains are thought to be better for construction contracts than private blockchains because they can be run by a group rather than a single community or company, which is more decentralized. They also have the same features of a private blockchain, such as transparency, privacy, and efficiency, without relying on a single party with the power to combine them. There are still numerous obstacles to overcome in the construction industry’s implementation of Smart Contracts. This includes payment transactions involving cryptocurrencies, which are not widely accepted in the construction industry at the moment, especially in Indonesia. However, with the advancement of the blockchain, it is no longer necessary for blockchain applications in construction contracts to be based on cryptocurrency. To facilitate the adoption of Smart Contracts in the construction industry, the terms of traditional standard contracts must be simplified to conform to the coding requirements of Smart Contracts. It is the process of interpreting complex contractual terms and converting them into language appropriate for simple contract terms, most notably time and monetary claims such as time extensions, retention payments and funds, and liquidated damages. However, even if Smart Contracts are used, it is suggested that traditional standard contract forms are still required as part of the binding contract document. While Smart Contracts cannot completely replace traditional construction contracts, they can act as an enforcement system, requiring construction actors to adhere to legally binding documents. Thus, the immutable distributed ledger used in the smart contract system

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will serve as critical evidence in the event of construction disputes, thereby increasing the efficiency of construction dispute resolution. With Smart Contracts, construction stakeholders can save time and money by avoiding the need to involve professional legal personnel in resolving disputes. In short, incorporating Blockchain Technology into construction contracts will increase the level of trust between the contract’s parties and facilitate the execution of the contract. Figure 2 describes the relationship between the issues in construction contracts, recommendations by previous researchers (Table 2) and how Smart Contract can be used.

Fig. 2. Issues in construction contracts, recommendations and solutions using Smart Contract

Nowadays, no companies in Indonesia have officially used a smart contract-based blockchain system to implement their work contracts. It is because Smart Contracts are still considered very new technology, and there is no clear law to legalize this system in Indonesia. However, many studies in Indonesia have begun to focus on the application of Smart Contracts in various fields, such as: 1. Examination of the legality of implementing Smart Contracts in agricultural insurance by Adhijoso (2019), 2. Traceability of capture fisheries products by Afrianto et al. (2020) 3. Use of Smart Contracts in E-Commerce by Ismanto et al. (2019) and Firdaus (2020) 4. Management of official documents for government services by Nugraha et al. (2019) Although many researchers have focused on the application of Smart Contracts in their field of expertise in Indonesia, it is still very rare that it can even be said that there has been no research on the implementation and readiness of Smart Contracts in the Indonesian construction industry. It is very unfortunate considering that the function of Smart Contracts makes a big contribution as a solution to contract management problems that often occur in Indonesian construction industry.

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In terms of readiness, Indonesian Government (2016) has issued the rules regarding Electronic Information and Transactions in Article 1 paragraph 17 of Law no. 11 of 2008, which was later revised into Law no. 19 of 2016, which reads, “Electronic contract is an agreement of the parties made through an electronic system.” The electronic system in question is a series of electronic procedures that prepare, collect, process, analyze, store, announce, transmit, and disseminate information electronically. Based on this definition, a smart contract can be considered an electronic contract to carry out an electronic transaction to bind the parties involved in an electronic system legally. However, according to Wardani and Afriansyah (2020), the legal model of the Electronic Information and Transaction Law (UU ITE) does not explicitly explain the form of the electronic contract itself. It creates a difference in knowledge and confusion about the meaning of an electronic agreement. They also emphasized that the rules governing electronic contracts have not been regulated in their entirety in the UU ITE, so there are many pros and cons in some circles. It can be one of the factors why there are no official companies in Indonesia, including the construction industry, that implement Smart Contracts in their work contracts. Apart from the legal aspect, knowledge and understanding of the Indonesian people, especially construction industry stakeholders, about blockchain and Smart Contracts is very much needed. Blockchain Technology based on Smart Contract is today’s advanced technology, so the readiness for Indonesian human resources to manage the technology needs to be considered.

4 Conclusions Smart Contract-based Blockchain Technology requires the readiness of adequate resources and knowledge to be applied in the world of construction management. Smart contracts are believed to resolve many problems that commonly occur in the construction industry, including in Indonesia. However, at this time, Smart Contracts have not been applied in the Indonesian construction industry. Even though their applicability is considerable. The reason is that smart contracts are still considered a new technology. Thus, many construction workers remain unaware of or do not fully understand smart contracts. Consequently, Indonesian construction workers need to learn more about this technology. Furthermore, Indonesian regulations are another reason the technology cannot be adopted yet. Although Indonesia has an Electronic Information and Transaction Law (UU ITE) that discusses electronic contracts, it does not clearly define electronic contracts, so it cannot accommodate Smart Contracts. It might also be the reason why no Indonesian company uses smart contracts.

5 Future Research After focusing on the literature review, future research will continue to the survey and interview stage about the readiness to implement blockchain-based Smart Contracts in the construction industry in Indonesia. It will be conducted to explore information about

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what the Indonesian construction industry needs to implement this advanced technology to improve the industry. Given that there are still many shortcomings regarding the resources and knowledge of the Indonesian people, especially stakeholders in the construction industry, the survey and interviews conducted will focus on the readiness of existing resources in Indonesia to implement Smart Contracts in contract management. Acknowledgements. This study was supported by the Collaborative Education Program under the ASEAN University Network/Southeast Asia Engineering Education Development Network (AUN-SEED/Net).

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Wang, J., Wu, P., Wang, X., Shou, W.: The outlook of blockchain technology for construction engineering management. Front. Eng. Manage. pp. 67–75 (2017) Wang, X., Ye, K., Arditi, D.: Embodied cost of collusive bidding: evidence from China’s construction industry. J. Constr. Eng. Manag. 147(6), 04021037 (2021) Wardani, N.K., Afriansyah, A.: Indonesian legal challenges regarding electronic contracts in international trade. Advances in Economics, Business and Management Research 130 (2020) Wohrer, M., Zdun, U.: Smart contracts: security patterns in the ethereum ecosystem and solidity. In: 2018 International Workshop on Blockchain Oriented Software Engineering (IWBOSE). IEEE, pp. 2–8 (2018) Xu, X., Pautasso, C., Zhu, L., Gramoli, V., Ponomarev, A., Tran, A.B., Chen, S.: The blockchain as a software connector. In: 2016 13th Working IEEE/IFIP Conference on Software Architecture (WICSA). IEEE, pp. 182–191 (2016) Yang, R., et al.: Public and private blockchain in construction business process and information integration. Autom. Constr. 118, 103276 (2020) Yu, A.T., Shen, Q., Kelly, J., Hunter, K.: Investigation of critical success factors in construction project briefing by way of content analysis. J. Constr. Eng. Manag. 132(11), 1178–1186 (2006) Zhang, Y., Wang, T., Yuen, K.V.: Construction site information decentralized management using blockchain and smart contracts. Comput.-Aided Civ. Infrastruct. Eng. (2021) Zheng, R., Jiang, J., Hao, X., Ren, W., Xiong, F., Ren, Y.: bcBIM: a blockchain-based big data model for BIM modification audit and provenance in mobile cloud. Mathematical Problems in Engineering 2019 (2019)

Construction Process Simulation Facing Digital Twin M. S. Dong1 , B. Yang1(B) , Y. L. Han2 , S. S. Jiang1 , and B. D. Liu1 1 College of Civil Engineering, Tongji University, Shanghai 200092, China

{2032594,yangbin,18538342,2010212}@tongji.edu.cn 2 Department of Construction Management and Real Estate, Tongji University,

Shanghai 200092, China [email protected]

Abstract. With the development of digitization, informatization, and intelligence in the field of civil engineering, a large amount of data has been accumulated during the construction process, forming engineering big data. How to effectively analyze the construction process by mining the relationship between these data to improve the management efficiency will be an important research direction. Graphs have natural advantages in describing complex association relationships between data and are widely used in the analysis and mining of association relationships. Therefore, this paper will make full use of the relationship between construction data based on the graph database to establish a process simulation framework facing digital twin. This framework consists of three parts. Firstly, data collection from BIM models, surveillance videos, and IoT networks is stored in a graph database. Secondly, the graph database will be imported into a discrete event simulation model to automatedly simulate the future construction process with the results written back to the graph database. This DES model will make full use of this data and its relationships to obtain a more reasonable result. Process information obtained from this DES, such as schedule information, resource information, cost information, will be directly connected to the components. Thirdly, the as-planned process, as-built construction process, and graph database-based process analysis results will be dynamically displayed on the digital twin model to support real-time decision-making. A case study is demonstrated to verify the proposed framework’s validity and feasibility. Keywords: Digital twin · Graph database · Discrete event simulation

1 Introduction Digital construction is the product of the deep integration of modern information technology and modern construction technology. Digital construction utilizes the integration of BIM technology (Eastman et al. 2011), digital twin (Kan and Anumba 2019), computer vision (Zhang et al. 2021) and information communication technology (Liu et al. 2021) to realize the comprehensive IoT and information fusion of construction projects. With the promotion of digital construction, the amount of construction data accumulated © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 264–283, 2023. https://doi.org/10.1007/978-981-19-7331-4_22

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in the process of digital construction will increase exponentially, forming engineering big data. A large amount of accumulated data includes the details of the model and the construction process. Through in-depth analysis and mining of the construction data, it is a problem worth exploring to further improve the application value of the construction data and provide the necessary support for the construction process management. Graphs have natural advantages in describing complex association relationships between data and are widely used in the analysis and mining of association relationships. Therefore, this paper will make full use of the relationship between construction data based on the graph database to establish a process simulation framework facing digital twin. With the objective of reducing resource idling time and improving site productivity, construction simulations have been applied to construction modeling processes in order to investigate time conflicts in allocating the utilization of resources (Wang et al. 2014). However, construction simulation’s practical applications remain two main questions. Firstly, although DES (discrete Event Simulation) method is widely applied in construction process simulation and has its advantages, its practical applications in construction are still limited. The large amount of input data required to build a simulation model has been one of the reasons that limit the application of DES in the construction industry (Abdelmegid et al. 2020). Manual data entry is not only time-consuming and has a high error rate, but also does not make full use of a large amount of valuable data accumulated in the construction process, making the simulation of construction progress very inefficient (Shrestha and Behzadan 2018). Therefore, some methods have been proposed to facilitate the construction of DES models using existing data. Huang et al. (2011) used computer-aided design (CAD) data as the data sources of data-driven simulations. Xu et al. (2003) extracted product information from the CAD into the simulation model in order to calculate the amount of earthwork and enable the user to input the input data into the simulation model. Lu et al. (2009) integrated 4D CAD and 3D animation of operations simulation to facilitate the construction planning. Wang et al. (2014) developed a stand-alone module (Visual Basic application) to read quantity information from MS Access and feed it as input into a predefined simulation model to generate construction schedules. From previous studies, data-driven simulation provides a possible solution to speed up the definition of DES models. However, the current research only focused on particular data sources, and there is no systematic and formal framework to study how to use the engineering big data accumulated in the whole construction process to promote the efficiency of construction simulation. To solve this problem, this paper will store construction information collected from BIM models, surveillance videos, and IoT networks in graph database, which is used to drive the DES model. Secondly, since it is difficult to effectively transfer the BIM model and the data collected on the construction site to the simulation model, the digital twin model cannot adjust the simulation results of the construction process in real-time, which does not meet the real-time needs of digital twins. This can be difficult because BIM is not compatible with IoT integration (Howell and Rezgui 2018), particularly due to a lack of integration with a semantic web paradigm (Boje et al. 2020). Existing construction knowledge representations such as the IFC Ontology lack description of manufacturing processes and how such data should be linked between construction products and the manufacturing process (Kalemi et al. 2020). The promising new developments for ontological

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approaches and semantic web (Wagner and Ruppel 2019) emphasize representation of product knowledge but do not attempt to include data from manufacturing. There is a need to formulate the requirements for a machine-readable language that can be used to pass specific manufacturing data from the production twin to the product twin. Without this, it becomes very difficult to retrieve any specific manufacturing-related data from final products in a true digital twin (Boje et al. 2020). Therefore, in order to solve these two problems, this paper will establish a construction schedule simulation framework based on graph database facing digital twin. The framework will help to carry out more accurate and efficient simulation of construction process by mining, transferring and applying a large amount of construction data accumulated in the construction process, thus laying a methodological foundation for the development of digital twin in the construction process.

2 Framework This paper developed a graph database-based framework to improve construction simulation. This framework consists of three parts, namely, data layer, logic layer, and presentation layer, as Fig. 1 illustrates. Firstly, the data layer collects data from BIM models, surveillance videos, and IoT networks is stored in a graph database. Secondly, logic layer will execute the construction process simulation. The graph database will be imported into a discrete event simulation model to automatedly simulate the future construction process with the results written back to the graph database. This DES model will make full use of this data and its relationships to obtain a more reasonable result. Process information obtained from this DES, such as schedule information, resource information, cost information, will be directly connected to the components. Thirdly, the as-planned process, as-built construction process, and graph database-based process analysis results will be dynamically displayed on the digital twin model to support real-time decision-making. 2.1 Data Layer 2.1.1 BIM Model’s Data For BIM data, most of the problems related to data storage and interoperation are solved by standardized file exchange formats, the most widely used of which is the IFC (Industry Foundation Classes) standard (Volk et al. 2014) published by buildingSMART. The latest official version of the IFC standard is IFC4 ADD2TC1 (ISO 16739-1:2018) (buildingSmart 2021), which is also the version of the IFC standard used in this paper. Although the IFC standard is widely used in various scenarios, IFC files are difficult to be used directly for big data mining (Pan and Zhang 2021), since they are pure texts. Therefore, how to map the IFC standard to a data format that can be more easily stored, updated, and analyzed is the core issue to effectively enhance the digitization of construction. A graph database is a NoSQL database that performs semantic queries in a graph structure and uses vertices, edges and attributes to represent and store data. Studies have pointed out that graphs are very efficient for representing and describing complex relationships

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Fig. 1. Framework

between building elements and data in BIM (Isaac et al. 2013), and transforming information models based on IFC standards into graph databases can greatly improve the efficiency of searching and analyzing related data in BIM models (Ismail et al. 2017). Therefore, graph data can better store the relationships between entities compared with other non-relational databases, thus facilitating the mining of relational information in IFC, which is not possible with other non-relational databases. Hence, this paper will establish an automatically mapping mechanism to map IFC information model to a graph database to lay the digital foundation for construction data mining. In order to meet the need of relationship mining among IFC-based construction information, the method architecture maps the IFC-based construction management information model described in the previous section to the graph database Neo4j (Yang et al. 2021). The graph database Neo4j is a Java-based implementation of NOSQL database, which is a kind of non-relational database. In this paper, the IFC architecture is mapped into Neo4j by establishing the mapping rules from IFC to Neo4j, and the mapping process is implemented through Java. A complete IFC data model consists of entities, attribute sets, quantity sets, types, functions and rules. Function set rules in the IFC model are used to calculate the attribute values of entities, to control the constraints to be satisfied by the entity attribute values, and to verify the correctness of the model, etc. Their content itself is included in the creation process of the IFC file, while for the established IFC file does not include the content of the function and rule entities. Therefore, the functions and rules are not parsed during the parsing of the IFC file, and they are not mapped to Neo4j. The mapping relationships for the remaining four data types are shown in Table 1. The result of mapping construction process’ information to graph database is as Fig. 2 illustrates.

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IFC

Data type

Java

Neo4j

Entity

IfcObjectDefinition’s subclass entities

Class

node

IfcRelationship’s subclass entities

Class

relationship

Property set and quantity set

IfcProertyDefinition’s subclass entities

Class

node

Type

BINARY

int

int

BOOLEAN

boolean

boolean

DOUBLE

double

float

INTEGER

int

int

LOGICAL

boolean

boolean

NUMBER

double

float

LIST

ArrayList

list

SET

ArrayList

list

STRING

String

string

ENUM

String

string

SELECT

String

string

Fig. 2. Result of mapping construction process information’s IFC model to graph database

2.1.2 Surveillance Videos’ Data Information about the lifting and installation of components at the construction site will be obtained by computer vision-based approach. Take the installation of prefabricated walls as an example. In this paper, Mask-RCNN and DeepSORT algorithms are combined to realize object detection, instance segmentation, and multiple-object tracking to collect precast walls’ location and temporal information from the surveillance videos recording the construction phase. Status information identified and collected is then sent to a corresponding component’s node in Neo4j to store this wall component’ installation information.

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2.2 Logic Layer 2.2.1 Construction Process Simulation The construction process simulation’s realization is divided into DES model’s establishment and simulation parameters’ input. Firstly, the DES model is established on the Matlab/Simulink-SimEvents. The tasks to be simulated in the graph database are extracted by the entity generator in Matlab and then routed to the execution process of different tasks through the route converter. The entity generation module consists of entity generator, entity storage pool, gate and queue as shown in Fig. 3. The entity generator extracts the tasks to be simulated in the graph database. When all the entities are generated in the system, the “Enable Gate” opens and the entities enter the queue from the storage pool and then leave the entity generation module and enter the subsequent activity processes through the routing converter. The tower resources are competing resources, i.e., when the tower resources are occupied by one entity, the activities of the remaining entities will be delayed, and only when the tower resources are released can the activities of the delayed entities proceed. In order to accurately simulate the occupancy of tower crane resources by component lifting activities, the “Resource Pool” module is used here, as shown in Fig. 4. When the lifting component entity passes through the “gate” and enters the “resource getter”, the component gets the crane resources from the “resource pool”, and after a period of occupation, it is released through the “resource releaser”. After a period of occupation, the crane resources are released through the “Resource Releaser” and returned to the “Resource Pool”. When the lifting of the components is finished, the component entities enter the installation module and are installed by the construction team.

Fig. 3. Entity generator module

Secondly, the simulation parameters’ input is the graph database obtained on the data layer. By using the association relationship of components in the graph database, more information associated with the components can be used as parameters to drive discrete event simulation, thus facilitating the simulation of construction process. The input parameters are divided into parameters of components to be simulated and parameters of tower crane. (1) Parameters of components to be simulated. For example, the prefabricated wall and its geometric coordinates are stored in the entity IfcWall and IfcCartesianPoint respectively in IFC. Therefore, it is more difficult to use the coordinates of the wall as the parameters of the simulation in the actual discrete

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Fig. 4. Components’ lifting module

event simulation. However, through the connection of association relations in the graph data, the coordinates of the plate can be obtained by looking up the relation [r1:ObjectPlacement]→[r2:RelativePlacement]→[r3:Location], which can be used as the input parameter of the component when performing discrete event simulation. (2) Parameters of tower crane. Since it’s hard to input the accurate tower crane’s parameter. In this paper, we will use the data on graph database to calculate the tower crane’s parameters in real time according to Formula (1)–(8) (Wu et al. 2020) and update them into the DES model.     i (1) = max Tvki , Thik + β × min Tvki , Thik + Tl + Tu Tk,m,n Tvki

=

  i Dz − Sz i  n m Vvki

    Thik = max T αki , T ωki + α × min T αki , T ωki T αki

=

  i   ρ D − ρ S i  n

m

V αki   2 2   2  ρ Dni + ρ Smi − lm,n 1 i     × arccos T ωk = 2ρ Dni ρ Smi V ωki       i − TCx i 2 + Sy i − TCy i 2 Sxm ρ Smi = m k k ρ



Dni



=

i = lm,n

 2  2 Dxni − TCxki + Dyni − TCyki



i Dxni − Sxm

2

  i 2 + Dyni − Sym

Among them: i = Tl + Thik + Tu = T αki + T ωki + Tl + Tu Tk,m,n

(2) (3) (4)

(5) (6) (7) (8)

Construction Process Simulation Facing Digital Twin

=

  i   ρ D − ρ S i  n m V αki

  TCxi , TCyi , TCz i  i k i ki k Sx , Sym , Szm  mi  Dxn , Dyni , Dzni i Tkmn Thik T αki T ωki Tvki Vvki Tl TU α β

271

  2 2   2  ρ Dni + ρ Smi − lm,n 1     + × arccos + Tl + Tu 2ρ Dni ρ Smi V ωki

the location of tower crane k on the i-th day the location of supply point m on the i-th day the location of demand point n on the i-th day one lifting time of tower crane from supply point m to demand point n on the i-th day horizontal movement time of the tower crane hook radial movement time of the tower crane trolley the slewing movement time of the tower crane jib vertical movement time of the tower crane hook the vertical velocity of the tower crane hook loading time unloading time the coordination degree of the hook movement in the radial and slewing directions in the horizontal plane the coordination degree of the hook movement in the horizontal and vertical planes.

Therefore, since we have obtained the coordinates of the components and the lifting time, we can use the least squares method to calculate the key parameters of the tower crane lifting, namely, V αki V ωki Tl, as formula (9) illustrates. These parameters are calculated in the graph database and used as input parameters for the tower crane in the DES model.

 ⎛ ⎞   ρ(D1i )2 +ρ(S1i )2 −(l1,1 )2 ρ(Di ) − ρ(S i ) arccos 1 1 1 ⎜ ⎟ 2ρ(D1i )ρ(S1i )

 ⎜ ⎟ i i 2 2 2  ⎜  ⎟⎛ ⎞ ρ(D2 ) +ρ(S2 ) −(l2,2 ) 1 ⎜ ρ(Di ) − ρ(S i ) ⎟ arccos 1 2 2 ⎜ ⎟ V αi 2ρ(D2i )ρ(S2i ) ⎜ ⎟⎜ k ⎟ ⎜ .. .. .. ⎟⎜ 1 i ⎟ ⎜ ⎟⎝ ⎠ . . . ⎜

i  ⎟ V ωk 2 +ρ(S i 2 −(l 2 ⎜ ⎟  Tl ρ(D ) ) ) n−1,m−1 n−1 m−1 ⎜ ρ(Di ) − ρ(S i ) arccos 1⎟ i i n−1 m−1 ⎜ ⎟ 2ρ(Dn−1 )ρ(Sm−1 ) ⎝  ⎠    ρ(Dni )2 +ρ(Smi )2 −(ln,m )2 ρ(Di ) − ρ(S i ) arccos 1 n m 2ρ(Dni )ρ(Smi ) ⎛ ⎞ i T1,1,1 − Tu1 ⎜ ⎟ i T ⎜ ⎟ 2,2,2 − Tu2 ⎜ ⎟ .. ⎟ (9) =⎜ . ⎜ ⎟ ⎜ i ⎟ ⎝ Tn−1,n−1,n−1 − Tun−1 ⎠ i Tn,n,n − Tun

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2.2.2 Schedule Network Analysis The schedule network of prefabricated buildings’ construction process can be automatically obtained after twinning the construction management information into the graph database without any manual work. Furthermore, this paper develops a graph-based algorithm to analyze the schedule network. The necessity to analyze the schedule network is reflected in two aspects. Firstly, the analysis of schedule networks can identify the tasks’ centrality in the schedule network, which can help managers adjust the resources’ allocation. Secondly, the parameters of schedule networks are significant in the Graph Neural Network (GNN), which will benefit further work in machine learning or deep learning. The algorithm calculates three parameters in the schedule network. Degree Centrality (DC): The DC is the total number of edges directed to a node and edges directed to others. The degree centrality of the node reflects the centrality of the construction task to other tasks. The greater degree centrality means that the delay of this node is more likely to cause the delay of other tasks in the construction network plan, which means the higher the risk caused by the delay of this task. Closeness Centrality (CC): The CC of a node is the average length of the shortest path between the node and all other nodes in the graph, which quantifies how close the node is to others. Closeness centrality reflects the difficulty of intercommunication between nodes. The larger the closeness centrality, the stronger the interaction between the construction tasks in the schedule network. Betweenness Centrality (BC): BC is the number of shortest paths that pass through the node and quantifies the number of times the node acts as a bridge along the shortest path between two other nodes. Betweenness centrality reflects the pivotal role of nodes in the network. The larger the betweenness centrality, the greater the construction task’s control effect on the schedule network’s other tasks. The calculation methods of degree centrality DC(x), closeness centrality CC(x), and betweenness centrality BC(x)are represented as follows: DC(x) = [Count(Ek |StartNode(Ek ) = x) + Count(Ek |EndNode(Ek ) = x)]/(N − 1) (10)  d (y, x) (11) CC(x) = 1/ y

BC(x) =

 y=x=z

d (y, x)

(12)

where x, y, z are different nodes, d (y, x) is the distance between nodes x and y, σyz (x) is the total number of shortest paths from node y to node z, σyz (x) is the number of those paths that pass through node x, and N is the total number of nodes in this network. 2.2.3 Delay Analysis In addition to the automatic analysis of the schedule network, automatic delay analysis plays a critical role in the graph database-based information model. The analysis of delays includes two parts. The first part is to calculate the project schedule network’s critical path and store the critical path’s information in the extended IFC schema, which can be automatically complete by the graph-based algorithm. The graph-based algorithm

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proposed in this paper calculates the critical path by finding the path that has the longest duration. The IfcTask entity identified in the critical path will be associated with the extended property set Pset_CriticalPath to store the critical path’s information. Furthermore, project managers are interested in the following properties of each construction task: Earliest Finish Time (EF), Earliest Start Time (ES), Latest Start Time (LS), Latest Finish Time (LF), Slack Time. These important properties’ calculation methods are as formula (13)–(17) illustrate. These insightful properties will also be easily calculated through the graph and then added to the graph, which is infinitely better than manually typing functions into several Excel cells. EFj = ESj + durationj

(13)

  ESj = max EFj−1

(14)

LSj = LFj − durationj

(15)

  LFj−1 = min LSj

(16)

EFj = LSj − ESj

(17)

The second part is to collect the construction information and analyze the delay. When the construction task is identified as its start time later than the last start time, its finish time later than the last finish time, or its delay time longer than the slack time, the IfcTask is associated with the extended property set Pset_DelayAnalysis. The result of the delay analysis is then be stored in the extended IFC schema, facilitating the managers to master the project process. Furthermore, the programming developed by this paper will also analyze the impact on the overall construction duration due to the delayed task based on whether the delayed task occurs on the critical path or whether the duration of the delay exceeds the slack time of the task, thus assisting managers in their decision making. 2.3 Presentation Layer The results of the logic layer will be displayed in the presentation layer, which is also used as the digital twin model’s presentation. In the process of making a schedule, the visualization of the schedules allows the project team to check the schedule for completeness and ensure that sequencing and constructability requirements are satisfied. During the actual construction, visualization of the construction process will present the delay tasks by extracting delay information and marking different colors, which will facilitate the project team’s control of the delay risks. In this section, Navisworks 2021 are used to visualize the digital twin model of construction process. This paper develops a plug-in for Navisworks to extract and display simulation results, process network analysis results, and delay analysis results stored in the graph database.

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3 Case Study The graph database-based framework is validated through an engineering case of prefabricated buildings. In this case study, the comprehensive process of construction process simulation is executed. The results illustrate that the framework proposed in this paper will help to carry out more accurate and efficient simulation of construction process by storing, mining, and applying a large amount of construction data accumulated in the construction process, thus laying a methodological foundation for the development of digital twin in the construction process. 3.1 Graph Database-Based Construction Process Simulation The specific process of conducting construction schedule discrete simulation is as follows. First, the construction information is stored in the graph database. According to the automatic mapping method established in the previous section, a complete construction information model based on graph database can be obtained. As shown in Fig. 5. The nodes with different colors in the figure represent different entity types, the edges between two nodes represent the relationship between two entities, and the properties of the entities are saved as the attributes of the corresponding nodes.

Fig. 5. Construction information model based on graph database

Next, the graph databased will drive the DES model in Matlab. The main purpose is to import the information in Neo4j into the discrete event simulation model created in Matlab. On the one hand, in this paper, the built-in function neo4j(urlm username, password) in Matlab is used to create a connection object Neo4jConnect to the Neo4j

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graph database and to retrieve the information in the graph data through this object. On the other hand, a model for discrete event simulation was created in Matlab using the Simulink toolbox. The construction process of the standard floor of the assembled building structure is shown in Fig. 6. Due to the large number of construction activities of the whole prefabricated building and the large volume of the simulation model, the task module, consisting of prefabricated wall lifting activities, internal wall column reinforcement lifting activities and internal and external wall formwork lifting activities. The discrete event simulation model in Matlab is shown in Fig. 6.

Fig. 6. Matlab model of discrete event simulation

Thirdly, tower crane parameters are inputted in the DES model. The tower crane model used at the construction site is STT373A. The construction data obtained from the construction site by means of computer vision are shown in Table 2, including the i , loading time Tl , installation time Tu , vertical transportation time total lifting time Tk,m,n Tv , and horizontal transportation time Th . Table 2. Lifting time obtained from construction site video based on computer vision method i The location of demand point n The location of supply point m Tk,m,n Tl

Tu

Tv

Th

(2100,2200,36800)

(− 2050,35677,0)

1247

271 592 272 112

(11125,2300,36800)

(− 2050,35677,0)

1076

243 454 271 108

(2007,2300,36800)

(− 2050,35677,0)

1110

189 532 273 116

(2300, 11150,36800)

(− 2050,35677,0)

1251

273 604 271 103

(2000,28200,36800)

(− 2050,35677,0)

1283

290 637 274 82

(11125,28100,36800)

(− 2050,35677,0)

1203

277 578 275 73

…

…

…

…

(20075,28100,36800)

(− 2050,35677,0)

1034

263 410 272 89

…

…

…

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The statistics were fitted in Matlab, where the loading time Tl and unloading time Tu obeyed the normal distribution, as shown in Fig. 7. The distribution expression of the fitted results for the loading time Tl is Tl ∼ Normal(269.3, 11.5), and the distribution expression of the fitted results for the unloading time Tu is Tu ∼ Normal(543.9, 15.7).

Fig. 7. Component loading time and unloading time fitting results (a) component loading time fitting results (b) component unloading time fitting results

Since the vertical movement time Tv and horizontal movement time Th are known, the tower crane trolley radial movement speed V αki = 666.6667 mm/s, the crane boom slewing speed V ωki = 0.1716 rad/s, and the hook vertical movement speed Vvki = 7357.6 mm/s can been calculated according to the formula (9). ⎛ ⎜ ⎜ ⎝

1 V αki 1 V ωki 1 Vvki

⎞

⎛ ⎟ ⎟=⎝ ⎠

⎞ 0.0015 (mm/s)−1 ⎠ 5.8278 (rad/s)−1 1.359 × 10−4 (mm/s)−1

⎞ ⎛ ⎞ 666.6667 mm/s V αki ⎝ V ωi ⎠ = ⎝ 0.1716 rad/s ⎠ k Vvki 7357.6 mm/s ⎛

Finally, the discrete event simulation is performed in Matlab. The graph database uses the connection object Neo4jConnect to pass the construction task to be simulated to Matlab, and the component type and component coordinates associated with the construction task are input to the simulation system as the input parameters of the simulation, so that the simulation results are calculated. Finally, the simulation results are rewritten into the diagram database. Take the actual project of exterior wall lifting as an example, the simulation results are shown in Fig. 8. The input is the prefabricated wall entity and its associated coordinate information. The output is the planned construction time of the prefabricated wall and the planned cost and consumed resources.

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Fig. 8. Result of discrete event simulation

3.2 Analyzing the Simulation Results 1. Schedule Network Analysis. This paper analyzes the complex schedule network of this engineering case. The degree centrality, closeness centrality, and betweenness centrality of this schedule network are calculated. The top 10 construction tasks in numerical value are shown in Table 3. Table 3. Top 10 tasks based on different centrality measures Tasks’ name

Degree centrality

Tasks’ name

Closeness centrality

Tasks’ name

Betweenness centrality

Task74

0.40000000

Task74

0.479233227

Task84

2712.615384615384

Task81

0.38888889

Task77

0.478214670

Task74

2702.000000000001

Task67

0.33333333

Task71

0.477200424

Task81

2668.384615384646

Task64

0.30000000

Task81

0.475687104

Task64

2624.153846153846

Task71

0.30000000

Task64

0.473684211

Task91

2624.153846153846

Task84

0.30000000

Task87

0.469728601

Task87

2613.538461538462

Task67

0.27777778

Task67

0.465838509

Task71

2613.538461538461

Task61

0.24444444

Task84

0.463917526

Task77

2592.307692307692

Task77

0.24444444

Task61

0.458248473

Task67

2561.435478256821

Task72

0.20000000

Task72

0.443240123

Task64

2487.346782493274

From the calculation results, it can be seen that Task74 is ranked in the top of all three parameters, which indicates the important position of Task74 in the whole progress construction network. Task74 represents the precast wall lifting task, and the

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vertical structure of this case is a precast wall, which has more lifting works than other components and materials, and occupies more tower crane resources in the construction process. Therefore, if this construction task is delayed, it will cause a large number of tasks in the schedule network to be delayed, which brings a great risk to the delay of the whole construction schedule. With this information, the manager should pay more attention to Task74 to avoid the delay of this task. This critical information will be stored in the extended attribute set Pset_ScheduleNetworkAnalysis and associated with the corresponding IfcTask entity, as shown in Fig. 9.

Fig. 9. Task74 and its related construction information

2. Delay Analysis. Automated construction delay analysis is an important application of the graph database-based framework. The construction schedule analysis consists of two parts. The first part is to calculate the critical path of the project schedule network and store the information of the critical path in the extended IFC attribute set. This part is a graph-based algorithm to automatically calculate the critical information of construction tasks. First, the parameters of the construction tasks represented by each node in the schedule network graph are calculated based on the correlation between the construction tasks in the project schedule network diagram: Earliest Start (ES), Earliest Finish (EF), Late Start (LS), Late Finish (LF), and slack time (FreeFloat, FF). These calculated values will be updated to the EarlyStart, EarlyFinish, LateStart, LateFinish, TotalFloat attributes of the corresponding nodes of IfcTaskTime entity in the graph database, respectively, as in Fig. 9. Second, the graph-based traversal algorithm is used to traverse all paths between the start and end points of the construction tasks in the project schedule network diagram, so as to find the path with the longest construction process duration, which is the critical path of the project. The calculated IfcTask entity on the critical path will be associated with the extended attribute set Pset_CriticalPath to store the information

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of the critical path, as shown in Fig. 10, which is the calculated critical path from the graphical database based information model.

Fig. 10. The critical path calculated from graph database-based information model

The second part is to analyze the delay of the progress. When a construction task is determined to have its start time later than the last start time, its end time later than the last end time, or its delay time longer than the slack time, IfcTask will be associated with the extended attribute set Pset_DelayAnalysis. The results of the delay analysis will be stored in the extended IFC schema, making it easy for managers to keep track of the project’s progress. In addition, delays resulting in changes in the attribute values of the node represented by the construction task will be placed in the entire construction network graph for analysis. The graph-based algorithm will analyze the impact of the change in the attributes of that node on the whole graph. That is, when there is a delay in a construction task, the impact of the delay on the construction task will first be analyzed, i.e., whether the delay exceeds the slack time. If the delay time exceeds the slack time, it will lead to the extension of the whole construction cycle, and the parameters of each construction task in the construction network diagram and the construction cycle will be recalculated and compared with the original construction cycle to get the extension of the overall construction cycle. The impact of the delayed tasks on the overall construction duration will be analyzed to help managers in their decision making. In fact, although the simulation object in this paper is components, if the simulation time of each component is compared with the actual construction time, it may be possible to analyze the schedule deviation for each component. This would result in a large number of calculations, but at the same time would have less practical significance for the project. Therefore, in this paper, we summarize the construction tasks of the same property and then compare the schedule delay analysis. For example, all the walls’ lifting tasks on the 8th floor is a summary task, and this summary task is used as the basic scale of analysis for the schedule delay analysis. In this case, monitoring equipment is installed at the construction site, so the actual construction time can be obtained from the video of the construction site as shown in Fig. 11.

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Fig. 11. Construction task time collected at the construction site

The simulation time and actual time of prefabricated walls construction schedule are shown in Tables 4 and 5, respectively. From the table, we can see that: (1) the wall lifting sequence of the simulation is different from the lifting sequence of the wall in the actual construction, so it is more reasonable to summarize the construction tasks and then analyze them than to analyze them at the granularity of the components. (2) The planned duration of the construction of the components obtained from the simulation is similar to the actual duration of the same components in the actual construction, which proves that the simulation results are reasonable. (3) The schedule start time of the prefabricated walls construction obtained from the simulation is 2021-3-21T08:10:00, and the schedule finish time is 2021-3-21T10:49:06, which lasts for 2 h, 39 min and 6 s in total. However, in the actual construction, the start time of the task was 2021-3-21T08:10:00, which was the same as the start time of the simulation, but the actual end time was 20213-22T16:48:25, which lasted a total of 1 day, 8 h, 38 min and 25 s. Therefore, the prefabricated facade construction task was delayed. Also, since the prefabricated wall task (Task73) is located on the critical path of the construction process, it is known that the delay of this task causes a delay of the total construction schedule by 1 day, 8 h, 38 min, and 25 s. (4) According to the records at the construction site, it is known that the main reason for the occurrence of this delay is that the precast wall elements 2351263, 2351247, 2351245, and 2351275 were not lifted as planned because they were not yet in the site at the time of lifting resulting in the elements not being lifted as planned.

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Table 4. Simulation time of prefabricated wall’s construction schedule The Walls’ number Schedule start time

Schedule finish time

Schedule duration

2351275

2021-3-21T08:10:00 2021-3-21T08:29:40

P0Y0M0DT00H19M40S

2351273

2021-3-21T08:29:40 2021-3-21T08:49:28

P0Y0M0DT00H19M48S

2351271

2021-3-21T08:49:28 2021-3-21T09:08:58

P0Y0M0DT00H19M30S

2351269

2021-3-21T09:08:58 2021-3-21T09:30:11

P0Y0M0DT00H21M13S

2351263

2021-3-21T09:30:11 2021-3-21T09:47:42

P0Y0M0DT00H17M31S

2351249

2021-3-21T09:47:42 2021-3-21T10:09:36

P0Y0M0DT00H21M54S

2351247

2021-3-21T10:09:36 2021–3-21T10:29:43 P0Y0M0DT00H20M07S

2351245

2021-3-21T10:29:43 2021-3-21T10:49:06

P0Y0M0DT00H19M23S

Total

2021-3-21T08:10:00 2021-3-21T10:49:06

P0Y0M0DT02H39M06S

Table 5. Actual time of prefabricated Wall’s construction schedule The Walls’ number Actual start time

Actual finish time

Actual duration

2351275

2021-3-21T08:10:00 2021-3-21T08:30:47

P0Y0M0DT00H20M47S

2351249

2021-3-21T08:30:47 2021-3-21T08:48:43

P0Y0M0DT00H17M56S

2351263

2021-3-21T08:48:43 2021-3-21T09:07:13

P0Y0M0DT00H18M30S

2351271

2021-3-21T09:07:13 2021–3-21T09:28:04 P0Y0M0DT00H20M51S

2351263

2021-3-22T15:20:04 2021-3-22T15:41:45

P0Y0M0DT00H21M41S

2351247

2021-3-22T15:41:45 2021-3-22T16:01:48

P0Y0M0DT00H20M03S

2351245

2021-3-22T16:01:48 2021-3-22T16:31:11

P0Y0M0DT00H29M23S

2351275

2021-3-22T16:31:11 2021-3-22T16:48:25

P0Y0M0DT00H17M14S

Total

2021-3-21T08:10:00 2021-3-22T16:48:25

P0Y0M1DT08H38M25S

3.3 Presenting the Simulation Results Facing Digital Twin Based on the above applications, the results of construction process simulation are finally obtained. As mentioned before, the construction information is extracted from the graph database-based construction management information model obtained in the previous steps to Navisworks via developed plug-in. The construction information includes tasks’ time information and corresponding cost information, schedule network analysis information, critical path information, and delay information. The screenshot of the animation in Navisworks is illustrated in Fig. 12. Through the construction simulation, the construction process, schedule network analysis information, delay analysis information, and critical path information can be known in real-time in the animation’s upper left corner. Additionally, the delay tasks also are identified with different colors. In this figure, the completed tasks are indicated by the color of the building facade, the unfinished tasks are indicated in green, and the red part indicates the delayed tasks.

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Fig. 12. Screenshot of animation in Navisworks.

4 Conclusions This paper makes full use of the relationship between construction data based on the graph database to establish a process simulation framework facing digital twin in order to solve two problems of construction simulation’s application: 1) The large amount of input data required to build a simulation model has been one of the reasons that limit the application of DES in the construction industry. 2) It is difficult to effectively transfer the BIM model and the data collected on the construction site to the simulation model, the digital twin model cannot adjust the simulation results of the construction process in real-time, which does not meet the real-time needs of digital twins. A case study verifies that this framework can help to carry out more accurate and efficient simulation of construction process by storing, mining, and applying a large amount of construction data on graph database. The simulation results are also analyzed by graphbased algorithms to analyze the schedule network and delay. Then the simulation results and the analysis results are presented in a digital twin model in real-time via a developed Navisworks-based plug-in. This framework lays a methodological foundation for the development of digital twin in the construction process. Acknowledgments. The study has been supported by the National Key R&D Program of China (Grant No. 2020YFD11004041).

References Abdelmegid, M.A., González, V.A., Poshdar, M., O’Sullivan, M., Walker, C.G., Ying, F.: Barriers to adopting simulation modelling in construction industry. Autom. Constr. 111, 103046 (2020). https://doi.org/10.1016/j.autcon.2019.103046 Boje, C., Guerriero, A., Kubicki, S., Rezgui, Y.: Towards a semantic construction digital twin: directions for future research. Autom. Constr. 114, 103179 (2020). https://doi.org/10.1016/j. autcon.2020.103179

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BuildingSmart: ISO 16739-1:2018 [WWW Document]. ISO (2021). URL https://www.iso.org/ cms/render/live/en/sites/isoorg/contents/data/standard/07/03/70303.html. Accessed 15 Mar 21 Eastman, C.M., Eastman, C., Teicholz, P., Sacks, R., Liston, K.: BIM Handbook: A Guide to Building Information Modeling for Owners, Managers, Designers, Engineers and Contractors. Wiley, Hoboken (2011) Huang, Y., Seck, M.D., Verbraeck, A.: From data to simulation models: component-based model generation with a data-driven approach. In: Jain, S., Creasey, R., Himmelspach, J. (eds.) Proceedings of the 2011 Winter Simulation Conference (WSC), pp. 3719–3729. IEEE, New York (2011) Isaac, S., Sadeghpour, F., Navon, R.: Analyzing building information using graph theory. In: ISARC Proceedings, pp. 1013–1020 (2013) Ismail, A., Nahar, A., Scherer, R., Dresden, T.: Application of graph databases and graph theory concepts for advanced analysing of BIM models based on IFC standard. Presented at the Proceedings of EGICE, pp. 161–173 (2017) Kalemi, E.V., Cheung, F., Tawil, A.-R., Patlakas, P., Alyania, K.: ifcOWL-DfMA a new ontology for the offsite construction domain. Presented at the Proceedings of the 8th Linked Data in Architecture and Construction Workshop, pp. 105–117 (2020) Kan, C., Anumba, C.J.: Digital Twins as the Next Phase of Cyber-Physical Systems in Construction, pp. 256–264 (2019). https://doi.org/10.1061/9780784482438.033 Liu, B., et al.: Review of optimization dynamically applied in the construction and the application potential of ICT. Sustainability 13, 5478 (2021). https://doi.org/10.3390/su13105478 Lu, M., Zhang, Y., Zhang, J., Hu, Z., Li, J.: Integration of four-dimensional computer-aided design modeling and three-dimensional animation of operations simulation for visualizing construction of the main stadium for the Beijing 2008 Olympic games. Can. J. Civ. Eng. 36, 473–479 (2009). https://doi.org/10.1139/L08-145 Pan, Y., Zhang, L.: A BIM-data mining integrated digital twin framework for advanced project management. Autom. Constr. 124, 103564 (2021). https://doi.org/10.1016/j.autcon. 2021.103564 Volk, R., Stengel, J., Schultmann, F.: Building information modeling (BIM) for existing buildings—literature review and future needs. Autom. Constr. 38, 109–127 (2014). https://doi.org/ 10.1016/j.autcon.2013.10.023 Wagner, A., Ruppel, U.: BPO: the building product ontology for assembled products. Presented at the Proceedings of the 7th Linked Data in Architecture and Construction Workshop, Lisbon, Portugal, pp. 106–119 (2019) Wang, W.C., Weng, S.W., Wang, S.H., Chen, C.Y.: Integrating building information models with construction process simulations for project scheduling support. Autom. Constr. 37, 68–80 (2014). https://doi.org/10.1016/j.autcon.2013.10.009 Wu, K., García de Soto, B., Zhang, F.: Spatio-temporal planning for tower cranes in construction projects with simulated annealing. Autom. Constr. 111, 103060 (2020). https://doi.org/10.1016/ j.autcon.2019.103060 Xu, J.F., AbouRizk, S.M., Fraser, C.: Integrated three-dimensional computer-aided design and discrete-event simulation models. Can. J. Civ. Eng. 30, 449–459 (2003). https://doi.org/10. 1139/L02-110 Yang, B., Dong, M., Wang, C., Liu, B., Wang, Z., Zhang, B.: IFC-based 4D construction management information model of prefabricated buildings and its application in graph database. Appl. Sci. 11, 7270 (2021). https://doi.org/10.3390/app11167270 Zhang, B., Yang, B., Wang, C., Wang, Z., Liu, B., Fang, T.: Computer vision-based construction process sensing for cyber-physical systems: a review. Sensors 21, 5468 (2021). https://doi.org/ 10.3390/s21165468

Establishment and Application of Multi-agent Simulation System Based on On-Site Construction Performers B. D. Liu, B. Yang(B) , Yilong Han, J. Z. Xiao, and M. S. Dong College of Civil Engineering, Tongji University, Shanghai 200092, China [email protected]

Abstract. Despite the literature on multiple decision agents in the construction process, questions regarding the on-site behaviour of construction performers and their interaction with the site remain unanswered. The study aims to simulate the construction process based on the behaviours of on-site construction performers. It first establishes a multi-dimensional simulation environment that includes construction procedures, work plane and component states. Then the Spatio-temporal attributes of the construction performs are encapsulated into the agents. And last, the interaction mechanism between the agents and the simulation environment is defined, that forming a multi-agent-based simulation system for the construction process. The proposed system is developed using Python code, which can be applied to simulate short-term construction process with agents modeling, environment modeling and agents’ strategies et al. information imported, and a real case study is carried out through this way. The case study shows that the result of the established system has passed the verification of the traditional discrete event simulation result. And a construction strategy testing proves that this system can help managers to test and quantify the impact of different construction strategies so as to choose the most effective one to execute. Keywords: Multi-agent-based simulation · Construction process · Discrete-event simulation · BIM

1 Introduction The construction process is a complex progressing system consisting of various procedures in which experiential management weighs more than scientific deduction. To describe a construction process with a complex hierarchical level, a widely used way is to break it down into a series of small procedures, such as the work break down structure (“Framework for a Generic Work Breakdown Structure for Building Projects | Emerald Insight” n.d.), which continuously decomposes it into sub-processes with pre-sub relationships, and a task network, or rather, the Petri net (Sawimey 1997) is formed. To study the possible time and resources consumption of tasks in the network, the discrete-event simulation (DES) method is adopted (Dori and Borrmann 2012)(Benevolenskiy et al. 2012). However, it is a simplified deduction of the actual construction process in which © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 284–304, 2023. https://doi.org/10.1007/978-981-19-7331-4_23

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the interaction of construction crews and individuals would have a minimal impact on this evolution (Ben-Alon and Sacks, n.d.). The multi-agent-based simulation is a powerful tool for studying the complex resource allocation in the concurrent construction procedures, which reorganizes the macro construction process in a buttom-up way, which insights into the complex system (Khodabandelu and Park 2021; Farshchian et al. 2017). However, current relevant studies are mainly focused on the large scale tasks such as the whole construction process of one floor (Ben-Alon and Sacks 2017), rather than the time-space behaviors of on-site actors when performing small scale-tasks, which is particularly important for on-site managers when managing short-term construction procedures. Without solving these problems, lean management is difficult to apply to on-site construction and can be combined with detailed construction data identified by emerging computer technologies. According to the motto of agent-based computational modeling: If you didn’t grow it, you didn’t explain its emergence (Epstein 1999). Therefore, a multi-agent system (MAS) that considers the detailed flow of construction resources (worker, materials and equipment) in the limited workspace is urgently needed to provide on-site managers with a reliable explanation and references of the entire construction process. This paper propose a novel MAS based on construction actors for space-time deduction of the construction process in floor plane. It first establishes a multidimensional simulation environment that includes work procedures, sites, and component states, then summarizes the spatio-temporal attributes of the construction actor and encapsulates them into the construction agents. And last, the interaction mechanism between the agents and the simulation environment and between agents are defined, forming a multi-agent-based construction simulation that considers the triple effects of the process, material, and time-space. The proposed system is developed using Python code, which can be applied to simulate short-term construction process with agents modeling, environment modeling and agents’ strategies et al. information imported, and a real case study is carried out through this way. Besides, the proposed MAS system has passed the verification of the traditional DES simulation method, whereas the MAS system can study more general emergence results through the adjustment of agent attributes. Compared with the existing MAS research in construction, the novelty of this study lies in the agent modeling of the construction actor agents rather than the construction process, and the simulation scale is more detailed down to the procedures of the component. The practical contribution is the established MAS realizes the emergent of the macroscopic construction process from the basic flow of crews and materials, which provides a reliable tool to predict the impacts of construction measures for on-site managers, and can help managers to test and quantify the impact of different construction strategies so as to choose the most effective one to execute.

2 Reviews 2.1 Multi-agent Based Construction Simulation Construction simulation is widely used to predict and validate the possible construction progress in an efficient approach (Halpin and Kueckmann 2002); and the MAS and DES are its main techniques (Zhang et al. 2011). MAS is a system modeling tool composed

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of a collection of entities with their characteristics, behavior rules, and interactions that enable the modeling of distinctive construction elements (Khodabandelu and Park 2021), which has been widely applied in constructions such as contractors bidding, planning and scheduling, equipment and labors analyze (Khodabandelu and Park 2021). The current MAS researches in construction mainly take the high-level construction procedures (Taghaddos et al. 2014), workflow (Hsieh and Lin 2015), the decision agents (Mostafavi et al. 2016), (sub)contractors (Kim and Paulson 2003), or projects (Farshchian et al. 2017) as agents, whose micro behaviors or rules are abstracted from real word and modeled as agent in system. For example, Ali et al. simulate the micro behaviors of state Departments of Transportation, private institutional investors, and the public in a multiagent system for ex-ante analysis of financing policies (Mostafavi et al. 2016). In most existing systems, agents are defined as the bidders and the resources such as construction resources, financial resources, or construction opportunities are taken as the sellers. In this way, the simulation of the actual system is transformed into the auction between bidders and sellers. And the additional auctioneer agent who controls the auction process can be added to form a hierarchy agents system (Mostafavi et al. 2014). Most of the current relevant studies do not consider the time-space behaviors of on-site actors when performing component-level tasks, which is particularly important for on-site managers when facing urgent short-term construction procedures. There is research that takes the crews as the agents to consider the space congestion caused by crew tasking in a work plane(Watkins et al. 2009). However, the congestion effect of agents’ movement is not considered, and the other materials and equipment flow are ignored, which could also affect the time of the construction process and the congestion of the work plane. Thus, there is a need for detailed agent simulation of the on-site construction actors and their interaction with materials and large equipment to study the time-space evolution of the short-term construction process. 2.2 The Time-Space Conflict or Congestion of Agents To simulate the detailed component-level construction process, the behavior and interaction of on-site actors with limited construction space and resources should be considered. Watkins et al. noticed that labor efficiency could be treated as an emergent property resulting from individual and crew interactions in space (Watkins et al. 2009). They used agent-based modeling methods to simulate space congestion on a construction site, to explore the impacts of individual interactions on productivity and labor flow. However, this study did not account for congestion caused by agent movements. Although few studies have considered the spatiotemporal properties of agents in construction process simulations, other fields of research for studying the collision or blocking caused by agent movements that can be referenced. Kim et al. (2010) proposed a MAS based on traffic agents to simulate earthmoving operations where vehicle speed, distance from other vehicles, and decision-making of lanes change are considered to assess the impact of traffic congestion. However, it is not applicable in a crowded work-plane where agents are slow. The other example is a meshed work-plane that records the agents’ positions and space occupation by girds. Li and Xu (2020) proposed a safety evacuation model that meshes the limited space and accommodates person agents in cells whose the state

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is either occupied or vacant. It brings such contradictory problems when studying the space-time congestion caused by agent movement, that if all the swept grids of an agent are taken as totally occupied in this time step, the space is obviously wasted. It also leads to how to simulate the congestion effects of soft constraints.

3 Multi-agents System Establishment Process The purpose of the proposed MAS is to simulate the time-space occupancy and congestion evolution of the short-term construction process with the participation of multiple construction actors. The modeling process of this system is adopted from the process described in (Kim and Kim 2010). It first divides the construction process into actors, work plane environment (with materials located), and the procedures environment. Then defines the crews, equipment et al. construction actors as the agents, extracts their spacetime attributes, and simulates their interactions with the environment or themselves from the actual process (Fig. 1). Besides, limited material is located at the work-plane and is replenished by agents who transport materials from the site. In this way, the five elements of man, machine, material, method, and space in the construction are both considered in the system simulation. They work together in the system to realize the space-time deduction of the construction in the work plane.

4 Mas Based on the Construction Actors This study defines agents as on-site construction actors who have specific target tasks and are considered whole when moving or tasking. A novel multi-agent system based on the on-site actors is proposed with three parts, the agents, work-plane environment, and construction procedures environment (Fig. 2). 4.1 Construction Procedures Environment The construction process can be decomposed and organized into a series of tasks with pre-success relationships. It is important to determine whether the decomposed tasks are executed exactly by one crew agent, especially construction tasks that often vary in size. This problem was resolved in our previous study (Yang et al. 2021), which established a flexible WBS structure for tasks organization that makes the tasks or multi-component tasks executable by one crew (allowing the assistance of public equipment). Thus, the organized tasks in (Yang et al. 2021) can be directly imported into the construction procedures environment of this system, which is the flow of tasks in the four task pools according to their attributes and the current system state (Fig. 3). The {task_wait} contains the tasks whose predecessors not finished; {task_quene} contains the tasks whose predecessors are finished; {task_on} contains the tasks under execution; {task_end} contains the finished tasks. Besides, the organized tasks contain the following attributes that will be passed for agents for time-space occupation mechanism: the involved components (or elements) of the task t ele , the position of the task t pos , which is the center of the involved components, the tasking scope t sco , represented as the component enclosing rectangle with working distance and safety distance extended (Fig. 4).

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Fig. 1. The establishing process of this MAS system

4.2 Work Plane Environment The work plane is the main container of agents, materials, and construction measurements Two kinds of constraints can be classified when agents behave. The first are the hard constraints that refuse the invasion of agents, whose geometric information mainly comes from the BIM model. The second are the soft constraints that hamper agents moving, such as temporary measurements, materials storages et al. To study the congestion effects caused by various factors on agent movements, the path blocks are proposed to consist of one of the work plane environments. 4.2.1 Hard Constraints Since the vertical components have structures such as survey lines and protruding steel bars before construction, they and openings can be regarded as hard constraints at the beginning. Hard constraint geometries can be imported into the system through the BIM

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Hard constraints {Ele_constraint}

Soft constraints {Storage_constrai nt}

Work plane environment Time-space path blocks: PT = Mj×k(p,t)

Shape

Tasks with predecessors unfinished {task_wait}

Time-space occupation

Finished tasks {task_end} Task flow

Construction procedures environment Performing tasks {task_on}

Attributes˖ t.pos , a.path, t.scope, t.quan/a.e

Tasks flow

Executable tasks {task_queue}

Attribute˖Target tasktype

Crew agents

Select Task flow Assign t.pos,t.scope,t.quan

Assign s.pos,t.scope,t.quan

Conges

Time-space occupation

Attributes˖a.r, c.ro,c.lift,c Interaction: Assist requirements

Request

Interaction˖Work chance competition

Public huge equipement

Attributes˖Work plan: c.Plan

Fig. 2. The proposed of MAS consists of three parts

Tasks with predecessors unfinished {task_wait} Finished tasks {task_end} Task flow

Construction procedures environment Performing tasks {task_on}

Tasks flow

Executable tasks {task_queue} Task flow

Fig. 3. The construction procedures environment of this system

Fig. 4. The diagram of task’s geometric attributes

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model as {C hard }. The BIM model will continue to provide the system with information about components, such as quantity, type, etc. 4.2.2 Soft Constraints There are always types of things in the work plane as soft constraints to hamper the agents’ movements. The soft constraint Csoft is defined as geometry with a congestion index IC in the work plane in this system. I C is used to describe the congestion degree of the soft constraint in a unit area. 0 represents no congestion, and 1 wholly blocked or hard constraint. Three types of soft constraints and their congestion indices are defined: the material storage are C m soft and I m C ; the task scope are C t soft and I t C ; the material storage are C m soft and I m C ; and the temporary measurement are C e soft and I e C . Different types of soft constraints have different ways to determine their I C value. For example, for a material yard, its I m C value depends on the ratio of its current reserves to its area, and the I m C value can be linearly related to the reserves, that is, when the reserves are 0, I m C = 0, and when the reserve exceeds a threshold its I m C is always = 1. The practical meaning is that the highly stacked storage completely hinders the agent’s movement. The I t C of the task scope is determined by the works number and activity level of the crew performing the task. 4.2.3 Path Blocks This study proposes the path blocks to simulate the movement congestion for agents based on the following assumptions: 1. To consider the security and management of the flow of workers and equipment, the movement of crews follows fixed paths in the work plane which can be concreted in the simulation; 2. Any overlapping parts of the constraints and path block will cause blocking effects, but because the flexibility of the agent, its impact can be evenly distributed over the blocks; 3. The congestion caused by the agent’s movement in a time step can be allocated to the passed blocks in proportion to the time the agent takes to pass the block. The actual meaning is that the longer the agent spends in the block, the greater the congestion impact it will cause. The path blocks is the discretization of the path area like Fig. 5. And each path block Pi will get an initial congestion matrix to record the current or future congestion degree of this block:   Pi _G = steps m×1 × [0] (1) where [steps] is an m × 1 column vector, representing the time steps of the system, which can be extended.

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Fig. 5. The diagram of path blocks

4.3 Construction Actor Agents This study defines construction actors as the crews or large equipment that constantly serve specific construction tasks are taken as the agents, and determines their attributes and rules. There are mainly two types of actor agents in this system. The first is the crew agent, which comprising one or more workers and a carried equipment, and the large public equipment that serves multiple tasks and crews, such as tower cranes and elevators. 4.3.1 Crew Agent Each crew agent a is responsible for a fixed type of task atype and moves around the work plane to the task location for construction. To simulate the time-space actions of crew agents in the construction process, the attributes of agent movement width in path awid , agent’s velocity av , the agent’s work efficiency ae , and the agent’s tasking scope t scope should be considerate. Among them, awid is based on crew size and the required safety distance when moving, and the attributes about the task are passed from the target task to the agent. 4.3.2 Public Equipment Agent The large-scale equipment in construction may have its operation logic and can work for various task types. The most important public equipment in the building construction is the tower crane, whose execution time has been well defined in research (Wu et al. 2020): One lifting time of tower crane is composed by lifting time T lift , loading time T l , and unloading time T u three parts. T l and T u are the given time, and Tlift needs to be calculated according to the Eqs. 2–9 (Wu et al. 2020). With the given tower crane k with position (TCk x , TCk y , TCk z ), the hop position H = (H x , H y , H z ) and the target position D = (Dx , Dy , Dz ), one lift time of tower crane k

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is Tk lift (H, D) that can be calculated: k (H , D) = max(Tvk , Thk ) + β × min(Tvk , Thk ) Tlift

Tvk =

|Dz − Hz | Vvk

Thk = max(Tαk , Tωk ) + α × min(Tαk , Tωk ) Tαk =

|ρ(D) − ρ(H )| Vαk

1 ρ(D)2 + ρ(H )2 − l 2 ) × arccos( 2ρ(D)ρ(H ) Vωk  ρ(H ) = (TCxk − Hx )2 + (TCyk − Hy )2

Tωk =

(3) (4) (5) (6) (7)

 (Dx − TCxk )2 + (Dy − TCyk )2

(8)

 (Dx − Hx )2 + (Dy − Hy )2

(9)

ρ(D) = l=

(2)

Tk v and Tk h mean horizontal and vertical movement time of the tower crane hook, β represents the coordination degree of the hook movement in the horizontal and vertical planes between 0 and 1, which assume to be 0.1 (Younes and Marzouk 2018); Tαk the radial movement time, Tωk the slewing movement time; Vαk the radial velocity of the trolley, Vωk the slewing velocity of the jib; α represents the coordination degree of the hook movement in radial and slewing directions in the horizontal plane between 0 and 1, which assume to be 0.25. The detailed description of the Eqs. 12–9 can be found in (Younes and Marzouk 2018). By identifying the operating status of the tower crane in the actual construction video, our team obtained the basic data of the tower crane operation: Vαk = 667 mm/s, Vωk = 0.172 rad/s, T u = 78.23 s, T l = 73.57 s. Besides, benefit from the continuity of the simulation of this system, the tower cane with a new mission retains its empty state of the previous time step; thus, the mission time of the tower cane can be calculated without distinguishing the empty or full load states: With the given tower crane k, the hop position S = (H x , H y , H z ), the target upload position D1 = (D1x , D1y , D1z ), and the target unload position D2 = (D2x , D2y , D2z ), the action time Tk act is: Tkact = Tklift (H , D1) + Tklift (D1, D2) + Tu + Tl

(10)

Since the tower crane is not on the same plane as the floor, its space occupation will only conflict with other tower cranes. And the time occupancy will cause the time and space occupation of the work plane through the interaction with the agent. The task targets performed by the tower crane come from the interactive requests of crew agents, mainly for task assistance, such as the hoisting of prefabricated components and the hoisting of materials.

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4.4 Time-Space Conflict and Congestion Mechanism The congestion in the work plan only considers the congestion impact on time-space path blocks, and only the task execution conflict. The following Time-space conflict and congestion mechanisms are defined: Task scope conflict mechanism: This system rules that the time and space occupied by different tasks must not conflict. For any task t that is about to start at the current step, its task’s space occupancy t sco must not conflict with any performing task in {Task_on} or agents’ registered tasks. Agents’ movements congestion on path blocks: The time for the agent to pass through each block is determined by its moving speed, the block’s width, and the current congestion value of the block. Since it is assumed that the blocking effect caused by the agent’s movement will be proportional to the passing time, assuming that the agent is stationary for a one-time step (S seconds), it will completely block its occupied area. When it takes s seconds to pass through a block, its congestion to this block is s/S compared to its inactivity. Tasks scopes congestion on path blocks: The overlapping area of the task scope and the path block is the task’s contribution to the path congestion during task performing. Temporary storages congestion on path blocks: Since agents are less hampered when passing the storage with fewer reserves. The contribution of the storage to the path’s congestion depends on its area and its current reserves. 4.5 The Actions of Crew Agents 4.5.1 Agents Targets and Paths Assume agent a gets an alternative target, the path between the agent’s position and the target can be found by the exhaustive method: The agent first enter into the closed path blocks Pi and keep moving into the following block to get closer to the target, until arriving the target’s closet block. The passing of the agent can’t make any path blocks completely blocked in the agent’s path. The agent’s potential targets are determined by its internal knowledge, such as task type, task pools statues, and workspace statues: (1) If an agent needs to acquire materials, its target is the corresponding material storage. (2) else, the agent chose a task from {task_quene} as its predetermined target tasks, which needs to satisfy three constraints: a. must be the same type with agent’s task type; b. not conflicts with any other tasks in {task_on} and targeted tasks by agents; c. The path to the target is fluent. 4.5.2 Agents’ Actions and Pathing The agent has two main actions; one is to perform the task, which occurs around the target components. In this system, the task is progressively advanced over time steps based on the agent’s efficiency, step length, and probability distribution until its reaches

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100% completed. Then the agent becomes idle, removing the task target and freeing the task scope. Another primary action is acquiring material, which occurs near the material yard and takes a certain time for the agent to acquire. When the assistance of the tower crane is required for these two types of actions, it takes additional time for the tower crane to lift the component or material, which Eq.x can calculate. The tower crane will also be occupied when assisting the task that the occupied time is determined by the assistant workload or work steps and the crew agent’s efficiency. The agent must reach the corresponding location through the path before performing the task or material acquisition action. In addition, the agent will also participate in the competitive action of determining the target and the action of initiating a request to the tower crane. 4.5.3 Agents Decision-Making Framework The agent will make a series of decisions and behaviors according to the current state of the system and its state, affect and change the internal properties of the agent and perform corresponding actions. The actions will further change the system state. At the beginning of each step, the agents who have determined their target may have reached the target’s position through the path. Identify the status of these agents to see if it is true, then identify whether the agent needs the assistance of tower crane. If there is no need, the agent starts its action (acquire materials or start task) in the target. The detailed decision-making process of the crew agent is shown in Fig. 6. 4.6 Agents’ Interaction The purpose of agent interaction is to solve the problem of insufficient space or public equipment caused by concurrent actions of multiple agents. The interaction between crew agents is mainly related the competition over limited space or task opportunities. While the interaction between the crew and equipment agents is primarily related the crew’s request for equipment’s assistance. 4.6.1 Interaction Between Crew Agent and Equipment Agent When the crew agent needs the assistance from the tower crane, it sends a request to the tower crane which is stored in the crane’s plan. There are two types of request: task assistance and materials hoist. If the request is material hoist, the material type and material quantity (optional) need to be declared in request. The tower crane can obtain the site location of the material from the internal knowledge of the system and the storage location in the work plane according to the material type. For task assistance request, the task type t type , the task location t pos , and the assistance workload t quan need to be declared in request, the assist time steps of crane is calculated by the assisting workload and agent work efficiency: t quan /ea , that the total steps of crane spend on task assistance is T assis = T lift + t quan /ea . In each step, after all crews send the requests, the tower crane selects the highest priority request in its plan to assist when it is idle. Generally, the priority of material lifting requests is higher than that of task assistance request.

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Acquire agent's and environment current states

Yes

Tasking?

Continue tasking

No Targeted?

Yes

No Get potential targets {Tar}a and validated paths {[P]ij}

Arrived? No Continue pathing

Yes

Occupy task scope, if needed No Need crane?

Start action

Yes No

Pre-targeted?

Continue idel

Send request

Yes

Start the competition with other agents Yes Target determined?

No

Continue idel

Yes Perform the interaction with the path block

End

Fig. 6. The crew agent decision-making process

4.6.2 Interaction Between Crew Agents At the beginning of the time step, all idle agents try to predetermine their targets according to the “Agent’s Target” and verify their paths that are passible. Owing to limited space and congestion paths, only some of the agents can determine its target and path at each step. The that agent determines its target earlier can preferentially register the corresponding spatiotemporal behavior, affecting the congestion matrix of the path block and the available space for tasking. For a predetermined target, its priority is affected by the target type, the number of its successor tasks, the length of paths, and the degree of target preparation. Each time, only the target with the highest score can be determined, and the agent begins its path to it, affecting the space-time congestion matrix of the path blocks and registering the task scope for tasking. After updating the system’s space-time conflict and congestion environment, re-validate other agents’ targets and paths that targets not validated are removed.

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4.7 The Development of the Proposed MAS The python code is used to develop the proposed system, which is widely used in developing related MAS systems that provide sufficient tools and references for the development of this system. The developed system contains a User Interaction Module (UI), where the user needs to set basic simulation parameters such as the actual duration of the time step, the maximum time step, and so on. In this module, users can add a temporary storage yard and specify the location, range, and initial reserve, set the number of agents used in the simulation, specify the initial position and status of the agents, and adjust spatiotemporal attributes of the agent instances. The main body of the program realizes the interactions between the agents and the environment and agents through Python code and driven by the discrete-time steps. The general execution processes are shown in Fig. 7.

Start step

Construction environment update Agents states update and decision-making Agent s with predetermined targets

Crew agents interaction Crane agent action End step Fig. 7. The execution process in each step of this system

1. Environment status update. Tasks stream between the four task pools according to their start time, end time, system’s current time step and completion status of the predecessors that updates the procedures environment. The finished tasks release the occupied task scope that updates the work plane environment. 2. Agents’ decisions and actions. Agents make a series of decisions and actions described in “Agents decision-making framework”, whose actions continuously affect and change the work plane environment.

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3. Crew agent’s competition and action. 4. Crane agent action. 5. End step: Mask supplementary records for the agents that have no recorded state at this time step, whose state is supplemented to idle, and the position remains unchanged.

5 Case Study A prefabricated structure in Shanghai was considered as a case study. To ensure the consistency of the work plane in the simulation, this case only involves the construction process of the vertical components of this structure, including 28 components in three types of prefabricated walls/columns, cast-in-place walls, and cast-in-place column. And the construction contains 4 types of tasks whose attributes are summarized in Table 1. Table 1. The task types in this case study Task Name

Abbreviation

Agents

Work distance (mm)

Safe distance (mm)

Material storage

PC wall Hoisting and Installation

PC

TC, PCW

1500

1000

Struts

Grouting

G

PW

800

300

Mortar

Reinforceing

R

RW

1200

300

Rebars

Formworking

F

F&SW

1500

500

Templates

5.1 The MAS of This Case 5.1.1 The Construction Procedures Environment Based on the previous research, the construction BIM model of this case was established: The existing building BIM model was used to generate process patterns at component levels, and the required multi-component tasks and tasks’ pre-successor relationships to form the tasks of the construction process, which is combined with the original BIM model to form a construction BIM model. Information such as task predecessors, taskrelated components, associated component locations, and associated component engineering quantities in the construction BIM model were extracted and imported into the system as task attributes. According to the task’ attributes and agent’ actions, the program drives tasks to flow in different task pools to form the process environment. 5.1.2 The Work Plane Environment The work plane environment of this system is composed of hard constraints, soft constraints and path blocks. In this case, the geometric information of the hard constraints,

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such as the working face shape and components, is obtained from the BIM model. Soft constraint information such as material yard and temporary measures on the working face can be obtained from the construction BIM model or specified by the user. For example, data such as the maximum storage yard, storage range, etc., or accompanying tasks for temporary measures. In this case, two storage yards are designated on the working face, namely the rebar storage, the Struts storage, the Mortar storage, and the template storage, the positions and scopes of which are shown in Fig. 8 also shows the path block used in this case.

Fig. 8. The layout of the work plane environment

5.1.3 Agents of Construction Actors To perform the tasks of this case, four types of crews and one tower crane were used. Crew agents and their temporal-spatial attributes are summarized in the following Table 2, which data were obtained from actual engineering. The tower crane agent uses the parameters in the section “Public equipment agent”. Table 2. The agents applied in the case study Agents

Work efficient /Duration

Movements width (mm)

Velocity (mm/s)

PCC

25 min

2000

6000

GC

9 min

1000

9000

RC

0.035 m3 /min

900

10000

FC

0.56 m2 /min

1300

7000

5.1.4 User Settings in the Main Body of the Program In this case, the simulation settings are shown below.

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Initial task environment status: All tasks are not started; Initial working face environment: Three temporary storage yards are placed, the reserves of all temporary storage yards are 0, and the space-time blockage of all path areas is [0]; Quantity setting of agents: reinforcement crews (RC) 2, PCs hoisting and install crew (PCC) 1, mortar grouting crew (MC) 1, formwork crew (FC) 2. Each agent is generated at the beginning of the simulation, inherits all the properties of the same type of agent in the program agent module, and is assigned an initial spatiotemporal log, which records all the historical and future actions of the agent. At the same time, the unique feature of this program is that the generated agent will not be recycled during the simulation process, which allows the user to trace all the agent’s actions through the agent for easy analysis. Simulation drive (other) setting: the set time step length is 10s in reality, then the team agent moves about 6–11m per step, and the tower crane agent rotates about 98° per step. 5.2 Simulation Results and the Comparison with DES Using the above settings to execute the developed MAS program, the simulation results of the construction process can be obtained and exhibited as the Gantt chart of each agent (Fig. 9). Which distinguishes three types of actions: idle (gray), move (yellow), perform a task (red). The Gantt chart reflects the participation of various agents on the work plane during the construction process, indicating that the proposed system successfully simulates the macro construction process from the basic agent modeling.

Fig. 9. The simulation results are shown in the agents Gantt chart

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To verify the reliability of the simulation result, it is compared with the result of the DES method. DES results represent a good verification tool for agent-based models that the nature of DES provides an accurate flow of resources, which allows for verifying the quantitative aspects of agent-based models(Jabri and Zayed 2017). There are several examples in the literature on the verification of ABMS outputs using DES results [6], [10]. In this case, the simulation object of the DES method is the task network of the case; each task consumes the same resources and takes the same probability time as this MAS, while does not consider the flow of resources (workers, equipment, and materials). The comparison between the DES simulation and the proposed MAS simulation is shown in Fig. 10, which shows that the proposed MAS takes more time to complete all tasks than the DES simulation. The reason is that this system considers the agent’s action and the related resource flow before the task start. By re-setting the agent and environment parameters of the system to make the moving speed of the agent extremely high, the initial material reserves of the site extremely large, and the moving volume of the agent to be extremely small, and re-run the proposed system to get a result, which compares with the DES results in Fig. 11. It shows that in this specific condition, the simulation results of this system have a very high consistency with traditional DES simulations, indicating that the system is verified with the traditional simulation method.

Fig. 10. The comparison of this MAS and traditional DES method in normal parameter

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Fig. 11. The comparison of this MAS and traditional DES method in the specific condition

5.3 Construction Strategy Application Experiment and Result Analysis To verify whether the established system can help managers test different construction strategies and understand the macro impact caused by them, the most commonly used construction strategy in practice is applied in this case, that is, changing the number of participants (crews) to test the system’s performance in different situations. The variable controlled in this experiment is the usage of rebar crews in 1 (case1, blue line), 2 (case2, orange line), 3 (case3, green line), and 4 (case4, red line) are tested (Fig. 12). It can be seen from the figure that the increase in steel bar teams accelerates the overall construction process, while the more the crews invested, the smaller the acceleration effect. It is in line with engineering experience that shows the proposed system successfully emergent the micro construction phenomenon from the adjustment of agents.

6 Conclusion The current construction-related MAS simulations lack consideration for the construction actors’ movement on the short-term limited working surface. This paper proposes a MAS based on the on-site construction actors, defines the agent’s spatiotemporal attributes, and further establishes the agent’s operation and interaction rules between agents and between agents and the environment. The proposed system is developed using Python code and verified with a real-life case of the standard floor’s construction of a prefabricated building in Shanghai. Besides, the comparison with the traditional

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Fig. 12. The simulation results of the four strategies

DES method and the experiment of different construction strategies are implemented. And the following conclusions can be drawn: 1. The program can record the action history of different agents and visualize it for the construction managers to read and understand intuitively. 2. In specific cases, the result from the developed system is highly consistent with the result from the traditional DES method in this case, which means that this system is compatible with DES in task network simulation and resource usage, and verifies the effectiveness of this system; 3. The simulation results of the system for different numbers of crews are consistent with the engineering experience, proving that the strategies applied on agents impact the macro construction process. The main contribution of this paper to related research fields is that it proposes a novel perspective for multi-agent modeling of the construction process. The simulation process can be more detailed based on the construction actor agents, and the measurements and preparations for tasks execution can be considered from the basic agents’ actions, which helps to emergent the macroscopic construction process from the basic flow of crews and materials. In practice, the proposed system can show managers a more detailed agent action status to help them understand the macro construction process and quantify the impact of different construction strategies on the overall process. A future of this system is to study the optimization method in the agents. Test the construction strategy about the usage of space in the work plane. For example, let the agent choose the task with a low degree of path congestion while with more performing tasks around, it is to avoid complete congestion of the path and free up contiguous non-task areas for the work plane as much as possible.

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Acknowledgments. The study has been supported by the National Key R&D Program of China (Grant No. 2020YFD11004045).

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Digital Fabrication for DfMA of a Prefabricated Bridge Pier T. K. Kim, D. C. Nguyen, and C. S. Shim(B) Department of Civil Engineering, Chung-Ang University, Heukseok-Ro, Dongjak-Gu, Seoul 06974, Korea {rlaxo1022,cuongnguyen,csshim}@cau.ac.kr

Abstract. Many countries have a strategy to increase the ratio of off-site construction. Design for manufacturing and assembly (DfMA) is a challenging requirement for a designer in the construction industry. Prefabricated structural members are widely utilized for bridge construction to minimize on-site activities. This paper proposes digital fabrication models for DfMA considering 3D concrete printing and CNC milling. Data-driven information delivery between the digital model and the robot arm was defined. Prefabricated bridge columns require strict geometry control, especially for match casting. Design for assembly procedure through digital models and robotic technology is proposed. Digital fabrication is essential for a fully prefabricated bridge. Consequently, a printed permanent formwork has been applied for a novel digital fabrication method of the prefabricated column segments. Keywords: DfMA · Bridge pier · 3D concrete printing · CNC milling · Digital model · Geometry

1 Introduction Prefabricated bridge construction has been developed to enhance construction productivity (Shim et al. 2010; Kim et al. 2016). Mainly, a prefabricated member is fabricated in better condition in the off-site factory. The prefabrication bridge industry expects the benefits of better quality control, mitigating labor shortage, and cost-effectiveness. Building Information Modeling (BIM) technology for bridge fabrication and design for manufacturing and assembly (DfMA) has been studied to accelerate the effort of prefabrication. DfMA method intends to improve design quality for ease of manufacturing and assembling bridge components (Kim et al. 2016). DfMA provides the potential to ensure the maximum combination of knowledge from design, manufacturing, and assembly at the early design stage. A prefabricated bridge requires highly standardized and customizable prefabricated elements. Chea et al. (2020) introduced the possibilities and advantages of robotic technologies in design, manufacturing, transportation, and structural assembly in the construction sector. Shim et al. (2018) proposed the three-dimensional information delivery methodology from design to maintenance of prefabricated bridge piers.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 305–310, 2023. https://doi.org/10.1007/978-981-19-7331-4_24

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Current practices in fabricated construction lack the automation and integrated information delivery between the design, fabrication, and assembly phases. This paper aims to study a methodology to establish the digital fabrication of a prefabricated bridge pier using a robot arm and combining parametric BIM and DfMA. The digital fabrication process includes 3D concrete printing and concrete milling. Furthermore, digital parametric models are integrated into each process to deliver information to the robot arm. The data flow of DfMA for a prefabricated pier is depicted in Fig. 1. Data for fabrication and assembly are generated in design and delivered to each stage.

Fig. 1. Data flow of DfMA for a prefabricated pier

2 Digital Fabrication Procedure Digital fabrication is developed for geometric freeform provided by 3D concrete printing (3DCP) that is used to liberate design thinking from conventional concrete techniques to realize the full architectural potential of 3DCP structures (Gaudillière et al. 2018; Anton et al. 2021). Digital fabrication requires a robot arm for 3D concrete printing and concrete milling. Figure 2 presents the whole process of digital fabrication of a prefabricated bridge pier. In this study, a permanent concrete formwork is performed by the 3DCP. It is considered a non-structural part. The geometrically complex segments were designed through the parametric modeling method. The twisted column form considering technical specifications of concrete printing, such as overhang capacity and level of geometric complexity, was implemented. Then, a reinforcement cage and ducts are installed in this formwork and cast concrete. When the segment is completed, the top surface is milled for matching. Finally, the segment can be prestressed and assembled.

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Fig. 2. Fabrication procedure of a prefabricated column segment

3 Digital Model for Concrete Printing The digital design model for concrete printing generates the printing parameters such as printing time, length layer thickness, and printing path (Fig. 3). The sliced model automatically generated the printing path based on the layer thickness and nozzle size parameter. The printing path generation is the first consideration in the early design stage to decide the level of structural complexity. The motion of the nozzle is simulated through G-code. The G-code data includes the coordinate of the spatial points on the defined printing path. The coordinate dataset presents the direction and speed of the printer nozzle. The small size of the designed column has been printed with printing parameters: 40 mm nozzle size, 20 mm layer height, 50 mm layer width, and 3000 mm/min speed (as shown in Fig. 4). Additionally, Fig. 5 describes the specifications of a 3D concrete printer operation. We generated a throwing section for stabilizing the mortar from the pump to the nozzle at the start. The vertical movement of the nozzle gradually rises from the start point to the endpoint of the layer. Moreover, the feed rate decreases at the curved part to control cracking and depositing. It is crucial to check whether printing to the target height is possible without elastic bucking and plastic collapse (Suiker et al. 2020). Furthermore, concrete properties need to be obtained on the hardened stage. Moreover, the tearing of layers needs to be detected (Buswell et al. 2018). Besides, the potential error should be considered to secure product quality (Anton et al. 2021).

Fig. 3. The segment dimension and printing path

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Fig. 4. Concrete printing process and parameters

Fig. 5. Specifications of a 3D concrete printer operation (a) generating a throwing section for stabilizing the mortar from the pump to the nozzle, (b) the vertical movement of the nozzle gradually rising, (c) decreasing the feed rate at the curved part

4 Digital Model for Concrete Milling Prefabricated segments with prestressing require perfect bonding to deliver a uniform compressive force. In this digital fabrication, joint surfaces are milled by a robot arm. To secure the inlet of the ducts, robot milling is performed using the central point of each duct model as a control point. The digital fabrication models provide geometries for final purposes and generate G-code for milling with parameters shown in Fig. 6. In the case of normal CNC processes, roughing and finishing techniques are included. Considering printed layer thickness, fabrication time, and cost, the maximum thickness for milling is limited by 15 mm. The 1% slope is designed to prevent rainwater penetration for the durability measurement at the joints when assembled.

5 Conclusions DfMA, a design method used in the manufacturing industry, has been applied to prefabricated bridge construction. This paper proposed the digital fabrication for DfMA of a

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Fig. 6. Milling the top surface of a prefabricated column surface by a robot arm

prefabricated bridge pier. In the procedures of formwork fabrication and creation of the joint surfaces of column segments, digital models contain the required information for robot arm operation at each process. The proposed digital model for DfMA enhances the centralization of production, standardization, and repetition that improves the flexible and accurate fabrication processes. Future works should be performed to predict and improve the quality of 3D concrete printing. Improving printing quality is the key to commercializing this prefabricated member. Acknowledgements. This research was conducted with the support of the “National R&D Project for Smart Construction Technology (No.22SMIP-A158708-03)” funded by the Korea Agency for Infrastructure Technology Advancement under the Ministry of Land, Infrastructure, and Transport, and managed by the Korea Expressway Corporation.

References Anton, A., et al.: A 3D concrete printing prefabrication platform for bespoke columns. Autom. Constr. 122 (2021).https://doi.org/10.1016/j.autcon.2020.103467 Bos, F., et al.: Additive manufacturing of concrete in construction: potentials and challenges of 3D concrete printing. Virtual Phys. Prototyping 11(3), 209–225 (2016). https://doi.org/10.1080/ 17452759.2016.1209867 Buswell, R.A., et al.: 3D printing using concrete extrusion: a roadmap for research. Cem. Concr. Res. 37–49 (2018). Elsevier Ltd., https://doi.org/10.1016/j.cemconres.2018.05.006 Chea, C.P., et al.: An integrated review of automation and robotic technologies for structural prefabrication and construction. In: Transportation Safety and Environment, pp. 81–96. Oxford University Press (2020). https://doi.org/10.1093/tse/tdaa007

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McKinsey & Company: Call for Action: Seizing the Decarbonization Opportunity in Construction. McKinsey Global Publishing, July 14 (2021). Available at https://www.mckinsey.com/ind ustries/engineering-construction-and-building-materials/our-insights/call-for-action-seizingthe-decarbonization-opportunity-in-construction Gaudillière, N., Duballet, R., Bouyssou, C., Mallet, A., Roux, P., Zakeri, M., Dirrenberger, J.: Large-scale additive manufacturing of ultra-high-performance concrete of integrated formwork for truss-shaped pillars. In: Robotic Fabrication in Architecture, Art and Design, pp. 459–472 (2018).https://doi.org/10.1007/978-3-319-92294-2_35 Kim, M.K., McGovern, S., Belsky, M., Middleton, C., Brilakis, I.: A suitability analysis of precast components for standardized bridge construction in the United Kingdom. Procedia Eng. 164, 188–195 (2016). https://doi.org/10.1016/j.proeng.2016.11.60 Tam, V.W.Y., et al.: Cutting construction wastes by prefabrication. Int. J. Constr. Manag. 6(1), 15–25 (2006). https://doi.org/10.1080/15623599.2006.10773079 Tam, V.W.Y., et al.: Towards adoption of prefabrication in construction. Build. Environ. 42(10), 3642–3654 (2007). https://doi.org/10.1016/j.buildenv.2006.10.003 Shim, C.S., Chung, C.H., Kim, I.K., Kim, Y.J.: Development and application of precast decks for composite bridges. Struct. Eng. Int. 20(2), 126–133 (2010). https://doi.org/10.2749/101686610 791283623 Shim, C.S., et al.: Three-dimensional information delivery for design and construction of prefabricated bridge piers. Struct. Eng. Int. 28(1), 6–12 (2018). https://doi.org/10.1080/10168664. 2018.1431378 Suiker, A.S.J., et al.: Elastic buckling and plastic collapse during 3D concrete printing. Cem. Concr. Res. 135 (2020).https://doi.org/10.1016/j.cemconres.2020.106016

Study on the Open Data System for Infrastructure Maintenance and Management Junha Hwang1(B) , Kei Kawamura1 , and Shuji Sawamura2 1 Graduate School of Sciences and Technology for Innovation, Yamaguchi University,

Tokiwadai 2-16-1, Ube City 755-8611, Yamaguchi Prefecture, Japan {b088vgv,kay}@yamaguchi-u.ac.jp 2 Yamaguchi Prefecture, 1-1 Takamachi, Yamaguchi City 753–8501, Yamaguchi Prefecture, Japan [email protected]

Abstract. In Japan, periodic inspection of social infrastructure is compulsory every five years. Consequently, after infrastructure inspection, many valuable data sets are accumulated. In Yamaguchi Prefecture, however, data are managed using an Excel file format. This makes it difficult and inefficient to extract information from data. Also, incorrect data input can occurs, because data are input manually by a person. In response to this problem, the authors developed a data extraction and conversion system. Which extracts a specific range of Excel format data and converts it to JSON format, making it easier to utilize information by correlating data based on bridge inspection data. By using such a data modification system with Google Map, incorrect data can be identified and corrected. Furthermore, an open data Web API system structure was developed, for future visualizations and analysis. The paper will conclude the authors assessment of the performance of those systems as well as their thoughts on the future utilization of bridge inspection data. Keywords: Web API · Open data · Infrastructure management · Infrastructure inspection · JSON

1 Introduction In 2014, the Japanese government enacted the Ordinance on Road Maintenance and Repair and required regular inspections of bridges and tunnels, every five years (Ministry of Land, Infrastructure, Transport and Tourism 2014). Yamaguchi Prefecture also conducts regular inspections in accordance with the above ordinances and notices, and 800–900 inspections are conducted for about 4500 bridges annually. Inspections of these bridges are carried out in accordance with Yamaguchi Prefecture’s Bridge Inspection Guidelines and summarized in Excel. Yamaguchi Prefecture’s Road Management Department performs maintenance and management based on the Master Data (Excel) recorded by transferring bridge ID, specification information, inspection schedule, and main inspection results from a separate © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 311–325, 2023. https://doi.org/10.1007/978-981-19-7331-4_25

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Inspection Table Record Form. Yamaguchi Prefecture has a database system for social infrastructure management, but due to the lack of fixed inspection guidelines and search requirements, it is difficult and expensive to renovate the database in a timely manner. Because road management personnel cannot use the database system, it is more efficient to manage the main data using Excel. Regular inspection results, such as the Inspection Table Record Forms, are managed by the person in charge according to the folder composition, folder naming rules, and file naming rules. As a result, there are many cases in which data are entered manually, thus regarding in errors in input and half-width/full-width typeset inconsistencies. One task of road management personnel in local governments is to report the results of regular inspections to the Ministry of Land, Infrastructure and Transport and Tourism (hereinafter referred to as “MLITT”) every year. Specifically, the data items required for reporting are extracted from the Master Data and the Inspection Table Record Form, and entered into the Ministry of Land, Infrastructure, Transport and Tourism’s reporting system. The purpose of this study is to develop a system that can improve the efficiency of this operation because data input is such a heavy burden on the person in charge. In their study on the management and utilization of maintenance data, Fujimoto et al. developed a system that displays files with incorrect file names and missing files as part of their data organization, and even created APIs as examples of open data (Fujimoto et al. 2020). Considering this background, the systems developed in this study have advantages. One reason for this is that the Bridge ID Correction System can accurately validate and rewrite incorrect data, while manual operations can lead to errors. Another is the Report Input Auxiliary system has similar advantages to reduce input errors. These two systems can reduce the time to perform repetitive tasks, which is time consuming for infrastructure administrators. Finally, the Web API system for the distribution of infrastructure data is likely to be used in the future, to visualize damage and other information in order to manage infrastructure.

2 System Overview Figure 1 shows the composition of the system proposed and developed in this study. This system attempts to extract the necessary data from both the Master Data of the bridge and the Inspection Table Record Form; however, discrepancies between the Master Data and the Inspection Table Record Form pose significant problems. From the beginning of the regular inspection, each bridge is given a facility number (hereinafter referred to as “the old ID”). MLITT has provided basic information regarding the provision of facility. IDs (Ministry of Land, Infrastructure, Transport and Tourism 2019), designed to facilitate the retrieval of data from the construction to maintenance stages in addition to correlating the various data stored in the system. The facility ID is generated as 18 digits, including latitude/longitude separated by commas. Yamaguchi Prefecture also shifted to data management using facility IDs (hereinafter referred to as “new ID”) based on this plan. In the Master Data, the old and new IDs of the bridges are recorded based on an electric calculated latitude/longitude. The primary issue is that, the old ID is not recorded in the Inspection Table Record Form. In addition, in the Inspection Table Record Form for bridges inspected in 2020,

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Fig. 1. Two simplified systems

there is a new ID column and a column describing the latitude/longitude as the location. Because the inspection company does not comply with the above latitude/longitude measurement standards, instead using GPS devices to measure and record them on its own, there are cases where data entries do not match the new ID of the Master Data. In the future, the bridge ID of the Master Data will be transferred directly to the Inspection Table Record Form, removing the need of enter, and the inspection table record form can be handed over to the inspection company. As for existing data, it is necessary to manually correct the bridge ID in the Inspection Table Record Form to ensure that the bridge names recorded in both the Master Data and Inspection Table Record Form match each other. But some other factors such as bridges sharing the same name, errors in input data, and differences in half-width/full-width characters limit matchable data to only 72%. Based on the above background, this study developed and verified a Bridge ID Correction System that matches the Master Data with the Inspection Table Record Form and then corrects the wrong ID with the correct ID. In addition, the Report Input Auxiliary System, which is extracts the data items required for reporting to the MLITT, from the correctly matched Master Data and Inspection Table Record Form before summarizing them in Excel, was also developed. Potential users of these systems are road management staff members of local governments. Furthermore, a Web API was prototyped to make data shared using the Report Input Auxiliary System public on the Web, as a method to improve the circulation of maintenance and management data.

3 Bridge ID Correction System 3.1 Overview of System Requirements As a solution to ID correction in the Inspection Table Record Form, a Bridge ID Correction System was developed using Google Maps for matching bridge IDs. The reason for

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using Google Maps is that system users have practical experience in road management and can quickly grasp the name of the road and the location of the bridge. In addition, it is necessary to determine the correct bridge name based on the bridge location and road name on the map because the bridge name of the Master Data and the Inspection Table Record Form may differ. Additionally, there are two types of Inspection Table Record Forms depending on the type of bridge structure, and it is necessary to determine which type of file is being referenced because the location of the data is different. Figure 2 shows a screen shot of the Bridge ID Correction System developed in this study.

Fig. 2. Part of the correction screen

On the map, the locations of bridges recorded in the Master Data are identified with red markers. Users click the red marker to display the bridge name and latitude/longitude recorded in the Master Data in the information window. Latitude/longitude entries recorded in the Inspection Table Record Form in need of confirmation are shown with a yellow marker. Users can click the yellow mark to display the bridge name, latitude, longitude, road name, inspection rank, date of inspection, inspector, bridge type recorded in the Inspection Table Record Form. System users can modify the bridge ID by comparing the red and yellow markers. 3.2 Technology Used in System Architecture This section describes the JSON format, XAMP software, and Google Map which are the main technologies used in the development of the Bridge ID Correction System. JSON is a file format standing for JavaScript Object Notation. As shown in Fig. 3, the data consists of a key and corresponding value, so it is easy to use for exchanging data between programs.

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Fig. 3. JSON file example

This system uses Google Maps to display the data on Web browsers, so it is appropriate to use JSON based on the above parameters. The key parameter describes the name of the data item as a string. Value describes a specific string, number, boolean, array, object or null for data items. For example, in Fig. 3, the left side of the colon is the entry key and the right side is its value, so data can be extracted from a collection of items based on a specific Key like “Id”. XAMPP is a tool that includes Web servers, databases, and so on. In this system, Google Maps is used to perform ID correction operations on the browser, while XAMPP is used to run the Web server. Google Maps is a digital map and has many convenient functions. In this system, marking function is mainly used, to display bridge location and information. 3.3 Bridge ID Correction Flowchart The bridge ID correction flowchart of this system is illustrated in Fig. 4. The system was developed in C# as shown in Fig. 5 and converts the specified data items into JSON format (hereinafter referred to as data conversion) before rewriting the bridge ID (hereinafter referred to as ID correction). Furthermore, it consists of the ID correction functions on web browsers developed using HTML and JavaScript (hereinafter referred to as matching functions). The buttons, search box, and correction status screen used in browser correction operations are shown in Fig. 6.

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Fig. 4. ID correction flowchart

STEP 1: This step performs the data conversion and converts the Master Data and Inspection Table Record Form into JSON format. The data in the Master Data is saved in the Output.json file, and the data in the Inspection Table Record Form is saved in Record.json. The Output.json file is created only once, unless the master data is changed. When the master data is altered, the user clicks the “Select Master Data” button (Fig. 5) of the data conversion function to create a new Output.json file. Record.json, on the other hand, extracts and converts data from all specified Inspection Table Record Forms and saves it. The Record.json file is created by executing steps 1 to 3 marked on Fig. 5. After creating these JSON files, the user initializes the matching function shown in Figs. 2 and 5 in their browser. STEP 2: Repeat the process shown in STEP 2 of Fig. 4 and perform ID correction. When the matching function is started, red markers based on the Output.json file and the first yellow marker to be confirmed will be displayed on the browser map. Red markers

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Fig. 5. User interface of a program with data conversion and ID rewrite functions

Fig. 6. Interface of the browser (matching function)

are always correct, but yellow markers may be incorrect. System users can view the marker information window by clicking on that marker. In addition, you can return to the previous bridge (yellow marker) by clicking the Return button. As a confirmation task, the system user first identifies the bridge name, road and coordinate (bridge ID) from the yellow marker information window, finds the corresponding red marker, and clicks. As shown in Fig. 6, a search box will appear in the system screen, and when the bridge name is entered, the red marker of the bridge will be displayed in the center of the map. If the coordinates of the yellow and red marker of the bridge are different, the coordinates of the yellow marker are incorrect, requiring the user to click the Decide button to save the correct coordinates as changes. However, if the coordinates of the marker are the same, click the Next button to proceed to the next correction. After clicking the Next button, the next yellow marker and information window will be displayed on the map. By clicking Finish, the Result.txt file containing the results of the change will automatically be downloaded to the download folder of the computer. STEP 3: The ID correction function is performed by clicking on the Rewrite Inspection Table Record Form button in Fig. 5, using the contents of Result.txt. This concludes the bridge ID correction operation.

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3.4 Data Verification Methods The data used for this study are from regular inspections conducted in 2020. The inspections were conducted separately by region, covering 12 bridges in Area 1, 24 bridges in Area 2, 96 bridges in Area 3, for a total of 132 bridges. The purpose of verification is to compare manual work with the time required for the Bridge ID Correction System. In other words, to demonstrate how much time can be reduced by using this correction system. As a premise, the verification operator should read the manual of the bridge ID correction system before using it. For manual work, the bridge ID must be retrieved from the Master Data and then entered in the Inspection Table Record Form. In addition, some folders will not follow the naming convention in the inspection report folder, so the folder name must be assumed for verification. Although it is possible to set exceptions programmatically, it is considered good practice to organize folders according to naming rules in order to prevent future errors, so no such programmatic measures were taken. 3.5 Verification Results The results of the verification are shown in Fig. 7.

Fig. 7. Verification results

The coordinate inconsistency on the graph refers to the number of objects that needed to be corrected. Overall, the use of the correction system reduced operation time to a modest change. This is partially because the verification process requires time for data convert to JSON files and to rewrite Excel contents. For example, in the case of Area

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3, it took 18 min to convert to JSON files. However, because people only need to wait for the system to finish converting, the actual time spent on the process is significantly reduced compared to manual work. In addition, manual work in Excel takes more time due to differences in inputting characters such as full-width/half-width kana, Chinese characters, and Arabic numerals. However, it is true that the overall time to complete the work is as shown in Fig. 7, so it is still necessary to improve the efficiency of algorithms and data conversion and rewriting. 3.6 Efficiency of Post-verification Correction Flow Since there is only a small difference in the overall time of the correction operation, a streamlining operation was implemented. Before, it was necessary to press the Next button even if the bridge ID was the same, but by adding a “Skip” function, only bridges with different bridge IDs need to be checked and corrected. For example, if there are 12 bridges and only the last bridge needs to be corrected, clicking the Skip button can automatically compare bridge IDs and display the twelfth bridge on the map. Although no verification has been carried out since the addition of this function, it can be thought that system efficiency will be increased compared to the time measured in verification.

4 Report Input Auxiliary System 4.1 Overview of System Yamaguchi Prefecture needs to report the results of regular inspections of bridges every year, so it manually extracts the necessary data from the Master Data and Inspection Table Record Forms and enters the report data into Excel. However, since two files are checked at the same time and entered one by one, it is burdensome for the operator and can result in input errors. The Report Input Auxiliary System is a system that automatically creates reporting data based on the Master Data and the Inspection Table Record Forms that can be matched by the correct bridge ID after using the bridge ID correction system. 4.2 Report File Creation Flow This section illustrates the flowchart of the Report Input Auxiliary System shown in Fig. 8. When the system is started, it automatically checks whether a text file extracted from the latest Master Data exists in a pre-specified folder. If there is no text file in that folder, corresponding to the latest Master Data, a new text file is created. The file name of the Master Data contains the date, and according to the file naming rules, ten characters from the beginning of the file name including the date are recorded as “YYYY.MM.DD” (year.month.day). In addition, the file name of the text file is recorded as “YYYYMMDD”, excluding the period. When the Report Input Auxiliary System is activated and the output key is clicked, the text file and the data in the Inspection Table Record Form are matched according

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Fig. 8. Report input auxiliary system flow

to the bridge ID. Subsequently, the items to be reported are extracted and Excel files with the date and time of creation as the name of the file are generated on the desktop as output from the system.

5 Data Distribution Using Web API 5.1 Overview of System In this section, to promote the utilization of maintenance data in bridge deterioration analysis, a method of distributing maintenance data in machine-readable JSON form through Web API was developed. API is an interface. Users can utilize data without connecting directly to the database system. Web APIs indicate the use of APIs in a Web environment. Figure 9 shows the overall structure of the Web API developed in this study. In addition, this paper deals with the distribution of infrastructure data related to bridges through the Web API, but the structure shown in Fig. 9 can be widely applied to other cases. The advantage of using Web API for data publication is that it utilizes public data to improve work efficiency and reuse services with high added value. For example, in the case of reporting from each local government to the government, if each local government can distribute machine-readable data as a Web API, the national system can automatically obtain and process data through programs, which would significantly reduce the burden of reporting. As another use case would, data-driven analysis has progressed in recent years, so if the Web API were to be overhauled, it would be easier to use it to obtain large amounts of data and analyze predict the deterioration of management facilities.

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Fig. 9. Structural diagram of data provision using API

5.2 Provision to Utilization Flow Figure 10 shows an example of flow, from data creation to data provision, for publication through the Web API. When creating Excel files in the Report Input Auxiliary System, a JSON file with the same content is created and used as publishable data. The data provider uploads the JSON file to the browser as shown in Fig. 11. Upon clicking the Transfer button, the JSON file is transferred to the server and saved in the Mongo database. Mongo databases are also known as NoSQL because they do not have limited data structures such as SQL and are suitable for managing dynamic structures such as JSON (Miki and Tanaka 2015, pp. 165–177). The stored data can be accessed via the API. If the user wants to use public data, the user can send a HTTP GET request through the Web API to obtain the data in the JSON file stored in the database. In the current test, the result is as shown in Fig. 12. HTTP GET involves sending a GET request to specific addresses (URLs, this time asterisk in Fig. 11) to obtain data from databases. This time, the test was conducted to return all the data by entering the address directly, but in the future it will be able to narrow down the contents of the returned data, increasing the usability of the function. In addition, the Web API of this paper has minimal basic functions, so it is necessary to consider issuing API keys and establishing security protocols in the future.

6 Conclusions In this paper, a Bridge ID Correction System was developed to correct the ID used to correlate files, and a Report Input Auxiliary System was developed to extract the necessary data items and create new files. Furthermore, considering future data utilization,

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Fig. 10. Flow from data provision to utilization

a structure was developed to distribute data in JSON form through a Web API. Since the value of data is increasing day by day, it is expected that the structure of matching and providing each data set will become very important in the future. It is necessary to match meaningful data to one another, combining information to derive new sets of data that will be considered useful in various fields. Because it predicts and prevents damage through future data provision and analysis, it is essential to organize periodic inspection data correctly. In addition, the conversion and deployment of data in JSON format, makes it possible to visualize the data in the future and expand the scope of utilization. Visualization of data has many advantages, such as finding meaningful patterns in large amounts of data (Masahiko and Yoshisuke 2015). Also, the JSON format is easy to use, so it can be reused many times as part of the API as well as visualization. A future improvement would be to fill automatically the contents of the Inspection Table Record Form into the Master Data to further reduce manual work and visualize the

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Fig. 11. Browser interface created for web API testing

inspection data to help maintain facilities. At this time, cloud systems such as Google Drive could be considered, but verification should be carried out after considering the inspection process and data storage. In addition, since there are no restrictions on the provision of current data, it is necessary to consider how to control the provision by authenticating users with keys when providing APIs (Google Cloud).

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Fig. 12. Saved contents (response to GET request)

Acknowledgements. I would like to express my gratitude to Professor Kei Kawamura (Supervisor), Shuji Sawamura (Yamaguchi Prefecture), and Associate Professor Zachary Robertson (Yamaguchi University).

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References Fujimoto, K., Kawamura, K., Sawamura, S.: Study on data management method for open data of periodic bridge inspection data. Intell. Inf. Infrastruct. [online] 1(J1), 78–85. Available at: https://www.jstage.jst.go.jp/article/jsceiii/1/J1/1_78/_article/-char/en (2020). Accessed 20 Feb 2022 Google Cloud: Why and when to use API keys. [online] Google Cloud. Available at: https://cloud. google.com/endpoints/docs/openapi/when-why-api-key (n.d.). Accessed 20 Feb 2022 Masahiko, S., Yoshisuke, S.: Data visualization: necessity and implication (Designing for Understanding). Inf. Sci. Technol. Assoc. [online] 65(11), 470–475. Available at: https://www.jst age.jst.go.jp/article/jkg/65/11/65_KJ00010079452/_article/-char/en/ (2015). Accessed 20 Feb 2022 Miki, M., Tanaka, M.: Database -Kiso kara netto shakai deno oyo made-. Kyoritsushuppan, pp.165–177 (2015) Ministry of Land, Infrastructure, Transport and Tourism: Enactment of Ordinance of the Ministry and Public Notice on Road Maintenance and Repair. [online] Available at: https://www.mlit. go.jp/common/001034659.pdf (2014). Accessed 6 Feb 2022 Ministry of Land, Infrastructure, Transport and Tourism: Reference materials for granting IDs to facilities subject to periodic inspection (proposed). [online] Available at: https://www.mlit.go. jp/road/sisaku/yobohozen/tenken/tenken-id.pdf (2019). Accessed 11 Feb 2022

Road Development Risks and Challenges in the Philippines Kenneth Edward Torrella Fernando1(B) and Michael Henry2 1 Division of Architecture and Civil Engineering, Graduate School of Engineering and Science,

Shibaura Institute of Technology, Tokyo 135-8548, Japan [email protected] 2 Department of Civil Engineering, Shibaura Institute of Technology, Tokyo 135-8548, Japan [email protected]

Abstract. The Philippines, as a fast-growing country, has had the highest road infrastructure investment to date for the past five years compared to the previous years. The infrastructure programs of the government as a solution to decongest Metro Manila and develop the countryside for economic growth are promising yet result in various risks and challenges. This research presents the road development issues from multiple sources; primary data from interviews of stakeholders of road development, secondary data from online news articles, social network services, government issuance, policies, and related literature. The Philippines is in a dire economic situation due to the Covid-19 outbreak that resulted in the country’s worst economic performance since the Asian financial crisis in 1998. The country’s economic managers pinned high hopes on the government infrastructure programs as a vital strategy to help pump-prime the economy towards recovery due to its job generation and multiplier effects. Hence, it implicates enormous risks and challenges such as low tax revenues, the trade-off with more urgent Covid-19 response measures, foreign and private companies support, unsolicited project proposals, inequitable distribution of infrastructures, and delays in construction activities. Various road development stakeholders also mentioned the need for strict road regulations, urban and regional planning, aesthetic improvement, urban renewal in aid of car-centric infrastructures, and routine maintenance on-road sections. The data are structured in various categories such as public involvement, environmental preservation, public policy, project planning, road design, road safety, economic recovery, and construction time. Lastly, the implications for future research directions are discussed. Keywords: Philippines · Road infrastructure · Risks and challenges · COVID-19

1 Introduction The Philippines, as a fast-growing country, has had the highest road infrastructure investment to date for the past five years compared to the previous years. The government’s plan in July 2017 to make the succeeding years the “Golden Age of Infrastructure” gave birth to the government’s “Build, Build, Build” (BBB) program from 2017 to 2022. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 326–339, 2023. https://doi.org/10.1007/978-981-19-7331-4_26

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The BBB Program is envisioned “to boost infrastructure development, and usher in the envisioned ‘Golden Age of Infrastructure’ of the country in the medium term by intensifying investments on public infrastructure while addressing implementation bottlenecks, ensuring the readiness of infrastructure programs and projects (PAPs) in the pipeline, and enhancing the absorptive capacities of implementing agencies in project preparation, development, and implementation.” (NEDA 2018). However, various risks and challenges arise in the outburst of road infrastructure if projects are poorly planned or executed. It resulted in creating numerous environmental, economic, and socio-political problems. Road proponents and stakeholders often proclaim the positive effects of new roads, but their potential risks are frequently downplayed. The study aims to summarize the most recent risks and challenges in the Philippines’ road infrastructure based on the literature review, Covid-19 related issues, online news articles, social network services, government issuance, policies, and primary data conducted through an interview questionnaire. This study structured the mentioned risks and issues. It gained a better understanding of road infrastructure’s unique risks and challenges based on the stakeholders’ perspective and related literature.

2 Literature Review Various reports in the past underscored the insufficient and underdeveloped infrastructure in the country. “Insufficient infrastructure has been a major constraint to economic growth and poverty reduction in the Philippines” (World Bank 2005). Inadequate infrastructure, particularly in electricity and transport, was identified as a critical constraint to investment and growth in the country (ADB 2007). Moreover, critical reforms in infrastructure did not keep pace with the growing population and increasing urbanization. Issues such as low-quality public transport, traffic congestion, poor road network quality, inadequate road safety features, and traffic in major container ports, among others, remained (NEDA 2017). There is a need for investments in urban development to address infrastructure deficits in big cities. Likewise, there is a need for increased investments in climate-resilient infrastructure to enhance interregional connections and competitiveness with the end given sustaining high inclusive growth (ADB 2018). The infrastructure hurdles in the Philippines are so huge in terms of the amount and effort to deliver in public. Aside from the challenge of completing the intended budgets for the infrastructure projects, there are more risks and challenges arising in the country, and it is aimed to discuss in the following sections based on the literature review, Covid19 related issues, online news articles, social network services, government issuance, and policies. 2.1 High Maintenance Costs in Wet Environments Maintenance costs for roads can be very high in wet tropical environments. Localized floods or surface flows promote potholes and rutting (Beevers et al. 2012; Douven and Buurman 2013; Sidle et al. 2006), such road-surface damage sharply reduces mean

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vehicle speeds while increasing traffic bottlenecks and accident risk, depressing the economic potential of the road investment. 2.2 Funding Maintenance Works vs. Construction In many developing nations, too much funding is being devoted to ambitious roadexpansion schemes and too little funding allocated to maintain and repair roads in the years following construction (Douven and Buurman 2013). 2.3 Poor Governance Road projects are also highly vulnerable to poor governance. Major infrastructure ventures that involve large budgets and myriad interactions among government decisionmakers, road proponents, local stakeholders, and construction contractors are highly exposed to such challenges. Poor governance is especially problematic in low- to middleincome nations, for which corruption (in its many guises) is a more significant daily economic impediment than in wealthier countries (Laurance 2004; World Bank 2016). 2.4 Financial Risks of Road Projects Cost-benefit analyses for road investments often fail to include critical factors, such as the effects of inflation, the expense of servicing project debt, and long-term environmental and social impacts (Ansar et al. 2014; Flyvbjerg 2009). The costs of road maintenance, ecological restoration, and unexpected outlay from corruption, political instability, or labor disputes (Laurance et al. 2008) can easily exceed expected project returns (Douven and Buurman 2013). 2.5 Socio-Political Risks of Road Projects Some road projects instigate serious social unrest (Rudel 1983). During the initial phases of development, real or perceived inadequacies in community consultation or forced land reclamations can be flashpoints for conflict. Community dissatisfaction may arise if benefits from roads are distributed inequitably, such as a lack of employment opportunities for local residents or perceived government corruption. 2.6 Environmental Impacts and Risks Road building can affect biodiversity both directly, as an immediate consequence of a road and its construction; or indirectly, as a result of human activities that are facilitated by new roads (Laurance et al. 2009; Trombulak and Frissell 2000). Road construction in mountainous areas also increases the risk of landslides (Leshchinsky et al. 2017; Sidle et al. 2006).

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2.7 Environmental Impact Assessments Environmental impact assessments (EIAs) are intended to identify many of the risks and potential liabilities of infrastructure projects and to minimize such risks with suitable mitigation and offset measures. However, relatively few EIAs are considered sufficiently robust or adequate in the scope (Laurance et al. 2015). For example, requirements and approvals for EIAs are typically determined by local or national government jurisdictions. As such, the EIA depends upon the enforcement capacity, willingness, and predilections (e.g., pro-development or not) of the jurisdiction. EIAs often lack consistency across local or national political boundaries, limiting their utility and comparability (Jaeger 2015). Such deficiencies of EIAs increase the risk of environmental damage, social conflicts, and litigation. This can lead to project delays, cost overruns, or even project cancellation (Laurance et al. 2015). 2.8 Unsolicited Proposals to Promote Public Interest Unsolicited proposals of road infrastructure projects have been one of the key risks and challenges in the Philippines. They were mired with vagueness and corruption with grossly disadvantageous terms to the government engendering significant contingent liabilities that have materialized and constituted major continuing fiscal burdens and represented legal and policy challenges that have yet to be resolved (Asian Development Bank 2017). Relatedly, projects with unsolicited proposals face Public-Private-Partnership (PPP) infrastructure projects. Recall that 18 out of the 29 IFPs for the PPP mode in the new BBB list are considered unsolicited proposals (Table 1). Unsolicited proposals refer to PPP projects, which are submitted at the initiative of the private firm rather than in response to a request by the government. The temptation to accept such projects is great because of the promise of a less budgetary burden on the part of the government. However, these proposals carry serious risks, which include the following: (i) they may not fit with other developments under consideration and overall infrastructure development plan; (ii) they have typically been pursued through direct negotiations with the soliciting private proponent with no competitive test that the government is getting good value from the arrangement; and (iii) supporting analyses made by the private party have been biased and solid fiscal impact analyses have not been undertaken (World Bank 2009). 2.9 Inequitable Distribution of Infrastructure Projects One of the primary strategies to solve traffic congestion in Metro Manila is decentralization, a way of outward economic progress in the adjacent regions of Metro Manila. However, a large part of the budget still goes to Metro Manila. Table 2 looks into the regional distribution of the budgets of the Department of Public Works and Highways (DPWH) and the Department of Transportation (DOTr), the two major infrastructure implementing agencies of the national government. The combined expenditure program of these departments at P810.9 billion accounts for roughly 18 percent of the P4.5 trillion national budget in 2021.

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K. E. T. Fernando and M. Henry Table 1. Unsolicited proposal—infrastructure flagship projects.

Projects

Cost (In P Billion)

New Manila International Airport

735.6

Ninoy Aquino International Airport

102.1

C5 MRT 10 Project

81.5

Cebu Monorail System

78.9

MRT 11

71.1

LRT 6 Cavite Line A/Modified LRT 6 Phase

50.4

Laguindingan Airport

45.8

Davao International Airport

39.5

TPLEX Extension Project

23.9

Cavite-Tagaytay-Batangas Expressway

25.2

TPLEX Extension Proiect

23.9

NLEX-SLEX Connector Road

23.3

Bacolod-Silay International Airport

19.2

Kanan Dam

14.4

Iloilo International Airport

4.6

Kalibo International Airport

3.8

New Bohol (Panglao) International Airport

3.8

Fort Bonifacio-Makati Sky Train

3.5

Total

1,350.50

Source National Economic Development Authority (NEDA)

2.10 Delays in Construction Activities Under the Construction Safety Guidelines for implementing infrastructure projects during the COVID-19 public health crisis, DPWH D.O. no. 35 series of 2020, subsequent implementation of social distancing measures beginning March 2020, and the critical issues on project financing could delay the timely completion of infrastructure projects. 2.11 Declining Public Infrastructure Expenditure In a recent news report, Fitch Solutions Country Risk and Industry Research has downgraded its growth forecast for the Philippine construction sector to 2.9 percent, noting that projects under the BBB Program will likely be delayed following the reduced budget for infrastructure this year. The infrastructure spending target for 2020 now stands at P833 billion, which is 15.8 percent lower than the P989 billion previously programmed for the year (Laforga 2020). Although 2.1 percent higher than the P816.2 billion disbursements in 2019, the public infrastructure budget this year is 10.9 percent lower than the P990.5 billion in 2018 (Fig. 1). Moreover, actual disbursements for infrastructure

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Table 2. Regional distribution of DPWH and DoTR budgets, 2021 (amount in million PHP). DPWH Amount

DOTr % Share

Amount

% Share

NCR

659,141.20

98.77

141,249.2

98.39

CAR

538.60

0.08

81.4

0.06

Region 1

493.50

0.07

172.7

0.12

Region 2

523.80

0.08

125.0

0.09

Region 3

706.70

0.11

245.1

0.17

Region 4A

661.60

0.10

307.0

0.21

Region 4B

447.70

0.07

66.9

0.05

Region 5

673.30

0.10

154.7

0.11

Region 6

655.60

0.10

173.3

0.12

Region 7

607.50

0.09

186.3

0.13

Region 8

575.90

0.09

160.1

0.11

Region 9

446.40

0.07

143.7

0.10

Region 10

542.30

0.08

134.9

0.09

Region 11

451.80

0.07

145.5

0.10

Region 12

417.50

0.06

118.5

0.08

Carga

440.80

0.07

97.3

0.07

0.00

0.00

0.00

667,334.20

100.00

143,561.60

BARMM Total

0.00 100.0

Source CPBRD Agency Budge Notes for DPWH and DOTr, FY 2021

and other capital outlays fell by 10.2 percent to P196.2 billion in January to April 2020 from P206.4 billion in the same period last year. 2.12 Low Tax Revenues Figure 2 compares government tax and non-tax revenues from January to May for 2010 to 2020. The low tax revenues impose more significant risks in the future. A runaway deficit is worrying because it could mean that public debt will surge shortly. Indeed, declining government revenues and rising budget deficits do not augur well with the government’s massive infrastructure program, which is supposed to be funded directly through the national budget.

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Fig. 1. Public infrastructure budget (amount in Php billion and as % to GDP). Source Department of Budget and Management (DBM). Notes 1 2000 to 2018 based on obligation. 2 2019 based on GAA level; 2018 to 2020 Nominal GDP projections based on December 2019 DBCC Meeting. 3 2021 to 2022 are based on DBM projections; 2021 to 2022 nominal GDP projections based on March 2019 DBCC Meeting.

Fig. 2. Tax and non-tax revenues (January to May, amount in Php million). Source of basic data: Cash Operations Report, Bureau of Treasury

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2.13 The Trade-off with More Urgent Covid-19 Response Measures One of the emergency powers given to the President in the “Bayanihan to Heal as One Act” (Republic Act No. 11469) is the power “to direct the discontinuance of appropriated programs, projects and activities (PAPs) of any agency of the executive department in the FY 2019 and FY 2020 General Appropriations Act (GAA) including unreleased appropriations and unobligated released allotments to augment the allocation for COVID-19 response measures. (Section 4 (v) of the “Bayanihan to Heal as One” Act (Republic Act No. 11469). Amid the pandemic, the government, acting as an economic agent with a limited number of resources, is facing a dilemma on what to pursue between large-scale infrastructure projects and the more urgent COVID-19 pandemic measures. 2.14 Low Absorptive Capacity The low absorptive capacity of agencies is indicative of their inability to effectively manage the increasing amount of funds entrusted to them due to insufficient physical delivery of target projects and activities. Notwithstanding the huge budgetary allocations for these significant infrastructure agencies, such as the DPWH and DOTr, they continue to experience difficulties in fully maximizing the use of their annual budgets. While these agencies’ obligation rates (percent of obligations incurred over-allotments) have grown over the years, their disbursement rates (percent of disbursements over obligations) have been perennially low (Table 3). Table 3. DPWH and DOTr obligation rates and disbursement rates (in percent). Obligation rates

Disbursements rates

DPWH

DOTr

DPWH

DOTr

2015

77.1

58

–

–

2016

77.5

67.1

73.2

79.2

2017

92.5

84.1

36.3

39.2

2018

92.6

90

42.9

40.7

2019

87.8

85.2

56.4

42.5

Note No data is available for the Disbursement rate in 2015. Source Statement of Appropriations, Allotments, Obligations, and Balances (SAOB), DBM

The major issues that affect the absorptive capacity of the agencies are road rightof-way (ROWA) problems; poor project preparation and planning; a deficit in technical capabilities; problems in bidding, contracting, and procurement; project design alteration and variation orders; difficulty in complying documentation requirements; issues on synchronization, complementation, and coordination with other government agencies including local government units (LGUs), among others (Rosales 2017) are the reported issues that contend the timely accomplishment or completion of road infrastructure projects.

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2.15 Foreign Assisted Funds Through the presidential adviser, the government admitted that it might be more challenging to secure financing from multilateral lenders, bilateral development partners, and even the private sector to roll out big-ticket infrastructure as the global economy suffers because of the COVID-19 virus (De Vera 2020). Multilateral lenders such as the IMF, ADB, the World Bank, and the Asian Infrastructure Investment Bank (AIIB) are currently prioritizing financing for COVID-19 response as borrower-countries worldwide scramble to fight the disease with more money needed to support vulnerable sectors and keep their economies afloat. Even the Philippines’ bilateral partners in the infrastructure rollout, such as China, Japan, and South Korea, are also grappling with their domestic COVID-19 outbreaks and possibly temporarily setting aside the grant of Official Development Assistance (ODA). 2.16 Uncertainties Over PPPs The strict implementation of the government community lockdowns affected the businesses at the height of the pandemic. It did not spare big companies participating in the Public-Private-Partnership (PPP) programs (Table 4). Table 4. Net income (loss) after tax of selected conglomerates/companies, Q1 2020 and Q1 2019. Conglomerates/companies

Net income (Loss) Income/(Decrease) (in %) after tax (In P milloin) Q1 2020

Q1 2019

Ayala Corporation

10,821.0

13,349.0

(18.9)

Metro Pacific Investments Corporation

3,690.0

5,660.0

(34.8)

JG Summit

3,998.4

9,721.8

(58.9)

SM Prime Holdings

8,396.9

9,721.8

(6.7)

San Miguel Corporation

1,093

8,995.3

(91.5)

Aboitiz Equity Ventures

2,998.3

12,825.0

(48.0)

Jollibee Foods Corporation

(2,073.5)

1,345.6

(253.1)

Filinvest Development Corporation

4,043.8

3,863.9

4.7

Source Philippines Stock Exchange (PSE) Edge (https://edge.pse.com.ph/financialReports)

This could weigh heavily on the prospects of some BBB projects supposed to be financed via the PPP mode as many of these private firms are expected to cut on their capital expenditures for the year.

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3 Interview Summary 3.1 Survey Overview The researchers are currently conducting a study on understanding the perspectives of various stakeholders of a suspended road widening project in the Philippines, a qualitative study using Q methodology. The Q methodology is a set of connected techniques designed to enable the study of subjectivity (views, opinions, beliefs, values, tastes, etc.) the perspectives of what people think and feel about concerning the questions” (Brown 1993). The study aims to understand various stakeholders affected by the road project socially and deal with environmental issues. A part of the study is to provide a questionnaire on the participant to distill the core meanings of the results. In the middle of the survey, a questionnaire was asked to 25 participants. The participants were local and national government officials, non-profit organizations, academia, business people, motorists, environmentalists, residents, and cyclists. The interview was done online via video telecommunication due to distance constraints. The question answered by the respondents was: “Do you have any strong views on the planning, design, construction, and maintenance of road improvement projects in the Philippines in general?”

4 Summary of Responses The responses were summarized into eight statements. Out of 25 participants, only 21 answered the question. Statements with similar meanings were combined. The exact answers were reconstructed so that the core meaning is still respected and presented. The summarized responses are enumerated in the following statements. • Unimplemented laws cause road infrastructure failure in the country; overloading, illegal parking, illegal settlers, traffic rules. • The government should continue the road projects until their completion, even with the change of political administration. • The mass transit system is a better approach than building more roads. • Road planning should always consider the long-term effect on the economy, society, and environment. • National roads in the Philippines are not well-illuminated. • Aesthetic improvement on road infrastructure is a suitable replacement if projects directly impact the environment. • Lack of urban planning caused the perennial problem of traffic congestions in urban areas. • The slow progress of contractors.

5 Summary and Discussions The abovementioned risks and challenges are structured in various categories such as public involvement, local impact, road safety, environmental preservation, project planning, construction time, and other social and environmental aspects of sustainability. The

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following table shows the risks and challenges of road infrastructure in the Philippines from primary and secondary data and sorted into various categories (Table 5). The risks and challenges of road infrastructure development in the Philippines vary widely between the primary and secondary data. Primary data shows the perspective of significant stakeholders based on their first-hand experience. They see the challenges in their personal view; political views, aesthetic, unimplemented laws, long-term effects, and quality of road infrastructure. Noticeably, their perspective areas are subjective but seem very practical and seen daily. On the contrary, secondary data from related literature, government policies, publication, and other sources showed evidence through Table 5. Structured risks and challenges of road infrastructure in the Philippines Category

Risks and challenges Primary data

Secondary data

The government should continue the road projects until their completion, even with the change of political administration

Socio-political risks of road projects

Environmental preservation Aesthetic improvement on road infrastructure is a suitable replacement if projects have a direct impact on the environment

Environmental impacts and risks

Public policy

Funding maintenance works vs. construction

Public Involvement

Unimplemented laws cause road infrastructure failure in the country; overloading, illegal parking, illegal settlers, traffic rules

Unsolicited proposals to promote public interest

Environmental impact assessments

Inequitable distribution of infrastructure projects Poor governance

Project planning

Road planning should always High maintenance costs in wet consider the long-term effect on environments the economy, society, and environment

Construction time

Slow progress of contractors

Road design

The mass transit system is a better approach than building more roads

Delays in construction activities Low absorptive capacity

Lack of urban planning caused the perennial problem of traffic congestions in urban areas (continued)

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Table 5. (continued) Category

Risks and challenges Primary data

Road safety

Economic recovery

Secondary data

National roads in the Philippines are not well-illuminated Financial risks of road projects Declining public infrastructure expenditure Low tax revenues The trade-off with more urgent COVID-19 response measures Foreign assisted funds Uncertainties over PPPs

the unequal distribution of infrastructure projects, national budget, tax revenues, low absorptive capacity, and foreign and private funding. The various data came from related literature, but it is straightforwardly quantifiable and in the state’s viewpoint. Not all the data falls to all categories of road infrastructure. The primary data are not only categorized in economic recovery and construction time. At the same time, the secondary data are not organized in road safety and road design.

6 Conclusions The risks and challenges in road infrastructure in the country were summarized based on the literature review and firsthand respondents. It went through 16 different points from the literature review and eight restated statements from respondents through an interview questionnaire. While it showed a wide variety of risks and challenges in many aspects, it was structured into eight categories: public involvement, environmental preservation, public policy, project planning, road design, road safety, economic recovery, and construction time. It helped the researchers compare and contrast the risks and challenges based on literature and perceived by respondents. However, this paper has no guarantees that all the risks and challenges are covered. For example, at the onset of the Covid-19 pandemic, new risks and challenges arose in road infrastructure development. More delays in the implementation were expected due to social distancing, tax revenues reduction due to financial crisis, same as the challenges in big companies and foreign countries that were not spared with the pandemic and made them shift other priorities than funding road infrastructure. Even the national government went through a trade-off with more urgent Covid-19 response measures. Moreover, the number of respondents (25) may not be enough to cover all the issues that stakeholders of road development perceived. A deeper study is recommended to cover all perceived risks and challenges among the stakeholders or even a proactive approach to

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safeguard the risks by prediction. This paper may be a good reference for future studies, e.g., subjective study on people’s perspectives on road infrastructure development. As mentioned in this paper, a Q methodology can be used as an excellent method to study the subjectivity of a specific topic. The above data can be used as statements needed to conduct the Q methodology. Statements that are the Q samples are vital in the process of Q methodology, which in this case is about road infrastructure development. Acknowledgements. The authors would like to thank the Japan International Cooperation Agency (JICA) for the financial support and providing the long-term training program – Road Asset Management Program.

References Ansar, A., Flyvbjerg, B., Budzier, A., Lunn, D.: Should we build more large dams? The actual costs of hydropower megaproject development. Energy Pol. 69, 43–56 (2014). https://doi.org/ 10.1016/j.enpol.2013.10.069 Asian Development Bank: Meeting Asia’s Infrastructure Needs (2017) Beevers, L., Douven, W., Lazuardi, H., Verheij, H.: Cumulative impacts of road developments in floodplains. Transp. Res. Part D Transp. Environ. 17, 398–404. (2012) https://doi.org/10.1016/ j.trd.2012.02.005 Brown, S.R.: A primer on Q methodology. Operant Subj. 16, 91–138 (1993) Douven, W., Buurman, J.: Planning practice in support of economically and environmentally sustainable roads in floodplains: the case of the Mekong delta floodplains. J. Environ. Manage. 128, 161–168 (2013). https://doi.org/10.1016/j.jenvman.2013.04.048 Flyvbjerg, B.: Survival of the unfittest: why the worst infrastructure gets built—and what we can do about it. Oxford Rev. Econ. Policy 25, 344–367 (2009). https://doi.org/10.1093/oxrep/ grp024 Jaeger, J.A.G.: Improving environmental impact assessment and road planning at the landscape scale. Handb. Road Ecol. 32–42 (2015) Laforga, B., 2020. Budget Cuts Seen Delaying Projects Dampening Growth in Construction Industry [WWW Document]. BusinessWorld Laurance, W.F.: The perils of payoff: corruption as a threat to global biodiversity. Trends Ecol. Evol. 19, 399–401 (2004). https://doi.org/10.1016/j.tree.2004.06.001 Laurance, W.F., Croes, B.M., Guissouegou, N., Buij, R., Dethier, M., Alonso, A.: Impacts of roads, hunting, and habitat alteration on nocturnal mammals in African rainforests. Conserv. Biol. 22, 721–732. https://doi.org/10.1111/j.1523-1739.2008.00917.x (2008) Laurance, W.F., Goosem, M., Laurance, S.G.W.: Impacts of roads and linear clearings on tropical forests. Trends Ecol. Evol. 24, 659–669 (2009) Laurance, W.F., et al.: Reducing the global environmental impacts of rapid infrastructure expansion. Curr. Biol. 25, R259–R262 (2015) Leshchinsky, B., Olsen, M.J., Mohney, C., Glover-Cutter, K., Crook, G., Allan, J., Bunn, M., O’Banion, M., Mathews, N.: Mitigating coastal landslide damage. Science (80-. ). 357, 981–982 (2017) NEDA: Public Investment Program 2017–2022 (2018) NEDA: Philippine Development Plan 2017–2022. Pasig City (2017) Rosales, J.P.: The philippines-national study: infrastructure financing strategies for sustainable development (2017)

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Rudel, T.K.: Roads, speculators, and colonization in the Ecuadorian Amazon. Hum. Ecol. 11, 385–403 (1983) Sidle, R.C., Ziegler, A.D., Negishi, J.N., Nik, A.R., Siew, R., Turkelboom, F.: Erosion processes in steep terrain—Truths, myths, and uncertainties related to forest management in Southeast Asia. For. Ecol. Manage. 224, 199–225 (2006). https://doi.org/10.1016/j.foreco.2005.12.019 Trombulak, S.C., Frissell, C.A.: Review of ecological effects of roads on terrestrial and aquatic communities. Conserv. Biol. 14, 18–30 (2000) The ADB: Philippines, 2018–2023 – High and Inclusive Growth. Country Partnership Strategy, Manila (2018) Turner, B.: Asian Development Bank. In: Turner, B. (ed.) The Statesman’s Yearbook 2008. TSY, pp. 68–69. Palgrave Macmillan UK, London (2007). https://doi.org/10.1007/978-1-349-740246_92 World Bank: Worldwide governance indicators (Washington, DC: World Bank) [WWW Document]. Washington, DC World Bank. (2016). http://info.worldbank.org/governance/wgi/index. aspxhome World Bank: Philippines: Meeting Infrastructure Challenges. World Bank, Washington, DC (2005)

Teaching and Learning During and After Pandemic

Understanding Sustainability Practices Through Sustainability Reports and Its Impact on Organizational Financial Performance Mavian Xin Yi Tay1 and Stephen En Rong Tay1,2(B) 1 Department of the Built Environment, 4 Architecture Drive, Singapore 117566, Singapore

{mavian.tay,stephen.tay}@nus.edu.sg 2 Solar Energy Research Institute of Singapore, 7 Engineering Drive 1, Singapore 117574,

Singapore

Abstract. Beyond publishing annual reports, which document organizational activities and their financial performance, organizations are increasingly publishing sustainability reports to inform stakeholders and the public about their sustainability practices. This raises the question as to whether there is a correlation between sustainability practices and financial performance. However, sustainability reports contain huge bodies of text, and much time is required to analyze the content manually. Hence, text mining was employed in this study, by which the top-ten sustainability-related words in the sustainability reports were identified. Subsequently, these ten words were mapped to 5 UN SDGs: (1) Goal 3: Good health and well-being, (2) Goal 8: Decent work and economic growth, (3) Goal 9: Industry, innovation, and infrastructure, (4) Goal 12: Responsible consumption and production, and (5) Goal 13: Climate action, which were categorized into three themes: (1) Social (Goal 3), (2) Economic (Goal 8 and 9), and (3) Environment (Goal 12 and 13). The relationship between organizational sustainability performance and financial performance was subsequently examined with correlation analyses. The results revealed that organizations with higher FTSE Russell ESG ratings had higher GTI scores, which indicates higher transparency in their reporting. Organizations with higher FTSE Russell ESG ratings also had lower net profits, although the average net profit for these organizations was positive. Furthermore, no statistically significant relationship between FTSE Russell ESG and ROE was found. These findings suggest that ESG-rated organizations are still profitable, and that there is value in investing in ESG-rated organizations. Findings from this study provide an overview of the sustainability practices that local organizations are practicing, and could serve as a reference for other organizations to move towards a green economy. Keywords: Sustainability reporting · UN SDG · Sustainability practices · Financial performance · Return on equity

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 343–352, 2023. https://doi.org/10.1007/978-981-19-7331-4_27

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1 Introduction In 2015, the United Nations (UN) Sustainable Development Goals (SDGs) were introduced with the aim of spurring global efforts to tackle climate change and obtain a sustainable future. Following the introduction of the SDGs, Singapore has also announced her goal to transform the nation into a sustainable city by 2030 with the SG Green Plan. One key highlight of the plan is to move the nation towards a green economy, by encouraging local organizations to engage in sustainable practices (SG Press Centre 2021). To encourage organizational sustainability practices, organizations listed under the Singapore Exchange (SGX) are required to publish annual sustainability reports, in addition to their annual reports, to inform stakeholders and the public about their sustainability practices (Liu et al. 2019). However, there is a lack of studies mapping organizational sustainability-related trends and themes to the UN SDGs. This is important as the UN SDGs serve as a framework to move towards global sustainability by 2030. Mixed results were reported in studies aiming to understand the relationship between organizational sustainability performance and financial performance. Specifically, most studies have found a positive correlation; some studies found no correlation; and a handful reported a negative correlation between corporate environmental responsibility and their financial performance as reported in a review by Peloza (2009). This difference in results was attributed to the different metrics used to measure environmental performance (Liu 2020), which ranged from measuring the level of environmental pollution in organizations to the environmental awards received (Peloza 2009). In recent years, market benchmarks for sustainability performance, such as the FTSE Russell ESG rating (FTSE Russell 2018), which captures the environmental, social, and governance (ESG) aspect in organizations has been developed to serve as a standardized benchmark to evaluate organizational sustainability performance. As such, the use of ESG ratings as a metric for measuring organizational sustainability performance has been encouraged (Liu 2020). However, there is a lack of studies examining the relationship between organizational ESG ratings and financial performance in the Asian context despite Asia having the largest regional economy (Tonby et al. 2019). Hence, this lack provides an impetus to look at ESG-rated organizations in the Asian context. In view of these gaps in literature, the current study has two aims: (1) Identifying the contributions by local organizations towards the SDGs through text mining, and (2) Determining the relationship between sustainability efforts and financial performance in local organizations. Organizations in Singapore were used as an Asian case study due to policies that required sustainability reports to be published, which would facilitate analysis. The results obtained in this study would contribute to our understanding on the current sustainability priorities in local organizations, as well as understanding the value of engaging in sustainability practices, in the context of Singapore as an Asian context.

2 Methodology 2.1 Data Collection To understand the relationship between sustainability practices and organizational financial performance, organizations that subscribe to sustainability reporting in SGX were

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shortlisted for data collection. Specifically, 3 types of indicators were extracted from the SGX website: (1) Sustainability performance indicator: FTSE Russell ESG rating, (2) Sustainability report transparency indicator: Governance and Transparency Index (GTI), and (3) Financial performance indicators: Net profit and Return on equity (ROE). In addition to net profit, ROE, which has been used in literature as a financial performance indicator for organizations (Prado et al. 2020), was included in this study as it measures organizational profitability in terms of shareholders’ equity. All values of the indicators were for the year 2021. The rationale for extracting the FTSE Russell ESG rating is due to the nature of the data being a scale variable, which allows for quantitative analyses with the other indicators. The FTSE Russell ESG rating, GTI, net profit, and ROE, were reported for 36 organizations. Analyses were conducted with these 4 indicators using IBM SPSS Statistics 26, and a two-tailed test at 0.95 confidence was used. The latest electronic copies of the organizational sustainability reports were downloaded from the website of 36 organizations. As the sustainability reports for 2021 will only be released by the first quarter of 2022, the sustainability reports for 2020 were used, since these were published by the first quarter of 2021. Out of the 36 organizations, 3 organizations did not publish a sustainability report for 2020 and 1 other organization had their sustainability report locked via password protection. Hence, a total of 32 sustainability reports for 2020 from 32 organizations were collected electronically for text mining. To overcome the voluminous amount of text, text mining was employed to analyze the content of organizational sustainability reports by identifying the trends and themes in their sustainability practices, which has been reported in literature (Liew et al. 2014; Modapothala et al. 2010). 2.2 Procedure for Text Mining 2.2.1 Gathering and Converting Sustainability Reports to Plain Text Format The 32 sustainability reports that were fully accessible were downloaded in portable document format (PDF) from the respective organization website. To facilitate the text mining process, all 32 PDFs were converted to plain text format with Adobe Acrobat Pro DC. To avoid repetition of information, cover pages, content pages, figures, and tables were removed during the conversion process. 2.2.2 Text Mining with RapidMiner Text mining was conducted with an open-sourced software, RapidMiner (Liew et al. 2014), with its Text Processing Extension. Eight steps were involved, which are presented in Table 1 together with its functions. In addition, pruning was conducted, such that words appearing in 2 or more sustainability reports were included for analyses. To understand the focus of sustainability practices in organizations, frequency statistics were collected during text mining. Specifically, 2 types of statistics were collected: (1) Organizational involvement, which measures the degree of involvement organizations have in a particular issue, and (2) Word occurrence, which measures the degree of occurrence for a term in the sustainability reports. The mathematical formulas to calculate

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the two statistics are presented below: No. of sustainability reports that contain a word ‘x’ Total number of sustainability reports × 100% (1)

Organizational involvement =

No. of times word ‘x’ appears in the sustainability reports Total number of words in the sustainability reports × 100% (2)

Word appearance =

Table 1. Steps used for text mining and its respective function Step

Function

Step 1: Transform cases

To ensure uniformity in text type, all texts were transformed into lower case

Step 2: Replace tokens

Words that are presented in different variations are replaced to the common term For example, the words “Covid pandemic”, “Covid19”, and “pandemic” were replaced with “Covid”

Step 3: Tokenize

To obtain smaller units of text, all texts were split at non-letters

Step 4: Filter tokens by length

Tokens were filtered by length, such that all filtered texts have a minimum length of 3 characters. This helps to remove single-lettered alphabets and two-lettered tokens that might be too short to have meaning

Step 5: Filter English stopwords Words were filtered by a list of built-in English stopwords in the software Step 6: Filter stopwords

To further refine the text, irrelevant words, such as the name of the organization, were entered as stopwords, and subsequently filtered away

Step 7: Generate n-Grams

n-Grams, with n < 2, were generated. This meant that only words, as opposed to phrases were generated. This step also helped in removing duplicated words in phrases

Step 8: Stemming

Stemming was conducted to remove suffixes, such as “-ing”, in the terms. This helps to further group words with the same stem together to avoid double counting

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3 Results and Discussion 3.1 Themes in Organizational Sustainability Practices The entire corpus of 32 reports yielded 20,022 words, and was reduced to 7286 words after text mining. From there, based on the highest percentage value for both organizational involvement and word appearance, the top-ten sustainability-related words were extracted manually, which are presented in Table 2. Table 2. Results of the top-ten sustainability-related words from text mining arranged in decreasing organizational involvement Rank

Word

Organizational involvement (%)

Word appearance (%)

1

Employee

96.88

39.69

2

Business

93.75

23.36

3

Environment

93.75

21.52

4

Energy

93.75

16.24

5

Training

93.75

10.50

6

Social

93.75

10.23

7

Community

93.75

9.40

8

Emissions

93.75

9.00

9

Safety

90.63

17.12

10

Health

90.63

13.63

3.1.1 Drawing Links to the UN SDGs To better understand the prioritized sustainability themes endorsed in local organizations, the top-ten sustainability-related words were mapped to the UN SDGs. Subsequently, themes relating to the SDGs were identified. The result of this mapping is presented in Table 3. Five SDGs, which belonged to three themes, were subsequently mapped in the analysis. First, Goal 8 and Goal 9 of the SDGs were mapped under the “economic” theme as they relate to initiatives, such as employee training, that would contribute to organizational economic growth. Apart from the “economic” theme, two non-economic related themes, “social” and “environment”, were identified. Goal 3 of the SDGs was parked under “social” as it aims to promote healthy lives and well-being for individuals at all age groups. Efforts under this theme extend beyond promoting employee welfare, to the local community. The third theme “environment” encompasses goals 12 and 13 of the SDGs, which focus on environmental efforts, such as the adoption of renewable energy to reduce carbon emissions, to act against climate change. Together, these three themes of economic, social, and environment, which encapsulate 5 SDGs, were identified as sustainable priorities in local organizations’ sustainability

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Theme

Social

Economic

SDG No

Goal 3

Goal 8

Goal 9

Goal 12

Goal 13

Name of SDG

Good health and well-being

Decent work and economic growth

Industry, innovation, and infrastructure

Responsible consumption and production

Climate action

Top-ten sustainability-related words

• • • •

• Employee • Business • Training

Social Community Safety Health

Environment

• Environment • Energy • Emissions

report for the year 2020. Beyond initiatives that solely boost economic growth, the value of expanding the organization’s focus to incorporate social and environmental initiatives for sustainability can also be seen in non-Asia profit-making organizations (Epstein et al. 2015). As a whole, these efforts towards sustainability contribute to the UN SDGs. 3.2 Relationship Between Sustainability Practices and Financial Performance Before correlation analyses were conducted, all variables were tested for normality with the Shapiro-Wilk test. The test revealed that the FTSE Russell ESG ratings (p = 0.980) and GTI scores (p = 0.667) follow a normal distribution, while data on the net profit and ROE did not follow a normal distribution (p < 0.05). Hence, the Pearson correlation was conducted for FTSE Russell ESG Ratings and GTI scores, while the Spearman correlation was performed with data on net profit and ROE. Results from the correlation analyses are presented in Table 4. Table 4. Results from the correlation analyses FTSE Russell ESG

GTI

Net Profit

ROE

FTSE Russell ESG

1

0.374a

−0.391a

0.075

GTI

–

1

−1.84

−0.31

Net Profit

–

–

1

0.427b

ROE

–

–

–

1

a Correlation is statistically significant at the 0.05 level b Correlation is statistically significant at the 0.01 level

With regards to organizational transparency in reporting, the average GTI score for the 36 organizations is 97.70, with a minimum and maximum of 61 and 128 respectively. The lowest score for GTI, 61, was two times more than the minimum score of 30 (Mak 2009), which convey a relatively high degree of transparency in organizational

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governance disclosure and practices, financial transparency, as well as investor relations. The result from the correlation analysis revealed that there is a statistically significant relationship between FTSE Russell ESG rating and GTI score. Specifically, organizations with a higher FTSE Russell ESG rating had a higher GTI score, suggesting that organizations with a higher sustainability performance were more transparent in reporting. This is supported by the agency theory, which suggests that organizations engage in sustainability disclosure to create value for shareholders (Omair Alotaibi and Hussainey 2016). This implies that organizations with a higher level of sustainability performance would engage in a higher level of disclosure and reporting, to promote the value of the organization to existing or potential shareholders. To understand the relationship between sustainability and financial performance, correlation analyses were conducted. A statistically significant negative relationship between FTSE Russell ESG rating and the organizations’ net profit was found. This finding is in line with research which found that organizations with a higher score on sustainability performance do not capitalize as much as those with lower sustainability performance (Xiao et al. 2018). One possible explanation to this finding is through the agency theory, which suggests that during times of low profitability, such as the ongoing Covid-19 pandemic, organizations engage in more sustainable practices for a competitive advantage over other organizations, as well as for long-term financial gains (Reverte 2009). As costs related to environmental management is increasing (Barbera and McConnell 1990), there is a trade-off between the level of sustainability practices engaged and immediate profit. In addition, it is worth noting that though a negative correlation was observed, the average net profit generated by these 36 organizations practicing sustainability is still positive, at 22.31%, in this study (refer to Table 5). This is supported by literature which found that positive financial performance is achieved in organizations with social and environmental initiatives (Margolis and Walsh 2003). Hence, explaining for the negative correlation between FTSE Russell ESG and organizations’ net profit. Table 5. Descriptive statistics of the indicators on sustainability and financial performance Range FTSE Russell ESG Net Profit (%) GTI ROE (%)

M

SD

Minimum

Maximum

1.20

4.00

2.70

0.61

−85.18

157.62

22.31

38.16

61.00

128.00

97.70

14.96

−21.13

33.87

6.53

9.18

In addition to net profit, a correlation analysis between FTSE Russell ESG rating and ROE was conducted. In contrast with net profit, which takes into account organizational revenue and costs, ROE measures the rate of return on the shareholders’ investment in the organization. A statistically significant correlation between FTSE Russell ESG rating and ROE was not found in this study. This suggests that there is no statistically

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significant relationship between sustainability performance and the profitability of organizations, in relation to their shareholders’ equity. This finding is similar to literature which did not find a statistically significant relationship between organizational sustainability performance and ROE (Castro Sobrosa Neto et al. 2020), and no cost in investing in organizations engaging in ESG (Limkriangkrai et al. 2017). Still, the average ROE for the 36 organizations is positive, at 6.53% (refer to Table 5), suggesting a positive degree of efficiency in utilizing shareholders’ equity to generate income for the organization. This is supported by the statistically significant positive correlation between net profit and ROE, where organizations with higher ROE have higher value in net profits. Thus, highlighting that there is still value in investing in companies with ESG ratings. During the text mining analyses, in addition to the top-ten words related to sustainability, the word “Covid” was also widely documented across the sustainability reports. Specifically, the organizational involvement and word appearance values were 96.88% and 16.79% respectively, which becomes the second most frequently documented word in the sustainability reports. This suggests that the Covid-19 pandemic has been identified as important to local organizations, which could have impacted net profits as discussed previously. As compared to pre-Covid-19, businesses from all over the world have reported a fall in earnings during the pandemic (Buckley et al. 2021). This implies that initiatives towards ESG would now need to take into consideration the ongoing pandemic. The average 2021 GTI score for the organizations in this study was 97.70, which is three times that of the minimum score of 30 (Mak 2009). In addition, organizations with higher FTSE Russell ESG ratings had statistically significant higher GTI scores. The findings are encouraging as it implies that these organizations are transparent in their reporting. Next, with the environmental and financial performance data from 2021, this study found that organizations with a higher FTSE Russell ESG rating had statistically significant lower net profits, which were still positive rather than negative. Furthermore, although there is no statistically significant relationship between FTSE Russell ESG rating and ROE, the average ROE is still positive, implying that there is still value in investing in organizations practicing ESG. Overall, these findings suggest that there is still a relationship between environmental and financial performance, and it is still valuable for companies to engage in ESG from the stakeholders’ point of view, when examined during the time of the Covid-19 pandemic. To better understand if there are differences between organizational environmental and financial performance pre- and post-Covid-19, future studies could expand beyond the current study to analyze organizational environmental and financial performance data published before 2020. Also, sustainability reports published before 2020 could be analyzed and compared against the period of the Covid-19 pandemic. Beyond the latest 2020 organizational sustainability reports and 2021 FTSE Russell ESG and financial performance data, future studies could build upon the current study to analyze subsequent sustainability trends in organizations.

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4 Conclusions Together, the results obtained in this study revealed the current sustainability priorities in local organizations in Singapore as the Asian context, as well as the relationship sustainability performance has with financial performance. With text mining, the top-ten sustainability-related words in the organizational sustainability reports were identified. From there, these ten words were mapped to 5 UN SDGs: (1) Goal 3: Good health and well-being, (2) Goal 8: Decent work and economic growth, (3) Goal 9: Industry, innovation, and infrastructure, (4) Goal 12: Responsible consumption and production, and (5) Goal 13: Climate action. These 5 SDGs were identified to be under three themes: (1) Social (Goal 3), (2) Economic (Goal 8 and 9), and (3) Environment (Goal 12 and 13). To understand the impact between sustainability practices and organizational financial performance, correlation analyses were conducted. It was found that the average GTI score for these local organizations were approximately three times higher than the benchmark score of 30. Also, organizations with higher FTSE Russell ESG ratings had higher GTI scores. This indicates that organizations engaged with ESG were transparent in their reporting. With regards to financial performance, organizations with higher FTSE Russell ESG ratings had lower net profits, though the average net profit was still positive, suggesting that there is still value in sustainability practices. There was no statistically significant relationship between FTSE Russell ESG and ROE. Still, the average ROE was positive, which implies that there is value in investing in ESG-rated organizations. The findings from this study provide an overview of the sustainability practices that local organizations are practicing, and could serve as material to help other organizations to move towards a green economy. In addition, the findings, which were based in Singapore as the Asian context, could be utilized by organizations beyond Singapore as they move towards sustainability practices specifically focusing in the Asian region.

References Barbera, A.J., McConnell, V.D.: The impact of environmental regulations on industry productivity: direct and indirect effects. J. Environ. Econ. Manag. 18(1), 50–65 (1990) Buckley, P., Barua, A., Samaddar, M.: The pandemic has forced corporate debt higher: but is that a bad thing? Deloitte (2021) Castro Sobrosa Neto, R., Lima, C.R.M., Bazil, D.G., Oliveira Veras, M., Andrade Guerra, J.B.S.O.: Sustainable development and corporate financial performance: a study based on the Brazilian Corporate Sustainability Index (ISE). Sustain. Dev. (Bradford, West Yorkshire, England) 28(4), 960–977 (2020) Epstein, M.J., Buhovac, A.R., Yuthas, K.: Managing social, environmental and financial performance simultaneously. Long Range Plan. 48(1), 35–45 (2015) FTSE Russell: FTSE Russell and Sustainalytics announce global ESG partnership. FTSE Russell (2018) Liew, W.T., Adhitya, A., Srinivasan, R.: Sustainability trends in the process industries: a text mining-based analysis. Comput. Ind. 65(3), 393–400 (2014) Limkriangkrai, M., Koh, S., Durand, R.B.: Environmental, social, and governance (ESG) profiles, stock returns, and financial policy: Australian evidence. Int. Rev. Financ. 17(3), 461–471 (2017) Liu, F.H.M., Demeritt, D., Tang, S.: Accounting for sustainability in Asia: stock market regulation and reporting in Hong Kong and Singapore. Econ. Geogr. 95(4), 362–384 (2019)

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Liu, Z.: Unraveling the complex relationship between environmental and financial performance—a multilevel longitudinal analysis. Int. J. Prod. Econ. 219, 328–340 (2020) Margolis, J.D., Walsh, J.P.: Misery loves companies: rethinking social initiatives by business. Adm. Sci. Q. 48(2), 268–305 (2003) Mak, Y.T.: Governance and transparency index: findings. Corporate Governance and Financial Reporting Centre (2009). https://bschool.nus.edu.sg/cgs/wp-content/uploads/sites/7/2019/02/ CGIO-SGTI-Forum-Presentation-2009.pdf Modapothala, J.R., Issac, B., Jayamani, E.: Appraising the corporate sustainability reports—text mining and multi-discriminatory analysis. In: Innovations in Computing Sciences and Software Engineering, pp. 489–494 (2010) Omair Alotaibi, K., Hussainey, K.: Determinants of CSR disclosure quantity and quality: evidence from non-financial listed firms in Saudi Arabia. Int. J. Discl. Gov. 13(4), 364–393 (2016) Peloza, J.: The challenge of measuring financial impacts from investments in corporate social performance. J. Manag. 35(6), 1518–1541 (2009) Prado, G.F., Piekarski, C.M., Luz, L.M., Souza, J.T., Salvador, R., Francisco, A.C.: Sustainable development and economic performance: Gaps and trends for future research. Sustain. Dev. (Bradford, West Yorkshire, England) 28(1), 368–384 (2020) Reverte, C.: Determinants of corporate social responsibility disclosure ratings by Spanish listed firms. J. Bus. Ethics 88(2), 351–366 (2009) SG Press Centre: Singapore Green Plan 2030 charts ambitious targets for next 10 years to catalyse national sustainability movement [Press release]. SG Press Centre (2021) Tonby, O., Woetzel, J., Choi, W., Eloot, K., Dhawan, R., Seong, J., Wang, P.: The Future of Asia: Asian Flows and Networks are Defining the Next Phase of Globalization. McKinsey & Company (2019) Xiao, C., Wang, Q., van der Vaart, T., van Donk, D.P.: When does corporate sustainability performance pay off? The impact of country-level sustainability performance. Ecol. Econ. 146, 325–333 (2018)

Broadening the Perspective of the Roles of Civil Engineers – A Freshmen Module on How Engineers Solve Real-World Problems Kevin Sze Chiang Kuang(B) and Weng Tat Chan Department of Civil and Environmental Engineering, 1 Engineering Drive 2, Singapore 117576, Singapore {ceeksck,noelchan}@nus.edu.sg

Abstract. Taking the role of a team of civil engineers, students working in a group of five prepare a bid for a civil infrastructural project for the government to address a pressing need in society. Students were guided using a framework where they identify, define, set goals, generate solutions, and evaluate alternatives from the financial, economic, environmental and society perspectives. This Year 1 module was conducted using a flipped classroom approach in the second semester over a 13-week period. A different theme could be assigned for every new semester and the theme of “Designing Infrastructural Solutions to Tackle the Effects of Climate Change” was adopted for the most recent run of the module to reflect the current interest on this topic. This paper will outline the philosophy behind the development of this module and other details including the format and learning support provided for students, student activities and deliverables, assessment and student feedback. A discussion of the main lessons learnt and some recommendations for future adoption of this learning approach in a civil engineering programme will also be presented. Keywords: Flipped classroom · Climate change · Holistic evaluation · Infrastructure and the environment

1 Introduction A majority of students joining the department as freshmen has a narrow view of what a civil engineer does, typically imagined as an individual performing technical calculations and analyses, running simulation on the computers to construct buildings or infrastructure. Students also commonly expressed the disconnect they feel between the various modules they have to take in the course of their programme as well as the relevance of the modules to the real-world problems they are expected to solve as professionals. As they progress to Year 2 or 3, it is not uncommon to have students feeling a sense of lostness as they maneuver through various modules but have little sense of the larger picture of how the profession contribute to solving complex world problems such as climate change, energy crisis, housing, access to clean water and others.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 353–359, 2023. https://doi.org/10.1007/978-981-19-7331-4_28

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Most students do not get the opportunity to experience the process of tackling problem as presented in real-life since students are more used to answering questions which have been designed for them to test narrow analytical knowledge associated to specific engineering skills taught to them. The ability to identify problems, to articulate the problems clearly and stepping through the process of setting objectives, innovating solutions, evaluating alternatives, applying decision making tools and deciding on the best solution holistically having considered the trade-offs in their analysis are generic skills that are highly desirable when they face complex real-world problems. Having a broad view of what civil engineering as a profession contributes to solving complex real-world problems not only inspires and motivates students as they have a clearer picture of their roles and the privilege position they will be in as professionals but also prepares them to tackle problems holistically, bringing an awareness of the impacts of their professional decisions in the workplace on the environment, society and economy. A Year 1 module was redesigned in response to this need and one of the key learning outcomes of the module is the awareness that real-world problems faced by engineers are, in many cases, complex and the solutions are often open-ended. Students learn that there is no one ‘correct’ solution but a range of alternatives which engineers need to evaluate from multiple perspectives to reach the ‘best’ or most suitable solution. It is emphasized in the module that the engineer is not so much the problem-solver but rather the problem-inventor (Harris 1980); ‘inventing’ or defining the problem is typically the most important and difficult phase in the project. The symptoms of a problem are easily identified, the actual problem itself, not necessarily so. The module also provide opportunities to develop generic skills such identification and articulation of needs given a complex problem, taking leadership roles, communication and working in a team, technique to evaluate solutions holistically, basic financial tools, decision-making methods, awareness of impact of solution on the environment - these being some of the desired learning traits of graduates outlined in the Student Learning Outcomes for IES/Engineering Accreditation Board (EAB) Accreditation Exercise. The underlying aim of the module is to broaden students’ view of civil engineering and exposing them to the higher level broad, up-stream questions and thought processes a civil engineer encounters, in particular the “what” and the “where” to construct and the “why” for the choice of solution rather than on the “how” to construct, typically a downstream tasks of engineering analysis, computation and design. In the subsequent sections, details of the module will be presented including module learning format, types of deliverables and assessments, rationale for choice of deliverables. A number of key lessons learnt from the module will be summarized followed by some concluding remarks.

2 Module Details Entitled Infrastructure and the Environment: Principles and Practice, a chosen theme was adopted for each semester ranging from issues related to Climate Change, Smart Cities or Energy Crises, to provide a direction for the type of projects students can proposed for their term project.

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Conducted in a flipped-classroom method, the university learning management system (LUMINUS® ) was utilized where an extensive resource organized by week has been carefully compiled and accessible by students. Students are expected to read selected reading materials, watch videos (YouTubes), explore links to relevant websites prior to attending the studio sessions for group work discussions, presentations and consultations with faculty members. A comprehensive student manual (64-page) containing details of the modules, guidelines, learning outcomes, details of resource, discussions questions, learning flow, schedule, expected deliverables and other important information was prepared to guide students through the module. 2.1 Teaching Format There are 3 types of teaching or learning activities: (1) Studio-based sessions (2) ROC (Realities-Outside-Classroom) (3) Selected bit-size lectures and learning from invited speakers (academics/professional engineers). 2.1.1 Studio-Sessions In addition to lecture style teaching, learning activities were carried out mainly in active learning classrooms similar to those studio-style classroom where students sit in groups around a configurable table setting which allow group discussions among peers in the group as well as interaction with faculty members or tutors to be carried out. As opposed to seminar or tutorial rooms with fixed rows of tables and chairs facing the front the classroom, the active learning classrooms allow optical group-based interaction and learning. Faculty members are able to move from group to group for closer interaction with ease. When necessary, the facilitator is also able to address the entire classroom equipped with wall-mounted displays and front projects. Figure 1 illustrates the learning environment of studio sessions adopted in this module.

Fig. 1. Students work in group during a studio-session in an active learning classroom environment.

2.1.2 Realities Outside Classroom Reality-Outside-Classroom (ROC) includes field trips to venues such as local government agency galleries such as the Urban Redevelopment Authority (URA) City Centre,

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Land Transport Authority (LTA) Gallery, Marina Public Utility Board (PUB) Sustainable Gallery where interactions with officers from these organizations further enhanced students’ appreciation of the role of civil engineers in defining problems and coming up with the ‘best’ solutions to address the infrastructural needs of Singapore. Following the visit of each site, a summary of their observations and learning points are compiled and submitted as a field report. Many have given feedback that these visits (locals and internationals) have helped them appreciate the infrastructure they use every day, and the amount of debate and deliberation that took place before the start of construction of these mega infrastructure projects. Not only have they realized the importance of holistic evaluation and the impact of infrastructure on the environment, society and economy the visits also served to inspire them to propose interesting projects and bond the team together fostering a positive team spirit to carry them through 13 weeks of the module. 2.1.3 Bit-Size Lecture by Faculty Members and Invited Speakers This part of learning support is carried out at Lecture Theaters and typically comprised of a few short 15–20 min talks by colleagues involved in infrastructural projects (Geotechnical, Transportation, Augmented/Virtual Reality, AI and Smart Construction) as well as practicing professional civil engineers from the industry to share their industrial experiences, showing the broad possibilities and trade-offs in the real-world and to inspire students to think broadly, to encourage innovation and to broaden their view of civil engineering. 2.2 Student Deliverables and Assessments The main deliverable of this module is the Term Project, where each team is required to propose a project of their choice which addressed the need of a society through an infrastructural solution. Each team is given the freedom to identify the societal needs and through the 13-week duration, generate and select the most appropriate solution. The process of getting to the solution involves several steps outlined in the Project Evaluation Process (PEP). The term project could be one that solves massive traffic jams in a specific city (e.g. in Dhaka), frequent destructive flooding at a particular area of choice (Wuhan, Kansai Airport, Yangtze River etc.), chronic lack of water supply (e.g. North-South water transport in China), frequent road accidents (e.g. the death highway in Manila), air and water-pollution problem, drought, water sufficiency (e.g. in Singapore), electrification of a under-developed region (inner Mongolia), lack of or inefficient public transportation system, facing threats of the Tsunami (e.g. Kamashi Japan etc.) that occur in any part of the world. The team could solve an existing problem (i.e. where a solution is not currently in existence for that site) or a project where an infrastructure solution is already in place. For the latter case, students are asked to step back in time to the time prior to the construction of the existing infrastructure, imagining themselves to be the consultants at that time having to decide on alternatives to fulfil the need at the time before the existing infrastructure was built. This allows them to assess whether the existing solution has indeed been the best solution based on the holistic framework introduced in the module.

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The exercise has helped students gained a wider appreciation of the importance of a holistic evaluation of alternative solutions to the problem they have identified. Through this approach, students can learn about the rationale and debates behind the constructions of many world-famous infrastructure. In addition, students also appreciate that existing solutions are not always the best solution (in some countries) based on the holistic model of project evaluation. Other deliverables expected from students are listed below (100% CA with individual Quizzes): 1. Interim Group Project Proposal Poster (8%) and Interim Group Oral Presentation (8%) 2. Quizzes (30%) 3. Final Group Presentation with Video Pitching Segment (15%) 4. Group Technical Consultant Report for Team Project (15%) 5. Individual Reflection Write-Up on the learning process (5%) 6. Individual Summary Notes – and peer sharing based on prior readings (10%) 7. Group End-of-Session Sharing and Participation (9%) Individual Peer Feedback from each member of the group for peer evaluation was also carried out to provide module coordinator information in assessing the marks and grades of each member of the group to address the issue of idling members. The deliverables above were chosen for specific pedagogical purposes: 1) Posters, Video Pitch Oral & Presentations and Technical Consultant Report – To mark their project milestone at various stages of the Project Evaluation Process. – To allow students the opportunity to convey information in a variety of medium of communications e.g. use of a single A1-size Poster, Oral presentations with slides and a Video Pitching segment embedded in their Final Presentation. 2) Individual Reflection Write-up – Students to reflect on their learning in this module (i.e. flipped classroom method, field trip) and on changes in their perspective of the role of a civil engineers. Three samples of the write-up are attached in the appendix. 3) Individual Summary Notes – Aim is to foster self-learning by writing their own summaries of paper they read and videos watched. 4) Individual Pre-Session Sharing (prior to main session, students share their readings in their groups) – This is to encourage bonding and peer learning from each member of the group as well as to encourage students to come prepared for each study session.

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5) Group end-of-session sharing – This comprises giving a short presentation by selected groups toward to the end of the class to help students sum up what was discussed. The various opportunities to present to peers help to build up their public speaking and questioning skill. 2.3 Lessons Learnt Three key lessons are summarized below based on the past three runs of the module. (1) Ambiguity in a flipped classroom format: The flipped-classroom approach adopted was found to be effective in a module such as this where the scope is broad with open-ended discussion opportunities. Close interactions with students is in a studio-style approach provides ample opportunities for the faculty member to work closely with each group them to guide them in their project. Although initially, some students found it challenging to have to adapt to a new learning format (most are not familiar with a flip-classroom studio style format) students also appreciated how this style of learning has stretched their minds and confidence to work in a group to deliver a challenging project. (2) Quality and Fast Feedback is important to student: In this module, significant amount of time is needed to spend in discussion with students during studio sessions (typically 25 groups per intake). It tends to be mentally demanding for the facilitator, as each group works on a unique project and the facilitator will need to understand the relevant issues related to the project in order to provide good feedback and to critique the project whilst encouraging the team and remain “upbeat” about the module as he visits every group. It has been encouraging that students are actually perceptive of the efforts put in by facilitators and are discerning of the quality of feedback given to them. Detailed written feedback for their interim project proposals were given by followed by discussions them during study sessions on the written feedback was highly valued by students. A recurrent comment in the student evaluation responses is their appreciation of the (fast) feedback students received as the teaching team responds to them via social media (WhatsApp) or email apart from the usual face-to-face or Zoom (optional sessions). It is clear from their comments, that students associate the fast response to their queries by the facilitator as indication of the care and commitment level of the facilitator have towards the students (Teven and McCroskey 1997). (3) Timing consuming - heavy workload In this module, students are required to do vast amount of reading around the topic of infrastructure in general and the background of the specific project they have chosen. Some students may find this approach of learning (without a set of power-point

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notes provided by lecturers) uncomfortable and time consuming. Having a flexible, selfdirected learning approach, is empowering for some students. They enjoy the process and grew from it while others find the experience “tedious and torturous”. The ability to learn quickly picking up relevant information and knowledge is a 21st century skill for every engineer and a mix of guided and self-directed learning would be a good balance of flexibility and more efficient use of learning time.

3 Conclusions This paper described a module where a flipped classroom model was adopted to create an interactive flexible learning environment where student groups role-play a technical consultant group to identify and solve a chosen infrastructure project to address the needs of a society using a holistic approach to evaluating alternative solutions whilst balancing the trade-offs of the decisions involved in the selection of the solution. Through this module, students had the opportunity to think broader addressing upstream questions on the “what”, “where” and “why” of infrastructure solutions in solving complex real-world problems. Evidence from student feedback have shown how the module has broaden their views of civil engineering and develop their problem solving skills preparing them to address complex real-world as they enter their career as professional civil engineers.

References Harris, A.J.: Can design be taught? In: Proceedings of the Institution of Civil Engineers, vol. 68, pp. 406–416 (1980) Teven, J.J., McCroskey, J.C.: The relationship of perceived teacher caring with student learning and teacher evaluation. Commun. Educ. 46, 167–177 (1997)

SafeSim Design: A Digital Game-Based Learning Approach to Address Design for Safety (DfS) Competency Sufiana Safiena, Juliana Tay, Yang Miang Goh(B) , and Michelle Lim Department of the Built Environment, National University of Singapore, 4 Architecture Drive, Singapore 117566, Singapore {bdgssak,jtay,bdggym,l.shm}@nus.edu.sg

Abstract. The Singapore government enacted the Workplace Safety and Health (Design for Safety) Regulations in 2015. However, the construction industry continues to be the nation’s main contributor to workplace injuries. As such, there is a need to develop competency in Design for Safety (DfS) within the industry so that designers (i.e., engineers and architects) can anticipate and “design out” construction, maintenance, and demolition hazards and risks. One way to improve the DfS competency of designers is through digital game-based learning (DGBL), a research-based educational approach developed to motivate and engage learners through interactive gameplay. Thus, this study developed SafeSim Design (SSD), a single-player digital game, to educate designers on the difference between design risks and occupational hazards, conduct risk evaluation, and design out risks through various design-related controls. SSD incorporated different game design elements that could effectively support the learning needs of designers. In addition, the game content is a collective effort from the authors and industry professionals in collating design-related case studies, ensuring fidelity and authenticity. This paper presents the development process of SSD, including the different game design elements and the incorporation of specific teaching strategies. The study also demonstrates how SSD can be an effective teaching tool for professional development (PD). Future studies will include an experimental study to evaluate the effectiveness of DGBL as an instructional tool in the context of the Built Environment. Keywords: Design for Safety · Digital game-based learning · Safety training · Workplace safety and health · Professional development

1 Introduction The construction sector remains one of the most dangerous industries worldwide due to the high percentage of workplace injuries and fatalities (Choi et al. 2019). Singapore’s construction industry remained the top contributor to workplace fatalities in 2021 (Ministry of Manpower 2021). Accidents can be caused by unsafe acts, unsafe conditions, or both (Abdelhamid and Everett 2000). Many fatalities can also be attributed to design © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 360–372, 2023. https://doi.org/10.1007/978-981-19-7331-4_29

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decisions and the lack of design planning for safety (Behm 2005), which in turn can be ascribed to designers who may lack understanding of the implications of their unsafe designs. Furthermore, Goh and Chua (2016) and Schulte et al. (2008) stated that hazards could be eliminated or controlled more effectively with early intervention, providing a safer workplace and construction processes.

2 Literature Review 2.1 Need for DfS Competency The construction sector in Singapore has consistently emerged as the top contributor to workplace fatalities over the years, and in Q1 2021, the rate of fatality is higher than the pre-COVID levels (Ministry of Manpower 2021). Besides the contractors, developers and designers can help to improve workplace safety and health (WSH) performance through conscious and collaborative effort to identify design risks and integrate the appropriate control measures upstream. In a bid to create a safer working environment, the Workplace Safety and Health (Design for Safety) Regulations 2015 (“WSH (DfS) Regulations”) was introduced in Singapore in 2016 (Government of Singapore 2016). Design for Safety (DfS) or Prevention through Design (PtD) is a process of identifying and removing potential occupational safety and health hazards and risks associated with construction and maintenance during the design and planning phases (Behm 2005; Workplace Safety and Health Council 2020). It requires stakeholders to anticipate and “design out” potential hazards and risks associated with the construction or maintenance processes (Schulte et al. 2008). The DfS Regulation requires stakeholders such as developers, designers, and contractors to work together to address the risks at the source and plan for safe work (Government of Singapore 2016). Despite the implementation of the DfS Regulation, there is still room for improvement for more effective practice of DfS in Singapore (Toh et al. 2017). First, DfS training is part of professional development, and it often requires adults to invest additional time and energy beyond their usual work schedule. Second, DfS training is typically lecturebased. Although lectures are useful to transmit information, they are not as effective for learning, especially for application-based content such as DfS. As an instructional tool, DGBL can deliver different types of information through short, interactive sessions. This can position DGBL as a viable instructional method. 2.2 Digital Game-Based Learning (DGBL) as an Alternative Solution The term DGBL was first created by Prensky (2001) to address “the coming together of serious learning and interactive entertainment into a newly emerging and highly exciting medium” (p. 5). Although some researchers have shown that digital game-based learning (DGBL) positively impacts learners’ interest and understanding of the topic (Goedert and Rokooei 2016), there are others who do not share the same conclusion (Dichev et al. 2014; Randel et al. 1992). A possible explanation is the digital game used. Some researchers chose to use existing off-the-shelf types of games, which could lead to issues such as relevance and the connection between the game type and instruction objectives

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(Nousiainen et al. 2018; Sanchez et al. 2010). Another explanation is the differences in research design within DGBL research. Some researchers found that the participants demonstrated better retention of the learning gained, when they were assessed with a delayed test, (Kao 2020; Randel et al. 1992). Differences from the field of DGBL research highlighted the need to consider such factors when investigating the effective of DGBL is a teaching tool. To implement DGBL successfully, educators and researchers need to consider the specific features of the digital game. Not all digital game design features are helpful to the players’ learning progress. Features such as storyline and avatar personalisation may help increase the amount of time players spend in the game, but they may not lead to better performance (Dankbaar et al. 2015; Ibrahim 2017; Proske et al. 2014). Conversely, features such as real-world context and the use of authentic tasks in digital games, were found to be useful to the players’ learning (Chang et al. 2020; Hwang and Chang 2020). These features allowed the players to anchor new knowledge with their prior experiences (Kebritchi and Hirumi 2008; Sanchez et al. 2010). Additionally, players were able to make mistakes in the digital world and learn through their mistakes the process and how their actions affect the outcome (Martin 2000). Another benefit of using DGBL is the design and duration of the games, which are important factors of consideration an upskilling course. Professionals need to invest time and energy beyond their usual work schedule to take an upskilling course and digital games can be designed to deliver different types of information through short interactive sessions, which could address the issues of time and energy (Smith and Sanchez 2010). However, there is limited research about the use of DGBL in the field of upskilling, as a result, the influence of DGBL remains unclear. Hence, we decided to adopt DGBL as an avenue for designers to learn about DfS and its concepts. This study introduces a DGBL prototype, SafeSim Design (SSD). It aims to help engineers and other designers learn about the importance of DfS, understand the difference between design risks and occupational hazards, conduct risk evaluation, and how to design out issues through design changes and design-related controls. Furthermore, this study aims to compile a list of design-related issues and their design-related controls to facilitate the development of a digital game aimed at improving the DfS knowledge of designers.

3 Methods See Fig. 1.

Initiation

Development

Testing

Refinement

Fig. 1. Stages of developing SafeSim Design (SSD) as a DfS training tool

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3.1 Initiation Stage During the initiation stage (refer to Fig. 1), case studies were collected from various engineering professionals who have experience conducting DfS reviews. Each case study provided the context, associated design risks, and possible design-related controls. These case studies were categorised based on their similarity and documented as a consolidated document (“DfS Library”). The DfS Library was then used to generate authentic contexts for SSD (Goh et al. 2021). The DfS Library has gone through several checks by different experts to ensure the design-related controls are feasible in Singapore. Additionally, a robust systematic literature review was conducted to understand the effectiveness and feasibility of adopting DGBL for adult learners in the context of professional upskilling. Several game features were also identified to satisfy the need of users and to ensure learning outcomes are met through the game. 3.2 Development Stage Cases from the DfS Library were extracted, mixed, and matched to generate different game development scenarios for SSD. Several gamification elements such as an award system, immediate feedback, role-playing, and hints were adopted to meet the learning outcomes. In addition, the authors worked closely with the game developers and industry experts to ensure that scenarios in the game were authentic and satisfied the learning outcomes. The following subsections will address SSD features based on the findings from the literature review. 3.2.1 Overview of SafeSim Design (SSD) SafeSim Design (SSD) is a prototype single-player digital game for designers to learn about design risks and hazards through a gameplay approach. SSD is developed based on the authors’ previous work on SafeSim Risk (SSR), a study where the authors developed the digital game (SafeSim Hazards (SSH)) based on the extended authentic learning framework (Safiena and Goh 2022). SSR, a successor of SSH, is designed to train players to identify hazards and good practices on a virtual construction site and understand the likelihood and severity of identified hazards (Safety and Resilience Research Unit (SaRRU) 2021). However, SSD extends beyond SSR, focusing on the implications of unsafe design throughout the project lifecycle. SSD aims to educate designers on the differences between design risks and occupation hazards, how to conduct risk evaluation, and how to design out these design risks through various design-related changes or controls. Therefore, SSD is a feasible option for designers, architects, and engineers to learn more about DfS along with opportunities to correct the identified design risks. SSD has four different scenarios, and each scenario addresses different design limitations. Each scenario is also designed to address different learning outcomes and has varying difficulty levels. The prototype SSD has a gameplay of 20 min for each scenario. Each player is required to log in using their provided credentials. Players may choose to complete all four scenarios in one sitting or complete each scenario separately. In each scenario, players will go through two phases: identification and mitigation. The progress of the player is encrypted and stored in the cloud database.

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3.2.2 Identification Phase

Fig. 2. Use of Mr Chief Designer (Mr CD) as a guiding tool

Upon logging in with their credentials, SSD will show a short cinematic to provide players with the context of the game. Players will be introduced to a non-playable character (NPC) called Mr Chief Designer (Mr CD), who will guide the players throughout the game (refer to Fig. 2). Mr CD will introduce the players to the game user interface (UI) and provide guiding prompts (refer to Fig. 3) to help players consider the situation from the DfS point of view and make the right decisions. Mr CD will also guide the players through capturing their first design risk and show an example of red herrings. Red herrings refer to operational risks that can be effectively managed by downstream controls and not design-related changes or controls. Players are required to identify any hazards within the site. Apart from correctly identifying the hazards, players must answer the question attached to obtain the total score. If the player responded to the question correctly and identified the design risk, they will get the maximum score of 100 points. However, if they fail to get the correct answer, 50 points will be deducted. Players receive immediate feedback and see explanations for their choices (refer to Fig. 4). Players can use the hint button to grey out one of the options. However, the use of hints will cost the player 200 points. Players are also expected to evaluate the identified design risk based on the severity and likelihood. Mr CD will explain the rationale of risk evaluation and guide the player through the first assessment. Players can see their rating against the recommended rating provided by Mr CD (refer to Fig. 5). Players are advised to complete the identification phase within 15 min. However, points will not be deducted if players take more than the recommended time. After identifying all the design risks within the identification phase, a window popup will appear, alerting the players to proceed to the mitigation phase (refer to Fig. 6).

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Fig. 3. Guiding prompts to help players ease their way into the content and the gameplay

Fig. 4. Use of hint will grey out one of the wrong options (left), and immediate feedback will be given after choosing an option (right)

Fig. 5. Risk evaluation based on its severity and likelihood (left) and checking against the recommended rating and explanation (right)

Players can choose to continue to explore the site. However, no marks will be given for capturing red herrings.

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Fig. 6. Window pop-up alerting players to move on to the next phase after finding all the design risks within the stage

3.2.3 Mitigation Phase Players are expected to implement the most suitable design-related control or changes to mitigate or eliminate the design risk in the mitigation phase. Players can hover over the options to see the design-related changes. Some of the options are not design-related controls or changes. Immediate feedback is provided to explain why the recommended solution is the best for that context (refer to Fig. 7). SSD also has an option for players to offer alternative solutions that were not covered by the choices. They can type out their answers in the box provided. Their answers will be uploaded to the forum, where other players can critique and comment on the feasibility of the solution provided. In Scenario 1 of the game, players are introduced to predefined multiple-choice (MCQ) options to correct the design. Later in subsequent scenarios, players are introduced to bonus rounds to earn more points. To unlock these bonus rounds, SSD alerts the players of the availability of bonus rounds when they first enter the mitigation phase (refer to Fig. 8). The bonus rounds are highlighted with a yellow border. Players are required to choose the best option before being able to unlock the bonus rounds. Examples of bonus rounds can be seen in Fig. 9, where on the left, players are required to shift the location of the photovoltaic (PV) panels on the grid, and on the right, players are to choose the best layout for the pipes. No points will be deducted if the players do not get the right answer. Players will also receive an explanation for the correct answer for the bonus round. At the end of each scenario, players will view a summary of their score, the number of design risks they have identified and rectified, and the top scorers (refer to Fig. 10). This scoreboard allows the players to review their performance in the scenarios and acknowledges their achievements. After completing each scenario, the players can either continue to the next scenario, replay the scenario, quit the game, or go to the forum to discuss their answers.

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Fig. 7. Three mitigation options with different numbers of ticks and the explanation

Fig. 8. Bonus rounds available from Stage 2 onwards

3.3 Testing Stages Throughout the development of SSD, the authors conducted continuous user testing with different groups to gather feedback on game flow, aesthetics, and authenticity of scenarios, as part of a pilot study. In User Test #1 (refer to Fig. 11), experts involved in developing the DfS Library assessed the first iteration of the SSD prototype. During this session, the experts only evaluated Scenario 1. Feedback from experts was compiled and used to refine the game for the subsequent versions. During the second user test (User Test #2), both students and practitioners (i.e., engineers and safety personnel)

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Fig. 9. Examples of bonus rounds: shifting of PV panels (left) and choosing the right layout plan for the pipes (right)

Fig. 10. Summary page after completing each scenario

User Test #1

Alpha Test

• Jul 2021

• Feb 2022

User Test #2 • Oct 2021

Fig. 11. Continuous testing was conducted to gather feedback

were invited to assess the game build. The second user test featured Scenarios 1 and 2. During the Alpha test, the past testers from User Test #1 and #2, as well as new practitioners and students, assessed the whole four scenarios. Researchers also observed the testers’ behaviour throughout the testing sessions, and all the testers were required to provide their feedback through an online questionnaire.

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3.4 Refinement Stages Feedback from all testers was collated and evaluated. This includes the field notes from the researchers’ observations. The research and development team carefully evaluated scenarios and user interface/experience (UI/UX) changes to ensure that the learning and game objectives were met. Aspects of the game, from the game layout, sound effects, guidance tool, and even the colour scheme went through many changes to suit the target audience’s needs.

4 Results and Discussion The questionnaire uses a 5-point Likert scale which measures the perceived effectiveness of three major aspects: (1) game design elements, (2) game-based learning, and (3) game content authenticity (i.e., 1 = strongly disagree, 3 = neutral, 5 = strongly agree). The questionnaire was distributed to the two groups of testers (i.e., students and practitioners). The mean rating and standard deviation (SD) of the questionnaire items for Alpha testing (i.e., the latest pilot study) are as follows (refer to Table 1). Table 1. Means and standard deviation (SD) of perceived effectiveness of SSD, using a 5-point Likert scale (1 = Strongly Disagree, 3 = Neutral, 5 = Strongly Agree) Students (n = 3)

Practitioners (n = 8)

Mean

SD

Mean

SD

Game design elements

4.46

0.60

4.26

0.76

Game-based learning

4.61

0.49

4.40

0.63

Game content authenticity

4.62

0.50

4.25

0.48

Components of perceived effectiveness

The practitioners’ ratings for all components are lower than the students’ ratings. Nevertheless, both groups have ratings over 4 (rating = “agree”), which means that SSD is perceived to be effective for learning DfS. Students rated the “Game Content” component the highest (4.62), and practitioners rated “Game-Based Learning” as the highest (4.40). The result for the students is as expected. Students do not have significant construction experience and having a virtual platform like SSD allows them to explore the construction site freely. SSD provided them with an avenue of authentic context. In contrast, practitioners are adult learners who may already have some experience in the field, and their need for professional upskilling differs from the needs of students. First, using the game as a learning tool to teach DfS is more interactive and intuitive for practitioners. Furthermore, the game is designed to be self-paced, and to provide immediate feedback. Researchers have highlighted the need for autonomy and self-directed learning and the influence of motivation in their learning process (Albert and Hallowel 2013). Additionally, SSD provides an avenue for practitioners to provide alternative solutions. This is a two-way process of applying from experience and applying what

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they have learned into the game scenario. Having this ability to apply their knowledge would encourage practitioners to perceive DGBL as effective. The questionnaire also has open-ended questions that ask the participants about their likes and dislikes of SSD, difficulties they faced during the game session, and any suggestions or comments to improve it. The majority said that SSD is authentic, interactive, and immersive. They also like that SSD provided them with immediate responses to review their materials and reinforce their learning. However, some exclaimed that the learning process is repetitive, and they may lose interest after a while. Some also mentioned that there is too much information within the game, causing them to forget specific details, and there is no avenue for them to review past information. Apart from the questionnaire, the authors and researchers also observed the participants’ behaviour during the testing sessions. Most participants were reluctant to use the clues when they were stuck during the scenario, and even when they were given for free. When asked about it, participants claimed they wanted to score the most points. This is not surprising as adult learners tend to be more competitive. They may also feel they have a reputation to uphold as they have experience in the field. Participants started off slowly in Scenarios 1 and 2 as they got used to the controls and game design. However, they were quicker in spotting design risks in Scenarios 3 and 4.

5 Conclusion It has been more than five years since the introduction of the Workplace Safety and Health (Design for Safety) Regulations 2015 (“DfS Regulation”). Still, the construction industry remained the top contributor to workplace fatalities in Singapore. Hence, there is a need to increase designers’ awareness and application of DfS during the design and planning phases. This study presented the development of the DfS Library and SafeSim Design (SSD), which are designed to address this need. The prototype digital simulation game aims to increase the awareness and knowledge of designers towards DfS. With authentic scenarios and feasible design-related controls, the designers can understand the difference between design risks and occupational hazards and design out issues through design-related controls. Practitioners evaluated the first iteration of SSD and provided constructive feedback and recommendations for improvement. Future studies will include an experimental study on two groups of designers. The control group will go through conventional online lectures. In contrast, the treatment group will go through digital game-based learning with SSD. Both groups will respond to a series of quizzes and questionnaires for the authors to analyse the impact of SSD on their learning. It is hypothesised that SSD would be more effective in teaching DfS than conventional online lectures. Furthermore, SSD can be further developed to include additional levels and a learning tool for training providers. Acknowledgements. This study is funded by SkillsFuture Singapore under the Workforce Development Applied Research Fund (WDARF) Grant. The contributions by the IES DfS workgroup and other anonymous practitioners are acknowledged and appreciated.

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References Abdelhamid, T.S., Everett, J.G.: Identifying root causes of construction accidents. J. Constr. Eng. Manag. 126, 52–60 (2000) Albert, A., Hallowel, M.R.: Revamping occupational safety and health training: integrating andragogical principles for the adult learner. Const. Econ. Build. 13, 128–140 (2013) Behm, M.: Linking construction fatalities to the design for construction safety concept. Saf. Sci. 43, 589–611 (2005) Chang, C.Y., Kao, C.H., Hwang, G.J., Lin, F.H.: From experiencing to critical thinking: a contextual game-based learning approach to improving nursing students’ performance in electrocardiogram training. Educ. Tech. Res. Dev. 68, 1225–1245 (2020) Choi, S.D., Guo, L., Kim, J., Xiong, S.: Comparison of fatal occupational injuries in construction industry in the United States, South Korea, and China. Int. J. Ind. Ergon. 71, 64–74 (2019) Dankbaar, M.E.W., Alsma, J., Jansen, E.E.H., van Merrienboer, J.J.G., van Saase, J.L.C.M., Schuit, S.C.E.: An experimental study on the effects of a simulation game on students’ clinical cognitive skills and motivation. Adv. Health Sci. Educ. 21(3), 505–521 (2015). https://doi.org/10.1007/ s10459-015-9641-x Dichev, C., Dicheva, D., Angelova, G., Agre, G.: From gamification to gameful design and gameful experience in learning. J. Cybern. Inf. Technol. 14(4), 80–100 (2014) Goedert, J.D., Rokooei, S.: Project-based construction education with simulations in a gaming environment. Int. J. Constr. Educ. Res. 12, 208–223 (2016) Goh, Y.M., Chua, S.: Knowledge, attitude and practices for design for safety: a study on civil & structural engineers. Accid. Anal. Prev. 93, 260–266 (2016) Goh, Y.M., Ng, Y.Q., Safiena, S. and The Institution of Engineers Singapore.: IES-NUS Design for Safety (DfS) library for designers: construction and maintenance design risks. The Institution of Engineers Singapore, Singapore (2021) Government of Singapore.: Workplace safety and health (design for safety) regulations 2015 (2016) Hwang, G.J., Chang, C.Y.: Facilitating decision-making performances in nursing treatments: a contextual digital game-based flipped learning approach. Interactive Learning Environments, pp. 1–16 (2020) Ibrahim, K.: The impact of ecological factors on game-based L2 practice and learning. Foreign Lang. Ann. 50, 533–546 (2017) Kao, C.W.: The effect of a digital game-based learning task on the acquisition of the English Article System. System 95, 1–13 (2020) Kebritchi, M., Hirumi, A.: Examining the pedagogical foundations of modern educational computer games. Comput. Educ. 51, 1729–1743 (2008) Martin, A.: A simulation engine for custom project management education. Int. J. Project Manage. 18, 201–213 (2000) Ministry of Manpower.: Workplace safety and health report (2021) Nousiainen, T., Kangas, M., Rikala, J., Vesisenaho, M.: Teacher competencies in game-based pedagogy. Teach. Teach. Educ. 74, 85–97 (2018) Proske, A., Roscoe, R.D., Mcnamara, D.S.: Game-based practice versus traditional practice in computer-based writing strategy training: effects on motivation and achievement. Educ. Tech. Res. Dev. 62, 481–505 (2014) Randel, J., Morris, B., Wetzel, C., Whitehill, B.: The effectiveness of games for educational purposes: a review of recent research. Simul. Gaming 23, 261–276 (1992) Safety And Resilience Research Unit (SARRU). SafeSim Risk [Online]. National University of Singapore, Singapore (2021). Available: https://cde.nus.edu.sg/dbe/cpfm/sarru/projects/risk/ [Accessed]

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Identification of Critical Factors Influencing Students’ Engagement and Satisfaction of Online Live Learning in Higher Education Lei Zhu1(B) , Lina Zhang1 , and Guifeng Zhu2 1 Department of Construction and Real Estate, Southeast University, #2 Southeast University

Road, Jiangning District, Nanjing 211189, Jiangsu Province, People’s Republic of China {seuzhulei,220191235}@seu.edu.cn 2 Zaozhuang Municipal Party School, Qilianshan North Road, Zaozhuang 277899, Shandong Province, People’s Republic of China [email protected]

Abstract. In response to the COVID-19 epidemic, online live teaching becomes the main teaching method rather than a choice. Considering the immediate habit change in education, this study aims to identify the critical factors influencing students’ engagement and satisfaction with the online live courses using a structural equation model and an online questionnaire survey. Through a comprehensive literature review, four critical factors influencing students’ engagement and satisfaction which are instructor behaviors, student characteristics, course organization, the state of health, wellbeing, and sense of community-related (HWC) issues were identified and their relationships as well as measurement indicators for each factor were proposed. Through a survey, 306 valid responses were collected from civil engineering students in China in 2020. The results showed that instructor behaviors and student characteristics have the highest impact on student engagement and perceived learning, respectively. Moreover, the mediating effects of student engagement between instructor behaviors and student characteristics and perceived learning and satisfaction are statistically significant. Furthermore, the state of HWC issues caused by intensive online learning does have a significant negative impact on student satisfaction. Besides, the relative importance of practices affecting student online learning effects was prioritized. The findings contribute to the body of knowledge of online teaching theories and strategies. Moreover, the instructor and the education manager can improve their online live arrangement by referencing the findings of this study. Keywords: Online live teaching · Engagement · Critical factors · SEM

1 Introduction The COVID-19 pneumonia has resulted in schools shut down across the world. Due to the advantages of online education, such as flexibility and interactivity, and the advancement in digital platforms, online education is now revolutionizing education. However,

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 373–387, 2023. https://doi.org/10.1007/978-981-19-7331-4_30

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because of the sudden change to intensive online learning environments, many reports indicated that online education leads to the decline of student performance and learning quality (Maslen 2020; UNESCO 2020). Moreover, the rush to offer online education has left many questions, for instance, what are the critical factors influencing student learning effects in intensive online learning environments. Besides, to what extent do the health, wellbeing, sense of community-related issues caused by intensive online learning effects (Roddy et al. 2017). Furthermore, whether online teaching will continue to persist post-pandemic (Li and Lanani 2020). Many factors affecting online learning effects have been well-documented (Eom et al. 2006; Erenler 2020; Frey et al. 2003). However, improvements are still needed considering the changing educational arrangements, advanced online platforms, social conditions. For instance, the emergence of COVID-19 changed many prerequisites for online education. Badia et al. (2017) indicated that the majority of instructors are still reluctant to integrate online teaching technologies in their teaching environment and students have little intention of using the e-learning programs. However, because of COVID-19, both teachers and students are forced to accept online education and gained rich online teaching and learning experiences (Bao 2020). Moreover, online platforms, such as Zoom and Tencent Meeting, improve rapidly. Therefore, this study aims to identify the determinants of online learning effects and their conduction mechanism in intensive online learning environments. The objectives include: 1) selecting potential factors; 2) proposing hypotheses and testing them; 3) analyzing data, drawing conclusions, and providing recommendations. The findings contribute to the body of knowledge in the field of engineering online education. Besides, the findings would advance engineering education practice for students, instructors, and educational administration by helping them be well-prepared for corresponding countermeasures or strategies.

2 Literature Review and Hypothesis Development This study adopted the Institution Analysis and Development framework (IAD) to form the conceptual framework. IAD helps to explore the governance structures in a social system and perceive complex collective action problems by dividing them into action arenas. Within each action arena, actors have choices and are influenced by the external environment such as institutional arrangements, social-economic conditions, and physical environments (Ostrom 2011). Eom et al. (2006) divided the factors which are antecedents of online learning effectiveness into human factors and design factors, partially supporting the current study. As the main actors, the instructor and the student perform teaching and learning on online platforms. Meanwhile, courses are organized by the educational administration. Along with the intensive online learning, the state of health, wellbeing, and sense of community-related (HWC) issues affect the outcomes of online education. Besides, student engagement is considered as a learning process; student perceived learning and satisfaction are considered as learning outcomes. Student engagement has mediating effects on student perceived learning and satisfaction. Structural equation modeling (SEM) was used to improve the degree to which a measure is “error-free” (Marks et al. 2005). The conceptual framework is shown in Fig. 1.

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Fig. 1. Conceptual framework

2.1 Learning Effects Student engagement is considered as one of the primary components of effective online learning (Ding et al. 2018; Gray and DiLoreto 2016). As a multi-faceted construct, student engagement can be measured from three dimensions including behavioral engagement, emotional engagement, and cognitive engagement (Fredricks, et al. 2004). Student engagement is proven to be a factor accounting for significant variance in student satisfaction and course performance (Bangert 2006; Choo et al. 2020). Perceived learning is considered as an indicator of the learning effect (Alqurashi 2019; Estévez et al. 2018). Perceived learning is someone’s judgment that their knowledge and understanding are constructed (Rovai 2002), or the changes in a learner’s perceptions of skills and knowledge levels before and after a learning experience (Alqurashi 2019). Studies indicated that student perceived learning is an influential factor in student satisfaction and efficacy of online courses (Erenler 2020; Wu et al. 2013). Student satisfaction is considered one of the key elements to evaluate the quality of online courses (Alqurashi 2019) and a significant predictor of learning outcomes (Eom et al. 2006). Student satisfaction reflects how learners view their learning experiences (Alqurashi 2019). Student satisfaction is highly related to students’ dropout rates, determination, motivation, and commitment to complete a degree online (Ali and Ahmad 2011; Marks et al. 2005). Considering the above, this study selected student engagement, perceived learning, and satisfaction as dependent variables and proposed the following hypotheses: (1) Hypothesis 1a: Student engagement will be positively related to student perceived learning; (2) Hypothesis 1b: Student engagement will be positively related to student satisfaction; (3) Hypothesis 1c: Student perceived learning will be positively related to student satisfaction.

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2.2 Instructor Behaviors Studies found that instructor behaviors are the most important explanatory variable for students’ satisfaction with online learning (Marks et al. 2005). Mishra and Koehler (2006) elaborated that the technical competence of online teaching should be highlighted alongside content proficiency and pedagogical knowledge. Other core teacher competencies required for effective online teaching include communication skills, provision of informative feedback, administrative skills, responsiveness, monitoring learning, and providing student support (Roddy et al. 2017). Considering the above, the following hypotheses were hypothesized: (1) Hypothesis 2a: Instructor behaviors will be positively related to student engagement; (2) Hypothesis 2b: Instructor behaviors will be positively related to student satisfaction; (3) Hypothesis 2c: Instructor behaviors will be positively related to student perceived learning. 2.3 Student Characteristics Student characteristics, including gender, learning style, self-control ability, selfregulated learning, attitude towards online learning, self-efficacy, and social presence, are frequently mentioned (Eom et al. 2006; Li 2019; Marks et al. 2005; Swan 2001). It is worth noting that online learning requires students to rely more on autonomous learning strategies (Galyon et al. 2015). Moreover, a student’s social presence and communication ability also affect perceived learning and satisfaction. Besides, a student’s attitude towards online learning also affects the satisfaction of an online course (Fredericksen et al. 1999). Considering the above, the following hypotheses were proposed: (1) Hypothesis 3a: Student characteristics will be positively related to student engagement; (2) Hypothesis 3b: Student characteristics will be positively related to student perceived learning; (3) Hypothesis 3c: Student characteristics will be positively related to student satisfaction. 2.4 Course Organization The education administration has the responsibility to make adjustments on the course arrangement for online courses (Marks et al. 2005; Roddy et al. 2017). Nuffer and Duke (2013) concluded that course length affects enrolment numbers and the learning effectiveness of online courses, respectively. Adamopoulos (2013) pointed out that the difficulty level of a course has a moderate effect on an online course. Besides, Gray and DiLoreto (2016) revealed that the course organization does have a statistically significant impact on both perceived student learning and student satisfaction. Moreover, the education administration also has the responsibility to provide academic and technology support (Roddy et al. 2017). E-learners often report the experiences of computer malfunctions and network jams (Federman 2019). Considering the above, the following hypothesis was hypothesized: (1) Hypothesis 4a: Course organization will be positively related to student engagement.

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2.5 State of HWC Issues Transitioning to university life and time management, transitioning to intensive online learning, the pressures of academic achievement, and the long-term home study create increasing stress among students. Moawad (2020) investigated pandemic and academic stress in university students after COVID-19 and found that the highest percentage of stress among students is their uncertainty over the end of semester exams and assessments. Moreover, Rovai (2002) found that online learners who have a stronger sense of community and perceive greater cognitive learning should feel less isolated and have greater satisfaction with their academic programs. It is worth noting that the rapid and widespread COVID-19 has resulted in the lack of time for HWC-related support in most universities. Considering the above, the following hypotheses were hypothesized: (1) Hypothesis 5a: Student characteristics will be positively related to the state of HWC issues; (2) Hypothesis 5b: The state of HWC issues will be negatively related to student satisfaction.

3 Research Method 3.1 Sampling The sample includes students who major in civil engineering and participated in live online courses in universities in China. Without limiting to any specific course, this study is a multi-course study that has methodological benefits such as external validity and increased statistical power (Marks et al. 2005). Moreover, the survey was conducted with anonymity. Students do not fear that instructors might match the respondents to their answers and affect their grades because there is no personal information or detailed course information (Frey et al. 2003). This study conducted a pre-survey and a formal survey mainly through the internet. A total of 306 valid copies of responses were collected from April to September 2020. 3.2 Measurements This study used a student self-report questionnaire to measure all variables in the conceptual framework. Asking the perception of students is proved to be a valid measure of cognitive learning (Nuffer and Duke 2013). Except for the measurement of the proportion of time that a student focuses on an online course, the other items were measured with a 7-point Likert scale (1 = strongly disagree; 7 = strongly agree). This study used four indicators to measure student engagement. They are: 1) the proportion of time that I focus on listening to the online course using a 100% scale (EG1); 2) my current feeling about the course in terms of the degree of enjoyment (EG2); 3) my current feeling about the course in terms of the degree of psychological involvement (EG3); 4) the degree that I would like to spend more time to learn and use the knowledge or theory related to the course after class (EG4). This study used five indicators to measure student perceived learning. They are: 1) I learned to interrelate the important issues of this course (PL1); 2) I learned to propose solutions to course-related problems by using the knowledge learned in this course

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(PL2); 3) I developed the ability to communicate clearly on topics related to this course (PL3); 4) I learned to summarize, refine, analyze or evaluate related issues by using the knowledge learned in this course (PL4); 5) I learned to innovate by using the knowledge learned in this course (PL5). This study used five indicators to measure student satisfaction. They are: 1) I was very satisfied with this course (SA1); 2) I was satisfied with the online platform which is very friendly and easy to access and use (SA2); 3) I was satisfied with the online course because it saved the time and cost of going to the classroom (SA3); 4) I was satisfied that I can choose my comfortable learning environment to study this course (SA4); 5) If I chose again, I would still choose the live online course (SA5). This study used seven indicators to measure instructor behaviors in online courses. They are: 1) the instructor is very familiar with the frontiers of the course-related research and industry development, and introduced this knowledge in class (IB1); 2) the instructor is humorous and the classroom atmosphere was very active (IB2); 3) the instructor actively and timely responded to the questions raised by the students (IB3); 4) the instructor timely communicated with students after class (IB4); 5) the instructor is familiar with online technology and proficient in using various common functions of online teaching platform (IB5); 6) the instructor wrote in the lecture notes (word/PPT), or used various auxiliary teaching tools (IB6); 7) the instructor opened camera for online teaching (IB7). This study used five indicators to measure student characteristics. They are: 1) my self-control ability is very strong (SC1); 2) my self-regulated learning ability is very strong (SC2); 3) I take the initiative to communicate with the instructor to clear my doubt (SC3); 4) I think that live online courses are more effective than offline courses (SC4); 5) I prefer group assignments or projects rather than personal assignments, where I can discuss with my classmates (SC5). This study used three indicators to measure course organization. They are: 1) the educational administration provided orientation, training, or guidance to students on online learning-related issues (ATS1); 2) the educational administration adjusted the curriculum arrangement for online live courses, such as time arrangement, providing e-books and other online learning resources (ATS2); 3) the educational administration recommended online platforms which are user friendly and easy to access and use (ATS3). This study used six indicators to measure the state of HWC issues, representing the social condition of students’ health, wellbeing, and sense of community. They are: 1) it is easily distracted when listening to live online courses (HWC1); 2) the intensive and longtime of online learning has caused me great psychological distress such as worry about my studies (HWC2); 3) the intensive and longtime of online learning has caused me stressful and irritating (HWC3); 4) the intensive and longtime of online learning has brought bad effects on my health such as poor eyesight and poor sleep quality (HWC4); 5) I hope that there will be an application with artificial intelligence that can capture the distracted and remind me (HWC5); 6) online learning made me feel no sense of belongingness and community (HWC6).

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4 Descriptive Results and Model Evaluation This study used the SEM software AMOS 24.0.0 and obtained parameter estimates by using maximizing likelihood function which is derived from the multivariate normal distribution. 4.1 Descriptive Results This study conducted an online questionnaire survey and received 306 valid responses from 19 universities in China. All students who responded to the questionnaire had experienced online learning. The proportions of male and female students are 54.58% and 45.42%, respectively. Because most of the students major in civil engineering, male students are more than female students. The survey covers both undergraduate (60.46%) and graduate students (39.54%). The average proportion of time that the student’ focus on online live classes is 74%. 4.2 Measurement Model Evaluation Table 1 shows the evaluation results of measurement models following the reporting practices in confirmatory factor analysis by Jackson et al. (2009). The results indicated that the indicator reliability is acceptable because all loadings are greater than 0.5 (Hulland 1999). The reliability of internal indicators within each factor is acceptable because the values of composite reliability (CR) are over 0.7 (Fornell and Larcker 1981). The values of the average variance extracted (AVE) are above 0.5 which ensures the convergent validity of the factors. This study also conducted the correlation analysis of the factors and cross-loading analysis for individual measurement items. The results first showed that the square root of the AVE of each factor is higher than its correlation with other factors. The results also showed that each measurement item has the highest loading on the corresponding factor. These together indicate a satisfactory discriminate validity of the factors. Besides, for models with cases more than 200, the chi-square is almost statistically significant (Kenny 2015). Overall, these results indicate that the measures in this study have adequate reliability and validity. 4.3 Structural Model Evaluation The hypothesis testing results of the conceptual model (Model 1) are shown in Table 2. The sample size of this study is larger than the minimum required sample size which is 231 according to the Hoelter 0.01 index. The results showed that, except for the hypotheses H1c and H2c, the other hypotheses are statistically significant. The results indicated that student perceived learning will not be positively related to satisfaction. Because H1c and H2c are insignificant, this study removed them to achieve the fitted model with standardized estimates (Model 2), as shown in Fig. 2. First, according to the results of unstandardized estimates, all path coefficients in the fitted model are statistically significant. Second, the results determine if the model is statistically valid. For

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L. Zhu et al. Table 1. Measurement model evaluation.

Factor

Indicator

Significance estimate Unstd.

Engagement

Perceived learning

Satisfaction

Instructor behaviors

Student characteristics

Course organization

Loading

S.E.

t-value

P

SMC

CR

AVE

0.901

0.698

0.972

0.874

0.912

0.678

0.935

0.672

0.898

0.644

0.914

0.781

EG1

1.000

0.753

0.567

EG2

0.077

0.005

16.526

***

0.903

0.815

EG3

0.084

0.005

16.407

***

0.924

0.854

EG4

0.073

0.005

13.597

***

0.745

0.555

PL1

1.000

0.900

0.810

PL2

1.043

0.036

28.922

***

0.943

0.889

PL3

1.069

0.037

28.988

***

0.946

0.895

PL4

1.065

0.036

29.305

***

0.957

0.916

PL5

1.121

0.042

26.638

***

0.928

0.861

SA1

1.000

0.648

0.420

SA2

1.362

0.112

12.176

***

0.758

0.575

SA3

1.934

0.157

12.281

***

0.895

0.801

SA4

1.969

0.154

12.809

***

0.930

0.865

SA5

2.054

0.165

12.425

***

0.855

0.731

IB1

1.000

0.792

0.627

IB2

1.081

0.064

17.007

***

0.854

0.729

IB3

0.956

0.062

15.528

***

0.798

0.637

IB4

1.085

0.064

17.071

***

0.857

0.734

IB5

0.996

0.058

17.322

***

0.866

0.750

IB6

1.007

0.063

15.869

***

0.811

0.658

IB7

0.998

0.069

14.453

***

0.755

0.570

SC1

1.000

0.913

0.834

SC2

0.918

0.037

24.550

***

0.914

0.835

SC3

0.941

0.048

19.637

***

0.818

0.669

SC4

0.880

0.059

14.887

***

0.700

0.490

SC5

0.748

0.059

12.568

***

0.625

0.391

ATS1

1.000

0.878

0.771

ATS2

1.009

0.949

0.901

0.045

22.422

***

(continued)

overall model fit assessment, the examined chi-square with degrees of freedom (x 2 /df ) is below three, which is acceptable (Hooper et al. 2008); the root mean square error of approximation (RMSEA = 0.070) is below the ideal model value 0.08, confirming

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Table 1. (continued) Factor

State of HWC issues

Indicator

Significance estimate

Loading

SMC

0.819

0.671

0.754

0.569

Unstd.

S.E.

t-value

P

ATS3

0.863

0.046

18.689

***

HWC1

1.000

HWC2

1.332

0.081

16.467

***

0.892

0.796

HWC3

1.391

0.082

16.876

***

0.912

0.832

HWC4

1.236

0.085

14.571

***

0.802

0.643

HWC5

0.728

0.084

8.684

***

0.501

0.251

HWC6

1.246

0.088

14.211

***

0.784

0.615

CR

AVE

0.904

0.618

Note: ***indicate that p < 0.001 Table 2. Hypothesis testing results of Model 1. Path

Estimate

S.E.

C.R.

P

Hypothesis

Learning

←

Engagement

0.043

0.006

6.558

***

H1a

Satisfaction

←

Engagement

0.025

0.006

4.367

***

H1b

Satisfaction

←

Learning

0.035

0.056

0.618

ns

H1c

Engagement

←

Instructor

6.771

0.971

6.972

***

H2a

Satisfaction

←

Instructor

0.161

0.055

2.923

**

H2b

Learning

←

Instructor

0.108

0.072

1.512

ns

H2c

Engagement

←

Student

3.62

0.647

5.593

***

H3a

Learning

←

Student

0.34

0.049

6.984

***

H3b

Satisfaction

←

Student

0.129

0.042

3.081

**

H3c

Engagement

←

Organization

1.268

0.726

1.746

*

H4a

Health

←

Student

Satisfaction

←

HWC

0.215

0.058

3.696

− 0.066

0.023

− 2.864

***

H5a

**

H5b

Note: ***p < 0.001, **p < 0.05, *p < 0.100, ns = not significant

the validity and significance of the model (Kenny 2015). For component fit assessment, the goodness of fit index and adjusted goodness of fit index (GFI = 0.796 and AGFI = 0.766) were a little lower than the acceptable model values 0.8. Overall, these results indicate the model fit is acceptable. To analyze the mediating effect of student engagement, this study first excluded “engagement” from the fitted model. Then this study added two direct paths which are “instructor” to “learning” and “organization” to “learning” to the model. The mediating model with standardized estimates (Model 3) is shown in Fig. 3. Combining Model 1, Model 2, and Model 3, this study concluded that the mediating effects of student

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Fig. 2. Fitted model with standardized estimates (Model 2)

engagement between two independent variables (instructor behaviors and student characteristics) and two dependent variables (student perceived learning and satisfaction) are statistically significant. To some extent, this finding is consistent with the findings from Gray and DiLoreto (2016).

5 Discussions 5.1 Influencing Factors on Student Engagement Model 2 shows that instructor behaviors, student characteristics, and course organization have significant impacts on student engagement in intensive online environments. Instructor behaviors have the leading role because it has the largest path coefficient (0.49) on student engagement. Besides, the impact of course organization on student engagement (path coefficient = 0.12) is significant only with a confident level of 90% (p = 0.077), indicating that a good course organization is an ingredient in student engagement (Pascarella and Terenzini 2005). However, most of the academic and technical supports of online courses, such as course orientation and guidance of online platforms, happen at the beginning of a course. Once there are problems during a semester, it is the instructor who made great efforts to find solutions for such problems and provide some support for students in China. This partially explains the high correlation between the course organization and instructor behaviors.

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Fig. 3. Mediating model with standardized estimates (Model 3). Note: ***p < 0.001, **p < 0.05, *p < 0.100, ns = not significant

5.2 Influencing Factors on Student Perceived Learning Model 3 shows that only instructor behaviors and student characteristics have significant impacts on student perceived learning. Student characteristics have the dominant role in student perceived learning because of the largest path coefficient (0.58). Because the path coefficients of student characteristics to engagement, engagement to learning, and student characteristics to learning are all significant in Model 2, this study further inferred that student perceived learning is obtained not only through in-class engagement but also via other out-of-class ways such as students’ self-learning after class. Model 2 shows that other out-of-class ways even have a larger contribution (path coefficient = 0.38). Besides, student engagement has a full mediating effect on the path from instructor behaviors to student perceived learning because the corresponding path in Model 1 is insignificant. This revealed that the instructor can influence students’ perceived learning only via motivating their active engagement. 5.3 Influencing Factors on Student Satisfaction Model 3 shows that the impact of student characteristics on student satisfaction is equal to that of instructor behaviors on satisfaction in intensive online learning environments. Besides, the results in Model 2 reveal that student satisfaction with online courses is not only caused by their educational experience via active class engagement but also by other factors such as the feeling of student-centeredness determined by student characteristics and education climate mainly formed by instructor behaviors during online teaching, which is consistent with the findings from Elliott and Healy (2001). It is worth noting that the current state of HWC issues in civil engineering does have a significantly negative impact on student satisfaction in intensive online learning environments. With the global spread of COVID-19 and the normalization of prevention and control, it is likely to lead

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to longer online learning. If the state of HWC issues is worsened in the future, the state of HWC issues may impact student perceived learning more. Finally, the results in Model 1 show that the relationship between student perceived learning and satisfaction is insignificant, which is consistent with the findings from Gray and DiLoreto (2016). 5.4 Important Measurement Indicators for Influencing Factors Indicators with greater path coefficients in Mode 2 are more important and recognized as better practices to achieve good outcomes of online learning. For instructor behaviors, IB1, IB2, IB4, IB5, and IB6 were recognized as important because their path coefficients are above 0.80. IB2 and IB4 are better practices because they got the highest path coefficient (0.86). A humorous instructor and a good classroom atmosphere (IB2) attract students to focus on the classroom. Moreover, timely feedback after class (IB4) improves student learning outcomes via informing students how well they are doing and via directing students’ learning efforts (Eom et al. 2006; Roddy et al. 2017). For student characteristics, SC1, SC2, and SC3 were emphasized because their path coefficients are above 0.8. In online teaching, an instructor becomes a facilitator who stimulates, guides, and challenges students via empowering students with freedom and responsibility. Selfcontrol (SC1) and self-regulated learning ability (SC2) become more important for online learning outcomes (Alqurashi 2019; Sun et al. 2018). For course organization, all indicators were valued as important to student engagement since all path coefficients are above 0.8. Given that students achieve course objectives via the whole semester’s online learning, it becomes critical that students feel continuously supported. For HWC-related issues, HWC2, HWC3, and HWC4 were emphasized because their path coefficients are above 0.8. A whole semester’s intensive online learning negatively impacts students’ health and wellbeing, resulting in a reluctance to continue online learning. For students in civil engineering, they should perform many engineering-related and out-of-class activities such as experiments, construction site visits, and project-related surveys (Simmons et al. 2018; Zhu et al. 2019). Because of the prevention and control measures of COVID-19, many activities were postponed or cancelled. Students in civil engineering face high pandemic and academic stress (Moawad 2020). Universities can help students to learn stress reduction methods to improve the students’ HWC conditions (Regehr et al. 2013). 5.5 Implications for Theories and Practices The findings of this study enrich online education theories in civil engineering. First, this study treated the complex collective actions of each main actor as a whole and treated the state of HWC issues as the social condition, enriching the theoretical analysis framework of online education. Second, this study explored the existence of the relationships among the actions, social state, and learning effects and prioritized the contributions of the actions and social state to learning effects in intensive online learning environments. The findings can provide theoretical support for the direction and focus of online teaching reform. Moreover, the findings of the current study have practical implications for online educators, students, and administrators in civil engineering. For instructors, they should

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change their role from a disseminator of knowledge to a guide to learning for online courses. Besides, the instructor should find ways to increase the self-regulated learning ability of students. For students, they should especially improve their self-control ability and self-regulated learning ability. For educational administration, they may extend support from the beginning of a course to the whole process of a course. Moreover, both instructors and educational administration should pay attention to HWC issues and find solutions to improve the current situations. Universities can invest in online counseling or self-help services to allow access for students from a diverse range of locations.

6 Conclusions and Recommendations Using a structural equation model and a questionnaire survey, this study identified the determinants of learning effects and their conduction mechanism in intensive online learning environments. The results of this study showed that: 1) instructor behaviors, student characteristics, and course organization significantly positively impact student engagement with the highest impact of instructor behaviors; 2) through the mediating effect of in-class engagement and other ways of learning, student characteristics in intensive learning environments have a higher impact on student perceived learning than instructor behaviors; 3) student characteristics and instructor behaviors have almost equal positive impact on student satisfaction while the state of HWC issues significantly negatively impact student satisfaction; 4) this study prioritized the relative importance of the measurement indicators which were recognized as good practices to achieve better outcomes of online learning. This study contributes to the body of knowledge in the field of civil engineering online education by clarifying the mechanism between determinants and learning effects. The findings also have practical implications for the online educator, students, and administrators for adjusting their online teaching or learning strategies, maximizing the chance of a successful online education. Although the objectives of this study are achieved, the limitations of this study should cause readers to take conclusions drawn from it with caution. For example, the respondents are mainly students from the civil engineering discipline. The extent to which they can be applied to students in other disciplinary is uncertain. Future research can focus on the development of best practices for each determinant. In addition, more research is required for appropriate prevention and intervention strategies for HWC issues in intensive online learning environments. Acknowledgements. This work was supported by the Social Science Foundation of Jiangsu Province (21SHB010) and the National Natural Science Foundation of China (NSFC-71801038).

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Preliminary Implementation of Adaptive Learning for Teaching Structural Systems to Non-engineering Students Xinping Hu1 , Yang Miang Goh1(B) , Alexander Lin1 , and Qizhang Liu2 1 Department of the Built Environment, 4 Architecture Drive, Singapore 117566, Singapore

{bdghx,bdggym,bdgal}@nus.edu.sg 2 Department of Analytics and Operations, 15 Kent Ridge Drive, Singapore 119245, Singapore

[email protected]

Abstract. The pandemic has caused a drastic shift to online teaching and learning. However, online teaching and learning still face similar problems to traditional teaching and learning, and one example is the “one-size-fits-all” approach. The ineffectiveness of such an approach is particularly pronounced in interdisciplinary teaching and learning. For example, non-engineering students entering engineering-related courses (e.g., engineering project management and facilities management) have diverse math, physics, and chemistry knowledge backgrounds. Correspondingly, students face different challenges in obtaining the necessary background knowledge for engineering-related courses. One solution to overcome the challenges is adaptive learning, an intelligent approach to providing personalised educational paths for each learner to learn more effectively and efficiently. This study proposes a preliminary framework for implementing adaptive learning for teaching structural systems, a subject in structural engineering, to students with diverse backgrounds. The framework consists of five modules: adaptation, content, learners, instructors, and feedback. The paper discusses a case study of a Structural Systems course for non-engineering students, which utilised the framework to implement adaptive learning in 2021. Preliminary findings show that students are generally satisfied with the adaptive learning approach. Furthermore, the preliminary framework can be adapted and applied to other interdisciplinary teaching and learning settings. Keywords: Adaptive learning · Preliminary framework · Non-engineering students · Online learning · Structural engineering

1 Introduction Since 2020, COVID 19 has drastically changed the education landscape. Shifting from traditional face to face teaching and learning to online teaching and learning imposed significant challenges on both teachers and students. In particular, the drawbacks of the traditional “one-size-fits-all” teaching approach are amplified under the online teaching mode. The lack of personalisation significantly compromises teaching quality and learning efficiency. In the context of the education of non-engineering undergraduates with © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 388–399, 2023. https://doi.org/10.1007/978-981-19-7331-4_31

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the aspiration of a career in the construction industry, such challenges have become bigger than ever before. One primary concern is that non-engineering students have diverse science knowledge backgrounds. To help students of different academic backgrounds to achieve the same set of learning outcomes, a framework and a prototype of an intelligent adaptive learning platform (IALP) are developed. This paper discusses the framework, features, and implementation of IALP.

2 Teaching Engineering Topics to Non-engineering Students 2.1 Interdisciplinary Engineering Education and Challenges Construction projects often require collaboration among several stakeholders, typically engineers, architects, project managers, and contract managers. Mutual understanding among stakeholders is crucial to construction project success. Interdisciplinary education is not only necessary for the STEM literacy of general graduates (Jonathan and Stephanie 2016; National Research Council 2015) but also necessary to equip graduates with adequate engineering literacy for a career in the construction industry. One of the main aims of such engineering courses is to familiarise non-engineering undergraduates with the engineering design process (National Academy of Engineering and National Research Council 2006). One example is that students enrolled in project and facilities management or similar construction-related non-engineering programmes should have engineering courses in their curriculums. Interdisciplinary engineering education has been increasingly common in higher education institutions (Van den Beemt et al. 2020). However, challenges for teaching and learning are inevitable in the context of interdisciplinary engineering education. For example, engineering courses often have critical mathematics and science prerequisites that non-engineering students do not necessarily equip (Krupczak et al. 2019). In addition, non-engineering students come from diverse backgrounds with a variety of STEM knowledge. One example is the Project and Facilities Management undergraduates at the National University of Singapore (NUS). Before enrolling in the program, their highest educational attainment in physics can vary from secondary school physics to polytechnic engineering courses. The diversity of background knowledge can be a significant challenge for interdisciplinary engineering education. 2.2 Potential Solutions There have been solutions proposed to assist non-engineering students in learning engineering courses better, such as flipped classrooms (Steven Chene et al. 2014) and handson activities (Lin et al. 2021; Hu et al. 2020). For the case of PF2102 Structural Systems (a module in the Project and Facilities Management programme), in which students learn the basics of structural engineering, previous efforts have been made to help students visualise abstract structural engineering concepts using augmented reality (AR) (Hu et al. 2021). Despite the solutions’ effectiveness, the diversity of non-engineering students’ knowledge backgrounds remains a challenge for both students and instructors. Such diversity demands differentiated teaching and learning strategies.

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Specifically for the challenge of teaching engineering concepts to non-engineering students, adaptive learning can potentially be the answer. By employing computer algorithms to provide personalised educational paths for each student, adaptive learning caters to the different learning needs of students from diverse backgrounds (Arsovic and Stefanovic 2020; Clark and Kaw 2019; Hsieh et al. 2013). Even though some studies stated that there is no significant change to learning outcomes with the employment of adaptive learning (Griff and Matter 2013; Kolpikova et al. 2019; Ross et al. 2018), it is generally the case that students who use adaptive learning systems (ALSs) tend to perform better than those who do not (Fautch 2019; Balasubramanian and Margret Anouncia 2018; Chrysafiadi and Virvou 2013; Lin et al. 2013; Ennouamani et al. 2020; Alsadoon 2020; Yang et al. 2013; Hsieh et al. 2013; Liu and Yu 2011; Jeong et al. 2012; Yao 2017; Wu and Chang 2020; Sfenrianto et al. 2018; Li 2019; Eichler and Peeples 2013; Maycock and Keating 2017; Sun et al. 2017; Dry et al. 2018; Benchoff et al. 2018; Arsovic and Stefanovic 2020). Besides, most studies agreed that ALSs help students to have higher enjoyment, higher motivation, and higher self-confidence in conceptual understanding, as they are presented with suitable learning materials and have a higher degree of autonomy in deciding their learning paths (Fautch 2019; Griff and Matter 2013; Chrysafiadi and Virvou 2013; Welbers et al. 2019; Yang et al. 2013; Huang and Shiu 2012; Yao 2017; Clark and Kaw 2020). Furthermore, from the instructors’ point of view, ALSs help to aid in presenting concepts in the optimal order tailored to each student (Al-Othman et al. 2017). Therefore, they help reduce the instructors’ workload, allowing them to focus more effectively on other aspects of instruction.

3 Intelligent Adaptive Learning Platform (IALP) 3.1 IALP Framework IALP is built on a modified general adaptive learning architecture. Different ALSs may focus on different adaptive aspects of learning and teaching as they cater to different learning goals and types of knowledge. As a result, researchers often described the general architecture of ALSs in three modules: content module, learner module and adaptation module (Arsovic and Stefanovic 2020; Wu et al. 2018; Balasubramanian and Margret Anouncia 2018; Moebert et al. 2016; Petersen and Gundersen 2019; Kostolányová et al. 2011). In addition, some researchers also highlighted the usefulness of feedback (Verdú et al. 2016) and instructor intervention (Martin and Whitmer 2016; Welbers et al. 2019; Van der Kleij et al. 2015; Wu et al. 2018). The architecture of IALP is shown in Fig. 1. Within the IALP, the content module consists of course content and additional background knowledge in math and physics in lecture notes, Internet resources, readings, quiz questions, lecture recordings, and discussions. The learner module consists of basic demographics, registered tutorial groups, background knowledge in math, learning styles based on the Felder-Silverman Learning Style Model (FSLSM), the performance of quiz attempts, including first attempt, best attempt and average attempt, knowledge unit (KU) proficiency levels, number of forum threads created, number of forum threads replied, timeliness of learning material downloads, timeliness of quiz attempts, number of quiz attempts, and average duration of quiz attempts. FSLSM is one of the most widely used

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Fig. 1. IALP framework.

learning style models in educational systems (Nafea et al. 2019). Scholars have recommended it as the most suitable learning style model for adaptive learning systems (García et al. 2007; Da˘g and Geçer 2009). In addition, FSLSM is easy to implement (Gwo-Jen et al. 2013). The adaptation module feeds content to students based on their learner profiles. The instructor module is about the instructor’s course supervision and student assistance. Finally, the feedback module is about receiving feedback from students to improve their learning experience. The program of IALP is hosted on a server of the National University of Singapore (NUS). The program is connected to NUS’s custom-developed Learning Management System (LMS), LumiNUS, through existing and custom-developed application programming interfaces (APIs). Students are granted the seamless experience of IALP on LumiNUS by minor User Interface (UI) adjustments made by NUS Centre for Instructional Technology (CIT). Instructors can access the IALP tutor dashboard by connecting to a website hosted on the NUS server. 3.2 Features of IALP 3.2.1 Overview of IALP Features Based on its system architecture, IALP has seven key features stored in the adaptation module, as listed in Table 1. Features 1 and 2 will be discussed in Sect. 3.2.2 Knowledge Unit (KU) Proficiency Tags, Features 3, 4, and 7 will be discussed in Sect. 3.2.3 Clustering, Personalised Announcements and Tutorial Teaming, and Feature 6 will be discussed in Sect. 3.2.4 Forum Recommender.

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X. Hu et al. Table 1. Key Features of Intelligent Adaptive Learning Platform (IALP)

S/N

Feature

Framework

1

Structuring module syllabus into hierarchical Content Module knowledge units (KUs) and linking the KUs with learning materials and self-learning quiz questions

2

Personalised proficiency tagging on each knowledge unit for each student

3

Student profiling based on clustering of students Learner Module using unsupervised learning algorithms

4

Personalised recommendations for learning Personalised Educational Paths strategy based on student profile and proficiency tags for knowledge units

5

Personalised forum recommendations based on text analytics

Personalised Educational Paths

6

Assessment of student participation and motivation based on analytics

Learner Module

7

Recommendations to teachers for tutorial discussion grouping based on students’ learning preferences, proficiency levels, and student profiles

Instructor

Personalised Educational Paths

3.2.2 Knowledge Unit (KU) Proficiency Tags In the content module, to optimise the adaptation accuracy and efficiency of IALP, the module syllabus is structured into hierarchical knowledge units (KUs). Learning materials and self-learning quiz questions are linked to the KUs. Based on students’ performance on self-learning quiz questions stored in the learner module, personalised proficiency tags are assigned on individual KUs for each student. This process is reflected from the adaptation module to personalised paths in the IALP framework. There are five proficiency levels for each KU, i.e., awaiting assessment, novice, beginner, intermediate, and advanced. The proficiency levels are modified based on established proficiency levels by the American Council on the Teaching of Foreign Languages (ACTFL) proficiency guidelines 2012 (Kissling and O’Donnell 2015) and the National Institutes of Health (NIH) Proficiency Scale (National Institutes of Health 2017). ACTFL proficiency guidelines include novice, intermediate, advanced, superior, and distinguished. At the first three levels, the proficiency is further divided into low, mid and high (Kissling and O’Donnell, 2015). NIH Proficiency Scale (National Institutes of Health 2017) measures individuals’ competency by five levels, i.e., fundamental awareness (basic knowledge), novice (limited experience), intermediate (practical application), advanced (applied theory), and expert (recognised authority). After deliberation of the profiles of non-engineering major undergraduates, IALP KU proficiency levels and their definitions developed by lecturers and researchers are listed in Table 2.

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Fig. 2. Knowledge Unit (KU) proficiency tags

IALP KU proficiency tags are integrated into LumiNUS UI, as shown in Fig. 2. KU proficiency levels of each student are processed by the adaptation module and stored in the IALP learner module. 3.2.3 Clustering, Personalised Announcements and Tutorial Teaming Clustering is a major component of the IALP adaptation module. Clustering utilises the data of students’ profiles stored in the learner module, which include the background knowledge in physics, learning styles based on the Felder-Silverman Learning Style Model (FSLSM), KU proficiency levels, learning behaviours such as the number of attempts of quiz questions, the timeliness of attempting quiz questions, and the timeliness of downloads of learning materials. In addition, the k-means clustering algorithm is applied due to its popularity and reliability to develop recommendation rules (Nafea et al. 2019; Wu 2012). Based on the clustering results, personalised announcements are scheduled for students every week. This is because students in the same clustering groups are assumed to have similar learning profiles and receive the same announcements. However, as students’ learning performance and behaviours might change over time, clustering results are scheduled to be updated on a weekly basis. One example of the personalised announcements is shown below. “You have practised a fair number of times and downloaded files early, but your weaker physics background may be your obstacle to attaining higher performance. You can attain higher performance by brushing up on your math and physics background. Are you familiar with the learning materials reviewing the background

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X. Hu et al. Table 2. Definitions of IALP Knowledge Unit (KU) proficiency levels

KU Proficiency

Description

Awaiting Assessment There is not enough data to assign a proficiency tag

Recommendation Complete relevant learning activities and quizzes based on the timeline of the learning flow

Beginner

You should have some basic Focus on learning the content in knowledge or understanding of the lecture notes and assigned fundamental techniques and learning activities concepts. Keep learning!

Novice

You should have gained some level of understanding of the knowledge taught in class. You are expected to review the learning materials and improve your ability to apply your knowledge in solving problems. If you have questions, do reach out to your peers and tutors for input and guidance, especially during the tutorial and end of each lecture. Keep learning!

Focus on understanding and applying the content in the lecture notes and improve your skills and knowledge through more practice and exercises. Work with your peers who have a stronger foundation in physics and math

Intermediate

You can solve quiz problems independently and apply the knowledge gained from classes. You may need to familiarise yourself with specific topics and learn how to apply knowledge in different situations

Focus on applying and enhancing knowledge in a wider range of questions and contexts. Assist your peers who may need help with some of the topics which you are already familiar with. As you teach, you strengthen your own understanding!

Advanced

You are already familiar with most Focus on solving more advanced of the content that has been tested problems and understanding to date content beyond what had been covered. Assist your peers with their learning, and you will strengthen your own knowledge along the way

knowledge for relevant math and physics? Have you discussed questions relevant to background math and physic concept during tutorials?” Another feature developed based on IALP clustering is discussion teaming during tutorials. During tutorials, students are often grouped to collaborate on solving exercise questions. Optimising the composite of each discussion group can improve discussion efficiency and help students learn more from each other. Background knowledge in physics, learning styles based on FSLSM, and clusters are three primary considerations when assigning students to discussion groups. To ensure the balance and variety of

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students in each tutorial team, IALP finds the optimal teaming by using the algorithm of solving a k-partition problem (Ghaddar et al. 2011). 3.2.4 Forum Recommender The Forum Recommender relies mainly on text analytics. Forum Recommender analyses the text-similarity between quiz questions and forum threads stored in the content module. Forum Recommender fetches the quiz attempt data from the learner module and recommends discussion threads most similar to questions each student failed to answer correctly. Two algorithms used for text analytics are TF-IDF (Bafna et al. 2016) and Word Embedding (Elekes et al. 2017).

4 Implementation of IALP in 2021 The prototype version of IALP was successfully implemented in LumiNUS from August 2021 to December 2021 for PF2102 Structural Systems, which characterised many of the teaching and learning challenges amplified by non-engineering students learning engineering courses. The module had 122 students enrolled during the implementation. PF2102 takes in students with diverse backgrounds, including non-science and science students with varying math and physics knowledge, which leads to significant challenges for the teachers. In addition, due to the ongoing COVID-19 pandemic, a significant portion of the module had been converted to remote learning, which amplifies the difficulty of teaching the module. Nevertheless, with the implementation of the features mentioned earlier, students gave generally positive feedback on IALP. Some of the testimonials from students are listed in Table 3. Table 3. IALP testimonials from students S/N

Testimonial

1

“I like that the IALP is a timely feedback system to serve as a ‘reminder’ to polish up certain points.”

2

“The feedback that it gives weekly to inform on my progress.”

3

“The KU proficiency tags are very useful in helping me to identify topics I am weak in quickly.”

4

“IALP system is a very systematic process that categorically breaks down all topics in the modules and ranks our efficiency on each and every one of the topics.”

5

“That we are able to share our own independent learning with the rest of the class and that there is a system informing me of my current progress for the module.”

6

“It allows me to know my weaker topics so that I am able to focus on my weaker topics.”

7

“I specifically like the KU features where it shows the progress of my learning and my weakness in certain topics. This allows me to take note of my weakness and practice more on those topics.”

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The successful implementation of IALP in PF2102 demonstrated the potential of adaptive learning in facilitating flexible interdisciplinary learning. However, the features of IALP at this first implementation were only preliminary. IALP is continually improved based on students’ feedback, and the version including improved features will be implemented in August 2022. A quasi-experimental study will be conducted in August 2022 to evaluate its impact on students’ learning.

5 Conclusions This study showcases a preliminary framework of an intelligent adaptive learning platform (IALP) and its application to teaching structural systems to non-engineering undergraduates. The framework is adapted from a general architecture of adaptive learning systems. IALP preliminary framework consists of five modules, adaptation, content, learner, instructor, and feedback. Based on the five modules, the prototype version of IALP with seven features is developed and implemented for teaching structural systems to non-engineering students. The prototype version of IALP was implemented in 2021 among 122 students. Student feedback was generally positive by the end of the course. The preliminary framework has the potential to assist interdisciplinary teaching and learning in similar educational settings. Acknowledgements. This study is funded by the Singapore Ministry of Education Tertiary Education Research Fund MOE2019-TRF-001.

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Resilient Infrastructural Solutions

Analysis of the Clearance Time of Roadblock Events Caused by Geohazards in Bhutan Dhan Raj Chhetri1(B) and Michael Henry2 1 Division of Architecture and Civil Engineering, Graduate School of Engineering and Science,

Shibaura Institute of Technology, 3 Chome-7-5 Toyosu, Koto City, Tokyo 135-8548, Japan [email protected] 2 Department of Civil Engineering, Shibaura Institute of Technology, Koto City, Tokyo, Japan

Abstract. The importance of providing precise Real Time Information (RTI) to road users has become one of the key roles for the concerned government agencies in Bhutan to ensure the safety of road commuters and also regulate the smooth flow of goods and people in the country. However, to date, the essence of RTI is usually compromised, owing to several unforeseen factors and a lack of sufficient resources at the site. Thus, this research studied and analyzed factors governing the clearance time of roadblock events caused by road geohazard such as landslide, rockfall, flood, etc. Statistical and Geospatial analyses were carried out on the roadblock data (2020) obtained from the Department of Roads. A Theissen Polygon technique in the GIS platform was constructed to obtain the rainfall intensity that was recorded during and after roadblock clearance time. Locations of predeployed machinery were also included to investigate the relationship between these two variables and the clearance time. Overall, it took an average of 12.2 h to clear the roadblocks that were recorded, with the longest and shortest times recorded in the Phuentsholing and Trongsa region, i.e., 360.2 h and 0.2 h, respectively. Concurrently, the locations that took the longest were those that did not have machinery on-site. The average time for clearing a block with and without machinery was 10.4 h and 13 h, respectively. Concerning the rainfall data, the clearance time was directly proportional to the accumulated rainfall intensity from the occurrence time to the clearance time. Thus, knowing such relationships and patterns can assist agencies in prioritizing locations and allocating necessary resources, as well as improving the predictability of tentative clearance times to reduce errors in sharing RTI with commuters so that they are not misinformed. Keywords: Bhutan · Roadblocks · Real-time information · Rainfall intensity · Machinery

1 Introduction Given the country’s geographical position and accompanying climate conditions, emergent natural incidents occur relatively regularly on Bhutan’s highways. These include natural hazards such as landslides, debris flows, rock falls, flooding, and so on, which not only impair traffic flow but also pose major threats to road users’ lives and substantial © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 403–415, 2023. https://doi.org/10.1007/978-981-19-7331-4_32

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economic loss. Monsoons in the summer months and snowfall and icing of the roads in the winter months have a significant impact on road conditions. During a road disaster or emergency, numerous players are involved in responding and restoring traffic normalcy as soon as possible, along with providing Real-Time Information (RTI) to road users for their essential route plans and adjustments. As of date, the country has a total of 2849.9 km of national highways (MOWHS 2020) with a daily traffic volume of about 48,499 vehicles in the country which are closely related to the daily functioning of various important sectors and industrial activities. Thus, the slightest delay in restoration and clearance of roadblocks can have a significant impact on the overall development and economic activities in the country as well as on the livelihood of the people who depend on road connectivity (Cheki and Shibayama 2008). The Department of Roads (DoR) is primarily involved in dealing with the physical restoration, the opening of the road infrastructure, and providing RTI to general road users. However, due to a lack of relevant research knowledge data and many other factors, the agencies’ actions at the site have been more reactive rather than preventive, making all of the hard work put forward less effective and efficient, thus, resulting in further delays in restoring the road’s normalcy. Records have shown that clearance of roadblocks in Bhutan is dependent on several factors, such as the unpredictability of weather (for example, incessant heavy rainfall during the response period), site preparedness in terms of manpower and machinery, the distance of the roadblock location from the nearest town & DoR site office, traffic volume, criticality/importance of the road section depending on its category, the magnitude of the failure event, and many others. Therefore, the purpose of this research is to analyze and investigate the clearance time of roadblock events in Bhutan by developing relationship patterns between the events and all the promising factors that impact the roadblock clearance time. The results of the studies are expected to assist relevant agencies in planning appropriate response measures by providing them with the critical areas/sections so that timely allocation of necessary resources in terms of manpower and equipment can be carried out. Furthermore, it is expected to help formulate a proper basis to correctly forecast the RTI, thereby reducing the associated risk and loss due to disruption in economic activities by enabling them to prioritize their plans and journeys accordingly.

2 Study Area An entire network of the National Highway in Bhutan is considered as a study area. It consists of 2849.9 km of road in total, which is further classified into three different categories. The classification of categories in descending order of its hierarchy of importance are Asian Highway-48(AH-48) 149.1 km, Primary National Highway (PNH) 1531.1 km, and Secondary National Highway (PNH) 1160.7 km, respectively. Except for the AH-48 and a few sections (379.6 km) of PNH and SNH that are looked after by Project Dantak, the entire National Highway falls under the DoR’s responsibility for maintaining the road’s serviceability and normal function, which is further divided among nine regional offices located at strategic locations across the country as shown in Fig. 1.

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Fig. 1. Map depicting the distribution of study area in 9 regional offices.

3 Methodology The overall methodology can be classified into three major steps: 1) Data Collection 2) Data Preparation and 3) Analysis (Statistical and Geospatial Analysis). 3.1 Data Collection 3.1.1 Roadblock Inventory Datasheet The roadblock inventory datasheet for the year 2020, which consists of all the roadblock events caused by road geohazard was obtained from DoR. The datasheet consists of information such as the name of the roads, name of the regional office, location of the block, failure types & occurrences and clearance date & time of the roadblocks. 3.1.2 Rainfall Data The rainfall data pertaining to the year 2020 was obtained from the National Center for Hydrology and Meteorology (NCHM), which is an autonomous scientific and technical organization under the Royal Government of Bhutan. The rainfall data consists of rainfall data in mm/day for the entire year along with the GPS coordinates (Latitude, Longitude, and Altitude) of the 20 rainfall gauging stations which are located across the country.

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3.1.3 Machinery Allocation Database The location and name of roads where pre-deployment of machinery done by the DoR was obtained. The database consisted of the types and numbers of machinery deployed for various days and expenditures incurred, especially during the monsoon period. 3.1.4 Traffic Count Database The traffic count for the year 2018 was obtained and utilized for the analysis. The database was considered because the normal flow of traffic was affected in recent years due to the countries‘ strategies and lockdown protocols to combat the novel Corona Virus, COVID19. The database consists of the name of the road, traffic types, and traffic counts that were carried out during September (15th–30th) for 15 consecutive days. 3.1.5 Geospatial Data The Following geospatial data were obtained from DoR: i.

Road Network Inventory Database. The shapefile consists of the entire national highway line file with information such as the name of the road, the name of the regional office, and the category of the road to which it belongs. ii. Location of Town Points, which consists of the name of the town and the district they belong to along with its category (Primary and Secondary Town). iii. Shapefile of DoR regional and locations of site office. 3.2 Data Preparation The roadblock datasheet contained a total of 102 different types of failure, the majority of which were duplicates or with similar meanings, and the remainder were redundant. To make the data homogeneous and to the required standard, the failure events were divided into seven separate types using Varnes’ classification of slope movements (Varnes 1978) without significantly affecting the uniqueness of the raw data. The categories are: 1) Landslide 2) Debris flow 3) Rockfall 4) Flooding, 5) Subsidence, 6) Scouring, and 7) Snowfall. A total of 692 roadblock entries were discovered after the cleaning process, which was further classified into Unique Locations (UL) and Unique Events (UE). This was necessary because some of the locations experienced multiple failure events during the course of the year and sometimes several locations were blocked at the same time and date. As a result, the overall datasheet was further classified into UL for the geospatial analysis and UE for the statistical analysis. A total of 309 UL and 888 UE were obtained. Furthermore, depending upon the number of failures a particular location had during the occurrence of the event, the failure types were classified into two categories namely, single-type and multi-type. The extraction of GPS coordinates for all UL points was then performed, where GPS coordinates for approximately 92.5% of the total UL points were acquired. The extraction process involved, the utilization of a road inventory map/database, Google Earth, and site surveys conducted by field personnel who initially collected the roadblock information

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in the datasheet. Finally, GPS coordinates were then presented on a GIS platform to generate the roadblock inventory map as shown in Fig. 2. In the second phase of the data preparation, the rainfall datasheet acquired from NCHM was cleaned, processed to the required format, and exported to the GIS software. Since the locations of rainfall gauging stations differ from the locations of the actual roadblock points, a Thiessen Polygon Method was adopted and applied to all 20 rainfall gauging stations in GIS using the “Voronoi Polygon” tool to obtain the amount of rainfall that most likely occurred at the block point at the date and time of the failure event, as shown in Fig. 2. Thiessen polygons are geographic process models, nonparametric point pattern analysis tools, organizational structures for showing spatial data, and information-theoretic approaches to point patterns (Mu 2009). The technique was applied because it is one of the most accurate and commonly used methods to calculate the areal average precipitation by weighting the area ratio of the Thiessen polygons enclosing the watershed stations (Kang et al. 2019). Since the roadblock inventory datasheet consists of block occurrence and clearance date/time, rainfall data for both the dates were obtained using the technique stated above, which was further analyzed to calculate a cumulative rainfall during occurrence and clearance dates. Hence, subtracting these two cumulative rainfalls would yield the observed accumulated rainfall intensity during the block clearance time. This method will provide a relationship between the total time taken for the block clearance and the total amount of recorded rainfall intensity during the clearance time.

Fig. 2. Thiessen polygon distribution pattern.

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In addition to the initial roadblock database, a new column containing “YES” and “NO” columns were created, which was then integrated with the machinery database to determine whether or not machinery was pre-deployed at block locations. The statistical analysis performed on the obtained database would allow us to see how the availability of machinery on-site affects the roadblock’s clearance time. Finally, all the collected geospatial data was exported to the GIS platform to carry out the necessary geospatial analysis. Firstly, the shapefiles were projected to the required projection, i.e., DRUKEF 03/Bhutan National Grid CRS, and then “v.distance” function under the vector tool was used to calculate the distance from block points to the nearest town points or DoR site office. Furthermore, a block clearance time of 10 h was considered as a threshold clearance time because all the recorded blocks that took less than 10 h to clear were on the same day of their occurrence, thus having less impact on the overall situation and the stagnant traffic at the block point. Similarly, though, severe weather conditions such as prolonged rainfall would impact the clearance time, a threshold of 53 mm/day was considered to be more critical because the intensity of such a magnitude is found to trigger further failure events such as earth slides or rockslides, thus, hampering the clearance work at the site (Dikshit et al. 2019). The two mentioned thresholds were considered for further detailed analysis processes as and when necessary. 3.3 Analysis The complete database was analyzed in Excel with pivot tables and cross-tabulation analysis methods. Further, the database was converted into.csv format and exported into GIS software, where various geospatial and overlay analyses were carried out yielding numerous results described in the result section of this paper.

4 Result and Discussion 4.1 Descriptive Statistical Analysis of the Roadblock Database 4.1.1 Relationship Between Roadblock Clearance Time and Types of Failure Events on a National and Regional Scale Statistical Analysis of the UE datasheet showed that on average it took 12.2 h to clear the roadblocks that were recorded in the year 2020, where 360.2 and 0.2 h were the maximum and minimum time taken respectively as depicted in Table 1. The further statistical results concerning average clearance time of different failure events showed that the roadblocks caused by snowfall, subsidence, and flooding types took longer average time to get cleared i.e., 147 h, 67.3 h, and 21.4 h respectively, although they occurred less frequently than compared to landslides, debris flow, and rockfalls which are the three predominant failure types with 70.6%, 16.1%, and 5.2% records of the total roadblock respectively. The detail of failure events and average, maximum, and minimum time of clearance for the respective single-types and multi-types of failure events are summarized in Table 1.

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After comparing the different statistics from the table, we can infer that the clearance of the failure event does not depend upon the frequency of its occurrence, but rather, it depends upon its type and magnitude. However, the magnitude data were not utilized in this study as it was not available due to the challenge and risk in the collection of such information at the block site. Roadblocks caused by snowfall are not pointel types unlike other failure events but instead, it usually occurs for a longer stretch of the road, therefore, requiring larger and special types of resources (machinery and manpower) thus, greater clearance time. In case of subsidence where the entire road width gets settled or wash out, it needs extra time for machinery to carry out formation cutting in high and hilly terrain mountains to obtain the extra sufficient road width to allow the vehicles to ply over. Finally, flooding events are found to be rare but of greater destruction and magnitude where the entire road stretch gets submerged by the swollen river or adjoining streams thus requiring a longer time for its clearance. Table 1. Relationship between failure events and clearance time (national scale). Failure events Landslide

Frequency

Clearance time (h) Average

Max

Min

416

13.3

322.6

0.2

Debris flow

95

4.6

20.3

0.5

Rock fall

31

17.6

315.6

0.7

Flooding

28

21.4

105.5

1.0

Subsidence

16

67.3

360.2

2.7

Snowfall

2

147.0

147.0

147.0

Scouring

1

9.0

9.0

9.0

90

4.8

27.6

0.5

Landslide/Debris flow Landslide/Rock fall

17

6.0

24.0

1.0

Debris flow/Rock fall

15

8.2

32.1

0.2

Landslide/Scouring

7

9.7

15.0

6.2

Landslide/Subsidence

3

5.3

7.0

3.7

Rock fall/Subsidence

1

3.8

3.8

3.8

Rock fall/Debris flow

1

5.2

5.2

5.2

Landslide/Debris flow/Subsidence

3

8.1

9.0

7.0

Landslide/Debris flow/Scouring

2

6.2

6.5

6.0

Rock fall/Debris flow/Scouring

1

13.5

13.5

13.5

Landslide/Subsidence/Scouring

1

11.7

11.7

11.7

Landslide/Debris flow/Rock fall/Flooding/Scouring

2

9.3

9.4

9.2

732

12.2

360.2

0.2

All data

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Furthermore, breaking down the block clearance time regionally as shown in Fig. 3 shows that the maximum and minimum time taken for clearance was reported from Phuentsholing and Trongsa regional offices respectively. However, in general, the average clearance time was longest for the roadblocks under the Lingmithang region followed by the Thimphu region with 37.6 h and 23.1 h respectively. On the other hand, Samdrup Jongkhar had the shortest average clearance time (4.7 h) followed by Lobeysa Region (5.5 h).

Fig. 3. Clearance time of roadblocks in each RO’s.

4.1.2 Relationship Between Roadblock Clearance Time and Availability of Machinery at the Site Results of clearance time concerning the availability of pre-deployed machinery at the site showed that the locations or the stretches of roads where the machinery was deployed before the occurrence of the failure event, took lesser clearance time when compared to the locations which didn’t have machinery at the site. The average time taken was 10.4 h and 13 h respectively. It was also observed that the locations where most of the regionals (except for Lingmithang and Lobeysa) took maximum clearance time, didn’t have machinery available prior to the failure occurrence at those sections of the road. Thus, it required more time for preparation and arrangement of machines from other nearby sources to reach the block location. Therefore, such a result would allow the

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agencies to timely prepare and plan necessary interventions such as better allocation of the resources depending upon the criticality, frequency of roadblock occurrence, and comparing the average time clearance by each RO. Detail result is summarized in Table 2. Table 2. Relationship between clearance time and availability of machinery at the site. Regional office Machinery available at the site Frequency

Machinery not available at the site

Clearance time (h)

Frequency

Average

Max

Min

Clearance time (h) Average

Max

Min

Lingmithang

24

46.1

198.4

1.33

11

23.2

147

3.3

Phuentsholing

3

8.23

14.5

3.2

70

19.5

360.2

0.2

Samdrup Jongkhar

48

4.4

37

0.7

109

4.9

29.8

0.4

Sarpang

136

7.8

105.5

0.6

92

19.5

109.5

0.8

Trongsa

17

9.4

82.3

0.4

81

8.5

59.9

0.2

Lobeysa

All the roadblock locations under these regions don’t have machinery at the site

28

5.5

36.1

0.5

Thimphu

22

23.2

59

1.5

Tingtibi

57

8.1

32

0.5

Trashigang All data

34 228

10.4

198.4

0.4

504

16.1

315.6

0.4

13

360.2

0.2

4.1.3 Relationship Between Roadblock Clearance Time with the Road Category and Traffic Volume The relation between roadblock clearance time with road category and traffic volume showed that the average clearance time for AH-48, PNH, and SNH were 8.2 h, 10.3 h, and 17 h which had an average traffic volume of 768, 452, and 134 vehicles/day respectively in the entire national highway of the country. This indicates that more priority to roadblock clearance was given to higher category and more important roads with higher traffic counts than compared to the road of less importance. The result is summarized in Table 3. 4.2 Exploratory Statistical Results of the Roadblock Database After Geospatial Analysis 4.2.1 Relationship Between Roadblock Clearance Time and Rainfall Data Under this section of the analysis, the cumulative rainfall for both roadblock occurrence and clearance dates were obtained through the Thiessen polygon technique as illustrated in the methodology section of this paper. The difference of these two cumulative gave

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Road category

Average traffic volume

Average clearance time (h)

3

768

8.2

PNH

520

452

10.3

SNH

209

134

17

All data

732

363

12.2

AH-48

Frequency

Fig. 4. Relationship between clearance time and accumulated rainfall intensity.

the total accumulated rainfall intensity in mm/days during the clearance period. The relationship between clearance time and accumulated rainfall results showed that the clearance time does depend upon the weather that followed the roadblock occurrence. A plot as shown in Fig. 4, was constructed between clearance time (greater than 10 h) Vs total accumulated rainfall intensity to see the pattern of total rainfall intensity for the roadblock which took clearance time greater than 10 h. The result shows that the roadblock clearance time increases with an increase in accumulated rainfall intensity and vice versa. Thus, such results would assist agencies to better predict the RTI value utilizing the weather forecast data and the equation derived from the relation after taking other relevant factors affecting the clearance time into consideration. Thus, minimizing the risk to the commuters and impact on the country’s overall development and economic activities by providing the relevant agencies as well as road users enough time to prioritize their plans and journeys accordingly.

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4.2.2 Relationship Between Roadblock Clearance Time and Distance Between Block Location from Nearest Town and DoR Site Office Location In general, no clear relationship pattern was observed between the block point and the distance values i.e., distance from the town and DoR site office to the block location. However, after further segregation of the distance values depending upon road categories, i.e., AH-48, PNH, or SNH, it was observed that the higher the road category in the hierarchy of importance, the lesser was the average distance of block points along those categories from the town or DoR site office. In addition, it was also observed that the average clearance time of those roadblocks was also dependent upon these two distance values as shown in Table 4. Table 4. Relationship between average clearance time and the average distance of block point from the town point and DoR site office. Road category

Frequency

AH-48

PNH

Average clearance time (h)

Average distance from town points

Average distance from DoR site office

3

8.2

3979.7

The road is not under DoR thus no DoR office is located nearby

520

10.3

5910.4

9365.5

SNH

209

17.0

9354.2

9854.3

Grand average

732

12.2

6824.5

9501.9

Distance factors have significant importance, especially when other influencing factors are favorable, such as good weather conditions, but there are no resources at the site due to the long distance to perform the task, thus, delaying the clearance time substantially even if the magnitude of failure events is relatively small. Therefore, to validate its importance and impact, roadblock events with values less than threshold rainfall intensity (greater than 53 mm/day) and clearance time greater than the threshold value (i.e., greater than 10 h) were only considered for further analysis, and a plot between distances from the two centers (town and DoR site office) and roadblock clearance time was developed as shown in Fig. 5. The result from the graph shows that the clearance time of roadblocks increases when the distance factors increase, and this could be because of the delay in the deployment of required resources at the site on time. However, it is also observed that the impact of the distance factor on the clearance time is very minimal compared to other factors.

5 Conclusions The study’s findings can be summarized as follows: 1. On average, it took 12.2 h to clear the roadblocks that were recorded in the year 2020, where 360.2 and 0.2 h were the maximum-minimum time taken, respectively.

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Fig. 5. Relationship between clearance time and distance from point of interest.

2. Roadblocks caused by snowfall, subsidence, and flooding types took a longer average time to get cleared, i.e., 147 h, 67.3 h, and 21.4 h respectively although they occurred less frequently than compared to landslide, debris flow, and rockfall. This could be because of various other factors such as rainfall intensity during clearance time, distance factors, the magnitude of failure, traffic volume, importance/category of road, etc. 3. From all the recorded roadblocks in the year 2020, Roadblocks under the jurisdiction of Phuentsholing and Trongsa region took the maximum and minimum average time of clearance, i.e. 360.2 h and 0.2 h respectively. 4. The block sites which didn’t have pre-deployed machinery at the site generally took a longer time to clear than those sites which had machinery. On average, the clearance time taken was 13 h and 10.4 h respectively. 5. The roadblocks on AH-48 were being cleared on an average of 8.2 h followed by 10.3 h on PNH roads and finally by 17 h on SNH. This indicates that the higher category roads are being prioritized and opened to traffic usually faster than compared to their consecutive lower category. 6. Higher rainfall intensity during the clearance of roadblocks means longer clearing times for the blocks. This could be because of hindrance due to active and continued failure events at the block location. 7. The farther the block points from town points or the DoR site office, the longer it took to clear the blocks. However, overall the distance factors didn’t have a significant impact on the clearance time of the roadblock. Therefore, such results in hand can immensely help the agencies involved in maintaining the normal function of the roads and also keep the general commuters well informed of the situation at the site. Thus, enabling various stakeholders, economic activities, and essential government sectors to plan and prioritize the activities to minimize the risk and impact that could be brought by such unfavorable and inevitable incidences. Acknowledgements. The authors would like to express their gratitude to the Japan International Cooperation Agency (JICA), Road Asset Management Platform, for providing all of the required

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funding and assistance to complete this study and also to the Bhutanese government agencies for contributing essential data that was substantially used in this research.

References Cheki, D., Shibayama, T.: Method for landslide risk evaluation and road operation management: a case study of Bhutan. J. Constr. Manag. JSCE 15, 23–31 (2008). https://doi.org/10.2208/procm. 15.23 Dikshit, A., Sarkar, R., Pradhan, B., Acharya, S., & Dorji, K.: Estimating rainfall thresholds for landslide occurrence in the Bhutan Himalayas. Water (Switzerland), 11(8) (2019). https://doi. org/10.3390/w11081616 Kang, B.-S., Yang, S.-K., Kang, M.-S.: A comparative analysis of the accuracy of areal precipitation according to the rainfall analysis method of mountainous streams. J. Environ. Sci. Int. 28(10), 841–849 (2019). https://doi.org/10.5322/jesi.2019.28.10.841 MOWHS: Road classification and network information of Bhutan (2020) Mu, L.: Thiessen polygon. In: International Encyclopedia of Human Geography, pp. 231–236. Elsevier (2009). https://doi.org/10.1016/B978-008044910-4.00545-9 Varnes, D.: Slope movement types and processes. Spec. Rep. 176, 11–33 (1978)

Research on Cumulative Plastic Deformation of the Soft Clay Under Cyclic Loading Xubing Xu1(B) , Zhendong Cui2 , and Yonglai Zheng1 1 Department of Hydraulic Engineering, Civil Engineering College, Tongji University,

Shanghai 200092, China [email protected], [email protected] 2 School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 221116, China [email protected]

Abstract. In coastal areas, the cumulative plastic strain development characteristics of soft clay foundation of wharf, airport, highway, etc., will change under long-term loads. In order to reveal the influence of the consolidation state and the drainage conditions on the cumulative plastic deformation of soft clay, a series of dynamic triaxial tests were carried out by the GDS triaxial apparatus, and then the cumulative plastic deformation of clay was analyzed and studied based on the fractional partial differential theory model. The test results show that the cyclic strain amplitude of drained triaxial test decreases with the increase of confining pressure, the base value creep curve decreases, and the cyclic strain amplitude also decreases; With the increase of vibration times, the hysteretic curve moves to the right and quickly tends to be dense. A certain amount of plastic strain will be accumulated in each loading cycle, but the accumulation decreases gradually. The plastic strain tends to be stable, and the elastic properties of soil become more prominent. Under different drainage conditions, the undrained cyclic strain curve is less than the drained cyclic strain curve, but the cyclic strain amplitude of the undrained cyclic strain curve is greater than that of the drained cyclic strain curve. Keywords: Soft clay · Cyclic loading · Cumulative plastic deformation

1 Introduction The loads, the aircraft landing load on the airport runway, the traffic load on the road, the container loading and unloading load on the wharf foundation and the tidal load on the breakwater and other structures, not only have long-term loads, but also have long-term cyclic loads. The soft soil foundation consolidated will have different degrees of settlement under cyclic load. The strain controlled dynamic triaxial tests were carried out to study the effects of loading times, dynamic strain amplitude, particle material content, particle size and effective confining pressure on the dynamic characteristics of hybrid clay (Jigheh and Soroush 2010). The results show that the damage degree of the sample increased with the

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 416–425, 2023. https://doi.org/10.1007/978-981-19-7331-4_33

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increase of loading times, strain amplitude and particle material content. Under different drainage conditions the triaxial creep tests were carried out by Cetin and Gokog (2013). The research indicates that soil samples in undrained creep test will be damaged at high strain level, while soil samples in drained creep test will be damaged at low strain level. The undrained dynamic triaxial tests were carried out to study the deformation characteristics of marine soft clay under long-term cyclic load (Wang et al. 2013; Guo et al. 2013). The results point out that the cumulative plastic strain after 1000 times and vibration times show an approximate linear relationship in the double logarithm space under different confining pressure and dynamic stress ratio. Hanna and Javed (2014) conducted a series of dynamic triaxial tests on sensitive clay. The results demonstrate that the effects of cyclic load, deviator stress, loading frequency, preconsolidation pressure, overconsolidation ratio, confining pressure, sensitivity, liquid index and saturation on the shear strength of sensitive clay, and put forward the concept of safe area. The undrained dynamic triaxial tests of offshore clay were carried out by Thian (2017). The results indicated that compared with the over consolidated sample, the normally consolidated sample shows better resistance to cyclic load, and the normally consolidated soil needs more vibration times to be damaged. Ling et al. (2017) studied the effects of dynamic stress amplitude, initial average stress and initial stress ratio on the cumulative plastic deformation of coarse-grained soil through the dynamic triaxial test of multistage loading. The results show that when the dynamic stress level is low, the cumulative rate of plastic strain decreases gradually with the increase of vibration times until it reaches an equilibrium state. The deformation characteristics of offshore silt with different sand content under cyclic load were studied by Jamali et al. (2018). The results reveal that the cumulative plastic deformation of the sample with 10% sand content is significantly greater than that of the sample with 0, 20 and 30% sand content under the action of different dynamic stress ratio. This study analyzes the variation law of soil strain under long-term cyclic load, provides theoretical guidance for the prediction of foundation settlement under longterm cyclic load, and focuses on the steady-state creep law of saturated soft clay under cyclic load, that is, the steady-state creep under specific frequency and dynamic stress amplitude.

2 Test Conditions Shanghai muddy saturated soft clay is selected for creep test under long-term cyclic load. The main test steps are back pressure saturation, bias consolidation and cyclic loading triaxial test, as shown in Fig. 1. During the tests, the vibration frequency is 0.5 Hz, and the specific test parameters are shown in Table 1.

3 Results 3.1 Selection of Cyclic Creep Characteristic Curve The soft clay of different confining pressure drainage creep shows similar creep characteristics under the cyclic load of the same dynamic stress amplitude, and the strain

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˄b˅Anisotropic consolidation

˄a˅Back pressure saturation

˄c˅Dynamic load

Fig. 1. Main test steps

Table 1. The schemes of samples creep tests under cyclic loading Effective confining pressure σ3 (kPa)

Initial deviatoric stress q0 (kPa)

σd (kPa)

f (Hz)

Test conditions

SD01

84

36

20

0.5

Drain

SD02

126

54

20

0.5

Drain

SD03

168

72

20

0.5

Drain

SD04

210

90

20

0.5

Drain

SD05

84

36

20

0.5

Undrain

development trend is roughly the same. A small section at the initial stage of long-term cyclic loading was selected to analysis. The six cyclic strain curves of the sample in the loading stage are shown in Fig. 2. Fifty data points are taken for each cycle. The creep curve is an approximate sinusoidal waveform, and the curve oscillation increases. In the strain curve of each cycle, there is a maximum strain point εmax and a minimum strain point εmin . Connecting the maximum strain points of each cycle will get the peak creep curve, and connecting the minimum strain points will get the valley creep curve. The strain at the midpoint of each cycle is defined as the base value point of strain. Connecting the base value points of each cycle will obtain the base value creep curve. As shown in Fig. 2, the recoverable strain generated during loading and unloading is called reversible strain. The strain that accumulates with the increase of cyclic vibration times is called cumulative plastic strain. Reversible strain reflects the elastic properties of soil, while cumulative plastic strain reflects the plastic properties of soil. 3.2 Analysis of Cyclic Creep Test Results The drainage creep characteristic curves of soft clay of the effective confining pressure of 84 kPa under cyclic loading are shown in Fig. 3. Figure 3 shows that the cyclic

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0.20

Test Peak value Valley value Base value

0.18 0.16

Axial strain (%)

419

0.14 0.12 Reversible strain

0.10 0.08 0.06 0.04

Cumulative plastic strain

0.02 0.00 780 782 784 786 788 790 792 794 796 798 800

Time (s) Fig. 2. The creep characteristic curve under cyclic loading

creep curve is included by the peak creep and valley creep curves, and increases with approximately sinusoidal waveform oscillation. The three creep characteristic curves have the same development trend. While the strain increases rapidly, the strain growth rate is decreasing, which indicates that the soil has hardened during the loading process. The cyclic creep is based on the base value creep and changes and increases within a certain cyclic strain amplitude range. With the increase of confining pressure, the reversible strain decreases. Figure 3(b) shows the change of excess pore water pressure of soft clay under cyclic load. In the initial stage, the excess pore water pressure rises rapidly. Because the cyclic creep is in the drainage state, the overall trend oscillation of the excess pore water pressure decreases with the increase of vibration times. Finally, the excess pore water pressure tends to be horizontal and stable as a whole, but compared with the creep curve, the waveform is slightly irregular and shows a step-by-step decline. This is due to the uncoordinated data acquisition frequency and loading frequency of GDS triaxial pore water pressure sensor, but the overall trend of pore water pressure is correct, which will not affect the analysis of soil deformation characteristics in this study. The same conclusion can be obtained in other drained cyclic creep tests under different confining pressures (SD02, SD03 and SD04). Figures 3(a), 4, 5 and 6(a) show that the cyclic creep of soft clay presents the characteristics of elasticity and plasticity at the same time. With the increase of cyclic loading times, the elasticity tends to be stable and obvious, and the plasticity gradually weakens. The creep curve is based on the base value creep and changes and develops within a certain cyclic strain amplitude. The strain amplitude is not a fixed value, but gradually tends to an approximate fixed value with the increase of loading time. With the increase of confining pressure, the cyclic strain amplitude decreases. When t = 10 h, the effective confining pressures are 84 kPa and 168 kPa, and the corresponding strain amplitude is 0.0502% and 0.0184% respectively.

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Figure 7 shows the undrained creep characteristic curve of soft clay under cyclic loading under effective confining pressure of 84 kPa. The SD05 parameters are the same as SD01 except for different drainage conditions. Compared with the drained cyclic creep test, the increase amount and growth rate of the three undrained creep characteristic curves are less than that of the drained cyclic creep characteristic curve. This conclusion can be obtained more intuitively from the comparison of the two base value creep curves in Fig. 8. Compared with the drained cyclic creep test, the excess pore water pressure in the undrained cyclic creep test oscillates and increases with the increase of vibration times, and does not decrease after reaching the maximum value. The excess pore water pressure and creep characteristic curve of undrained cyclic creep test have the same development trend. While the excess pore water pressure increases, the growth rate of excess pore water pressure decreases. In the loading process of undrained cyclic creep test, the excess pore water pressure bears most of the pressure, which is the internal factor of the slow growth of soil strain, as shown in Fig. 7(b).

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4 Discussion Figure 9 shows the base value creep curve of cyclic loading drainage creep under different confining pressures. The analysis shows that the base value creep curve decreases with the increase of confining pressure, which shows that confining pressure is an important factor affecting the creep characteristics of soft clay. Figure 10 shows the hysteretic curve of deviatoric stress-strain relationship of drainage cyclic creep of soft clay under different confining pressures. The curve moves to the right and quickly tends to be dense, which indicates that Shanghai soft clay has good viscoplasticity; Three clusters of hysteretic curves representing the initial, middle and late loading stages are selected from the figures. The plastic strain will be accumulated in each loading cycle, but the cumulative amount will gradually decrease, that is, the plastic strain will gradually accumulate, but the cumulative rate will gradually decay. With the increase of loading times, the soil becomes more and more dense, the

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growth of cumulative plastic strain tends to be stable, and the soil shows more elastic properties. The same conclusion can be obtained from other hysteretic curves. However, with the increase of confining pressure, the hysteretic curve slows down to the right, and the maximum strain becomes smaller. The hysteretic curve of the partial stress-strain relationship of soft clay is shown in Fig. 11. The overall development trend of the hysteretic curve of undrained cyclic creep test is basically consistent with that of drained cyclic creep test, but the hysteretic curve of undrained cyclic creep test moves slowly to the right and is too sparse. Compared with the drained cyclic creep test, the cumulative plastic strain of the undrained cyclic creep test increases slowly, but the strain amplitude is large.

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5 Conclusions The cyclic triaxial tests were carried out to study the variation law of soil cyclic creep characteristics and hysteretic curve with the increase of vibration times. The effects of different test conditions on soil cyclic creep characteristics were analyzed, and the following conclusions were obtained. 1. The excess pore water pressure of the cyclic drainage creep test of soft clay under cyclic load increases rapidly in the initial stage. With the increase of vibration times, the overall trend of excess pore water pressure oscillation decreases, and finally the overall excess pore water pressure tends to be horizontal and stable. 2. The hysteretic curve of the deviatoric stress-strain relationship of soft clay moves to the right and quickly tends to be dense. A certain amount of plastic strain will be accumulated in each loading cycle, but the accumulation will gradually decrease. With the increase of vibration times, the plastic strain tends to be stable, and the elastic properties of soil become more prominent. 3. The cyclic strain amplitude of the cyclic drainage creep test of soft clay decreases with the increase of confining pressure, the base value creep curve decreases, and the cyclic strain amplitude also decreases. 4. The undrained cyclic creep curve is less than the drained cyclic creep curve, but the cyclic strain amplitude of the undrained cyclic creep curve is greater than that of the drained cyclic creep curve.

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References Cetin, H., Gokog, L.A.: Soil structure changes during drained and undrained triaxial shear of a clay. Soils Found. 53(6), 628–638 (2013) Guo, L., Wang, J., Cai, Y.Q., et al.: Undrained deformation behavior of saturated soft clay under long-term cyclic loading. Soil Dyn. Earthq. Eng. 50, 28–37 (2013) Hanna, A.M., Javed, K.: Experimental investigation of foundations on sensitive clay subjected to cyclic loading. J. Geotech. Geoenviron. Eng. 140(11), 04014065 (2014) Jigheh, H.S., Soroush, A.: Cyclic behavior of mixed clayey soils. Int. J. Civ. Eng. 8(2), 99–106 (2010) Jamali, H., Tolooiyan, A., Dehghani, M., et al.: Long-term dynamic behaviour of Coode Island Silt (CIS) containing different sand content. Appl. Ocean Res. 73, 59–69 (2018) Ling, X.Z., Li, P., Zhang, F. et al.: Permanent deformation characteristics of coarse grained subgrade soils under train-induced repeated load. Adv. Mater. Sci. Eng. (2017) Thian, S.Y., Lee, C.Y.: Cyclic stress-controlled tests on offshore clay. J. Rock Mech. Geotech. Eng. 9, 376–381 (2017) Wang, J., Guo, L., Cai, Y.Q., et al.: Strain and pore pressure development on soft marine clay in triaxial tests with a large number of cycles. Ocean Eng. 74, 125–132 (2013)

Improved Vehicle Scanning Method for Bridge Damage Detection D. S. Yang1,1(B) , C. M. Wang2 , and W. H. Duan1 1 Department of Civil Engineering, Monash University, Clayton, VIC 3800, Australia

[email protected], [email protected] 2 School of Civil Engineering, The University of Queensland, St Lucia, QLD 4072, Australia

[email protected]

Abstract. In this paper, the bridge damage is detected by improved vehicle scanning method. In order to extract the narrowband signals from the vehicle response, the improved VSM uses a designed elliptic filter. These narrowband signals generally have a good signal-to-noise ratio. Therefore, the signals can reconstruct vibration modes accurately. For a damaged bridge, the kinks on the vibration modes reveal the damage locations. It has been found this improved VSM yields a better result with a series of vehicles passing over the bridge. In addition, the reconstructed mode shapes reveal a more noticeable kink. It can be used to point out the damage location when compared to the use of existing VSMs. As a result, the improved VSM can distinguish the damage locations directly with little to none post-process. This is unlike the other VSMs generally need to compare baseline model, construct damage index, etc. to determine the damage. Keywords: Filter · Damaged beam · Moving load · Signal processing · Beam structure

1 Introduction Owing to the development of the moving load problem in recent years, the dynamic response of the vehicle-bridge-interaction system has gained lots of attention (Yang and Lin 2005). Conventionally, most researchers have been targeted on the bridge’s dynamic response (Biggs 1964; Saller 1921). The safety of the bridge structure subjected to the load moves in space was the main purpose (Chan and O’Connor 1990). Upon studying the dynamic response of the vehicle, Yang et al. (2004) proposed to use vehicle response to extract the bridge frequency. This work opened a new path for identifying the bridge’s dynamic properties, also recognized as the vehicle scanning method (VSM) (Lin and Yang 2005; Bu et al. 2006). Upon applying the VSM to the SHM, it is crucial to study the vibration characteristic of a non-prismatic beam, i.e., a damaged beam. By reducing the elasticity modulus, Pandey et al. (1991) proposed to detect the damage from curvature changes in the mode shapes. To consider a damaged beam with cracks, a handbook was published by Tada et al. (2000) with an extensive source of crack stress analysis. Followed by introducing © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 426–436, 2023. https://doi.org/10.1007/978-981-19-7331-4_34

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the internal hinge to a classical (Euler-Bernoulli), the equivalent rotational stiffness could be simulated as a crack (Wang and Wang 2001; Weaver et al. 1990). To determine the damage in the beam structure, studies have found that using the frequency-based method is less effective than the mode-shape-based method (Jassim et al. 2013; Kim et al. 2003). To further consider a damaged steel bridge, Chang and Kim (2016) suggest that sufficient modal frequencies, e.g., the first three or four, are regarded as effective features to identify the damage. While the field of the VSM developed, many studies have sought the application of VSM on bridge SHM (Mousavi et al. 2019; OBrien et al. 2017; Zhang et al. 2012). Researchers has developed various method to identify bridge damage, e.g., baseline model (Oshima et al. 2014), instantaneous amplitude squared (Zhang et al. 2018), regional mode shape curvature (He et al. 2018) and modal assurance criterion (Zhan et al. 2021). Inspired by the VSM on bridges, lots of researchers have developed some measurements based on the vehicle’s response. However, it has been challenging to adopt the extracted mode shape to point out damage directly. This paper adopts the improved VSM method to perform SHM of the beam (Yang and Wang 2022a, 2022b). The outline of this study is given below. In Sect. 2, the definition of the problem will be given. Section 3 layouts the damaged beam modeling and the improved VSM. Section 4 presents two numerical examples of the adoption of improved VSM for damage detection. First, a testing vehicle over a bridge is considered. Secondly, a testing vehicle is further extended to a series of testing and exciting vehicles. Section 5 draws the conclusions.

2 Problem Definition By adopting a testing vehicle driving over a simply supported bridge. Figure 1 shows the bridge is modelled as a simply supported beam and the testing vehicle is simplified as a sprung mass. The bridge has a span L, flexural rigidity EI , mass per unit length m, and damping ratio ζb , and the testing vehicle has a stiffness of k v , damping coefficient cv , vehicle and wheel masses M v and M w . The testing vehicle is adopted to extract the bridge’s modal properties.

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3 Method of Solution This section presents identification of beam’s modal properties using improved VSM. In the first step, the response of the dynamic system is formulated and calculated. Next, the natural frequency of the beam will be extracted from CP response, and the CP responses will be decomposed by the designed filter. Finally, the reconstructed mode shape from the analytic signal and will be used to determine the bridge damage from the mode shape. 3.1 Formulation for Vehicle-Bridge Interaction The dynamic system of a vehicle and a bridge without damage can be formulated as ∂ 4w ∂ 2w + 2 = fc (t) · δ ∗ (x − xc ) ∂x4 ∂t   ∂wv ∂wc ∂ 2 wv − =0 μ 2 + kv (wv − wc ) + cv ∂t ∂t ∂t where the nondimensional terms are x= μ=

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The governing equations, along with the boundary and initial conditions, will be solved with FEM and time integration scheme, e.g., the Newmark beta method. 3.2 Open Crack Modelled as Internal Hinge In this study, an open crack in transverse direction is presumed to be the bridge damage. To model this open crack, we adopt an internal hinge model which includes an elastic rotational stiffness Kr . It is worth noting that the axial stiffness is assumed to be undamaged throughout the beam, and the rotational spring stiffness at the crack location can be expressed as (Tada et al. 2000):    2   −1 2h α 2 3 4 Kr = 5.93 − 19.69α + 37.14α − 35.84α + 13.12α (6) EI 1 − α where the severity of damage parameter α = a/h can be measured as a ratio of crack of depth a and thickness of the beam h. When the parameter α ≈ 0, it refers no crack, and when the parameter α ≈ 1, the crack goes through the transverse direction of the beam.

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3.3 Identifying Bridge Frequency Based on the bridge response, the bridge’s natural frequencies can be determined (Yang et al. 2018). Due to the testing vehicle passing through the beam in longitudinal direction, the CP response can capture most vibration modes, even though the CP response may contain minimal noise from the moving vehicle (Corbally and Malekjafarian2021; Nayek and Narasimhan, 2020; Zhang et al. 2018). The bridge’s natural frequency can be captured by applying the Fourier transform to the CP response. By using the acceleration (as against velocity or displacement) of CP response, one can acquire a better frequency spectrum (Yang et al. 2004). As the spectrum peaks may be the natural frequency of the beam, it is important to identify the frequency accurately, e.g., adopting zero-padding to improve recognition (Yang and Wang, 2022a). 3.4 Modal Identification Upon extracting the natural frequency of beam from previous section, the CP response can be decomposed to give an understanding of the vibration mode. The CP response will be dissembled into the narrowband signals by adopting the bandpass filter. Each of the narrowband signals constitutes the whole dynamic system. As a result, a decent band pass filter design plays an essential role in seeking the distilled narrowband signal. The design of an infinite impulse response (IIR) bandpass filter must acknowledge the targeted natural frequencies and discard frequencies above and below. By introducing the passband ripple and stopband ripple to the typical IIR filter (Butterworth filter), the newly designed filter becomes the Elliptic filter (Yang and Wang, 2022a). In comparing IIR filters, the impulse responses from the Butterworth filter and Elliptic filter are shown in Fig. 2. It can be seen the Elliptic filter’s transition band has a steep frequency, despite some ripples at the passband. Knowing the study herein is targeting the desired natural frequency with a small passband width, the passband ripple does not affect much obtaining the narrowband signal. As a result, the Elliptic filter will be adopted to distill the signal. 3.5 Reconstruction of BRIDGE’S Mode Shape Upon extracting a distilled signal s(t) in the last section, one can obtain the mode shape from the Hilbert transform. The Hilbert transform can be regarded as a unit impulse function 1/π t that convolutes a time series s(t). Hence, it keeps most of the local information in s(t). The analytic signal can be calculated, and the instantaneous amplitude can be defined (Yang et al. 2014). As the distilled signal s(t) is a narrowband time series, the instantaneous amplitude A(t) is therefore physically meaningful and can be viewed as the envelope function of s(t) and also as the mode shape of the beam (Bracewell 1978).

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4 Example Problems In this section, we demonstrate the improved VSM in two example problems. The properties of bridge and testing vehicle are similar to those used by Yang and Yau’s work (1997). The beam has a length L = 25 m, flexural rigidity EI = 2.75 × 108 N+m2 , mass m = 2000 kg/m, and the sprung mass has a body mass M v = 1200 kg, wheel mass M w = 100 kg, suspension stiffness k v = 170 kN/m, damping ratio ζv = 5% and with a low constant speed v = 3 m/s. In our simulation, we adopt the Newmark parameters α = 0.5, β = 0.25, the time step size  t = 1/2000 and the beam is discretized into 10 elements. Two example problems will be demonstrated by adopting the same damage parameters. In the first problem. A testing vehicle is adopted to extract the bridge’s dynamic properties. In the second example, a series of testing and exciting vehicles passing over the bridge is considered. Initially, a couple of exciting vehicles will pass over the bridge to enlarge the bridge vibration. And, the testing vehicle will soon follow, same as first example, to extract the bridge’s dynamic properties. 4.1 A Testing Vehicle Passing Over a Bridge Consider a simply supported beam is subjected to a sprung mass. The beam is presumed to have a single crack at 0.3L from the left end of the beam, and the crack has a damage parameter α = 0.6. While the testing vehicle is collecting data from its CP response, the

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testing vehicle excites the beam at the same time. The damage detection with the use of the improved VSM will be tested out. Figure 3 shows the comparison of the beam’s mode shape extracted from a testing vehicle and the theoretical result. Due to the narrowband signal, the physical meaning of the instantaneous amplitude can be represented as the extracted mode shape of the bridge. On the other hand, the theoretical mode shape is determined by the eigenvector. In each mode, the result agrees very well. 10-4

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Figure 4 shows the comparison of the damaged beam’s mode shape extracted from a testing vehicle and the theoretical result. The mode shape extracted from the testing vehicle and theoretical results is obtained by adopting the same method as the undamaged beam. Both results match well around the location without any damage. However, the extracted mode shape does not fit well around the location with damage owing to the low signal-to-noise. The extracted result for the mode shape can be refined by enlarging the beam’s vibration.

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4.2 A Series of Vehicle Passing Over a Bridge In this example, a series of testing and exciting vehicles pass over a bridge, as shown in Fig. 5. The bridge’s parameters are adopted the same as Example 4.1. However, the vehicles are led by two sprung masses that can be viewed as exciting vehicles and followed by the same testing vehicle to measure the bridge vibration. The pair of the exciting vehicles will have a distance of d1 = 0.75L to each other while the testing vehicle will have a distance of d2 = 1.1L to the last exciting vehicle. The testing vehicle parameters are adopted the same as Example 4.1, but the exciting vehicles have heavier masses and different parameters, as shown in Fig. 5. Therefore, the exciting vehicle will introduce a greater bridge vibration. And the testing vehicle will measure the induced vibration by itself and the exciting vehicle. Figure 6 compares the undamaged and damaged beams’ frequency subjected to a series of vehicles. The frequency spectrum has shown the difference between the undamaged and damaged beams. With the addition of the exciting vehicles, the peak spectrum has improved greatly in its signal-to-noise ratio than Example 4.1. The result of the frequency spectrum has exceeded the one excited by a single testing vehicle only.

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Figure 7 compares the damaged beam’s mode shape extracted from a series of vehicles and theoretical results. It has shown that both results in a good agreement. Especially for higher mode, both results fit very well throughout the beam. Moreover, there is a small hump in the extracted mode shape at the damage location. This small hump can also be used as a damage indicator.

5 Conclusions Presented herein is an improved VSM for damage detection of a simply supported bridge. With the adoption of the FEM and an appropriately designed elliptic filter, the damaged bridge’s mode shape can be reconstructed by the improved VSM. From the above illustrative examples, the following conclusions may be drawn:

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• when a single test vehicle is adopted to extract the bridge mode shape, the result from an undamaged bridge generally has better accuracy than a damaged beam. By comparing extracted mode shape to the theoretical solution, the result from the undamaged bridge matches very well. • when the bridge damage is considered, it is better to adopt a series of vehicles to extract the mode shape. The small hump of the extracted mode shape is usually magnified compared to the theoretical mode shape. This can be used as an indicator for the damage location. • the extracted mode shape from the higher mode, e.g., second or third mode, suffice better accuracy, which can indicate the beam damage. The illustrative example problems demonstrate the capability of damage detection using the improved VSM. This makes advancements for the reliability of structural health monitoring of bridges/beam structures.

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Acknowledgements. The financial support by the Australian Research Council (IH150100006) and the Department of Transport and Main Roads (TMR) Chair Professor Grant at The University of Queensland is gratefully acknowledged.

References Biggs, J.M.: Introduction to Structural Dynamics. McGraw-Hill Inc, New York (1964) Bracewell, R.: The Fourier Transform and its Applications. McGraw-Hill, New York, United States (1978) Bu, J.Q., Law, S.S., Zhu, X.Q.: Innovative bridge condition assessment from dynamic response of a passing vehicle. J. Eng. Mech. 132, 1372–1379 (2006) Chang, K.C., Kim, C.W.: Modal-parameter identification and vibration-based damage detection of a damaged steel truss bridge. Eng. Struct. 122, 156–173 (2016) Corbally, R., Malekjafarian, A.: Examining changes in bridge frequency due to damage using the contact-point response of a passing vehicle. J. Struct. Integr. Maintenance 6, 148–158 (2021) He, W.Y., He, J., Ren, W.X.: Damage localization of beam structures using mode shape extracted from moving vehicle response. Measurement 121, 276–285 (2018) Jassim, Z.A., Ali, N.N., Mustapha, F., Abdul Jalil, N.A.: A review on the vibration analysis for a damage occurrence of a cantilever beam. Eng. Fail. Anal. 31, 442–461 (2013) Kim, J.T., Ryu, Y.S., Cho, H.M., Stubbs, N.: Damage identification in beam-type structures: frequency-based method vs mode-shape-based method. Eng. Struct. 25, 57–67 (2003) Lin, C.W., Yang, Y.B.: Use of a passing vehicle to scan the fundamental bridge frequencies: an experimental verification. Eng. Struct. 27, 1865–1878 (2005) Mousavi, M., Holloway, D., Olivier, J.C.: Using a moving load to simultaneously detect location and severity of damage in a simply supported beam. JVC/J. Vibr. Control 25, 2108–2123 (2019) Nayek, R., Narasimhan, S.: Extraction of contact-point response in indirect bridge health monitoring using an input estimation approach. J. Civ. Struct. Heal. Monit. 10(5), 815–831 (2020). https://doi.org/10.1007/s13349-020-00418-z OBrien, E.J., Malekjafarian, A., González, A.: Application of empirical mode decomposition to drive-by bridge damage detection. Eur. J. Mech. A/Solids 61, 151–163 (2017) Oshima, Y., Yamamoto, K., Sugiura, K.: Damage assessment of a bridge based on mode shapes estimated by responses of passing vehicles. Smart Struct. Syst. 13, 731–753 (2014) Pandey, A.K., Biswas, M., Samman, M.M.: Damage detection from changes in curvature mode shapes. J. Sound Vib. 145, 321–332 (1991) Saller, H.: Einfluss bewegter Last auf Eisenbahnoberbau und Brücken. Kreidels Verlag, Berlin und Wiesbaden (1921) Tada, H., Paris, P., Irwin, G.: The Stress Analysis of Cracks Handbook. ASME Press, New York (2000) Chan, T.H.T., O’Connor, C.: Vehicle model for highway bridge impact. J. Struct. Eng. 116, 1772– 1793 (1990) Wang, C.Y., Wang, C.M.: Vibration of a beam with an internal hinge. Int. J. Struct. Stab. Dyn. 01, 163–167 (2001) Weaver, W., Timoshenko, S.P., Young, D.H.: Vibration Problems in Engineering. Wiley, New York (1990) Yang, D.S., Wang, C.M.: Modal properties identification of damped bridge using improved vehicle scanning method. Eng. Struct. 256, 114060 (2022) Yang, D.S., Wang, C.M.: Bridge damage detection using reconstructed mode shape by improved vehicle scanning method. Eng. Struct. 263, 114373 (2022)

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Yang, Y.B., Li, Y.C., Chang, K.C.: Constructing the mode shapes of a bridge from a passing vehicle: a theoretical study. Smart Struct. Syst. 13, 797–819 (2014) Yang, Y.B., Lin, C.W.: Vehicle-bridge interaction dynamics and potential applications. J. Sound Vib. 284, 205–226 (2005) Yang, Y.B., Lin, C.W., Yau, J.D.: Extracting bridge frequencies from the dynamic response of a passing vehicle. J. Sound Vib. 272, 471–493 (2004) Yang, Y.B., Yau, J.D.: Vehicle-bridge interaction element for dynamic analysis. J. Struct. Eng. 123, 1512–1518 (1997) Yang, Y.B., Zhang, B., Qian, Y., Wu, Y.: Contact-point response for modal identification of bridges by a moving test vehicle. Int. J. Struct. Stab. Dyn. 18, 1850073 (2018) Zhan, Y., Au, F.T.K., Zhang, J.; Bridge identification and damage detection using contact point response difference of moving vehicle. Struct. Control Health Monit. (2021) Zhang, B., Qian, Y., Wu, Y., Yang, Y.B.: An effective means for damage detection of bridges using the contact-point response of a moving test vehicle. J. Sound Vib. 419, 158–172 (2018) Zhang, Y., Wang, L., Xiang, Z.: Damage detection by mode shape squares extracted from a passing vehicle. J. Sound Vib. 331, 291–307 (2012)

Positioning Accuracy Comparison of RTK Receivers Used for Disaster Investigation Toru Yamano1(B) , Kai Kiriyama1 , Osamu Okamoto3 , and Kei Kawamura2 1 Chuden Engineering Consultants, 2-3-30 Deshio, Minami-ku, Hiroshima-shi,

Hiroshima-ken 734-8510, Japan [email protected] 2 Yamaguchi University, 2-16-1 Tokiwadai, Ube-Shi,Yamaguchi-Ken 755-8611, Japan 3 National Institute of Technology (KOSEN) Ibaraki College, 866 Nakane, Hitachinaka-shi,Ibaraki-ken 312-8508, Japan

Abstract. In recent years, heavy rains that cause great deal of human damage have occurred in the northern Kyushu and the Chugoku regions, and severe sedimentrelated disasters have been caused. In the event of sediment-related disasters, a prompt survey is required to prevent the spread of damage. Therefore, the authors have developed a disaster investigation support system that aims to enhance the safety of investigators and their work efficiency by using a multi-band receiver. In this paper, the fixed-point positioning accuracy of some RTK receivers was evaluated at the disaster recovery site in Hiroshima Prefecture, where the sediment disaster surveys were actually conducted. In experiments on sabo dam aimed at confirming fixed-point positioning accuracy in a poor radio environment, it has been confirmed that the variation in horizontal positioning results is 22 mm (2DRMS) or less. Our experiments for the positioning performance in the forest have shown the variation in the horizontal positioning results being 0.65 m or less (2DRMS). Keywords: RTK · Disaster investigation · GNSS · Low-cost

1 Introduction There are many places where housing development is progressing near the valley exits such as mountainous areas near cities. If landslides or debris flows occur due to heavy rain, there is a risk of serious damage. In the northern Kyushu and the Chugoku region, heavy rain damages such as “July 2017 heavy rain in northern Kyushu” and “July 2018 heavy rain” have occurred, and sediment-related disasters were caused by heavy rains. Rapid surveys are important to prevent the spread of damage caused by sediment-related disasters. In order to confirm the damage state of structures, disaster investigations have two major tasks: measuring displacement of structures and monitoring the displacement of huge rocks at risk of sliding. In addition, it is necessary to accurately keep track of the current position and movement route for the investigators to grasp the work position and ensure safety. Surveys in areas where sediment-related disasters have occurred may be © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 437–447, 2023. https://doi.org/10.1007/978-981-19-7331-4_35

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more dangerous due to sudden changes in the weather. Therefore, it is important for the headquarters to know the exact position of the investigator. Furthermore, accurate grasp of the disaster location is useful for facility design at the time of reconstruction. In the current survey method, paper-based survey materials using medical records dangerous stream of debris flow chart and maps are brought to the site for taking photographs and sketching on maps. Therefore, it takes more time to complete the field survey and to compile the survey results. Kawaguchi et al. have developed a disaster investigation support system that improves work efficiency and the safety of investigators by utilizing ICT equipment such as smartphones and unmanned aerial vehicles (hereinafter referred to as UAVs) to solve above problems in sediment-related disaster investigations. This system uses a receiver built into the smartphone to acquire location information. In an environment where there are forests and/or structures for disaster investigation, there is a problem that the positioning value jumps of several tens of meters or more due to the multipath peculiar to the high-sensitivity receiver. To solve this problem, the authors have developed a disaster investigation support system that employs the RTK (Real Time Kinematic) method using a low-cost multi-band receiver (hereinafter referred to as this system). The RTK method is a satellite positioning method that is expected to be applied to autonomous driving of vehicles and robots. In recent years, the entry of consumer receiver manufacturers into the market has made it possible to use the RTK method with multi-band receivers at a cost of tens of thousands of yen. Compared to the conventional range of utilization of the RTK method by low-cost single-band receivers, it is expected that position information can be obtained with an accuracy of several centimeters in a variety of environments. The authors conducted a trial experiment on November 29, 2018 at a disaster recovery site in the Yagi district of Asaminami-ku, Hiroshima-shi, Hiroshima Prefecture. Compared to single-band receivers, multi-band receivers have a higher Fix rate in an environment with surrounding forests and structures, and there are no jumps in positioning points in the forest, which means the surveyor’s movement route was confirmed to be traceable. In this paper, the authors confirmed (1) the variation of the positioning results of the multi-band receiver and (2) the deviation of the positioning results of the multi-band receiver and the survey results of the total station in sabo dams and forests at disaster recovery sites. Based on these results, the authors evaluated the performance of the multi-band receiver used in the disaster investigation support system.

2 Existing Research and Coventional Technology 2.1 Existing Studies As previous research on disaster investigations, systems with GIS functions and investigations using UAVs are attracting attention. Ito et al. Developed a disaster investigation support system using GPS positioning. In this system, the results of positioning with a portable GPS can be automatically displayed on a map, the survey record sheet can be linked, and the results can be written on the sheet. Shibayama et al. has conducted research on disaster information sharing using a disaster information collection support system. In their system, investigators use terminals that have a GIS function and a GPS function linked to the map to improve the efficiency of the survey. Miura et al. reported on the utilization of GIS systems at disaster sites. The purpose of their system

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is to improve the efficiency of field surveys and information sharing by implementing GIS on tablet PCs. These studies do not use high-precision satellite positioning, and it is difficult to use them in a harsh environment for satellite positioning. In addition, Araki et al. conducted a trial study of an emergency survey using UAVs in a large-scale sediment-related disasters. In their study, they conducted a demonstration experiment using UAVs in an emergency survey of a natural dam, and confirmed the effectiveness of being able to grasp the situation at disaster sites from a bird’s-eye view by creating orthoimages. However, in order to effectively utilize this information in the next step such as field survey, accurate location information of the investigator is required. By adopting a low-power multi-band receiver with excellent portability for the system proposed by the authors in this section, highly accurate position information can be obtained at the disaster site. As a result, it is expected that the efficiency of disaster investigation and the safety of investigators will be improved. 2.2 About Satellite Positioning Method Figure 1 shows the classification of satellite positioning methods, and Fig. 2 shows the outline of the RTK method.

Fig. 1. The classification of satellite positioning methods

The satellite positioning method is divided according to the number of receivers, such as a positioning method that uses only one unit for independent positioning and two units for relative positioning. Furthermore, relative positioning is classified into code differential positioning and interference positioning. The Code differential positioning is a positioning method that uses a code transmitted from a satellite and has an accuracy of about several meters. The Interference positioning is a positioning method that requires observation of carrier phase, and is classified into static positioning and kinematic positioning (RTK method). This RTK method was used in this system reported in this paper. The RTK method is a positioning method that measures the relative position by simultaneously observing the carrier wave at a reference station with known coordinate values and a mobile station with unknown coordinate values. The observation data of the reference station is transmitted to the mobile station in real time by some communication means, and the position of the mobile station is obtained with an accuracy of several cm in the horizontal direction. Figure 2 shows the case of IP communication by mobile

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Fig. 2. The outline of the RTK method

router and that by radio as communication means. There are two solutions in the RTK method: the FLOAT solution and the FIX solution. The FLOAT solution for which the number of carrier phases is not calculated shows a range of accuracy from several tens of centimeters to several meters. The FIX solution for which the number of carrier phases has been calculated has an accuracy of several centimeters. The time from the start of positioning calculation until the solution is found and converged to the FIX solution is called the initialization time.

3 Overview of Disaster Investigation Support System The authors have been developing the disaster investigation support system that uses smartphones and UAVs in sediment-related disaster investigations to enhance the safety of investigators and their work efficiency. Figure 3 shows the outline of this system. The users of this system consist of a disaster response headquarters, a ground survey team, and a UAV survey team. The ground survey team surveys disaster sites using wearable cameras and smartphone applications, and shares the survey results with the disaster response headquarters. The UAV survey team surveys dangerous places that the ground investigation team cannot enter and shares the survey results with the disaster response headquarters. The disaster response headquarters grasps the site situation based on the survey results, gives instructions to the survey team, and confirms the safety. In addition, this system has a GIS function, and the location of the investigator and photos of the site are shared with the disaster response headquarters via a cloud server. However, this system, which is under development, uses a receiver built into the smartphone to detect the current position of the investigator. Therefore, the positioning results may be jumped over several tens of meters due to the multipath peculiar to the high-sensitivity receiver. Therefore, by using a small, low-power, low-cost, multi-band compatible RTK

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Fig. 3. The outline of this system

receiver instead of the receiver built into the smartphone, highly accurate positioning results can be obtained by which the investigator’s accurate position can be grasped and the efficiency of inspection of structures can be expected. Table 1 is a comparison table of the case where the receiver built in the smartphone is used and the case where the RTK receiver is used in this system. Table 1. System comparison table for different GNSS receivers Receiver

Positioning accuracy

Cost

Reliability

Reference station

Waiting time until positioning starts

Smartphone built-in receiver

Several meters

Low

Relatively high

Unnecessary

None

RTK receiver

A few centimeters

High

Relatively low

Necessary

About a few minutes

4 Positioning Performance Evaluation at Disaster Recovery Sites 4.1 Outline of Positioning Performance Evaluation Disaster sites are in a poor observation environment for satellite positioning because there are obstacles that block the sky, such as trees and sabo dams. In this experiment,

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positioning performance is evaluated using the receiver used in this system at the disaster recovery site in the Yagi district of Asaminami-ku, Hiroshima-shi, Hiroshima-ken, where an actual disaster survey was conducted. The receivers used were u-blox’s ZEDF9P (hereinafter, multi-band receiver) and u-blox’s NEO-M8T (hereinafter, single-band receiver). Table 2 shows the two receivers used in the experiment. Table 2. The two receivers used in the experiment Model

Equipped with RTK engine

Satellite system used

Dimensions/weight

GPS

GLONASS

BeiDou

Galileo

Multi-band receiver(F9P)

◯

L1/L2

G1/G2

B1/B2

E1/E5b

57[mm] × 55[mm] × 18[mm] /About 50[g]

Single-band receiver(M8T)

× (RTKLIB)

L1

–

B1

E1

57[mm] × 55[mm] × 18[mm] /About 50[g]

As the multi-band receiver does not support QZSS in RTK positioning, GPS, GLONASS, BeiDou, and Galileo were used for positioning calculation. As the single band receiver, GPS, BeiDou, and Galileo were used because the use of GLONASS and BeiDou is exclusive. The positioning of the multi-band receiver was calculated inside the receiver, and the positioning of the single-band receiver was calculated by post-processing on the PC using the open source program package RTKLIB 2.4.3b31. Figure 4 shows the installation status of the reference station and the sky view. The reference station was set up on the roof of the Yagi branch office of the Hiroshima West mountain range Sabo Office, Chugoku Regional Development Bureau, Ministry of Land, Infrastructure, Transport and Tourism, about 1 km away from the disaster recovery site. There are no obstacles around the reference station, and the sky is sufficiently open. For both the reference station and mobile station, the TW3870GP from Ritto (TW3870 from Tallysman with a 10 cm ground plane) was used. The mobile station connected one antenna to two receivers using a distributor. The reference station used a multi-band receiver and transmitted the correction data to the mobile station by IP communication of the mobile router. 4.2 Evaluation of Positioning Accuracy at the Sabo Dam In this experiment, the authors confirmed the positioning accuracy of the multi-band receiver used in this system at the sabo dam. The experiment was conducted at 10:00 am (hereinafter, JST) on March 29, 2019. Figure 5 shows the experimental environment at the sabo dam. The two points on the upstream side of the dam was surrounded by walls, and the sky was covered by about 70%. In the experiment, the antenna was leveled while looking at the bubble tube of the survey pole at each of the four positioning points, and the antenna remained stationary for 45 s. Figure 6 shows the horizontal positioning

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Fig. 4. The installation status of the reference station and the sky view

results of the experiment on the dam. The FIX solution was obtained in an environment where about a quarter of the sky was open, and the variations in the positioning results were 0.016 m, 0.022 m, 0.009 m, and 0.010 m (2DRMS), respectively. The deviations between the average value of the positioning results of the RTK method and the survey results of the total station were 0.013 m, 0.044 m, 0.019 m, and 0.025 m, respectively. Since this positioning results were obtained by leveling by human hand while looking at the bubble tube, it is necessary to consider hand shake.

(a) Experiment environment

(b) Positioning location and sky

Fig. 5. The experimental environment at the sabo dam

4.3 Evaluation of Positioning Performance in the Forest In this experiment, the authors confirmed the positioning performance of the multi-band receiver used in this system in the forest. The experiment was conducted at noon on

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Fig. 6. The horizontal positioning results of the experiment on the dam

March 29, 2019. Figure 7 shows the experimental environment and experimental route in the forest.

Fig. 7. The experimental environment and route in the forest (Taken from east to west)

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The experimental route was set to go around a fixed course including that in the forest, and the authors installed four tripods on the route. Three out of the four tripods were installed in the forest where there were trees with a diameter at breast height of about 20–30 cm around them, which is a harsh environment for satellite positioning. In the experiment, the authors set the antenna on a tripod at the starting point, converged on the Fix solution, moved in the forest, set the antenna on the tripod again, and positioned it for 30 s. In the experiment, the authors moved around the experimental route for positioning work multiple times. The characteristic results are introduced here. Figure 8 shows the results of horizontal positioning in the forest. In the positioning results of the single band receiver shown in Fig. 8 (a), jumps of positioning points of several tens of meters or more were found. The positioning results of the multi-band

(a) Posioning result of single band receiver

(b) Posioning result of mul-band receiver and sky view Fig. 8. The results of horizontal positioning in the forest

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receiver shown in Fig. 8 (b) were 9.1% for the FIX solution, 88.4% for the FLOAT solution, and 2.5% for the DGPS. In addition, there was a positioning point where a missed FIX was suspected that the positioning result was jumping about 5 m, and the positioning result of the stationary point after that was also offset by about 5 m. Figure 9 shows an enlarged view of the positioning results.

Fig. 9. Enlarged view of positioning results

The variations in the positioning results were 0.165 m, 0.177 m, 0.467 m, and 0.641 m (2DRMS), respectively. The deviations between the average value of the positioning results of the RTK method and the survey results of the total station were 1.273 m, 0.646 m, 5.046 m, and 4.228 m, respectively.

5 Conclusions In this paper, the authors confirmed the positioning performance of the latest multi-band receivers. In the positioning accuracy evaluation of the sabo dam, it was confirmed that the variation of the positioning result was 22 mm or less and the result compared with that of the total station was 44 mm or less even in the environment where about a quarter of the sky was open. In addition, in the evaluation of positioning performance in the forest, the positioning results of the single band receiver showed jumps of positioning points of several tens of meters or more. In the same environment, it was confirmed that the variation in the positioning results of the multi-band receiver was 0.65 m or less, and the result compared with that of the total station was 5.1 m or less.

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From the results of this experiment, it is expected that the efficiency of disaster investigation and the safety of workers will be improved by using highly accurate position information by GNSS positioning for the disaster investigation support system. In addition, when a disaster occurs, it is expected to be applied to measure the displacement of structures such as sabo dams in disaster investigations. Acknowledgements. In the trial experiment at the disaster recovery site, the authors received cooperation from the Chugoku Regional Development Bureau of the Ministry of Land, Infrastructure, Transport and Tourism and the Hiroshima West Mountain range Sabo Office, such as providing the location for the reference station and the landslide disaster site field.

Bibliography Aoyagi, H., Maeda, Y., Okamoto, O., Kobayashi, A.: Evaluation of usefulness low cost RTK-GNSS positioning. In: 18th System Integration Division Lecture(SI2017), 1F3_05 (2017) Araki, Y., Kinoshita, A., Hata, M., Kawai, M., Kotake, T., Yamada, T., Shibata, S., Kamei, M., Matsuoka, K., Minamiguchi, Y.: A study of emergency survey using unmanned aerial vehicle of large-scale disasters. In: 10th Symposium on Sediment-Related Disasters, pp. 73–78 (2020) Chiba, F., Sada, T., Ishizaka, T.: Fundamental study on the Measurement of Vehicle Trajectory using RTK-GPS. J. Japan Soc. Civil Eng. F3 68(2), II_37–II_42 (2012) Ito, Y., Toyoda, M., Nakamura, D.: Development and utilization of the disaster investigation support system. Japanese Geotech. J. 4(2), 197–204 (2008) Japan Meteorological Agency, (Obtained 2020.10.14): List of meteorological, earthquake, and volcanic phenomena named by the Japan Meteorological Agency. Kawaguchi, Y., Yoshimura, G., Esumi, N.: Utilization of SMART SABO for emergency survey after sediment-related disaster. J. Japan Soc. Erosion Control Eng. 73(1), 58–61 (2020) Miura, H., Sato, K.: Utilization of GIS system at disaster site—Example of utilization in Typhoon No.12 TEC-FORCE-. Japan Institute of Country-Technology (2012) Oizumi, T., Kawai, M., Saruwatari, Y., Kiriyama, K., Akutsu, A., Kawano, K., Araki, Y., Moriyasu, S., Takada, T., Okamoto, O.: Performance evaluation of RTK receiver for disaster investigation. J. Appl. Survey Technol. 32 (2019) Shibayama, A., Hisada, Y., Murakami, M.: A study on intelligence sharing using the support system for disaster information collection with information and communication technology. J. Japan Assoc. Earthq. Eng. 9(2) (Special Issue) (2009) Takasu, T., Kubo, N., Yasuda, A.: Development, evaluation and application of program library RTKLIB for RTK-GPS. In: GPS/GNSS Symposium 2007 Textbook, Institute of Positioning, Navigation, and Timing, pp. 213–218 (2007)

Corrosive Behavior of Structural Steel and Hot Dipped Galvanized Steel in the Central Part of Thailand by Atmospheric Exposure Test Bunya Chea1,2(B) , Taweep Chaisomphob1 , and Takashi Matsumoto3 1 Department of Civil Engineering and Technology, Sirindhorn International Institute of

Technology, Thammasat University, Bangkok 12120, Thailand [email protected] 2 Graduate School of Engineering, Hokkaido University, Sapporo 060-0808, Japan 3 Faculty of Engineering, Hokkaido University, Sapporo 060-0808, Japan [email protected]

Abstract. Central part of Thailand consists of several kinds of areas like metropolitan area and non-packed area. Those kinds of characteristics could cause different corrosion rates based on the atmospheric conditions and environmental pollutions. In this paper, atmospheric exposure test study with six test locations for bare steel and hot dipped galvanized steel is illustrated. The chosen test locations conformed to ASTM G50 standard. Environment parameters have been collected at the test locations. The meteorological data from the governmental website has also been collected to complete the gap. After exposure, the specimens have been collected and analyzed based on ASTM and ISO standards. This study result shows the thickness loss for bare steel and hot dipped galvanized steel at each test location and how important and effective the galvanized coating is in the test locations. Keywords: Bare steel · Hot dipped galvanized steel · Coating · Environmental parameters · Corrosion

1 Introduction In tropical climates, wet and dry conditions with a combination of high temperature, high humidity, and considerable amount of rainfall are commonly found (Corvo et al. 2008). Different meteorological parameters and environmental pollutants affect the corrosion rate of bare steel and hot dip galvanized steel. Air pollutants like SO2 , CO2 , NO2 , and so on which can be transported by the wind, while sometimes with moisture, to touch with the structure are the key factors for steel corrosion in central part of Thailand. Those air pollutants can form with the rain to be acid rain that consequently provides the deterioration of the structures. Specific environmental events played a dominant role in corrosion behavior of the steel (Lloyd et al. 1990). Higher corrosion values are generally associated with higher SO2 levels (Rios-Rojas et al. 2016).

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 448–457, 2023. https://doi.org/10.1007/978-981-19-7331-4_36

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Central part of Thailand (Bangkok, Pathum Thani, Ayuttaya, and Saraburi) combines with metropolitan area, urban with some industrial places, and low activities area. The aim of this study is to demonstrate the corrosion rate of the steel and hot dipped galvanized, and the influence of those kinds of atmosphere characteristics.

2 Experimental Procedure 2.1 Specimen Properties Two grades of carbon steel, SS400 and SM490, have been chosen. The dimensions of the specimens are 100 × 150 × 4.5 mm following ASTM G92-86. SS400 specimen has been conformed to JIS G3101 and SM490 has been conformed to JIS G3106 (Tables 1 and 2). 2.2 Specimen Preparation The surfaces of the bare steel specimens have been cleaned for the rust by removing the mild skin with the sandblasting method and have been smoothed by sandpaper with removal machine. For HDG steel specimens, the surface has been smoothed by sandpaper. After smoothing the surface for all specimens, the dust, oil, and other chemical substance have been removed with DI water and Acetone. Afterward, those specimens have been dried by air dryer and stored in the desiccator boxes prior to exposure. All the cleaning processes conformed to ASTM G1 and ASTM G31 standards. 2.3 Exposure Conditions Six test locations have been selected throughout the central part of Thailand. Atmospheric conditions like temperature, relative humidity, and rainfall have been collected at the test sites and meteorological data from a government website have been collected. Sulfur dioxide data has also been collected from a government website (Fig. 1; Table 3). Exposure rack has been put toward the South and the angle of the exposure is 30 degrees following ASTM G50. For the weather station, the design followed ISO 9225. The station height has to be higher than one meter from the ground. The period of exposure are 3 months, 6 months, and 1 year. After reaching those periods, specimens have been collected to analyze and calculate corrosion rate. For the test locations in this paper, the exposure test was carry out in March, 2021 (Fig. 2). 2.4 Analyzing Procedure The collected exposure specimens, both bare steel and HDG specimens, have been cleaned to remove rust and weighted to know the mass loss for calculating the corrosion rate of each exposure time following ASTM G1 standard. The mass loss has been weighted with the digital balance which has the ability to weight 0.001g. The exposed

0.117

0.199

SM490

C

1.220

0.430

Mn

0.010

0.014

Si

0.014

0.012

P

Chemical composition (% by wt)

SS400

Steel types

0.010

0.009

S

0.042

0.050

Al

0.013

0.011

Ni

0.030

0.020

Cr

0.007

0.003

Mo

0.002

0.000

V

Table 1. Chemical composition of bare steel.

0.008

0.017

Cu

0.0000

0.0000

B

0.41

0.023

Cr + Mo

0.26

0.051

Cu + Ni + Cr + Mo

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Table 2. Type of specimens. Specimens

Coating layer Binder Thk

Bare steel

–

–

Hot-dip galvanized (HDG)

Zn

100 µm

Standards ASTM A123

Note: Hot dip galvanized is a bare steel coating with zinc

Fig. 1. Test locations.

Table 3. Name list of test locations. No

Location

Category

Total number of rack

Province

1

Saraburi province

Center

2

Saraburi

2

Thai Metal Trade Company Limited (Wangnoi)

Center

1

Ayutthaya

3

Sangcharoen Galvanizing Limited

Center

1

Pathum Thani

4

Sirindhorn International Institute of Technology (SIIT)

Center

2

Pathum Thani

5

Thai Metal Trade Company Limited (Bangkok)

Center

1

Bangkok

6

Iron and Steel Institute of Thailand

Center

2

Bangkok

area of the specimen has been measured with the digital caliper which has an accuracy ± 0.2 mm. The thickness loss has been calculated by following formula below: C=

W × 104 D×A

(1)

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Fig. 2. Exposure racks.

where C is thickness loss (µm), W is weight loss (g), A is the specimen exposed area (cm2 ), and D is the density of steel (7.86 g/cm3 ) or the density of Zinc (7.13 g/cm3 ) in case of HDG specimens.

3 Results and Discussions 3.1 Meteorological Data Thailand is a tropical country with wet and dry conditions. Thailand’s rainy season continues from May to October and dry season continues from November to April. Monthly average temperature and relative humidity are shown in Fig. 3. Figure 3(a) shows that Bangkok is the highest temperature zone among other provinces since Bangkok is a metropolitan area and that Bangkok is followed by Pathum Thani. The lower temperature zones are Saraburi and Ayutthaya. In Fig. 3(b), Ayutthaya and Saraburi were observed to have higher relative humidity (RH). Relative humidity shows downward trend from October to December based on the graph since the dry season starts from October. The bar chart in Fig. 4 illustrates that all the zones have higher rainfall from August to October. Overall, the highest rainfall month is September. Rainfall rate is found higher in Bangkok and Pathum Thani compared to Saraburi and Ayutthaya. The chart demonstrates that the peak value of rainfall is 316 mm in Pathum Thani and 357 mm in Bangkok. All the data have been collected at the test site and also collected from meteorological data of a government website (Thai Meteorological Department). 3.2 Pollution Data When steel or iron (Fe) reacts with sulfur dioxide (SO2 ) and oxygen (O2 ), it will become iron (II) sulfate (FeSO4 ) that is the rust product of steel (Peter et al. 2011). Based on ISO 9225, sulfur dioxide is one of the mandatory for the purpose of corrosivity estimation. It is noticeable in the graph of Fig. 5 that Bangkok shows the highest concentration of SO2 in the air since it is a metropolitan and business area. In that kind of area, SO2 comes out

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Fig. 3. Meteorological data for central part of Thailand. (a) Monthly average temperature. (b) Monthly average relative humidity.

Fig. 4. Meteorological data for central part of Thailand: monthly rainfall.

mainly from the use of fossil fuels with sulfur content such as diesel or gasoline (RiosRojas et al. 2016). Next to Bangkok, Pathum Thani has also higher SO2 concentration while this province is an urban area combined with some industrial places. The lowest are observed in Saraburi and Ayutthaya because those provinces have low activities in term of business and industrial. 3.3 Thickness Loss of Bare Steel The thickness loss of carbon steel in six different test locations are shown in Fig. 6. The thickness loss of bare steel shows the same tendency with the behavior of meteorological parameters and environmental pollutant. It is noticeable that thickness loss of bare steel for Saraburi and Ayutthaya are lower than Pathum Thani and Bangkok. According

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Fig. 5. Environmental pollutant: SO2 . (Source: Pollution Control Department Thailand)

the meteorological data, Bangkor and Pathum Thani have higher concentration of SO2 pollutant and higher rainfall values that consequently provide higher corrosion rate of bare steel. However, the corrosion in Pathum Thani is not significantly different from both sites in Bangkok. The thickness loss of bare steel after six month exposure for the central part of Thailand range from 8 micron to 11 micron. From the graph, it can be observed that corrosion rate from 3 to 6 months exposure gradually slows down for some of the stations since, for the period of 3 to 6 months, corrosion products act like a barrier layer to aggressive agents (water, oxygen and pollutants) that might cause the decrease of corrosion rate (Castano et al. 2009). Thickness loss of SM490 grade of bare steel was found higher than SS400 grade of bare steel. Based on the chemical compositions of the steel in Table 1, percentage of carbon of SM490 was found a little bit higher than SS400, and percentage of copper (Cu) of SM490 is lower than SS400. Copper (Cu) is one of the chemical composition to protect steel from corrosion. However, the rate is not far different from each other since both kinds of the steel are carbon steel. 3.4 Thickness Loss of Hot Dip Galvanized Steel In Fig. 7, it can be observed that thickness loss of HDG in Saraburi and Ayutthaya is lower than Pathum Thani and Bangkok as the same trend with bare steel that showing the same tendency with the behavior of meteorological parameters and environmental pollutant. The thickness loss of HDG after six months exposure for the central part of Thailand range from 0.2 to 0.33 micron. Thickness loss of SM490 HDG steel was found higher for some stations but for other stations, thickness loss of SS400 HDG steel is higher. However, both grades are not significantly different since Zinc coating layer sacrificed itself rather than the base steel. The thickness loss of HDG is the loss of zinc coating (not the steel).

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3.5 Corrosion Rate of Bare Steel Versus Hot Dip Galvanized Steel It is noticeable from the graph in Figs. 6 and 7 that thickness loss of HDG is remarkably low compared to bare steel without 52coating. After 6 months exposure, HDG thickness loss is lower in the range of 30–40 times compared to thickness loss of bare steel for the central part of Thailand. It can be determined that HDG coating can withstand well with atmospheric and pollutant impact and can protect the steel from corrosion.

Fig. 6. Thickness loss of bare steel (a-f) for two different grades SS400 and SM490

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Fig. 7. Thickness loss of HDG steel (a-f) for two different grades SS400 and SM490

4 Conclusions Atmospheric corrosion of bare steel and HDG steel have the same tendency with the behavior of meteorological parameters and environmental pollutant. As result, it can be observed that thickness loss in Bangkok and Pathum Thani are higher than in Saraburi and Ayutthaya. After 6 months exposure, thickness loss of bare steel ranged between 8 and 11 micron and thickness of HDG steel ranged between 0.2 and 0.33 micron (30–40 times lower than bare steel). These results show the effectiveness of the HDG coating that can withstand the atmospheric and pollutant impact to protect steel from corrosion.

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Currently, the exposure test is still continuously being conducted. To assure confidently the results, one year exposure is currently being performed in order to complete the cycle of the season, and the result will be coming in a further publication. Acknowledgements. The authors wish to acknowledge Thai Galvanizing Association for the financial support for the research. This work was partially budget supported by AUN/SEED-Net sponsored by JICA. Conducting this research would never have been done without the help and support. The authors would like also to express thanks for all the institutions and companies that provide us the test location and help.

References ASTM G50-2015: Standard Practice for Conducting Atmospheric Corrosion Tests on Metals (2015) ASTM G92-86 (Reapproved 2010): Standard Practice for characterization of atmospheric test sites (2010) ASTM A123-2017: Standard Specification for Zinc (Hot-dip Galvanized) coatings on Iron and Steel Products (2017) ASTM G1-2011: Standard Practice for Preparing, Cleaning, and Evaluating Corrosion Test Specimens (2011) ASTM G31-72 (Reapproved 2004): Standard Practice for Laboratory Immersion Corrosion Testing of Metals (2004) Corvo, F., et al.: Time of wetness in tropical climate: considerations on the estimation of TOW according to ISO 9223 standard. Corr. Sci 50(2008), 206–219 (2008) Castano, J.G., et al.: (20010), Atmospheric corrosion of carbon steel in Colombia. Corros. Sci. 52, 216–223 (2010) JIS G3101: Rolled steels for general structure (2015) JIS G3106: Rolled steels for welded structure (2004) Lloyd, B., Manning, M.I.: The episodic nature of the atmospheric rusting of steel. Corrosion Sci. 30, 77 (1990) Peter, M., Peter, P.: Handbook of hot-dip galvanization, Wiley-VCH, Weinheim: Strauss GmbH. Morlenbach, Germany (2011) Rios-Rojas, J.F., et al.: Annual atmospheric corrosion rate and dose-response function for carbon steel in Bogota. Atmosfera 30(1), 53–61 (2016) Thai Meteorological Department, Retrieved from https://www.tmd.go.th/en/ Thai Pollution Control Department, Retrieved from http://air4thai.pcd.go.th/webV3/#/Home

High Performance Materials and Structures

Experimental Investigation of Circular Reinforced Concrete Columns Exposed to Elevated Temperatures Jia Xu(B) and Riyad Aboutaha Department of Civil and Environmental Engineering, 151 Link Hall, Syracuse, NY 13210, USA {jxu26,rsabouta}@syr.edu

Abstract. This paper presents an experimental study on thermal and structural performance of fire-damaged circular reinforced concrete (RC) columns with medium and high strength concretes. A total twelve circular RC columns were exposed to elevated temperatures following the ISO 834 standard fire curves up to 120 min. The investigation focused on the effect of concrete compressive strength and fire duration on the residual axial capacity. The paper presents the temperature radiation into the column’s section versus duration and exterior temperature levels. In addition, detailed deterioration damage of the columns, residual axial load carrying capacity and load-displacement response of columns are presented. Detailed review of experimental work done by others is also presented. Keywords: Circular RC column · HSC · Post-fired · ISO 834 standard fire · Elevated temperature damage

1 Introduction Fire leads to serious threats to people’s lives and properties. Reinforced concrete (RC) structure shows relatively good fire resistance due to the thermal properties of concrete— low thermal conductivity and high heat capacity. Therefore, concrete cover could be considered as a shield to protect the reinforcements and concrete core during fire event. The understandings of RC column exposed to fire are important since column performed as the fundamental structural member for the bearing capacity of the building. It is essential to estimate the residual axial capacity of fire-damage RC columns for both safety concerns and repair purposes. Along with the increasing number of skyscrapers, high strength concrete (HSC) has been widely used in high-rise buildings, especially in columns. It is important to understand the structural behavior of fire-damaged RC columns for both NSC and HSC. Many experimental studies have been conducted to estimate the residual strength of RC columns damaged by fire in since 1980s. Lie did a series of tests on full-scaled RC columns for up to 3-h ASTM E119 standard fire (ASTM E119-20 2020) exposure to study the effects of axial loading, cross-sectional dimensions, moisture content, aggregate types, thickness of concrete cover and amount of steel on the residual strength of RC columns with NSC. Test results indicated that load, cross-section © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 461–468, 2023. https://doi.org/10.1007/978-981-19-7331-4_37

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size and type of aggregate had significant influence on the fire resistance of RC columns (Lie and Lin 1985). Jau and Huang tested six rectangular RC columns with concrete strength of 22.7 MPa under 2- and 4-h ISO 834 standard fire exposure to investigate the effect of fire duration, reinforcement ratio and concrete cover thickness on the residual strength. The test results indicated that longer fire duration, lower reinforcement ration and thicker concrete cover could lead to lower the residual strength (Jau and Huang 2007). Chen et al. tested nine full-sized square RC columns with concrete strength up to 30 MPa for 2- and 4-h ISO 834 standard fire exposure (ISO 834 1999) and concluded that the reduction in residual stiffness is more significant than in ultimate load (Chen et al. 2009). Kodur et al. tested five full-scaled RC square columns with concrete strength up to 98 MPa for 2- and 4-h ASTM E119 standard fire exposure and indicated that HSC columns experienced higher loss in the ultimate load capacity than NSC columns due to the occurrence of spalling (Kodur et al. 2013). Nair and Salem investigated ten square RC columns with NSC to study the effect of fire duration and load ratios and concluded that load ratio had much less effect on the residual strength of post-fire RC column than fire duration (Nair and Salem 2020). Although there were numbers of studies conducted on determining the residual strength of RC column with NSC, the investigations on post-fire behavior of RC columns with HSC is quite limited. This paper presented the experimental investigations of RC columns exposed to ISO 834 standard fire up to 120-min, and the concrete compressive strength ranged from 44.6 to 90 MPa.

2 Experimental Program This experimental program aimed to investigate the effect of fire duration and concrete compressive strength at room temperature on estimations of residual bearing capacity for fire-damaged RC columns. The experimental program obtained two phases—fire tests and uniaxial compressive tests. A total of twelve spiral circular RC columns were tested. 2.1 Specimen Details All specimens were identical, 300 mm in diameter and a length of 1000 mm. Columns were reinforced with six 16 mm diameter longitudinal reinforcing bars with equal spacing throughout the cross-section and transversely reinforced with 6 mm diameter spirals with 40 mm pitch throughout the length. The clear concrete cover was 25 mm for all columns. Figure 1 shows the cross-sectional details for the columns. Columns with the same concrete strength were casted from the same batch. Each column was instructed with four type-K thermocouples at the mid-height at casting, and the locations of thermocouples are shown in Fig. 2. Columns were divided into three groups—group N, group M and group H based on the concrete compressive strength at 28-day under room temperature. The average compressive concrete strength for group N, group M and group H were 44.6 MPa, 63.6 MPa and 90.1 MPa, respectively. Each group contained four specimens—the reference column, column with 50-min fire exposure, column with 90-min fire exposure and column

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Fig. 1. Cross-section details.

Fig. 2. Thermocouples locations.

with 120-min fire exposure. Columns were labelled in accordance with the designated fire exposure time. For instance, RC column with 44.6 MPa concrete compressive strength and 60-min fire exposed time was named as column N60. 2.2 Fire Tests Columns were exposed to fire for 60, 90 and 120-min in the gas furnace, and the temperature in the furnace followed the ISO834 standard fire curve (ISO 834 1999). The temperature in the furnace was controlled by two type-K thermocouples attached on the furnace walls, and the average of these two temperatures represented the temperature in the furnace and the surface temperature for columns. After the designated fire exposure time reached, the furnace was turned off, and the door was opened to let columns cool down to the ambient temperature by air. The maximum temperatures recorded by embedded thermocouples are plotted in Figs. 3, 4 and 5 for 60-min, 90-min and 120-min fire exposure, respectively.

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Fig. 3. Maximum experienced temperature for 60-min fire exposed columns.

Fig. 4. Maximum experienced temperature for 90-min fire exposed columns.

Fig. 5. Maximum experienced temperature for 120-min fire exposed columns.

The thermocouple on the steel bar of specimen N-60 was damaged during casting, so no data was recorded through the fire test. It could be observed that large temperature gradient was developed inside column, and columns with higher concrete strength showed higher temperature at the same location. A large crack in the longitudinal direction was

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observed on column M120, which contributed to the highest temperature observed at steel bar and 100 mm from concrete center in this column. The maximum temperature at concrete core for 120-min fire exposed columns is approximately twice than 60-min fire exposed columns. As shown in Fig. 6, spalling was observed for all columns in group-H, 90- and 120min fire exposed columns in group-M, and 120-min fire exposed column in group-N. It showed the agreement that concrete with higher strength is more in frequency of spalling due to the dense microstructure and less permeability (Kodur 2014). No steel reinforced was directly exposed to the fire through the heating cycle, which indicated that concrete cover could effectively slow the degradation on the strength of reinforcement and concrete core.

(a)

(f)

(b)

(c)

(g)

(d)

(h)

(e)

(i)

Fig. 6. Columns after fire test (a) column N60; (b) column N90; (c) column N120; (d) column M60; (e) column M90; (f) column M120; (g) column H60 (h) column H90 (i) column M120

2.3 Uniaxial Compression Tests The columns were subjected to monotonic loading by a vertical positioned 10,000 kN actuator, as shown in Fig. 7. Load was applied using load control of 1 kN/s until failure.

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Two steel plate with 300 mm in diameter were placed at both ends of the testing column to distribute load uniformly.

Fig. 7. Uniaxial compressive test setup

Test results are summarized in Table 1. Columns in group N showed a gentle reduction on the axial capacity compared with columns in group M and group H, because NSC showed slower strength degradation than HSC. Column M120 showed the greatest reduction on residual axial capacity, since large crack formed in the fire test caused further strength degradation of concrete core. A typical concrete crushing failure was observed for all specimens. Fire exposed columns in group N and group M showed ductile failure. Large cracks were observed in the longitudinal directions when columns in prior to failure followed by concrete cover peeled off. All columns in group H showed brittle and explosive failure mode with a very loud bang, and spiral fracture was observed. Figures 8, 9 and 10 represented load-displacement responses for column in group N, group M, and group H, respectively. Fire-exposed columns showed reduction on axial capacity and stiffness but improvement on ductility.

3 Conclusions This paper presents an experimental study on thermal and structural performance of post-fire circular reinforced concrete (RC) columns to investigate the effect of concrete compressive strength and fire duration on the residual axial capacity. Large temperature gradient could be developed between concrete core and concrete cover under fire exposure, and columns with higher concrete strength showed higher temperature at the same location. Spalling occurred more in frequency in HSC columns. Fire-exposed columns showed reduction on axial capacity and stiffness but improvement on ductility.

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Table 1. Uniaxial compressive test results. Specimen

Fire exposed time (min)

Axial strength (kN) 3957

Decrease (−) with respect to reference column (%)

N0

0

N60

60

3465.1

12.4

N90

90

3222.8

18.55

N120

120

3004.9

24.06

M0

0

4438

M60

60

3498

–

– 21.18

M90

90

3053.1

31.3

M120

120

3031.7

31.69

H0

0

6213.7

H60

60

4802.4

22.71

H90

90

4723.7

23.98

H120

120

4735.3

23.79

–

Fig. 8. Load-displacement response for columns in group N

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Fig. 9. Load-displacement response for columns in group M

Fig. 10. Load-displacement response for columns in group H

References ASTM E119-20: Standard Test Methods for Fire Tests of Building Construction and Materials. ASTM International, West Conshohocken (2020) Chen, Y., Chang, Y., Yao, G., Sheu, M.: Experimental research on post-fire behaviour of reinforced concrete columns. Fire Saf. J. 44, 741–748 (2009) ISO 834: Fire resistance tests—Elements of building construction—Part 1: General requirements. International Organization for Standardization, Switzerland (1999) Jau, W., Huang, K.: A study of reinforced concrete corner columns after fire. Cem. Concr. Compos. 30(2008), 622–638 (2007) Kodur, V.: Properties of concrete at elevated temperatures. IRSN Civil Eng. 2014, 1–15 (2014) Kodur, V., Raut, N., Mao, X., Khaliq, W.: Simplified approach for evaluating residual strength of fire-exposed reinforced concrete columns. Mater. Struct. 46, 2059–2075 (2013) Lie, T., Lin, T.: Fire performance of reinforced concrete columns. ASTM Special Technical Publication, pp. 176–205 (1985) Nair, A., Salem, O.: Experimental determination of the residual compressive strength of concrete columns subjected to different fire durations and load ratios. J. Struct. Fire Eng. 11(4), 529–543 (2020)

Mechanical Model for Parallel-to-Grain Withdrawal Failure of Self-tapping Screws in Glulam Lijing Fang(B) , Wenjun Qu, and Shengdong Zhang Department of Structural Engineering, Tongji University, Shanghai 200092, China {lijing-fang,quwenjun.tj,zhangsh_d}@tongji.edu.cn

Abstract. In response to the goal of carbon neutrality under the background of global climate crisis, timber as a kind of bio-based material regains a new attention in the field of building. When the building industry hopes to promote timber structure in practice, existing connection techniques are in urgent need of innovation. Currently the improving screw manufacturing process can supply the threaded fasteners such as self-tapping screw or threaded rod with sufficient lengths and optimized threads to the market, which provides a promising technical solution to realize the strong and stiff timber connections. Distinguished from the common laterally-loaded metal fasteners such as dowel and bolt, the selftapping screw can be regarded as a kind of fastener capable of load transfer along the direction of its axis. Before the application of this axially-loaded threaded fastener in timber connection, the withdrawal failure mechanism of self-tapping screw in wood should be researched in depth to avoid the withdrawal failure at first. Different from existing models based on the classical theory of Volkersen, a new mechanical model for parallel-to-grain withdrawal failure of self-tapping screws in glulam is proposed in this paper. “Assembly unit”, which can be assembled to the whole fastener surrounded with failure wood and disassembled to some discrete parts, is first introduced as a mechanics analysis unit in this model to research the withdrawal failure of self-tapping screws in glulam and calculate the anchorage length of self-tapping screws in glulam. The model considers the distinctive mechanical behaviors caused by the thread of the screw: the local stress of wood filled in the screw pitch and the discontinuous transfer of shear stress/force on the failure surface. The theoretical calculations achieve an acceptable agreement with the results of two experimental investigations, and the reasons affecting the accuracy of the model are discussed for further improvement. Keywords: Glulam structure · Connection technology · Self-tapping screw · Withdrawal failure · Mechanical model

1 Introduction General research approaches for withdrawal property of self-tapping screws in wood include experimental research, theoretical analysis and numerical simulation, with their respective advantages and limits. Experimental research usually carries out regression © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 469–481, 2023. https://doi.org/10.1007/978-981-19-7331-4_38

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analysis based on test results, and proposes empirical formulas for withdrawal capacity or strength of self-tapping screws, as well as further modification and optimization of such formulas. Some research results (Blaß et al. 2006) have been provided for corresponding codes or technical approvals (CEN 2004). However, regression formulas largely rely on the test data and hardly reveal the failure mechanism of self-tapping screws. Numerical simulation based on finite element method can be adopted to investigate the withdrawal property of self-tapping screws at the stress and strain level, but the accuracy of numerical results is not widely recognized mainly due to the lack of an appropriate constitutive model of wood with shear failure as the main failure criterion and reliable information about contact property in relevant finite element programs. Most analytical models for withdrawal property of axially-loaded fasteners in wood can be traced back to the theory of Volkersen (1938), which was initially developed for the rivet load distribution in lap-joints, and then gradually applicable for other fasteners such as glued-in hardwood dowel (Jensen et al. 2001), glued-in rod (Jensen et al. 2011), lag screw (Jensen et al. 2011, 2012) and threaded rod (Stamatopoulos and Malo 2015) by means of modification and introduction of new physical parameters. The mechanical behavior of axially-loaded threaded fasteners in wood is similar to the anchorage behavior of deformed steel bar in concrete, while the compressive or shear strength of wood is less than that of concrete, which means the influence of the thread on the mechanical behavior should deserve special attention. Since the theory of Volkersen in essence is not specific to the mechanical behavior caused by the thread of fasteners, the modifications and improvements for initial theory of Volkersen mostly focused on bond behavior and failure criterion can hardly reflect the distinctive features of axially-loaded threaded fasteners. Therefore, a new mechanical model for parallel-to-grain withdrawal failure of self-tapping screws in wood will be presented in this paper. Through the observation for experimental phenomena, the shear failure surface will be redefined when withdrawal failure occurs. Enlightened by the ideology of finite element method, “assembly unit”, which can be assembled to the whole fastener surrounded with failure wood and also disassembled to some discrete parts, is introduced as a mechanics analysis unit in this model to preliminarily investigate the local deformation and compression of wood, and the discontinuous transfer of shear stress on the shear failure surface, as the mechanical behaviors caused by the thread of self-tapping screws.

2 Theory 2.1 Experiment Investigation The typical withdrawal failure phenomena of an axially-loaded self-tapping screw embedded in wood are shown in 0. Through observations for the longitudinally and radially cut wood (0a), the screw surrounded with failure wood (0b) and the wood fragments with a length of the screw pitch (0c), the features of withdrawal failure are summarized as follows: (I) The withdrawal failure is primarily the shear failure that occurs in wood, and the shear failure surface is a circumferential surface, the diameter of which is the thread diameter of the screw. (II) As can be seen from the wood fragments falling off at random positions in 0c, the shear failure wood could be divided by threads into fragments with a length of the screw pitch, which implies that the shear stress on

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Fig. 1. Typical withdrawal failure phenomena of a self-tapping screw in wood: (a) the longitudinally and radially cut wood; (b) the screw surrounded with failure wood; (c) wood fragments with a length of the screw pitch

the shear failure surface is no longer transferred continuously along the axial direction (Fig. 1). 2.2 Model Simplification The mechanical model for parallel-to-grain withdrawal failure of self-tapping screws in wood is based on the following assumptions: (I) Wood is regarded as a kind of transversely isotropic material, which applies particularly to homogeneous glulam. (II) As illustrated in 0, essential screw geometric characteristics such as the thread depth denoted as t (namely the difference between the thread radius and the core radius of the screw) and screw pitch denoted as s will be retained but the lead angle, thread angle (α) and flank angle (α1 ) of the screw ignored, which means the screw is treated as having an annular rather than a helical thread. In accordance with these assumptions, the complex three-dimensional mechanical problem in reality can be simplified to an ideal one-dimensional axisymmetric model (Fig. 2).

Fig. 2. Simplification of screw geometric characteristics

The three-dimensional visualization for the mechanical model is illustrated in 0, with the terms and concepts borrowed from assembly/disassembly process in mechanical engineering. An integrated self-tapping screw with failure wood is shown in 0a. Cut into segments in length of the screw pitch, the screw with failure wood is disassembled into a finite number of assembly units, and one of them is presented in 0b. The assembly unit can be separated into four discrete parts (metal top-cover, metal rod, wood tube, metal

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bottom-cover) shown in 0c, and the internal relations among these parts can be revealed by the radially cut assembly unit shown in 0d. The wood wrapping the rod in an assembly unit could be regarded as a thin-walled circular tube whose imaginary undeformed and deformed shape are respectively provided in 0e and 0f. The radial sections of the wood tube, indicated by the red lines, change from the rectangular sections in 0e to the nonrectangular sections in 0f, which is assumed to be caused by the vertical dislocation between the inner and outer walls of the wood tube and will be transformed into the shear deformation of failure wood during the establishment of the governing differential equation. Opposite to the disassembly process, these discrete parts can be combined to an assembly unit (a process termed component assembly), and then progressively to a whole model capable of vertical force transferring (a process termed final assembly) (Fig. 3).

Fig. 3. Discreteness and disassembly process of a whole model: (a) the screw surrounded with failure wood; (b) a standard assembly unit; (c) four parts in an assembly unit; (d) a radially cut assembly unit; (e) undeformed wood tube; (f) deformed wood tube; (vertical dislocation between the inner and outer walls, and shape change of the radial sections)

2.3 Formula Derivation For the sake of conciseness and convenience, the mechanical model is constructed from discrete parts to an assembly unit and finally to an integrated screw with failure wood. The main schematic diagrams such as the deformation of an assembly unit, internal structure of an assembly unit, and component/final assembly process are shown in 0, 0 and 0, respectively. The symbols in the diagrams and subsequent equations, with their physical meanings, will be interpreted in the following text. The deformations of the wood tube and the screw rod in an assembly unit are shown in 0. The failure wood wrapping the rod can be regarded as a thin-walled circular tube,

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the inner diameter, outer diameter and length of which are respectively denoted as d 1 , d, s, namely the core diameter, thread diameter and pitch of the screw. When focused on the axial deformations of the wood tube and the screw rod, it is assumed that the tensile displacement of the rod denoted as us (y) and the compressive displacement of longitudinal fibers on the outer wall of wood tube denoted as uwσ (y) are the function of the height of the rod (or wood tube) denoted as y in an assembly unit. Considering that the thickness of wood tube denoted as t (namely the thread depth) is far less than the core diameter of the screw, on the inner and outer walls of the wood tube, the couples of corresponding nodes (indicated by the red dots)divided along the height can be connected in the form of imaginary straight lines. These horizontal straight lines on the radial section of undeformed wood tube (0e) become a group of inclined straight lines after deformation (0f) (Figs. 4 and 5). Within the range of a screw pitch, the internal structure of an assembly unit is represented in 0. The screw can be regarded as a rod with variable cross section due to the existence of threads. Vertical tension denoted as F1 and F2 is respectively located on the top-cover at the position y = s and bottom-cover at the position y = 0 (here the thickness of thread is ignored). The tensile stress of the rod denoted as σs (y) uniformly distributed on the cross section without threads. Since the wood tube is extremely thin, along the radial direction, the compressive stress of other longitudinal fibers within the range of thickness is approximately equal to the compressive stress of longitudinal fibers on the outer wall of wood tube denoted as σw (y). The vertical stress along the height of the rod is simplified as friction per unit area denoted as q(y); q(y) and q (y) are a pair of equal and opposite stresses between the rod surface and the inner wall of wood tube. The outer wall of wood tube is just the shear failure surface separated from the wood, with the shear stress denoted as τ (y). According to the assumption of axisymmetric model, σw (y), q(y) and τ (y) stay the same around the circumference of rod or wood tube. At the position y = s, the compressive stress is denoted as σw1 , and σw1 · Aw is the compressive force located on the top cross section of wood tube, with the area of the top cross section of wood tube denoted as Aw ; additionally, σs1 is the tensile stress and σs1 · As is the tensile force located on the top cross section of the rod, with the area of the top cross section of the rod denoted as As . At the position y = 0, the symbols of σw2 , σw2 · Aw , σs2 and σs2 · As with their physical meanings are completely similar. On the outer wall of wood tube, τ1 and τ2 are respectively shear stress at the position y = s and y = 0, and shear stress could be aggregated through integral operation to obtain the shear force denoted as Q (Fig. 6). An assembly unit composed of wood tube, rod, top-cover and bottom-cover can work as a vertical force-transferring unit, and an integrated self-tapping screw with failure wood can be finally assembled by multiple assembly units, schematically shown in 0. F1 (i), F2 (i), Q(i) satisfy the vertical static equilibrium equation in an assembly unit with serial number (i). As we know, except the discontinuous transfer of shear stress on the shear failure surface, the vertical tension can be transferred continuously in the screw, which implies the relationships among multiple assembly units: F1 (i) is equal to F2 (i − 1) from the previous assembly unit (i − 1), and through the force-transferring action of the current assembly unit (i), F2 (i) as the tension to be transferred to the next assembly unit (i + 1) is equal to F1 (i + 1). This vertical force-transferring behavior

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Fig. 4. Deformations of the wood tube and the screw rod in an assembly unit: (a) rectangular radial section of undeformed wood tube; (b) non-rectangular radial section of deformed wood tube; (c) radial section of undeformed assembly unit; (d) radial section of deformed assembly unit; (e) imaginary horizontal lines on the radial section of undeformed wood tube; (f) imaginary inclined lines on the radial section of deformed wood tube

among multiple assembly units is the mechanical interpretation for the final assembly process. The vertical dislocation between the inner and outer walls of wood tube could be transformed into the rotation of the imaginary horizontal lines mentioned above, which is directly related to the shear deformation of failure wood, schematically shown in 0f. Thanks to the rigid displacement constraints exerted by the rod, top-cover and bottomcover, it is assumed that there is no relative slip between the rod surface and inner wall of wood tube, and then the displacement of longitudinal fibers on the inner wall of wood tube is equal to the tensile displacement of the rod us (y). Note that the compressive displacement of longitudinal fibers on the outer wall of wood tube is uwσ (y). The difference (us − uwσ ) quantifying the vertical dislocation between the inner and outer

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Fig. 5. Internal structure of an assembly unit

Fig. 6. Component assembly and final assembly process

walls of wood tube for each couple of nodes, and in the case of small deformation, the ratio of this difference to the thickness of wood tube, defining the change of right-angle at a node located on the outer wall of wood tube, namely shear strain denoted asγ (y) at a node, are indicated in 0f. Also note that the outer wall of wood tube is just the shear failure surface, the shear strain can be determined by the generalized Hooke’s law of shear stress and shear strain in elastic mechanics. Therefore, the governing differential

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equation of an assembly unit is provided in Eq. (1), where GLR is shear modulus of wood in L-R plane. Take the second derivative with respect to the variable y on both sides of equations (1)–(3) are respectively the equation of geometry and constitution in elastic mechanics, with elastic modulus of steel Es and parallel-to-grain elastic modulus of wood Ew,0 . us − uwσ τ = tan γ = γ = t GLR

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During the derivation, the rod and the wood are assumed to work in linear elasticity σw in Eq. (4) are determined by the vertical equilibrium equations range. The ddyσs and ddy of an infinitesimal small slice dy (0), namely Eqs. (5) and (6) (Fig. 7).

Fig. 7. Vertical static equilibrium of an infinitesimal small slice

  d σs σs + dy · As − σs · As − q · π d1 · dy = 0 dy   d σw σw · Aw − σw + dy · Aw − τ · π d · dy + q · π d1 · dy = 0 dy After the substitution of ddyσs and assembly unit can be expressed as:

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about the relationship between τ(y) and q(y) in Eq. (7). The parameter H is introduced as: q (8) H= τ where H is an unknown independent of the height, but related to the geometrical characteristics, material properties and stress state of an assembly unit. Thus, Eq. (7) can be simplified into a second-order differential equation with constant coefficients: τ  − [C1 + H (C2 − C3 )]τ = 0

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The similar derivation for ∇ < 0 is omitted in this paper to save space. Eq. (11) as the common solution of Eq. (9) is the distribution function of the shear stress along the height of wood tube in an assembly unit. In order to consider the local deformation and compression of wood, it is also necessary to make some assumptions about the displacement function on the left side of Eq. (1). In view of the exponential form of τ (y) in Eq. (11) and simple subtraction on the left side of Eq. (1), the function form of us (y) is assumed to be the exponential form with undetermined coefficients: us = meλy + ne−λy + la

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where la is a constant independent of the height (to avoid too many undetermined coefficients during the differential operations), aimed to adjust the tensile displacement of the rod in an assembly unit, and ensure the continuity and compatibility of the tensile displacement between two adjacent assembly units in the assembly process. Due to the limitation of space and the need for smooth writing, this paper focuses on the establishment of mechanical model and omits the mathematical process of simplification of undetermined coefficients in Eqs. (11) and (13). Please refer to (Fang et al. 2022) for details. After mathematical processing, the governing differential equation requires two independent conditions to determine all undetermined coefficients, and the vertical static equilibrium of an assembly unit can be expressed as: ⎧ F = σs1 · As − σw1 · Aw ⎪ ⎪ ⎨ 1 s Q = π d × ∫ τ dy (14) ⎪ 0 ⎪ ⎩ F2 = F1 − Q

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As discussed previously, since the tension can be transferred continuously in the screw during the assembly process, F1 (i) in the current assembly unit (i) is equal to F2 (i-1) from the previous assembly unit (i − 1), which is the first condition to determine the undetermined coefficients. Obviously, the model needs a condition about the stress state of the wood to identify the occurrence of withdrawal failure. As can be seen from 0, on the outer wall of wood tube, the position y = 0 is the contact area around the thread edge, which are the extremely unfavorable positions in a state of fairly complicated and highly concentrated stress. With the increase of the external axial load, once shear cracks appear at this position, they will gradually expand along the height of the outer wall of wood tube and penetrate through more and more assembly units until the screw is pulled out at a certain moment. Therefore, it is assumed that when withdrawal failure occurs, at least at the position y = 0 in each assembly unit, the shear stress reaches the parallel-to-grain shear strength of wood (Fig. 8).

Fig. 8. Unfavorable positions on the outer wall of wood tube

2.4 Algorithm Design The vertical force-transferring behavior between two adjacent assembly units when withdrawal failure occurs can be expressed by Eqs. (15) and (16). When i = 1, the tension F1 (1) is the external axial load P applied on the screw. The undetermined coefficients a1 , k1 , λ1 , the unknown shear force Q (1) and tension F2 (1) of the first assembly unit can be completely determined thanks to the known axial load P and the shear stress τ2 at the position y = 0 equal to the parallel-to-grain shear strength of wood fv,0 . When i = 2, the tension F1 (2) is equal to the tension F2 (1), all unknowns can be determined by the same calculation method. This kind of procedural calculation can be extended to more assembly units until the tension F2 (N) is less than 0, for obvious reason that an assembly unit is impossible to transfer compressive force in the vertical force-transferring behavior. The calculation termination means the fulfillment of the assembly process.  ⎧ πd ⎪ ⎪ F1i = λi ai (eλis − ki e−λis ) × ki C4 + C1 ⎪ ⎪ ⎪ ⎪ τ2i = ai + ai ki = fv,0 ⎨ LR (15) N =i: λ2i = ki GLR πC4dG Aw t ⎪

λis +Ew,0  ⎪ π D ⎪ ⎪ Qi = λi · ai · e − ki e−λis + ki − 1 ⎪ ⎪ ⎩ F2i = F1i − Qi > 0

Mechanical Model for Parallel-to-Grain Withdrawal  ⎧ ⎪ F1(i+1) = F2i = λ(i+1) a(i+1) (eλ(i+1)s − k(i+1) e−λ(i+1)s ) × k(i+1) C4 + πCd ⎪ ⎪ 1 ⎪ ⎪ ⎪ τ2(i+1) = a(i+1) + a(i+1) k(i+1) = fv,0 ⎪ ⎨ π dGLR λ2(i+1) = k N=i+1: ⎪  (i+1) GLR C4 +Ew,0 Aw t ⎪ ⎪ ⎪ Q(i+1) = λ π d · a(i+1) · eλ(i+1)s − k(i+1) e−λ(i+1)s + k(i+1) − 1 ⎪ ⎪ (i+1) ⎪ ⎩ F2(i+1) = F1(i+1) − Q(i+1) > 0

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The collated Eq. (15) or Eq. (16) is turned into a transcendental equation without analytical solution. In order to obtain the numerical solution of the equation and realize the whole assembly process, this procedural calculation can be written into a loop program in C language. N is the loop control variable in the program and also associated with the required number of assembly units when an integrated screw subjected to axial load P is pulled out. Note that the last assembly unit is not included due to the occurrence of compressive force, the effective embedment length of parallel-to-grain withdrawal P corresponding to axial load P is failure of self-tapping screw in wood denoted as lem given by: P lem = [(N − 1) × s]

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P . More genThe goal of the model is to calculate the effective embedment length lem erally, the relationship curve between withdrawal failure load and embedment length can be obtained by entering the information about geometry, material and axial load into the model. Among the input values, the axial load starts from 0 and gradually increases to the ultimate tensile capacity of the screw, which means each axial load corresponds to an embedment length and the withdrawal failure occurs prior to the tensile failure of the screw. For the system of screw and timber capable of vertical force transferring, there exists an anchorage length (namely the withdrawal failure will be avoided if the embedment length exceeds the anchorage length) limited by the geometrical characteristics and material properties.

3 Verification and Discussion 3.1 Model Verification Douglas-fir glulam and the WRT-type self-tapping screws produced by SFS intec were used in withdrawal experiments conducted by our research group. A total of 120 specimens were divided into 24 groups with 5 replicates in each group, according to the 4 different embedment lengths (65 mm, 130 mm, 195 mm, 260 mm) and 6 different screwto-grain angles (0°, 15°, 30°, 45°, 60°, 90°). The pull-push loading configuration was adopted in withdrawal test, with the purpose-made steel shelf for specimen installment and type SHT4106D electro-hydraulic servo universal testing machine for withdrawal test (Fang et al. 2022). In addition, this paper also uses the test data of parallel-tograin withdrawal failure of threaded rods by Stamatopoulos and Malo (2015) for model verification (Fig. 9). Considering that the withdrawal experiments by our research group are similar to the verification experiments by Jensen (2012), theoretical results based on the theory

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Fig. 9. Experimental and theoretical relationship curves between failure load and embedment length

of Jensen are also presented in 0a. It should be pointed out that the mode II fracture energy of wood adopts the same value provided by Jensen (2012), and the initial shear stress as an empirical fitting parameter is tried in two cases, 0 and 1. Since the theory of Jensen does not clearly suggest the calculation method for the compressive area of the wood involved in formulas, the calculation for theoretical failure loads based on the full cross section area of 200 × 200 mm2 similar to Jensen (2012), may lead to conservative results. However, the basic shape of the relationship curves between failure load and embedment length will not be changed. 3.2 Discussion In general, an acceptable agreement has been achieved between experimental results and theoretical predictions from the current model. A nearly linear relationship between withdrawal failure load and embedment length is predicted by the model. The main reasons affecting the accuracy of the model are summarized as follows: (I) The solution of the governing differential equation of assembly unit contains a lot of assumptions, among which the friction between the wood tube and screw rod is simplified to be proportional to the shear stress on shear failure surface; however, the influence of the simplification on the deformation and stress of the wood tube and screw rod is hard to evaluate. (II) The role of stress function or displacement function on an assembly unit is similar to the role of shape function on an element in the finite element method. Just as the calculation precision lies on the authenticity of the shape function, the stress function or displacement function will affect the availability of the assembly unit, and then the final precision of the whole model. (III) Now that the wood between threads is simplified into separate thin-walled wood tube, the stress state at the moment of withdrawal failure which relates to the assumption of failure criterion for the whole model is very necessary to be further researched. At present, the model adopts the maximum shear stress criterion for each assembly unit. When the number of assembly units is large; namely the embedment length is long, a rough assumption of failure criterion will inevitably lead to the inaccuracy of prediction. (IV) If the shear strength

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of wood under combined shear-compressive stresses is not concerned in the model, the theoretical prediction may not be accurate enough.

4 Conclusions Through the introduction of assembly unit, a new mechanical model for parallel-tograin withdrawal failure of self-tapping screws in wood is presented in this paper. The local deformation and compression of wood, and the discontinuous transfer of shear stress on the shear failure surface, as the distinctive mechanical behaviors caused by the thread of the screw, are reflected and investigated in the aspects of model simplification, formula derivation and algorithm design. In general, an acceptable agreement is achieved between theoretical predictions and experimental results, and a nearly linear relationship between withdrawal failure load and embedment length is predicted by the model. At last, the reasons affecting the accuracy of the model are discussed in detail for further improvement in the follow-up research.

References Blaß, H.J., Bejtka, I., Uibel, T.: Tragfähigkeit von Verbindungen mit selbstbohrenden Holzschrauben mit Vollgewinde. Universitätsverlag Karlsruhe (2006). https://doi.org/10.5445/ KSP/1000004810 CEN: European Committee for Standardization, EN 1995-1-1:2004: Design of timber structures. Part 1–1: General—Common rules and rules for buildings, Brussels, Belgium (2004) Fang, L.J., Qu, W.J., Zhang, S.D.: Mechanical model for withdrawal failure of self-tapping screws in glulam. Eng. Mech. 39(6), 212–225 (2022). https://doi.org/10.6052/j.issn.1000-4750.2021. 11.0866 Jensen, J.L., Koizumi, A., Sasaki, T., et al.: Axially loaded glued-in hardwood dowels. Wood Sci. Technol. 35, 73–83 (2001) Jensen, J.L., Nakatani, M., Quenneville, P., et al.: A simple unified model for withdrawal of lag screws and glued-in rods. Eur. J. Wood Wood Prod. 69, 537–544 (2011) Jensen, J.L., Nakatani, M., Quenneville, P., et al.: A simplified model for withdrawal of screws from end-grain of timber. Constr. Build. Mater. 29, 557–563 (2012) Stamatopoulos, H., Malo, K.A.: Withdrawal capacity of threaded rods embedded in timber elements. Constr. Build. Mater. 94, 387–397 (2015) Nakatani, M., Komatsu, K.: Development and verification of theory on pull-out properties of lagscrewbolted timber joints. In: Proceedings of the 8th World Conference on Timber Engineering (WCTE), pp. 95–99 (2004) Ellingsbø, P., Malo, K.A.: Withdrawal capacity of long self-tapping screws parallel to grain direction. In: Proceedings of the 12th World Conference on Timber Engineering (WCTE), pp. 228–237 (2012) Volkersen, O.: Die nietkraftverteilung in zugbeanspruchten nietverbindungen mit konstanten laschenquerschnitten (the rivet load distribution in lap-joints with members of constant thickness subjected to tension). Luftfahrtforschung 15, 41–47 (1938)

Behaviors of Steel-Concrete Composite Structures at Cold-Region Low Temperatures Jia-Bao Yan(B) and Jian Xie Key Laboratory of Coast Civil Structure Safety of Ministry of Education, School of Civil Engineering, Tianjin University, Tianjin University, Tianjin 300350, China {yanj,xiejian}@tju.edu.cn

Abstract. This paper delivers the recent research progress on steel-concrete composite structures at cold-region low temperatures, which aims on the engineering constructions in the Arctic/cold regions. This paper summarizes the recent research progress of the authors on the ultimate strength behavior of steel-concrete composite structural members at low temperatures. The paper firstly reported the research progress on the low-temperature mechanical properties of constructional materials in the CFSTs that included mild steel and high strength steel Q690. Secondly, the steel-concrete bonding behaviors of CFSTs at low temperature were also studied through full-scale tests. Thirdly, the axial low-temperature compression behavior of CFSTs using mild steel tubes and NWC were experimentally studied. Finally, the ultimate strength behavior of steel-concretes-steel (SCS) sandwich composite beams at cold-region low temperatures. The influences of different parameters on low-temperature ultimate strength behaviors of SCS sandwich composite beams were discussed and analyzed. All these studies built the foundations and clear the obstacles of application of steel and composite structures used in the Arctic and cold regions with low-temperature environments. Keywords: Composite structures · Low temperatures · Arctic structures · Steel structures · Cold region

1 Introduction Steel-concrete composite (SCC) structure combines the advantages of concrete compression and steel tension, which is a relative new type of structures and has been extensively applied in engineering structures. The increasing applications of SCC structures (SCCSs) in cold regions provide big opportunities for their engineering practices, e.g., the SCC bridge in Canada (Long et al. 1975; Dalen 1983), Lasa River bridge in Northern China, and the Arctic oil platforms (Yan et al. 2014), as shown in Fig. 1. In cold regions, the cooling environment with varying low temperatures in different seasons brings challenges to engineering constructions. According to the reports by Stjpanova (Stepanova 1958), the lowest temperature near the Arctic circle at Verkhoyansk Siberia was −72 °C. Meanwhile, the lowest temperature in the record of Northern China could drop to −53.4 °C (Yan et al. 2020a). These low temperatures definitely © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 482–490, 2023. https://doi.org/10.1007/978-981-19-7331-4_39

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affect mechanical properties of structural materials, steel-concrete interfacial bonding, and performances of SCCSs. Thus, it is of interest to perform necessary studies to investigate the behaviors of materials and structures of SCCSs exposed to the col-region low temperatures. This paper performed a series of studies on low-temperature ultimate strength behaviours of SCCBs from the material, component, and structural levels. These studies revealed the influences of cold-region low temperatures on these mechanical behaviors.

2 Mechanical Properties of Construcitonal Materials at Low Temperatures 2.1 Mechanical Properties of Mild Steel and High Strength Steel at Low Temperatures Low-temperature mechanical properties of mild were obtained from tension tests according to GB/T 13239 (2006) and GB/T 1228 (2002). Figure 2(a) shows geometry of steel coupons. Figure 2(a) shows the tension test setup. LNG was also used to realize the low temperature environment. During the testing, the PT100 thermocouples were installed on the coupons to measure their temperatures. Linear strain gauges (LSGs) and extensometer (gauging length = 50 mm) were adopted to instrument the strains in coupons. Four low temperature levels of 20, −30, −60, and −80 °C. Figure 2(b) and (c) plots the low-temperature stress-strain curves of mild steel Q355 and high strength steel Q690 at varying low temperatures. These figures show that the

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low temperatures significantly improved the yield and ultimate strength of Q355 and Q690, and their ductility was slightly increased. With the decrease of T from 20 to −30, −60, and −80 °C, the f y (or f u ) of Q355 is averagely improved by 13% (13%), 19% (25%), and 19% (30%), respectively; meanwhile, the average increments of f yT value for Q690 plate are 2%, 6%, and 12%, respectively; the f uT values of HSS Q690 plate are averagely increased by 4%, 8%, and 12%, respectively;

3 Low-Temperatrue Steel-Concrete Bonding Behaviors of CFSTS To study the influence of low temperatures on steel-concrete bonding in concrete-filled steel tubes (CFSTs), specimens C1~4 were tested at temperatures of 30 °C, −30 °C, − 60 °C and −80 °C, respectively (Yan et al. 2019a). Figure 3 shows the details of pushout test specimens used for low-temperature bonding. Each specimen, consisting of a steel tube and a concrete core, measures 133 mm (or 120 mm) in diameter (or width) and 400 mm in length, respectively except those prepared for the length to diameter (or width) ratio. All the specimens were reserved a gap of 10 mm at the top to locate the steel block for the loading purpose. Figure 4 plots the shear bonding stress (τ ) versus slip S at the loading end curves for the tested four CFST columns. It shows that the low temperature T exhibits significant improvements on the ultimate bond strengths for the circular CFSTs. It can be also found that the ultimate bond strengths of CFST increase almost linearly as the temperature decreases. As the T value drops down from 30 °C to −30 °C, −60 °C, and −80 °C, the

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τ u value of the CFST column was significantly increased by 190%, 248%, and 287%, respectively. Thus, the influences of low temperatures on the bonding strength of CFSTs requires careful consideration in the design of CFSTs. 3.6

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4 Low-Temperatrue Compression Behaviors of CFST There are four circular CFST (C-CFST) stub columns (C1~C4) and four square CFST (S-SCFST) stub columns (S1~S4) prepared in this study (Yan et al. 2019b). And they were tested at four low temperature levels, i.e., 20 ºC, −30 ºC, −60 ºC, and −80 ºC. All the C-CFST stub columns measure 400 mm in height (L = 400 mm), and the nominal

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external diameter of steel tube, D, is 133 mm with the L/D ratio of three. Similar to C-CFST columns, all the S-CFST columns measure 400 mm in height, and they were designed with square cross section with width of 120 mm. Normal weight concrete (NWC) C40 was used to fabricate the CFST columns. Figure 5 shows the typical setup of compression tests on CFST columns at low temperatures.

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Figure 6(a) and (b) show the effects of low temperature T on load-shortening behaviours of C-CFST and S-CFST columns, respectively. These two figures reflect that the low temperature generally improves the load-shortening behaviours of CFST columns. As T decreases from ambient 20 ºC to −30 ºC, −60 ºC, and −80 ºC, Pu of C-CFST (or S-CFST) column is averagely increased from 1396 kN (or 1107 kN) to 1512 kN (or 1233 kN), 1555 kN (or 1339 kN), and 1561 kN (or 1416 kN), respectively that correspond to increments of 8% (or 11%), 11% (or 21%), and 12% (or 28%), respectively. This is due to that the low temperatures improve the compression strength of both steel tubes and concrete core. Moreover, the frozen ice at steel tube-concrete interface improves the confinement that improves the compressive resistance of CFSTs.

5 Ultimate Strength Behaviours of Double Skin Composite Beams at Low Temperatures TO study the ultimate strength behaviors of double skin composite beams (DSCBs) at low temperatures, four DSCBs, namely B1-B4, were prepared for the two-bending tests that were tested at four low temperature levels of 20, −30, −50, and −70 °C, respectively (Yan et al. 2020b). Figure 7 plots the geometric details of these DSCBs. The top and bottom faceplates, concrete core, and headed shear studs are the three major types of components in the beam. Each DSCB measure 200 and 1600 mm in width and length, respectively. Its nominal depth of the concrete core equals to 100 mm with steel-faceplate

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thickness of 2.71 mm. Figure 8 depicts the experimental setup of two-point loading tests on DSCBs at different low temperatures. Before the testing, the low temperature level for DSCBs specimens were maintained at least 48 h in a cold storage. After this cooling process, the DSCB was then fast moved into the cooling chamber (see Fig. 8) with insulation materials surrounding the specimen. After that, LNG was sprayed into the cooling chamber to recover the lost temperature during the installation and balance the testing low temperature level during the testing process. After installation of the DSCB into the cooling chamber, quasi-static displacement loading in a 0.1 mm/min rate was applied to a spreading beam by a 100-ton actuator and then spread to the two hinge supports.

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Figure 9 displays the influences of T on P-δ curves of DSCB. It can be found that all the DSCBs exhibits ductile load-deflection behaviours at different T within 20 to−70 °C and the flexural failure mode was not changed within this temperature varying range. Figure 10(a) and (b) shows the effects of T on strength and stiffness of DSCBs. It shows that (1) positive linear relationship can be found between stiffness indexes (initial stiffness K 0 and elastic stiffness K 1 ) and decreasing temperature from 20 to −70 °C; (2) the strength of DSCB including cracking (Pcr ), elastic limit (Pe ), yielding (Py ) and ultimate strength (Pu ) are in linear-positive correlation with the decreasing T values. As T decreases from 20 to −30, −50, −70 °C, the K 0 (or K 1 ) was averagely increased by 5% (22%), 29% (19%), and 33% (24%), respectively; the cracking resistance is increased by 2%, 25%, and 55%; elastic limit load Pe is increased by 27%, 30%, and 31%; yielding load Py is improved by 14%, 21%, and 24%, and Pu is improved by 8%, 14%, and 16%, respectively. These improvements on both strength and stiffness indexes benefitting from the low temperature are due to that the improved strengths and modulus of both concrete and steel materials in DSCB, which can be explained by that at low temperatures the water in the porous micro-structure of concrete tends to be frozen to the ice, which increased both stiffness and strength of the concrete.

6 Conclusions The following conclusions can be draw from those experimental studies; 1. Decreasing T from 20 to −80 °C significantly improved the yield and ultimate strength of Q355 and Q690, and their ductility was slightly increased. 2. Decreasing T from 20 to −80 °C significantly improves ultimate bond strengths of the CFSTs. 3. The low temperature from 20 to −80 °C generally improves the load-shortening behaviors of CFST columns.

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4. The decreasing low temperature from 20 to −80 °C improves the stiffness and strengths of DSCBs, and the decreasing low temperature shows positive linear relationship with those stiffness and strength indexes of DSCBs.

Acknowledgements. The authors would like to acknowledge the Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration (Grant No. 2019EEEVL0504). The authors gratefully express their gratitude for the financial supports.

References Dalen, K.V.: The strength of stud shear connectors at low temperatures. Can. J. Civ. Eng. 10(3), 429–436 (1983) Long, A.E., Dalen, K.V., Csagoly, P.: The fatigue behavior of negative moment regions of continuous composite beams at low temperatures. Can. J. Civ. Eng. 2(1), 98–115 (1975) Yan, J.B., Liew, J.R., Zhang, M.H., Wang, J.Y.: Mechanical properties of normal strength mild steel and high strength steel S690 in low temperature relevant to Arctic environment. Mater. Des. 61, 150–159 (2014)

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Yan, J.B., Xie, J., Ding, K.: Stress relaxation behavior of prestressing strands under low temperatures. PCI J. 65(1), 41–56 (2020) Yan, J.B., Dong, X., Wang, T.: Flexural performance of double skin composite beams at the Arctic low temperatures. Steel Compos. Struct. 37(4), 431–446 (2020) Yan, J.B., Xie, W.J., Zhang, L., Lin, X.: Bond behaviour of concrete-filled steel tubes at the Arctic low temperatures. Constr. Build. Mater. 210, 118–131 (2019) Yan, J.B., Dong, X., Zhu, J.: Compressive behaviours of CFST stub columns at low temperatures relevant to the Arctic environment. Constr. Build. Mater. 223, 503–519 (2019)

Development of Novel Sigma-shaped Self-locking Inter-modular Joints for Robust Modular Steel Buildings Kashan Khan1(B) , Zhihua Chen1,2,3 , Xingwang Liu1 , Jia-Bao Yan1,3 , and Jiadi Liu1 1 Department of Civil Engineering, Tianjin University, Tianjin, China

[email protected] 2 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin, China 3 Key Laboratory of Coast Civil Structure and Safety, Ministry of Education, Tianjin University,

Tianjin, China

Abstract. Modular Steel Buildings (MSBs) are a new structure consisting of fully assembled volumetric units. The inter-modular connections are essential components contributing to MSB’s onsite assembly and structural safety. It is necessary to have a precise and valuable intermodular joining system that allows for efficient load transfer, safe handling, and the most efficient use of the modular components’ strength. The majority of inter-module connections are currently manual vertical column-to-column welded, bolted, or prestressed, which has a lot of shortcomings, including poor quality, inefficient construction, lack of space, full connectivity, and incompatibilities with interior design. Moreover, due to a discontinuous horizontal diaphragm and vertical walls, the lack of horizontal and vertical beam-to-beam connections between modular units reduces in-plane and out-of-plane stiffness and uniform lateral force transmission. To overcome the concerns mentioned above, this study first presents a unique self-locking automatic vertical column-to-column inter-modular connection that uses connection boxes with spring-loaded tenons and mortises with tongues and grooves to achieve vertical connectivity. Then, to guarantee horizontal diaphragm continuity, a horizontal beam-to-beam interlocking connection with a continuous group of interlocking clips with sigma-shaped tongues and grooves is proposed, welded on modular floor beams. Then, a vertical beam-to-beam interlocking connection with a group of interlocking clips is developed, welded on beams offsite to achieve vertical diaphragm continuity. The proposed vertical and horizontal connections satisfy simple splicing, non-welding, easy installation, complete and robust connectivity, and reliable connection characteristics. Furthermore, finite element analysis revealed that developed connections enhance in-plane rigidity and improve MSB vertical and horizontal connectivity, maximizing modular building assembly benefits. Keywords: Discontinuous modular steel buildings · Column-to-column automatic connection · Beam-to-beam vertical diaphragm connection · Beam-to-beam horizontal diaphragm connection · Finite element analysis

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 491–505, 2023. https://doi.org/10.1007/978-981-19-7331-4_40

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1 Introduction Modular steel buildings (MSBs) are high-performance prefabricated buildings that transport modular units fabricated in the factory to the site and assemble the vertical and horizontal modules. They have unique development potential and application prospects due to their outstanding advantages such as fast construction efficiency, green construction process, saving human resources and material resources, but their development and application in pure MSBs are mainly concentrated in low-rise buildings, such as Wuhan Huoshenshan Hospital, Leishenshan Hospital, Xiong’an Citizen Service Center, Tianjin Jinghai Ziya Shanglin Garden Project (Fig. 1), etc. However, for achieving height, MSB relies upon other stabilizing systems, such as concrete cores, infilled frames, continuous bracings, and damping systems. These have been used in many high-rise buildings, such as the Australian Styles Hotel, the US B2 tower, the British Croydon Building, and so on (Fig. 2).

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Due to the unique construction method of MSB, components such as horizontal and vertical force-transmitting components, i.e., columns, floors, ceilings, and walls

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diaphragms, are spliced into an overall structure through the number of vertical and horizontal connections between the modular units. Thus, diaphragms, columns, bracings, and walls, have prominent discontinuous characteristics, influencing the stability of MSBs, which hampers the development of pure MSBs to achieve more considerable heights, relying on lateral stabilizing systems (Fig. 2). Moreover, the manual intermodular column-to-column connections have a lot of shortcomings, including poor quality, inefficient construction, lack of space, full connectivity, and incompatibilities with interior design. Various inter-modular connections, more columns and beams, discontinuous features of columns, walls, bracings, and diaphragms make MSB vastly different from traditional steel structures. This makes the force transmission law different, complex, and unable to achieve robust structures (Fig. 3). Thus, it is crucial to establish accurate inter-modular connection systems between columns and beams in the vertical and horizontal directions. This could ensure structural members’ safety, robustness, resilience, and continuity to develop pure high-rise MSB without relying on lateral stabilizing systems.

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2 Literature Review Three main types, welded, bolted, and prestressed connections, are frequently used for manually operating joints. Meanwhile, all of these connections have been shown to have sufficient earthquake resistance, but they do have difficulties. The onsite work of welded connections is extensive, and full welding cannot be achieved (Annan et al. 2009). Bolted connectors have strict operational space requirements and lower production efficiency (Lacey et al. 2019). Prestressed connections are complex to build. The corners and external interface may be bolted or welded from the outside by laborers. However, some connections cannot tighten the final module because of the module units’ wall panels and slabs, mainly due to a lack of construction clearance for the jointing. Fully column welded (Annan et al. 2009), rotary connection (Chen et al. 2019b, 2020; Liu et al. 2020),

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beam-to-beam vertical bolted connections (Chen et al. 2017a, 2017c), beam and column fully bolted joints (Khan and Yan 2020), fully bolted joints (Zhang et al. 2021), columnto-column prestressed joint (Chen et al. 2017b; Yu et al. 2019) are some examples of manual connections. As a result, automatic joints that do not require any functional space have recently been developed to address the issues raised above. The researchers designed a sliding bloc connection that uses self-locking technology (Chen et al. 2021). Another researcher (Dai et al. 2019) also devised a self-locking bolted device, using springs to install easily. On the other hand, these self-locking connectors overlook construction or deformation tolerances, requiring a high precision level. Thus, further studies are highly motivated on robust automatic joints to achieve complete high-rise modularization. Modular steel buildings’ in-plane and out-of-plane stiffness and nonuniform lateral transmission of forces are always critical. It is due to the discontinuity between the horizontal ceiling, floor diaphragms, and vertical wall diaphragms. Due to the impact of lateral forces on high-rise buildings and the inability of joints to withstand them, lateral stability systems such as braces, shear walls, diaphragm walls, cores, base-isolation systems, and viscoelastic damping connections have been developed. The discontinuous features of the floor and ceiling diaphragms and the wall diaphragms cannot be resolved entirely, affecting MSB’s lateral force-resisting performance. Thus, a beam-to-beam horizontal joint utilizing tongues and grooves between floor beams was recently discovered; however, when subjected to higher subsequent shear forces, the grooves and tongues are easily misplaced, proving the joint ineffective (Chen et al. 2019a). Another method joins modules horizontally by field bolting angles welded to beam flanges, which necessitates onsite labor and a work area for bolting, making MSB unsustainable (Memari and Sagiroglu 2015). Sharafi et al. devised a system for horizontal and vertical beam connections that can withstand shear forces but not tensile forces (Shara et al. 2018).

3 Development and Working Mechanism of Inter-modular Joints 3.1 Automatic Vertical Column-to-Column Inter-modular Joint Figure 4 depicts the exterior corner, middle, and interior middle connections between two, four, and eight modular units. Manual connections are typically incapable of connecting all eight modules on the interior middle connection location while maintaining MSB’s sustainability and physical aesthetics. Figure 5 shows the developed connection system that supports eight modular units by interlocking sigma-shaped central tenon male parts with teeth while spring and bolt-supported female parts for vertical and horizontal MSB stacking. The springs and bolts systems and the upper and lower connection boxes are primarily responsible for assembling both male and female parts of the connection system. Fillet welding is used to attach the connection boxes to the columns and beams. Spring links to connection boxes support the female parts. Fixed bolts on top prevent spring stretching and female part separation. On the other hand, rotating bolts allow female parts to rotate in collision with male parts during the assembly of modular units. When the modular unit is mounted, sigma-shaped male part tenons are embedded into connection boxes and collide with female parts, causing the springs to stretch and allow male parts to enter. When the male part’s teeth and head are fully inserted in the

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female part’s head and teeth, springs are automatically pulled back and fixed due to stiffness, preventing the male and female parts from being separated. During axial, tension, compression, lateral-torsional loadings throughout a severe earthquake, this keeps the upper and lower eight modular units together without affecting the MSB’s sustainability. The disturbance is produced when the bending moment is applied to the top of the column. Bearing stresses develop as a gap forms between the upper and lower parts connection system. The locking behavior of male and female parts’ teeth and heads, on the other hand, can withstand any increase in uplift force.

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3.2 Beam-to-Beam Sigma-shaped Horizontal Inter-modular Joint To meet the rapid installation of modular buildings, current connection systems primarily use connections at corners between modular unit columns. However, because the floor and ceiling diaphragms in both the longer and shorter directions are discontinuous, unlike traditional buildings, a discrete floor and ceiling diaphragm results in no involvement of connections, becoming non-rigid. The modular building’s overall in-plane and out-ofplane rigidity are not as impressive as traditional steel structures due to the discontinuity of the floor and ceiling diaphragm. This has a massive impact on column-to-column corner connections; thus, pure MSB height is limited to low-rise buildings. With the increasing use of modular buildings, it is necessary to improve the horizontal connection between modular units and the overall in-plane and out-of-plane rigidity of modular buildings in shorter and longer directions while ensuring rapid assembly. Furthermore,

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the uniform, lateral transmission of force is a significant issue for the immediate solution of modular buildings. In order to address the aforementioned technical issues while maintaining sustainability and structural integrity, the study proposes a horizontal interlocking connection between floor and ceiling beams in both directions for modular structures. As shown in Fig. 6, the connection is composed of a series of interlocking sigma-shaped clips with tongues and grooves welded to the modular floor and ceiling beams. The proposed horizontal connection between modular units has simple automatic locking, requires no bolting or welding. It is a reliable connection that can withstand bending and shear forces in both directions caused by massive earthquakes, thus improving the rigidity of modular horizontal diaphragms. The male and female sigma parts are locked into each other and become a single unit when the modular unit is mounted, making the connection between beams rigid and capable of resisting tremendous shear forces. It increases the building’s in-plane rigidity, maximizing the benefits of modular building assembly for high-rise MSBs without the need for traditional unsustainable stabilizing systems. 3.3 Automatic Beam-to-Beam Vertical Inter-modular Joint Because the floor and ceilings in both the longer and shorter directions are discontinuous in the middle, there is always a gap between upper and lower modular units; thus, unlike traditional buildings, a discrete vertical wall through-diaphragm results in a non-rigid wall system. The modular building’s in-plane and out-of-plane stiffness are critical due to the spacing between the floor and ceiling diaphragms. Because the vertical diaphragms, such as corrugated shear walls, diagonal braces, and double skin steel plate shear walls, are discontinuous as a result of the splicing of modular units, external lateral stabilizing structures are required when the modular structure system is applied to multi-high-rise

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buildings. This mitigates the benefits of rapid MSB construction. As a result, developing a connection system capable of converting discontinuous vertical diaphragms into nearly continuous or rigid diaphragm systems is critical to research. As a result, a single connection system was developed between upper and lower modular units in both longer and shorter direction beams to achieve vertical diaphragm continuity, laying a theoretical foundation for using the modular support structure system in high-rise buildings. The connection is a group of interlocking solid regular-shaped clips with male and female parts welded on the modular floor and ceiling beams, as shown in Fig. 7. The proposed beam-to-beam vertical connection between modular units provides simple automatic locking, no bolting or welding on site, and a reliable connection to resist bending

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and shear forces in both directions caused by massive earthquakes, thus improving the rigidity of modular vertical diaphragms. When the female part of the upper modular unit is mounted on the male part of the lower modular unit, both male and female parts automatically interlock at a specific position, making the connection between beams rigid and demonstrating the ability to withstand tremendous shear forces.

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4 Numerical Studies on Column-to-Column Inter-modular Joint ABAQUS/CAE was used to develop FE models, while ABAQUS/Standard type solver was used to perform nonlinear analysis on models (ABAQUS 2013). All FE modeling

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was done following the methodology from the author’s previous studies, applying all four types of nonlinearities, i.e., geometric, material, boundary, and interaction properties (Khan and Yan 2017, 2020; Khan et al. 2021a, 2021b). Mild steel Q345B was used for columns. On the other hand, joint components were of cast steel, including ZG35, G20Mn5QT, and ZG310-570. The material properties were taken from joints studies (Chen et al. 2017a, 2017c). All structural steel members were modeled with bi-linear material behavior with kinematic hardening, using Poisson’s ratio: υ = 0.3 for elasticity, while plasticity was introduced using the standard yield strength and ultimate tensile strength. In all structural components, hexagonally structured mesh controls were applied. Surface to surface (standard) with finite sliding and “hard contact” in the normal direction and the tangential direction as “penalty friction formulation” was used. All the components of joints were modeled to derive accurate conclusions; thus, the mesh model for the study is shown in Fig. 8. Additionally, the rotational stiffness of the rotary joint was examined (Chen et al. 2019b). The current study validated the FE analysis and conducted additional nonlinear finite element analyses on a joint developed in this study using the experimental findings from the studies mentioned above. 4.1 Bending Performance of Column-to-Column Inter-modular Joint The bending behavior of the joint was investigated by applying a lateral displacement load to the top edge of the free end column, as described in the reference. On the other hand, the bottom end column was kept fixed (Chen et al. 2019b). The moment-rotation relationship and the von Mises stresses related to the formation of plastic hinges in joint members were used to assess the connection’s static behavior. Since the lateral loading was displacement-controlled, the reaction force was tracked at the tip of the upper column to plot the moment by multiplying with the lever arm in the monotonic curve. Figure 9 shows that the joint showed a high moment capacity of 176 kN m, ductile force transferring behavior, and higher initial stiffness than the connection validated in the study. When the joint was in the elastic stage, the lateral load created no gap between the upper and lower connection boxes. A slight decrease in tangent stiffness occurred following this point as the force increased, indicating the onset of elastoplastic behavior. Following yielding, plastic behavior propagated due to gaping, followed by increased tangent stiffness, indicating the formation of a plastic hinge in the bottom plate of the upper connection box. At this point, neither the male nor female parts of the connection were stressed, indicating the connection’s rigid bending performance. However, the load resistance of the joint was reduced in a ductile manner due to the plate punching, leading to a massive gaping of 48 mm caused by the lateral load. The stress contour demonstrates that the joint has a greater tendency for force distribution than the structural components to which it is connected. In a limited or severe applied loading scenario, all connection parts, and columns at the bottom and top welded ends demonstrated minimal concentration. Compared to the fixed boundary conditions at the bottom, the rotation difference between the upper and lower regions imposed the most significant stress on plates with a much thinner thickness than the plates in other regions; this suggested thickening the connection box plates. The failure modes were

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perfectly consistent with the joint case study. Additionally, the connection’s plastic rotation angle was greater than 0.03, indicating that it is well suited for energy dissipation in high seismic zones. 4.2 Tensile Performance of Column-to-Column Inter-modular Joint According to the reference, the tensile behavior of the joint was investigated by applying vertical upward displacement load to the top edge of the female part of the joint while leaving the bottom female part fixed (Chen et al. 2020). The primary goal was to test the tensile bearing capacity of joint components because the primary function of the joint is to resist uplift forces. When the models were located in an elastic-plastic state, the load-displacement curve revealed necking phenomena in the middle male part. Figure 10 shows that increasing the load increases the gap between the head and teeth of male and female parts due to necking phenomena. Even though the teeth region showed extreme stress accumulation, the teeth region was responsible for the rigid bonding between male and female parts. While after necking, the majority of the load was resisted by the heads interlocking of both components, indicating that the joint’s plastic region stiffness

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and capacity were still increasing. In tensile load-bearing, necking of the male part teeth region was crucial. A suitable thickness for this region should be used to achieve better results. Similarly, the equivalent tensile behavior was comparable to Chen et al.’s (2020) connection strength and stiffness, showing the current joint possessed better interlocking performance than joints in case studies. Furthermore, the case study joint was manual, requiring onsite tight bolting of the huge bolt. Furthermore, due to a lack of working space, the joint was unable to tighten the last modular unit; thus, the automatic

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4.3 Numerical Model Validation Finite element analysis results were compared to the lateral P-Δ curves of two test specimens of plugin joint and moment-rotation curves of a rotary joint, as shown in Fig. 11. The results discovered that FE models accurately simulated test specimens’ ultimate capacity, stiffness, and ductility. Experiment failure modes were compared to von Mises stress distributions in FE models, as illustrated in Fig. 12. The primary failure events in plugin joint test specimens were gap development and enlargement, slicing of column or beam welds, local column buckling, and beam tearing. Similarly, the test results were accompanied by accurate simulations of gap generation of 25 mm between corner fittings and their outward buckling, such as the gap generation of 27 mm demonstrated by FE models for rotary joints. As a result of the FE simulation’s accuracy and efficiency, additional joint studies are performed.

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5 Conclusions The study’s primary objective was to resolve issues concerning the assembly of all modular units in MSBs and concerns about discontinuous component features. These issues were addressed by proposing new inter-modular joints between columns and between floor and ceiling beams, improving the sustainability, in-plane and out-of-plane stiffness, and uniform lateral force transmission of MSBs in high-rise buildings. The following significant conclusions are drawn: 1. The development of sigma-shaped automatic column-to-column, beam-to-beam horizontal, and beam-to-beam vertical connections has demonstrated that they are safe, capable of achieving fully rigid and robust continuity between components, and efficient at achieving sustainable MSB. This justifies their use in the conceptual design of future inter-modular connections.

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2. The automated column-to-column connection demonstrated bolt- and weld-free interlocking behavior, providing comparable seismic performance to conventional designs by achieving a plastic rotation angle greater than 0.03, demonstrating the connection’s suitability for use in high seismic zones. 3. Under tensile performance, the connection’s components showed no signs of premature failure. It achieved a perfect elastic-plastic stage with higher bearing capacity than previously reported connections, demonstrating a solid interlocking structural response that supports its applications. 4. When FE results were compared to test results, it was determined that the developed FE models accurately captured initial stiffness, ultimate bearing capacity, and failure behavior, demonstrating the accuracy of FE modeling.

Acknowledgements. The authors would like to express their gratitude for the research grant from the National Natural Science Foundation China (Grant No. 51978457). Additionally, the first author wishes to express his heartfelt appreciation to the China Scholarship Council for its kind financial assistance.

References ABAQUS: User manual Version 6.13. DS SIMULIA Corp, Providence, RI, USA. DS SIMULIA, pp. 1–847 (2013) Annan, C.D., Youssef, M.A., El Naggar, M.H.: Seismic overstrength in braced drames of modular steel buildings. J. Earthq. Eng. 13(1), 1–21 (2009). https://doi.org/10.1080/136324608022 12576 Chen, Z., Liu, J., et al.: Experimental study of an innovative modular steel building connection. J. Constr. Steel Res. 139, 69–82 (2017). https://doi.org/10.1016/j.jcsr.2017.09.008 Chen, Z., Li, H., et al.: Research on pretensioned modular frame test and simulations. Eng. Struct. 151, 774–787 (2017). https://doi.org/10.1016/j.engstruct.2017.08.019 Chen, Z., Zhong, X., et al.: Horizontal interlocking connection structure for modular building (in Chinese). China (2019a) Chen, Z., Liu, Y., et al.: Rotational stiffness of inter-module connection in mid-rise modular steel buildings. Eng. Struct. 196, 109273 (2019). https://doi.org/10.1016/j.engstruct.2019.06.009 Chen, Z., et al.: Tensile and shear performance of rotary inter-module connection for modular steel buildings. J. Constr. Steel Res. 175, 106367 (2020). https://doi.org/10.1016/j.jcsr.2020.106367 Chen, Z., et al.: Seismic behavior and moment transfer capacity of an innovative self-locking inter-module connection for modular steel building. Eng. Struct. 245, 112978 (2021). https:// doi.org/10.1016/j.engstruct.2021.112978 Chen, Z., Liu, J., Yu, Y.: Experimental study on interior connections in modular steel buildings. Eng. Struct. 147, 625–638 (2017). https://doi.org/10.1016/j.engstruct.2017.06.002 Dai, X.M., et al.: Experimental study on seismic behavior of a novel plugin self-lock joint for modular steel construction. Eng. Struct. 181, 143–164 (2018). https://doi.org/10.1016/j.engstr uct.2018.11.075 Khan, K., Chen, Z., Liu, J., Khan, A.: Numerical and parametric analysis on compressive behaviours of continuous-supported wall systems in MSB. Structures 33, 4053–4079 (2021). https://doi.org/10.1016/j.istruc.2021.07.001 Khan, K., Chen, Z., Liu, J., Yan, J.: Simplified modelling of novel non-welded joints for modular steel buildings. Adv. Steel Constr. (2021)

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Khan, K., Yan, J.-B.: Development and study on the seismic behavior of novel joint in prefabricated modular steel building. Tianjin University (2017). https://doi.org/10.1017/CBO978 1107415324.004 Khan, K., Yan, J.-B.: Finite element analysis on seismic behaviour of novel joint in prefabricated modular steel building. Int. J. Steel Struct. 20(3), 752–765 (2020). https://doi.org/10.1007/s13 296-020-00320-w Lacey, A.W., et al.: Review of bolted inter-module connections in modular steel buildings. J. Build. Eng. 23, 207–219 (2019). https://doi.org/10.1016/j.jobe.2019.01.035 Liu, Y., et al.: Lateral stiffness evaluation on corner-supported thin walled modular steel structures. Thin-Walled Struct. 157, 106967 (2020). https://doi.org/10.1016/j.tws.2020.106967 Memari, A.M., Sagiroglu, M.: Evaluation of connection systems in modular constructions. In: World Congress and Exhibition on Construction and Steel Structure (Steel Structure-2015), pp. 16–18 (2015) Shara, P., et al.: Automation in construction interlocking system for enhancing the integrity of multi-storey modular buildings. 85, 263–272 (2018). https://doi.org/10.1016/j.autcon.2017. 10.023 Yu, Y., Chen, Z., Chen, A.: Experimental study of a pretensioned connection for modular buildings. Steel Compos. Struct. 31(3), 217–232 (2019). https://doi.org/10.12989/scs.2019.31.3.217 Zhang, G., Xu, L., Li, Z.: Development and seismic retrofit of an innovative modular steel structure connection using symmetrical self-centering haunch braces. Eng. Struct. 229, 111671 (2021). https://doi.org/10.1016/j.engstruct.2020.111671

Shear Performance of Interface Between Normal Concrete and Ultra-high Performance Concrete in Cryogenic Circumstance Yujie Chen1 , Jian Xie1(B) , Ercong Kang1 , and Chenglong Tong2 1 School of Civil Engineering/Key Laboratory of Coast Civil Structure Safety of Ministry of

Education, Tianjin University, Tianjin 300350, China {cyjztd,xiejian}@tju.edu.cn, [email protected] 2 3Rd Construction Co., LTD of China Construction 5Th Engineering Bureau, Wuhan, China [email protected]

Abstract. Ultra-high performance concrete(UHPC) is known for its high strength, high toughness and durability, which makes UHPC be seen as a promising repairing material for normal concrete(NC). In order to make sure the application of UHPC in reinforcement, especially in cryogenic circumstance, it is critical to characterize the bonding performance between UHPC and NC. Through 11 sets of normal concrete and ultra-high performance concrete specimens (UHPC-NC specimens) were tested by double shear tests, the shear properties of UHPC-NC specimens in normal and cryogenic environment (−60 °C) were evaluated and discussed. Different interface treatments were used, including untreated, water jetting and using retarder. The effect of interface agent was also studied. The results show that the shear strength of the interface was improved by increasing surface roughness degree. The failure mode presented brittle failure, no matter what kind of interface treatments. Cryogenic circumstance can improve the bonding strength of UHPC-NC, and the group without interfacial agent had a more significant improvement. The performance of interfacial agent in low temperature limits the improvement of interfacial bonding strength to a certain extent. Keywords: UHPC · NC · Interface · Shear performance · Cryogenic circumstance

1 Introduction Due to the existing harsh natural environments, concrete structures will be damaged and destroyed to some extent. In China, there are a lot of cryogenic circumstance, and the lowest temperature can reach −53.3 °C [1]. In addition, the rich resources in the polar region have attracted more and more attention to polar construction, but the climate conditions in the polar region have made the local infrastructure construction quite different from that in inland regions. Through the repair of damaged concrete structures, the safety and service life of them can be effectively improved. Ultra-high performance concrete (UHPC) is famous © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 506–514, 2023. https://doi.org/10.1007/978-981-19-7331-4_41

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for its high strength, high toughness [2, 3] and durability [4–6], which makes UHPC can be used in repairing engineering. Based on this, many scholars have studied the bonding performance of UHPCNC. By slant shear test and splitting tensile test, Harris et al. [7] obtained that interface roughness has influence on the bonding performance between UHPC and NC. The results showed that there was a relatively excellent bonding performance between UHPC and NC, and appropriate interface treatment could make the bonding strength of UHPC-NC be superior to the strength of NC substrate. Jang et al. [8] adopted five different interface treatment methods and found that high-pressure water jetting is the most effective method to improve the bonding strength. Zhang et al. [9–11] carried out systematic research on the bonding performance of UHPC-NC specimens through a variety of test methods, such as splitting tensile, direct tensile, slant shear and push-out tests. These researches proved that no matter what test method was adopted, the bonding strength between UHPC and NC was better than that of NC-NC interface, and was approach to or slightly stronger than the strength of NC whole casting specimen. Tayeh et al. [12] conducted research on the bonding strength of UHPC-NC when the age of UHPC was 3, 7 and 28 days. The results demonstrated that with the increasing age of UHPC, the bonding strength of the specimen increases. The research on the bonding performance of UHPC-NC is concentrated mainly on the conventional environment. And the bonding performance of UHPC-NC in cryogenic circumstance can be one of the key factors influencing the reliability of UHPC in concrete repair engineering. Thus, it is necessary to conduct experiment on the bonding behaviors of UHPC-NC specimens at low temperature. This paper focused on the bonding performance of UHPC-NC specimens in cryogenic circumstance. 11 sets of UHPC-NC double shear specimens were prepared. The influence of low temperature, interface treatments and interface agent were figured out.

2 Experimental Program 2.1 Materials 2.1.1 Normal Concrete (NC) The NC in this test was designed as Grade-40, using Portland cement (42.5), crushed stone (5–10 mm), natural river sand, and water. Table 1 listed the mix proportions of NC. 2.1.2 Ultra-high Performance Concrete (UHPC) UHPC powder is produced by Demin Construction Technology (Shanghai) Co., LTD. The steel fiber produced by Shanghai Zhijian Engineering Technology Co., LTD. The length of steel fiber is 16 mm and the diameter of it is 0.22 mm. The volume content of steel fiber in UHPC is 2.4%. Table 1 shows the mix proportions of UHPC. 2.2 Test Specimens The composite specimens were designed according to CECS 13:2009 [13]. These specimens have a dimension of 100 mm × 100 mm × 300 mm, consist of the NC part at

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Y. Chen et al. Table 1. Mix proportions of NC and UHPC (kg/m3 )

Materials

Constituents

Amount

C40

Sand

574

Gravel

1021

Cement

575

UHPC

Water

230

Permix

2100

Steel fiber

186.9

Water

207.9

the two ends and the UHPC part in the middle. The sizes of each part are 100 mm × 100 mm × 100 mm. The form of specimens is shown in Fig. 1.

Fig. 1. Test specimens

2.3 Preparation of Concrete Substrates The NC parts were first cast and then demolded after 1d. After demolding, the NC parts were roughened as needed. The surface treatment methods were untreated, water jetting and using retarder. Figure 2 exhibits the different concrete surfaces tested in this research. Among them, specimens treated with retarder were named as R group, which means the specimens with rough surface. Different from the other surface treatments, after the NC specimen was poured for 12 h, the R group specimens were demolded. At this time, the cement slurry of group R was soft and not completely hardened. Water gun was used to continuously wash the surface of the specimen until the slurry that was not completely hydrated was washed away and coarse aggregate was exposed. Then, the interface treatment of group R was completed.

Shear Performance of Interface Between Normal

509

Interface agent is one of the commonly used bonding methods in actual engineering. Thus, the interface agent was introduced into the test. After interface processing, the NC parts were cured in nature for 28d.

(a) M:smooth

(b) W:water jetted

(c) R:rough

Fig. 2. Different NC surfaces

After roughing the NC part surface, the sand filling depth was used to define the interfacial roughness. The data of the sand filling depth was listed in Table 2. Table 2. Interfacial roughness (mm) Samples

Interfacial roughness

Samples

Interfacial roughness

CG-M

0.10

0.09

CG-W

0.89

0.85

0.09

CGJ-M

0.08

0.09

–

0.75

CGJ-W

0.75

0.74

0.58

CG-R

1.20

1.48

1.40

CGJ-R

1.07

1.30

1.20

L-W L-R

0.79

0.92

0.95

LJ-W

0.67

0.59

0.74

1.70

1.25

1.43

LJ-R

1.28

1.28

1.20

LJ-M

0.08

0.06

0.06

2.4 Placing UHPC Limited by the construction method of specimens, the surfaces were in dry condition in the test. The UHPC part was mixed by a high viscosity mixer. Before pouring the UHPC, the interface agent was applied on the side wall of the NC section for specimens which designed to use interface agent. The interface agent is epoxy resin product produced by Carbon Technology Group Co., LTD. During the pouring process, the UHPC should be poured within 30 min after the coating of interface agent is completed. After pouring, plastic sheets were used to cover the UHPC-NC bonding specimens, and the mold were removed 3d later. The UHPC-NC specimens were cured for 28d in nature.

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2.5 Test Procedure According to CECS 13:2009, the double shear test was designed. The double shear test adopted displacement loading method, as shown in Fig. 3. The loading speed was 0.2 mm /min. This test used Eq. (1). fD =

F 2A

(1)

where fD = bonding strength of push-out test. F = maximum applied load (kN), and A = the area of the bonding plane (mm2 ). There were 3 specimens in each group. The average value was taken as the finial bonding strength.

Fig. 3. Sketch of tests

The specimens were precooled with the ultra-low temperature refrigerator. Before double shear test, the specimens were placed in the ultra-low temperature refrigerator one day in advance. The target temperature of the specimens was −60°C and should be held for 4 h. Take out the specimen and place it in the thermal insulation loading device, as shown in Fig. 3, when the test started. During the double shear test at cryogenic circumstance, the liquid nitrogen was used to maintain the target temperature. The temperature was measured by embedded thermal couples.

3 Results and Discussion 3.1 Double Shear Test 3.1.1 Failure Modes IN Fig. 4, the failure modes caused by the double shear tests are shown. There are five main failure modes of UHPC-NC specimens: (i) Partial interface failure and partial NC failure(B/C): the specimen was damaged at the interface, combined with partial NC failure, part of NC slurry and aggregate were attached to the UHPC; (ii) NC failure(C): NC near the interface was damaged, and only a small amount of UHPC was attached to the concrete part; (iii) Interface agent failure(J): the damage of interface agent mainly occurred at the interface between interface agent and UHPC and delamination failure of interface agent itself; (iv) Partial interface agent failure and partial NC failure(J/C): the specimen was damaged at the interface agent, combined with partial NC failure; (v) Mixed destruction(H): multiple failure modes can be observed on the specimen, including NC failure, interface agent failure and steel fiber pulled out.

Shear Performance of Interface Between Normal

NC

UHPC

NC

(a) B/C

NC

511

UHPC (b) C

UHPC

NC

(c) J

UHPC (d) J/C

NC

UHPC (e)H

Fig. 4. Failure types of double shear test

3.1.2 Test Results The bonding strengths (fD ), the coefficient of variation (Cov) and failure modes of each group in double shear tests are gathered in Table 3. Compressive strength of concrete and UHPC specimens at the same age of UHPC-NC specimens were 52.81 MPa and 129.98 MPa respectively. In Table 3, the specimens was named after the following notations: environment (CG = conventional environment, L = cryogenic circumstance), with or without the interface agent (J = with interface agent), concrete surfaces (M = smooth, W = water-jetted, R = rough). The Covs of the bonding strength of the UHPC-NC specimens in conventional environment range from 5.81% to 51.41%, which is much higher than the other tests. The Covs of UHPC-NC specimens in cryogenic circumstance vary from 0.86% to 10.42%, with an average of 5.64%. Therefore, the specimens in cryogenic circumstance share smaller discreteness.

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Y. Chen et al. Table 3. Results of double shear test

Item

Temperature/°C

fD /MPa

Cov/%

Proportion of Failure mode/% B/C

CG-M

J

J/C

H

1.20

31.12

100

0

0

0

0

CG-W

1.71

14.63

100

0

0

0

0

CG-R

3.31

9.98

0

100

0

0

0

CGJ-M

1.24

51.41

0

0

100

0

0

CGJ-W

2.04

14.99

0

0

100

0

0

CGJ-R

3.65

5.81

0

0

0

0

100

0

0

0

0

0

0

L-W

20

C

−60

3.87

10.00

L-R

5.09

10.42

100

33.33

66.67 0

LJ-M

0.80

0.86

0

0

LJ-W

2.36

7.68

0

0

100

0

0

LJ-R

3.88

6.14

0

0

100

0

0

66.67

33.33

0

3.1.3 Effects of Cryogenic Circumstance Figure 5 exhibits the effect of cryogenic circumstance on the bonding strength of each specimen. It can be seen that, except for the group LJ-M, the interface bonding strength of specimens in low temperature environment is generally improved. The bonding strength of group LJ-M at low temperature was 35.48% lower than that of CGJ-M group. For group L-W and group LJ-W, the bonding strength was 126.32% and 15.69% higher than that in the conventional environment, namely, the group CG-W and the group CGJ-W, respectively. Group L-R and group LJ-R were 53.78% and 6.30% higher than group CG-R and group CGJ-R, respectively. Thus, cryogenic circumstance shows a positive effect on the bonding properties of UHPC-NC specimens without the use of interface agent. According to Xie et al. [14], the freezing of pore water in NC will lead to the improvement of the compressive strength of NC. In addition, water icing in the interfacial pores can promote the densification of the interface structure and enhance the bonding strength. At cryogenic circumstance, the bonding strength of group L-W and group L-R is 1.64 times and 1.31 times than that of group LJ-W and group LJ-R, respectively, and the bonding strength of group LJ-M decreases more in low temperature than that of conventional environment. Therefore, the performance of interface agent in cryogenic circumstance limits the improvement of bonding strength to a large extent.

4 Conclusions In this paper, the bonding performance between UHPC and NC at low temperature were investigated by double shear tests. According to the results of each mechanical and environmental loading states, the following conclusions can be derived:

Shear Performance of Interface Between Normal 4.50

CG-M CGJ-M LJ-M

1.20

L-W LJ-W

Bonding strength/MPa

Bonding strength/MPa

1.80

513

CGJ-W

3.00

CG-W

1.50

0.60

0.00

0.00 0

0.05 0.1 Interfacial roughness/mm

0.4

0.15

0.6 0.8 Interfacial roughness/mm

(a) M

1

(b) W

Bonding strength/MPa

6.00

4.00

L-R

2.00

LJ-R CG-R CGJ-R

0.00 0.8

1.2 1.6 Interfacial roughness/mm

2

(c) R Fig. 5. Influence of cryogenic circumstance on bonding strength

(1) In double shear test, there are five main failure modes of UHPC-NC specimens. (2) The roughness of the interface has a certain impact on the performance of the UHPC-NC specimens. (3) In cryogenic circumstance, the UHPC-NC specimens without interface agent presented more improvement on the bonding strength than the specimens with interface agent. For the specimens using interface agent, the performance of interface agent in cryogenic circumstance has more influence on the bonding performance of UHPC-NC.

Acknowledgements. The authors would like to acknowledge the research grant 51978459 received from National Natural Science Foundation of China for the works reported herein. The authors gratefully express their gratitude for the financial supports.

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References 1. Qiao, Y., Wang, H., Cai, L., et al.: Influence of low temperature on dynamic behavior of concrete. Constr. Build. Mater. 115, 214–220 (2016) 2. Kusumawardaningsih, Y., Fehling, E., Ismail, M.: UHPC compressive strength test specimens: cylinder or cube? Proc. Eng. 125, 1076–1080 (2015) 3. Yoo, D.Y., Banthia, N., Yoon, Y.S.: Flexural behavior of ultra-high-performance fiberreinforced concrete beams reinforced with GFRP and steel rebars. Eng. Struct. 111, 246–262 (2016) 4. Kim, M.J., Yoo, D.Y., Kim, S., et al.: Effects of fiber geometry and cryogenic condition on mechanical properties of ultra-high-performance fiber reinforced concrete. Cem. Concr. Res. 107, 30–40 (2018) 5. Wang, Y., An, M.Z., Yu, Z.R., et al.: Durability of reactive powder concrete under chloride-salt freeze–thaw cycling. Mater. Struct. 50(1), 18 (2017) 6. Reju, R., Jacob, G.J.: Investigations on the chemical durability properties of ultra high performance fibre reinforced concrete. In: Proceedings of International Conference on Green Technologies, New York, USA, pp. 181–185 (2012) 7. Harris, D.K., Sarkar, J., Ahlborn, T.M.: Characterization of interface bond of ultra-highperformance concrete bridge deck overlays. Transp. Res. Rec. 2240, 40–49 (2011) 8. Jang, H.O., Lee, H.S., Cho, K., et al.: Experimental study on shear performance of plain construction joints integrated with ultra-high performance concrete (UHPC). Constr. Build. Mater. 152, 16–23 (2017) 9. Zhang, Y., Zhu, P., Liao, Z.Q., et al.: Interfacial bond properties between normal strength concrete substrate and ultra-high performance concrete as a repair material. Constr. Build. Mater. 235(C) (2020) 10. Zhang, Y., Zhang, C.Y., Zhu, Y.P., et al.: An experimental study: various influence factors affecting interfacial shear performance of UHPC-NSC. Constr. Build. Mater. 236(C) (2020) 11. Zhang, Y., Zhu, P., Wang, X.W., et al.: Shear properties of the interface between ultra-high performance concrete and normal strength concrete. Constr. Build. Mater. 248 (2020) 12. Tayeh, B.A., Abu Bakar, B.H., Megat Johari, M.A., et al.: Mechanical and permeability properties of the interface between normal concrete substrate and ultra high performance fiber concrete overlay. Constr. Build. Mater. 36 (2012) 13. CECE 13-2009: Standard Test Methods for Fibre Reinforced Concrete. China Planning Press, Beijing, China (2010) (in Chinese) 14. Xie, J., Yan, J.B.: Experimental studies and analysis on compressive strength of normal-weight concrete at low temperatures. Struct. Concr. 19(4), 1235–1244 (2018)

Effects of Arctic Low Temperatures and Freeze-Thaw Cycles on Mechanical Properties of Ultra-high Performance Concrete Ercong Kang1 , Jian Xie1,2 , Jiabao Yan1,2,2(B) , and Jing Tang3 1 School of Civil Engineering, Tianjin University, Tianjin 300350, China

[email protected], [email protected], [email protected] 2 Key Laboratory of Coast Civil Structure Safety of Ministry of Education, Tianjin University,

Tianjin 300350, China 3 Department of Infrastructure Construction, Hainan University, Hainan 570228, China

[email protected]

Abstract. Ultra-high performance concrete (UHPC) has a significant advantage in complex structures relevant to Arctic environment conditions such as longspan bridges and offshore platforms due to its high strength, high toughness and excellent durability. To explore the compressive response of UHPC at low temperatures and after freeze-thaw cycles, two series tests were conducted. Firstly, the compressive strength of UHPC exposed to low temperatures was experimentally investigated. The UHPC cubes had good integrity after failure due to the bridging effect of continuous steel fibers. The compressive strength of UHPC increased almost linearly with reducing temperature in the range of 20–80 °C. Then, a total of 17 groups of UHPC and NWC cubes were prepared to explore the compressive response of UHPC after freeze-thaw cycles. The investigated parameters include freezing temperature (−30, −60, and −80 °C) and number of freeze-thaw cycles (25, 50, 75, and 100). With the increase of number of freeze-thaw cycles and the decrease of freezing temperature, the degradation in compressive strength of UHPC gradually became distinguished. Finally, the regression analysis was conducted to establish the empirical formulae for the compressive strength of UHPC at different low temperatures and after freeze-thaw cycles. The accuracy of the developed formulae was validated by the experimental results. Keywords: UHPC · Low temperature · Freeze-thaw cycles · Compressive strength · Empirical equations

1 Introduction Ultra-high performance concrete (UHPC) is a type of cement-based composite material, which has exhibited high mechanical strengths, dense matrix structure, and superior workability. Thus, UHPC is regarded as a cost-efficient engineering material that can be utilized in various harsh circumstances, such as marine environment, Arctic Circle, and cold regions. In Asia, Europe, and North America areas, there are quite a few bridges © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 515–524, 2023. https://doi.org/10.1007/978-981-19-7331-4_42

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utilizing UHPC as a major or part building materials, such as Peace Bridge, American Mars Hill Bridge, and Wild Bridge. The offshore concrete structures, including oil and gas offshore platforms, gravel island, floating structures, pipelines, and airstrips, tend to exposed to the severe environmental conditions with low temperature of about −70 °C in the Arctic and −50 °C in northern China. The exploration of oil and gas resources has further enhanced the demand for construction offshore structures. More importantly, these bridges and offshore structures are continuously exposed to the freeze-thaw cycles during their service lives due to the climate change. To avoid unnecessary restrictions on UHPC applications in these cold regions, the investigations of its compressive response at low temperatures and after freeze-thaw cycles become quite important. In the past four decades, extensive studies have been carried out to examine the performance of UHPC at ambient temperature, consisting of ingredients, design methodologies, hydration, and mechanical properties (Shi et al. 2015; Wang et al. 2015; Du et al. 2021). To extend the application of UHPC in commercial Liquid Natural Gas (LNG) tanks, Kim et al. (2017, 2018) examined the mechanical properties of UHPC under different temperature conditions. The results showed that the compressive strength of all types of UHPC at −162 °C increased by 36% on average compared with ambient temperature and cause no detrimental effect on the compressive strength from a single freeze-thaw cycle. However, this research only focused on the −162 °C temperature level and only experiencing one cryogenic freeze-thaw cycle. Graybeal and Tanesi (2007) reported that the relative dynamic modulus of UHPC was at least 96% after 690 cyclic freezing cycles between 4.4 and −18 °C, indicating that UHPC has excellent freeze-thaw degradation resistance. However, the specified lower temperature target value for the freezing circumstance only reached −18 °C and the compressive response of UHPC was not involved. Consequently, current studies provided very limited information for UHPC applications in cold regions (about −80 °C). Accordingly, the specific objectives of this paper are to evaluate the effect of low temperatures and freeze-thaw cycles on the mechanical properties of UHPC. Firstly, a total of 21 uniaxial compressive tests of UHPC at four temperature levels (T ) were conducted. The failure mode and compressive strength of UHPC at different temperatures were obtained. Followed, seventeen groups of cubic UHPC and normal weight concrete (NWC) specimens were prepared to investigate the influence of freezing temperatures (T ) and number of freeze-thaw cycles (N) on the compressive strength of UHPC. Finally, based on the test results, empirical equations were developed to evaluate the compressive strength of UHPC suffering low temperatures and freeze-thaw cycles.

2 Testing Progrem 2.1 Details of Specimens In this study, same mixture proportion with a low w/b ratio of 0.22 was adopted to examine the compressive response of UHPC at low temperatures and after freeze-thaw cycles, as listed in Table 1. The measured moisture content of UHPC was 1.77%. In contrast with the normal weight concrete (NWC), the coarse aggregate was eliminated from the UHPC mixture. Furtherly, straight brass-coated steel fibers with a length-todiameter ratio (l f /d f ) of 65 (13.0 mm/0.2 mm) were incorporated evenly at a volume

Effects of Arctic Low Temperatures and Freeze-Thaw Cycles …

517

fraction of 2.0% to enhance the ductility of UHPC. The tensile strength and elastic modulus of steel fibers are 2500 MPa and 200 GPa, respectively. Table 1. Mix proportions of UHPC (kg/m3 ) Item

w/b

Cement

Silica fume

Ground quartz

Silica sand

Steel fibers

Water

SP

UHPC

0.22

708.6

212.6

212.6

949.5

185

193.3

6.7

C50

0.40

515

205

Sand

Gravel

605

1075

w/b denotes the water-to-binder ratio; SP denotes superplasticizer

All tests were classified into two parts according to the temperature conditions. Eighty cubic specimens with a side of 100 mm were tested under axial loading condition. Twenty-one were from Part I whereas the other fifty-nine were from Part II. To explore the effect of temperature levels (T ), the compressive tests of UHPC were performed at 20 °C, −30 °C, −60 °C, and −80 °C, corresponding to the specimens of A-N0-T1, A-N0-T2, A-N0-T3, and A-N0-T4, respectively. Three and six identical UHPC cubes were prepared for tests at ambient temperature and low temperatures, respectively. Fiftynine specimens of Part II could be further divided into two series. Thirteen groups of UHPC cubes with three identical samples in each group, i.e., 39 samples in total, were prepared for Series B. The investigated parameters were freezing temperatures (−30, −60, and −80 °C) and number of freeze-thaw cycles (25, 50, 75, and 100). Series C with Grade C50 NWC was designed as control specimens to analyze the difference in freezing resistance between UHPC and NWC. Mix proportions of NWC are listed in Table 2. The coarse aggregates are crushed gravels with continuous grading of 5−25 mm. The fine aggregates are river sands with fineness module of 2.8. To explore the effect of T, C-N0-T1, C-N12-T2, C-N12-T3, and C-N12-T4 with the freezing temperature of 20 °C, −30 °C, −60 °C, and −80 °C, respectively, were tested under compression after 12 freeze-thaw cycles. Five identical NWC cubes were prepared for each group. More details are summarized in Table 2. 2.2 Test Procedure Specimens were immersed in a water bath for 4 days before the freeze-thaw cycling. The freezing is carried out in the cold storage freezer. The specimens were maintained at the target low temperature for 4 h, and then brought back up to ambient temperature in the water bath. The compressive tests after freeze-thaw cycles were conducted at ambient temperature. A 200 tons universal testing machine with a sealed cooling chamber was used for compressive strength testing at different temperatures. Liquid Nitrogen was injected into the chamber to maintain the target temperature condition throughout the whole experiment. PT100 thermocouples were attached to the chamber and embedded in specimens to monitoring the corresponding temperatures. According to GB 50081-2019, the stress speed of 0.8 MPa/s was adopted during the compressive testing.

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3 Test Results 3.1 Mechanical Properties of UHPC at Low Temperatures 3.1.1 Failure Mode Figure 1 depicts the typical failure modes of UHPC cubes at different temperatures. It is noticeable that low temperature had quite limit effects on the failure modes of UHPC cubes under compressive loading. The specimens remained intact after destruction due to presence of steel fiber. Most of the cracks developed along the loading direction. Peeling of the UHPC was also observed near the cracking locations. 3.1.2 Influence of Low Temperature on the Compressive Strength of UHPC The compressive strength values (f c ) of UHPC at different low temperatures are summarized in Table 2. Besides, Fig. 2 shows the relationship between the compressive strength of UHPC and temperature. This figure indicates that the increase in f c was proportional to the decrease in temperature. As T increased from +20 to −30, −60, and −80 °C, the f c of UHPC was averagely increased by 11.95, 19.78, and 28.78%. The improvement in compressive strength of UHPC exposed to low temperatures was mainly associated with the frozen process of water in capillary pores. When the temperature lower below 0 °C, the water in capillary pores started freezing. The ice gradually filled the capillary pores with the decreasing T and could support part of external loading. Furthermore, the increasing rate of f c was relatively limited due to the low w/b ratio and moisture content of UHPC. 3.2 Mechanical Properties of UHPC After Freeze-Thaw Cycles 3.2.1 Influence of Freezing Temperature Figure 3 (a) and (b) present the effect of freezing temperature (T ) on the compressive strength (f c ) of UHPC and NWC, respectively. These figures show that as the freezing temperature decreased, the compressive strength of UHPC and NWC were both decreased. For UHPC specimens, after 25 (50) freeze-thaw cycles, the f c values averagely decreased by 0.41% (0.35%), 0.81% (1.61%), and 0.97% (3.19%), corresponding to T of −30 °C, −60 °C, and −80 °C, respectively. It could be concluded that when the number of freeze-thaw cycles (N) did not exceed 50, the effect of T on the f c of UHPC was marginal and the reduction ratio were all less than 5%. As T dropped from −30 to − 60 °C, the reduction ratio of f c after 75 (100) freeze-thaw cycles increased from 1.21% (1.37%) to 2.78% (4.90%); as T dropped from −60 to −80 °C, the reduction ratio of f c after 75 (100) freeze-thaw cycles increased from 2.78% (4.90%) to 10.18% (14.55%). These results revealed that the influence of freezing temperature on the compressive strength of UHPC was quite relevant to the number of freeze-thaw numbers. When N exceeded 50 times and T was below −60 °C, the influence of freezing temperature on the compressive strength of UHPC gradually became significantly and the reduction rate on f c were over 10%. In addition, Fig. 3 (b) depicts that after 12 freeze-thaw cycles, the reduction ratio in f c of NWC averagely increased by 10.61%, 28.06% and 30.58%, corresponding to

UHPC

UHPC

I

II

100

−80

B-N100-T4

12

75

−80

B-N75-T4

−80

50

−80

B-N50-T4

C-N12-T4

25

−80

B-N25-T4

12

100

−60

B-N100-T3

12

75

−60

B-N75-T3

−60

50

−60

B-N50-T3

−30

25

−60

B-N25-T3

C-N12-T3

100

−30

B-N100-T2

C-N12-T2

75

−30

B-N75-T2

0

50

−30

B-N50-T2

+20

25

−30

B-N25-T2

C-N0-T1

0

0

−80

A-N0-T4

+20

0

−60

A-N0-T3

B-N0-T1

0

0

+20

−30

N

A-N0-T1

T (°C)

A-N0-T2

Specimen

35.01

35.22

46.42

56.84

111.92

120.50

128.16

134.35

132.64

126.96

128.79

131.80

133.07

135.42

135.89

137.99

138.01

156.08

133.41

127.52

125.43

f c1 (MPa)

35.62

37.35

43.69

48.74

114.61

118.18

130.36

132.82

123.85

129.67

136.41

131.12

135.08

141.96

127.82

127.53

130.83

165.69

137.73

129.52

126.38

f c2 (MPa)

33.37

37.86

47.89

52.67

116.81

122.23

130.46

130.74

125.62

134.00

130.16

135.62

128.17

119.58

136.71

134.63

132.97

154.15

155.10

152.38

122.11

f c3 (MPa)

35.72

37.40

41.47

50.47

170.90

165.63

149.98

f c4 (MPa)

39.19

37.57

50.89

48.98

164.51

156.31

138.25

f c5 (MPa)

151.73

147.55

f c6 (MPa)

35.78

37.08

46.07

51.54

114.45

120.30

129.66

132.64

127.37

130.21

131.79

132.85

132.11

132.32

133.47

133.38

133.94

160.51

149.29

139.53

124.64

f c (MPa)

0.033

0.038

0.046

0.079

0.021

0.017

0.010

0.014

0.036

0.027

0.031

0.018

0.027

0.087

0.037

0.040

0.028

0.039

0.077

0.099

0.018

COV

0.854

0.898

0.968

0.990

0.951

0.972

0.984

0.992

0.986

0.988

0.997

0.996

1.000

1.288

1.198

1.119

1.000

I fc

0.910

0.923

0.941

0.973

0.934

0.947

0.966

0.999

0.971

0.985

1.004

1.038

1.275

1.217

1.130

0.985

I fcP

121.93

123.62

126.05

130.32

125.14

126.88

129.37

133.75

130.12

131.93

134.52

139.07

158.42

151.32

140.66

122.89

f cP (MPa)

T denotes temperature level; N denotes number of freeze-thaw cycles; COV denotes coefficient of variation; f c and f cP denote experimental and predicted cubic compressive strength, respectively; I fc and I fcP denote the experimental and predicted strength changing factor, respectively

NWC

Concrete type

Part

Table 2. Details of specimens

Effects of Arctic Low Temperatures and Freeze-Thaw Cycles … 519

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Fig. 1. Failure modes of UHPC at different low temperatures

200

fc (MPa)

160

120 y = -0.36x + 130 R² = 0.64 80

40 -90

-60

-30 T (°C)

0

30

Fig. 2. Compressive strength of UHPC at different low temperatures

the freezing temperature of −30 °C, −60 °C, and −80 °C, respectively. Compared with UHPC, it can be drawn that the reduction of freezing temperature caused more severe effects on the compressive strength of NWC. This may be attributed to the different pore structures of NWC and UHPC. Through optimization of the particle packing density, UHPC achieved a very low water-to-binder ratio (w/b = 0.22) and a discontinuous pore structure that relatively reduced the ingress of liquid (Kang et al. 2018; Xie et al. 2020). The low moisture content of UHPC further weakened the damage of frozen ice. 3.2.2 Influence of Number of Freeze-Thaw Cycles Figure 4 depicts the influence of the number of freeze-thaw cycles (N) on f c values of UHPC. It can be obtained that the compressive strength (f c ) of UHPC decreased with the increase of N. For UHPC specimens after 25, 50, 75, and 100 freeze-thaw cycles, the f c values of UHPC with the freezing temperature of −30 °C averagely decreased by 0.41%, 0.35%, 1.21%, and 1.37%, respectively; the f c values of UHPC with the freezing temperature of −60 °C averagely decreased by 0.81%, 1.61%, 2.78%, and 4.90%, respectively; the f c values of UHPC with the freezing temperature of −80 °C averagely decreased by 0.97%, 3.19%, 10.1%, and 14.55%, respectively. These results

Effects of Arctic Low Temperatures and Freeze-Thaw Cycles … 160

80

N=25

N=50

60

120

fc (MPa)

140 fc (MPa)

521

N=75

40

N=100 N=25 N=50 N=75 N=100

100

y = 0.168 x + 48.92 R² = 0.83

20

0

80 -90

-60

-30 T(°C)

0

30

(a) Effect on UHPC

-90

-60

-30 T (°C)

0

30

(b) Effect on NWC

Fig. 3. Effect of freezing temperature on compressive strength of UHPC

showed that for UHPC specimens suffered freeze-thaw cycles within 100 times, the reduction ratio of f c was less than 5% when the freezing temperature T ≥ −60 °C. In these cases, the effect of N on f c values of UHPC was quite limited. However, when freezing temperature reached −80 °C, the effect of N on f c eventually became distinguished and the reduction ratio of f c exceed 10% after 75 freeze-thaw cycles. 160

+20°C~ -30°C

fc (MPa)

140

+20°C~ -60°C

120

T= -30°C T= -60°C

+20°C~ -80°C

T= -80°C

100 0

25 50 75 100 Number of freeze-thaw cycles

Fig. 4. Effect of N on compressive strength of UHPC

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4 Regression Analysis and Discussion 4.1 Evaluation of Compressive Strength of UHPC at Low Temperatures As shown in Fig. 5, the compressive strength increased almost linearly with dropping temperature. The increasing ratio (I fcT ) was adopted to estimate the effect of low temperature on f c . Thus, for UHPC with w/b ratio close to 0.22 and W c close to 1.8%, the formula to predict the compressive strength at low temperatures was determined as follows; IfcT =

fcT = −0.0029T + 1.043 fca

(1)

where, T is temperature level, in °C, and −80 °C ≤ T ≤ 20 °C; f cT and f ca denote compressive strength of UHPC at low temperature T and ambient temperature, respectively, in MPa. 1.6

fcT/fca

1.3

1.0

y = -0.0029x + 1.043 R² = 0.64

0.7

0.4 -90

-60

-30 T (°C)

0

30

Fig. 5. Effect of T on f cT /f ca of UHPC 1.4

Test-to-predicted ratio

+15%

1.2

1.0

0.8

-15% Mean 1.00 COV 0.06

0.6 0

6

12 18 Test number

24

Fig. 6. Test-to-predicted ratios for I fcT

Figure 6 depicts the relationship between predicted compressive strength and experimental results. The average test-to-predicted ratio is 1.00 with a COV of 0.06 and all

Effects of Arctic Low Temperatures and Freeze-Thaw Cycles …

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predictions fall within the scope of ± 15%. These results confirm that the developed equation estimates well the compressive strength of UHPC exposed to low temperatures. In addition, the Eq. (1) was established based on limited test results and further verifications were required. The empirical equation is available for UHPC with freezing temperature above −80 °C and the number of freeze-thaw cycles of 0−100. 4.2 Evaluation of Compressive Strength of UHPC After Freeze and Thaw Cycles Figure 7 (a) and (b) show that freezing temperature (T) and number the freeze-thaw cycles (N) have a remarkable effect on the compressive strength (fc) of UHPC. The strength deterioration factor Ifc of UHPC was proposed for determining the f c of UHPC after free-thaw cycles. Thus, regression analysis was conducted to develop the prediction formula of UHPC compressive strength (f c ) considering T and N. Based on the 39 experimental results of UHPC after freeze-thaw cycles, the empirical model for UHPC with w/b ratio close to 0.22 and W c close to 1.8% was proposed as follows; Ifc = 1.26e0.0013T N −0.048

(2)

where, T denotes freezing temperature, in °C, and −80 °C ≤ T ≤ 20 °C; N denotes the number of freeze-thaw cycles, 0 < T ≤ 100. As presented in Fig. 7 (c), the mean value and COV of test-to-predicted ratios are 1.00 and 0.04 and they are within the range of ± 10%. Herein, it could be derived that the proposed formula provides a reasonable prediction for the compressive strength of UHPC subjected to freeze-thaw cycles. Furthermore, since the reduction ratio in f c of UHPC gradually became significant when N ≥ 75 and T = −80 °C, the compressive response of UHPC subjected to freeze-thaw cycles over 100 times merits further study. The proposed Eq. (2) is applicable for UHPC suffered freeze-thaw cycles with 0 < N ≤ 100 and 0 °C < T ≤ −80 °C. 1.2

1.4 +20°C~ -30°C

N=25

N=50

1.0 fc/fc0

fc /fc0

1.0 N=75 N=100

0.8

N=25 N=50 N=75 N=100

0.6 -90

-60

-30 T(°C)

0

(a) Effect of T

+20°C~ -60°C 0.8 T= -30°C

+20°C~ -80°C

Test-to-predicted ratio

1.2

1.2

+10%

1.0

-10%

0.8

T= -60°C T= -80°C

0.6 30

Mean 1.00 COV 0.04

0

25 50 75 Numer of freeze-thaw cycles

(b) Effect of N

0.6 100

0

10

20 30 Test number

40

(c) Test-to-predicted ratios for Ifc

Fig. 7. Effect of T and N on f c of UHPC after freeze-thaw cycles

5 Conclusions Based on the tests and regression analysis conducted in the manuscript, the main conclusions could be drawn as follows;

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(1) Low temperature had quite limited influence on the failure patterns of UHPC cubes under axial loading. The compressive strength of UHPC increased almost linearly with dropping temperature, which appeared to be related to the frozen ice in capillary pores. The increments in f cT values of UHPC was about 28.78% as T dropped from 20 to −80 °C. (2) With the decrease of freezing temperature and the increase of number of freezethaw cycles, the degradation on compressive strength of UHPC gradually became distinguished. (3) The developed Eqs. (1) and (2) could provide a relative reasonable prediction for compressive strength of UHPC subjected to low temperatures and freeze-thaw cycles.

Acknowledgements. The authors would like to acknowledge the research grant 51978459 received form National Natural Science Foundation of China for the works reported herein. Further financial support of this research project was also granted by the China Scholarship Council (CSC) (202006250220). The authors gratefully express their gratitude for those sponsors for financial support.

References Chinese Standard: Standard for test methods of concrete physical and mechanical properties, GB 50081-2019. China Architecture and Building Press, Beijing, China (2019) Du, J., et al.: New development of ultra-high-performance concrete (UHPC). Compos. B Eng. 224, 109220 (2021) Graybeal, B., Tanesi, J.: Durability of an ultra-high-performance concrete. J. Mater. Civ. Eng. 19(10), 848–854 (2007) Kang, S.H., Hong, S.G., Moon, J.: The effect of superabsorbent polymer on various scale of pore structure in ultra-high performance concrete. Constr. Build. Mater. 172, 29–40 (2018) Kim, M.J., Yoo, D.Y., Kim, S., Shin, M., Banthia, N.: Effects of fiber geometry and cryogenic condition on mechanical properties of ultra-high-performance fiber-reinforced concrete. Cem. Concr. Res. 107, 30–40 (2018) Kim, M.J., Kim, S., Lee, S.K., Kim, J.H., Lee, K., Yoo, D.Y.: Mechanical properties of ultra-highperformance fiber-reinforced concrete at cryogenic temperatures. Constr. Build. Mater. 157, 498–508 (2017) Shi, C.J., Wu, Z.M., Xiao, J.F., Wang, D.H., Huang, Z.Y., Fang, Z.: A review on ultra high performance concrete: Part I Raw materials and mixture design. Constr. Build. Mater. 101, 741–751 (2015) Wang, D.H., Shi, C.J., Wu, Z.M., Xiao, J.F., Huang, Z.Y., Fang, Z.: A review on ultra high performance concrete: Part II Hydration, microstructure and properties. Constr. Build. Mater. 96, 368–377 (2015) Xie, J., Fu, Q.H., Yan, J.B.: Compressive behaviors of concrete stub columns with SFRCC jacket under cold-region marine environments. J. Cold Reg. Eng. 34(3), 04020021 (2020)

Compressive Behavior of High Strength Steel Wire-Mesh Reinforced Concrete Filled Steel Tubular Columns Fangyuan Gao, Mingxiang Xiong(B) , and Fengming Ren(B) School of Civil Engineering, Guangzhou University, Guangzhou 510006, China {cvexmx,rfm}@gzhu.edu.cn

Abstract. Square steel tube cannot provide effective confinement to core concrete in a concrete filled steel tubular (CFST) column, in this regard, the transverselyplaced high-strength steel wire mesh (SWM) is proposed to enhance such confinement. The enhancement mechanism of SWM is rather different from traditional CFST columns where the confinement is provided from inside of core concrete through the interactions between SWM and surrounding concrete, such confinement reduces the dilation of concrete. The compressive behavior of high strength SWM reinforced square CFST columns were investigated experimentally, it is found the load-carrying capacity of square CFST columns can be largely improved. Keywords: Concrete filled steel tubular column · Steel wire mesh · High strength · Compression

1 Introduction Confinement to concrete core is generally low in square concrete-filled steel tubular (CFST) columns compared to their circular counterparts. To improve such confinement, many measures have been sought, such as longitudinal stiffener plates (Tao et al. 2005), tab stiffeners (Petrus et al. 2010), diagonal tie bars (Ding et al. 2016), perforated plates (Gan et al. 2019), horizontal tie bars (Yang et al. 2014), binding bars (Cai and He 2006), CFRP jackets (Tao et al. 2007), etc. These measures have demonstrated their efficiency to prevent local buckling of the square steel tube and improve the load-carrying capacity of the square CFST columns. However, there are disadvantages when they are used, for example, large amounts of hot welding work and cold cutting or drilling work are needed, which impairs the strength of steel tube. Setting against this background, a new stiffening measure employing high strength steel-wire-mesh (SWM) is proposed to improve the compressive performance of square CFST columns without incurring welding and cutting work in this study. Layers of SWM are evenly placed along with the column height. The stiffening mechanism of SWM is rather different from that of the abovementioned measures in terms of confinement to the concrete core. The abovementioned measures use stiffened steel tube to confine the concrete core from outside of concrete. However, for the concrete core reinforced by

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 525–530, 2023. https://doi.org/10.1007/978-981-19-7331-4_43

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SWM, the confinement is applied from inside of concrete through the dragging force which is mainly contributed from the mechanical interlocking of the ribbed steel wire and concrete with a minor contribution from the adhesion and friction between the steel wire and concrete. In this study, the compressive behavior of high-strength SWM reinforced square CFST columns is investigated experimentally.

2 Experimental Program A total of 13 SWM reinforced square CFST column specimens were prepared and tested under axial compression. The height of all specimens is 800 mm. The width of the square section is 350 mm. The effects of steel tube thickness, steel wire diameter, width of concrete core enclosed by SWM, longitudinal spacing, horizontal spacing, and steel wire ratio, were investigated, they are provided in Table 1. The cubic strength of concrete is 38.6 MPa, the yield strength of 4 mm and 8 mm steel tubes are 254 MPa and 245 MPa, and those of 5 mm and 7 mm steel wire are 1440 MPa and 1420 MPa, respectively. Table 1. Details of SWM reinforced CFST columns under axial compression Tube Wire Width of Spacing Spacing Steel thickness diameter SWM Dc sl (mm) sh (mm) wire t (mm) dw (mm) (mm) ratio ρw

Test load capacity (kN)

S8-1

8

\

\

\

\

7871

S8-2

8

7

300

200

60

0.77% 8004

S8-3

8

7

300

100

100

1.03% 8240

S8-4

8

7

300

100

60

1.54% 8975

S8-5

8

7

240

100

60

1.60% 7820

S8-6

8

5

300

51

60

1.54% 9582

S8-7

8

5

240

51

60

1.60% 8292

S8-8

8

5

240

100

26.7

1.63% 8245

S4-1

4

\

\

\

\

0

S4-2

4

7

300

200

60

0.77% 5529

S4-3

4

7

300

100

100

1.03% 5828

S4-4

4

7

300

100

60

1.54% 5937

S4-5

4

7

240

100

60

1.60% 5115

0

Dc

Sh

Specimens

Sl

Sh

4946

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3 Test Results and Discussions 3.1 Effect of Horizontal Spacing The horizontal spacing of SWM plays a key role in affecting the confinement to the concrete core and then affecting the load-carrying capacity and ductility of the column. As seen from Fig. 1a, without SWM, the load applied on the column ascended with the increase of vertical displacement of column head but dropped abruptly after the peak load. The abrupt drop of load is attributed to the crush of concrete. When the concrete core is reinforced by SWM with a horizontal spacing of 100 mm, there is no such abrupt drop of load, indicating the reinforcement from SWM delayed or even suppressed the brittle crush of concrete. When the horizontal spacing is reduced to 60 mm, there is no abrupt load drop either and the load descended slower. Besides, the axial load-carrying capacity in terms of the peak load is also improved by using SWM. The inset in Fig. 1a shows that the improvement of load-carrying capacity is 4.7% when the horizontal spacing is 100 mm and 14.0% when it is 60 mm.

Fig. 1. Effect of horizontal spacing on load-displacement curve.

Figure 1b shows the load-displacement curves of columns with a thinner steel tube. The load drop after the peak load can still be seen in the column without SWM but less abrupt compared to its counterpart with a thicker steel tube, this could be because the peak load of it is lower. With the increase of horizontal spacing, the abrupt load drop becomes less noticeable but the load descending rates after their peak load are quite comparable. This implies that the use of SWM can effectively suppress the brittle crush of concrete at peak load but cannot improve the ductility behavior after the peak load. Besides, compared to that of a column without SWM, the increase of load-carrying capacity is 17.8% and 20.0% when the horizontal spacings of SWM are 100 mm and 60 mm, respectively. This indicates the use of SWM is more effective to improve the load-carrying capacity of the CFST column with a thinner steel tube.

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3.2 Effects of Longitudinal Spacing The effects of longitudinal spacing on the load-displacement response are illustrated in Fig. 2. Generally, the increase of longitudinal spacing affected significantly the loadcarrying capacity and brittle crush of concrete at peak load but had little effect on the ductility after the peak load. For the columns with thicker tubes shown in Fig. 2a, the improvement in load-carrying capacity by using SWM with a longitudinal spacing of 200 mm is low (i.e., 1.7%), but largely increased when said spacing is doubled (i.e., 14.0%). For the columns with thinner tubes shown in Fig. 2b, the improvement are 11.8% and 20.0% when the longitudinal spacings are 200 mm and 100 mm. The improvement in columns with a thinner tube is also higher.

Fig. 2. Effect of longitudinal spacing on load-displacement curve.

3.3 Effects of Area of SWM Reinforced Concrete Core Figure 3a, b show the effects of the area of SWM reinforced concrete core on the thickwalled columns. The 7-mm steel wires were placed in S8-4 and S8-5 whereas the 5-mm steel wires were used in S8-6 and S8-7. It is found that the improvement to the loadcarrying capacity is insignificant when said area is 240 mm. This is because the load capacity was governed by the crush of concrete not reinforced by SWM (concrete outside SWM). When the reinforced area increased to 300 mm which is very close to the full area of inner concrete, the improvement in load capacity is high. The effects of the area of SWM reinforced concrete core on the thin-walled columns are similar to those on the thick-walled columns. Hence, it is recommended that the full area of inner concrete should be reinforced by SWM to achieve a higher load-carrying capacity. 3.4 Effects of Diameter of Steel Wire Two pairs of columns are compared in Fig. 4. The steel wire ratios are the same in each pair of columns but the diameters of steel wire are different. It is found that the

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Fig. 3. Effect of area of SWM reinforced concrete core on load-displacement response.

Fig. 4. Effects of diameter of steel wire ratio on load-displacement response.

load-carrying capacity of the column with a smaller diameter steel wire is higher, this is because the contact area of the 5-mm steel wires with the surrounding concrete is more when the steel wire ratios are the same, this leads to a higher dragging force and then the higher confinement to concrete.

4 Conclusions A new confinement measure using high-strength steel wire mesh (SWM) is proposed to improve the compressive behavior of square concrete-filled steel tubular (CFST) columns. The confining mechanism of SWM is different from traditional measures because it confines the concrete core from inside of it to outside continuously through dragging force. It is found that the compressive load-carrying capacity of the square CFST column can be improved by 21.7% with a steel wire ratio of 1.54%. SWM possesses other advantages over traditional improvement measures, for example, no hot

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welding work and cold binding or drilling work are involved, therefore saving labor costs. The disadvantage is concrete casting that may be congested when the spacings of the steel wires are small, this requires concrete to have good flowability. Overall, the use of SWM is promising in terms of its construction feasibility and improvement to the compressive performance of square CFST columns. Acknowledgements. The authors would like to acknowledge the financial support of the Guangzhou Science and Technology Program (Project No.: 202102010407) and Guangdong Natural Science Foundation (Project No.: 2021A1515012390).

References Cai, J., He, Z.Q.: Axial load behavior of square CFT stub column with binding bars. J. Constr. Steel Res. 62, 472–483 (2006) Ding, F.X., Lu, D.R., Bai, Y., Zhou, Q.S., Ni, M., Yu, Z.W., et al.: Comparative study of square stirrup-confined concrete-filled steel tubular stub columns under axial loading. Thin-Walled Struct. 98, 443–453 (2016) Gan, D., Zhou, Z., Zhou, X.H.: Axially loaded thin-walled square concrete-filled steel tubes stiffened with diagonal binding ribs. ACI Struct. J. 116, 265–280 (2019) Petrus, C., Hamid, H.A., Ibrahim, A., Parke, G.: Experimental behaviour of concrete filled thin walled steel tubes with tab stiffeners. J. Constr. Steel Res. 66, 915–922 (2010) Tao, Z., Han, L.H., Wang, Z.B.: Experimental behaviour of stiffened concrete-filled thin-walled hollow steel structural (HSS) stub columns. J. Constr. Steel Res. 61, 962–983 (2005) Tao, Z., Han, L.H., Zhuang, J.P.: Axial loading behavior of CFRP strengthened concrete-filled steel tubular stub columns. Adv. Struct. Eng. 10, 37–46 (2007) Yang, Y.L., Wang, Y.Y., Fu, F.: Effect of reinforcement stiffeners on square concrete-filled steel tubular columns subjected to axial compressive load. Thin-Walled Struct. 82, 132–144 (2014)

Prefabricated Construction and Composite Structures

Numerical Study on Out-of-Plane Mechanical Performance of New Type Precast Shear Wall with Unspliced Vertical Distribution Bars Qiang Fu(B) , Zhiwei Cao, and Heng Dong Department of Structural Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China {1910327,1610222}@tongji.edu.cn

Abstract. To eliminate the shortcomings in the grouting sleeve in precast shear wall structure induced by the poor grouting, difficult quality assurance and low construction efficiency, a new type of precast shear wall structure with unspliced vertical distributed bars (SGBL precast shear wall) was proposed. In this paper, a numerical study was carried out to preliminary explore the out-of-plane mechanical performance of SGBL precast shear wall based on the verified finite element simulation method. The influence of different parameters on the out-ofplane mechanical performance of SGBL precast shear wall was investigated by FE analysis. The results show: 1. The out-of-plane mechanical performance of SGBL shear wall is similar to that of cast-in-situ shear wall; 2. The axial compression ratio is the key factor of out-of-plane mechanical performance of shear wall and increase of wall thickness can significantly improve the out-of-plane bearing capacity. Finally, several engineering suggestions were proposed to control the out-of-plane safety of SGBL precast shear wall. Keywords: New type precast shear wall · Unspliced vertical distribution bars · FE analysis · Out-of-plane mechanical performance

1 Introduction Compared with the traditional construction methods, precast buildings are environmentally friendly and can significantly reduce the on-site construction work (Xiao et al. 2019; Pavese and Bournas 2011; Gu et al. 2019). Under the support and promotion of the government, the precast buildings have been widely carried out in China, especially in residential buildings. Shear wall structure has been widely used in multi-high-rise residential buildings due to its advantages of large lateral stiffness, large bearing capacity and regular interior (Yee 2001). Therefore, scholars from domestic and overseas have carried out extensive and deeply studies on the performance of precast shear wall structure. Reliable reinforcement connection is the key to ensure the performance of precast shear wall structure (Kramar et al. 2010). Currently, the commonly used vertical reinforcement connection method includes sleeve grouting, mechanical connection and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 533–544, 2023. https://doi.org/10.1007/978-981-19-7331-4_44

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grouting anchor connection (Wu et al. 2015; Chen et al. 2013; Guo et al. 2019) and the application of grouting sleeve connection is more than 70%. However, grouting sleeve connection has the following shortcomings: 1. The quantity of grouting sleeve is large and costly; 2. The number of connecting reinforcements is large and the reinforcements are difficult to place accurately; 3. More importantly, the quality of on-site grouting is difficult to guarantee (Xiao et al. 2019). In order to reduce the vertical reinforcement connection, many scholars proposed different vertical reinforcement connection methods for precast shear wall (Cao et al. 2002; Zhang et al. 2012), but the problem of decreasing the bearing capacity and ductility of walls still exists. To solve the problems, our research group proposed a new type precast shear wall with unspliced vertical distribution bars as shown in Fig. 1. The studies on the in-plane seismic performance (Xiao et al. 2021a, b; Liao et al. 2021; Fu et al. 2021; Zhang et al. 2021) were carried out. Previous studies have shown that the in-plane seismic performance of SGBL precast shear wall is equivalent to that of the cast-in-situ shear wall and some performance is slightly better than that of the cast-in-situ shear wall. SGBL precast shear wall eliminates the grouting sleeve greatly reduces the project cost, completely solves the difficulty of vertical reinforcement connection and greatly improves the construction efficiency. More importantly, the construction quality can be effectively controlled. However, SGBL precast shear wall improved the utilization rate of reinforcements by changing the way of reinforcement arrangement, which reduced the area of vertical reinforcements connection. The effect of this change on the out-of-plane mechanical performance of SGBL precast shear wall need to be studied.

Fig. 1. SGBL precast construction

In this paper, a preliminary numerical study on out-of-plane mechanical performance of SGBL precast shear wall was investigated by verified FE simulation method. Firstly, the difference of out-of-plane mechanical performance between SGBL precast shear wall and cast-in-situ shear wall was compared. Then the influence of axial compression ratio, height to thickness ratio, longitudinal reinforcement ratio of cast-in-situ edge member

Numerical Study on Out-of-Plane Mechanical Performance

535

and shear-span ratio was investigated by analyzing the load- displacement curve and bearing capacity. Finally, some suggestions were put forward for out-of-plane safety of SGBL precast shear wall.

2 Finite Element Modeling 2.1 Material Modeling The damaged plasticity model provided by the ABAQUS library was used to simulate the nonlinear behavior of concrete. The definition of the uniaxial compressive stress–strain curve, tension-softening curve, and definition of damage evolution for the concrete can be referred to GB-50010. The constitutive relationship for reinforcement are represented by a bilinear constitutive model, which is assumed to be elastic followed by perfectly plastic (GB-50010). 2.2 Interface Modeling Cohesive Behavior can be used to define the bond and friction between concrete interface in ABAQUS. It can be defined as a two-line model as shown in Fig. 2. In this paper, old and new concrete interface property parameters can be referred to the study conducted by Mohamad et al. (2017). In order to accurately simulate the shear action of reinforcements at old and new concrete interface, the shear-slip model of reinforcement adopts the shear-slip model of stud shear connector (Eurocode 4) to simulate in this paper. Embedded contact method was adopted to simulate the contact between reinforcements and concrete, which indicated that the no slip occurred between reinforcements and concrete.

Fig. 2. Cohesive behavior interaction model

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2.3 Element Type and Mesh 3D solid element (C3D8R) with eight-node reduced integration was used to simulate the behavior of concrete parts. The reinforcement was simulated with two-node linear three-dimensional truss elements (T3D2). The spring element was adopted to model the behavior of the reinforcement connection at old and new concrete interface. According to the SGBL precast shear wall construction method, the cast-in-situ loading beam, edge member and ground beam are combined as a whole. The reinforcement of the ground beam, cast-in-situ edge member and loading beam is combined as a whole and the reinforcement of the precast wall is combined as a whole. The reinforcement parts are embedded in the corresponding concrete parts. After trial calculation, a mesh size of 100 mm × 100 mm can achieve favorable results with the balance of accuracy and efficiency. 2.4 Boundary and Loading Conditions According to the experimental conditions, the displacements in the x, y direction for the bottom of the wall were constrained in this FE model. The loading is divided into two analysis steps. The initially constant axial load was applied to the top of the wall in the first analysis step. The horizontal loading was then applied at the top of the wall by displacement. 2.5 Model Verification In order to verify the accuracy and rationality of the FE model, the experimental results (Xiao et al. 2021a, b; Liao et al. 2021) are simulated and compared with the FE results as shown in Fig. 3. It can be seen from Fig. 3 that the simulation results agree well with the test results, which accurately reflect the loading and displacement development of the specimens.

Fig. 3. Comparison between FE results and test results

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3 Numerical Parameter Analysis In order to explore the influence of different parameters on the out-of-plane mechanical performance of SGBL precast shear wall, the size, reinforcement, material and other information of SGBL precast shear wall were refer to a practical project. Based on the verified FE model, 40 FE models were established by considering different axial compression ratio, height to thickness ratio, longitudinal reinforcement ratio of cast-insitu edge member and shear-span ratio. The details of specimens are shown in Table 1. All specimen’s height is 2900 mm, hw is shear wall length, L p is cast-in-situ edge member length (0.2hw ), t is the wall thickness, n is the design axial compression ratio, ρ is the longitudinal reinforcement ratio of cast-in-situ edge member, R is cast-in-situ edge member reinforcement, K for precast shear wall vertical distribution reinforcement, S is precast shear wall horizontal distribution reinforcement, G is stirrup reinforcement of cast-in-situ edge member. Table 1. Specimen parameters No.

hw /mm

L p /mm

t/mm

n

ρ/mm

R

K

S

G

XS1-5

1700

400

200

0.1–0.5

1.50%

6C14

8@200

8@200

8@200

PS1-5

1700

200

0.1–0.5

1.50%

6C16

8@300

8@200

8@200

P6-10

1700

240

0.1–0.5

1.50%

8@300

8@200

8@200

P11-15

1700

280

0.1–0.5

1.50%

8@300

8@200

8@200

P16-20

1700

200

0.1–0.5

2.40%

6C20

8@300

8@200

8@200

P21-25

1700

200

0.1–0.5

3.40%

6C25

8@300

8@200

8@200

P26-30

2500

500

200

0.1–0.5

1.50%

8C16

8@300

8@200

8@200

P31-35

3300

600

200

0.1–0.5

1.50%

10C16

8@300

8@200

8@200

3.1 Axial Compression Ratio Figure 4 is the horizontal load-displacement curve of cast-in-situ shear wall and SGBL precast shear wall under different axial compression ratio. Figure 5 is the peak load-axial compression ratio curve. It can be seen from figures that the horizontal load drops faster after reaching the peak load with the increase of axial compression ratio. The difference of peak horizontal load between SGBL precast shear wall and cast-in-situ shear wall become smaller and the peak horizontal load is decrease with the increase of axial compression ratio. With the increase of axial compression ratio, the effect of vertical load on out-of-plane mechanical performance of shear wall is gradually significant than horizontal load. Due to it has significant second-order effect in out-of-plane direction, the actual moment is M = VH + N . Moment-displacement curve of cast-in-situ shear wall and SGBL precast shear wall is shown in Fig. 6. Figure 7 is the axial compression

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ratio-ultimate moment curve. It can be seen from figures that the specimens showed good ductility when axial compression ratio is small and the moment drops faster after reaching the ultimate moment with the increase of axial compression ratio when n ≥ 0.3. With the increase of axial compression ratio, the bearing capacity of SGBL precast shear wall exceeds that of cast-in-situ shear wall. The bearing capacities of cast-in-situ shear wall is about 5.3% higher than that of SGBL precast shear wall under lower axial compression ratio.

Fig. 4. Horizontal load-displacement curve

Fig. 5. Peak load-axial compression ratio

The out-of-plane mechanical performance of SGBL shear wall is similar to that of cast-in-situ shear wall. The axial compression ratio-ultimate moment curve of specimens is similar to that of compression-flexural members. The axial compression ratio is the key factor of out-of-plane mechanical performance of shear wall. So, the design

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Fig. 6. Moment-displacement curve

Fig. 7. Compression-moment curve

axial compression ratio of shear wall without flange should not exceed 0.3 in actual engineering. 3.2 Height to Thickness Ratio Figure 8 is the peak load-axial compression ratio curve. With the increase of wall thickness from 200 mm to 280 mm, the maximum horizontal load of specimens increased from 26.29 kN to 87.16 kN, an increase by 231.5%. Figure 9 is the axial compression ratio-ultimate moment curve. As the height to thickness ratio decreases, the specimens still have a large bearing capacity and the improvement of bearing capacity is more obvious under higher axial compression ratio. With the increase of wall thickness from 200 mm to 280 mm, the ultimate moment of specimens increased by 129% when n = 0.5.

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Fig. 8. Peak load-axial compression ratio

Fig. 9. Compression-moment curve

3.3 Longitudinal Reinforcement Ratio of Cast-In-Situ Edge Member Figure 10 is the peak load-axial compression ratio curve. With the increase of longitudinal reinforcement ratio from 1.5% to 3.4%, the maximum horizontal load of specimens increased from 26.29 kN to 46.37 kN, an increase by 76.4%. Figure 11 is the axial compression ratio-ultimate moment curve. With the increase of longitudinal reinforcement ratio from 1.5% to 3.4%, the ultimate moment of specimens increased from 202 kN m to 282 kN m when n = 0.3. The longitudinal reinforcement ratio increases by 126.7% and the ultimate moment increases by 59.4%.

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Fig. 10. Peak load-axial compression ratio

Fig. 11. Compression-moment curve

3.4 Shear-Span Ratio Figure 12 is the peak load-axial compression ratio curve. With the increase of shear wall length from 1700 mm to 3300 mm, the maximum horizontal load of specimens increased from 26.29 kN to 48.07 kN, an increase by 82.8%. Figure 13 is the axial compression ratio-ultimate moment curve. With the increase of shear wall length from 1700 mm to 3300 mm, the ultimate moment of specimens increased from 202 kN m to 273 kN m. The shear wall length increases by 94.1% and the ultimate bending moment increases by 35.1% when n = 0.3. In conclusion, the axial compression ratio is the key factor of out-of-plane mechanical performance of shear wall. In actual engineering, the axial compression ratio of shear wall without flange should not exceed 0.3. Otherwise, flanges should be set or edge members

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Fig. 12. Peak load-axial compression ratio

Fig. 13. Compression-moment curve

should be strengthened. The increase of wall thickness can significantly improve the out-of-plane ultimate bearing capacity.

4 Conclusions Based on the verified FE simulation method, the out-of-plane mechanical performance of SGBL precast shear walls with different parameters were preliminarily explored by analyzing load-displacement curves and bearing capacity of specimens. The main conclusions are listed as follows: 1. The out-of-plane mechanical performance of SGBL shear wall is similar to that of cast-in-situ shear wall. The bearing capacity of SGBL precast shear wall is weaker

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than that of cast-in-situ shear wall when axial compression ratio is lower and the maximum weakening value is about 5.3%; 2. The axial compression ratio is the key factor of out-of-plane failure of shear wall. When n ≥ 0.3, the second-order effect becomes significant and the moment drops faster after reaching the ultimate moment with the increase of axial compression ratio. The increase of wall thickness can significantly improve the out-of-plane bearing capacity of shear wall. 3. In actual engineering, the axial compression ratio of shear walls without flange should not exceed 0.3. Otherwise, flanges should be set or edge members should be strengthened.

Acknowledgements. This work was financially supported by National Natural Science Foundation of China (Grant No. 52078360).

References Cao, W.L., Zhang, J.W., Tian, B.F., Song, W.Y., Wang, H.C.: Experimental study on seismic behavior of mid-rise RC shear wall with concealed bracings. J. Build. Struct. 23(6), 26–32, 55 (2002) Chen, Y.G., Liu, J.B., Guo, Z.X., Zhang, J.X.: Test on seismic performance of precast shear wall with reinforcements grouted in holes and spliced indirectly in horizontal connections. J. Harbin Inst. Technol. 45(6), 83–89 (2013) DD ENV 1992-1-1 Eurocode 2: Design of Concrete Structures—Part 1: General Rules and Rules for Buildings[S]. British Standards Institution, London (1992) Fu, Q., Cao, Z.W., Liao, X.D., Liu, Y.N., Zhang, S.Q.: Quasi-static test and simplified analysis method of a new type precast shear wall with unconnected vertical distributed reinforcements. J. Build. Eng. 47, 103794 (2021) Guo, W., Zhai, Z.P., Cui, Y., Yu, Z.W., Wu, X.L.: Seismic performance assessment of low-rise precast wall panel structure with bolt connections. Eng. Struct. 181, 562–578 (2019) Gu, Q., Dong, G., Wang, X.: Research on pseudo-static cyclic tests of precast concrete shear walls with vertical rebar lapping in grout-filled constrained hole. Eng. Struct. 189, 396–410 (2019) GB 50010-2010: Code for Design of Concrete Structures. China Building Industry Press, Beijing (2010) Kramar, M., Isakovi, T., Fischinger, M.: Seismie collapse risk of precast industrial buildings with strong connections. Earthq. Eng. Struct. Dyn. 39(8), 847–868 (2010) Liao, X.D., Zhang, S.Q., Cao, Z.W., Xiao, X.W.: Seismic performance of a new type of precast shear walls with non-connected vertical distributed reinforcement. J. Build. Eng. 44, 103219 (2021) Mohamad, M.E., Ibrahim, I.S., Abdullah, R.: Finite element modeling of the interfacial behavior at surface roughness concrete without the projecting steel. Int. J. Adv. Mech. Civ. Eng. 3(4), 125–130 (2017) Pavese, A., Bournas, D.A.: Experimental assessment of the seismic performance of a prefabricated concrete structural wall system. Eng. Struct. 33(6), 2049–2062 (2011) Wu, D.Y., Liang, S.T., Guo, Z.X., Xiao, Q.D.: Bending bearing capacity calculation of the improved steel grouted connecting precast wall. J. Harbin Inst. Technol. 47(12), 112–116 (2015) Xiao, X.W., Cao, Z.W., Liu, X., Liao, X.D.: Status, problems and countermeasures of prefabricated buildings in China. Build. Struct. 19, 6–9, 29 (2019)

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Xiao, X.W., Cao, Z.W., Zhang, S.Q., Liao, X.D.: Quasi-static test and strut-and-tie modeling of precast concrete shear walls with unconnected vertically distributed reinforcements. Struct. Concr. 22(4), 2258–2271 (2021a) Xiao, X.W., Cao, Z.W., Liu, X., Liao, X.D.: Experimental study on seismic performance if precast shear wall with unconnected vertical distributed reinforcement. Build. Struct. 51(17), 5–9, 24 (2021b) Yee, A.A.: Structural and economic benefits of precast/prestressed concrete construction. PCI J. 46(4), 34–42 (2001) Zhang, W.J., Qian, J.R., Yu, J.S., Qin, H., Liu, G.Q.: Tests on seismic behavior of precast shear walls with cast-in-situ boundary elements and vertical distributed reinforcements spliced by a single row of steel bars. Chin. Civil Eng. J. 45(10), 89–97 (2012) Zhang, S.Q., Chen, Y.S., Liu, Y.N., Ma, X.X., Liao, X.D., Xiao, X.W.: State of the art in connection of vertically distributed reinforcements for precast shear wall. J. Southwest Jiaotong Univ. 56(4), 828–838 (2021)

Lightweight and Advance Precast Concrete System for Modular Building Construction Junxuan Wang, Kian Hau Kong(B) , and J. Y. Richard Liew Department of Civil and Environmental Engineering, 1 Engineering Drive 2, 117576 Singapore, Singapore [email protected], {leonghien,ceekkh,ceeljy}@nus.edu.sg

Abstract. Productivity and efficiency are the critical aspects emphasised by the present Singapore construction industry, and these demands are addressed from two key approaches: construction materials and methods. These aspects involve the intensive coordination amongst various stakeholders in construction, prompting a need to collaborate and utilise highly intricate technologies such as Design for Manufacturing and Assembly (DfMA) in Advanced Precast Concrete System (APCS) and Prefabricated Pre-Finished Volumetric Construction (PPVC). DfMA is a systematic quality control method of construction that is vital to Singapore’s Construction Industry Transformation Map. PPVC system taps on the 3-dimensional modular production technology, fabricating modules off-site, and later installed on-site. However, the limitation for incorporating Concrete PPVC in Healthcare and Institutional buildings lies in the mismatch between PPVC module dimensions and the predominant design philosophy of the flat slab system. Thus, there is a need for a more flexible PPVC construction methodology to allow the construction to tap on the benefits of DfMA. The proposed Large Panel System (LPS) is used in conjunction with Concrete PPVC to overcome the rigidity in the design and construction of healthcare and institutional buildings. In the present study, a typical cast-in-situ Lightweight Concrete (LWC) building and a PPVCLPS Hybrid LWC building are modelled and analysed using a 3D Non-linear Structural Finite Element software. Both buildings are designed based on various design limit states from the Eurocode 2 (EC2) section of Structural Lightweight Aggregate Concrete (LWAC), and their performances are compared. This paper aims to study the viability of the PPVC-LPS Hybrid LWC construction for healthcare and institutional buildings. Compared to the conventional cast-in-situ method, the innovative hybrid construction is found to be more superior due to its rapid connection method, meeting the structural integrity performance of cast-in-situ buildings. Keywords: DfMA · Prefabrication · Precast · Hybrid · Flat slab

1 Introduction Resources, safety, and sustainability are common topics that the construction industry has continuously been working on in recent years. These topics are further exemplified © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 545–564, 2023. https://doi.org/10.1007/978-981-19-7331-4_45

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through various problems encountered by the industry, namely labour intensiveness, accident-prone, potential environmental degradation, and fluctuation in construction quality. This emphasised the need for improvement in terms of construction, and the improvement can be addressed from two key aspects of construction material(s) and construction method(s). On top of that, cast-in-situ construction often poses a problem when it comes to the disposal of construction waste and the industry finds it hard to address the issue (Jallion and Poon 2007). Light-weight Concrete (LWC) or Light-weight Aggregate Concrete (LWAC) has been adopted by the construction industry for many years. Compared to the regular reinforced concrete, LWC has a lower density while maintaining the concrete strength level. This is mainly contributed by the lightweight aggregate used in the concrete. Many studies on high-performance lightweight concrete have been done and the material is subjected to various settings to establish a well-rounded study for the material property of LWC or LWAC (Rossignolo et. al. 2003). Design for Manufacturing and Assembly (DfMA) is a game-changing method of construction that involves construction being designed for manufacturing off-site in a controlled environment, before being assembled on-site (Building and Construction Authority 2020). DfMA is a widely adopted technology in today’s industry as it effectively addressed the concerns over resources, safety, and sustainability.

2 Technological Development 2.1 Design for Manufacturing and Assembly (DfMA) The innovative and advanced DfMA solutions are characterised by their unique features. These features include the optimization of building components, which includes optimization in all aspects such as size, shape, and configurations. Furthermore, the optimization also comes in constructability of the DfMA components, the components are self-supporting and do not require temporary props or supports at the temporary stage. Other features of DfMA also consist of the strategic use of different materials, innovative and efficient jointing solutions, high level of integration between architectural/MEP and structural elements, ease of manufacturing and transport, and fast on-site installation methods. An empirical study showed that there is a positive correlation between the overall constructability, quality, and productivity of the project when the DfMA method is adopted. These factors are the quintessential indicators of the progress of the project and the uncertainties involved in the project. Statically, DfMA technology can increase the efficiency of structural trades up to 40%, and MEP and architectural trades up to 70% (Building and Construction Authority 2020). 2.2 Limitations DfMA has conventionally been used for the construction of residential buildings, namely HDB estates. A hybrid usage of PPVC modules and precast elements can be found in the floor plans used for HDB estates. Prefabricated bathroom units and prefabricated household shelters are often used in conjunction with precast large panel slabs and facades.

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Fig. 1. DfMA technology used in HDB construction (Image extracted from Housing & Development Board Website)

The prefabricated and precast elements are stitched together to reduce the construction cycle, as compared to the traditional cast-in-situ construction (Fig. 1). However, due to various reasons, DfMA construction methods such as Precast Prefabricated Volumetric Construction (PPVC), are often not considered for the design of healthcare and institutional buildings. One of the most critical reasons for the lack of implementation of DfMA methods in healthcare and institutional buildings is the mismatch between the size restriction during modular fabrication and the strive to create more open and usable space in large floorplans. Transportation is one of the critical determinants to the effective implementation of the DfMA technologies, and to achieve savings for the projects (Turai and Wsghmare 2015). In Singapore context, typical PPVC modules are designed in line with the restrictions given by the Land Transport Authority of Singapore (LTA). In compliance with LTA’s traffic regulation, Police Escort will be required for transportation if the PPVC modules exceed any or more of the following dimensions (Land Transport Authority 2020) (Table 1). Table 1. PPVC modular parameters limitation for road transportation without traffic escort Height

< 4.5 m (inclusive of truck height)

Width

≤ 3.4 m

Laden Weight

< 80 tons

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Requiring police escort results in an increase in logistic complexity and cost for the project, as such defeating the inherent benefits of DfMA technologies. As a result, PPVC modules are often only applicable for the use of small rooms with a very restrictive column-to-column spacing. Healthcare and institutional buildings require a larger column-to-column spacing to cater to the flexibility in floor usage, and to increase the space provision for unique spaces due to specific functional requirements. The restriction in one or both directions of column-to-column spacing(s) deters the utilisation of PPVC in healthcare and institutional buildings. Furthermore, reviews have been done to show that the precast concrete structure performs remarkably well with the design and construction consideration of seismic design (Khare et al. 2011). While there is still much to explore in terms of a PPVCLPS hybrid structure, and the further incorporation of LWC for the constructability consideration.

3 PPVC—Large Panel System Hybrid Light Weight Concrete Construction 3.1 Idealised Floor Plan The adaptation of the PPVC technology available in the market is accompanied by the innate limitations of PPVC modular transportation. These restrictions are legislated by authorities such as LTA to ensure safety for both the transportation vehicle and the public. As such, the conventional 6-sided cladding modular unit design used in the market reduced the flexibility of implementation of the PPVC technology in larger floor plans/layouts such as healthcare and institutional buildings. This paper aims to address the restrictions through exploring a more viable and open floor plan, and its composition. The flexibility of the floor plan is achieved through the combined usage of various DfMA technologies such as PPVC and Precast technology. 3.2 PPVC-LPS Hybrid LWC Building According to the LTA traffic regulatory requirements, the maximum dimension of a single modular PPVC unit that can be transported on the road, without requiring escort, has to be kept within 3.4 m (width) × 3 m (height) × 12 m (length). To meet this requirement and to maximise usage of modular construction in large floor plans such as healthcare and institutional buildings, a new PPVC modular design is proposed. In contrast to the conventional four-column, six-sided precast modular design is proposed. The new design consists of two columns and one flat slab, the two columns act as the support for vertical loads. The proposed precast modular structure mitigated the conventional design of 6-sided wall cladding or box-like 4 column PPVC modules, thereby negating the need to have small (3.5 m and below) column-to-column spacing within the floor plan while tapping on the prefabrication advantage of PPVC construction. The exclusion of walls from the precast module increases the flexibility in customizing modular units, thereby being more versatile in catering to multiple building requirements and floor plans. Furthermore, walls or partitions can be constructed at a later stage to bring segregation and definition to spaces (Fig. 2).

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Fig. 2. Proposed new concrete precast modular unit design

A unique point to highlight is that the proposed precast module does not conform with the conventional definition of PPVC modular units. The new modular unit eliminates the fixture in physical space of the traditional four column structure. However, fixtures, furnishings, and M&E modules can still be installed to the LPS while fabrication at the workshops, prior to transportation onsite, thereby minimising the needs to perform works at height for installation and ensure safety. The ability and ease to access, inspect and maintain the M&E spaces within the facilities is another critical factor for enabling efficient routine servicing and maintenance works (Building and Construction Authority 2019). Therefore, the combination of the PPVC modular stitching and M&E system space provision will bring about efficiency and constructability in both provisions of opening for inspection and maintenance in the future. The proposed modular unit is a non-stereotypical design for the PPVC structure. On one hand, the lack of 3D definition forfeited a certain degree of prefinishing. However, the inherent flexibility of a 2-column module allows the incorporation of DfMA construction in taller and larger floor plans. Thereby, catering to more demanding designs such as healthcare and institutional buildings. 3.3 PPVC Installation Sequence Ease of construction is essential to the success of DfMA construction in elevating the manpower and resource efficiency of construction process. Technologies such as the precast modular construction technique allow the simple stack and stitch construction of the structure. However, such efficiency can only be utilized with careful planning of the sequence, minimising any possible downtime and wastage of resources in construction. The planned sequence is as (Fig. 3):

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3.3.1 Stage 1 The first floor of the building will consist of a cast-in-situ level, acting as a foundation and guide to the PPVC-LPS LWC module installation. The initial cast-in-situ structure have an initial height of 7.5 m (including 4.5 m of 1st floor and 3 m stump at 2nd floor), and a center-to-center distance of 8.4 m in both directions. 3.3.2 Stage 2 The PPVC-LPS LWC modules transported to the site will be lifted and placed onto the cast-in-situ LWC stumps. The duo-pillar configuration will be fitted onto the original cast-in-situ stump. Due to the unique configuration of the modular units and the presence of unbalance forces during stitching, temporary supports or struts will be needed to stabilise the PPVC-LPS LWC module for stitching with the precast slab. 3.3.3 Stage 3 The precast stitching slab will act as a connecting element between two PPVC-LPS LWC modules. The design of the stitching slabs is the same as the flat slabs used in PPVC-LPS LWC modules, this ensures the uniformity of the elements, and minimising any uneven deformation. The slab has a width of 3.9 m and a length of 8.4 m. These precast slabs will be manufactured off-site and delivered for Just-In-Time installation. The temporary strut will only be removed when there is no more construction work to be done on and around the PPVC module, or when the entire floor is completed.

4 Finite Element Software Analysis 4.1 Preliminary Element Sizing Eurocode 2 clause 11.3.1.3 mandated that when LWC is used for design, the strength of the concrete shall be reduced by a factor. Hence a lower compressive strength (fck ) of 37.82 kPa is used for Grade 40 lightweight concrete (C40). Grade 50 regular concrete (C50) is used for the shear wall to simulate the higher performance and rigidity in the structure during analysis. Given that the quasi-permanent loading condition is considered for the design, the long-term effects namely the creep and shrinkage will be accounted for in the initial design calculation. The effect of creep and shrinkage is represented via a 50% reduction in the Young’s modulus of the concrete. Furthermore, the effect of temperature differential on the contraction of concrete has been considered. However, given the relatively constant temperature of Singapore, thermal effects are ignored. A minimum concrete cover depth (40 mm) is catered for as regulated by Singapore Annex SS-EN 1992-2 clause 4.4.1.2. 4.2 Finite Element Modelling and Analysis To provide a fair gauge of the performance of the PPVC-LPS Hybrid LWC system, a cast-in-situ model of similar dimension and configuration will be modelled to obtain

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Fig. 3. Schematic assembly sequence for PPVC-LPS Hybrid LWC building

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analytical results for comparison. Furthermore, the same load case, loading, and load combination will be applied to the two models. This allows the parameters of the analysis to be similar and provide a fair comparison for the performance of the two buildings. The main software used in this analysis will be SAP2000, which is Non-linear Finite Element analysis software. The software analysis mainly involves the analysis of two structures: (1). Cast-in-situ LWC building; (2). PPVC-LPS Hybrid LWC building. The Cast-in-situ LWC building (Fig. 4.) has a total height of 45 m, length 113.4 m, and width of 42 m. The floor height is equally distributed amongst 10 floors, with each floor height at 4.5 m. On top of that, the spacing between columns is standardised at 8.4 m, both horizontally and laterally. Furthermore, there are in total 4 sets of shear walls, including 2 staircase cores and 2 groups of lift cores.

Fig. 4. Cast-in-situ LWC building modelled in SAP2000

The PPVC-LPS Hybrid LWC building (Fig. 5.) has a total height of 45 m, length 114.3 m, and width of 42.1 m. The floor height is equally distributed amongst 10 floors, with each floor height at 4.5 m. The total height of the PPVC-LPS LWC module is 4500 mm, and the width of the module is 4500 mm, while the columns will be joined at every 3m above each floor level (Fig. 2). Stitching precast LPS slabs will be used to join the PPVC-LPS LWC modules. 4.3 Load Case and Load Combination Load cases refer to the predetermined conditions for the inherent or applied load use for analysis. Suitable design guides are developed to regulate the magnitude of loadings

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Fig. 5. PPVC-LPS Hybrid LWC building modelled in SAP2000

that are deemed to be adequate for developing building elements, with the consideration of safety and structural integrity. The load cases considered in the experimental analysis consist of Dead Load (Selfweight), Live Load, Superimposed Dead Load, Wind Load, Seismic Action, and Imperfection (EHF). All loadings are designed according to Eurocode 2 and modified to align with the Singapore National Annex to Eurocode 2. While the load combinations considered are Ultimate Limit State (ULS), Long Term Service Limit State (SLS), Seismic Analysis, and Staged Construction Analysis. To simulate staged construction analysis, maximum deflection is taken at various intermediate construction stage of the building, thereby highlighting potential excessive deflection of the building during construction, if any. The result from staged construction analysis ensures that the building is constructible even at the intermediate phase. Aside from stage construction, other mode of analysis such as ULS and SLS are taken at the final stage. At this stage, the full building has been constructed and the complete frame has been connected (Tables 2 and 3).

5 Result(s) and Discussion 5.1 Modal Period, Frequency, and Load Participation Ratio The fundamental natural period (T) is an inherent characteristic of a building. Conventionally, the fundamental natural period of a building, up to 20 storeys, is in the range of 0.05–2.00 s. Natural frequency of a building is the frequency that the building sways in

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Load Comb

1

2

3

Dead Load

1

1

1

Superimposed Dead Load

0.6

0.6

0.6

Live Load

0.6

0.6

0.6

Wind Load X

0

0

0

Wind Load Y

0

0

0

Imperfection/EHF (Dead Load−Global X Axis)

0

1

0

Imperfection/EHF (Dead Load−Global Y Axis)

0

0

1

Imperfection/EHF (Live Load−Global X Axis)

0

0.6

0

Imperfection/EHF (Live Load−Global Y Axis)

0

0

0.6

Imperfection/EHF (Superimposed Dead Load−Global X Axis)

0

0.6

0

Imperfection/EHF (Superimposed Dead Load−Global Y Axis)

0

0

0.6

when it recovers from its disturbed position, it is measured as the number of oscillations completed per unit time. Both Cast-in-situ LWC building and PPVC-LPS Hybrid LWC building, the period falls within 0.7–1.2 s. Comparing, the performance of the two buildings, the average period increased approximately by 7.7% (as shown in Table 4.). However, the period still falls within the range of 0.05–2.00 s, and within the expected range determined prior to the analysis. 5.2 Ultimate Limit State Analysis The load assigned to the structure in the ultimate limit state analysis includes the selfweight of the structural elements, live load, and superimposed dead load. The significant deviation of the analysis result comes in the Maximum Shear force on the columns in the Global Y axis. The maximum shear force on column at the Global Y axis for the PPVCLPS Hybrid LWC building is 138 kN, while the similar component in the Cast-in-situ LWC building is 37.6% higher, at a magnitude of 221 kN. This difference indicates a significant variation in the characteristics of the buildings, there might be a change in the load path when PPVC modular units and precast elements are connected. In other aspects, the performance under Ultimate Limit State is similar for both Cast-in-situ LWC building and PPVC-LPS Hybrid LWC building (Table 5).

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Table 3. Factors used for ultimate limit state analysis load combinations Load Comb

1

2

3

Dead Load

1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35

Superimposed Dead Load

1.5

Live Load

1.05 1.5

1.05 1.5

1.05 1.5

1.05 1.05 1.05 1.5

1.05 1.05

Wind Load X

0

0

0

0

0.75 0

1.5

1.5

Wind Load Y

0

0

0

0

0

Imperfection/EHF (Dead Load−Global X Axis)

1.35 1.35 0

0

1.35 1.35 1.35 1.35 0

Imperfection/EHF (Dead Load−Global Y Axis)

0

1.05 1.5

0

4

5

1.05 1.5

1.35 1.35 0

Imperfection/EHF 1.5 (Live Load−Global X Axis)

1.05 0

0

Imperfection/EHF 0 (Live Load−Global Y Axis)

0

1.5

1.05 0

Imperfection/EHF 1.05 1.5 (Superimposed Dead Load−Global X Axis)

0

0

Imperfection/EHF 0 (Superimposed Dead Load−Global Y Axis)

1.05 1.5

0

1.5

6

7

8

9

1.05 1.05 1.05 1.5

0.75 0

0

0

10

12

1.05 1.05 1.05

0

0.75 0

1.5

0

0

11

0

0.75 0

1.5

0

0

0

1.35 1.35 1.35 1.35

1.05 1.05 1.05 0

0

0

1.05 1.05 1.05

0

0

1.5

1.05 1.5

1.05 1.05 0

0

0

0

0

0

1.05 1.5

0

0

0

0

1.05 1.05

Table 4. Modal period and frequency CIS LWC building and PPVC-LPS Hybrid LWC building Cast-in-situ LWC building

PPVC-LPS Hybrid LWC building

Mode 1 Mode 2 Mode 3 Average Mode 1 Mode 2 Mode 3 Average Period (Sec) 1.07

0.96

0.71

0.91

1.18

1.01

0.75

0.98

Frequency 0.94 (Cycle/Sec)

1.04

1.41

1.13

0.85

0.99

1.34

1.06

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Table 5. Ultimate limit state analysis results for CIS LWC building and PPVC-LPS Hybrid LWC building Max. shear force on column (kN)

Max. overall deflection (%)

Global X

Global Y

Global X

Global Y

Cast-in-situ LWC building

259

221

0.0094

0.0108

PPVC-LPS Hybrid LWC building

259

138

0.0120

0.0124

Difference (%)

–

−37.6

–

–

5.3 Long Term Service Limit State Analysis Long term service limit state analysis is also carried out to analyse the performance of the two buildings under service limit state, taking into consideration the effect of creep and shrinkage in the long run. This is critical to ensure that the building designed is of satisfying performance within the design life required. The horizontal deflections for both the Cast-in-situ LWC building and the PPVC-LPS Hybrid LWC building are within the acceptable deflection limit of 0.4% (Table 6.). However, the deflections for the PPVC-LPS Hybrid LWC building are generally greater than the cast-in-situ LWC building using the same loading condition. This suggests that the overall strength of the PPVC-LPS Hybrid LWC building is lower than the Cast-in-situ LWC building. Alternatively, it might also suggest that there is a knock-on effect in the displacement of the PPVC or precast elements which might have resulted in the greater deflection. Table 6. Long term service limit state analysis results for CIS LWC building and PPVC-LPS Hybrid LWC building Max. displacement as a percentage of overall height

Cast-in-situ LWC Building (%)

PPVC-LPS Hybrid LWC Building (%)

Difference (%)

Global X

0.063

0.073

+0.010

Global Y

0.058

0.073

+0.015

Limit

0.4

0.4

–

5.4 Seismic Analysis The seismic analysis on the building is done in two aspects: Inter-storey drift and Separation from the property line. The design limit for inter-storey drift (dr ) of the building is calculated to be 47 mm or 0.047 m. Under seismic loading combinations, the maximum inter-storey drift of the buildings in both directions are below 0.02 m, below the limit

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of 0.047 m. Hence, the inter-storey drifts of the buildings are acceptable. Both buildings satisfy the requirement whereby separations from the property line in both axes are within the limit of 0.047 m (Fig. 6).

Fig. 6. Maximum Inter-storey drift for PPVC-LPS Hybrid LWC building and CIS LWC building

However, the overall building drift for the PPVC-LPS Hybrid LWC building is higher than that of the Cast-in-situ LWC building (Table 7). This may suggest that the PPVCLPS Hybrid LWC building tends to undergo larger displacement than the Cast-in-situ LWC building when it is subjected to the same seismic loading conditions. Table 7. Separation from property line for CIS LWC building and PPVC-LPS Hybrid LWC building Cast-in-situ LWC building

PPVC-LPS Hybrid LWC building

EQx drift−Global X (m)

0.0935

0.1174

EQy drift−Global Y(m)

0.0774

0.0846

Separation from property line (m)

Dx Separation (Global X)

0.1122

0.1409

Dy Separation (Global Y)

0.0929

0.1015

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5.5 Staged Construction Staged construction is solely applied to the PPVC-LPS Hybrid LWC building, where the building is analysed at each interim stage of construction. This is critical for DfMA construction, especially PPVC, where the construction is done in phases and the temporary stage might experience excessive deflection/deformation, resulting in structural failure. The staged construction simulates the actual construction sequence of the PPVCLPS Hybrid LWC building, where the cast-in-situ foundation will be constructed first, followed by the subsequent floors in stages. Results from Staged Construction analysis show that the deflections, for both Global X and Global Y axes, are within the deflection limit. Hence, there is no excessive deflection in the PPVC-LPS Hybrid LWC building during construction (Table 8). Table 8. Maximum displacement of PPVC-LPS Hybrid LWC building in staged construction analysis

PPVC-LPS Hybrid LWC building

Max. displacement (m)

Percentage of overall height (%)

Limit (%)

Global X

0.0102

0.0227

0.4

Global Y

0.0109

0.0242

0.4

6 Buildability The implementation of DfMA has emphasized the ever-so-important consideration of the constructability of the designed building. To allow the building to be more constructible, the building elements involved have to be simple, standardised, and safe. It is further highlighted that module assembly is a critical consideration when designing the joining techniques to be adapted in all projects (Pang et al. 2016). These characteristics are thereby exemplified through the utilisation of innovative and effective joining techniques, several joining techniques are considered for the PPVC-LPS Hybrid LWC building (Fig. 7). 6.1 Integrated Digital Delivery Integrated Digital Delivery (IDD) is the utilization of technologies to present a more holistic perspective of the full life cycle of a project via the integration of design, manufacturing and fabrication, construction, and facility management. IDD enables seamless collaboration between various stakeholders in the project and increases the efficiency of collaboration. There are two fundamental elements of IDD, Building Information Modelling (BIM) and Virtual Design and Construction (VDC). These elements complement each other and collaborate to simplify the different stages of a construction project, hence improving

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Fig. 7. Novel joint techniques implemented for PPVC-LPS Hybrid LWC building

the project in terms of time, cost, profit, and floor efficiency (Building and Construction Authority 2022). IDD is instrumental in ensuring the buildability of the PPVC-LPS Hybrid LWC construction, where both the construction process and design can be simulated and visualized before construction onsite. Furthermore, the usage of IDD allows the novel joints proposed to be of structural satisfaction. 6.2 Lotus Root Joint Lotus root joint is proposed for the vertical joint for the PPVC modules. Cast-in protruding reinforcement bars are included in the columns, these reinforcement bars are paired with the grout sleeve in the upper column to form the grouted splice sleeve. The lapping length to be used for the grout sleeve shall be designed to ensure the performance of the lotus root joint is satisfactory based on the preliminary assumed conditions. Ultimate limit state design is considered to ensure the safety of the design, and further optimization can be made to ensure the efficiency of design for practical purposes (Fig. 8). 6.3 Pour Stripe Pour stripes are essential for the effective incorporation of DfMA technologies. Most major roads and highways are subjected to the maximum transportable size limit imposed by the local authorities. As a result, to ensure that the modular units transported onsite are assembled desirably, and the constructed structure is monolithic, pour stripes are designed for the structure. The pour stripe should be sealed with proper grouting upon installation, while the rebar ratio and concrete grade used for the pour stripe shall be uniform with the slabs

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Fig. 8. Schematic diagram of lotus root connection for PPVC-LPS Hybrid LWC construction

joined to reduce the difference in expansion and displacement of the elements (Figs. 9 and 10).

Fig. 9. Schematic diagram of pour stripe for PPVC-LPS Hybrid LWC construction

6.4 Mechanical Connector The concealed mechanical connector is designed to connect the PPVC modules at the drop panel level. The mechanical connector utilises a lock and key mechanism, where the metal plate acts as a key and secures the connecting elements together upon installation on site. Having a mechanical connector concealed within the drop panel allows the mechanical space of the PPVC module to be uninterrupted and avoid any clash in utility

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Fig. 10. Schematic construction process showing pour stripe between PPVC-LPS Hybrid LWC modules and flat slab

installation. This also maximized the efficiency of the M&E space and allows better ventilation and airflow while the space is utilized later (Figs. 11 and 12). 6.5 Shear Key Shear key connection is calculated and designed to be located at every 1.5 m vertical interval along the column to along a more uniform and monolithic structure of the building. The shear key will utilize grouting of similar concrete grade to the other concrete elements so as to allow a more uniform expansion and displacement (Fig. 13).

7 Conclusions and Recommendations Comparing the analysis results, the two building models have similar model outputs for natural building characteristics such as building period and frequency. The analysis is done using three analysis conditions (1). Ultimate Limit State; (2). Long Term Service Limit State; and (3). Seismic Analysis. The analysis results show that the PPVC-LPS Hybrid LWC building’s performance is less desirable as compared to the Cast-in-situ LWC building. However, the deviation is within the acceptable range and the building

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Fig. 11. Schematic diagram of mechanical joint for PPVC-LPS Hybrid LWC construction

Fig. 12. Installation process of mechanical connector between adjacent PPVC-LPS Hybrid LWC construction

performance is still within the performance allowance stipulated by design code or authority requirements. However, there is a significant lower shear force on column surface in the PPVC-LPS Hybrid LWC building as compared to the Cast-in-situ LWC building. This difference in the results could be attribute to the load distribution and load path in the PPVC-LPS Hybrid LWC building might be different from that of the Cast-in-situ LWC building. The analysis mainly focused on the global analysis of the PPVC-LPS Hybrid LWC building. To simulate the horizontal connection between PPVC columns, a short horizontal beam is modelled as a simple pin joint. The actions at joints are to be further analysed and adopted with market available joint designs (for example lotus root joint

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Fig. 13. Schematic design of shear key between columns for PPVC-LPS Hybrid LWC construction

or shear key) or proposed novel joint for the PPVC-LPS Hybrid LWC building. Other aspects of constructability can also be studied to further improve the efficiency of implementation, these constructability aspects include the design of lifting frame and lifting hook position for the PPVC module and LPS flat slab panel. There are limited experiments and studies done on the crack mechanism and crack propagation within the light-weight concrete elements, especially large panel system. Future experimental data and studies might suggest a more holistic approach to the design, thereby improving the structure viability. In conclusion, the proposed PPVC-LPS Hybrid LWC building is analytically feasible. However, the constructability and installation need to be further developed to increase the viability of implementing this hybrid construction in the industry.

References Building and Construction Authority: Design for maintainability guide (Non-residential). Singapore: s.n. (2019) Building and Construction Authority: Design for manufacturing and assembly (DfMA). [Online] (2020). Available at: https://www1.bca.gov.sg/buildsg/productivity/design-for-manufacturingand-assembly-dfma. Accessed 27 Sept 2021 Building and Construction Authority: Benefits of adopting IDD. [Online] (2022). Available at: https://www1.bca.gov.sg/buildsg/digitalisation/integrated-digital-delivery-idd/benefits-ofadopting-idd. Accessed 3 Feb 2022 Housing & Development Board: Prefabrication technology. [Online] (2018). Available at: https://www.hdb.gov.sg/about-us/research-and-innovation/construction-productivity/ prefabrication-technology. Accessed 30 Apr 2022 Jallion, L., Poon, C.: Advantages and limitations of precast concrete construction in high-rise buildings. Hong Kong Case Studies. s.l., s.n (2007)

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Khare, R., Uma, S., Manlyar, M.M.: Seismic performance and design of precast concrete building structures: An overview. J. Struct. Eng. (Madras) 272–284 (2011) Land Transport Authority: Design for manufacturing and assembly (DfMA)—prefabricated prefinished volumetric construction. Singaproe: s.n. (2020) Pang, S.D., Liew, J.Y.R., Dai, Z., Wang, Y.: Prefabricated prefinished volumetric construction joining techniques review. Steel Struct. 249–256 (2016) Rossignolo, J., Agenesini, M., Morais, J.: Properties of high-performance LWAC for precast structure with Brazilian lightweight aggregates, s.l.: Elsevier Science Ltd. (2002) Turai, V., Wsghmare, A.: A study of cost comparison of precast concrete versus cast-in-place. Int. J. Recent Innov. Trends Comput. Commun. 3(11), 6235–6238 (2015)

Study of Initial Imperfection of Concrete-Filled Square Steel Tube Columns for Direct Analysis Zijuan Zhang1 , Jiale Xing1 , Yao-Peng Liu2,3(B) , and Guochang Li1 1 School of Civil Engineering, Shenyang Jianzhu University, Shenyang 110168, China 2 Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University,

Hong Kong, China [email protected] 3 NIDA Technology Company Limited, Hong Kong Science Park, Hong Kong, China

Abstract. The initial imperfection and residual stress play important roles in the buckling resistance of both structural system and structural members. The latest Standard for Design of Steel Structures (GB50017-2017) firstly introduces the direct analysis method for the stability design of steel structures in China. The equivalent initial imperfections for steel members have been well specified in this code. However, as an important part of modern structures, there is limited research on the initial imperfections of steel-concrete composite members in relevant regulations in China. Therefore, it is urgent to study the equivalent initial imperfections of steel-concrete members for direct analysis. This paper collects extensive experimental data on concrete-filled square steel tube columns (CFSSTC) for calibration of finite element models using software ABAQUS. The key factors affecting CFSSTC’s behaviors such as section dimensions, grades of steel and concrete, and width-to-thickness ratios have been taken into account. A comparative analysis for the CFSSTC with and without initial imperfections will be presented. From this study, the equivalent initial imperfection for CFSSTCs will be proposed for practical direct analysis of steel-concrete composite structures to achieve a safer and economical design without use of conventional effective length method. Keywords: Concrete-filled square steel tube column · Initial imperfection · Direct analysis method · Finite element analysis (FEA)

1 Introduction In the concrete-filled steel tube columns (CFSTC), the steel tube is used as a component to restrain the lateral expansion of the inner filled concrete, while the infilled concrete can prevent the local buckling of the outer steel tube. Thus, the steel tube and the concrete can fully exert their respective properties and the mechanical performance of the CFSTC can be significantly improved. In addition, the steel tube can be used as the pouring formwork of concrete to shorten construction time and minimize environmental impact. With the rapid development of China’s economic construction, the building structures are constantly breaking through in span and height, while the building shape has become more complex. At the same time, various high-strength and high-performance materials © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 565–580, 2023. https://doi.org/10.1007/978-981-19-7331-4_46

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are continuously introduced. These factors make the slenderness ratios of the structures and structural elements larger with significant increase of second-order effects. Also, the load path becomes complex. Thus, the conventional linear analysis method cannot provide a good prediction on the structural responses. The effective length method based on linear analysis for stability design faces great challenges in practical engineering. CFSTCs are widely used in building structures because of their high bearing capacity, good ductility and superior seismic performance. The uncertainty in determination of effective length for stability design of CFSTCs will limit their application. The direct analysis method for stability design based on structural system can adapt to the development of various new systems, new shapes and new materials, with consideration of the influence of second-order effects and other nonlinear factors in the analysis process. By doing so, the most unfavorable internal force distribution can be obtained and therefore only the strength checking is needed without assumption of effective length, leading to a safe design and economic design. In the numerical simulation of the concrete-filled square steel tube columns (CFSSTC) under axial compression, the section capacity of CFSSTC without initial imperfection deviates from the test results, which may be due to the ignorance of the possible imperfection such as the initial bowing of the column. Therefore, it is necessary to consider the equivalent initial geometric imperfection in the practical design. The shape of equivalent initial geometric imperfection can follow the lowest buckling mode. However, due to the different sensitivity of different structural forms to imperfection, each design code may specify the amplitude of the imperfection value according to the characteristics of the structural system. The latest Standard for Design of Steel Structures (GB50017-2017) introduces the direct analysis method for the first time, and makes corresponding provisions on the design of steel structures by the direct analysis method. The equivalent initial geometric imperfection of steel members lays a foundation for the overall analysis of steel structures. Not that as an important part of modern structures, the steel-concrete composite members are rarely mentioned in China’s relevant codes or regulations, resulting in engineers having no relevant code provisions to consult when designing steel-concrete composite structures. Therefore, it is necessary to carry out comprehensive research on CFSTC from traditional design methods to experimental research considering various section sizes, loading conditions and materials. A large number of research studies on CFSSTC can be found in the literature (Han and Tao 2019; Cai and Jiao 1984; Kenji et al. 2004; Masahide 1977; Zhang and Zuo 1985; Han 2002). For CFSSTC, the experimental tests and finite element analysis are carried out accounting for different parameters such as design strength, width-to-thickness ratio, slenderness ratio and so on. There are few studies on the initial imperfection of CFSSTC. For this reason, this paper takes axially compressed CFSSTC members (Joachim 2018) as the research object. In order to put forward the equivalent initial geometric imperfection of CFSSTC suitable for Chinese standards, the test results from China, American and other countries on CFSTC are collected. This paper provides theoretical and design basis for the direct analysis method of CFSSTCs.

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2 Concrete Filled Square Steel Square Tube Column Considering Imperfection 2.1 Initial Geometric Imperfection In steel standards, the mode of initial imperfection in the component geometry can be defined as: πx δ0 = e0 sin (1) l in which, x is the distance from the first end of the member; δ0 is the initial deformation at x; e0 is the initial bowing at the middle of the member; l is the member length. The equivalent geometric imperfection of the member (Du et al. 2019a, b) is shown in Fig. 1.

Fig. 1. Equivalent geometric imperfection

2.2 Residual Stress of Steel Initial material imperfection generally refers to residual stresses that are widely existing in hot-rolled or welded steel members. Residual stress is mainly caused by processes such as rolling, welding and cold forming. Residual stresses are self-balancing stresses in the members, and the stress distribution patterns have a great correlation with the shape of the cross-section. As an initial mechanical imperfection, residual stress will cause early yield and cracks of the member, and is also one of the factors affecting the stability performance of the axially loaded members. Therefore, the influence of residual stresses also needs to be considered in the design of CFSTCs.

3 Experimental Test Data In order to study the influence of initial imperfection on CFSSTC, this paper collects nearly 100 sets of test data from literature. The data sources are shown in Table 1. The specimens adopted in this study are listed in Table 2. According to the section sizes and boundary conditions of CFSSTC in literatures, the finite element models are established in ABAQUS. Among them, considering the introduction of different initial imperfection, it’s necessary to introduce different amplitudes as scale factors for buckling mode shape. The scale factor is generally a few thousandths of the length of the member or a few percent of the shell thickness. The details and the procedure of introduction of initial geometric imperfection will be described in Sect. 46.3.

568

Z. Zhang et al. Table 1. Summary of experimental test data

No.

Number of specimens

Source of experimental tests

1

20

Han and Tao (2001)

2

48

Kenji et al. (2004)

3

6

Slawomir and Muhammad (2019)

4

8

Han and Yang (2001)

5

6

Han and Yao (2004)

6

10

Guo et al. (2008)

4 Finite Element Model To study the influence of initial imperfections, a finite element model for an axially loaded CFSSTC member with pinned-pinned boundary condition is established in ABAQUS. 4.1 Constitutive Model of Materials 4.1.1 Constitutive Model of Steel The stress-strain relationship of low-carbon steel such as Q235, Q345 and Q390 can generally be divided into five stages (Han 2016), which is expressed in Eq. (2) below: ⎧ ⎪ Es εs εs ≤ εe ⎪ ⎪ ⎪ 2 ⎪ ⎨ −Aεs + Bεs + C εe < εs < εe1 fy εe1 < εs < εe2 σs = (2) ⎪ εs −εe2 ⎪ ⎪ f [1 + 0.6 ] ε < ε < ε y e2 s e3 ⎪ εe3 −εe2 ⎪ ⎩ 1.6fy εs > εe3 with

⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

εe = 0.8fy /Es εe1 = 1.5εe εe2 = 10εe1 εe3 = 100εe1 ⎪ ⎪ ⎪ A = 0.2fy /(εe1 − εe )2 ⎪ ⎪ ⎪ ⎪ B = 2Aεe1 ⎪ ⎪ ⎩ C = 0.8fy + AεE2 − Bεe

(3)

4.1.2 Constitutive Model of Concrete The constitutive relationship model of concrete adopts the model of longitudinal stress (σ)-strain (ε) of core concrete proposed by Han (2016):  2x − x2 (x ≤ 1) (4) y= x β0 (x−1)η +x (x > 1)

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Table 2. Details of CFSSTC specimens No.

Specimen

B×t×L (mm)

Steel fy (MPa)

Steel fu (MPa)

Concrete fcu (MPa)

Resistance Nc (kN)

1

CFSSTC-1

120 × 3.8 × 360

330.1

528.16

52.5

1078.0

2

CFSSTC-2

140 × 3.8 × 420

330.1

528.16

54.6

1499.4

3

CFSSTC-3

120 × 5.9 × 360

321.1

513.76

52.5

1372.0

4

CFSSTC-4

140 × 5.9 × 420

321.1

513.76

54.6

1906.1

5

CFSSTC-5

200 × 5.9 × 600

321.1

513.76

17.6

1960.0

6

CFSSTC-6

180 × 1.49 × 553

222.7

356.32

55.6

1788.0

7

CFSSTC-7

150 × 1.45 × 463

222.7

356.32

55.6

1300.0

8

CFSSTC-8

135 × 1.44 × 418

222.7

356.32

55.6

1216.0

9

CFSSTC-9

120 × 1.49 × 372

222.7

356.32

54.3

916.0

10

CFSSTC-10

140 × 5.9 × 420

321.1

513.76

16.3

1342.6

11

CFSSTC-11

120 × 5.9 × 360

321.1

513.76

25.8

1080.0

12

CFSSTC-12

120 × 5.9 × 360

321.1

513.76

30.0

1117.2

13

CFSSTC-13

140 × 3.8 × 420

330.1

528.16

16.0

940.8

14

CFSSTC-14

140 × 3.8 × 420

330.1

528.16

16.7

921.6

15

CFSSTC-15

120 × 3.8 × 360

330.1

528.16

27.3

882.0

16

CFSSTC-16

120 × 3.8 × 360

330.1

528.16

31.2

921.2

17

CFSSTC-17

120 × 3.8 × 360

330.1

528.16

49.3

1080.0

Note: B/t is ranging from 20.3 to 120.8

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⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

x = ε/ε0 y = σ/σ0 σ0 = fc ε0 = εc + 800ξ 0.2 × 10−6 ⎪ εc = (1300 + 12.5fc ) × 10−6 ⎪ ⎪ ⎪ ⎪ η = 1.6 + 1.5/x ⎪ ⎪ √ ⎪ ⎪ = (fc )0.1 /(1.2 1 + ξ ) β ⎪ 0 ⎪ ⎩ ξ = (fy As )/(fck Ac )

(5)

4.2 Finite Element Model The finite element model of the CFSSTC column subjected to axial compression is established in ABAQUS. All the components of the column are modeled by solid element C3D8R. The steel tube-concrete interface adopts friction contact and hard contact with a friction coefficient of 0.6. The end plate-concrete adopts hard contact, while the end plate and steel pipe are connected by tie elements. The boundary conditions and applied load are shown in Fig. 2. 4.3 Procedure of Consideration of Initial Imperfections 4.3.1 Eigenvalue Buckling Analysis To impose the initial imperfection for a member, the linearized buckling analysis should be carried out to obtain the buckling mode: |KL + λKG | = 0

(6)

in which, KL is the linear stiffness matrix; KG is the geometric stiffness due to the loads. 4.3.2 Geometrical and Material Nonlinearity Analysis Before performing geometrical and material nonlinear analysis, the initial imperfection should be taken into account by offsetting the nodal coordinates by following the buckling mode shape. The keywords “*imperfection, file = buckle” (the job name of the eigen buckling analysis), step = 1” command is required to introduce the initial deformation. In the nonlinear analysis allowing for geometrical and material nonlinearity, the displacement control plus correction of the arc length method is adopted for incrementaliterative nonlinear solution. 4.3.3 Amplitude of Initial Imperfection for CFSSTC According to GB50017 (2017), the initial member imperfections vary from L/400 to L/250 for steel members. There is no doubt that the ultimate bearing capacity of CFSSTC will be reduced if the initial imperfection is included. However, there is limited research on the determination of initial imperfections for steel-concrete composite members. Thus, this paper aims to study the amplitude of initial imperfection for CFSSTC members.

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Fig. 2. Finite element model in ABAQUS

4.4 Calibration of Finite Element Model To study the influence of initial imperfections, a finite element model is established using the commercial software ABAQUS to predict the axial resistance of the CFSSTCs. As no initial imperfections were reported in the literature, three equivalent initial geometric imperfections are assumed to study the sensitivity of amplitudes on the ultimate bearing capacity of the CFSSTCs, as listed in Table 3. To clearly demonstrate the contribution of initial imperfection, a model “0” without imperfection is also presented. The comparison of axial resistance with different imperfections are shown in Tables 4 and 5. Table 3. Sensitivity study of initial geometric imperfection Model

Initial bowing imperfection, e0

0

0 (no imperfection)

1

3L/1000

2

L/1000

3

L/3000

In Tables 4 and 5, Nc is the ultimate bearing capacity obtained from the experimental test, while Nei is obtained from the proposed finite element model with different amplitude of initial imperfection. From Table 4, it can be clearly seen that the numerical results without consideration of initial imperfections are higher than the test results, which demonstrate that the initial imperfections should be included in the finite element model. Note that both the constitutive models of steel and concrete do not contain the material imperfection and therefore they may over-predict the capacity of CFSSTCs. Similarly, Du et al. (2019a,

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Z. Zhang et al. Table 4. Comparison of axial resistance with different imperfections (e0 = 0)

Specimen

Nc (kN)

Ne0

Ne0 /Nc

CFSSTC-1

1078.0

1161.0

1.157

CFSSTC-2

1499.4

1614.9

1.074

CFSSTC-3

1372.0

1477.6

1.085

CFSSTC-4

1906.1

2052.9

1.002

CFSSTC-5

1960.0

2110.9

1.031

CFSSTC-6

1788.0

1925.7

1.033

CFSSTC-7

1300.0

1400.1

1.137

CFSSTC-8

1216.0

1309.6

1.034

CFSSTC-9

916.0

986.5

1.107

CFSSTC-10

1342.6

1503.7

1.120

CFSSTC-11

1080.0

1123.3

1.040

CFSSTC-12

1117.2

1158.7

1.037

CFSSTC-13

940.8

1059.3

1.126

CFSSTC-14

921.6

1069.5

1.160

CFSSTC-15

882.0

926.1

1.050

CFSSTC-16

921.2

1038.8

1.128

CFSSTC-17

1080.0

1123.4

1.040

b) recommends additional geometric imperfection of L/500 is required for noncompact and slender concrete-filled steel tube members using effective stress method. From Table 5, the bearing capacity is reduced by about 6% when the initial imperfection (e0 = 3L/1000) is considered, compared with that without considering the initial imperfection. The bearing capacities assuming initial imperfections e0 = L/1000 and e0 = L/3000 are very close, which are greater than the case of e0 = 3L/1000. From the above, it can be concluded that the initial imperfection will reduce the bearing capacity of the CFSSTCs.

5 Contrastive Analysis 5.1 Influence of Amplitude of Initial Imperfections When the amplitude of equivalent initial geometric imperfection e0 for scaling the firstorder mode introduced is less than L/1000, the ultimate bearing capacity of CFSSTCs does not change significantly. However, when the amplitude e0 is assumed as 3L/1000, the ultimate bearing capacity of CFSSTC is reduced largely. Therefore, the amplitude e0 from L/1000 to 3L/1000 are studied for CFSSTCs. Totally five equivalent initial imperfections as listed in Table 6 are investigated. The bearing capacities of CFSSTCs

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Table 5. Comparison of axial resistance with different imperfections Specimen

Nc (kN)

e0 = 3L/1000

e0 = L/1000

e0 = L/3000

Ne1

Ne1 /Nc

Ne2

Ne2 /Nc

Ne3

Ne3 /Nc

CFSSTC-1

1078.0

1013.3

0.940

1072.6

0.995

1075.8

0.998

CFSSTC-2

1499.4

1415.4

0.944

1490.4

0.994

1493.4

0.996

CFSSTC-3

1372.0

1293.8

0.943

1364.5

0.995

1366.5

0.996

CFSSTC-4

1906.1

1797.5

0.943

1896.5

0.995

1898.6

0.996

CFSSTC-5

1960.0

1844.4

0.941

1950.2

0.995

1952.2

0.996

CFSSTC-6

1788.0

1689.7

0.945

1779.1

0.995

1782.6

0.997

CFSSTC-7

1300.0

1220.7

0.939

1293.5

0.995

1294.8

0.996

CFSSTC-8

1216.0

1134.5

0.933

1209.9

0.995

1211.1

0.996

CFSSTC-9

916.0

861.0

0.940

912.3

0.996

913.3

0.997

CFSSTC-10

1342.6

1266.1

0.943

1335.9

0.995

1338.6

0.997

CFSSTC-11

1080.0

1019.5

0.944

1074.6

0.995

1076.8

0.997

CFSSTC-12

1117.2

1052.4

0.942

1112.7

0.996

1113.8

0.997

CFSSTC-13

940.8

887.2

0.943

936.1

0.995

938.0

0.997

CFSSTC-14

921.6

870.0

0.944

917.0

0.995

918.8

0.997

CFSSTC-15

882.0

830.8

0.942

877.6

0.995

879.4

0.997

CFSSTC-16

921.2

868.7

0.943

916.6

0.995

917.5

0.996

CFSSTC-17

1080.0

1018.4

0.943

1073.5

0.994

1077.8

0.998

Table 6. Initial geometric imperfection for parametric study Model

Initial bowing imperfection, e0

4

L/900

5

L/800

6

L/700

7

L/600

8

L/500

with the different amplitude of initial imperfections obtained from the finite element model are presented in Tables 7, 8, 9 and 10. As the behaviours of CFSSTC-1 to CFSSTC-17 are similar, only CFSSTS-1 and CFSSTC-2 are discussed as follows. Figure 3 shows the deformed shape of CFSSTS1 and CFSSTC-2 under axial load with consideration of initial imperfections. Figure 4 shows the load-axial strain curves of CFSTCC-1 and CFSSTC-2 with different amplitude of initial imperfections. Clearly, the introduction of initial imperfections will reduce the

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Z. Zhang et al. Table 7. Axial resistance of CFSSTC-1 to CFSSTC-4

Specimen

CFSSTC-1

CFSSTC-2

CFSSTC-3

CFSSTC-4

1161.0

1614.9

1477.6

2052.9

Test result

Ne0 (kN)

Model 4 (e0 = L/900)

Ne4

1154.0

1605.2

1468.7

2036.4

(Ne4 /Ne0 )

(0.994)

(0.994)

(0.994)

(0.992)

Model 5 (e0 = L/800)

Ne5

1144.7

1595.5

1461.3

2032.3

(Ne5 /Ne0 )

(0.986)

(0.988)

(0.989)

(0.990)

Model 6 (e0 = L/700)

Ne6

1138.9

1585.8

1446.5

2015.9

(Ne6 /Ne0 )

(0.981)

(0.982)

(0.979)

(0.982)

Model 7 (e0 = L/600)

Ne7

1125.0

1568.0

1433.2

1993.3

(Ne7 /Ne0 )

(0.969)

(0.971)

(0.970)

(0.971)

Model 8 (e0 = L/500)

Ne8

1121.5

1558.3

1427.3

1974.8

(Ne8 /Ne0 )

(0.966)

(0.965)

(0.966)

(0.962)

Table 8. Axial resistance of CFSSTC-5 to CFSSTC-9 Specimen Test result

CFSSTC-5 CFSSTC-6 CFSSTC-7 CFSSTC-8 CFSSTC-9 Ne0 (kN)

2110.9

1925.7

1400.1

1309.6

986.5

Model 4 Ne4 2087.7 (e0 = L/900) (N /N ) (0.989) e4 e0

1906.4

1388.9

1297.8

980.6

(0.990)

(0.992)

(0.991)

(0.994)

Model 5 Ne5 2083.5 (e0 = L/800) (N /N ) (0.987) e5 e0

1894.9

1377.7

1288.6

977.622

(0.984)

(0.984)

(0.984)

(0.991)

1875.6

1367.9

1278.2

966.8

Model 6 Ne6 2060.2 (e0 = L/700) (N /N ) (0.976) e6 e0

(0.974)

(0.977)

(0.976)

(0.980)

Model 7 Ne7 2037.02 (e0 = L/600) (N /N ) (0.965) e7 e0

1854.5

1352.5

1263.8

954.9

(0.963)

(0.966)

(0.965)

(0.968)

Model 8 Ne8 2022.2 (e0 = L/500) (N /N ) (0.958) e8 e0

1846.8

1339.9

1254.6

953.9

(0.959)

(0.957)

(0.958)

(0.967)

bearing capacity of CFSSTCs. As shown in Fig. 5, the abscissa is the model number representing the different initial imperfections, while the ordinate is the ratio of each case to the no initial imperfection case. From Fig. 5 and Tables 7, 8, 9 and 10, when the amplitude e0 is L/600, the bearing capacity of the specimen has dropped significantly, the decline is about 3%, at this time the impact of the initial imperfection on the bearing capacity cannot be ignored; when the amplitude e0 is L/500, the impact of the initial imperfection on the bearing capacity is more obvious, and the bearing capacity drops by about 3.5%.

Study of Initial Imperfection of Concrete-Filled Square Steel

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Table 9. Axial resistance of CFSSTC-10 to CFSSTC-13 Specimen

CFSSTC-10

CFSSTC-11

CFSSTC-12

CFSSTC-13

1503.7

1123.3

1158.7

1059.3

Test result

Ne0 (kN)

Model 4 (e0 = L/900)

Ne4

1494.7

1115.4

1150.6

1052.9

(Ne4 /Ne0 )

(0.994)

(0.993)

(0.993)

(0.994)

Model 5 (e0 = L/800)

Ne5

1485.7

1110.9

1143.6

1048.7

(Ne5 /Ne0 )

(0.988)

(0.989)

(0.987)

(0.990)

Model 6 (e0 = L/700)

Ne6

1475.1

1099.7

1135.5

1038.1

(Ne6 /Ne0 )

(0.981)

(0.979)

(0.980)

(0.980)

Model 7 (e0 = L/600)

Ne7

1455.6

1090.7

1121.6

1026.5

(Ne7 /Ne0 )

(0.968)

(0.971)

(0.968)

(0.969)

Model 8 (e0 = L/500)

Ne8

1451.1

1081.7

1117.0

1023.3

(Ne8 /Ne0 )

(0.965)

(0.963)

(0.964)

(0.966)

Table 10. Axial resistance of CFSSTC-14 to CFSSTC-17 Specimen

CFSSTC-14

CFSSTC-15

CFSSTC-16

CFSSTC-17

Test result

Ne0 (kN)

1069.5

926.1

1038.8

1123.4

Model 4 (e0 = L/900)

Ne4

1062.0

918.7

1031.5

1116.7

(Ne4 /Ne0 )

(0.993)

(0.992)

(0.993)

(0.994)

Model 5 (e0 = L/800)

Ne5

1054.5

914.1

1025.3

1108.8

(Ne5 /Ne0 )

(0.986)

(0.987)

(0.987)

(0.987)

Model 6 (e0 = L/700)

Ne6

1049.2

908.5

1017.0

1100.9

(Ne6 /Ne0 )

(0.981)

(0.981)

(0.979)

(0.980)

Model 7 (e0 = L/600)

Ne7

1039.6

897.4

1007.6

1088.6

(Ne7 /Ne0 )

(0.972)

(0.969)

(0.970)

(0.969)

Model 8 (e0 = L/500)

Ne8

1031.0

894.6

1002.4

1081.8

(Ne8 /Ne0 )

(0.964)

(0.966)

(0.965)

(0.963)

It can be seen that the initial imperfection will reduce the bearing capacity of CFSSTCs. When the scale factor (e0 ) of the first-order mode introduced is less than L/600, the impact of the initial imperfection on the bearing capacity is not obvious, while it is greater than L/600 the impact of the initial imperfection on the bearing capacity cannot be ignored.

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Z. Zhang et al.

(a) CFSSTC-1

(b) CFSSTC-2

Fig. 3. Deformed shape of CFSSTCs

(a) CFSSTC-1

(b) CFSSTC-2

Fig. 4. Load-axial strain curves

5.2 Comparison with Specification In order to verify the accuracy of the proposed equivalent initial imperfection for CFSSTCs, the simulation results of the model without imperfection are compared with the design results based on the Technical code for concrete filled steel tubular structures (GB 50936-2014). The structural detailing requirements in the parametric study are complied with this code.

Study of Initial Imperfection of Concrete-Filled Square Steel 1.2

1.2 0.994

0.986

0.981

0.969

1.0

0.966

0.8

Nei / Ne0

Nei / Ne0

1.0

0.6

0.2

0.2

5

6 Model

7

8

0.988

4

5

0.982

0.971

0.965

7

8

0.6 0.4

4

0.994

0.8

0.4

0.0

577

0.0

(a) CFSSTC-1

6 Model

(b) CFSSTC-2

Fig. 5. Comparison of calculation results for different imperfections

For the axial compression CFSSTCs, GB50936-2014 provides the equations as below to determine the bearing capacity N0 : ⎧ ⎪ N0 = fsc Asc ⎪ ⎪ ⎪ ⎪ f = (1.212 + Bθ + Cθ 2 )fc ⎨ sc (7) B = 0.131f 213 + 0.723 ⎪ 0.070fc ⎪ ⎪ C = − + 0.026 ⎪ 14.4 ⎪ ⎩ θ = As f /Ac fc in which, Asc is the section area of CFST; B is coefficient of influence of cross-sectional shape on the hoop effect; fsc is the characteristic compressive strength of CFST; f is the characteristic compressive strength of the steel; fc is the characteristic concrete compressive strength; θ is the coefficient of confinement effect; N0 is the bearing capacity of axial compression member. 5.3 Comparison of Axial Resistance By using Eq. 7, the bearing capacity N0 of the CFSSTCs are calculated and compared with the test results in Table 11. From Table 11, the design results from the GB50936-2014 are lower than the test results and on the safe side with μ = 0.840 and σ = 0.053. Thus, it is proved that the bearing capacity of the CFSSTCs meets the requirements of the specification. The finite element model with the proposed equivalent initial imperfection also meets the requirements of the specification.

6 Influence of Width-to-Thickness Ratios Based on the above analysis, five finite element models for CFSSTC 1 under axial load are established with different thicknesses of steel tube (i.e. t from 3 mm to 8 mm) to study the influence of width-to-thickness ratio. The settings for boundary conditions and

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Z. Zhang et al. Table 11. Comparison of axial resistance of 17 CFSSTCs

Specimen

N0

N0 /Ne0

N0 /Ne8

CFSSTC-1

1068.8

0.921

0.953

CFSSTC-2

1409.8

0.873

0.905

CFSSTC-3

1251.7

0.847

0.877

CFSSTC-4

1645.9

0.802

0.833

CFSSTC-5

1869.5

0.886

0.924

CFSSTC-6

1657.3

0.861

0.898

CFSSTC-7

1173.4

0.838

0.876

CFSSTC-8

963.5

0.736

0.768

CFSSTC-9

763.9

0.774

0.801

CFSSTC-10

1170.9

0.779

0.807

CFSSTC-11

1004.2

0.894

0.929

CFSSTC-12

1035.5

0.894

0.927

CFSSTC-13

847.4

0.800

0.828

CFSSTC-14

855.5

0.800

0.830

CFSSTC-15

795.4

0.859

0.889

CFSSTC-16

835.5

0.804

0.833

CFSSTC-17

1032.9

0.919

0.955

Note: N0 is determined from GB 50936(2014); Ne0 is from experimental test; Ne8 is from finite element analysis with consideration of initial imperfection of L/500

Table 12. CFSSTC 1 with different B/t ratios Model

B×t×L

B/t

fy (MPa)

fcu (MPa)

CFSSTC 1-1

120 × 4 × 600

30.0

345

40

822.1

CFSSTC 1-2

120 × 5 × 600

24.0

345

40

923.7

CFSSTC 1-3

120 × 6 × 600

20.0

345

40

1012.9

CFSSTC 1-4

120 × 7 × 600

17.1

345

40

1087.0

CFSSTC 1-5

120 × 8 × 600

15.0

345

40

1142.9

Nu (kN)

Note: Nu is the ultimate bearing capacity from finite element analysis

applied load of the finite element model are shown in Fig. 2. The specific parameters and the numerical results are shown in Table 12. Figure 6 shows the load-axial strain curves of the CFSSTC 1, taking account of different width-to-thickness ratios (B/t) and the equivalent initial imperfections (e0 ). It can be seen that when the amplitude e0 is L/600 and the B/t is increased from 15.0 to 40.0, the decrease range of the ultimate bearing capacity of CFSSTCs increases from

Study of Initial Imperfection of Concrete-Filled Square Steel

(a) e0 =L/600

579

(b) e0 =L/500

Fig. 6. Influence of width-to-thickness ratio

2.2% to 3.1%. When the amplitude e0 is L/500 and the B/t is increased from 15.0 to 40.0, the decrease range of the ultimate bearing capacity of CFSSTCs increases from 3.1% to 3.7%.

7 Conclusions In this paper, the equivalent initial geometric imperfection of CFSSTCs for direct analysis are studied by using finite element analysis against the experimental test data. The influence of width-to-thickness ratio is also studied in this paper. The following conclusions can be drawn from the scope of the study in this paper: 1) The initial imperfection will reduce the bearing capacity of the CFSSTCs. Thus, the initial imperfection should be included in the numerical simulation or in the direct analysis without use of effective length for stability design. 2) When the amplitude of initial geometric imperfection e0 is L/500, the bearing capacity of CFSSTCs is reduced by about 3% and therefore the impact of the initial imperfection cannot be ignored. It is recommended that the equivalent initial geometric imperfection of CFSSTCs in the direct analysis of practical projects should be not less than L/500. 3) When considering the initial imperfections, the bearing capacity of the CFSSTCs reduces with increase of the width-to-thickness ratio. The influence of slenderness ratio and confinement effect have not been included in current study, which will be reported in our future works.

References Cai, S.-H., Jiao, Z.-H.: Behavior and ultimate strength of short concrete-filled steel tubular columns. J. Build. Struct. 06, 13–29 (1984)

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Du, Z., et al.: Second-order elastic-plastic analysis for direct analysis method. Build. Struct. 49(16), 72–77 (2019a) Du, Z.-L., Liu, Y.-P., He, J.-W., Chan, S.-L.: Direct analysis method for noncompact and slender concrete-filled steel tube members. Thin-Walled Struct. 135, 173–184 (2019b) Guo, L., et al.: Behavior of concrete-filled SHS steel tubes under different loading conditions. Eng. Mech. 09, 143–148 (2008) GJB 4142-2000: Technical specifications for early-strength model composite structure used for navy port emergency repair in wartime. The general logistics department of PLA.2001 (2001) Han, L.-H., Zhong, T.: Study on behavior of concrete filled square steel tubes under axial load. China Civil Eng. J. 02, 17–25 (2001) Han, L.-H.: Tests on stub columns of concrete-filled RHS sections. J. Constr. Steel Res. 58(3) (2002) Han, L.-H., Yang, Y.-F.: Influence of concrete compaction on the behavior of concrete filled steel tubes with rectangular sections. In: Advances in Structural Engineering, vol. 4(2) (2001) Han, L.-H., Yao, G.-H.: Experimental behaviour of thin-walled hollow structural steel (HSS) columns filled with self-consolidating concrete (SCC). In: Thin-Walled Structures, vol. 42(9) (2004) Han, L.-H.: Concrete Filled Steel Tubular Structures-Theory and Practice, 3rd edn. Science Press, Beijing (2016) Joachim, L., Kuhlmann, U., Jörg, F.: Initial bow imperfections e0 for the verification of flexural buckling according to Eurocode 3. Part 1-1—Additional considerations. Steel Constr. 11(1), 30–41 (2018) Kenji, S., Hiroyuki, N., Shosuke, M., Isao, N.: Behavior of centrally loaded concrete-filled steeltube short columns. J. Struct. Eng. 130(2) (2004) Masahide, T.: Experimental studies on concrete filled steel tubular stub columns under concentric loading. In: Proceedings of International Colloquium on Stability of Structures Under Static and Dynamic Loads, SSRC/ASCE/Washington, DC. (1977) Slawomir, K., Muhammad, O.A.: Concrete-filled steel tubular (CFTS) columns subjected to eccentric compressive load. AIP Conf. Proc. 2060(1) (2019) Standard for design of steel structures:GB50017-2017[S]. China Architecture & Building Press, Beijing (2018) Zhang, Z., Zuo, M.: Study on basic performance of concrete filled square steel tubular short columns under short-term primary static load. J. Zhengzhou Univ. Technol. 02, 19–32 (1985)

Nonlinear Coupled Thermal-Structural Analysis of Monolithic and Precast Concrete Corbel Beam-to-Column Connection Noor Azim Mohd. Radzi, Shanmugam Muniandy, Fadlin Sakina Ismasafie, and Roszilah Hamid(B) Department of Civil Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D. E.,, Malaysia {p100973,a165894,a165633}@siswa.ukm.edu.my, [email protected]

Abstract. In this paper, a nonlinear coupled thermal-structural analysis is executed using ANSYS Workbench to simulate the fire performance of monolithic and precast concrete corbel beam-to-column connection at high temperatures. The monolithic models, namely M22-S and M600-S, represent the testing temperatures of 22 °C and 600 °C. The precast concrete corbel models, namely C22-S and C400-S, represent the testing temperatures of 22 °C and 400 °C. The models are simulated to failure under incremental point loads at the end of the beam that produced hogging moments to the connections. The response of the models is validated against the load-deflection curves and toughness of connections from the previous experimental test. The relative connection performance at ambient and high temperatures is evaluated and discussed. The load-deflection curves for connections M22, M600, and C22 show a good agreement between the simulation and experimental results. The load-deflection curves are reduced with increasing temperatures. The toughness for connections M22, M600, and C22 (simulation and experimental) has verified the accuracy and applicability of the proposed simulation model. The toughness results show that the connection at ambient temperature (M22 and C22) has higher fracture resistance than at high temperatures (M600 and C400). The validation result of nonlinear coupled thermal-structural analysis executed using ANSYS Workbench gives good efficiency for predicting the fire performance of monolithic and precast concrete corbel beam-to-column connection at high temperatures. Keywords: Nonlinear analysis · Finite element · Fire test · Concrete corbel · Beam-to-column connections

1 Introduction The precast concrete frame structure developed by the construction industry has resulted in high production efficiency, better product quality, and low labour intensity (Hollý and Harvan 2016; Turai and Waghmare 2016). Connections between the precast elements are critical in ensuring structural integrity, adequate strength, energy dissipation, stiffness, and ductility of the designed structures (Hollý and Harvan 2016; Elliott 2017; He et al. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 581–596, 2023. https://doi.org/10.1007/978-981-19-7331-4_47

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2017). Precast concrete corbel beam-to-column connection has been used extensively in precast concrete construction where the connections’ visual aesthetics are unnecessary and heavy loads are transferred (Elliott 2017). However, like other precast connections, corbel exhibits a semirigid behaviour with intermediate stiffness between fully rigid and perfectly pinned. Even though it has finite stiffness and moment resistance, these connections are weaker than the connected elements (Fatema 2006; Lacerda et al. 2018). Exposure to fire could considerably further reduce the strength and stiffness of the precast concrete corbel beam-to-column connection (Raouffard and Nishiyama 2016). During a fire, precast concrete structures have a relatively low integrity and are more vulnerable to progressive collapse (Qian et al. 2019). Reports of actual fire incidents involving precast concrete buildings show that the structures’ post-fire condition sustained severe damage because of the failure and collapse of the beam-column connections (Kose et al. 2006; Gales et al. 2011; Wróblewski et al. 2016). However, such findings were not validated by laboratory tests. Most large-scale fire tests were conducted on rigid connections than semirigid ones (Radzi et al. 2020). Besides, the essential post-fire moment-rotation-temperature characteristics and the thermal-structural response at the cooling phase for the precast concrete corbel beam-to-column connection are not yet understood and require further investigation (Radzi et al. 2021). To overcome these limitations, a nonlinear coupled thermal-structural analysis is executed using ANSYS Workbench to simulate the fire performance of monolithic and precast concrete corbel beam-to-column connection at high temperatures. The models are simulated to failure under incremental point loads at the end of the beam that produced hogging moments to the connections. The response of the models is validated against the load-deflection curves and toughness of connections from the previous experimental test. The relative connection performance at ambient and high temperatures is made by referring to the experimental specimens tested at an ambient temperature test result.

2 Description of Specimens This study adopted the experimental test results by Eid et al. (2017) for the monolithic model and Teja et al. (2019) for the precast concrete corbel model, as shown in Table 1. The test setup, detail of the test specimen, material properties, and test procedure are summarised in this section. More details of this experiment can be found in the paper (Eid et al. 2017; Teja et al. 2019). The monolithic specimens, namely M22-E and M600-E, represent the testing temperatures of 22 °C and 600 °C. The precast concrete corbel specimens, namely C22-E and C400-E, represent the testing temperatures of 22 °C and 400 °C. The symbol E stands for experimental. The 28-day average compressive strength of cubes tested for monolithic and precast concrete corbel specimens was 46 N/mm2 and 24.4 N/mm2 , respectively. The test setup for monolithic specimens used a fire resistance test furnace to produce fire exposure according to the standard cellulose fire test curves. The specimen was exposed to a temperature of 600 °C within 6 min from starting of the fire. Then, the temperature was maintained constant for another 60 min before entering the decay phase. For precast concrete corbel specimens, the test setup used a gas burner to produce fire exposure to the specimen. Initially, the specimen attained the 400 °C temperature in 20 min. Then,

Nonlinear Coupled Thermal-Structural Analysis of Monolithic

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the temperature was maintained constant for another 60 min before entering the decay phase. The detail of the test specimen for monolithic and precast concrete corbel are shown in Figs. 1 and 2. The specimens M22-E and C22-E were selected as a reference to study the performance of connections at ambient temperature (22 °C). The load was applied to the specimen to obtain the first crack load (initial load) and ultimate load. Then, the specimens M600-E and C400-E were exposed to 600 °C and 400 °C for 60 min with the initial load to study the performance of connections subjected to high temperature. After fire exposure, the gradual load was applied to the end of the beam to allow for beam failure. Finally, the load-deflection curves and toughness of connections from ambient and high temperatures were compared and evaluated. Table 1. Experimental specimens. Specimens

Designation

Compressive strength, fcu (N/mm2 )

Fire exposure Maximum temperature (°C)

Duration (min)

Method

Monolithic (Eid M22-E et al. 2017) M600-E

46

−

−

−

46

600 °C

60

Furnace

Precast concrete C22-E corbel (Teja C400-E et al. 2019)

24.4

−

−

−

24.4

400 °C

60

Gas burner

3 Numerical Model 3.1 Simulation Procedures The nonlinear coupled thermal-structural analysis using ANSYS Workbench was performed to validate the experimental result. This sequential coupling technique was chosen to connect thermal and structural analysis. The simulation procedures inside the ANSYS program are illustrated in Fig. 3. The monolithic models, namely M22-S and M600-S, represent the testing temperatures of 22 °C and 600 °C. The precast concrete corbel models, namely C22-S and C400-S, represent the testing temperatures of 22 °C and 400 °C. The symbol S stands for simulation. In Step 1, the transient structural analysis was executed for models M22-S and C22-S. The material properties at ambient temperature and structural boundary conditions were assigned to the model. The gradual load was applied to the end of the beam to allow for beam failure. Then, the ultimate capacity of the structure at ambient temperature was evaluated. In Steps 2 and 3, the transient thermal and structural analyses were executed for models M600-S and C400-S. Transient thermal analysis was performed firstly and followed by transient structural analysis. The temperature-dependent thermal

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Fig. 1. Monolithic connection M22-E and M600-E (Eid et al. 2017).

properties and thermal boundary conditions were assigned to the model. The temperature of 600 °C and 400 °C were applied to the model based on the experimental fire curve. The temperature solution at a high temperature was evaluated. Then, the computed temperature solution was used as input data to determine the deformation and thermal stress of the structure at high temperatures. The geometry models of M22-S and M600-S consist of rigid reinforced concrete beam-to-column connections, as illustrated in Fig. 4. The geometry models of C22-S and C400-S consist of the precast concrete column with corbel, precast concrete beam, rubber pad, grout, and cleat angle with stiffeners, as illustrated in Fig. 5. The designated element size meshed for both models was 25 mm, which convenient for analysis purposes and accuracy of results. The fixed support was assigned at the top and bottom of the precast concrete column. The interface between rebar elements and concrete was assumed to be fully bonded using the discrete reinforcing method. The explosive spalling phenomena on the concrete surface during heating were neglected.

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Fig. 2. Precast concrete corbel connection C22-E and C400-E (Teja et al. 2019).

3.2 Thermal and Structural Elements The element characteristics were described by ANSYS (ANSYS Inc. 2010). For transient thermal analysis, SOLID278 was assigned to simulate the concrete element. SOLID278 has a 3-D thermal conduction capability. The element has eight nodes with a single degree of freedom and temperature at each node. For transient structural analysis, SOLID278 was replaced by SOLID185 to simulate the concrete element. SOLID185 was selected for 3-D modelling of solid structures. It is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element

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Fig. 3. Simulation procedures.

Fig. 4. Geometry configuration of monolithic models M22-S and M600-S.

has plasticity, hyperelasticity, stress stiffening, creep, large deflection, and large strain capabilities. REINF264 was assigned for the transient thermal and transient structural

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Fig. 5. Geometry configuration of precast concrete corbel models C22-S and C400-S.

analysis to reinforce the elements. REINF264 has plasticity, stress stiffening, creep, large deflection, and large strain capabilities. 3.3 Materials Properties The thermal and mechanical material properties assigned in the simulation were according to Eurocode (European Committee For Standardization 2011) and previous studies (Tjitradi et al. 2017; Elshorbagy and Abdel-Mooty 2020). The isotropic thermal conductivity and specific heat constant pressure are varied with respect to temperature. The density, isotropic elasticity (Young’s modulus and Poisson’s ratio), multilinear isotropic hardening of concrete (plastic stress-strain), and bilinear isotropic hardening of reinforcement (yield strength-tangent modulus) are varied with respect to temperature. 3.4 Process of Data Analysis The two main results obtained from the experiments and simulations were the loaddeflection curves and the toughness of the connections. 3.4.1 Load-Deflection Curves The load-deflection curves were used to find the point in a beam where the maximum deflection occurs. The load-deflection curves were generated based on the incremental loads applied at the end of the beam plotted along the vertical axis. The vertical directional deformation data recorded from these loads were plotted along the horizontal axis. The relative load of connections at ambient and high temperatures was analyzed to show the percentage reduction of load-deflection curves with increasing temperatures.

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3.4.2 Toughness of the Connections Toughness of the connections is the energy absorption capability of the connections to resist larger deflection and rotation. The magnitude of toughness depends directly on the geometrical characteristics of the test specimen and the loading system. In this study, the toughness of the connections was calculated based on the area under the load-deflection curves. The relative toughness of connections at ambient and high temperatures was analysed by referring to the experimental specimens tested at ambient temperature test results (M22 and C22). ASTM C1018-97 and JSCE SF-4 provide the method to evaluate the flexural toughness of fibre-reinforced concrete in terms of areas under the load-deflection curve obtained in a simply supported beam setup (Sukontasukkul 2004). The same method was used in a previous study (Teja et al. 2019; Zainal et al. 2021) to determine the beam-tocolumn connection’s toughness by evaluating the areas under the load-deflection curve in a cantilever beam setup. Variations in structural toughness cause differences in displacement ductility, which directly affects the specimen’s yield and ultimate displacement capacity.

4 Validation Results 4.1 Load-Deflection Curves 4.1.1 Monolithic Connection Figure 6 illustrates the load-deflection curves for monolithic connections M22-E and M22-S at ambient temperature. The experimental result (M22-E) shows that the deflection is 23 mm with an ultimate load of 35.3 kN. Using ANSYS (M22-S), the deflection is 22.5 mm with an ultimate load of 33 kN. Figure 7 illustrates the load-deflection curves for monolithic connections M600-E and M600-S at 600 °C. The experimental result (M600-E) shows that the deflection is 17.5 mm with an ultimate load of 28.9 kN. Using ANSYS (M600-S), the deflection is 18 mm with an ultimate load of 26.2 kN. The percentage difference of the ultimate load between experimental and simulation connections is 6.5% and 9.3%, which verifies the accuracy and applicability of the proposed simulation model. The load-deflection curves show a good agreement between the simulation and experimental results. The initial slope of the simulation curves is parallel to the test results. However, the middle slope of simulation curves is slightly stiffer than the experiment curves. This behaviour might be because the simulation models are based on the smeared crack theory and use the perfect bond assumption described by Panedpojaman et al. (2016) (Panedpojaman et al. 2016). In the simulations, the concrete cracks cannot have large crack openings, while large crack openings and bond-slip between concrete and steel cause large beam deflections and large rebar strains. The relative load for the monolithic connections M22-E, M22-S, M600-E, and M600S as a function of displacement is illustrated in Fig. 8. The figure shows reduced loaddeflection curves with increasing temperatures up to 600 °C. The relative load reduction for experiments (E) and simulations (S) is 18.1% and 20.5%, respectively. The monolithic connection has more stiffness than the precast concrete corbel connections. It has

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Fig. 6. Load-deflection curves for monolithic connections M22-E and M22-S at ambient temperature.

Fig. 7. Load-deflection curves for monolithic connections M600-E and M600-S at 600 °C.

the maximum hogging moment and minimum rotation at the support. However, monolithic connections experience a permanent loss of stiffness and strength during a fire, which is known as thermal damage and thermal decohesion (Radzi et al. 2020). During a fire, the deterioration of yield strength and modulus of elasticity of steel reinforcements affect monolithic connections’ performance. Steel reinforcements lose yield and ultimate strength at 200 °C and 300 °C, respectively. Exposure to temperatures higher than 400 °C could cause a considerable expansion of the reinforcements.

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Fig. 8. Relative load of monolithic connections M22-E, M22-S, M600-E, and M600-S as a displacement function.

4.1.2 Precast Concrete Corbel Connection Figure 9 illustrates the load-deflection curves for precast concrete corbel connections C22-E and C22-S at ambient temperature. The experimental result (C22-E) shows that the deflection is 30 mm with an ultimate load of 14.25 kN. Using ANSYS (C22-S), the deflection is 29.86 mm with an ultimate load of 12.85 kN. The percentage difference of the ultimate load between experimental and simulation connections is 9.8%, which verifies the accuracy and applicability of the proposed simulation model. The curve shows a good agreement between the simulation and experimental results.

Fig. 9. Load-deflection curves for precast concrete corbel connections C22-E and C22-S at ambient temperature.

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Figure 10 illustrates the load-deflection curves for precast concrete corbel connections C400-E and C400-S at 400 °C. The experimental result (C400-E) shows that the deflection is 29 mm with an ultimate load of 11 kN. Using ANSYS (C400-S), the deflection is 29.17 mm with an ultimate load of 10.5 kN, close to the deflection and ultimate load observed experimentally. However, the initial to middle slope of simulation curves are slightly stiffer than the experiment curves. The deflection for the simulation curve at load 0 to 7 kN is only 8 mm compared to the experimental result with 13 mm. The substantial curve difference is possibly contributed by the neglected explosive spalling phenomena and the thermal effect on the rubber pad during the initial 60 min fire simulation. In a standard building fire, spalling starts at between 250 and 420 °C, depending on the heating rate and concrete properties. Concrete spalling will impact the moment of inertia of the concrete and directly affect the strength of the model and its deflection value. The fire exposure as early as 200 °C on the rubber pad caused excessive bulging at the sides and contributed to the earlier deflection of the beam.

Fig. 10. Load-deflection curves for precast concrete corbel connections C400-E and C400-S at 400 °C.

The relative load for the precast concrete corbel connections C22-E, C22-S, C400E, and C400-S as a function of displacement is illustrated in Fig. 11. The figure shows reduced load-deflection curves with increasing temperatures up to 400 °C. The relative load reduction for experiments (E) and simulations (S) is 22.8% and 18.3%, respectively. This value appears to be almost the same for monolithic connections (18.1% and 20.5%). However, these similarities cannot illustrate that the behaviour of these two connections is the same. Several factors need to consider in making comparisons. The compressive strength of concrete for monolithic connections is almost double that of precast concrete corbel connections. The tension reinforcement of monolithic connections (16 mm Ø) is larger than the precast concrete corbel connections (10 mm Ø). Furthermore, the cantilever beam length for monolithic connections (1050 mm) is more significant than precast concrete corbel connections (570 mm).

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The precast concrete corbel connections have a lower stiffness than the precast connection. The cleat angle with bolted connection installed at the top of the connection is an essential component to restrain the upward lifting of the beam. An increase in deformations of the cleat angle with bolted connection during a fire was governed by the thermal expansion and degradation of material strength and stiffness. Figure 12 illustrates the failure mode of bolted connection at a cleat angle. As the strength and stiffness are reduced with higher temperatures, the bolt connection at the beam (Bolt B) stretches more than the bolt connection at the column (Bolt A) by following the direction of the beam at the failure condition.

Fig. 11. Relative load of precast concrete corbel connections C22-E, C22-S, C400-E, and C600-S as a displacement function.

Fig. 12. Failure mode of bolted connection at a cleat angle.

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4.2 Toughness of the Connections Table 2 shows the toughness of experimental and simulation connections. The percentage difference of toughness for monolithic connections M22-E, M22-S, M600-E, and M600S is between 8.3% to 8.6%, which verifies the accuracy and applicability of the proposed simulation model. A similar result is seen on the precast concrete corbel connections C22-E and C22-S at ambient temperature, where the percentage difference of toughness is only 6.7%. However, the toughness for precast concrete corbel connections C400-E and C400-S at 400 °C (1.90 × 105 Nmm) is 11.6% lower than the simulation result (2.15 × 105 Nmm). The substantial percentage difference is contributed mainly by a gradual increase in load-deflection slope at the beginning of the loading, as shown in Fig. 10. Table 2. The toughness of experimental and simulation connections. Specimens

Designation Toughness (×105 Nmm)

Percentage different (%)

Experimental Simulation Monolithic (Eid et al. 2017)

M22

5.38

5.87

8.3

M600

3.08

3.37

8.6

Precast concrete corbel C22 (Teja et al. 2019) C400

2.95

2.75

6.7

1.90

2.15

11.6

The relative toughness of monolithic connections and precast concrete corbel connections as a function of temperature is illustrated in Figs. 13 and 14. It appears that the relative toughness is reduced with increasing temperatures. For the precast concrete corbel connections, exposure to 400 °C causes the relative toughness value to decrease to 64% to 73% from the control specimens, as shown in Fig. 13. For the monolithic connections, further exposure up to 600 °C causes the relative toughness value to decrease to 57% to 63% from the control specimens, as shown in Fig. 14. The result indicates that the toughness of the monolithic and precast concrete corbel connections at ambient temperature (M22-E, M22-S, C22-E, and C22-S) has higher fracture resistance than high temperatures (M600-E, M600-S, C400-E, and C400-S). The toughness of the beam-to-column connections is consequently decreased when the fire exposure damages the structural stiffness and integrity between them due to different reasons such as reduction of bending or tensile strength, decreased compressive strength, and loss of shear or shear torsional strength. The beam-to-column connections subjected to fire have damaged the beam’s structural stiffness and damaged the integrity between the beam end and the column faces, consequently decreasing the toughness of the connections, as reported by Teja et al. (2019). However, the toughness depends upon exactly how they are determined experimentally. The factors to be considered include test configuration, type of testing machine, specimen geometry, and how specimen deflections are determined.

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Fig. 13. Relative toughness for precast concrete corbel connections C22 and C400 as a function of temperature.

Fig. 14. Relative toughness for monolithic connections M22 and M600 as a function of temperature.

5 Conclusions Based on the results presented in this paper, the following conclusions can be drawn from the nonlinear coupled thermal-structural analysis of precast concrete corbel beamto-column connection: a. The load-deflection curves for connections M22, M600, and C22 show a good agreement between the simulation and experimental results. The percentage difference of ultimate load for simulation and experimental is 6.5%, 9.3%, and 9.8%, respectively. b. The load-deflection curves are reduced with increasing temperatures. The relative reduction of applied load between experiments (E) and simulations (S) for all connections is between 18.1 and 22.8%. c. The toughness for connections M22, M600, and C22 (simulation and experimental) has verified the accuracy and applicability of the proposed simulation model. The

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percentage difference in toughness for connections M22, M600, and C22 are 8.3%, 8.6%, and 6.7%, respectively. d. The toughness results show that the connection at ambient temperature (M22 and C22) has higher fracture resistance than at high temperatures (M600 and C400). The relative reduction of toughness for precast concrete corbel connection (exposed to 400 °C) and monolithic (exposed to 600 °C) is between 64% to 73% and 57% to 63%, respectively. e. During a fire, monolithic connections experience a permanent loss of stiffness and strength. In contrast, the cleat angle with bolted connection experienced a thermal expansion and degradation of material strength and stiffness for precast concrete corbel connection. f. The validation result of nonlinear coupled thermal-structural analysis executed using ANSYS Workbench gives good efficiency for predicting the fire performance of monolithic and precast concrete corbel beam-to-column connection at high temperatures. The nonlinear coupled thermal-structural analysis method can be used as an alternative to the laboratory’s large-scale fire test.

Acknowledgements. The authors acknowledge the financial support from Universiti Kebangsaan Malaysia through Research University Grant (grant no. DIP-2019–002 and MUTIARA-A165894) and laboratory facilities provided by the Department of Civil Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia.

References ANSYS Inc.: Mechanical APDL Element Reference (2010) Eid, F., Heiza, K., Elmahroky, M.: Behavior and Analysis of Reinforced Self-Compacted Concrete Beam Column Connection Subjected to Fire. Am. J. Sci. Eng. Technol. [Preprint] (2017). https:// doi.org/10.11648/j.ajset.20170204.15 Elliott, K.S.: Precast Concrete Structures, 2nd edn. CRC Press (2017) Elshorbagy, M., Abdel-Mooty, M.: ‘The coupled thermal-structural response of RC beams during fire events based on nonlinear numerical simulation. Eng. Fail. Anal. [Preprint]. (2020). https:// doi.org/10.1016/j.engfailanal.2019.104297 European Committee For Standardization: Eurocode 2: Design of concrete structures - Part 1–2: General rules - Structural fire design (2011) Fatema, T.: Study on connection between precast concrete beam and cast-in-situ column in prefabricated building frames. J. Eng. Appl. Sci. 1(1), 33–38 (2006) Gales, J., Bisby, L.A., Gillie, M.: Unbonded post tensioned concrete in fire: a review of data from furnace tests and real fires. Fire Saf. J. 46(4), 151–163 (2011). https://doi.org/10.1016/j.firesaf. 2011.01.004 He, W., et al.: A review of precast concrete building development in different countries. In: Proceedings of 128th The IIER International Conference, Auckland, New Zealand, pp. 8–11 (2017) Hollý, I., Harvan, I.: Connections in precast concrete elements. Key Eng. Mater. 691, 376–387 (2016). https://doi.org/10.4028/www.scientific.net/KEM.691.376 Kose, M.M., Temiz, H., Binici, H.: Effects of fire on precast members: a case study. Eng. Fail. Anal. 13(8), 1191–1201 (2006). https://doi.org/10.1016/j.engfailanal.2005.12.003

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Lacerda, M.M.S., et al.: Influence of the vertical grouting in the interface between corbel and beam in beam-to-column connections of precast concrete structures – an experimental analysis. Eng. Struct. 172(May), 201–213 (2018). https://doi.org/10.1016/j.engstruct.2018.05.113 Panedpojaman, P., Jina, P., Limkatanyu, S.: Moment capacity and fire protection of the welded plate joint for precast members. Arch. Civ. Mech. Eng. 16(4), 753–766 (2016). https://doi.org/ 10.1016/j.acme.2016.04.017 Qian, K., et al.: Progressive collapse resistance of precast concrete beam-column sub-assemblages with high-performance dry connections. Eng. Struct. 198(2019). https://doi.org/10.1016/j.eng struct.2019.109552 Radzi, N.A.M., et al.: A review of precast concrete beam-to-column connections subjected to severe fire conditions. Adv. Civ. Eng. 2020, 1–23 (2020). https://doi.org/10.1155/2020/883 1120 Radzi, N.A.M., et al.: A review on structural fire performance tests of beam-to-column connections. Fire Safety J. [Preprint] (2021) Raouffard, M.M., Nishiyama, M.: Residual load bearing capacity of reinforced concrete frames after fire. J. Adv. Concrete Tech. [Preprint]. (2016) https://doi.org/10.3151/jact.14.625 Sukontasukkul, P.: Toughness evaluation of steel and polypropylene fibre reinforced concrete beams under bending. Int. J. Sci. Technol. Thammasat 9(3), 3–9 (2004) Teja, C.S., et al.: Effect of fire on prefabricated concrete beam column connections. Int. J. Recent Technol. Eng. 8(2), 1433–1436 (2019). https://doi.org/10.35940/ijrte.b2092.078219 Tjitradi, D., Eliatun, E., Taufik, S.: 3D ANSYS numerical modeling of reinforced concrete beam behavior under different collapsed mechanisms. Int. J. Mech. Appl. 7(1), 14–23 (2017). https:// doi.org/10.5923/j.mechanics.20170701.02 Turai, V., Waghmare, A.: A study of cost comparison of precast concrete vs. Cast-in-Place. Int. J. Adv. Eng. Res. Appl. 2(2), 112–122 (2016) Wróblewski, R., et al.: Fire and collapse modelling of a precast concrete hall. Struct. Infrastruct. Eng. 12(6), 714–729 (2016). https://doi.org/10.1080/15732479.2015.1042885 Zainal, S.M.I.S., Hejazi, F., Rashid, R.S.M.: Enhancing the performance of knee beam–column joint using hybrid fibers reinforced concrete. Int. J. Concrete Struct. Mater. 15(1), 1–28 (2021). https://doi.org/10.1186/s40069-021-00457-w

Mechanical Performance of Novel UHPFRC Grouted SHS Tube-Sleeve Connection: Experiments, Numerical Simulation and Analytical Approaches Zhenyu Huang1,2,3(B) and Weixiong Deng1,2 1 Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen

University, Shenzhen 518060, China [email protected] 2 Key Laboratory of Impact and Safety Engineering, Ministry of Education, Ningbo University, Ningbo 315211, China 3 Key Laboratory for Resilient Infrastructures of Coastal Cities, Shenzhen University, Ministry of Education, Shenzhen 518060, China

Abstract. This paper presents the axial and lateral performance of a novel ultrahigh-performance fiber-reinforced concrete (UHPFRC) grouted SHS tubeSleeve connection for prefabricated prefinished volumetric constructions (PPVC). The experimental study tested 18 full-scale specimens with varying shear key spacings, inner tube lengths, inner tube heights, and volume proportions of steel fiber in UHPFRC. The results showed that the connection have adequate resistance and ductility to resist tension and bending moment. The failure modes in tension mainly include the shear failure of the UHPFRC and the fracture of the inner tube, while the failure modes in bending mainly include the fracture of the inner tube and the slip of the grout. To further understand the load transfer mechanism of the connection, the advanced finite-element (FE) models were built to simulate the axial and lateral load–displacement behavior, strain and crack development of the grout. Thereafter, new design formulas are developed and evaluated to predict the axial and lateral resistance of the grouted connections. Validation against the test results showed that the new formulas can provide reasonably effective and accurate predictions of the axial-load and lateral-load resistance of the novel grouted connection. Keywords: Grouted sleeve connection · UHPFRC · Axial-load resistance · Lateral-load resistance · Finite element analysis (FEA)

1 Introduction Modular construction, by which the modules are prefabricated off-site and assembled on-site, has become a popular trend in construction industry due to its higher efficiency and productivity, better quality and safety, as well as lesser labor force and pollution. Depending on the degree of off-site manufacturing, the modular unit varies from simple © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 597–613, 2023. https://doi.org/10.1007/978-981-19-7331-4_48

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stick frame systems, like pre-cast concrete or prefabricated bathroom pods, up to fully prefabricated prefinished volumetric constructed (PPVC) module (Liew et al. 2019). As a special modular construction, PPVC pre-finishes the internal elements such as mechanical, plumping and electrical, etc., before the installation of the modules and thus owns the highest prefabrication rate. One of the most critical issues affecting the integrity and safety of the modular building is the connection between the PPVC module (Dai Pang et al. 2016). PPVC modules are normally connected externally for minimization of interior decoration on-site (Liew et al. 2019). According to the joint location, the connections are classified as corner connection, perimeter connection and interior connection. Although bolted connections are widely used, some critical issues still exist. Firstly, the accumulation of geometric and positioning deviations may easily cause alignment issues especially for the high-rise modular buildings (Generalova et al. 2016). Secondly, corrosion is a critical problem for bolted connections exposed to humid weather environment (Singapore and Authority 2017). Thirdly, the extensive usage of bolted connection would reduce the productivity of modular construction and cause collision problems during the assembly process (Sanches et al. 2018). To overcome these issues, a shear key-grouted column connection of square hollow section (SHS) has been proposed, which connects the upper column and lower column through the grout in the annulus of the connection (Huang et al. 2021; Sui et al. 2020). These investigations conclude that for the connection under axial compression, the load is transferred from the upper outer tube to the lower outer tube. The load resistance is dominated by the geometric sizes and material properties of the outer tubes. For the connection under axial tension, the load is transferred from the upper outer tube to the inner tube through the infilled grout. The failure mechanism is more complex and the load resistance is difficult to predict. Dai et al. (2021, 2020) conducted experimental and numerical studies on the axial and bending resistance of SHS column connections for modular construction, which effectively supplemented the availability of the connection. However, there is no analytical model of axial resistance and the number of lateral-load specimens is insufficient. As a continuation and deeper investigation, the current study designs a novel SHS column connection, as shown in Fig. 1, which is an improvement of the column connection reported by Sui et al. (2020). Then the study tests ten full-scale specimens under axial tension and eight specimens under lateral compression to examine the failure modes and load resistances. Then, advanced FE simulation is performed to get more information on the stress and crack development of the infilled grout. Finally, two analytical models are proposed to predict the axial and lateral resistance of SHS column connections. Among them, the axial analytical model considers the influence of section shape and bond slip, while the lateral analytical model is calculated based on the elastic-plastic design theory.

2 Experimental Programme 2.1 Material Properties To check the influence of material properties on the failure mode and load resistance of the column connection, three types of UHPC with 0, 1 and 2% of steel fiber have been developed. To achieve the same level of compressive strength around 100 MPa, the three

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Fig. 1. Fabrication procedure of the column connection.

types of UHPC are designed with slightly different mix proportions, as shown in Table 1. The tensile strength and elastic modulus of fibers are around 2750 MPa and 200 GPa, respectively. For each mixture, the experimental program tests three 100 × 200 mm concrete cylinders according to ASTM C39/C39M (International 1999) to determine the compressive strength, and five concrete coupons according to JSCE-2008 (Yokota et al. 2008) to determine the tensile strength. Table 2 lists the material properties of concrete. The compressive strength of the three types of UHPC are around 100 MPa. The experimental program has extracted curved coupons from the corner region of the tubes, and flat coupons from the flat region of the tubes, as well as flat coupons from the steel plates. Table 3 summarizes the Young’s modulus, 0.2% offset yield strength, and ultimate strength of the steel tubes, steel plates and rebars, respectively. Table 1. Mix proportion of UHPFRC (kg/m3 ) Mix

W/B

W

OPC

SF

GGBFS

S

F

HWRA

SRA

UHPC

0.19

209.5

823.3

135.5

170.1

1060.0

0

7.29

6.29

UHPFRC (1%)

0.21

213.9

750.0

130.5

165.1

1120.0

78.0

7.15

6.42

UHPFRC (2%)

0.24

229.1

705.0

120.5

155.1

1150.0

156.0

5.81

6.87

Notes W/B = water to binder ratio; W = water; OPC = ordinary Portland cement; SF = silica fume; GGBFS = mineral power; S = sand; F = steel fiber; HWRA = high Water reducing agent; SRA = shrinkage reducing agent; R = retarder

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Concrete

f cu (MPa)

E c (GPa)

f t (MPa)

Poisson’s ratio

96.6

41.4

5.4

0.185

UHPFRC (1%)

105.8

42.6

6.0

0.182

UHPFRC (2%)

108.9

44.2

6.1

0.192

UHPC

Table 3. Material properties of the steel components Component

Material

E s (GPa)

f y (MPa)

f u (MPa)

Inner tube flat

Mild steel

205.3

260.5

405.6

Inner tube corner

202.2

482.5

522.1

Outer tube flat

202.1

323.5

457.7

Outer tube corner

208.4

461.7

541.6

Steel plate Shear key

HRB 4006

206.2

377.6

546.8

193.6

357.0

485.0

2.2 Test Specimens Figure 2 shows the configuration of the SHS column connection. Table 4 lists the geometric parameters of the 18 SHS column connections. The main geometric parameters include the outer diameter, thickness and radius of the round corner of the outer tube (Bo , t o and r o ), the inner diameter, thickness and radius of the round corner of the inner

Fig. 2. Configuration of the tube grouted connection.

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tube (Bi , t i and r i ), the length and thickness of the infilled grout (L g and t g ), and the shear key spacing (s). The shear keys, in the form of steel bar with w = 6 mm height and h = 12 mm width, are welded to the both inner surface of the upper outer tube and the outer surface of the inner tube. These specimens vary with different shear key spacings (s = 60 mm, 80 mm, 120 mm), inner length (Bi = 160 mm, 170 mm, 180 mm), inner tube height (L g = 300 mm, 360mm, 420 mm), and volume proportions of steel fiber (V s = 0%, 1%, 2%). 2.3 Test Set-Up, Loading and Measurement Figure 3 shows the test set-up and Linear Variable Displacement Transducers (LVDTs) measurement scheme. Digital Image Correlation (DIC) technology is used for cross verification of lateral-load specimens. The experimental program adopts a computercontrolled servo hydraulic actuator with a load capacity of 5000 kN. The actuator applies an axial tensile force on the top of the specimen and a lateral force in the middle of the specimen through displacement control mode with a loading rate of 0.2 mm/min. The loading rate increases to 1 mm/min when the specimen starts to fail or the loading force starts to drop down.

3 Test Results 3.1 Failure Modes Figure 4 (a) and (b) show the typical failure modes observed for SHS column connections under axial tension, while Figs. 4 (c) and (d) show failure modes under lateral load. For the axial tension test, generally, if the grouted region is strong enough, the outer and inner tubes would yield and the inner tube may fracture at the intersection with the steel plate; if the grouted region is not stiff enough, the infilled grout would crush with obvious bond-slip between the upper outer tube and inner tube, and the steel tubes yield. The crack patterns are also classified into two types. The first type is the diagonal line crack linking the staggered two shear keys on the inner surface of the outer tube and the outer surface of the inner tube, respectively (Fig. 8). The two adjacent parallel diagonal line cracks form the compression strut, through which the load is transferred from the outer tube to the inner tube. The second type is the large-area crush along the outer surface of the inner tube. For the lateral load test, the concrete slip and inner tube fracture are the main failures. Firstly, the cracks of concrete are typically distributed in the tensile area of the connection, and the specimens S80T170L300V0-L have obvious shear cracks. In addition, the failure of most specimens is that the gap between the upper and lower column is open, and the inner tube reaches the fracture state. This may be due to the synergistic contradiction between the shear performance of UHPFRC and the fracture performance of steel. 3.2 Load-Displacement and Moment-Curvature Curves Figure 5 displays the load-displacement curves of all the eighteen SHS column connections. P indicates the external load applied by the actuator, and δ indicates the vertical

170 × 12 × 25 170 × 12 × 25 160 × 12 × 25 180 × 12 × 25 170 × 12 × 25 170 × 12 × 25

250 × 8 × 30 250 × 8 × 30 250 × 8 × 30 250 × 8 × 30 250 × 8 × 30 250 × 8 × 30

S60T170L300V1-L

S80T160L300V1-L

S80T180L300V1-L

S80T170L360V1-L

S80T170L420V1-L

S80T170L420F0-A

S80T170L300V0-L

250 × 8 × 30

S80T170L420F1-A

170 × 12 × 25

170 × 12 × 25

250 × 8 × 30

S80T170L360F1-A

250 × 8 × 30

170 × 12 × 25

250 × 8 × 30

S80T180L300F2-A

S80T170L300V1-L

180 × 12 × 25

250 × 8 × 30

S80T160L300F2-A

170 × 12 × 25

160 × 12 × 25

250 × 8 × 30

S80T170L300F2-A

170 × 12 × 25

170 × 12 × 25

250 × 8 × 30

S80T170L300F1-A

250 × 8 × 30

170 × 12 × 25

250 × 8 × 30

S120 T170L300F0-A

250 × 8 × 30

170 × 12 × 25 170 × 12 × 25

250 × 8 × 30

S60 T170L300F0-A

S120T170L300V1-L

170 × 12 × 25

250 × 8 × 30

S80 T170L300F0-A

Axial-loading

Lateral-loading

Bi × ti × ri (mm × mm × mm)

Bo×to×ro (mm × mm × mm)

Specimen

Table 4. Geometric dimensions of test specimens

80

80

80

80

60

80

80

120

80

80

80

80

80

80

80

120

60

80

s (mm)

420

360

300

300

300

300

300

300

420

420

360

300

300

300

300

300

300

300

Lg (mm)

1

1

1

1

1

0

1

1

0

1

1

2

2

2

1

0

0

0

Vs (%)

602 Z. Huang and W. Deng

Mechanical Performance of Novel

603

Fig. 3. Test setup and measurement scheme.

Fig. 4. Failure modes

displacement measured at the top end plate. For axial loading, the curve of external load to vertical displacement is drawn in Fig. 5 (a) - (b). For three-point bending, the curve of bending moment versus upper column curvature is shown in Fig. 5 (c) - (d). All the curves exhibit a similar trend before reaching the peak load resistance. The load-displacement relationship is initially elastic, and then enters into the nonlinear stage due to the crack

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of the infilled grout. After reaching the peak load resistance, the curve drops down either due to the fracture of the inner tube or due to the crush of the infilled grout. Under axial loading, the peak load resistance of the specimen is positively related to the strength of the grout. The specimen with the longest inner tube height, S80T170L420F0-A has the largest capacity at the grouted connection and the peak load resistance reaches 3005.2 kN. The specimen S80T170L420F1-A is supposed to have the same load level with S80T170L420F0-A. The specimen with the shortest inner tube height and largest shear key spacing, S120T170L300F0-A, has the smallest capacity at the grouted connection and the peak load resistance is only 1404.6 kN. During lateral loading, there is a sharp decrease for bending moment except S80T170L300V0-L and S80T160L300V1-L. This is due to the fracture of the steel in the tensile area of the inner tube. Since the upper and lower limits of lateral bearing capacity are controlled by the section properties, S80T180L300V1-L and S80T160L300V1-L have the maximum and minimum resistance, which are 280.5 kN·m and 252.5 kN·m, respectively. Obviously, S80T170L300V0-L has superior ductility behavior compared with other specimens, thus 1% fiber addition may not be necessary. Moreover, the increase of the inner tube height results in a more significant fracture trend. The reason is that not only there are more shear keys within the grout to form more grout struts, but also the bond area between concrete and steel tube increases, which cumulatively increase plastic deformation. It is worth noting that for the whole connection, when fracture failure occurs, the connection is regarded as the limit state.

Fig. 5. Load-displacement and moment-curvature curves.

4 Finite Element Modelling 4.1 Material Model The FE analysis adopts the concrete damage plasticity (CDP) model to represent the behavior of the UHPC and UHPFRC. The CDP model specifies the inelastic behavior of concrete as isotropic damaged elasticity in combination with isotropic tensile and

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compressive plasticity. Sui et al. (2020) have discussed the compressive and tensile constitutive relationship for UHPFRC and UHPC, respectively, and plotted the nondimensional stresses-inelastic strain curves and nondimensional damage variables-inelastic strain curves, which are used in this study. In ABAQUS, engineering stress and strain are transferred by inputting the trues stress and strain of steel. The fracture simulation in the three-point bending experiment requires specification of the relationship between the equivalent strain-to-fracture and stress triaxiality. ABAQUS provides several models to define the ductile damage, and this study adopts the Johnson–Cook criterion model. The fracture locus and failure parameters need to be calibrated by experiments (Zhang et al. 2020). 4.2 Validation of FE Model Figures 6 and 7 compare the load–displacement curves of the 18 grouted connections obtained from the tests and FE simulations. The predictive load resistances are very close to the test values. When approaching the peak axial-load, a significant number of cracks are generated in the grout. The load resistance of the specimen is reduced due to the shear crushing of the grout, and the load–displacement curves show dramatic decreases. The strength of the grouted connection is negatively related to the shear key spacing and positively related to the inner tube height, as shown in Fig. 6(a) and (b). This is because the number of shear keys will affect the formation of compression struts bearing axial force in grouting. The load-displacement behavior and the peak load resistance of the three specimens are very close to each other, indicating that the inner tube length has marginal effect on the axial-load capacity of the SHS column connection, as shown in Fig. 6(c). The reason is that the increase of inner tube length only changes the angle of the compression strut, but does not change the number of shear keys and the contact area between the concrete and steel tubes. Regarding the effect of steel fiber in concrete, the results obtained from axial-load specimens and lateral-load specimens are quite different. As shown in Figs. 6(d) and 7(d), grout containing fibers can improve ductility under axial loading, but lead to tube fracture under lateral loading. The development of inner tube fracture is mainly due to the opening of the outer tube of SHS column connection after lateral loading test, resulting in the fracture strain of the inner tube contributing to the lower limit of lateral resistance. As shown in Fig. 7(c), the moment-curvature curves show that the peak resistance increases only significantly with the increase of the inner tube area in the midspan section. 4.3 Development of Crack and Fracture Compared with the test results, the validated FE model provides a convenient and useful tool to extract detailed information on the development of crack in the grout. For the axial-load specimens failed by grout shear crushing, the crack pattern in the grout initially was diagonal between two staggered shear keys on the inner surface of the outer tube and the outer surface of the inner tube. At the peak load, the diagonal line cracks developed rapidly, leading to severe crushing along the longitudinal direction and large bond-slip between grout and steel tubes. For the specimens in Fig. 8(i) and (j) with longer inner tube height, only minor diagonal line cracks formed and the grout was not crushed.

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Fig. 6. Comparison of load–displacement curves under axial loading: (a) with different shear key spacing; (b) with different inner tube heights; (c) with different inner tube lengths; and (d) with different volume proportions of steel fiber.

Among the specimens with tube fracture, the concrete only develops diagonal damage in the area with the largest curvature, while the specimens with obvious bond slip are observed with damage at the diagonal of each shear key in the tensile area (Fig. 9). Generally, the proposed FE model was able to reproduce satisfactorily the damage in the grout observed from the tests.

5 Theoretical Model 5.1 Prediction of Axial-Load Resistance 5.1.1 Axial Load Resistance To provide guidance for the design of UHPFRC grouted SHS tube sleeve connections, this section derives a theoretical model based on the load transfer mechanism of the sleeve connection to predict the axial-load resistance. The axial load resistance consists of the resistance contribution of the shear key interlock, friction and adhesion as given by: Pu = 4Bi Lg τu

(1)

where the ultimate shear stress can be obtained: τu = τb + τs

(2)

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Fig. 7. Comparison of load–displacement curves under lateral loading: the meaning of (a) – (d) are the same as Fig. 6 (a) – (d).

Fig. 8. Development of crack in the grout under axial loading.

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Fig. 9. Development of crack in the grout under lateral loading.

where τb is the bond strength due to friction and adhesion; τu is the ultimate shear strength; τs is the shear key interlock strength; Bi , h, s and L g are the width of the inner tube, shear key height, shear key spacing, and height of inner tube, respectively.

Fig. 10. Shear key interlock.

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5.1.2 Friction and Adhesion for UHPFRC Grouted SHS Tube Sleeve Connection Based on the previous study of the CHS concrete-filled steel tubes and SHS concretefilled steel tubes reported by Lyu and Han (2019), an equation considering the shape effect is proposed:      2ro to 2ro + 1100 + 3800 (3) τb = 0.043 + 0.028 Bo Bo Bo2 where r o is radius of the round corner of the outer tube; t o is thickness of the outer tube. 5.1.3 Shear Key Interlock for SHS Column Connection The shear strength contributed by the shear keys needs to be calculated according to the tension and compression strut model, as shown in Fig. 10(a). The effect of confined concrete needs to be considered. Therefore, the confined concrete model is adopted for the SHS connection confined by steel tubes with round corners, as shown in Fig. 10(c) (Wang and Wu 2008). Since the sharp square column has weak confining effect, the confined concrete strength for the sharp square column is assumed as fcu∗ = fcu . Then, the shear strength contributed by the shear keys is given by:     h h h h a Ps = 1+ τs = fcu = ξ fcu 1 + (4) o 4Bi Lg Bi s Bi s a − 8.2r Bo R where a is side length correction coefficient of critical triangle in grout (Fig. 10a); n = L g /s is the number of shear keys; fcu∗ is the confined concrete strength; ξ is ratio of fcu∗ to f cu ; r o is radius of the round corner of the outer tube. 5.2 Prediction of Lateral-Load Resistance TO predict the bending moment of the grout connection, a fiber element model for composite structure is developed. To conservatively predict the load resistance, the section stress state is defined based on the elastic-plastic limit state. 5.2.1 Assumptions To simplify the calculation and ensure the accuracy of the predictions, the following assumptions are adopted: (a) plane sections remain plane; (b) ignore the section corner radius; (c) strain-compatibility condition and (d) ignore the contribution of the area below both sides of the outer tube and the tensile area of the concrete (the part exceeding h0 ). Three typical ultimate limit state design (ULSD) methods are taken into consideration as the failure criterion: (a) elastic; (b) elastoplastic; and (c) plastic method, which are shown in Fig. 12. 5.2.2 Constitutive Model The stress-strain curves of UHPFRC and steel are shown in Fig. 11. This paper adopts the concrete model proposed by Wee et al. (1996) that can well represent the strain

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softening behavior and post-peak behavior of concrete after the peak point. As a strain hardening material, based on simple mixing parameters, the rising stage and next stage of the UHPFRC uniaxial tensile stress-strain relationship can be analyzed by the study of Isa et al. (2021). As for structural steel, the perfect elastic-plastic model is used.

Fig. 11. Constitutive models for martials.

5.2.3 Fiber Element Analysis The composite section is divided into strip fiber elements. The stress distribution in each fiber element is calculated based on the plane section assumption and the material constitutive model. The current study focuses on the elastic-plastic limit state of the structure. Thus, the stress is distributed nonlinearly with the neutral axis of the section. It needs to be assumed that the material enters the plastic stage after the elastic stage. Generally speaking, when the concrete strain develops to the ultimate strain, the failure occurs (Fig. 12).

Fig. 12. Plane section assumption and force equilibrium of grout connection.

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5.3 Validation The validation of the proposed analytical model on the axial load resistance of SHS column connections adopts the test results of the ten specimens tested in this study and the four specimens tested by Dai et al. (2020).The verification of lateral load resistance adopts the test results of eight specimens in this study and two specimens tested by Dai et al. (2021). Figure 13 plots the ratios of the predicted results to the test results. The mean value of the ratios (axial-load and lateral-load) are 0.85 and 0.92 while these standard deviations are 0.12 and 0.13, respectively. Thus, the proposed analytical model is satisfactory to predict the axial and lateral load resistance of SHS column connections, and the prediction is relatively conservative for practical design.

Fig. 13. Test results and predicted results.

6 Conclusions A novel UHPFRC grouted SHS tube sleeve connection was developed and its load resistance behaviour were investigated experimentally, numerically, and theoretically. The research work reported in the paper supports the following conclusions: (1) Under axial loading, for the SHS column connection with sufficient strength of the grouted region, the connection fails by fracture of the inner tube at the intersection with the steel plate; for the SHS column connection with insufficient strength of the grouted region, the connection fails by bond-slip and concrete crush. Under lateral loading, the connection fails either by the fracture of the inner tube or bond slip between tube and concrete. (2) The increase of steel fibre content and inner tube height can effectively improve the axial resistance of SHS column connection, but it will reduce the lateral ductility. The increase of inner tube length has little effect on the axial bearing capacity of SHS column connection, but it significantly improves the lateral bearing capacity.

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(3) The FE model has successfully illustrated the load transfer mechanism of the SHS column connection under axial and lateral loading. It effectively reproduces the crack development, bond slip and fracture of inner tube in grouting. (4) The proposed axial-load analytical model considered the effects of cross-section shape and corner radius on the strength of confined concrete. For the prediction of bending moment resistance of grout connection under lateral load, an elasticplastic model based on the plan section assumption is proposed. The predictive load resistances agree well with the test values.

Acknowledgements. The authors would like to acknowledge the research grant received from the National Natural Science Foundation of China (Grants No.51978407, 52108159), Key Laboratory of Impact and Safety Engineering (Ningbo University) Ministry of Education (Grants No.cj202005). Natural Science Foundation of Guangdong Province (Grants No.2021A1515010932, 2022B1515020037), Shenzhen International Science and Technology Joint Project (Grants No. GJHZ20200731095802008), and Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering (SZU) (Grant No. 2020B1212060074).

References Dai Pang, S., Liew, J.Y.R.L., Dai, Z., Wang, Y.: Prefabricated prefinished volumetric construction joining techniques review. In: Modular and Offsite Construction (MOC) Summit Proceedings, pp. 2562–5438 (2016) Dai, Z., Cheong, T.Y.C., Dai Pang, S., Liew, J.Y.R.: Experimental study of grouted sleeve connections under bending for steel modular buildings. Eng. Struct. 243(112614), 110141–110296 (2021) Dai, Z., Dai Pang, S., Liew, J.Y.R.: Axial load resistance of grouted sleeve connection for modular construction. Thin-Walled Struct. 154(106883), 100263–108231 (2020) Generalova, E.M., Generalov, V.P., Kuznetsova, A.A.: Modular buildings in modern construction. Procedia Eng. 153(167–172), 1877–7058 (2016) Huang, Z., Zhang, W., Fan, S., Sui, L., Ye, J.: Axial-load resistance of a novel UHPFRC grouted SHS tube-sleeve connection: experimental, numerical, and theoretical approaches. J. Struct. Eng. 147(04021184), 04020733–04029445 (2021) International, A.: ASTM C39/C39M-99-Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens (ASTM International West Conshohocken) (1999) Isa, M.N., Pilakoutas, K., Guadagnini, M.: Determination of tensile characteristics and design of eco-efficient UHPC. Structures 32, 2174–2194 (2021) Liew, J.Y.R., Chua, Y.S., Dai, Z.: Steel concrete composite systems for modular construction of high-rise buildings. Structures 21, 135–149 (2019) Lyu, W.-Q., Han, L.-H.: Investigation on bond strength between recycled aggregate concrete (RAC) and steel tube in RAC-filled steel tubes. J. Constr. Steel Res. 155(438–459), 0143-0974X (2019) Sanches, R., Mercan, O., Roberts, B.: Experimental investigations of vertical post-tensioned connection for modular steel structures. Eng. Struct. 175(776–789), 0141–0296 (2018) Singapore, B.C.A., Authority, C.: Design for manufacturing and assembly (DfMA): prefabricated prefinished volumetric construction. Singapore: Singapore BCA (2017) Sui, L., Fan, S., Huang, Z., Zhang, W., Zhou, Y., Ye, J.: Load transfer mechanism of an unwelded, unbolted, grouted connection for prefabricated square tubular columns under axial loads. Eng. Struct. 222(111088), 110141–110296 (2020)

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Wang, L.-M., Wu, Y.-F.: Effect of corner radius on the performance of CFRP-confined square concrete columns: test. Eng. Struct. 30(493–505), 0141–0296 (2008) Wee, T.H., Chin, M.S., Mansur, M.A.: Stress-strain relationship of high-strength concrete in compression. J. Mater. Civ. Eng. 8(70–76), 0899–1561 (1996) Yokota, H., Rokugo, K., Sakata, N.: JSCE-2008 Recommendations for design and construction of high performance fiber reinforced cement composites with multiple fine cracks (HPFRCC). Jpn. Soc. Civ. Eng. (2008) Zhang, W., Choo, Y.S., Yang, P., Shen, W., Huang, Z.: Nonlinear behaviour of fully grouted CHS X joints and associated representation for overall frame analysis. Thin-Walled Struct. 152(106761), 100263–108231 (2020)

Effects of Gap Arrangement on the Compression Behavior of Square Tubed Steel Reinforced-Concrete Columns Biao Yan1 , Quanlin Zhou2 , and Dan Gan2(B) 1 School of Highway, Chang’an University, Xi’an 710064, China

[email protected] 2 School of Civil Engineering, Chongqing University, Chongqing 400045, China

[email protected], [email protected]

Abstract. For a tubed concrete column, generally, the tube gaps are arranged at column ends to avoid the steel tube carrying loads directly. This paper experimentally and numerically investigated the behavior of square tubed steel reinforced concrete (TSRC) columns with an additional gap at the mid-height of the steel tube. Four square intermediate TSRC columns were tested under axial and eccentric compression, and the main test parameters were the load eccentricity ratio and width-to-thickness ratio of steel tube. The failure modes and ultimate strength were analyzed. The test results demonstrated that the columns with two types of gap arrangement schemes showed similar failure modes. The axial compression strength of the column with an additional gap at mid-height was slightly higher than that of the column with gaps at the column ends, while the eccentric compression strength of column showed the opposite result. A detailed finite element (FE) model was developed and verified, in which the material nonlinearity and initial geometric imperfection were considered. Further parametric analysis was carried out based on the verified FE model. Keywords: Steel tube confined concrete · Steel reinforced concrete · Finite element analysis · Column · Eccentric compression

1 Introduction A tubed steel reinforced concrete (TSRC) column can be seen as an improved steelreinforced concrete (SRC) column in which the reinforcement cage is replaced by the outer thin-walled steel tube (Zhou and Liu 2010a, b). The outer thin-walled steel tube is usually terminated at the ends of the columns (see Fig. 1(a)). Therefore, the outer steel tube does not directly carry the longitudinal load, delaying the local buckling of the steel tube (Gan et al. 2011). The outer steel tube can provide more effective confinement on core concrete. Besides, the steel tube of the TSRC column can be used as a formwork and facilitate concrete pouring (Liu et al. 2015). Over the past few decades, the structural behavior of TSRC columns was extensively investigated. To prevent shear failure of reinforced concrete short columns, the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 614–624, 2023. https://doi.org/10.1007/978-981-19-7331-4_49

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tubed-reinforced-concrete column was proposed by Tomii et al. (1985). Qi et al. (2011) investigated the axial load behavior of square TSRC short columns. It was concluded that the confinement effect increased the strength and ductility of concrete, so the TSRC column had higher axial load capacity than that of the SRC column with the same steel ratio. Zhou et al. (2015) reported test results on eight slender square TSRC columns under eccentric compression. It was found that local buckling of the square tubes was delayed since the axial load was not directly applied on the steel tube. Wang et al. (2016) carried out tests on twelve short square TSRC columns under eccentric compression. It was found that the average confinement of steel tube was close to that of the columns under axial compression. Zhou et al. (2017) investigated seven circular TSRC columns under combined constant axial compression and lateral cyclic load. It was found that the TSRC columns exhibited excellent ductility and plastic deformation ability. Liu et al. (2018) investigated the hysteretic behavior of square TSRC columns. The test results indicated that the confinement from steel tubes effectively improved the ductility and plastic deformation capacity of the specimens, while the shear studs on the steel shape affected little on the coworking behavior between the concrete and the steel shape. Liu et al. (2019) investigated the seismic behavior of short circular TSRC columns. It was found that the short TSRC columns that failed in shear failure mode still showed good ductile behavior due to the effective confinement from the steel tube. Yan et al. (2019a) investigated the influence of slenderness on axially loaded square TSRC columns. It was found that the axial load carried by square tube due to friction and bond of the interface increased with the increase of slenderness ratio, while the confinement effect of tube was just the opposite. In general, TSRC columns have high load bearing capacity, good ductility, and superior seismic performance. Therefore, TSRC columns have potentials in practical engineering application, as shown in Fig. 1a. Steel section Steel tube weld

Weld

Steel tube

Steel beam

Gap Steel tube

(a) TSRC column

(b) Welding position of steel tube

Fig. 1. Tubed SRC column

In practice, the outer steel tube of a TSRC column sometimes needs to be lapped and welded along the tube height direction (see Fig. 1(b)). However, welding generates large

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welding residual deformation and stress in the steel tube which is usually cold formed, and the residual deformation and stress will adversely affect the performance. As the length of the steel tube increases, the bond and friction between the steel tube and the concrete will generate large longitudinal stress and may reduce the confinement effect of the steel tube on the core concrete. Besides, the in-field welding is laborious. Therefore, this paper experimentally and numerically investigated the behavior of square TSRC columns with an additional tube gap at the mid-height.

2 Experimental Study 2.1 Specimen Details Table 1 gives the details of eight specimens. Four Type-A specimens had gaps only at the column ends, and four Type-B specimens had an additional gap at the mid-height (see Fig. 2). The nomenclature of the specimens in the table can be explained by the example of specimen S-1.5-0-A: S denotes square TSRC column; 1.5 represents the thickness of steel tube in millimeters; 0 denotes the load eccentricity in millimeters; Parameters for the test specimens included the tube thickness (t = 1.5 mm and 2.0 mm) and eccentricity (e = 0 mm and 25 mm). A cold-formed steel plate was used to fabricate the outer square tube, and the encased steel section was a hot-rolled H section. The average yield strengths are presented in Table 1, where f yt is the yield strength of the tube, and f ys is the yield strength of the steel section. The cubic strength of concrete (f cu ) was determined by three 150 mm cubes. Figure 2 depicts the instrumentation layout for the specimens. Note that the experimental results of Type-A specimens without the additional tube gap can be found in Zhou et al. (2015). The four specimens in Zhou et al. (2015) were renumbered in this paper for the convenience of comparison.

V-shaped hinge LVDTs

100

B

L

Gap

Weld seam

8

6

B Cross section Type-A

Type-B

Stiffener

Grooved plate

e Loading

Fig. 2. Details of the specimens and the test up

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Table 1. Detail information of specimens Specimen

Group

L (mm)

B (mm)

t (mm)

S-1.5-0-A

A

1200

200

1.5

S-1.5-25-A

1200

200

1.5

S-2-0-A

1200

200

S-2-25-A

1200

f yt (MPa)

f cu (MPa)

f ys (MPa)

N ue (kN)

Source

0

324.4

80.61

285.4

2726.7

Zhou et al. (2015)

25

324.4

80.61

285.4

2108.9

Zhou et al. (2015)

2

0

290.1

80.61

285.4

3044.1

Zhou et al. (2015)

200

2

25

290.1

80.61

285.4

2142.9

Zhou et al. (2015)

1200

200

1.5

0

324.4

80.61

285.4

3070.3

This investigation

S-1.5-25-B

1200

200

1.5

25

324.4

80.61

285.4

2091.4

This investigation

S-2-0-B

1200

200

2

0

290.1

80.61

285.4

3268.9

This investigation

S-2-25-B

1200

200

2

25

290.1

80.61

285.4

2065.2

This investigation

S-1.5-0-B

B

e (mm)

2.2 Experimental Results 2.2.1 Failure Mode Figure 3 illustrates the failure modes of the specimens. For the axially loaded specimens (e = 0 mm), local buckling of the steel tube was observed near the top or bottom ends. Concrete was crushed at the location where tube terminated. Similarly, for the eccentrically loaded specimens (e = 25 mm), local buckling was also observed at the location near the end of the specimens. However, the buckling occurred at two or more locations and was more severe. The damage degree of Type-A specimens was more serious than that of Type-B specimens. There was no significant difference in failure modes between Type-A and Type-B specimens. From the test observations, it is recommended that the thin-walled steel tube of both Type-A and Type-B specimens should be stiffened at the column ends to improve the composite effect. 2.2.2 Load-Deformation Relationship Axial load (N) versus mid-height lateral deflection (um ) curves for all the specimens are presented in Fig. 4. The specimens of group t = 1.5 mm and t = 2.0 mm are shown in Fig. 4(a) and (b), respectively. The ultimate strength N ue of the column is summarized in Table 1. For the axially loaded specimens (e = 0 mm), the steel tube longitudinal stress of the Type-B specimen with an additional gap at the mid-height became smaller due to the less bonding and friction between the steel tube and the concrete. The ultimate strengths N ue of Type-B specimens were higher than those of the Type-A specimens: N ue of the t = 1.5 mm specimen was 12.6% higher and t = 2 mm specimen 7.4% higher. For the eccentrically loaded specimens (e = 25 mm), the steel tube on the tensile side of the Type-B specimen was detached, so the tube near the mid-height gap was

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Initial geometric

Local buckling Local buckling

Cracks

Cracks

S-2-0-A

S-2-0-B

S-1.5-25-A

S-1.5-25-B

Fig. 3. Comparison of failure modes

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3 Nonlinear Analysis 3.1 Model Description The finite element model of the TSRC column was established. The meshing and boundary conditions are shown in Fig. 5. In the model, the S4R element was used to simulate all the steel tubes and steel. The C3D8R element was used for the concrete. The concrete was simulated by the damage plastic model (Yu et al. 2010). The stress-strain relationship of concrete under compression was defined by Yan et al. (2019b), which was modified

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from the stress-strain relationship of Mander et al. (1988). The elastoplastic model was used for steel and steel tube. A surface-to-surface contact interaction was applied at the interface of the steel tube and concrete column, by specifying a hard contact in the direction normal to the interface plane and using Mohr-Coulomb friction model with a fiction coefficient of 0.6 for the tangential behavior (Zhou et al. 2018). The interface element allowed separation of the surfaces under tensile force. However, both contact elements were not allowed to penetrate into each other.

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3.2 Effect of Local Geometric Imperfection The shape of local geometric imperfection is often assumed to be the same as that of the first-order buckling mode (Dawson and Walker 1972), as shown Fig. 6(a). The firstorder buckling shape showed outward deformation since the in-filled concrete provides a rigid support for the steel tubes. The amplitude of the imperfection was taken as 0.01B (Han 2016). It can be seen from Fig. 6(b) and (c) that when considering the local geometric imperfection of the steel tube, the average value of the ultimate strength of the specimen decreased by 1.2% only. However, the initial geometric imperfection reduced the ultimate strength of concrete-filled steel tubular columns by 3.7% (Tao et al. 2009). Therefore, the influence of the local geometric imperfection of the steel tube was not considered in the following parameter analysis to reduce calculation cost. 3.3 Effect of Residual Stress The square steel tube was formed by welding two cold-formed U-shaped steel plates. The residual stress distribution of the steel tube was treated using the simplified model in Fig. 7(a) (Tao et al. 2007, 2009). Taking specimen S-2-25-B as an example, when the residual stress of the steel tube was considered, the ultimate strength decreased by 0.6%

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only, as shown in Fig. 7(b). However, the residual stress reduced the ultimate strength of concrete-filled steel tubular columns by 1.0% (Tao et al. 2009). Since the steel tube was thin and did not directly carry the longitudinal load, the residual stress was not considered in the following parametric analysis. 3500 3000

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3.5 Parametric Study The width of the standard column was chosen as 600 mm. The considered parameters included gap patterns (Type-A and Type-B), width-to-thickness ratio of steel tube (B/t), eccentricity ratio (2e/B), and length-to-width ratio (L/B). The values of these parameters are listed in Table 2. Figure 9 shows the comparison of the ultimate strength of the Type-A and Type-B specimens. The ultimate strength of the Type-B specimen was slightly lower than that of the Type-A counterpart, and the difference in the ultimate strength of the two types of

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specimens ranged between 4.9% and 11.4%. With the increase of length-to-width ratio (L/B) and eccentricity ratio (2e/B), the difference in the ultimate strength between the two types of specimens increased slightly. This is because the specimens failed by flexure, and the additional gap in the steel tube of the Type-B columns reduced the bending resistance, while the Type-B specimens also showed good ductility. From the numerical analysis and test results, the axial compressive capacity between Type-A and Type-B specimens showed opposite trend, and this issue also confused the authors. According to the author’s speculation, the numerical analysis results were reasonable. Table 2. Values of studied parameters Parameter

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4 Conclusions (1) Both Type-A and Type-B specimens showed similar tube buckling and concrete crushing failure patterns. The additional gap in the middle-height of the column tube did not affect the failure mode. The additional gap could delay and improve the local buckling of the steel tube. It is recommended that the thin-walled steel tube of both Type-A and Type-B specimens should be stiffened at the column ends to improve the composite effect. (2) For the axially loaded specimens, the test ultimate strength of Type-B specimens was 7.4–12.6% higher than that of Type-A specimens. For the eccentrically loaded specimens (2e/B = 0.25), the test ultimate strength of Type-B specimens was 1.0– 3.6% lower than Type-A specimens, while the ductility was better.

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(3) The finite element analysis results demonstrated the ultimate strength of the tubed STRC specimens with initial geometric imperfection and residual stress of the steel tube only decreased by 0.6–1.2%. The initial imperfection of the steel tube on tubed column could be ignored in the finite element analysis, and the influence is much smaller than that of concrete-filled steel tubular columns. (4) For the axially and eccentrically loaded specimens (2e/B = 0.00, 0.25, 0.5, 0.75, 1.00), the parametric analysis results showed that the ultimate strength of a Type-B specimen was slightly lower, ranging between 4.9% and 11.4% than that of its counterpart Type-A specimen, and the difference became larger with increasing eccentricity. The finite element analysis and test results on the axial compression capacity showed different trend, and this issue needs further experimental researches.

Acknowledgements. The authors greatly appreciate the financial support provided by the National Natural Science Foundation of China (Nos. 51908045 and 51878097). However, the opinions expressed in this paper are solely the authors’ own.

References Dawson, R.G., Walker, A.C.: Post-buckling of geometrically imperfect plates. J. Struct. Div. 98(1), 75–94 (1972) Gan, D., Guo, L., Liu, J.: Seismic behavior and moment strength of tubed steel reinforced-concrete (SRC) beam-columns. J. Constr. Steel Res. 67(10), 1516–1524 (2011) Han, L.: Concrete Filled Steel Tubular Columns-Theory and Practice, 7th edn. Science Press, Beijing, China (2016).(in Chinese) Liu, J., Li, X., Zang, X., Chen, Y.F., Wang, X.: Hysteretic behavior and modified design of square TSRC columns with shear studs. Thin-Walled Struct. 129, 265–277 (2018) Liu, J., Li, X., Zang, X., Wang, X., Chen, Y.F.: Seismic behavior of shear-critical circular TSRC columns with a shear span-to-depth ratio of 1.3. Thin-Walled Struct. 134, 373–383 (2019) Liu, J., Wang, X., Qi, H.: Behavior and strength of circular tubed steel-reinforced-concrete short columns under eccentric loading. Adv. Struct. Eng. 18(10), 1587–1595 (2015) Mander, J.B., Priestley, M.J.N., Park, R.: Observed stress-strain behavior of confined concrete. J. Struct. Eng. 114, 1827–1849 (1988) Qi, H., Guo, L., Liu, J., Gan, D., Zhang, S.: Axial load behavior and strength of tubed steel reinforced-concrete (SRC) stub columns. Thin-Walled Struct. 49, 1141–1150 (2011) Tao, Z., Han, L.H., Wang, D.Y.: Experimental behaviour of concrete-filled stiffened thin-walled steel tubular columns. Thin-Walled Struct. 45(5), 517–527 (2007) Tao, Z., Uy, B., Han, L.H.: Analysis and design of concrete-filled stiffened thin-walled steel tubular columns under axial compression. Thin-Walled Struct. 47, 1544–1556 (2009) Tomii, M., Sakino, K., Xiao, Y., Watanabe, K.: Earthquake resisting hysteretic behavior of reinforced concrete short columns confined by steel tube. In: Proceedings of the International Speciality Conference on Concrete Filled Steel Tubular Structures, Harbin, China, pp. 119–125 (1985) Wang, X., Liu, J., Zhou, X.: Behaviour and design method of short square tubed-steel-reinforcedconcrete columns under eccentric loading. J. Constr. Steel Res. 116, 193–203 (2016) Yan, B., Gan, D., Zhou, X.: Influence of slenderness on axially loaded square tubed steel-reinforced concrete columns. Steel Compos. Struct. 33(3), 375–388 (2019)

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Yan, B., Zhou, X., Liu, J.: Behavior of circular tubed steel-reinforced-concrete slender columns under eccentric compression. J. Constr. Steel Res. 155, 342–354 (2019) Yu, T., Teng, J.G., Wong, Y.L., Dong, S.L.: Finite element modeling of confined concrete-I: Drucker-Prager type plasticity model. Eng. Struct. 32, 665–679 (2010) Zhou, X., Liu, J.: Seismic behavior and strength of tubed steel reinforced concrete (SRC) short columns. J. Constr. Steel Res. 66, 885–896 (2010a) Zhou, X., Liu, J.: Performance and Design of Steel Tube Confined Concrete. Science Press, Beijing, China (2010b) (in Chinese) Zhou, X., Yan, B., Liu, J.: Behavior of square tubed steel reinforced-concrete (SRC) columns under eccentric compression. Thin-Walled Struct. 91, 129–138 (2015) Zhou, X., Yan, B., Liu, J., Gan, D.: Axial load behavior of circular tubed reinforced concrete with different length-to-diameter ratios. J. Build. Struct. 39(12), 11–21 (2018). (in Chinese) Zhou, X., Zang, X., Wang, X., Liu, J., Frank Chen, Y.: Seismic behavior of circular TSRC columns with studs on the steel section. J. Constr. Steel Res. 137, 31–36 (2017)

A Modified Beam-to-Column Connection for Steel Modular Structures with Enhanced Repairability Jiajia Xu1 , Xudong Qian1(B) , Chengguang Xu2 , and Ran Tao2 1 Department of Civil and Environmental Engineering, 1 Engineering Drive 2,

Singapore 117576, Singapore [email protected], [email protected] 2 China Harbour Engineering Co., Ltd., Beijing 100027, China {cgxu,rtao}@chec.bj.cn

Abstract. This paper presents an investigation on the static strength of a modified beam-to-column connection in steel modular structures. The modified beam-tocolumn connection aims to enhance the repairability of the connection after an extreme loading condition. The onsite installation of the connection entails only bolt connections with the welding procedure completed in the pre-fabrication procedure in a factory. The current study examines the static strength of the beam-tocolumn connection under static loading conditions, and confirms that the proposed connection demonstrates sufficient moment resistance under static conditions. The parametric investigation examines three different effects on the moment resistance of the proposed connection scheme. Keywords: Modular frame structure · Bolt connection · Beam-column connection · Steel structure

1 Introduction Modular construction has become increasingly popular in the current construction industry. Compared to the traditional construction, modular construction has advantages on standardization of the construction units, reduction in the construction waste, savings in the transportation and construction cost. Modular construction comprises prefabricated units that are installed on-site as load-bearing “building blocks”(Lawson et al. 2012). The modular concept allows the building to be divided into different types of units with diverse functions. Each unit can be freely combined and assembled to form a complete structure according to required functions. Meanwhile, the module units are relatively independent, they can be disassembled, replaced and recycled after the current design life cycle. The connection remains one of the most critical structural components for modular structures. There are different types of connections in a modular structure, including the intra-module connection, module-to-module connection, module-to-frame connection and module-to-foundation connection. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 625–634, 2023. https://doi.org/10.1007/978-981-19-7331-4_50

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The intra-module connection connects the members within the same modular units. Compared to other types of connection, the intra-module connection has the lowest requirement for load bearing capacity. Doh et al. (2016) investigated and analyzed a hollow cube steel bracket connection. Each face of the cube has 4 bolt holes, and two opposite faces are made hollow to facilitate the transportation. Dhanapal et al. (2019) analyzed a typical corner vertical connection made of VectorBloc connector. This connection can be used for both the intra-module connection and module-to-module connection. The experimental results showed that its failure mode is ductile and the failure load is much higher than the anticipated design loads. Module-to-module connections, also known as the inter-module connections, provide horizontal and vertical connections for different modular units. Chen et al. (2017) proposed a beam-to-beam bolt connection, which provides easy working access without being affected by the structural members. The module-to-module connection often utilizes a combination of bolts and end plates (Sendanayake et al. 2019; Gunawardena 2016). Sendanayake et al. (2019) analyzed the seismic performance of a column-tocolumn connection. The interlayer between the upper and lower columns consists of resilient layers and steel connector plates to provide ductility and energy dissipation capacity. Gunawardena (2016) focused on the behavior of the proposed connection under various lateral loading conditions and simulated the end plate as spring elements. The module-to-module connection may also adopt the post-tensioned rods and tie plates (Chua et al. 2020; Lacey et al. 2019). The module-to-foundation connection transfers the loading and moment from the upper modules to the foundation. Park et al. (2016) introduced an embedded steel column-to-foundation connection for modular structural systems. Their research demonstrate that the proposed connection is able to develop full strength of the column under seismic action. The module-to-frame connection connects the box module units with the outer frame, typically found in stacked module structures (Deng et al. 2020). Such structures exhibit strong resistance against lateral actions, such as the wind load and earthquake actions. Many existing connections in prefabricated structure can be improved and modified for these module-frame hybrid structures. For example, to protect the column under critical loading, Li et al. (2003) introduced a connection to transfer the plastic hinges outward by adding a weakened beam end. Yang et al. (2021) proposed a new type of H shape beam-column connection which is convenient to install. Similarly, Chen et al. (2006) investigated a weakened square column tree moment resistance connection which is suitable to combine with in-fill box module structure. However, the repairability and reproducibility of modular connections are more demanding than those of conventional prefabricated structures. This paper presents an improved H shape beam-to-column connection, to be applied in inter-module or module-to-frame structures, with enhanced repairability and ductility of connecting components. The calibrated numerical analysis examines the static strength of the proposed connection.

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2 Calibration of Finite Element Analysis 2.1 Reference Connection Figure 1 illustrates the configuration of the beam-to-column connection originally proposed by Yu (2013). As shown in Fig. 1, the beam-to-column connection entails both welding and bolt details, with the welding fabricated in a factory and the onsite construction includes only the bolting process. Figure 2 illustrates the application of the module to frame structure where the connection shown in Fig. 1 is typically applied. Figure 3 and Table 1 presents the material properties for the base metal and the bolt adopted by Yu et al. (2014) and Yang et al. (2021) in their numerical analysis. Yu et al. (2014) have previously validated their numerical analysis against the experimental study. Both the beam and column are made of the Q235B steel. The elastic modulus for the steel material equals 206 GPa, with a Poisson’s ratio of 0.3. The bolts utilize the frictional high-strength bolt of Grade 10.9, while the coefficient of friction between different surfaces equals 0.45. The column has a section 300 mm × 300 mm with the web thickness equal to 10 mm and the flange thickness 15 mm. The beam section has a depth of 400 mm, a width of 200 mm, a web thickness of 8 mm and a flange thickness of 13 mm. The flange splice plate has the dimension (length × width × thickness) of 610 mm × 240 mm × 10 mm, while the web splice plate has the dimension 340 mm × 210 mm × 10 mm.

Fig. 1. Configuration of the module-to-frame connection [Yu (2013)]

The beam-to-column connection shown in Fig. 1 employs splicing plates, as illustrated in Fig. 4. The bolt for both the flange and web utilizes the M20 bolts.

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Fig. 2. Module-frame hybrid structures.

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Fig. 4. Splicing plate details for the flange and web.

2.2 Finite Element Modeling The current study generates the finite element model using the pre-processing software Patran (MSC Software Corporation 2021), with the numerical analysis performed in ABAQUS (Dassaault Systemes 2019). The finite element model employs 20-node solid elements with reduced integration (C3D20R in ABAQUS element library). The material properties defined in the finite element analysis follows the properties presented above. All contact surfaces assume the general face-to-face contact, except for the contact between the bolt and plate surfaces, which employs the tied contact. The boundary condition of the joint follows that of the reference study, illustrated in Fig. 5a. The numerical analysis adopts a displacement-controlled load, with a final displacement of 120 mm. 2.3 Comparison of the Connection Behavior Figure 5b shows the finite element model used in the current numerical analysis. Figure 5c illustrates the comparison between the load-deformation curve estimated from the current finite element analysis with that from the reference study (Yu et al. 2014). The displacement in Fig. 5c refers the displacement along z-axis (Fig. 5a) at the free end of the beam. The reasonable agreement between the two studies demonstrate the validity of the current finite element analyses. The connection entails sufficient stiffness and bending capacity required for a rigid full-strength connection.

3 Proposed Connection Scheme Both the current numerical analyses and the investigations reported by Yu et al. (2014) and Yang et al. (2021) indicate that the above connection design incurs plastic deformations near the beam-to-column regions under large displacement loadings. To enhance

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the repairability of the connection after extreme loading events, the connection design requires further improvement, by relocating the plastically deformed region from the beam-to-column area to the splicing plates, which is easily replicable. The modified connection design should, however, maintain a similar stiffness and moment resistance as the original connection design. To achieve the above requirements, the current study proposes a modification to the flange splicing plate, by introducing a twin splicing plate, as shown in Fig. 6. The top and bottom of the beam flange now connect through two splicing plates, with an opening in the exterior splicing plate. The exterior plate with an opening, aims to function as an energy dissipation plate, and requires replacement after an extreme loading event, while the interior splicing plate remains connected to withstand the gravity load of the structure during repair and replacement. The shape of the opening shown in Fig. 6 minimizes the stress concentrations in the splicing plates and therefore leads to improved ductility, as evidenced from an investigation reported by Xie et al. (2004). Similar to the original connection design, the proposed connection requires installation of the bolts only during the onsite construction, with all welding procedures completed in factory prior to the onsite installation.

4 Parametric Study on Connection Performance This section presents the parametric investigation on the static strength for the proposed connection with different joint geometry and material parameters. The parametric analysis covers the following three aspects: 1) the effect of opening size for the twin splice plates; 2) the effect of opening size in the single splice plate; and 3) comparison between the twin splice plate and the single splice plate. 4.1 Effect of Opening Size for Twin Splice Plates To understand the impact of the opening size on the connection performance, the numerical analysis includes four different models: the connection without an opening and

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Fig. 6. A pair of proposed twin splicing plates on the beam flange.

three different connections with different moment capacities compared to the plastic moment capacity of the beam. Both the beam and column sizes are the same as those in the reference study. The material properties are the same as presenting in Table 1. Assuming that the plastic moment capacity of the beam is equal to Mp,beam , the moment capacity in the three connections with openings corresponds to Mp,beam , 0.9Mp,beam and 0.8Mp,beam . The corresponding opening size D is equal to 36 mm, 79.2 mm and 123.2 mm, respectively. Figure 7 demonstrates the negligible effect of the opening size on the load-deformation responses of the connection. 4.2 Effect of Opening Size for Single Splice Plates In a similar effort to understand the effect of opening size in the single splice plate, this study builds three additional connection models with a single splice plate, instead of the twin splice plate. In the single splice plates, the nodes on the contact surfaces of the exterior and interior plates are equivalent to simulate a no-slipping behavior. The thickness of single splice plate is equal to 14 mm, which is the same the total thickness of the twin splice plate. The yield strength of the single splice plate is 235 MPa. The openings in the single splice plate are 80, 110 and 152 mm, which yield a moment capacity of 0.7Mu,beam , 0.65Mu,beam and 0.576Mu,beam , respectively. Figure 8a illustrates the typical finite element model for the connection with a single splice plate with an opening. Figure 8b compares the load-deformation responses the connection with a single splice plate with different opening sizes. The increased opening size leads to slight decreases in the load resistance of the connection.

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4.3 Twin Splice Plates Versus Single Splice Plate The twin splice plates, in contrast to the single splice plate, enhances the repairability of the connection after the extreme loading events, with additional processes in the installation procedure. The twin splice plate requires bolting of a new layer of plates during the onsite construction. This section thus compares the load-deformation responses for the connection with twin splice plate and single splice plate. Figure 9 shows the negligible difference in the load-deformation responses of the two different connection schemes.

5 Conclusions This paper proposes a modified connection scheme by using the twin splice plates in the beam-to-column connection for modular steel construction. The current study calibrates the finite element analysis from a previous study with a similar joint configuration. The subsequent numerical analyses examine the key parameters in the static strength of the proposed connection scheme. The above study supports the following conclusions:

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1. The twin splice connection with different openings demonstrates sufficient moment resistance, as reflected by the load-deformation curves of the connection. The plastic moment capacity of the beam corresponds to an applied load of 218 kN. 2. The opening in the exterior plate of the twin splice plate does not impose significant effect on the static strength of the connection. The current study recommends an intermediate opening size with the connection plastic moment capacity corresponding to 80% of the beam moment capacity. 3. The twin-splice plate connection exhibits similar load-deformation responses as compared to the single splice plate connection.

References Chen, C.-C., Lin, C.-C., Lin, C.-H.: Ductile moment connections used in steel column-tree moment-resisting frames. J. Constr. Steel Res. 62, 793–801 (2006). https://doi.org/10.1016/ j.jcsr.2005.11.012 Chen, Z., Liu, J., Yu, Y.: Experimental study on interior connections in modular steel buildings. Eng. Struct. 147, 625–638 (2017). https://doi.org/10.1016/j.engstruct.2017.06.002 Chua, Y.S., Liew, J.Y.R., Pang, S.D.: Modelling of connections and lateral behavior of high-rise modular steel buildings. J. Constr. Steel Res. 166, 105901 (2020). https://doi.org/10.1016/j.jcsr. 2019.105901 Dassaault Systemes: ABAQUS User’s Manual, Version 6.19. Dassault Systèmes Simulia Corp, United States (2019) Deng, E.-F., et al.: Seismic performance of mid-to-high rise modular steel construction—a critical review. Thin-Walled Struct. 155, 106924 (2020). https://doi.org/10.1016/j.tws.2020.106924 Dhanapal, J., Ghaednia, H., Das, S., Velocci, J.: Structural performance of state-of-the-art VectorBloc modular connector under axial loads. Eng. Struct. 183, 496–509 (2019). https://doi.org/ 10.1016/j.engstruct.2019.01.023 Doh, J.-H., Ho, N.M., Miller, D., Peter, T., Carlson, D., Lai, P.: Steel bracket connection on modular buildings. Steel Struct. Constr. 121 (2016). ISSN 2472-0437

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Gunawardena, T.: Behaviour of prefabricated modular buildings subjected to lateral loads. PhD thesis, University of Melbourne (2016) Lacey, A.W., Chen, W., Hao, H., Bi, K., Tallowin, F.J.: Shear behaviour of post-tensioned intermodule connection for modular steel buildings. J. Constr. Steel Res. 162, 105707 (2019). https:// doi.org/10.1016/j.jcsr.2019.105707 Lawson, R., Ogden, R., Bergin, R.: Application of modular construction in high-rise buildings. J. Arch. Eng. 18 (2012).https://doi.org/10.1061/(ASCE)AE.1943-5568.0000057 Li, Q.C., Su, P.Z., Gu, Q., Chen, A.G.: Experimental study on frictional energy-dissipation behavior of bolted steel beam splicing in rigid frame. Jian Zhu Jie Gou Xue Bao 24, 54–59 (2003). https:// doi.org/10.3321/j.issn:1000-6869.2003.04.008 MSC Software Corporation. MSC Patran User’s guide (2021) Park, K.-S., Moon, J., Lee, S.-S., Bae, K.-W., Roeder, C.W.: Embedded steel column-to-foundation connection for a modular structural system. Eng. Struct. 110, 244–257 (2016). https://doi.org/ 10.1016/j.engstruct.2015.11.034 Sendanayake, S.V., Thambiratnam, D.P., Perera, N., Chan, T., Aghdamy, S.: Seismic mitigation of steel modular building structures through innovative inter-modular connections. Heliyon 5, e02751 (2019). https://doi.org/10.1016/j.heliyon.2019.e02751 Xie, X., Yang, N., Yang, Q.: Parameter analysis of steel reduced beam section connection. Steel Struct. 19, 50–52 (2004) Yang, W., Yu, Y., Zhang, H.: A study on the mechanical properties of HU-shaped assembly connection strengthened by steel frame flange. Prog. Steel Build. Struct. 23 (2021) Yu, Y.: A Steel Structure Beam Column of Assembled Rigid Joint (2013). 201220089213 Yu, Y., Wei, L., Fu, G., Wang, Y.: Nonlinear static analysis of a new beam-column assembly rigid connection. World Earthq. Eng. 30, 50–56 (2014)

Numerical Analysis of Precast Shear Wall with Opening and Unspliced Vertical Distribution Bars Qi Cai1 , Xiaobin Song1(B) , and Xuwen Xiao1,2 1 College of Civil Engineering, Tongji University, Shanghai 200092, China

[email protected] 2 China Construction Engineering Corp, Beijing 100037, China

Abstract. To investigate the effect of opening on the lateral behaviour of precast concrete shear wall with unspliced vertical distribution bars, a series of nonlinear numerical analyses is carried out. Cohesive elements and nonlinear springs are adopted to simulate the joints around the precast wall panel and the steel bars across the joints, respectively. The numerical analysis model was verified based on test results of the lateral behaviour of precast shear wall with unspliced vertical distribution bars. Based on the verified model, parametric studies are carried out for the influence of the opening’s characteristic parameters and the length of the boundary element. The results show that the influence of the area ratio and location of the opening on the lateral behaviour of the precast shear wall is similar to that of cast-in-situ shear walls with openings. Compared with the cast-in-situ shear wall with opening, the load-carrying capacity and stiffness of the precast shear wall similarly decreased with the increasing opening area ratio; and the stiffness of the precast wall decreased up to 47.6%. The wall beneath the window opening can slightly compensate for the weakening effect of the unspliced vertical bars on cracking, but the vertical location of the opening had little effect on the lateral behaviour of the precast shear wall with unspliced vertical distribution bars. Finally, the length of the cast-in-situ boundary elements of the precast shear wall was more influential in the stiffness rather than the load-carrying capacity of the shear walls. Keywords: Precast concrete shear wall · Opening · Unspliced vertical distribution bars · Lateral behaviour · Numerical analysis

1 Introduction Compared with the traditional cast-in-situ concrete structure construction, the precast concrete structure has competitive advantages in economy, technology and ecological environment. By virtue of the great lateral resistance and space regularity, the precast concrete shear wall structure is widely applied to residential buildings (Zhang et al. 2015; Xue et al. 2019). Especially, the performance of splicing between precast components plays a crucial role in the mechanical performance of the precast concrete shear wall structure. At © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 635–647, 2023. https://doi.org/10.1007/978-981-19-7331-4_51

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present, the grouting sleeve and grouting anchor connection are frequently utilized for splicing. Previous studies discovered that under the premise of guaranteed grouting quality, the precast shear wall could exhibit superior seismic performance like cast-insitu shear wall (Qian et al. 2017; Jiang et al. 2011). Nevertheless, the concrete shear wall structure is generally designed with a large quantity of small-diameter steel bars, then the grouting sleeve connection could induce a lot of construction, more cost and longer construction period. Besides, the construction quality of grouting sleeves is hard to guarantee (Gao et al. 2018a, b). Fortunately, an innovative precast shear wall with unspliced vertical distribution bars can avoid the grouting for the assembly joints. The innovative precast concrete shear wall structure is shown in Fig. 1. The vertical bars of the precast wall panel are not spliced at the bottom, and the bottom of the precast wall panel rests on a layer of high performance mortar; the protruding bars on the other three sides of the precast wall panel are assembled with the surrounding components through post-cast concrete. Xiao et al. (2021) and Zhang et al. (2021) concentrated the vertical reinforcement in the boundary element areas according to the equivalent flexural load-carrying capacity. Their experimental results showed that the load-carrying capacity, stiffness and energy dissipation of such shear walls without opening were the same as those of cast-in-situ shear walls.

slab

Upper precast wall panel

slab

Unsplicing vertical bars Post cast boundary element Lower precast wall panel (a) Assembly components

(b) Joint to be casted

Fig. 1. Assembly process for precast shear wall with unspliced vertical bars

However, due to architectural considerations such as lighting, windows and doors, the load-carrying capacity, energy dissipation, stiffness and other mechanical properties of shear walls will decrease with the inevitable existence of opening. The mechanical performance of the shear wall is affected by a series of factors such as the area ratio and location and shape of the opening. Wang et al. (2009) found that the larger the opening, the lower the load-carrying capacity and energy dissipation were. Alimohammadi et al. (2019) numerically analysed the influence of the shape of the opening on the mechanical performance of shear walls. It was found that the shear wall with a circular opening had

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the best performance. MegHdadian and Ghalehnovi (2019) and Lin and Kuo (1988) showed that the configuration of oblique bars at the corner of the opening reduced the oblique cracking and compensated for the weakening effect of opening on the loadcarrying capacity and deformation. Similarly, the mechanical performance of precast concrete shear walls with openings is also affected by the splicing of the vertical distribution bars. Wang et al. (2012) compared the composite shear wall with opening and the cast-in-situ shear wall with opening, and found that they had nearly identical mechanical properties. Nonetheless, the unsplicing of vertical bars in precast wall panel induced different failure pattern in shear wall with opening. Yang et al. (2020) conducted quasi-static tests on precast walls with door opening and unspliced vertical distribution bars. The result showed that the cracks at the bottom of the precast wall mainly appeared on the boundary elements, and no crack was observed at the bottom of the walls beside opening. Thus, it’s necessary to further study the performance of the precast shear wall with opening and unspliced vertical bars. For this reason, a numerical model was developed and verified based on the test results of the lateral behaviour of the precast shear walls with and without opening. Then a series of parametric study is carried out to investigate the influence of such parameters as the area ratio and location of opening and the length of the boundary element on the performance of the innovative precast shear wall.

2 Development of the Finite-Element Model 2.1 Numerical Model To study the effect of opening in the precast shear wall with unspliced vertical bars, many numerical models were developed with ABAQUS software. 2.1.1 The Basic Information About Models Based on Appendix C in the specifications in Chinese code for design of concrete structure (GB50010-2010), the uniaxial stress-strain relationship and the corresponding damage factor were determined. For modelling concrete plastic behaviour, the concrete damage plasticity model(CDP) in ABAQUS was adopted. And the primary parameters of CDP model are listed in Table 1. The elastic-linear hardening model with the hardening rule of kinematic was chosen for the reinforcement. Poisson’s ratio and elastic modulus of reinforcement were taken as 0.3 and 200 GPa, respectively. Table 1. The primary parameters for CDP model Dilation angle

Eccentricity

f b0 /f c0

K

Viscosity parameter

30

0.1

1.116

2/3

0.005

As Fig. 2 shows, C3D8R element and T3D2 element were used for concrete and steel bars, respectively, in the numerical model. All bars were embedded in the concrete

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element at the same location without considering the bond-slip between steel bars and concrete. The two types of element share the same nodes. Additionally, the monotonic horizontal displacement load was applied at the top face of the wall. To analyse more walls with various openings, modelling and analysis were automated in ABAQUS with the assistance of python.

(a) Concrete element

(b) Reinforcement element

(c) precast concrete with opening

Fig. 2. Finite element model of the precast shear wall

2.1.2 Precast Joints Interface Simulation As we know, the precast joints around the precast wall panel may be fragile. Cohesive contact was employed to simulate the joints around the precast wall panel, to consider the effect of the joints on the lateral behaviour of precast shear wall. Cohesive contact allows the joint interface to transmit limited tensile stress, shear stress and infinite compressive stress. In this way, the cohesive property comparatively coincides with the mechanical behaviour of concrete, a brittle material with weak tensile capacity. The maximum normal tensile stress of cohesive contact was taken from the tensile strength of concrete, and the tangential strength could be calculated according to Eq. (1) (Mohamad et al. 2015), and the interface roughness Rpm was taken as 5 mm (Fig. 3). τ = 0.2363e0.237Rpm + 0.8766Rpm

(1)

Additionally, aiming to avoid estimating the mechanical behaviour of the joints other than the bottom joint where no bars cross the interface, the spring connector element was adopted to simulate the dowel action of the reinforcement (Fig. 4). The ideal elastoplastic model was used for the connector. According to the Europe code for design of concrete structures (DD ENV 1992-1-1 Eurocode 2), the shear capacity V max and the stiffness K s were calculated by Eqs. (2) and (3), respectively. Vmax =

0.8fu (π ds2 /4) 1.25

0.5Vmax  Ks =  −3 80 × 10 − 86 × 10−5 fc ds

(2) (3)

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Fig. 3. Cohesive law for traction-separation

V connector

Vmax

Ks δVmax

S

Fig. 4. Spring connector in the joint interface and corresponding constitutive model

2.2 Model Verification The area ratio of opening is the primary parameter affecting the mechanical performance of shear wall. The smaller the opening, the more similar performance to the shear wall without opening the shear wall exhibits. (Wang et al. 2009). In an effort to facilitate the study of the effect of various openings on the performance of the prefabricated shear wall, it is essential to verify the numerical model with the shear walls with and without opening. In this way, the numerical model will have better applicability for the precast shear walls with various openings. A specimen of shear wall without opening and a specimen of shear wall with opening were picked for validating the finite element model, and the vertical bars of the precast panels of two specimens were not spliced at the bottom interface.

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2.2.1 Verification for Precast Shear Wall Without Opening and Splicing Vertical Distribution Bars Based on the test specimen PF-1 which is a precast shear wall without opening and splicing vertical distribution bars (Xiao et al. 2021), the corresponding numerical model was established in ABAQUS. The dimensions of the specimen PF-1 and the numerical model are shown in Fig. 5. As can be seen from Fig. 6, for the precast shear wall without splicing vertical distribution bars and opening, the numerical model results agreed well with the experimental results.

Boundary element

Prefabricated panel

(a) Dimension details of specimen PF-1

(b) FE mesh model of specimen PF-1

Load /KN

Fig. 5. Overall schematic diagram of specimen PF-1

4000 3000 2000

PF-1

1000

FEM

0 -40

-20

-1000

0

20

40 60 Displacement /mm

-2000 -3000 -4000 Fig. 6. Comparison of the test result and numerical analysis

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2.2.2 Verification for Precast Shear Wall with Opening and Unspliced Vertical Distribution Bars A precast shear wall with an opening area of 34% was the second test specimen for verification. As Fig. 7 shows, the shear wall size was 4200 mm × 3020 mm × 140 mm, and the opening size was 1800 mm × 2400 mm. With more details in the literature (Yang et al. 2020), a numerical model and a pushover analysis for the specimen were conducted with ABAQUS. Figure 8 shows the comparison of the experimental and numerical skeleton curves, and the stiffness and load-carrying capacity calculated by the numerical model were in good agreement with the test result. Moreover, due to the non-splicing of vertical steel bars in the precast wall panel, a non-identical failure pattern was shown in the precast shear wall with opening. As can be seen from Fig. 8, there was no tensile damage to the precast wall panel beside the opening.

Prefabricated panel

Boundary element

Boundary element

Foundation Unit:

Fig. 7. Dimensions of the precast shear wall (Yang et al. 2020)

FEM

Load / KN

600

Test

400 200 0

-40

-30

-20

-10 -200

0

10

20 30 40 Displacement/ mm

No tensile damage

-400 -600

Fig. 8. Comparison of the test result and numerical analysis

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3 Analysis Plan In order to study the effects of opening on the lateral behaviour of precast concrete shear wall with unspliced vertical distribution bars, 159 finite element models were analyzed. All models were single-story shear walls with a height of 2900 mm, a width of 3300 mm and a thickness of 200 mm. The reinforcement ratio of all shear wall models in this analysis was consistent with that of the PF-1 specimen in the literature (Xiao et al. 2021). And the axial compression ratio was 0.2. As Fig. 1 shows, the boundary element with splicing vertical bars plays a comparatively vital role. Therefore, besides such primary character parameters of the opening as area ratio and location, the length of boundary element should be considered in the analysis plan (Table 2). Table 2 lists the details of all models in this analysis. Table 2. Parameters and details of models No

Length of boundary element /mm

Width of opening /mm

Height of opening /mm

Vertical location of opening/mm

Splicing vertical bars or not?

Quantity of models

Type of shear wall

Primary parameter for analyzing

1

400

0

0

–

Yes

1

Cast-in-situ

2

400

0

0

–

No

1

Precast

Control wall without opening

3

400

900–1800

900–2400

0

Yes

24

Cast-in-situ

4

400

900–1800

900–1800

600

Yes

16

Cast-in-situ

5

400

900–1800

900–2400

0

No

24

Precast

6

400

900–1800

900–2100

300

No

20

Precast

7

400

900–1800

900–1800

600

No

16

Precast

8

400

900–1800

900–1500

900

No

12

Precast

9

500

900, 1200

900–1800

600

No

8

Precast

10

600

900, 1200

900–1800

600

No

8

Precast

11

700

900, 1200

900–1800

600

No

8

Precast

12

800

900, 1200

900–1800

600

No

8

Precast

13

900

900, 1200

900–1800

600

No

8

Precast

Area ratio and location of opening Area ratio and location of opening

The length of boundary element

4 Discussion of Numerical Results In general, with the same opening, the failure pattern of precast shear wall was similar to that of the cast-in-situ shear wall. Figure 9 shows the damage distribution of the walls. The mechanical performance of the innovative precast wall with opening was severely affected by the area ratio, location of opening and the length of boundary element, and the specific influence is discussed as follows. To distinctly characterize the effects of the characteristic parameters of the opening on the lateral behaviour of the shear wall, the stiffness and load-carrying capacity were normalized to those of the corresponding shear wall without opening.

Numerical Analysis of Precast Shear Wall Tensile damage

Tensile damage

Compressive damage

(a) cast-in-situ shear wall

643

Compressive damage

(b) precast shear wall

Fig. 9. Comparison of failure pattern of cast-in-situ shear wall and precast shear wall

4.1 The Effect of Opening Ratio Firstly, the opening area ratio was not surprised to have the greatest influence on the mechanical performance of the precast shear wall with opening. It can be seen from Fig. 10 that there are minor differences between the load-carrying capacity of the castin-situ shear wall with opening and precast wall with opening. However, compared with the cast-in-situ shear wall with opening, the stiffness of precast shear wall with opening decreased up to 47.6% (Fig. 11).

(a)

0.8

1

cast-in-situ precast

0.6

0.4 0.2

Load carrying capacity

Load carrying capacity

1

(b)

cast-in-situ

0.8

precast

0.6 0.4 0.2 0

0 0

0.2 0.4 Area ratio

0.6

0

0.1

0.2 Area ratio

0.3

0.4

Fig. 10. Influence of opening area ratio on the load-carrying capacity: (a) door opening; (b)window opening

4.2 Effect of Opening Vertical Location The lower the wall beneath the opening, the less tensile cracks appeared on the walls beside the opening. Figure 12 shows the comparison of tensile damage distribution of the precast wall. Due to the wall beneath the window opening slightly compensating for the weakening effect of the unspliced vertical bars, there were more tensile cracks in the precast wall panel beside window opening than door opening. In addition, as shown in Fig. 13, the load-carrying capacity of the precast wall with opening didn’t change significantly with various vertical locations of the opening. But the lower wall beneath opening, the greater rigidity of the coupling beam was. In this way, the stiffness of the precast shear wall with the lower wall beneath opening was also relatively greater.

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(a)

(b)

cast-in-situ

0.8

precast Stiffness

Stiffness

0.8

1

cast-in-situ

0.6 0.4

precast

0.6 0.4 0.2

0.2

0

0 0

0.2 0.4 Area ratio

0

0.6

0.2 Area ratio

0.4

Fig. 11. Influence of opening area ratio on the stiffness: (a) door opening; (b) window opening

(a)

(b)

Fig. 12. Comparison of tensile damage distribution of precast shear wall concrete: (a) door opening; (b) window opening

(a)

1

0

0.8

load carrying capacity

1

300

Stiffness

600

0.6

900

0.4 0.2

(b)

0

0.8

300 600

0.6

900

0.4 0.2

0

0 0

0.2 0.4 area ratio

0.6

0

0.2

0.4 area ratio

0.6

Fig. 13. Influence of opening vertical location on (a) stiffness and (b) load-carrying capacity of precast shear wall

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4.3 Effect of the Length of Boundary Element As mentioned above, boundary elements are the most significant vertical splicing. The amount of splicing vertical bars in the precast shear wall is determined by the length of boundary element. Thus, the length of boundary element can theoretically affect the lateral behaviour of the shear wall with opening and unspliced vertical bars. As can be seen from Figs. 14 and 15, for the precast wall with the same opening, the loadcarrying capacity and stiffness changed to a certain extent with the change in the length of the boundary element. And compared with the influence of the length of boundary element on load-carrying capacity, the influence on stiffness was greater. The maximum difference between the precast walls with various length of the boundary element could be 29%. (a)

1

400

500

600

700

800

0.6 0.4 0.2

(b)

900 Load carrying capacity

Load carrying capacity

1 0.8

0

400

500

600

700

800

900

0.8 0.6 0.4 0.2 0

Dimension of opening/ mm

Dimension of opening/ mm

Fig. 14. Influence of the length of boundary element on the load-carrying capacity of precast shear wall: (a) door opening; (b) window opening

(a)

400

500

600

700

800

1

900

(b) 0.8

0.6

0.6

Stiffness

Stiffness

1 0.8

0.4

500

600

700

800

900

0.4

0.2

0.2

0

0

Dimension of opening/ mm

400

Dimension of opening/ mm

Fig. 15. Influence of the length of boundary element on the stiffness precast shear wall with unspliced vertical bars: (a) door opening; (b) window opening

5 Conclusions Based on the discussion of the numerical analysis, we can draw the following conclusions:

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(1) The influence of the area ratio and vertical location of the opening on the lateral behaviour of the precast shear wall is similar to that of cast-in-situ shear walls with openings. (2) The wall beneath the window opening could slightly compensate for the weakening effect of the unspliced vertical bars on cracking, but the vertical location of the opening had little effect on the lateral behaviour of precast shear wall with unspliced vertical distribution bars. (3) The length of the cast-in-situ boundary elements of the precast shear wall was more influential to the stiffness rather than the load-carrying capacity of the precast shear walls.

Acknowledgements. This study was financially supported by the National Natural Science Foundation of China (No. 52078360), and China construction technology R&D Program (No. CSCEC-2016-Z-16). The authors thank all sponsors and all anonymous reviewers very much.

References Alimohammadi, H., Mesfahani, M.D., Yaghin, M.L.: Effects of openings on the seismic behavior and performance level of concrete shear walls, 6(10), 34–39 (2019) Gao, R.D., Li, X.M., Xu, Q.F.: Existing problems and solutions of sleeve grouting in prefabricated monilithic concrete building. Construct. Technol. 47(10), 1–4 (2018) Gao, Z.X., Zhu, W., Chen, Y.F.: Research and application status of non-destructive testing technology for steel sleeve grouting fullness. Guangzhou Architect. 46(5), 20–23 (2018) Jiang, H.B., Chen, Z.X., Zhang, J.Q., et al.: Quasi-Static test of precast reinforced concrete shear wall structure. J. Build. Struct. 32(6), 34–40 (2011) Lin, C.Y., Kuo, C.L.: Behavior of shear wall with opening. In: Proceedings of Ninth World Conference on Earthquake Engineering (1988) Meghdadian, M., Ghalehnovi, M.: Effects of the opening on the behavior of composite steel plate shear wall (CSPSW). J. Rehabil. Civ. Eng. 7(3), 139–152 (2019) Mohamad, M.E., Ibrahim, I.S., Abdullah, R., et al.: Friction and cohesion coefficients of composite concrete-to-concrete bond. Cement Concr. Compos. 56, 1–14 (2015) Qian, J.R., Han, W.L., Zhao, Z.Z., et al.: Pseudo-dynamic substrucutre test on a 3-story full-scale model of prefabricated concrete shear wall structure with rebars splicing by grout sleeves. J. Build. Struct. 38(3), 26–38 (2017) Wang, J., Lou, W., Tanaka, H.: Influence of opening type on seismic behavior of reinforced concrete structural walls. J. Build. Struct. 30(S2), 41–46 (2009) Wang, Z.J., Liu, W.Q., Ye, Y.H., et al.: Experimental study on seismic behavior of reinforced concrete composite shear wall with opening. J. Build. Struct. 33(7), 156–163 (2012) Xiao, X.W., Cao, Z.W., Zhang, S.Q., et al.: Quasi-static test and strut-and-tie modeling of precast concrete shear walls with unconnected vertically distributed reinforcements. Struct. Concr. 22(4), 2258–2271 (2021) Xue, W.C., Hu, X.: State of the art of studies on precast concrete shear wall structures. J. Build. Struct. 40(2), 44–55 (2019) Yang, B.K., Wang, E.C., Liu, K., et al.: Experimental study on seismic behavior of open wall with low-rise fabricated concrete wall panel structure. Sci. Technol. Eng. 20(34), 14213–14222 (2020)

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Zhang, S.H., Ye, Y.H., Sun, R., et al.: Experimental study on seismic performance of profile steel concrete composite shear wall. J. Nanj. Tech. Univ. (Nat. Sci. Edition) 37(6), 87–93 (2015) Zhang, S.Q., Chen, Y.S., Liu, Y.N., et al.: State of the art study on vertical connection degree for precast shear wall structure system. J. Southwest Jiaotong Univ. 56(4), 828–838 (2021)

Structural Health Monitoring and Sensor Technologies for Civil Infrastructure

Evaluation of the Application of Unmanned Aerial Vehicle Technology on Damage Inspection of Reinforced Concrete Buildings Jiehui Wang(B) and Tamon Ueda Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China {wangjiehui,ueda}@szu.edu.cn

Abstract. As for the damaged structures that suffered a destructive earthquake, damage inspection is essential to evaluate the seismic safety as well as assess the long-term performance for planning a suitable structural rehabilitation strategy for further service. However, the conventional inspection method by human hands is time-consuming, highly costly, and highly risky for inspectors’ life safety in the fieldwork. To summarise the current situation for structural damage inspection and explore the future potentials of newly-developed technology in this field, the application and usage of unmanned aerial vehicles (UAVs) that are commonly known as drones have been reviewed and evaluated herein. Presented in this study is the basic concept of the UAV-based damage inspection, in which drones are employed as useful tools to inspect and monitor the damaged condition of buildings by collecting photography data. Besides, a conceptual comparison with the conventional approach is consequently given for understanding the advantages and limitations of the UAV-based damage inspection approach. Also, discussions composing of instructions, recommendations, existing challenges, and future directions to address the UAV-based damage inspection approach into further practice are suggested. Keywords: Life cycle management · Reinforced concrete building · Damage inspection · Unmanned aerial vehicle technology

1 Introduction Life cycle management (LCM) is noticed and used to achieve a sustainability goal related to different fields from civil and building engineering perspectives in recent years. The LCM includes all phases of the service life, from planning, conceptual and detailed design, execution, to operation, maintenance, repair, and decommissioning to optimize the life-cycle aspects of a structure (Frangopol and Soliman 2016). Within all these phases, structural maintenance and repair are important issues for ensuring life safety and supporting the normal manner of the people living or working there. Particularly structures that are damaged in disasters such as earthquakes needed to be paid attention to their maintenance and retrofitting to elongate their lifetime for further service. Also, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 651–666, 2023. https://doi.org/10.1007/978-981-19-7331-4_52

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appropriate retrofitting strategies for these damaged structures are usually related to saving resources, improving the use efficiency, which contributes to a resilient city and global sustainability. To process a retrofitting or renewing of these earthquake-damaged structures, there is a critical need to capture structural damages and understand current conditions for a decision on rehabilitation and maintenance in a near future. Thus, an appropriate damage inspection can provide the most basic information as the first action. Considering all types of structures, post-earthquake damaged buildings are particularly concerned in this work since they are playing an important role in people’s daily life rather than other structural types. Once an earthquake occurs, especially strikes large cities, destructive damage (both structural and nonstructural damages) could happen to buildings, including residential and official buildings, for instance as given in previous post-earthquake investigation reports (e.g. the 1995 Hyogo-ken Nanbu Earthquake, 2011 Tohoku Earthquake (NILIM and BRI 2012), and the 2016 Kumamoto Earthquake (NILIM and BRI 2016) in Japan), as shown in Figs. 1 and 2. For these damaged buildings, a critical issue following the major earthquake is to assess the damage conditions for repairing quickly in a short time for preventing more severe damage from secondary earthquakes due to potential aftershocks and providing information for the next-step building repair, or for further usage from a sustainability perspective. Considering these needs, damage inspection with high effectiveness and accuracy is expected. A damage inspection on these post-earthquake damaged buildings can provide necessary information for experts, building owners, or government to identify whether or not these buildings can maintain enough seismic performance and should be used continually with a quick temporary structural repair done in the case of aftershocks for people’s life safety. Besides, damage inspection can also give valuable information to help people determine buildings that should be repaired requiring a further well-prepared retrofitting strategy for long-term rehabilitation.

Fig. 1. Building damages in the 2011 Tohoku Earthquake (NILIM and BRI 2012).

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Fig. 2. Building damages in the 2016 Kumamoto Earthquake (NILIM and BRI 2016).

Based on these considerations, a well-organized damage inspection with high efficiency and accuracy is the very beginning action needed to be taken prior to further rehabilitation procedures. A damage inspection always includes an overall damage survey of the entire building, a detailed damage investigation of structural components, and even for critical non-structural components, finally reaching an overall damage rating. For a quick inspection in a short time after the earthquake, when a building is considered nearly collapsed or structurally unsafe, experts intend to make a decision not to enter anymore. However, in the situation that no obvious evidence shows the building is unsafe, it is hard to simply determine safe or not to continually use this building, thus it is of significant importance from the investigators’ point of view to assess the actual structural condition and damage level. On the other hand, for a long-term community restoration plan, it is as well important to determine and prepare repair or renovation plans as soon as possible. Thus, it is expected to give perspective suggestions for both quick and further long-term retrofitting strategy organization at both structural member-and overall levels. To perform appropriate damage inspection after earthquakes, a technical guideline, the Japanese Guideline for Post-Earthquake Damage Evaluation and Rehabilitation (JBDPA 2017) originally developed by the Japan Building Disaster Prevention Association in 1991 and revised in 2001 and 2017 (subsequently referred to as JBDPA Guideline) based on lessons from historical earthquakes over the Japanese archipelago such as the 1995 Hyogo-Ken-Nambu (Kobe) and 2011 Pacific coast of Tohoku (Tohoku) earthquakes has been improved and applied in practice in Japan. According to this guideline, a post-earthquake damage inspection is always performed in two phases, a quick inspection phase, and a more precise detailed inspection phase. The quick damage inspection is usually performed urgently within a short time just after an earthquake. In contrast, the detailed damage inspection on all structural components and some of the critical nonstructural components, and an evaluation on the damage condition are quantitatively performed for providing directions for the next-step rehabilitation. According to the JBDPA Guideline (JBDPA 2017), the damage inspection is always performed visually by engineers, based on the inspection results (type of damages,

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damage locations, numbers, configurations of cracks, etc.), damages to each structural member are classified into one of the damage ranks I through V. However, several disadvantages and inconvenience have been noticed using the mannul approach, such as (i) a damage inspection on buildings that cannot be confirmed stable and safe is with potentially high risk for investigators’ life safety concerning secondary disaster due to the potential aftershocks or collapse, (ii) in densely populated large cities, the number of damaged buildings after an earthquake that need to be inspected might be enormous, which requires a large number of investigators at the same time, (iii) it could take a significant amount of time (several days or even several months) to finish the full inspection for a large number of damaged buildings, which may lead to severe consequences, such as some progressive collapse in buildings without timely major repair or structural maintenance, (iv) some large-scale or high-rise buildings are difficult for investigators to access, or needs additional instruments such as temporary ladders or scaffolds, as well as traffic block or other inconvenience potentially brought to the society, (v) the quick visual damage inspection and damage level identification is occasionally determined only based on the outside inspection of the building surface, it is hard to enter in or access to investigate the damage condition of some critical structural members even though the condition of these members are highly influencing the seismic performance and safety of the entire building, (vi) the damage evaluation and rating result highly relies on the knowledge, experience, and understanding local building codes by the investigators, which might bring inaccuracy and discrepancy to the inspection and damage rating results according to different investigators, and (vii) it is difficult to synchronize and update damage inspection results in a real time manner by the conventional approach. Thus, there is a need to seek a safer, more convenient, efficient, accurate, and time and human resource-saving approach for building damage inspection. In recent times, unmanned aerial vehicles (UAVs) that rapidly developed are noticed and have begun to be applied to the damage inspection field. This study intends to provide a summary and evaluation focusing on the use of UAV technology to meet structural damage inspections including the basic concept, conceptual comparison with the conventional method, as well as instructions, recommendations, limitations, challenges faced by this new inspection approach for a practical application. Furthermore, potential future directions for practical application have been also suggested.

2 Unmanned Aerial Vehicle (UAV) Technology UAVs are generally defined as aircraft such as drones without any human pilots and can be controlled remotely by human beings via the computer on the ground autonomously or semi-autonomously. Drones were initially invented and mainly employed for military use around the 1970s and 1980s while small and light drones, such as that shown in Fig. 3, have been developed and extended to applications in various fields in recent times due to their capacity of ease controlling and large-scale for flight. Particularly in recent decades, various activities and applications, such as in the fields of agriculture photography, geographic mapping, traffic monitoring, civil and building construction management, infrastructure inspection, engineering surveys, commercial imaging flights, and so on, have been widely expanded. Regarding the building damage inspection concerned in

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this work, lots of advantages of these high-tech pieces of equipment can be expected. The machines equipped with remote sensing instrumentations can bring more flexibility to the inspection process, it is much easier to be moved and controlled by the remoting control system than conventional human-based investigation. A much safer inspection can thus be performed without manual investigations for inaccessible buildings or places rather than the conventional inspection way. As well, convenience and ease of operation of the data (image, video, or location data) acquisition, synchronization, and analysis can be expected. A comprehensive damage inspection including both the quick and detailed phases might thus be potentially established, which leads to improving the quality and efficiency of the damage inspection simultaneously.

Fig. 3. A commercial drone system example.

3 Background Lots of researchers have investigated and conducted a variety of research focusing on the state-of-the-art practice related to various applications including damage inspection using UAV technology. Adams and Friedland (2011) pointed out that UAV usage for imagery collection had a variety of advantages of flexibility, safety, ease of operation, and relatively low cost of ownership and operation in disaster investigation, data acquisition for post-disaster assessments, rapid response, management, and monitoring situations by performing a survey obtained in Hurricanes Katrina, Wilma and Ike; Typhoon Morakot; and the 2009 L’Aquila, 2010 Haiti and 2011 Japan Earthquakes. Hallermann and Morgenthal (2013, 2014) discussed the application of remotely controlled UAVs equipped with highdefinition photo and video cameras based on two practical examples of the chimney and historical tower inspections. They indicated that the immense potential of this visual inspection platform concerning the quality of the recorded images could suggest a large number of analysis applications, such as 3D geometry reconstruction of structures and automatic damage pattern detections on a variety of structural properties in the future. Choi and Kim (2015) conducted an experimental test and discussed an image acquisition

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concept for inspection of structures by a small aerial vehicle-based system. They found that the UAV-based inspection performed well on building safety inspection and intended to be applied more in the future even though there were still several technical issues to be solved. Fujino (2016) pointed out that it was hard to say the new inspection method could completely replace the conventional human visual inspection method at the current stage, but it was expected to improve the new technology to be a good assistant and efficient for both time and human resource-saving way. Particularly in the infrastructural field, Salaan et al. (2018) designed an inspection system by applying a UAV with a passive rotating spherical shell and analyzed its performance through simulated and actual bridge inspections. Seo et al. (2018) conducted a comprehensive project focusing on evaluating drones as supplemental bridge inspection tools by performing a structural damage identification on two pedestrian timber deck bridges. In their study, the efficiency of using the drone was demonstrated throughout application cases on different types of structural bridge damages. Jordan et al. (2018) as well conducted a literature review on the state-of-the-art technologies for UAV inspections in their work, including relevant previous research from 27 articles relating to UAV power facility and infrastructure inspections focusing on (i) power lines, (ii) bridges, (iii) industrial facilities, buildings, and facades, (iv) geographical mapping and inspection, (v) sewers, (vii) railways, and (vii) wind turbines. They pointed out that even though the advancements and the continual development of UAVs in several decades have been proved the possibility to reduce the cost and labor of civil structural inspection operations, the system and concept are still considered to be in the early stages, which leads to various challenges and potential opportunities in the structural inspection field. Hasuike et al. (2018, 2020) studied the application of these new technologies on steel bridge inspection by conducting field tests of two selected steel bridges in Gifu prefecture, Japan, and proved that the image quality taken by drones has reached almost the same level as the human visual approach. Nooralishahi et al. (2021) conducted a review and case studies on the drone-based non-destructive inspection of industrial sites. In their work, a brief review of the history of the UAVs, along with a comprehensive review of case studies focused on UAV-based structural inspection have been as well provided. They pointed out that lots of research and application cases using the UAVs have been conducted involving in inspection and monitoring of electrical power, monitoring buildings and urban planning, monitoring archaeological and cultural heritage sites, agriculture, oil and gas, construction, mining, telecommunication towers, and so on. Kapoor et al. (2021) also conducted a literature review on structural health monitoring and management with UAVs. They indicated that bridge structures have been considered as the testbed to evaluate the efficacy of UAV application for visual damage inspection in the civil structure field. It was summarized in their work that the engagement of the latest robotic technologies, especially the UAVs was highlighted to facilitate a rather revolutionary era for efficient structural information collection and management of structures counteracting several limitations of conventional methods. For the building damage inspection, Miyauchi (2018) conducted research on the visibility of deformation and degradation on building envelopes by both 20- and 100megapixel cameras and compared the photography quality of the building deterioration including surface cracks and materials. They pointed out that the drones were applicable

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for photography data collection while a significant effect on the data quality would be brought by using different resolution cameras. Miyauchi (2018) and Nimura et al. (2018) compared the inspection approaches by using a drone and conventional human visual investigation focusing on 4 aspects, the inspection range and accuracy, the cost, the period, and the safety based on the results of an experimental test on a 6-story full-scale building. They found that (i) the drone system could provide a wide-range and reasonably accurate data collection by taking photos without any blind spots, (ii) even though a lower cost could be obtained by using the drone compared to the conventional way but it possibly needed more human resources to process the data analysis, (iii) it required less time for the fieldwork than the conventional way while more time for the desk work by using the drone system, and 9iv) the drone flight safety should be a major issue when conducting the drone photography inspection. They as well indicated that (i) it was more time-saving and efficient by designing a flight route with fewer downs for the drone flying plan, (ii) the impact on flight stability due to the use of leads was small, and (iii) automatic shooting is more accurate compared to manual shooting for the photography settings. Ma et al. (2018) analyzed the images obtained using the UAV approach and discussed typical characteristics of different types of building surface cracks. They collected imagery data of building surface cracks using a four-rotor aerial UAV, processed digital image identification, extraction, and measurement of these detected cracks, and consequently proposed improvements on the efficiency of the drone-based approach on surface cracks of buildings. Some other research (Wu and Lin 2019; Guo 2020) focusing on building damage inspection was as well carried out in recent years and showed that the UAVs had great practical application value combined with visual technology in surface crack checking and maintenance for buildings. Besides, lots of research related to the drone application in building inspection has been conducted in recent times, such as the survey on the pollution level of building exterior walls (Kodama et al. 2017), crack investigation of the external tile finishing wall (Hayakawa et al. 2017), inspection trial on middle-rise apartment houses (Kameyama et al. 2019), inspection on the building exterior wall using infrared thermography based on the hammering test method mounted on the drone (Ohba 2019; Makatayama et al. 2021), trial experimental tests of an analysis system for building damage using a drone (Miyauchi et al. 2020), safety inspection technology for high-rise buildings using drone system (Nimura et al. 2020), the effectiveness of utilizing micro drones for inspection of the interior and narrow spaces in the building (Ishida and Miyauchi 2020; Saito et al. 2020). Also, a variety of research has been conducted to explore and discuss the use and potential of drone technology for wider applications, such as building inspections (Chan et al. 2015; Otero et al. 2015; Ohno et al. 2017; Endo et al. 2018; Kerle et al. 2020; Ballesteros Ruiz et al. 2021), bridges (Zink and Lovelace 2015; Khaloo et al. 2017; Jongerius 2018; Feroz and Dabous 2021), dams (Henriques and Roque, 2015), big industrial plants (Moranduzzo and Melgani 2014), and other types of structures, construction site management (Irizarry and Costa 2016; Ashour et al. 2016), geomatics surveying or mapping (Calantropio et al. 2018).

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4 Discussions for Practical Application It can be known that UAVs have been widely used in various fields and proved effective particularly for collecting photography data for external surface investigation of building structures, thus considered potentially applicable to replace the traditional human visual way to collect imagery data (photos and videos) for a damage inspection with high-efficiency and accuracy. This section intends to present discussions regarding the practical application, particularly in the field of damage inspection focusing on post-earthquake damaged buildings, including a conceptual comparison with the current conventional inspection approach, instructions, recommendations, limitations, and challenges, as well as possible future directions for further research. 4.1 Comparison with Current Inspection Methods Based on the previous research and case studies previously summarized in the background section, the basic concept and advantages of the UAV-based building damage inspection are presented by giving a conceptual comparison with the conventional approach (visual inspection conducted by investigators) herein. For the purpose of building damage inspection, the requirements of data needed to be collected should be figured out first. Thus, UAVs are considered to equip with highresolution cameras to capture images and record videos and other additional attachments according to the building condition and data requirements, such as flashlights for unilluminated areas, or additional cameras for a wider scope of photography, and other needs. Next, to ensure the quality of the required imagery data, a variety of potential influencing factors, such as flight time, camera numbers, camera resolution, video resolution, etc. needed to be discussed for selecting suitable machines and planning a reasonable data collection strategy. By solving these two key issues, the efficiency of the UAVs as an effective inspection tool can be expected. For both UAV-based and conventional inspection approaches, it is noted that photos or videos can be taken at a distance from the target building either by cameras carried by investigators or the UAV platform, between which there is not much difference on the digital image data quality (Yamauchi et al. 2018) discovered. However, in the conventional approach, investigators are required to get into or at least get close to the post-earthquake damaged buildings with measurement tools to inspect damages, which may need a large amount of time and human resources and still be dangerous for investigators’ life safety, particularly just after the mainshock of an earthquake. In contrast, investigators can operate drones to get close to the damaged building for taking photos or videos by applying the UAV platform, which is much more convenient without any accessibility. Also, high-quality photography data can be captured by drones at some difficultly accessible locations so that high accuracy of data analysis could be achieved. Furthermore, it can be expected the UAV-based approach is a time- and human resourcesaving way to collect data, because drones can take photos or videos in a much larger scope of the target building. On the other hand, in some cases that even though investigators have succeeded to get inside the damaged buildings, several damages located in hard-to-reach places are difficult to be inspected and measured by human hands, such as concrete spalling,

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delamination, and cracking near joints or at corners, on the beam and girders top, on the ceilings, or underside slab components, such as shown in Fig. 4, investigators may need additional instruments or equipment to inspect damages located in girders or ceilings, while it might be more conveniently and efficiently to be recorded by operating drones. Besides, in the conventional approach according to the current standards, the inspection is usually performed in a phase-separated manner, a quick inspection, and a detailed inspection. However, there is a possibility to perform these two independent phases integrated using the UAV-based approach, by which photography data collection on both structural-component and overall building levels can be achieved in a short time just after an earthquake with time- and human resource-saving procedures.

Fig. 4. Additional instruments for damage data collection.

4.2 Instructions and Recommendations Based on the conceptual advantages, instructions and recommendations of the UAVbased data collection for building damage inspection in the current stage are presented. 1. Due to the complexity of the residential buildings compared to infrastructures, such as the interior layout, decoration layers, separating components, non-structures, and so on, the situation of damage inspection particularly the interior space is much more complex than other types of structure. Thus, it is highly recommended to prepare a pre-observation of the outer surface and an information preparation including technical documents, built construction plans, structural design details, historical inspection reports, and other related documents before the inspection. Based on a good understanding of the target building, an effective and applicable data collection

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plan and operation path of drones can be designed for supporting efficient data collection. 2. Considering the inspection team using the UAV-based approach, it is recommended to consist of at least two investigators, one should be a well-trained pilot who can operate the drones for collecting photography data, another one should have the ability and necessary knowledge to synchronize and process the following work based on raw data using computer-based technologies, such as data examining, sorting, modeling and so on. 3. The data collection should be started with an overall investigation, which can provide valuable information for investigators to determine whether there is severe damage experienced by the target building, such as obvious collapse, an inclination of the floor, or any other indicators showing the building is obviously unsafe. In situations where it is difficult to determine the damage level for the target building, a more detailed inspection using the UAV-based approach could be arranged and performed consequently. It is also of significant importance from a high-effectiveness perspective. Considering the above-mentioned points, the critical role of drone technology applied to the building damage inspection field is to collect damage information with high efficiency and accuracy. Thus, to systemically collect photography data about building damage conditions using the UAV-based approach as a supplementary tool for the conventional inspection approach at the current and to be developed as the next-generation inspection approach in a near future, a basic five-stage protocol and a workflow (see Fig. 5) was recommended herein. Step 1: Once the target building is determined, it is recommended to consider the type of the building, such as a residential building or official building, different design features and preferences might significantly influence the data collection design for the following procedures. Step 2: Perform a pre-observation before the inspection (including the current state of the target building and the surroundings that could affect the inspection, evaluating the approximate damage condition, inspection risk, and if possible pre-consider the current damage state of structural components theoretically and visually to find potential damage areas that needed to be inspected.) Step 3: Prepare necessary information about the target building, such as technical documents (as-built construction plans, structural design details, historical inspection reports, etc.), which are important references for determining vital information such as dimensions and locations of structural components, and increasing the accessibility across its elements for the drone. For instance, locations of critical structural elements such as girders can be determined by reviewing the plans and this can help develop an efficient strategy for their inspection under limited and complicated approachability conditions using the drone. Also, a review of the plans and inspection reports allows for efficient damage collection on structural components using the drone. These reports should be considered as the basis prior to machine operation. Step 4: Operate drones to collect data following the preplanned approach of capturing overall section views first and then proceeding to sections specific to each structural component. To appropriately process the inspection, an overall view/shoot of the whole

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structure should be captured first, by which some obvious damage areas or locations needed to be special checked are noticed, and then detailed views of critical structural components determined based on the review of the construction plans or the type of the structure and previous inspection reports, and the sections that needed to be checked in detail based on the overall view, are inspected accordingly. Step 5: Perform the analysis of image data collected using drones and select highquality data required for damage identification and quantification according to the local codes.

Fig. 5. Recommended UAV-based data collection protocol.

4.3 Limitations and Challenges Some difficulties that the UAV-based inspection cannot perform well are noticed throughout the current discussion are drawn as follows, 1. Weather condition needs to be considered when designing the inspection plan based on the pre-observation results, such as the strong wind can make the drone operation unstable and unsafe, the low-illumination condition can make taking photos difficult, or high-illumination condition can cause the camera overexposure to affect the data quality significantly, rain or snow can cause overloading of the drones, and other potentially influencing factors, such as stability limited by the drone itself, distance away from the target, size limitation for entering enclosed space and so on, that could make collected imagery data unclear, blurry or hard-to-recognize for the next-step damage identification. 2. Even though drones are proved effective and have been usually used for collecting data on the outer surface of buildings and can be used occasionally in large internal spaces according to the literature review, based on which the UAV-based approach can be considered potentially the most suitable for collecting data for interior spaces of buildings. However, it is needed to pay attention to their orienteering capacity for some hard-to-reach locations in the complex interior space with obstacles such as enclosed and limited internal space. 3. Due to the small payload of the drones, only small format and light digital compact cameras can be carried and employed for data collection. Furthermore, only

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limited battery packs are allowed of the limited payload, which leads to a relatively short working time. Thus, it is essential to design a scientific and time-saving data collection route for time-limited flights. 4. The possibility for a fully automatic flight mode is limited by the type of drones. On one hand, for the drones that are not equipped with a global positioning system (GPS), we can at most perform a semi-automatic flight mode, which might require sufficient training and a well-prepared investigator to handle these machines for successful data collection. Thus, the data collection plan, flight path, is as well limited and needed to be considered carefully to ensure the operation distance and height within the remote limitation. While in contrast for drones with GPS installed, a fully automatic flight mode can be expected. Thus, the installment of GPS and the capacity to navigate under GPS signal is another important issue that should be considered regarding the UAV-based platform. In the situation that a GPS has been installed in drones, the remote control distance limitation and GPS signal connection can cause a positive change from the semi-automatic flight or moving mode for the drones. 5. Flight permission for drones is always required, particularly in large cities, which is also limiting the extensive application of UAV-based data collection and damage inspection in the practice. 4.4 Future Directions Potential future directions for further research based on the current discussions are considered and presented here, 1. To extensively discuss the UAV-based damage inspection, more studies focusing on influencing factors of the data quality (such as image features of the noise, sharpness, contrast, color accuracy, blurriness, etc. that refer to the level of image accuracy) are still needed and expected. 2. The damage identification and analysis methods based on the imagery data collected by the UAV-based approach using computer-based methods, such as different ways for image identification or intelligent video analysis can be furtherly discussed. 3. To improve the UAV-based damage inspection approach, further research focusing on both the experimental test and data analysis is still needed. Also, for further damage identification using the collected data obtained from drones, it is not sufficient to only identify the location of the damage, more detailed information, such as configurations (length, width, damage types), its effect on the structural components where it is located, and an integrated effect on the overall structural performance and then estimate the long-term behavior of buildings are as well expected. Thus, it is as well required to discuss the necessary information related to damage inspection that should be provided by the UAV-based data collection approach in further research. 4. By applying drones, semi- or fully automatic imagery data for building damage inspection can be expected, while for the following data processing, such as damage identification, or damage analysis, automatic damage identification combining the UAV technology and real-time data streaming can be as well expected for the next stage.

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5 Conclusions This study was intended to propose a summary and evaluation of the application of the UAVs for the damage inspection of post-earthquake damaged buildings, based on which the following conclusions can be drawn, 1. A comprehensive summary of the previous research, particularly on the practice of drone application in the damage inspection field has been conducted. 2. The basic concept for the practical application of the UAV application on the damage inspection, and a conceptual comparison with the conventional approach have been presented. 3. A discussion including instructions, recommendations for the practical applications has been provided. Also, limitations and challenges that were noticed based on the present study have been presented. It was as well pointed out that even though this UAV approach can be expected with lots of advantages in comparison with the current conventional approach, there were still several limitations when applying this system in practice due to the pieces of equipment themselves. 4. Based on these considerations, potential future research directions for an effective damage inspection by applying the UAVs have been also provided.

Acknowledgements. The authors acknowledge Professor Koichi Kusunoki from The University of Tokyo for providing experimental photos, and all members of the Ueda laboratory at Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, College of Civil and Transportation Engineering, Shenzhen University, particularly Ms. Cui Di for her kindness during this work.

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Morgenthal, G., Hallermann, N.: Quality assessment of unmanned aerial vehicle (UAV) based visual inspection of structures. Adv. Struct. Eng. 17(3), 289–302 (2014) Moranduzzo, T., Melgani, F.: Monitoring structural damages in big industrial plants with UAV images. In: 2014 IEEE Geoscience and Remote Sensing Symposium, pp. 4950–4953 (2014) Ma, G., Lu, J., Han, Y.: Research on detection methods of building surface cracks based on UAV image acquisition. Master Thesis, Jiangsu University, Jiangsu, China (2018) Miyauchi, H.: Visibility of deformation and degradation on building envelope by 100-millionpixel camera mounted on drone. Summaries of technical papers of annual meeting Architectural Institute of Japan, vol. 2018, pp. 567–568 (2018) Miyauchi, H., et al.: Development of analysis system for building damage using drone. Summaries of technical papers of annual meeting Architectural Institute of Japan 2020, 1029–10310 (2020) Makatayama, M., Miyauchi, H., Kanematsu, M., Sato, D., Kawabe, S., Okude, M.: Experiment using the buildings of external wall investigation using infrared thermography mounted on the drone. AIJ J. Technol. Des. 27(65), 75–80 (2021) National Institute for Land and Infrastructure Management (NILIM) & Building Research Institute (BRI): Reconnaissance Report of the 2011 Tohoku-Pacific Ocean Earthquake Disaster, Japan (2012) National Institute for Land and Infrastructure Management (NILIM) & Building Research Institute (BRI): Quick Report of the Field Survey and the Building Damage by the 2016 Kumamoto Earthquake, Japan (2016) Nimura, K., Tsutimoto, T., Miyauchi, H., Yamagishi, N.: Test results of inspection by drone on the building envelope of 6-story test building, part2: establishment of flight method and photographing method by drone. Summaries of technical papers of annual meeting Architectural Institute of Japan 2018, 571–572 (2018) Nimura, K., Miyauchi, H., Itoda, K.: Development of safety inspection technology for highrise buildings using drone: Observation and consideration of the behavior of unmanned aerial vehicles near buildings. Summaries of technical papers of annual meeting Architectural Institute of Japan 2020, 1031–1032 (2020) Nooralishahi, P., et al.: Drone-based non-destructive inspection of industrial sites: a review and case studies. Drones 5(4), 1–29 (2021) Otero, L.D., Gagliardo, N., Dalli, D., Huang, W. H., Cosentino, P.: Proof of concept for using unmanned aerial vehicles for high mast pole and bridge inspections. Final Report. Tallahassee, FL: Florida Department of Transportation, Research Center (2015) Ohno, K., Okada, Y., Harashima, S., Yokoe, M.: Unmanned aerial vehicle for supporting close visual inspection of bridges. J. Jpn Soc. Precis. Eng. 83(12), 1066–1070 (2017) Ohba, Y.: A study on utilization of drone technology: efficiency and generalization for building inspection by drone technology. Summaries of technical papers of annual meeting Architectural Institute of Japan 2019, 689–690 (2019) Saito, K., Miyauchi, H., Aoki, K., Nanbu, Y.: Effectiveness of utilizing micro drones for inspection of interior and narrow spaces in building. Summaries of technical papers of annual meeting Architectural Institute of Japan 2020, 1035–1036 (2020) Salaan, C., et al.: Close visual bridge inspection using a UAV with a passive rotating spherical shell. J. Field Robot. 35(6), 850–867 (2018) Seo, J., Duque, L., Wacker, J.: Drone-enabled bridge inspection methodology and application. Autom. Constr. 94, 112–126 (2018) Wu, S., Lin, J.: Research on surface crack detection technology of large buildings based on UAV Vision. Master Thesis, Guangxi University, Guangxi, China (2019) Yamauchi, N., Tsutimoto, T., Miyauchi, H., Nimura, K.: Test results of inspection by drone on the building envelope of 6-story test building, part 1: comparison of the existing inspection and drone-inspection. Summaries of technical papers of annual meeting Architectural Institute of Japan 2018, 569–570 (2018)

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Capture of Crack Evolution for Evaluation of Concrete Properties Using Dynamic Mode Decomposition Jixing Cao1,2 , Ser-Tong Quek1(B) , and Yao Zhang3 1 Department of Civil and Environmental Engineering, National University of Singapore,

Singapore 117576, Singapore {ceecaoj,st_quek}@nus.edu.sg 2 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, China 3 School of Safety Engineering and Emergency Management, Shijiazhuang Tiedao University, Shijiazhuang 050043, China [email protected]

Abstract. Cracks on concrete surface provide the earliest indication in structural damage diagnosis and durability evaluation. Currently, most image-based crack detection methods focus on static image, which is not optimal for tracking the evolution of cracks. To address this shortcoming, a novel crack detection method based on dynamic mode decomposition (DMD) of video images is developed. The DMD spectrum, based on two-dimensional matrix formed by a sequence of video frames, is employed to identify cracks from each video frame according to the distribution of eigenvalues. The method is demonstrated using the flexural test of ultrahigh-performance concrete (UHPC) in the laboratory. The surface cracks identified agree well with those of the original image. The total crack area and its projections on two major directions were computed. The relationship between crack development and force-displacement state was investigated. The crack propagation of UHPC and its effect on mechanical characteristics were revealed from analysis of the captured images. In this crack detection procedure, the cracks of concrete surface do not require any special marks and the video can be recorded using a smartphone. The simplicity of the proposed method and its ability to produce good results make it attractive for practical applications. Keywords: Crack detection and evolution · Crack area evaluation · Dynamic mode decomposition · Ultrahigh-performance concrete

1 Introduction Ultrahigh-performance concrete (UHPC) exhibits better compressive strength, durability and workability compared with ordinary concrete (Gu et al. 2015; Graybeal and Tanesi 2007). This is because various types of fibers, such as steel fibers, polyethylene fibers and calcium carbonate whisker, are added into concrete. Multiscale fibers can restrain

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the propagation of macro- and micro-cracks, effectively enhancing the crack behavior including the post-cracking strength, toughness, and deformation capacity of UHPC. Accordingly, the flexural behavior of UHPC reinforced with multiscale fibers depends significantly on the crack initiation, propagation path, and distribution. Studying the crack development in UHPC is necessary and important. Several different techniques have been employed to analyze the crack propagation of concrete and its effect on the mechanical properties (Yao 2014; Cao et al. 2021). The acoustic emission technique (Ohno and Ohtsu 2010; Van et al. 2012) characterizes the crack features through the difference of transmission signals during the cracking process. Since this method relies on the signal transmission, the setting of the average frequency and rise time has a significant influence on detecting cracks, which requires careful calibration. Digital image correlation (DIC) (Gehri et al. 2020; Golewski 2021) is another popular technique for inspecting cracks and measuring the strain field. The basic idea is to compare two images of a component before and after deformation. Even if the DIC method can achieve high accuracy, the object surface needs to be marked, which is not convenient in practical applications. Recently, image processing technique gains wide popularity for crack detection. Typical algorithms, such as Otsu algorithm (Chen et al. 2019) and local thresholding algorithm (Wang et al. 2019), can identify cracks well. Most of them focus on a single image, whereas the crack development is a dynamic process. This paper presents the study on crack development of UHPC using dynamic images and the analyses on the relationship between crack development and mechanical characteristics. A novel method of dynamic crack detection based on dynamic mode decomposition (DMD) is proposed, and verified using laboratory experiments conducted on UHPC. The surface cracks will be identified and the crack area calculated to yield the relationship between the total crack area and applied force so as to understand the crack propagation in UHPC.

2 Dynamic Mode Decomposition for Crack Detection Concrete specimens are usually tested in the laboratory to study their mechanical properties. To observe and record the development of cracks, the use of video recording has gained popularity. Image processing technique is utilized to separate the cracks from the background contents. The video stream is decomposed into a sequence of frames. Each frame is vectorized and all frames are stacked in time as y1 , y2 , · · · , yp , in which p denotes the total number of frames. The dataset is divided into two overlapping matrices p−1 p Y 1 and Y 2 as follows: ⎡ ⎡ ⎤ ⎤ | | | | | | | | p−1 p Y 1 = ⎣ y1 y2 · · · yp−1 ⎦, Y 2 = ⎣ y2 y3 · · · yp ⎦. (1) | | | | | | | | p

p−1

Since Y 2 is time shift from Y 1 linear operator A, that is,

, it is approximately related by a time-independent p

p−1

Y 2 = AY 1

,

(2)

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The linear map A can be estimated through the method of least-squares  

 p p p−1 † p−1 2 A = argminY 2 − AY 1  = Y 2 Y 1 , F

A

(3)

p−1 † is the pseudo-inverse that can be calculated where ·F is the Frobenius norm, Y 1 by singular value decomposition, i.e., 

p

Y 1 = USV T

, p−1 † Y1 = VS−1 U T

(4)

in which U and V are left and right orthogonal matrices; S is a diagonal matrix. The linear operator A is given by A = Y 2 VS−1 U T , p

(5)

The eigenvalues and eigenvectors of matrix A are calculated using eigen decomposition AW = WΛ,

(6)

where W is an eigenvector matrix and Λ is a diagonal matrix. Then, the DMD mode is obtained by (Tu 2013) p −1 Φ = Y 2 VS

W , (7) ωj = log λj /t where matrix Φ contains DMD modes, t is the time interval between two frames; ωj is the DMD frequency; λj is an eigenvalue corresponding to the j-th column of Λ; A dynamic video can separate the foreground from the background, in which the foreground contains components that changes (such as the development of cracks) and the background are components that do not change or change very slowly. Mathematically, the background can be interpreted as having low-frequency dynamic mode components and those of the foreground are the high-frequency mode components. The procedure can be formulated as (Tu 2013) p Y2

=L+S≈

n 

 bj φj exp ωj t ,

(8)

j=1

in which L and S are low-rank and sparse matrices, respectively;φj is the j-th column of matrix Φ, bj is the initial amplitude of each mode; t is time; Based on a pre-setting threshold τ , the modes for the background are   low-frequency formed by components with frequency ωj  ≤ τ , that is, L≈

 |ωj |≤τ

 bj φj exp ωj t ,

(9)

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The remaining modes are utilized to construct the foreground signal matrix, 

 bj φj exp ωj t , S≈ |ωj |>τ

(10)

In application to concrete, the extracted foreground contains information on cracks and other movement components (such as the loading). A specified mask is designed to remove irrelevant parts (that is, the background) and maintain the information on the evolution of concrete cracking. According to the detected cracks, some statistical properties of cracks, such as total area and its projected area, are computed. Figure 1 illustrates the procedure of crack detection and assessment of crack properties. It starts with decomposing a video into a set of frames. If each frame is a color image, all images will be converted to grayscale to reduce the data size. The grayscale images are stacked column-wise according to time, forming a data matrix. The DMD method is applied to the matrix to yield the different modes, corresponding amplitudes and time evolution. The high frequencies and corresponding DMD modes are utilized to reconstruct the foreground information on the evolving cracks. Postprocessing is performed to highlight the cracks and their principal directions as shown in Fig. 1. The statistics of crack features (such as their area) and their relationship with mechanical parameter (such as force) can be studied, which may help understand the propagation behavior of concrete.

3 Crack Detection Technique Applied in UHPC 3.1 UHPC Under Three-Point Bending Tests Three-point bending test of UHPC was carried out to study their flexural properties, using a specimen with dimension of 40 mm × 40 mm × 160 mm (see Fig. 2a). The mix of the UHPC specimen consisted of PO 52.5 Portland cement, first-grade fly ash, silica fume and 0.1–1 mm quartz sand. Polycarboxylate superplasticizer was used to increase workability in view of the low water content. To improve the ductility, 1% by volume fraction of 13-mm-long micro-smooth steel fibers having diameter of 0.12 mm were added. Displacement-controlled vertical line load was applied at a constant rate of 0.5 mm/min on the upper surface at the mid-span of the specimen. The load corresponding to each displacement was recorded using the load cell. Figure 2b shows the stress-displacement curve obtained. The force reached a maximum value of 7800 N at a displacement of 1.38 mm, and the surface cracks are shown in Fig. 2c. The specimen failed at 2.9 mm with a load capacity of 2560 N with the crack shown in Fig. 2d. To observe the crack development of the UHPC specimen, a video was recorded at a speed of 30 frames/s for 361 s using an OPPO Find X3 mobile phone during the test. The resolution of each frame is 1920 × 1080 pixels. 3.2 Crack Detection The video stream was decomposed into a sequence of frames. All color images were transformed to grayscale images and every 180 frames were grouped together to form a

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Fig. 1. Crack detection and assessment of crack properties.

data matrix for DMD analysis. To give a sense of the practicality of the DMD method, a set of data matrices was used for illustration. Figure 3a plots the imaginary part and real part of the eigenvalue analysis. The data points (eigenvalues) formed conjugate pairs, symmetrical about the horizonal axis, and are distributed within the unit circle. The latter implies that the modes are stable. Recall that the frequency ωj = ln λj /t, hence ωj = 0 if λj = 1. This means that components on or close to the unit circle can be used for the stationary background reconstruction. Figure 3b depicts the amplitude evolution of several DMD modes. The amplitude in black is almost the constant, whereas the amplitude in other colors reduces with increasing frame index. The amplitude in black is much higher than the amplitude in other colors. According to the eigenvalue distribution in Fig. 3a, modes with eigenvalues lower than 0.002 were used to reconstruct the background and other modes were used to reconstruct the foreground. Figures 4a and b show the reconstructed background and foreground images. The foreground contains the movement of load cell and the cracks, as shown in Fig. 4c. To correctly capture the cracks and discard the unwanted components, the procedure was executed as follows: the Hough transform (Brummer 1991) was first used to detect the circle and outline of the load cell in the original image. The outline

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Fig. 2. UHPC beam experiment: (a) specimen, (b) force-displacement curve, (c) cracking at the maximum load-carrying capacity, (d) cracking at failure.

Fig. 3. Eigenvalue analysis and its amplitude evolution, (a) eigenvalues, (b) amplitude evolution.

of the load cell was filled with black and the other region was set to white, forming a specific mask (Fig. 4d). Then, the boolean operation “and” was performed using the specific mask and the binary foreground, as shown in Fig. 4e. The motion components of load cell were removed and the detected cracks showed good agreement with the original cracks (Fig. 4f). The whole video stream was broken into 60 segments, each of which contained 180 frames. Every segment is analyzed individually according to the procedure introduced in

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Fig. 4. Procedure of crack detection, (a) background, (b) grayscale foreground, (c) binary foreground, (d) specific mask, (e) detected cracks, (f) detected cracks superimposed on the original image.

Fig. 1. The detected cracks in the last frame of each segment is selected to be used to assess the behaviour of the specimen. Figure 5a describes the relationship between total crack area and the load-carrying capacity of the UHPC specimen over time. The total crack area increases as time becomes large, even if its load-carrying capacity decreases. Since crack width at the bottom surface is the largest, the trend along with time increasing is presented in Fig. 5b. The crack width increases rapidly from 48 to 72 s, and then increases almost linearly. The total area only gives an overall sense of crack development, while the detailed shape of cracks may not be captured. The detected cracks projected on both vertical and horizontal directions provide supplementary information. Figure 6a illustrates the projection of a binary image onto two major directions. In general, projection gives a compact representation perpendicular to the projection direction. It is achieved by

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Fig. 5. Relationship of force and crack properties over time (a) crack area, (b) crack width.

partitioning each pixel into bins and finding all pixels that are perpendicular to each bin. More specific, the cracks projected on the horizontal (Hi ) and vertical directions Vj are, respectively, defined as ⎧ n  ⎪ ⎪ bij ⎨ Hj = i=1 , (11) m  ⎪ ⎪ bij ⎩ Vi = j=1

where bij is a value of the pixel in row i and column j. The cracks in Fig. 4e are projected on both horizontal and vertical directions, as shown in Fig. 6b. The cracks show two obvious regions. The upper region is small and concentrated; whereas the bottom region is long and narrow.

Fig. 6. Pixel count of crack projected on two orthogonal directions, (a) concept, (b) UHPC specimen.

According to the definition of crack projection on two major directions, the projection of crack patterns for each video frame can be obtained. When the projected cracks are stacked in time, the evolution of vertical projected cracks along with time and position in 3D is shown in Fig. 7a. Most cracks are concentrated on the position between 147 and 367. The maximum number of pixels of vertical projected cracks is no more than 77

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pixels. Figure 7b presents the evolution of horizontal projected cracks along with time and position in 3D. The number of pixels shows an overall increase along with time increase and the maximum value is no more than 83 pixels. All cracks are concentrated between the position 367 and 508. Since the evolution of crack patterns is not easy to capture, this work tries to describe the development of cracks using different features, which is helpful for better understanding crack propagation in UHPC.

Fig. 7. Crack evolution with time and position, (a) vertical projection, (b) horizontal projection.

4 Conclusions This paper presents a study on the crack propagation of ultrahigh-performance concrete (UHPC) under bending tests, and the relationship between crack and the loading. A novel approach based on dynamic mode decomposition (DMD) is proposed to separate cracks from the background. The method was verified using laboratory bending test of a UHPC specimen. Some characteristics of detected cracks were calculated and compared. Some conclusions are drawn as follows: (1) DMD can accurately separate cracks from the background based on the distribution of eigenvalues. DMD can perform continuous detection by stacking video frames column-wise to facilitate analysis of dynamic crack development. (2) The total area and crack width increase as the loading time becomes large. The projection of crack regions in two major directions provides a supplementary description of crack development. (3) The proposed crack detection method does not need any special markings on the concrete surface and the video can be recorded using a smartphone. These conditions can be easily satisfied, making this method promising for practical applications.

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Acknowledgements. The first author would like to acknowledge the support from the 2022 Open Project of State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University (No. HESS-2218).

References Brummer, M.E.: Hough transform detection of the longitudinal fissure in tomographic head images. IEEE Trans. Med. Imaging 10(1), 74–81 (1991) Cao, J., Xiong, H., Ghahari, S.F., Taciroglu, E.: A validated lateral response model for mass timber frames with knee-braces. Eng. Struct. 239, 112278 (2021) Chen, B., Zhang, X., Wang, R., Li, Z., Deng, W.: Detect concrete cracks based on OTSU algorithm with differential image. ipi, 1: 0 (2019) Graybeal, B., Tanesi, J.: Durability of an ultrahigh-performance concrete. J. Mater. Civ. Eng. 19(10), 848–854 (2007) Gu, C., Ye, G., Sun, W.: Ultrahigh performance concrete-properties, applications and perspectives. Sci. China Technol. Sci. 58(4), 587–599 (2015). https://doi.org/10.1007/s11431-015-5769-4 Gehri, N., Mata-Falcón, J., Kaufmann, W.: Automated crack detection and measurement based on digital image correlation. Constr. Build. Mater. 256, 119383 (2020) Golewski, G.L.: Validation of the favorable quantity of fly ash in concrete and analysis of crack propagation and its length—using the crack tip tracking (CTT) method—in the fracture toughness examinations under Mode II, through digital image correlation. Constr. Build. Mater. 296, 122362 (2021) Ohno, K., Ohtsu, M.: Crack classification in concrete based on acoustic emission. Constr. Build. Mater. 24(12), 2339–2346 (2010) Tu, J.H.: Dynamic Mode Decomposition: Theory and Applications. Princeton University (2013) Van Tittelboom, K., De Belie, N., Lehmann, F., Grosse, C.U.: Acoustic emission analysis for the quantification of autonomous crack healing in concrete. Constr. Build. Mater. 28(1), 333–341 (2012) Wang, Y., Zhang, J.Y., Liu, J.X., Zhang, Y., Chen, Z.P., Li, C.G., Yan, R.B., et al.: Research on crack detection algorithm of the concrete bridge based on image processing. Procedia Comput. Sci. 154, 610–616 (2019) Yao, Y., Tung, S.T.E., Glisic, B.: Crack detection and characterization techniques—an overview. Struct. Control. Health Monit. 21(12), 1387–1413 (2014)

Model Updating with Neural Network Based on Component Model Synthesis Zihan Cao(B) and Tao Yin School of Civil Engineering, Wuhan University, Wuhan, People’s Republic of China 430072 {czh1999,tyin}@whu.edu.cn

Abstract. Structural health monitoring usually depends on an accurate finite element (FE) model. Due to the complexity of the structures of long-span bridges, the initial FE model usually needs updating to reduce model errors and improve prediction accuracy. Neural network, relying on its strong ability of pattern matching, has gradually received more attention in the research fields of structural model updating. However, for large-scale complex structures, the amount of degrees of freedom of the model and the parameters need to be updated is huge. When using a single neural network for model updating, the required set of training data will be extensive to ensure the density of training samples, which leads to low efficiency or even infeasibility of network training. In this paper, a method of model updating with neural network method based on Component Model Synthesis (CMS) is proposed. In the proposed method, the sizeable full structure model is first divided into several substructures, and then each substructure is updated by a small neural network, respectively. After that, the updated substructures are assembled by the Craig-Bampton method, where the information of updating parameters from all substructures to the original complete structure, resulting in an updated full structural model. The feasibility and effectiveness of the proposed method are verified by a numerical simulation example of a FE model updating of a plane truss. Keywords: Structural model updating · Neural networks · Substructure · Craig-Bampton method

1 Introduction In recent years, the digital twins between FE models and actual civil structures is a hot topic of structural health monitoring that need an accurate model. In the practical use of civil structures, the changes of material parameters and section parameters will inevitably occur due to shrinkage, creep, corrosion and fatigue, resulting in the FE models established using the original parameters cannot sufficiently adapt to the actual structures (Avci et al. 2021). Hence, it is necessary to update the FE models to reduce model errors and improve prediction accuracy. It is a typical inverse problem of predicting material parameters through structural modal data. The parametric correction method selects some physical parameters for updating, takes the residual between the FE calculation result and the measured data as an objective function, and iteratively adjusts parameters to

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 677–684, 2023. https://doi.org/10.1007/978-981-19-7331-4_54

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minimize the objective function (Yin and Zhu 2018). With the development of computer technology and the improvement of computer computing power, artificial neural network (ANN) is widely used in model updating (Nobari and Aliabadi 2018). At the same time, the current bridges are becoming larger and more complex. Directly using a single-stage ANN to update the complete FE model will be laborious and timeconsuming due to the huge amount of degrees of freedom (DOFs) of the model and the parameters needing to be updated. This causes the size of the training data set of the neural network to be extensive. Thus, divide a large structure into several substructures, and a set of small neural networks are trained to update the substructure model. For large-scale structures, such as long-span bridges, the number of DOFs of substructures may still be very considerable. In this case, using the reduced model for each substructure would further improve the computational efficiency. However, it is difficult, if not impossible, to obtain the measurement data of the substructure in practical measurement. It is necessary and critical to transfer the modal information from the complete structure to the substructures. In this paper, the whole structure is divided into two substructures, and a multi-stage neural network is adopted. In the first step, the information of the frequency and vibration mode of the complete structure is mapped to two substructures using the reduced model, respectively. In the second step, a set of small-sized neural networks are adopted to update substructural models respectively, compared with the results of using the singlestage neural network to update the entire model. The comparison results show that the method proposed in this paper shortens training time significantly and ensures accuracy, proving the flexibility of the proposed method.

2 Theoretical Background 2.1 The Component Model Synthesis (CMS) In the early 1960s, Hurty first established the basic framework of this method (Hurty 1965), and then Craig and Bampton improved further it (Craig and Bampton 1968). The constraint modes of a substructure are defined by producing a unit displacement of each boundary freedom in turn, with all other boundary freedoms fixed and with all interior freedoms unconstrained, as shown in Fig. 1.

Fig. 1. Global and partitioned structural models: (a) global structure; (b) substructures

The undamped vibration equation can be expressed by Mu¨ + Ku = f

(1)

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where M and K are the global mass and stiffness matrices, u and f are global displacement ¨ = d2 ()/dt 2 with the time variable t. and force vectors. () So the global eigenvalue problem is   K − λ j M φj = 0 (2) where λj and φj are the square of the jth natural frequency and the corresponding mode shape in structural dynamics, respectively. Using the eigenvectors obtained from Eq. (2), the global displacement vector u is represented by u = q

(3)

where  and q are the global eigenvector matrix and its generalized coordinate vector, respectively. For each substructure, the eigenvalue problem is     Kii Kib Mii Mib , Ms = (4) Ks = K bi Kbb Mbi Mbb (Ks − λs Ms )φs = 0 where subscript i, b, s denote internal, boundary and substructures, respectively. Then the transformation matrix is   s −Kii−1 Kib T= 0 Ib

(5)

(6)

where s is eigenvector matrix of substructure and Ib is an identity matrix for the interface boundary. From Eq. (6), we can obtain reduced system equations   K − λj M φj = 0 (7) K = TT KT M = TT MT

(8)

where K and M are the reduced mass and stiffness matrices, respectively, and λj and φj are the eigenvalue and eigenvector of the jth mode calculated from the reduced model. 2.2 Neural Network ANN is a powerful computational model inspired by a biological neural network system to approximate functions which are generally unknown. The neural networks take advantage of learning procedures with parallel and distributed processing for performance improvement. Utilizing the ANN method, the FE model updating problem is equivalent to predicting multiple target variables representing model updating parameters from input vectors representing modal characteristics by adjusting adaptive network

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parameters. Through the modal analysis based on the structural FE model, the input of the network is obtained as x = G(t)+η, where G : RNO → RNI represents the FE model of the model parameters extracted from the model parameter space generated by the uniform distribution assumption to predict the modal parameters, η is the noise vector, from a zero-mean Gaussian distribution with a standard deviation of a certain level, adding into the computational modality to ensure the robustness neural network  of the trained     (Yin and Zhu 2020). We denote the data by D = x1 , t1 , x2 , t2 , . . . , xN , tN . The standard performance index of neural network training is the sum of squares of the error of the network on the training set: N

ED = (ti − ai )2

(9)

i=1

where ai indicates the output of the network, ED is the sum of squares of errors on the training data. Unfortunately, the minimization of Eq. (9) can fall into one of many local minima, not in the global minimum (Burden and Winkler 2008). In a Bayesian regularized neural network, the regularization adds an additional term and then an objective function to penalize large weights that may be introduced to obtain smoother mapping (Kayri 2016). In this case, a gradient-based optimization algorithm is preferred for minimizing the objective function S(w), i.e., S(w) = αEw + βED

(10)

NW where Ew = j=1 wj , the sum of squares of network weights, α and β, are hyperparameters that need to be estimated. For a given model M, the Bayesian inference for the weights w can be written as (Bishop and Nasrabadi 2006) P(w|D, α, β, M ) =

1 P(D|w, β, M )P(w|α, M ) = exp[−S(w)] P(D|α, β, M ) Zs

(11)

where w is weight, D is training data, α, β is hyperparameters. S(w) can be written as a Taylor expansion about the most probable (MP) value of the weights, wMP , S(w) ≈ S(wMP ) + 21 (w − wMP )T G(w − wMP ) and if G is the Hessian matrix of the total error function, S(wMP ), the distribution of w can be approximated as a Gaussian, 1 1 P(w|D, α, β, M ) ∼ = ∗ exp[−S(wMP )] − wT Gw ZS 2

(12)

where w = w − wMP and ZS∗ is a normalizing function. The inference for the hyperparameters α and β is P(α, β|D) =

P(D|α, β)P(α, β) P(D)

(13)

Only the evidence,P(D|α, β), needs to be maximized, and the priors P(D) and P(α, β) can be ignored (Nabney 2002). Hence, the log of the evidence for α and β can be written as 1 NW ND ND log P(D|α, β) = −α − β − ln|D| − ln α − ln β − log 2π (14) 2 2 2 2

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which is maximized with respect to α and β. NW is the number of weights and ND is the number of data points. The new values of α and β are reevaluated as α = γ /2EW β = (ND − γ )/2ED γ =

NW

i=1

λi = NP − αtrace G−1 λi + α

(15)

This cannot be achieved using backpropagation as for a simple ANN, and the use of a procedure such as a conjugate-gradient method is required, and need to calculate the Hessian matrix. The objective function will change when the regularization parameters are re-estimated each time, so the minimum point is always changing. If the next minimum point is moved on the performance surface, the new estimation of regularization parameters will be more accurate.

3 Model Updating of a Truss In this section, the proposed method is validated by numerical simulation of a planar truss, as shown in Fig. 2. Meanwhile, the basic information of the three FE models is shown in Table 1. The natural frequencies and mode shapes of the first four modes are calculated from each model. The red part of the models indicates the sections where the parameter of modulus of elasticity needs to be updated. The blue circles point out the master DOFs of each model, which corresponds to the measurement points in practice.

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According to each substructure, there will be a multi-stage ANN. The first ANN will transfer modal information from the complete structure to two substructures, and

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then two ANNs will finish parameters updating for each substructure. At the same time, a relatively single-stage ANN directly updates the parameters of the whole structure as a comparison. The input parameters come from one-mean Gaussian with standard deviations of 0.2 and only keep samples greater than 0.4 and less than 1. The inputoutput training data D of mapping, substructures and complete structures are generated with a size of 1000, 1000, 2000, respectively. The training data of the substructure is obtained from the reduced model. The training data of mapping and the single-stage ANN is obtained from the complete model. With a suitable number of neurons, one layer is sufficient to approximate any functional relationship between input and output (Cybenko 1989). On this note, we take a single hidden layer neural network, and the hidden layer √ neurons are estimated by (Ward Systems Group, Inc. 2000) NH = (NI + NO )/2 + N . Where NI is the number of input neurons, NO is the number of output neurons, and N is the number of sets in the training data. The natural frequencies and mode shapes of the first four modes are taken as network input. Frequencies and mode shapes are divided into two parts which are mapped to substructures, respectively. The number of input neurons, output neurons and hidden layer neurons is shown in Table 2. To mimic the measurement noise on the natural frequencies and mode shapes in practice, the noise vector from a zero-mean Gaussian distribution with a standard deviation of 1% is imposed on the training data of modal parameters. To validate the accuracy of the proposed method, two groups of training data are randomly generated and input into the neural network. The neural network prediction results are compared with the actual input results, and two different neural network prediction results are also compared, as shown in Fig. 3. Meanwhile, the comparison of used time is also given in Table 3. Table 2. The architecture of each ANN Input neurons ANN of frequency mapping

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Figure 3 shows the result of two random cases, respectively calculated by multistage ANN and single-stage ANN. It is clearly seen that the results of the two methods are consistent with the input data, which shows that the proposed multi-stage ANN guarantees the accuracy of parameter identification. The multi-stage ANN consists of four small neural networks, and every network is trained separately. The time taken to train each neural network and the single-stage networks is shown in Table 3. From the time comparison in Table 3, we can clearly see the superiority of the proposed method

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in reducing time consumption, which expects to be more significant for large-scale structural models.

4 Conclusion This paper proposes a FE model updating technology based on CMS and neural networks. The modal parameter information of the global structure is mapped to the substructures through the neural network, which is used to overcome the difficulty of practical measurement of substructures. Then the model of each substructure is updated by a set of small neural networks, which reduces the number of parameters that need to be updated. Compared with the model updating of the global structure with a single-stage network, this method ensures accuracy and dramatically shortens the time required for training. In

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addition, the uncertainty in parameter measurement can be further considered to make the training process and prediction results of the neural network more robust. Acknowledgement. The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grants No. 51778506).

References Avci, O., Abdeljaber, O., Kiranyaz, S., Hussein, M., Gabbouj, M., Inman, D.J.: A review of vibration-based damage detection in civil structures: from traditional methods to machine learning and deep learning applications. Mech. Syst. Sig. Process. 147, 107077 (2021) Bishop, C.M., Nasrabadi, N.M.: Pattern Recognition and Machine Learning, vol. 4(4), p. 738. Springer, New York (2006) Burden, F., Winkler, D.: Bayesian regularization of neural networks. Artif. Neural Netw. 458, 23–42 (2008) Craig, R.R., Jr., Bampton, M.C.: Coupling of substructures for dynamic analyses. AIAA J. 6(7), 1313–1319 (1968) Cybenko, G.: Approximation by superpositions of a sigmoidal function. Math. Control Sig. Syst. 2(4), 303–314 (1989) Hurty, W.C.: Dynamic analysis of structural systems using component modes. AIAA J. 3(4), 678–685 (1965) Kayri, M.: Predictive abilities of Bayesian regularization and Levenberg–Marquardt algorithms in artificial neural networks: a comparative empirical study on social data. Math. Comput. Appl. 21(2), 20 (2016) Lam, H.F., Yuen, K.V., Beck, J.L.: Structural health monitoring via measured Ritz vectors utilizing artificial neural networks. Comput.-Aided Civil Infrast. Eng. 21(4), 232–241 (2006) Nabney, I.: NETLAB: Algorithms for Pattern Recognition. Springer Science & Business Media (2002) Nobari, A.S., Aliabadi, M.F. (Eds.): Vibration-Based Techniques for Damage Detection and Localization in Engineering Structures, vol. 10. World Scientific (2018) Ward Systems Group, Inc.: NeuroShell 2 Manual (2000) Yin, T., Zhu, H.P.: An efficient algorithm for architecture design of Bayesian neural network in structural model updating. Comput.-Aided Civil Infrast. Eng. 35(4), 354–372 (2020) Yin, T., Zhu, H.P.: Probabilistic damage detection of a steel truss bridge model by optimally designed Bayesian neural network. Sensors 18(10), 3371 (2018) Yuen, K.V., Lam, H.F.: On the complexity of artificial neural networks for smart structures monitoring. Eng. Struct. 28(7), 977–984 (2006)

Crack Assessment of Beam Using Machine Learning with Augmented Sensing J. H. Hwang1 and H. W. Park2(B) 1 Department of ICT Integrated Ocean-front Smart City Engineering, 37 Nakdong-Daero

550beon-gil Saha-gu, Busan 49315, South Korea [email protected] 2 Department of ICT Integrated Ocean-front Smart City Engineering, Dong-A University, 37 Nakdong-Daero 550beon-gil Saha-gu, Busan 49315, South Korea [email protected]

Abstract. The modal frequency of a cracked beam is known to be smaller than that of an intact beam because cracks in the beam do not change the mass and only reduce the rigidity. Most previous studies have focused on assessing the crack location and depth by using the fractional reduction of the modal frequency based on the Euler–Bernoulli (E–B) beam theory. Because the effects of rotational inertia and shear deformation are disregarded in the E–B beam theory, the high-frequency dynamic behavior cannot be predicted appropriately. Furthermore, more than three cracks cannot be identified because 2n modal frequencies are required to assess n cracks, whereas the maximum number of available modal frequencies is six at most, based on previous studies. In this study, the broadband modal frequencies of a cracked beam are accurately predicted by using the Timoshenko beam theory. The use of broadband modal frequencies alleviates the sparsity of measurement information for crack assessment. Using the closed-form solution of the modal frequency for a Timoshenko beam with multiple incipient cracks, the computational cost can be reduced significantly during data augmentation. Data augmentation allows for augmented sensing, thereby providing machine learning with a sufficiently huge database of broadband modal frequencies associated with multiple cracks of arbitrary depths and locations on the beam. The proposed method is validated through the numerical simulation in which the number of cracks is estimated in free-free cracked aluminum beams with up to four cracks. Keywords: Crack assessment · Beam · Modal frequency · Machine learning · Augmented sensing · Data augmentation

1 Introduction In structural health monitoring (SHM), Crack assessment is an important research topic (Dimarogonas 1996; Fan and Qiao 2011; Salawu 1997). Studies regarding the assessment of the location and size of cracks have been widely conducted based on the fractional reduction of the modal frequency of a cracked beam (Salawu 1997). Most previous studies pertaining to crack assessment have focused on the detection of cracks in beams © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 685–690, 2023. https://doi.org/10.1007/978-981-19-7331-4_55

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by using narrowband low-frequency modes ranging from the first to the fifth bending mode (Dimarogonas 1996; Fan and Qiao 2011; Kam and Lee 1992; Kim and Ryu 2003; Lele and Maiti 2002; Lee and Chung 2000; Patil and Maiti 2005; Salawu 1997; Sha et al. 2019; Vestroni and Capecchi 2000). Previous studies are limited to narrowband low-frequency modal frequencies because of the following two reasons: First, previous studies are based on the Euler–Bernoulli (E–B) beam theory; however high-frequency modal behaviors cannot be predicted accurately because the rotational inertia and shear deformation effects of the beam are disregarded. Second, mesh refinement of finite element analysis is required to predict the modal frequencies numerically in the highfrequency range resulting in huge computational cost. Furthermore, the number of cracks is assumed to be known a priori for assessing multiple cracks in the previous studies. No studies have been conducted to identify the number of cracks from the measured modal frequencies so far to the best of authors’ knowledge. We propose a new technique to identify the number of multiple cracks reliably by using machine learning incorporated with augmented sensing. The fractional reduction data of broadband modal frequencies are augmented by using the approximate solution of a cracked Timoshenko beam considering all possible crack scenarios in terms of crack locations and crack depths. The use of the approximate solutions allows for augmented sensing of a sufficiently large dataset for machine learning which is impossible to acquire from a real experiment. The validity of the proposed method is presented through the numerical simulation in which the number of cracks is identified in free-free cracked aluminum beams.

2 Augmented Sensing A significant amount of data is required to train a machine-learning classification model to estimate the number of cracks in a beam. As the number of cracks increases, the number of crack scenarios required for training increases as well. Augmented sensing is very useful to obtain a sufficient dataset for machine learning when it is difficult to acquire experimental data considering all possible crack scenarios. In augmented sensing, the fractional reduction data of broadband modal frequencies can be augmented by using either analytical or numerical methods for the crack scenarios of interest. This study adopted an analytical method that predicts the fractional reduction of the broadband modal frequencies of a Timoshenko beam with multiple cracks (Park and Hwang 2022). The huge computational cost can be reduced during the data augmentation through the analytical method. Figure 1 shows the examples of augmented sensing using the analytical method (Park and Hwang 2022). The fractional reduction data of the broadband modal frequencies from the augmented sensing are consistent with those from the finite element analysis and experimental results. This demonstrates the validity of the augmented data provided for machine learning.

3 Machine Learning Figure 2 presents the configuration of the training set for training the classification model. Using a randomly generated crack scenario for the input, augmented sensing was performed using 500, 500, 4500, 5000, and 5000 NMFS data for intact, one crack, two

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cracks, three cracks, and four cracks, respectively. Here, NMFS stands for the normalized modal frequency shift which corresponds to the fractional reduction of the modal frequency of a cracked beam (Park and Lim 2018). The number of cracks associated with the NMFS data was labeled in the target set. The training set consisting of input and target pairs was provided to the MATLAB classification learner (Mathworks.com 1997–2022). A support vector machine with the highest training accuracy was selected. Figure 3 shows an example of the training result. When the classification model training was completed, the training performance was presented through a confusion matrix. The diagonals of the confusion matrix represent the accuracies of target prediction for the given training set. The upper triangular part of the confusion matrix presents false-positive target prediction in which the number of cracks is overestimated than the correct one. The lower triangular part of the confusion matrix shows a false negative target prediction underestimating the number of cracks than the correct number.

Fig. 2. Train set for the machine learning

Figure 4 shows the comparison results of the training results with respect to the number of modal frequencies. The training model using the narrowband modal frequencies of less than six modes exhibited a lower overall training accuracy compared with the training model using the broadband modal frequencies, furthermore, the standard deviation that can be regarded as the training precision was rather large. Figure 5 shows the comparison results of the mean accuracy and the precision of classification model training with respect to the number of modal frequencies. As the

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number of modal frequencies increased, both the accuracy and precision of the classification model improved. The overall model performance improved as well with respect to the number of modal frequencies. When the narrowband modal frequencies were used, the existence of cracks might be identified. However, it is difficult to estimate the number of cracks when assessing cracks. As the number of modal frequencies increases, the number of cracks was identified more accurately. This shows the limitations of previous studies of crack assessment that used less than six modal frequencies. The comparison of model performance in Fig. 5 implies that the use of broadband modal frequencies is necessary for the reliable identification of the number of multiple cracks. It also should be noted that machine learning with augmented sensing is a promising tool to implement multiple crack assessment without a need for knowing the number of cracks a priori.

4 Conclusions In this study, a new technique was presented to identify the number of multiple cracks through machine learning incorporated with augmented sensing. An analytical method is employed to augment fractional reduction data of the broadband modal frequencies of a cracked Timoshenko beam for augmented sensing. The use of analytical method enabled augmented sensing of a sufficiently large dataset for machine learning with low computational cost considering all possible crack scenarios. The proposed method

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identified the number of cracks up to four satisfactorily in free-free aluminum beams. In particular, the overall model performance was approximately 85% when the number of modal frequencies exceeds 12. In the future study, the proposed method will be adopted for implementing a crack assessment technique with no need for knowing the number of cracks a priori. Acknowledgements. This research was conducted with the support of the “National R&D Project for Smart Construction Technology (No. 21SMIP-A156444-02)” funded by the Korea Agency for Infrastructure Technology Advancement under the Ministry of Land, Infrastructure, and Transport, and managed by the Korea Expressway Corporation. And supervised by the Korea Expressway Corporation, Furthermore, this research was supported by National Research Foundation “Establishment of science and engineering research base project (R&D) (2021R1I1A3051224)” funded the Ministry of Education.

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References Dimarogonas, A.D.: Vibration of cracked structures: A state of the art review. Eng. Fract. Mech. 55(5), 831–857 (1996) Fan, W., Qiao, P.: Vibration-based damage identification methods: A review and comparative study. Struct. Health Monit. Int. J. 10(1), 83–111 (2011) Kam, T.Y., Lee, T.Y.: Detection of cracks in structures using modal test data. Eng. Fract. Mech. 42(2), 381–387 (1992) Kim, J.T., Ryu, Y.S., Cho, H.M., Stubbs, N.: Damage identification in beam-type structures: Frequency-based method vs mode-shape-based method. Eng. Struct. 25(1), 57–67 (2003) Lele, S.P., Maiti, S.K.: Modelling of transverse vibration of short beams for crack detection and measurement of crack extension. J. Sound Vib. 257(3), 559–583 (2002) Lee, Y.S., Chung, M.J.: A study on crack detection using eigenfrequency test data. Comput. Struct. 77(3), 327–342 (2000) Mathworks.com: Classification learner, [online] Available at: https://www.mathworks.com/help/ stats/classificationlearner-app.html. Accessed 30 Apr 2022 (1994–2022) Patil, D.P., Maiti, S.K.: Experimental verification of a method of detection of multiple cracks in beams based on frequency measurements. J. Sound Vib. 281(1–2), 439–451 (2005) Park, H.W., Hwang, J.H.: Generic frequency equation for one-dimensional waveguides with incipient cracks based on the phase closure principle. J. Sound Vib. 521, 116675 (2022) Park, H.W., Lim, T.: Investigating a common premise in structural health monitoring: Are higher modal frequencies more sensitive to an incipient crack on a beam than lower ones? Eng. Struct. 176, 385–395 (2018) Salawu, O.S.: Detection of structural damage through changes in frequency: A review. Eng. Struct. 19(9), 718–723 (1997) Sha, G., Radzie´nski, M., Cao, M., Ostachowicz, W.: A novel method for single and multiple damage detection in beams using relative natural frequency changes. Mech. Syst. Signal Process. 132, 335–352 (2019) Vestroni, F., Capecchi, D.: Damage detection in beam structures based on frequency measurements. J. Eng. Mech. 126(7), 761–768 (2000)

Structural Health Monitoring of Steel-Concrete Composite Beams Using Acoustic Emission Dan Li1(B) , Jia-Hao Nie2 , Jia-Bao Yan3 , Chen-Xun Hu2 , and Peng Shen2 1 School of Civil Engineering, Southeast University, Nanjing 211189, China

[email protected] 2 School of Civil Engineering, Hefei University of Technology, Hefei 230009, China 3 School of Civil Engineering, Tianjin University, Tianjin 300350, China

Abstract. Steel-concretes composite structures have been widely used in buildings and bridges during the past decades. However, in the hogging moment regions of steel-concrete composite beams, the concrete slabs are vulnerable to cracks and the connection interfaces are subject to debonding and slip. These damages could substantially reduce the stiffness, strength and durability of the beams. Structural health monitoring of steel-concrete composite beams is thus of interest. In this study, acoustic emission (AE) is applied to detect and characterize damages in steel-concrete composite beams. The damage induced AE sources were located based on Akaike information criterion (AIC)and genetic algorithm (GA), where AIC helped to determine the arrival time of AE waves more accurately in the presence of noise and GA helped to find the optimal location considering AE waves received by all the sensors. With located AE sources, the damage size could also be estimated. After that, the crack types and orientations were diagnosed based on MTA. Through inversed four-point bending test, the proposed method was proved to be able to identify concrete cracks and steel-concrete debonding damages in steel-concrete composite beams with different sizes of headed studs. The beam with studs of lower shear capacity behaved with higher concrete crack resistance, and the dominant damage mechanism in the concrete slab was found to be tensile-mode cracks. Keywords: Steel-concrete composite beams · Structural health monitoring · Acoustic emission · Genetic algorithm · Moment tensor analysis

1 Introduction Steel-concrete composite beams have been widely used in high-rise buildings and longspan bridges during the past decades. Taking advantage of the high tensile strength of steel and compressive strength of concrete, they are of greater load-carrying capacity, lighter self-weight, superior mechanical performance, and accelerated structure construction (Nie and Cai 2003; Yan et al. 2018; Su et al. 2012; Su et al. 2015; Wang et al. 2020). However, in the hogging moment regions of steel-concrete composite beams, the concrete slabs are vulnerable to cracks and the connection interfaces are subject to debonding and slip. These damages could substantially reduce the stiffness, strength and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 691–701, 2023. https://doi.org/10.1007/978-981-19-7331-4_56

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durability of the beams. Numerous researches have been done to investigate the bearing capacity of the steel-concrete composite beams (Lam et al. 2017; Zhang et al. 2018; Su et al. 2012), and to improve the crack resistance of concrete through prestressing techniques (Su et al. 2015; De Silva et al. 2008), ultra-high-performance concrete (Pyo et al. 2016; Zhang et al. 2020) and different types of shear connectors (Zhang et al. 2020; Han et al. 2015). However, limited attention has been paid to structural health monitoring of steel-concrete composite beams that enables early damage detection and timely maintenance to prevent disastrous failures. Ultrasonic non-destructive testing techniques behave with high potential in local damage detection of steel-concrete structures (Chen et al. 2021). Qin et al. (2015) utilized piezoelectric-based smart aggregates to detect the initiation and development of bond slip of steel plate and concrete beams. Xu et al. (2017) studied active interfacial debonding detection for rectangular concrete-filled steel tubular columns using embedded piezoelectric sensors. Magdalena et al. (2018) assessed structural adhesives in steelconcrete composite systems during push-out tests through ultrasonic waves excited and registered by means of surface-bonded piezoelectric transducers. As a passive ultrasonic technique, acoustic emission has also been applied to the health monitoring of steel-concrete composite structures. Farhidzadeh et al. (2015) implemented unsupervised pattern recognition of AE measurements to evaluate infill concrete cracks of steelconcrete composite shear walls subjected to cyclic loadings. Du et al. (2019) integrated the mechanical behavior of a FRP/Steel-concrete hybrid rider with AE response, identifying critical states and providing warnings of catastrophes. Overall, these researches were mainly focused on a certain type of damage. More comprehensive and quantitative monitoring of steel-concrete composite structures is demanded. AE refers to the energy emitted in the form of transient elastic waves (generally 20–1000 kHz) due to various damages in the material, such as crack initiation and propagation, impact, plastic deformation and fracture. Compared with other ultrasonic approaches, AE technique, which does not need artificial excitations, is highly sensitive to microstructural damages, less susceptible to complex structural geometry, and suitable for relatively remote detection and continuous in-service monitoring (Grosse and Ohtsu 2008). It provides a promising approach for health monitoring of mechanical, aerospace and civil engineering structures (Maillet and Morscher 2015; Hasan et al. 2019; Vetrone et al. 2021; Nair and Cai 2010; Li et al. 2021). Besides of the aforementioned references, AE has successfully introduced to detect concrete and steel damages. Ohno et al. (2010) proposed two methods, parameter-based method and moment tensor analysis (MTA)based method, to classify tensile mode and shear mode cracks in concrete. Burud et al. (2021) assessed damages of plain concrete during the fracturing process using AE energy. Li et al. (2017) developed theoretical models to evaluate the size of fatigue cracks in steel using crack propagation-induced and crack closure-induced AE signals, respectively. Li et al. (2022) brought forward a novel method based on time-frequency analysis and deep learning to process AE signals for crack location in steel bridge decks. Taking advantage of AE, this study investigates the health monitoring of steelconcrete composite beams. Based on Akaike information criterion (AIC) and genetic algorithm (GA), the locations of damages can be identified more accurately. After that, MTA of AE events is implemented to characterize the micro mechanisms of damages.

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Through inverted four-point bending test, the proposed method is proved to be able to quantitatively diagnose different damages in steel-concrete composite beams.

2 Methodology 2.1 Damage Location Based on AIC and GA In order to accurately locate and quantify the damages, the first step should be identifying the damage induced AE signals and their arrival times at the sensor. Traditionally, the arrival time of AE waves is picked up by the first threshold-crossing of waveform amplitude. However, it is difficult to fix an optimal threshold in practical applications due to the dissipation and reflection of AE waves along with propagation, as well as varying operational noise of civil engineering structures. Hence, AIC is introduced to determine the exact arrival time of AE waves. The wave is divided into two parts at a certain moment via an autoregressive process. The moment where AIC value is minimized is picked as the arrival time of AE wave. The AIC function is defined as (Akaike 1974; Kurz et al. 2005) AIC(t)=t log10 (var(x[1, t])) + (T − t − 1) log10 (var(x[t+1, T ]))

(1)

Here, x(t) with t = 1, 2, .., T is the selected characteristic component. var(x[1, t]) is the variance of time series x[1, t], and var(x[t+1, T ]) is that of time series x[t+1, T ]. After the arrival times of AE wave at sensors are identified, the damage location, i.e. AE source, can then be determined. In a three-dimensional structure, the location process requires at least four sensors. For an AE source at the location (x0 , y0 , z0 ), its arrival times at N sensors installed at locations of (xi , yi , zi ) are denoted as ti (i = 1, 2, · · · , n). The wave propagation velocity is assumed constant, which is denoted as vp , and the propagation path is assumed straight. The source location (x0 , y0 , z0 ) can be estimated by solving the equation below.   (x0 − xi )2 + (y0 − yi )2 + (z0 − zi )2 − (x0 − xj )2 + (y0 − yj )2 + (z0 − zj )2 = di − dj = vp (ti − tj ), with i, j = 1, 2, · · · , n, and i = j (2) where di is the distance between the source and the ith sensor location. As the solution, a hyperbolic surface could be formed for each sensor pair. The hyperbolic surfaces of all the sensor pairs will cross at one point, theoretically, which is the source location. However, it is difficult to be achieved due to inconstant wave propagation velocity, complex propagation path, and noise pollution. A better solution for AE source estimation is to define an error function:    2 [(ti − tj ) − di − dj /vp ] (3) E(x0 , y0 , z0 ) = The objective is to minimize the value of E(x0 , y0 , z0 ), which ideally equals zero at the source location.

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The source location problem is transformed into a three-variable optimization problem. GA is then introduced to search for the optimal solution. It is a bionic optimization algorithm inspired by the conceptions of biological evolution and genetic variation. Potential solutions to a specific problem are encoded on simple chromosome-like data structures. Genetic operators, including selection operator, crossover operator and mutation operator, are implemented on these structures to reserve crucial information (Barricelli 1957; Fraser and Burnell 1970; Golberg 1989). GA has robust global parallel search ability and helps to avoid local minima. 2.2 Damage Characterization Based on MTA AE waves are generated by dislocation motions at the crack inside the solid material. According to the elastic wave dynamics (Grosse and Ohtsu 2008; Ohtsu 1991), the kinematics of crack location, motion direction and crack type, can be quantitatively determined through MTA (Ohno and Ohtsu 2010; Shigeishi and Ohtsu 2001). The crack can be modeled by crack-motion vector b and unit normal vector n to the crack surface F. Crack motion at point y is defined as b(y)lS(t), where b(y) is the magnitude of crack displacement, l is the direction vector of crack motion, and S(t) is the source-time function of crack formation. AE wave motion received at point x can be represented as (Ohtsu 1995)  Cpqkl Gip,q (x, y, t)[b(y)lk S(t)nl ]dS = Gip,q (x, y, t)Mpq S(t) (4) ui (x, t) = F

where Gip,q is the spatial derivative of Green’s function and Mpq is the moment tensor. The following integration on the crack surface leads to the moment tensor:  Cpqkl [b(y)lk nl ]dS = [Cpqkl lk nl ]V = Mpq (5) F

where Cpqkl is the tensor of elastic constants, V is the crack volume. In the isotropic material, the moment tensor is expressed as Mpq = [λlk nk δpq + μlp nq + μlq np ]V

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Re(s, r) rp Mpq rq R

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where A(x) is the amplitude of the first motion and CS is the calibration coefficient related to the sensor sensitivity and material properties. r is the direction vector of distance R from the source to the observation point, which is derived from the results of AE source location. Re(t, r) is the reflection coefficient with s referring to the direction of sensor sensitivity. It should be noted that Mpq is a symmetric tensor of the second order. The number of independent components of Mpq is thus six, and all the components can be calculated using the amplitudes of P-wave first motions from more than six channels.

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After that, eigenvalue analysis of the calculated moment tensor Mpq is performed. The three eigenvalues, e1 , e2 and e3 , are represented by combinations of shear component X , deviatoric component Y , and hydrostatic component Z. X =

e2 − e3 2(e1 − 2e2 + e3 ) e1 + e2 + e3 , Y = , Z= e1 3e1 3e1

(8)

Cracks can then be classified into shear cracks for X ≥ 60%, tensile cracks for X ≤ 40%, and mixed-mode cracks for 40% < X < 60%. The direction and normal vectors of the crack surface are derived as below.   l = ( 2 + 2lk nk · e1 + 2 − 2lk nk · e3 )/2 (9)   n = ( 2 + 2lk nk · e1 − 2 − 2lk nk · e3 )/2 where e1 , e2 and e3 are the unit eigenvectors.

3 Experimental Procedure Two 2500mm-long steel-concrete composite beams, named SCB1 and SCB2, were fabricated for static loading test in the laboratory. As shown in Fig. 1, they were consisted of H-section steel beams, reinforced concrete slabs, and headed studs. The height and width of the steel beams were 240 mm and 200 mm, respectively. The top and bottom flange and the web were all of 8mm thick. As the shear connectors, two rows of headed studs were welded to the top flange with a longitudinal spacing of 100 mm and transverse spacing of 120 mm. The height of headed studs was 80 mm, and the diameters were 10 mm and 13 mm, respectively for SCB1 and SCB2, in order to obtain different failure modes. The steel beams and headed studs were of grade Q235 (Chinese standard GB 50017-2017). The thickness and width of the concrete slabs were 100 mm and 500 mm, respectively. The strength grade of the concrete was C30 (Chinese standard GB/T50081-2019), and the mix ratio of cement: water: fine aggregate: coarse aggregate by weight was 1: 0.38: 1.11: 2.72. Two layers of HRB400 rebars (Chinese standard JTG D62-2018), 8mm in diameter and 100mm in spacing, were designed in the concrete.

Fig. 1. Schematic of the steel-concrete composite beams.

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Fig. 2. Setup of inversed four-point bending test.

Fig. 3. AE energy of SCB1 with 10 mm-diameter studs during loading test.

To simulate the hogging moment region of continuous steel-concrete composite beams, inverted four-point bending test was carried out. The loading span was 2400 mm with the pure bending span of 500 mm. The load was transferred through a hydraulic jack and controlled by a pressure transducer. The loading step was 20 kN. A DH5922N-GD data acquisition (DAQ) system was used to record the load data with a sampling rate of 10 Hz. The test setup is illustrated in Fig. 2. Eight AE sensors with 150 kHz resonant frequency, named S1-S8, were attached to the surface of the concrete slab, as marked in Fig. 1. Considering the symmetry of the tested beams, only half of the whole span was of interest. A multi-channel DAQ system supplied by Physical Acoustics Corporation was employed to collect AE waves. The sampling rate was 2 MHz. The gain of preamplifier was 40 dB. The triggering threshold of data acquisition is set to 35 dB for filtering potential noise signals.

4 Results and Discussion 4.1 AE Parameter Analysis of Damage Development The variation and accumulation of AE energy received by sensor S1 during loading test for SCB1 with 10 mm studs and SCB2 with 13 mm studs are shown in Figs. 3

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Fig. 4. AE energy of SCB2 with 13 mm-diameter studs during loading test.

and 4, respectively, where the damage evolution process is marked. There were totally six cracks formed in the loading span of SCB1, three of which were not completely penetrated, and four through cracks in that of SCB2. The first crack of SCB1 was developed at the loading stage of 60 kN, and that of SCB2 was formed at the loading stage of 40 kN. Steel-concrete debonding was found at the end of SCB1 at the loading stage of 160 kN, while two macrocracks were observed at the end of SCB2 at the loading stage of 140 kN, as can be seen in Figs. 5 and 6. These phenomena indicated that the tensile stress in the concrete slab of SCB2 was higher than that of SB1 under the same hogging-moment loading conditions, due to the stronger restraint provided by the 13 mm-diameter studs. The beam with studs of lower shear capacity behaved with higher concrete crack resistance, as some of the strain energy was released due to interface debonding and stud deformation. The cumulative energy curves behaved with stepwise increases during the loading test of both SCB1 and SCB2. The curve of SCB1 maintained a steady increase at each loading stage, which corresponded to the slow and continuous formation of multiple macrocracks. The curve of SCB2 rose significantly only at 40, 60, 80 and 120 kH. Here, the stages of 40, 80, and 120 kN were correlated with the formation of the four through cracks, and the stage of 60 kN was related to the propagation of the first crack. It should be noted that the marked cracks in Figs. 3 and 4 generally lagged behind the AE activities. This was because the cracks were checked at the end of each loading stage and, more importantly, the cracks could be observed only when they propagate to a certain size. In summary, AE was highly sensitive to crack initiation and propagation in steel-concrete composite beams. The AE energy was able to qualitatively reveal the damage development process, but difficult to characterize and quantify the damages. 4.2 Damage Location and Characterization For each AE event that triggered at least six channels, source location and MTA were performed. Crack locations, types and orientations are visualized in Figs. 5 and 6, where arrow vector and circular plate represent crack motion vector and crack surface, respectively. The tensile-mode, mixed-mode and shear-mode microcracks are indicated by blue, green and red, respectively. Besides, the black lines show the location of actual

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Fig. 5. Results of damage location and characterization in SCB1 with 10 mm-diameter studs.

Fig. 6. Results of damage location and characterization in SCB2 with 13 mm-diameter studs.

concrete slab cracks, and those small dark grey columns are AE sensors. As can be seen, the AE sources were recognized mainly around observed macrocracks, and the interface debonding of SCB1 and end cracks of SCB2 were successfully identified. According to the location of AE events, the number of cracks and the size of debonding area could be estimated. In addition, it is worth noting that there were 251 events identified in SCB1 while only 164 events identified in SCB2, although sensor S1 of SCB2 received more AE hits and higher AE energy as presented in Figs. 3 and 4. This was because the damages in SCB2 were more serious. The wider through cracks in SCB2 introduced more reflection, scattering and dispersion, which would change the propagation path and velocity of AE waves significantly, and made it difficult for the AE events to be detected by at least six sensors. Through MTA, more than 70% of the cracks in the loading span of both SCB1 and SCB2 were found to be tensile-mode cracks. It was much higher than those of normal reinforced concrete beams in four-point bending tests as reported in the literature. This was because that the deflection of concrete slab and the shear slipping motion of cracks were greatly restrained by the steel beam with remarkable flexural stiffness, and that the limited thickness of concrete slab hindered the generation of shear cracks in the shear region. Thus, the dominant motion of microcracks in the concrete slab under hogging moment was tensile. As microcracks developed approaching through cracks,

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the proportion of shear cracks grew slightly. At the debonding area of SCB1, both shearmode and tensile-mode microcracks were found, while at the end of SCB2, only tensilemode microcracks were detected. Obviously, MTA of AE waves could characterize the mechanisms of damages in the steel-concrete composite beams.

5 Conclusions This study proposes a quantitative health monitoring method for steel-concrete composite beams using AE measurements. Based on AIC and GA, the damages that were regarded as AE sources could be located more accurately, and based on MTA, the crack types and orientations could be identified. Two steel-concrete composite beams with different sizes of headed studs were tested under hogging moment. The beam with studs of lower shear capacity behaved with higher concrete crack resistance, as some of the strain energy was released due to interface debonding and stud deformation. The AE location results successfully revealed and quantified the concrete cracks and steel-concrete debonding. Through MTA, the dominant motion of microcracks was found to be tensile. This was because the shear deformation of concrete slab was significantly limited by the steel beam. As microcracks developed approaching through cracks, the proportion of shear cracks grew slightly. The results demonstrated that the proposed method provided a promising approach for structural health monitoring of steel-concrete composite beams. In addition, due to the existence of aggregates with heterogeneous sizes, headed studs and rebars, the influence of complex interfaces introduced by cracks, and the interference of operational noise, the propagation path, velocity and arrival time of AE waves are difficult to be determined, which lead to location errors in steel-concrete composite beams. More accurate location methods would be further explored in future work. Acknowledgements. Financial support from National Natural Science Foundation of China (No. 51708164) is acknowledged.

References Akaike, H.: Markovian representation of stochastic processes and its application to the analysis of autoregressive moving average processes. Ann. Institute of Statal Math. 26(1), 363–387 (1974) Barricelli, N.A.: Symbiogenetic evolution processes realized by artificial methods (1957) Burud, N.B., Kishen, J.C.: Response based damage assessment using acoustic emission energy for plain concrete. Constr. Build. Mater. 269, 121241 (2021) Chen, H., Nie, X., Gan, S., Zhao, Y., Qiu, H.: Interfacial imperfection detection for steel-concrete composite structures using NDT techniques: A state-of-the-art review. Eng. Struct. 245, 112778 (2021) De Silva, S., Mutsuyoshi, H., Witchukreangkrai, E.: Evaluation of shear crack width in I-shaped prestressed reinforced concrete beams. J. Adv. Concr. Technol. 6(3), 443–458 (2008) Du, F., Li, D., Li, Y.: Fracture mechanism and damage evaluation of FRP/steel–concrete hybrid girder using acoustic emission technique. J. Mater. Civ. Eng. 31(7), 04019111 (2019) Farhidzadeh, A., Epackachi, S., Salamone, S., Whittaker, A.S.: Bayesian decision and mixture models for AE monitoring of steel–concrete composite shear walls. Smart Mater. Struct. 24(11), 115028 (2015)

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Fraser, A., Burnell, D.: Computer models in genetics (1970) Golberg, D.E.: Genetic algorithms in search, optimization, and machine learning, Addion Wesley (102), 36 (1989) Grosse, C.U., Ohtsu, M.: Acoustic emission testing. Springer Science & Business Media (2008) Han, Q., Wang, Y., Xu, J., Xing, Y.: Static behavior of stud shear connectors in elastic concrete–steel composite beams. J. Constr. Steel Res. 113, 115–126 (2015) Hasan, M.J., Islam, M.M., Kim, J.-M.: Acoustic spectral imaging and transfer learning for reliable bearing fault diagnosis under variable speed conditions. Measurement 138, 620–631 (2019) Kurz, J.H., Grosse, C.U., Reinhardt, H.W.: Strategies for reliable automatic onset time picking of acoustic emissions and of ultrasound signals in concrete. Ultrasonics 43(7), 538–546 (2005) Lam, H., Lin, W., Yoda, T.: Performance of composite twin I-girder bridges with fatigue-induced cracks. J. Bridg. Eng. 22(9), 04017056 (2017) Li, D., Kuang, K., Koh, C.G.: Fatigue crack sizing in rail steel using crack closure-induced acoustic emission waves. Meas. Sci. Technol. 28(6), 065601 (2017) Li, D., Nie, J.-H., Ren, W.-X., Ng, W.-H., Wang, G.-H., Wang, Y.: A novel acoustic emission source location method for crack monitoring of orthotropic steel plates. Eng. Struct. 253, 113717 (2022) Li, D., Wang, Y., Yan, W.-J., Ren, W.-X.: Acoustic emission wave classification for rail crack monitoring based on synchrosqueezed wavelet transform and multi-branch convolutional neural network. Struct. Health Monit. 20(4), 1563–1582 (2021) Magdalena, R.: Failure monitoring and condition assessment of steel-concrete adhesive connection using ultrasonic waves. Appl. Sci. 8(3), 320 (2018) Maillet, E., Morscher, G.N.: Waveform-based selection of acoustic emission events generated by damage in composite materials. Mech. Syst. Signal Process. 52, 217–227 (2015) Nair, A., Cai, C.S.: Acoustic emission monitoring of bridges: Review and case studies. Eng. Struct. 32(6), 1704–1714 (2010) Nie, J., Cai, C.S.: Steel–concrete composite beams considering shear slip effects. J. Struct. Eng. 129(4), 495–506 (2003) Ohno, K., Ohtsu, M.: Crack classification in concrete based on acoustic emission. Constr. Build. Mater. 24(12), 2339–2346 (2010) Ohtsu, M.: Simplified moment tensor analysis and unified decomposition of acoustic emission source: application to in situ hydrofracturing test. J. Geophys. Res. Solid Earth 96(B4), 6211– 6221 (1991) Ohtsu, M.: Acoustic emission theory for moment tensor analysis. Res. Nondestr. Eval. 6(3), 169–184 (1995) Pyo, S., Alkaysi, M., El-Tawil, S.: Crack propagation speed in ultra high performance concrete (UHPC). Constr. Build. Mater. 114, 109–118 (2016) Qin, F., Kong, Q., Li, M., Mo, Y., Song, G., Fan, F.: Bond slip detection of steel plate and concrete beams using smart aggregates. Smart Mater. Struct. 24(11), 115039 (2015) Shigeishi, M., Ohtsu, M.: Acoustic emission moment tensor analysis: development for crack identification in concrete materials. Constr. Build. Mater. 15(5–6), 311–319 (2001) Su, Q.T., Yang, G.T., Bradford, M.A.: Behavior of a continuous composite box girder with a prefabricated prestressed-concrete slab in its hogging-moment region. J. Bridge Eng. 20(8), B4014004.1–B4014004.13 (2015) Su, Q.T., Yang, G.T., Wu, C.: Experimental investigation on inelastic behavior of composite box girder under negative moment. Int. J. Steel Struct. 12(1), 71–84 (2012) Vetrone, J., Obregon, J.E., Indacochea, E.J., Ozevin, D.: The characterization of deformation stage of metals using acoustic emission combined with nonlinear ultrasonics. Measurement 178, 109407 (2021) Wang, Y.-H., Yu, J., Liu, J.-P., Zhou, B.-X., Chen, Y.F.: Experimental study on assembled monolithic steel-prestressed concrete composite beam in negative moment. J. Constr. Steel Res. 167, 105667 (2020)

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Predicting the Modal Frequencies of a Cracked Beam Considering Crack Modes I and II Taejeong Lim1 and Hyun Woo Park2(B) 1 Department of Civil Engineering, Dong-A University, 37 Nakdong-Daero 550beon-gil

Saha-gu, Busan 49315, South Korea [email protected] 2 Department of ICT Integrated Ocean-Front Smart City Engineering, Dong-A University, 37 Nakdong-Daero 550beon-gil Saha-gu, Busan 49315, South Korea [email protected]

Abstract. Surface-mounted piezoelectric wafers allow for the evaluation of the dynamic characteristics of a cracked beam in the high-frequency range. The modal coupling between the adjacent axial and bending modes of the cracked beam was observed in the high-frequency range. The modal frequencies do not change in the low-frequency range owing to a crack located on the bending node of an intact beam. However, mode II crack causes a reduction in modal frequencies, particularly in the high-frequency range, in the presence of the crack on the bending node. When a crack is arbitrarily located on a beam, modal frequencies in the highfrequency range are simultaneously affected by mode I crack, which is associated with the axial-bending mode coupling, and mode II crack. The effect of mode I crack on the reduction in the modal frequency is dominant, except for the crack on the bending node. Mode II crack became more sensitive to the reduction in the modal frequency as the mode number increased. Therefore, crack modes I and II should be taken into account simultaneously for the accurate prediction of the modal frequency, which enables reliable crack diagnosis of a beam. In this study, the modal frequencies of cracked beams were predicted by considering both crack modes I and II. The characteristic equations of the cracked beam were derived from the compatibility equation corresponding to crack modes I and II, equilibrium equations, and boundary conditions. The modal frequencies calculated from the characteristic equations were verified through a comparison with the finite element analysis and experimental results. Keywords: Cracked beam · Modal frequency · Mode I crack (opening crack mode) · Mode II crack (sliding crack mode) · Frequency equation

1 Introduction Most previous studies have focused on the frequency prediction of beams with a transverse crack for a few lower bending modes (Carneiro and Inman 2002; Chinchalkar 2001; Rizos et al. 1990). Existing modal test equipment, such as the impact hammer and shaker mode tests, have a limit in obtaining a frequency of 20 kHz or higher (Chinka © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 702–709, 2023. https://doi.org/10.1007/978-981-19-7331-4_57

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et al. 2021; Chen et al. 2005). Recently, surface-mounted piezoelectric wafers have been used to evaluate the dynamic characteristics of a cracked beam in the high-frequency range (Park et al. 2003). Kang et al. (2019) observed the axial-bending mode coupling that affects when the axial and bending modes are adjacent to one another in the highfrequency range. Park and Lim (2020) proposed the closed frequency equation of a crack beam considering the axial bending mode coupling and accurately predicted the modal frequencies caused by a crack on a bending antinode. The modal frequency of a certain bending mode tended to decrease as the mode number increased, although the crack was located on a bending node. This phenomenon conflicts with the premise reported in previous studies, which stated that a reduction in the bending modal frequency does not occur when the crack is located on a bending node (Lim and Park 2022). Lim and Park (2022) investigated the modal behaviors of a beam with a transverse crack on a bending node and revealed that this premise does not hold, particularly for a deep crack on a high-frequency bending node. The cracked beam considering mode I crack accurately predicted the frequency when the crack was located at the bending antinode. The cracked beam considering mode II crack accurately predicted the frequency when the crack was on the bending node. When a crack is arbitrarily located on a beam, modal frequencies in the high-frequency range are simultaneously affected by mode I crack accounting for axial-bending mode coupling and mode II crack accounting for in-plane shear behavior at the crack. The effect of mode I crack on the reduction in the modal frequency is dominant, except for the crack near a bending node. Mode II crack became more sensitive to a reduction in the modal frequency as the mode number increased. Therefore, crack modes I and II should be considered simultaneously for the accurate prediction of the modal frequency, which enables reliable crack diagnosis of a beam. In this study, the modal frequencies of the cracked beams were predicted by considering both crack modes I and II. The characteristic matrix of the cracked beam was derived from the compatibility equation corresponding to crack modes I and II, equilibrium equations, and boundary conditions. The modal frequencies calculated from the characteristic matrix were verified through a comparison of the finite element analysis and experimental results.

2 Formulation 2.1 Spectral Solution Figure 1 shows a cantilever beam with a transverse crack at an arbitrary location. The spectral solutions of the axial displacements of a beam are provided as two parts at both sides of the crack, as follows (Doyle 1989): uL (x1 ) = A1 e−ik(a−x1 ) + A2 e−ikx1 uR (x2 ) = B1 e−ikx2 + B2 e−ik(b−x2 )

(1)

where uL , uR and k denote the axial displacements at the left and right sides of the crack and the axial wave number in Fig. 1, respectively. The spectral solutions for the

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transverse displacements and rotational angles of the cracked beam are expressed using the bending wave number yields (Mei and Mace 2005): wL (x1 ) = A3 e−ik p (a−x1 ) + A4 e−ik p x1 + A5 e−k e (a−x1 ) + A6 e−k e x1 wR (x2 ) = B3 e−ik p x2 + B4 e−ik p (b−x2 ) + B5 e−k e x2 + B6 e−k e (b−x2 ) θL (x1 ) = −iPA3 e−ik p (a−x1 ) + iPA4 e−ik p x1 − NA5 e−k e (a−x1 ) + NA6 e−k e x1 θR (x2 ) = −iPB3 e−ik p x2 + iPB4 e−ik p (b−x2 ) − NB5 e−k e x2 + NB6 e−k e (b−x2 )

(2)

where wL , wR , θL and θR denote the transverse displacements and rotational angles at the left and right sides of the crack, respectively. P and N represent the coefficients relating the rotational angles to the transverse displacement. k p and k e denote the propagating and evanescent bending motions, respectively. Details of the dispersion equations and wave numbers corresponding to the axial and bending motions in Eqs. (1) and (2) were provided by Park and Lim (2020).

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2.2 Derivation of Characteristic Matrix for Cantilever Cracked Beams Four unknowns exist in the axial motion in Eq. (1), and eight unknowns owing to the bending motion in Eq. (2). Twelve equations are derived from three equilibrium equations, three compatibility equations at the crack, and six boundary condition equations at both ends of the beam, respectively as follows: i.

Compatibility of axial displacement at C (Fig. 2a) uR − uL = Faa uL + Fab θL ⇒ (1 − ikFaa )A1 e−ika + (1 + ikFaa )A2   − Fab k p PA3 e−ik p a + k p PA4 − k e NA6 − B1 − B2 e−ikb = 0

(3)

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ii. Compatibility of rotational angle at C (Fig. 2b) θR − θL = Fbb θL + Fba uL     ⇒ ikFba A1 e−ika − A2 + iP + k p PFbb A3 e−ik p a     − iP − k p PFbb A4 − N + k e NFbb A6 − iPB3 + iPB4 e−ik p b − NB5 = 0 (5) iii. Compatibility of transverse displacement at C (Fig. 2c)   wR − wL = Fss wL − θL         ⇒ 1 − i k p − P Fss A3 e−ik p a + 1 + i k p − P Fss A4     + 1 + k e − N Fss A6 − B3 − B4 e−ik p b − B5 = 0

(a) ′

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v.

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Shear force equilibrium at C   κGA −wL + θL + wR − θR = 0       ⇒ −i P − k p A3 e−ik p a + i P − k p A4 − k e − N A6       + i P − k p B3 − i P − k p B4 e−ik p b − k e − N B5 = 0

(6)

(7)

Moment equilibrium at C EI θL = EI θR ⇒ k p PA3 e−ik p a + k p PA4 − k e NA6 − k p PB3 − k p PB4 e−ik p b + k e NB5 = 0

(8)

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vii. Axial displacement boundary condition at A uL = 0 ⇒ A2 = −A1 eika

(9)

viii. Transverse displacement boundary condition at A wL = 0 ⇒ A3 + A4 e−ik p a + A5 = 0 ix.

(10)

Rotational angle boundary condition at A θL = 0 ⇒ −iPA3 + iPA4 e−ik p a − NA5 = 0

x.

(11)

Axial force boundary condition at B EAuR = 0 ⇒ B2 = B1 e−ikb

xi.

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(12)

(13)

xii. Moment boundary condition at B EI θR = 0 ⇒ −k p PB3 e−ik p b − k p PB4 + k e NB6 = 0

(14)

Equations (3)-(14) can be expressed as a characteristic equation matrix:

(15)

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Fig. 3. Cantilever beam with a transverse crack for validation

3 Validation The characteristic equation matrix of a cracked beam considering crack modes I and II was verified through comparison to numerical results from the finite element analysis. Figure 3 shows the geometry of the cantilever-cracked beam. The crack is located 158.4 mm away from the left end of the beam. The crack-depth ratio was set from 0 to 0.7 with the increment being 0.1. The elastic modulus, Poisson’s ratio, and density of the beam are 69 GPa, 0.34, and 2700 kg/m3 , respectively. Finite element analysis was performed using the ABAQUS 6.14/standard at NURION of the KISTI Super Computing Center. Figure 4 presents comparison results of the normalized modal frequencies from the 4th to the 17th bending mode using the equation presented by Park and Lim (2020) and those from the finite element analysis. Here, the normalized modal frequency is obtained by dividing the modal frequency of a cracked beam by that of the intact beam. The black solid line corresponds to the frequency equation of a cracked beam considering the axial-bending coupling related to mode I crack in Park and Lim (2020) while the red dotted line corresponds to Eq. (15). ‘x’ corresponds to numerical results from the finite element analysis. Compared with the results of Park and Lim (2020), Eq. (15) agreed better with the numerical results from the finite element analysis. The effect of mode II crack does not exist at all in the 4th bending mode that belongs to low-frequency bending modes. However, the influence of mode II crack increases deviating approximately 2% from the solid line for crack depth ratio of 0.7 at the 17th bending mode. Crack modes I and II should be taken into account simultaneously for the accurate prediction of the modal frequency, which enables reliable crack diagnosis of a beam.

4 Conclusions In this study, the modal frequencies for the bending of cracked beams were predicted by considering both modes I and II crack. The characteristic equation matrix of the cracked beam was derived from the compatibility equation corresponding to crack modes I and II and the equilibrium equations at the crack and boundary conditions at the supports. The proposed matrix was validated through comparison with the numerical results of the finite element analysis using a cracked cantilever beam. The crack was arbitrarily placed on the beam so that the crack is as distant as possible from nodes and antinodes within the frequency range of interest. The proposed equation matrix successfully predicted

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Fig. 4. Normalized modal frequencies with respect to crack depth ratios: (a) 4th bending mode; (b) 8th bending mode; (c) 11th bending mode; (d) 13th bending mode; (e) 15th bending mode; (f) : axial-bending coupling, x: Finite element analysis, : proposed 17th bending mode ( frequency equation)

the fractional reduction of axial and bending modal frequencies compared to numerical results from the finite element analysis. Acknowledgements. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2019R1F1A1058483 and NRF-2021R1I1A3051224) and Ministry of Education (NRF-2021R1A6A3A13039289).

References Carneiro, S.H., Inman, D.J.: Continuous model for the transverse vibration of cracked Timoshenko beams. J. Vib. Acoust. 124(2), 310–320 (2002) Chinka, S.S.B., Putti, S.R., Adavi, B.K.: Modal testing and evaluation of cracks on cantilever beam using mode shape curvatures and natural frequencies. In: Structures, vol. 32, pp. 1386–1397. Elsevier (2021) Chinchalkar, S.: Determination of crack location in beams using natural frequencies. J. Sound Vib. 247(3), 417–429 (2001) Chen, X.F., He, Z.J., Xiang, J.W.: Experiments on crack identification in cantilever beams. Exp. Mech. 45(3), 295–300 (2005) Doyle, J.F.: Wave Propagation in Structures. Springer, New York (1989) Kang, J.K., Lim, T., Park, H.W.: Predicting the modal frequencies of a cracked beam considering axial-bending coupling. Trans. Korean Soc. Noise Vib. Eng. 29(2), 270–279 (2019)

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Lim, T., Park, H.W.: Investigating the modal behaviors of a beam with a transverse crack on a high-frequency bending node. Int. J. Mech. Sci. 107217 (2022) Loya, J.A., Rubio, L., Fernández-Sáez, J.: Natural frequencies for bending vibrations of Timoshenko cracked beams. J. Sound Vib. 290(3–5), 640–653 (2006) Mei, C., Mace, B.R.: Wave reflection and transmission in Timoshenko beams and wave analysis of Timoshenko beam structures. J. Vib. Acoust. 127(4), 382–394 (2005) Park, G., Sohn, H., Farrar, C.R., Inman, D.J.: Overview of piezoelectric impedance-based health monitoring and path forward. Shock Vib. Digest 35(6), 451–464 (2003) Park, H.W., Lim, T.: A closed-form frequency equation of an arbitrarily supported beam with a transverse open crack considering axial–bending modal coupling. J. Sound Vib. 477, 115336 (2020) Rizos, P.F., Aspragathos, N., Dimarogonas, A.D.: Identification of crack location and magnitude in a cantilever beam from the vibration modes. J. Sound Vib. 138(3), 381–388 (1990)

Deep Learning-Based Crack Detection and Classification for Concrete Structures Inspection C. K. Nguyen1(B) , K. Kawamura2 , and H. Nakamura2 1 MienTrung University of Civil Engineering, 195 Ha Huy Tap, Tuy Hoa, Phu Yen 620000,

Vietnam [email protected] 2 Graduate School of Science and Technology for Innovation, Yamaguchi University, Tokiwadai-Ube, Yamaguchi 755-8611, Japan

Abstract. Automatic crack detection is a main task in a crack map generation of the existing concrete infrastructure inspection. This paper presents an automatic crack detection and classification method based on genetic algorithm (GA) to optimize the parameters of image processing techniques (IPTs). The crack detection results of concrete infrastructure surface images under various complex photometric conditions still remain noise pixels. Next, a deep convolution neural network (DCNN) method is applied to classify crack candidates and non-crack candidates automatically. Moreover, the proposed method compared with the different deep learning methods for crack detection. The experimental results validate the reasonable accuracy in practical application. Keywords: Crack detection · Deep learning · Concrete structure inspection · Genetic algorithm

1 Introduction Crack detection and classification of concrete structures is main task of the preliminary inspection progress. The concrete components of the existing large-size structures such as many bridges, and tunnels have suffered from different loading and environmental conditions cause to cracks, spall, leakage…which influence to operational quality of the civil building. There are many non-destructive testing methods conducting some of different image data captured from ultrasonic device, infrared and thermal device, laser scanning, and commonly digital cameras. Image processing techniques consist of three approaches: edge detection, threshold technique (Fujita et al. 2006) [1] and mathematical morphology (Nguyen et al. 2016) [2]. Therefore, they applied to detect and classify concrete infrastructure surface cracks. In recently years, many automatic crack detection and classification methods based on a combination of image processing techniques (IPTs) and machine learning algorithms (MLAs) are implemented as decision tree (DT) (Kei et al. 2013) [3], support vector machine (SVM), k-clustering nearest neighbour (K-NN), and artificial neural network (ANN) (Zhang et al. 2014) [4]. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 710–717, 2023. https://doi.org/10.1007/978-981-19-7331-4_58

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This research incorporates deep learning with image processing technique (IPT) to crack detection and classification on the concrete structure surface. Furthermore, the parameters of the IPT were optimized using genetic algorithm to find the best values of the parameters. Data acquisition collected from the tunnel lining surface images and various concrete structure images. The experiment results demonstrate that the proposed method has the significant effectiveness compared to the other methods.

2 Proposed Method See Fig. 1.

Optimized parameters

End

Start

Initial / Next population

Evaluation of each individual

Stopping criterion

Input image

Filter image

Dilation/ Erosion

Yes

GA Fitness function

Contrast Enhancement

No

Evolution

Selection

Crossover

Binary image

Binarization Dilation/Erosion

Mutation

Input Layer

Output Layer

Deep convolution neural network

Linear degree

crack

Output Image

Noncrack

Crack candidates Stage-1 Convolution layer Batch-normalization Activation function Max-Pooling

Stage-2

Stage-3

FCL 128 neurons

Fig. 1. Pipeline of the automatic crack detection and classification using GA-CNN [5]

2.1 Image Processing Techniques (IPTs) Figure 1 shows a pipeline of automatic crack detection and classification based on the image processing techniques (IPTs) combined with deep learning. Namely, there are filtering image part, binary image part, and crack extraction part. Therein, filter image part comprises of morphological filter transform and contrast enhancement. The second part consists of binarization, and dilation-thinning transformation. The final part comprises of labeling and length threshold. The purpose of the filtering image part is firstly to smooth images as well as eliminate noises, shading so that make the sharpness of crack edge. For an example, Fig. 2b shows the result of smooth image M. Figure 2c shows crack enhancement after morphology filter is applied to smooth the original image.

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The purpose of the binary image is to segment crack image into binary image. The output image only has two values 255 (white is background) and 0 (black is crack or noise). Furthermore, in this study, to evaluate the effectiveness of the binarization, the accuracy of crack detection used global optimized threshold as shown in Fig. 2d. The aim of a dilation operation is to connect crack fragment meanwhile noises are separated from the cracks. Therefore it results in loss reduction. However, widths of crack pixels increase along with crack shape. The size of structuring element of the dilation operation is considered as an adjusted parameter to optimized value by GA. Shape of structuring element is predefined as “square” type. The rule of the dilation operation is if any pixel in the input neighbourhood is “1”, the output pixel is “1”. Otherwise, the output pixel is “0”. After that, Erosion to a binary image is a morphology operator used to remove noise surrounding crack pixels illustrated in Fig. 2e.

(a)

(b)

(c)

(e)

(d)

(e)

(f)

(a): Original image; (b): Morphological filter; (c): Contrast enhancement; (d): Binarization; (e): Dilationthinning transform; (f): Final crack image.

Fig. 2. The illustrative results of image processing procedure.

Finally, the length threshold implemented to the image result of the crack detection as shown in Fig. 2f. 2.2 Application of GA to the Optimization of Image Processing Parameters In this study, the GA is applied to search optimal values of the image processing parameters (IPPs) because its advantage is to avoid local optimization as other conventionally evolutional algorithms. (1) Represented chromosome design for solution candidates No losing generality, assumption that a solution candidate is represented by a chromosome of an individual in the population. The chromosome contains information in term

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of tuned parameter values which is encoded by binary strings. A population comprises of 20 individuals. Weak individual will be removed and the quality of population is improved by performing genetic operations in each generation. Firstly, the IPPs are combined to create an individual in a population. Secondly, each individual is represented by a chromosome encoded to a binary string, as shown in Fig. 2. Namely, the size of structuring element (st) is assigned by 6 bits, the threshold value of binarization (bi) is expressed by 8 bits, dilation transform parameter (di) is expressed by 4 bits, the threshold value of object area is designed by 6 bits. Finally, an initial population was generated randomly with a predetermined size. After that, the linear degree is expressed by 6 bits. Table 1 shows some parameter values. Therein, the ranges of the shown values are based on the preliminary experiments.

Fig. 3. A represented chromosome for solution candidates.

Table 1. Properties of parameter. Variable

Range

Steps

Bits

st bi

[1 127]

2

6

[0 255]

1

8

di

[1 31]

2

4

li

[0 32.5]

0.5

6

(2) Genetic algorithm Figure 3 shows an operated mechanism of GA including into the crucial three stages. Namely, they consist of the initial population generation, fitness evaluation of each individual in the current population, and evolution operation to create the next generation. Therein, the evolution operation comprised of selection, crossover, and mutation is repeated until finding best solution. Namely, the detailed steps are presented as the following three steps: Step1. Generate initial population randomly: An initial population was generated randomly with a predetermined size to start fitness evaluation. The larger number of individuals means the faster convergence. However, the running time of the program is slow. The semi-automatic and fully automatic methods select 15 and 20 individuals in a generation, respectively. To assess the fitness of the individual in the current population, an objective function to assess crack detection accuracy is defined as the Eq. (1). Loss and noise are computed based on comparison between a processed image and a target image.

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As a result, the objective function (f ) has to ensure the accuracy of extracted crack information with the minimum noises and losses as much as possible.  f2 f2 f = 1 − 1 + 2 , f ∈ [01] 2 2 Loss Noise f1 = ; f2 = (1) Crack Back where, f 1 , f 2 are loss rate and noise rate, respectively. f measures the accuracy of crack detection. f is larger value, the accuracy is higher. Step2. Evolution operation: Selection progress is to mimic the natural survival of the creatures. Each string has a corresponded fitness value. The probability of each string to be selected proportional to its fitness value based on the roultte wheel rotation randomly. The process repeated for the second parent. Two elite members are kept forward to the next generation. To improve quality of individual fitness, the crossover operation is used to create two new children from two selected parents with predefined probability. Crossover point is point laid on between 0 to the end of chromosome length. In this study, the single crossover point is selected. The part of the first parent chromosome that runs until the crossover point is spliced with the part of the second parent chromosome that includes, and runs after, the crossover point chose the middle point of the parent string. The whole new generation is selected in this manner. The mutation of bit strings ensue through bit flips at random positions. The purpose of the mutation operation is to create genotype diversification in the population in order to avoid local optimization leading to finding the best solution. Mutation point is taken randomly. However, mutation rate is very small under 1% to avoid collapsing the genetic structure of the current population. (3) Stopping criterion: Evaluation of each individual meets the predefined maximum generation, or the best value of the objective function met. 2.3 Deep Convolution Neural Network (DCNN) The output results of the image processing technique are crack images including crack pixels and crack-like non-crack pixels. The brightness of crack-like non-crack pixels is similar to the brightness of the crack pixels. The brightness is intensity value of pixel of binary image in 0 (black) or 255 (white). As a result, the crack image contains many noise and crack like non-crack. The major challenge is how to classify them automatically in order to only keep true crack pixels. 2.3.1 Convolution Layer The deep learning method (DL) composed of three stages. Each stage comprises of convolution layer, batch-normalization layer, max-pooling layer with drop out, and activate function. The last layer is fully-connected layer so as to map noise candidates or crack candidates.

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Table 2 indicates dimension of layers of the proposed method and the Cha-2017Architect [6] shown in Fig. 1 as well as parameters of stride and padding. Where C1, C2, and C3 are the convolution layers; M-Pl, M-P2, and M-P3 are the max pooling. FCL1and FCL2 are fully-connected layers. Dr1and Dr2 are drop out with a predefined probability ratio (Tong et al. 2018) [7]. In this paper, these probability ratios are 0.4.

3 Experiment Results The accuracy of the classification is expressed as the following equation: ACC =

TP + TN TP + TN + FP + FN

(2)

where TP is the total of crack images detected correctly, TN is the total of non-crack images detected correctly. FP is the total of the crack images detected incorrectly. FN is the total of the non-crack images detected incorrectly. Figure 4 shows comparison of the training accuracy between the proposed method, transfer Alexnet and Cha_2017 method. In that, the transfer Alexnet keeps first three layers. The result expresses that the proposed method outperforms the others, and it gains maximum accuracy at epoch 30. Further, the experiment results of the proposed training model with various image data sizes. Training maximum accuracy (ACC) is 96.1%, the test data accuracy is 91% with 3000 images for each class. Table 2. Dimension of layers and parameters Proposed method-Architecture Layer Number Size name of filter

Cha-2017-Architect

Stride Padding Layer Number Size name of filter

Stride Padding

C1

32

16 × 16 2

2

C1

24

20 × 20 2

M-P1

1

3×3

2

–

M-P1

1

7×7

Dr1

1

Dr1

0

C2

64

7×7

2

2

C2

48

15 × 15 2

M-P2

1

3×3

2

–

M-P2

1

4×4

C3

128

6×6

2

2

C3

96

10 × 10 2

2

M-P3

1

2×2

2

–

M-P3

1

2×2

2

2

Dr2

0.4

Dr2

0.4

FCL1 1

128

–

–

FCL1 1

96

–

FCL2 1

2

–

FCL2 1

2

–

2

2 2

2

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4 Conclusion This paper found the optimization of parameters of IPTs using GA. Moreover, the IPTs results combined with DCNN method resulted in high automatic crack detection. The accuracy of training model is depending on the diverse of input data. The difference of accuracy between training and testing is large. It is necessary to improve more deep CNN layers to get high score. The final purpose was to create crack map therefore requiring the pixel-level accuracy automatically. Disadvantage of DCNN method needed a large number of input data so as to gain the high fixed accuracy. More, the computation of DCNN model is heavy relied on GPU and computer configuration.

Results of different methods

Accuracy of Training data

120

100

Proposed-method

80

Cha-2017 60

40

Transfer-Alexnet

1

21

41

61

81

101

121

141

161

181

201

221

241

261

281

301

321

341

Fig. 4. The comparison results of different deep learning method

References 1. Fujita, Y., Mitani, Y., Hamamoto, Y.: A method for crack detection on a concrete structure. In: ICPR2006: IEEE 18th International Conference, on Pattern Recognition, vol. 3, New York, pp.901–904 (2006) 2. Nguyen, C., Kawamura, K., Tarighat, A.: A study on semi-automatic concrete cracks detection using interactive genetic algorithm. JCI 38(1), 2061–2066 (2016) 3. Kawamura, K., Yoshino, K., Nakamura, H., Sato, Tarighat, A.: A valid parameter range identification method of a digital image processing algorithm for concrete surface cracks detection using genetic algorithm and decision tree. Proc. Japan Soc. Civ. Eng. 69 (2013) 4. Zhang, W., Zhang, Z., Qi, D., Liu, Y.: Automatic crack detection and classification method for subway tunnel safety monitoring. Sensors 14, 19307–19328 (2014)

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5. Nguyen, K., Kawamura, K., Tarighat, A.: Automatic Crack Detection for Concrete Infrastructures Using Image Processing and Deep Learning (2020). https://doi.org/10.1088/1757-899X/ 829/1/012027 6. Cha, Y., Choi, W.: Deep learning-based crack damage detection using convolutional neural networks. Comput.-Aided Civ. Insfrastrure Eng. 32, 361–378 (2017) 7. Tong, Z., Gao, J., Sha, A., Hu, L.: Convolution neural network for asphalt pavement surface texture analysis. Comput.-Aided Civ. Infrastructure Eng. 0, 1–17 (2018)

Bayesian System Identification of Civil Engineering Structures: Development and Application

Finite Element Model Updating Based on Neural Network Ensemble Yuxuan He(B) and Tao Yin School of Civil Engineering, Wuhan University, Wuhan 430072, P. R. China {2017301550123,tyin}@whu.edu.cn

Abstract. Over the last few decades, structural health monitoring (SHM) has been gaining more and more attention, especially in civil engineering. Due to the assumptions and uncertainties in finite element (FE) modelling, there are inevitably various errors between the dynamic characteristics predicted by the FE model and the measured data. So it is necessary to calibrate the initial structural model, which is a typical inverse problem, and generally ill-posed. As a powerful artificial intelligence technology, artificial neural network (ANN) has been widely used in model updating due to its excellent pattern recognition ability. Compared with the traditional ANN approach, the Bayesian Neural Network (BNN) method is more robust to noise. However, with the increase in the number of dimensions and hidden neurons, the amount of samples required for training neural networks and the corresponding time consumption shows catastrophic growth, especially for training a single neural network to update large-scale FE models of civil engineering structures. To make progress, the ensemble of multiple neural networks fed with divided training sample sets is a feasible strategy. It is expected to improve the generalization performance compared to a single network for handling large-scale FE models, which is seldom emphasized in the current literature related to the FE model updating. This paper proposes a FE model updating method that utilizes the strategy of neural network ensemble by utilizing the modal flexibility matrix as the training input. The entire set of training samples is further divided into a series of smaller sample sets and used to train multiple BNNs, the final identification result is obtained by summing the outputs weighted by the evidence of each individual model. A truss model is employed in this paper to validate the feasibility and effectiveness of the method. Keywords: Structural health monitoring · Finite element model updating · Neural network ensemble

1 Introduction In recent years, SHM of civil engineering structures has been gradually concerned. An accurate FE model is generally necessary and serves as a vital baseline for SHM and structural condition assessment. Since there are boundary errors, material parameter errors and discretization errors in the initial FE model, the static and dynamic properties of the ideal model must be different from the actual structure. So it is necessary to © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 721–729, 2023. https://doi.org/10.1007/978-981-19-7331-4_59

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carry out the FE model updating to improve the model accuracy by adjusting the model parameters. FE model updating is an inverse problem of structural dynamics in highdimensional parameter space. This problem has been vastly investigated in the past few decades, including the deterministic methods and probabilistic methods (Behmanesh and Moaveni 2015). Model updating is essentially an iterative process of systematically adjusting parameters of the FE model by minimizing the objective function, which always defined by the difference between the measured and model-predicted results (John et al. 2010; Yuan et al. 2019; Ni et al. 2012; Jafari and Akbari 2019). Machine learning (ML), especially the ANN method, has a strong pattern recognition ability and has been applied to more and more fields with the rapid improvement of computer computing power (Avci et al. 2021). The learning process carried out in the Bayesian framework, i.e., the Bayesian Neural Network (BNN), is more robust to the noise than the traditional ANN, which has received more and more attention nowadays (Marwala and Sibisi 2005; Hernández-Lobato and Adams 2015; Springenberg et al. 2016 Goan and Fookes 2020). The FE model updating of large-scale civil engineering structures generally requires considerable computational overhead. For the model updating of a large-scale structural model, training a single neural network will require more time and more computing memory, which is expected to be solved by adopting the strategy of neural network ensemble (Hansen and Salamon 1990; Barber and Bishop 1998). This paper focuses on the structural FE model updating by a strategy of the BNN ensemble. By utilizing the Bayes’ theorem to infer the posterior probability distribution of the neural network ensemble, the prediction results of the network ensemble are the combined posterior predictive distributions weighted by the evidence of each component network. The proposed BNN ensemble method is employed to update the FE model of a plan truss structure.

2 Theoretical Background Many researchers point out that the modal flexibility matrix contains both structural natural frequency and mode shape information which is expected to be more sensitive than the commonly used natural frequencies and mode shapes and is thus more suitable for SHM (Zhao and DeWolf 1999). For undamped free systems, the differential equation can be expressed as ..

M u +Ku = 0

(1)

where M and K denote the mass and stiffness matrices of the structural system, respectively, and u is the displacement vector. Orthogonalizing the mass and stiffness matrices with respect to the mode shape ϕ, we can get, ϕ T Kϕ = Λ, ϕ T Mϕ = I −1  K = ϕ T ϕ = ϕ−1 ϕ T

(2,3) (4)

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where  is the diagonal matrix of the system’s eigenvalues, and I is an identity matrix. The flexibility matrix is defined as the inverse of the stiffness matrix and can be expressed as, F = K−1 = ϕ−1 ϕ T

(5)

In the following, an approximation of the flexibility matrix based only on the mode shapes and frequencies of the first few modes is introduced. The structural modal flexibility matrix is redefined as (Doebling 1995; Yan et al. 2004), T Fm×m = ϕm×n −1 n×n ϕm×n

(6)

where ϕm×n is the mass-normalized mode shape matrix, m is the number of measured degrees of freedom, and n is the extracted mode order. In this paper, the proposed algorithm focuses on a single hidden layer feedforward BNN. we denote the BNN model by M, then the outputs can be expressed as y(x, w; M) ∈ RNO ×1 , x ∈ RNI ×1 is the vector-valued inputs of the neural network, NI and NO represent the number of neurons in the input and output layers, respectively. All weights and biases are stacked into a weight vector w ∈ RNW ×1 , NW = NH (NI + NO + 1) + NO represents the total number of elements contained in the network parameters, and NH denotes the number of neurons in the hidden layer. In the proposed method, we take the flexibility matrix as input, and then the FE model updating problem is equivalent to predicting multiple target variables representing model updating parameters from input vectors representing modal characteristics by adjusting adaptive network parameters. Through the modal analysis based on the structural FE model, the input of the network is obtained as x = G(t) + η, where G : RNO → RNI represents the FE model with the model parameters extracted from the model parameter space generated by the uniform distribution assumption to predict the modal parameters. η is the noise vector, from a zero-mean Gaussian distribution with a standard deviation of a certain level to ensurethe anti-noise robustness     of the  trained neural network. We denote the data by D = x1 , t1 , x2 , t2 , . . . , xN , tN , where N is the number of data sets, then the training process of the neural network can be regarded as seeking the posterior probability of unknown weights w providing the measurement data D, p(w|D, M) =

p(D|w, M)p(w) p(D|M)

p(D|M) = ∫ p(D|w, M)p(w|M)d w

(7) (8)

where p(w) denotes the prior probability distribution of network parameters w before training, p(D|w, M) is called likelihood, which is the probability of data D given w, p(D|M) is called the evidence of the model class M. We assume that the prior and likelihood are Gaussian distributions, then we can get (Bishop and Nasrabadi 2006), p(w|D, M) =

p(D|w, M)p(w|M) 1 = exp(−S(w)) p(D|M) ZS

(9)

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where ZS is aa normalization factor. Thus, our goal is to minimize the negative logarithm of p(w|D, M ), which is equivalent to minimizing the objective function, S(w) =

Nw N 2 α  β  y(x; w) − tn + wi2 2 2 n=1

(10)

i=1

When we have the posterior distribution for the weights, we can get the distribution of the network output. By utilizing the Laplace approximation, one can seek a Gaussian approximation to the posterior distribution p(w|D, M) at a local maximum of the posteˆ If we approximate p(w|D, M) to a sufficiently narrow Gaussian rior distribution, say w. distribution, we can get the output distribution as (Yin and Zhu 2018)  T





ˆ J x, w ˆ ˆ H−1 w ˆ M , βˆ −1 INO + J x, w (11) p(y|x, D, M) ≈ N t|y x, w; where J = ∇y(x, w; M)|w=wMP is the x-dependent Jacobian matrix of the vector-valued

ˆ Mj )] is the Hesˆ and H w ˆ = −∇∇ ln[p(w|D ˆ N , α, network function evaluated at w, ˆ β, ˆ ˆ α, sian matrix of negative log posterior evaluated at w. ˆ β denotes the hyperparameters ˆ and I is an identity matrix. of the BNN at w, We further consider the ensemble of the Bayesian neural network. If we denote Mj as the jth neural network model, the posterior probability of the model is given by using the Bayes’ Theorem as,





p D|Mj p Mj |M (12) p Mj |D, M = p(D|M)

where p(D|Mj ) is the evidence of the model, p Mj |M is the prior, and p(D|M) = Nm Here the prior probability is considj=1 p(D|Mj )p(Mj |M) is the normalization factor.

ered to be a noninformative distribution, that is p Mj |M = 1/Nm , j = 1, 2, ..., Nm , Nm represents the total number of the neural network model (Lam and Ng 2008). By using the Laplace approximation, the evidence can be approximated as,







− 1 Nm 2 ˆ Mj p w|M ˆ j (2π ) 2 det H w ˆ p D|Mj ≈ p D|w, Take the logarithm and further simplify it to,

  

 ˆ Mj ] ˆ α, ln p D|Mj ≈ NNO ln βˆ − ln(2π ) − 1 + NW ln αˆ − ln |H w; ˆ β,

(13)

(14)

  ˆ Mj is the Hessian matrix of negative logarithm of the posterior, and ˆ α, where H w; ˆ β, it can be given by (Yin and Zhu 2020),     

1 ˆ w; ˆ Mj |w=wˆ = ˆ Mj = −∇∇ ln p w|D, α, ˆ Mj + αI ˆ α, βH ˆ β, H w; ˆ β, ˆ Nw 2 (15)

ˆ Mj ∈ RNw ×Nw is the Hessian matrix of ED . From this, the evidence where H w; p(D|Mj ) of the model can be calculated. Since the prior and normalization factor of the

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model are the same for each model, the distribution of its output is combined according to the evidence of the model to obtain the final result as

Nm 

p D|Mj p(y|x, D) = p y|x, D, Mj (16) Nm j=1 p(D|Mj ) j=1 where p(y|x, D) denotes the probability density function of the BNN ensemble, and the posterior predictive distribution p y|x, D, Mj for each model class Mj is given by Eq. (11).

3 Case Studies In this paper, the proposed method is validated by numerical simulation of a planar truss, as shown in Fig. 1. The cross-sectional area, modulus of elasticity, and mass density of the nominal model are taken to be 12.5 cm2 , 220 GPa, and 7.85 × 103 kg/m3 , respectively. The FE model of the truss consists of 6 nodes and 11 truss elements. The total number of degrees of freedom is 9. The natural frequencies and mode shapes of the first five modes are calculated from the model. There are 11 stiffness scaling parameters assigned to each element, and the total number of model parameters to be updated is 11. Considering cases with no stiffness reductions, only one reduction and two reductions simultaneously, with four extents, i.e., 20, 40, 60 and 80%. The total number of patterns to be considered is 925 (Lam et al. 2006). 4

3

3m

5

6 8

10

7 9

11

1

2

4m

4m

Fig. 1. The truss model used to validate the proposed method

The adopted neural network consists of 81 input neurons (NI = 81) and 11 output neurons (NO = 11), corresponding to each element of the modal flexibility matrix and each potential stiffness reduction location. As one layer is sufficient to approximate any functional relationship between input and output (Cybenko 1989), we take a single

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hidden layer neural √ network, and the hidden layer neurons are estimated by NH = (NI + NO )/2+ N (Ward Systems Group, Inc. 2000), where N is the number of datasets in the training dataset. Since the modal flexibility matrix contains the information of frequencies and mode shapes, using more modes expects a better approximation of the modal flexibility matrix. Therefore, in the proposed method, we divide different stiffness reduction cases into multiple parts to reduce the size of the data set Nj used to train each component network. To validate the efficiency of the proposed strategy of neural network ensemble, two different neural network architectures denoted by method 1 and method 2, respectively, are investigated in this paper. The first one is to train a single neural network to predict the stiffness reductions, and the second is to train several neural networks with the segmented data and combine the prediction results. To ensure that each neural network in the ensemble has better regularization capability, each segmented sub-dataset contains the information corresponding to the data of intact status, single reduction case and evenly distributed data of double reduction case. In this way, each sub-dataset includes Nj = 265 sets of data. Two testing cases are considered in this study. In Case 1, Element 6 has 30% stiffness reduction, and in Case 2, Elements 5 and 8 have 30 and 50% stiffness reduction, respectively. It is noted that none of the above two cases is included in the training set. To mimic the noise effect in the measurement, 1 and 3% noise levels are added to the frequencies and mode shapes in the training data, respectively.

Fig. 2. The output of sub-BNNs for the two testing cases (upper sub-figure: case 1; lower subfigure: case 2)

The output of the ensemble method is shown in Fig. 2. It is clear from this figure that, compared to the actual stiffness reduction, the prediction results given by each sub-BNNs are relatively accurate, which means that each subset of training data can

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provide enough information. At the same time, there still exist some notable differences between the output of sub-BNNs, and it is partly due to the effect of measurement noise. As the evidence information is needed in our network ensemble method, the evidence for sub-BNN in method 2 is calculated and shown in Table 1. Table 1. The logarithm of evidence and ratio of evidence for models in method 2

  ln p D|Mj

    ln p D|Mj − ln p(D|M1 )

p D|Mj /p(D|M1 )

Sub-BNN1

Sub-BNN2

Sub-BNN3

Sub-BNN4

39519

39381

39655

39601

0

−138

136

82

1

1.31 × 10−60

1.23 × 1059

4.84 × 1035

Calculating the covariance matrix of the output distribution of the BNNs in the two methods, we can get the probability density functions as shown in Fig. 3. It can be seen from this figure that the accuracy of the two methods is almost equivalent. In addition, the standard deviation of the output distribution of method 2 is slightly more significant than method 1 due to the smaller training data size for each neural network component.

Probability

30

Method 1 Method 2

20 10 0

0

0.1

0.2

0.3

0.4

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0.6

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0

0.1

0.2

0.3

0.4

0.5 case 2

0.6

0.7

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Probability

20 10 0

Fig. 3. Probability density of the stiffness scaling parameters predicted by two methods (upper sub-figure: case 1; lower sub-figure: case 2)

The means of the final results of the two methods are shown in Fig. 4. It is found from the figure that for the numerical cases, both methods can successfully detect the prescribed stiffness reductions of the truss model. Also, the accuracy of method 2 is slightly lower than that of method 1, which is mainly due to the fact that each subdataset only has a partial set of data, resulting in somewhat poor robustness to noise. As for the computational efficiency, the time consumed for methods 1 and 2 was 1225 sec and 415 sec, respectively, provided that the network ensemble is trained in a parallel

Y. He and T. Yin

Reduction degree

Reduction degree

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Actual Method 1 Method 2

0.2 0.1 0 1

2

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8

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11

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6 Element

7

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Fig. 4. Comparison of the accuracy of two methods (upper sub-figure: case 1; lower sub-figure: case 2)

manner. Although there is a 66% reduction in the used time for the present simple numerical example, this difference becomes more significant as the model becomes more complex.

4 Conclusion This paper proposes a structural FE model updating method based on Bayesian neural network ensemble. By carefully dividing the entire set of training samples into some smaller sets, the computational cost for training each component neural network is reduced, and further improvement of computational efficiency can be achieved by training all the component neural networks in a parallel way as compared to a single neural network architecture. Due to the intrinsic uncertainty of the BNN output, the weighted summation of the predictive output distribution of each sub-BNN is achieved based on the Bayesian evidence statistic. The proposed BNN ensemble strategy can explicitly quantify the uncertainties of the predictive outputs and also expects to improve the anti-noise robustness. Acknowledgements. The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grants No. 51778506).

References Avci, O., Abdeljaber, O., Kiranyaz, S., Hussein, M., Gabbouj, M., Inman, D.J.: A review of vibration-based damage detection in civil structures: from traditional methods to machine learning and deep learning applications. Mech. Syst. Signal Process. 147, 107077 (2021) Barber, D., Bishop, C.M.: Ensemble learning in Bayesian neural networks. Neural Netw. Mach. Learn. 215–237 (1998)

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Behmanesh, I., Moaveni, B.: Probabilistic identification of simulated damage on the Dowling Hall footbridge through Bayesian finite element model updating. Struct. Control. Health Monit. 22(3), 463–483 (2015) Bishop, C.M., Nasrabadi, N.M.: Pattern Recognition and Machine Learning, vol. 4, no. 4, p. 738. Springer, New York (2006) Cybenko, G.: Approximation by superpositions of a sigmoidal function. Math. Control Signal. Syst. 2(4), 303–314 (1989) Doebling, S.W.: Measurement of structural flexibility matrices for experiments with incomplete reciprocity (Doctoral dissertation, University of Colorado at Boulder) (1995) Goan, E., Fookes, C.: Bayesian neural networks: an introduction and survey case studies. In Applied Bayesian Data Science, pp. 45–87. Springer, Cham (2020) Hansen, L.K., Salamon, P.: Neural network ensembles. IEEE Trans. Pattern Anal. Mach. Intell. 12(10), 993–1001 (1990) Hernández-Lobato, J.M., Adams, R.: Probabilistic backpropagation for scalable learning of bayesian neural networks. In: International Conference on Machine Learning, pp. 1861–1869. PMLR (2015) Jafari, M., Akbari, K.: Global sensitivity analysis approaches applied to parameter selection for numerical model-updating of structures. Eng. Comput. 36(4), 1282–1304 (2019) Lam, H.F., Ng, C.T.: The selection of pattern features for structural damage detection using an extended Bayesian ANN algorithm. Eng. Struct. 30(10), 2762–2770 (2008) Lam, H.F., Yuen, K.V., Beck, J.L.: Structural health monitoring via measured Ritz vectors utilizing artificial neural networks. Comput.-Aided Civ. Infrastruct. Eng. 21(4), 232–241 (2006) Marwala, T., Sibisi, S.: Finite element model updating using Bayesian framework and modal properties. J. Aircr. 42(1), 275–278 (2005) Mottershead, J.E., Link, M., Friswell, M.I.: The sensitivity method in finite element model updating: a tutorial. Mech. Syst. Signal Process. 25(7), 2275–2296 (2011) Ni, Y.Q., Xia, Y., Lin, W., Chen, W.H., Ko, J.M.: SHM benchmark for high-rise structures: a reduced-order finite element model and field measurement data. Smart Struct. Syst. 10(4), 411–426 (2012) Springenberg, J.T., Klein, A., Falkner, S., Hutter, F.: Bayesian optimization with robust Bayesian neural networks. Adv. Neural Inf. Process. Syst. 29 (2016) Ward Systems Group, Inc.: NeuroShell 2 Manual (2000) Yan, A.M., De Boe, P., Golinval, J.C.: Structural damage location by combined analysis of measured flexibility and stiffness. In: Progress in Structural Engineering, Mechanics and Computation, pp. 635–640 (2004) Yin, T., Zhu, H.P.: Probabilistic damage detection of a steel truss bridge model by optimally designed Bayesian neural network. Sensors 18(10), 3371 (2018) Yin, T., Zhu, H.P.: An efficient algorithm for architecture design of Bayesian neural network in structural model updating. Comput.-Aided Civ. Infrastruct. Eng. 35(4), 354–372 (2020) Yuan, Z., Liang, P., Silva, T., Yu, K., Mottershead, J.E.: Parameter selection for model updating with global sensitivity analysis. Mech. Syst. Signal Process. 115, 483–496 (2019) Zhao, J., DeWolf, J.T.: Sensitivity study for vibrational parameters used in damage detection. J. Struct. Eng. 125(4), 410–416 (1999)

Damage Statistics and Integrity Assessment of Brick Masonry Structures in Historic Buildings Haiyang Qin1 , Yongjing Tang2(B) , Jiao He3 , and Zhiwang Gu3 1 College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China

[email protected] 2 Tongji Zhejiang College, 168 Business AvenueZhejiang Province, Jiaxing 314051, China

[email protected] 3 Shanghai Construction No.4(Group)Co.,LTD., 928 Guilin Road, Shanghai 201103, China

[email protected], [email protected]

Abstract. Deterioration faced by brick masonry structure of historical buildings is more and more concerned. In this paper, two methods, statistical classification and quantitative mapping, have been carried out to analyze the damage apperance of the southeast and northwest facades based on a historical building project in downtown Shanghai. Then damage distribution characteristic and integrity assessment have been further analyzed. Statistics show that the damage area ratios on southeast and northwest facade are 8.71% and 8.06%, respectively. Specifically, dampness, saltpetering and peeling are three main damage features to these two facades. The damage distribution curves of the both in vertical direction have the similar appearance, Both show that the sum of damage reaches the maximum value at the level of 2 m above ground surface, and then gradually decreases with the elevation increase. In addition, the total damage length also increases near height of 9 m. Keywords: Historical building · Damage statistic · Integrity assessment · Health monitor

1 Introduction Brick, as one of the oldest building materials, has many good properties such as pressure resistance. However, compared with concrete structure, brick masonry structures have several disadvantages of heavier self-weight, lower strength, and poor overall durability and earthquake resistance. In addition, the high void ratio of bricks material leads to relatively serious weathering degree in the environment over time, which would inevitably affect the structural safety and visual enjoyment of brick masonry buildings. A large proportion of historical buildings are made of brick materials, which have a relatively long time span and are sensitive to environmental conditions, inevitably threatening the safety and inheritance of historical buildings. Herein, we take a historical building in Shanghai as an example to analyze its integrity assessment and damage

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 730–738, 2023. https://doi.org/10.1007/978-981-19-7331-4_60

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distribution characteristics of the south and north facades. Field investigation and statistics methods are employed. Our findings could be a reference for the protection and repair work of historical buildings and the coming health monitoring action.

2 Project Overview Figure 1 shows the location and facade of this historical building in downtown of Shanghai. This building was built in 1927. It is a three-story black-brick masonry and decorated with horizontal ribbon-shaped red bricks. Its doors and windows are decorated with red bricks as traditional arches. In almost one hundred years, its masonry walls have repeatedly suffered from different degrees of weathering damage.

Fig. 1. Location and structure of northwest facade

3 Site Investigation During the site investigation before a new round of repair work in 2019, we found that deterioration in the facade of this building is severe. Specifically, Fig. 2(a) shows the surface peeling, the damage area is usually less than 1 m2 , and the exposed area is often accompanied with saltpetering. Figure 2(b) shows the mortar failure, which is often characterized by the cracking and loosening of the bonding mortar, and the affected area is usually a little large. Figure 2(c) shows the cracks, which usually occurs locally or in a small area. The wall bulging damage shown in Fig. 2(d) is actually the further deterioration of the wall cracking damage. Figure 2(e) shows the dampness damage on the wall surface, which often occurs at the same time as the saltpetering damage shown in Fig. 2(f), The affected area is usually larger and the bricks are usually accompanied by a color change. Two methods of statistical classification and quantitative mapping were carried out on the southeast and northwest facade of this historical building after site investigation. Damage forms described in Fig. 2 is mainly classified into four categories, including dampness, saltpetering, peeling, and mildew damage. Damage distribution of the four categories is marked on each facade in the form of cloud map, and the results are shown in Figs. 3(a)-(b).

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(a) peeling

(b) mortar failure

(d) bulging

(e) dampness

(c) cracking

(f) saltpetering

Fig. 2. Damage problems photographed during site investigation

(a) southeast facade

(b) northwest facade

Fig. 3. Damage distribution of four categories

4 Statistics and Analysis In PHOTOSHOP software, the total pixels Ni ’ of each facade, the pixels Ni of four categories area, and the pixels Nij of each category area could be obtained (Among

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them, i = 1, 2, representing the southeast facade and northwest facade, respectively; j = 1, 2, 3, 4, representing dampness damage, saltpetering damage, peeling damage, mildew damage, respectively). The ratio of total damaged area to the total area could be calculated by applying the following formula (1), which could be used to evaluate the affected area of four categories. The following formula (2) could be used to calculate the area ratio of each category of damaged area to the total damaged area, which could be applied to determine the main form of damage categories of the facade. In addition, since the area Si ’ of each facade is known, so the total damage area Si could be calculated by the following formula (3), and the classified damage area Sij could be obtained by the following formula (4). Total damage percentage Wi : 4 j=1 Nij Wi = (1) Ni Classified damage percentage Wij : Nij Wij = 4

(2)

Si = Si Wi

(3)

Sij = Si Wi Wij

(4)

j=1 Nij

Total damage area S i :

Classified damage area S ij :

Figures 4 and 5 show the classified damage maps for the southeast and northwest facades, respectively. The height of each facade is 8.10 m, and the horizontal length is 55.73 m, so the total area of each facade could be calculated to S1 ’ = S2 ’ = 451.41 m2 .

(a) dampness

(c) peeling

(b) saltpetering

(d) mildew

Fig. 4. Classified damage map of southeast facade

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(a) dampness

(c) peeling

(b) saltpetering

(d) mildew

Fig. 5. Classified damage map of northwest facade

It can be calculated from Fig. 4 through the “information statistics” function of PHOTOSHOP software that in the southeast facade, the total pixels are N1 ’ = 168775, and the total pixels of the damaged area are N1 = 14704, including N11 = 2990 in dampness area, N12 = 6659 in saltpetering area, N13 = 4282 in peeling area, and N14 = 773 in mildew area. In the northwest facade of Fig. 5, the total pixels are N2 ’ = 168775, and the total pixels of the damaged area are N2 = 13598, including N21 = 1674 in dampness area, N22 = 8379 in saltpetering area, N23 = 3340 in peeling area, and N24 = 205 in mildew area. As a result, the damages conditions of both facades can be obtained as shown in Table 1 based on the above analysis and calculation. Damage conditions of two facades in Table 1 could be drawn into pie charts, as shown in Fig. 6. It can be found that the total damage proportions of the southeast and northwest facade are 8.71% and 8.06% respectively, which are very close. Proportion of each damage category was further compared and analyzed. In southeast facade, the dampness, saltpetering and peeling are the main damage factors, their classified damage percentage are 20.33%, 45.29% and 29.12% respectively. By comparison, the facade damage caused by mildew factors is relatively small, its classified damage percentage is only 5.26%. In northwest facade, the dampness, saltpetering and peeling are still the main damage factors, their classified damage percentage are 12.31%, 61.62% and 24.56% respectively, the classified damage percentage of mildew damage is only 1.51%. The above analysis comprehensively explains that dampness, saltpetering and peeling are three main damage categories of both facades. By comparison, the damaged area caused by mildew factor is relatively small.

5 Damage Distribution in Vertical Direction Damaged area of each facade is marked, then the total length Li ’ and the total pixels Ni ’ in horizontal direction could be obtained, as shown in Fig. 7(a) (where i = 1 and 2, representing the southeast and northwest facades, respectively). In the second step, each damaged area is divided into several horizontal strips so as to obtain different pixels Ni corresponding to different heights, as shown in Fig. 7(b). In the third step, the following formula (5) could be used to calculate the damage length x of the facade at different

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Table 1. Damage conditions of both facades Damage category Calculation Southeast facade (total pixels N1 ’ = 168775; Total area S1 ’ = 451.41 m2 )

Northwest facade (total pixels N2 ’ = 168775; Total area S2 ’ = 451.41 m2 )

Dampness j=1

Total pixels of damage area N1

14704

Classified pixels of damage area N1j

2990

Total damage area S1

39.31 m2

Classified damage area S1j

7.98 m2

Total damage percentage W1

8.71%

Classified damage percentage W1j

20.33%

Total pixels of damage area N2

13598

Classified pixels of damage area N2j

1674

Total damage area S2

36.36 m2

Classified damage area S2j

4.47 m2

Total damage percentage W2

8.06%

Classified damage percentage W2j

12.31%

Saltpetering j=2

Peeling j=3

Mildew j=4

6659

4282

773

17.81 m2

11.45 m2

2.07 m2

45.29%

29.12%

5.26%

8379

3340

205

22.41 m2

8.93 m2

0.55 m2

61.62%

24.56%

1.51%

heights, and then the distribution curve of the total damage and the classified damage in vertical direction could be generated by fitting method, As shown in Fig. 7(c). This fitting curve could be applied to analyze the distribution characteristics of damage conditions of each facade in vertical direction.   (5) x = Li Ni / Ni In southeast facade, the total length and the total pixels in horizontal direction is L1 ’ = 55.73 m and N1 ’ = 1061, so the damage distribution curve of the southeast facade in vertical direction could be drawn as shown in Fig. 8 according to method in Fig. 7. In northwest facade, the total length and the total pixels in horizontal direction is L 2 ’ = 55.73 m and N1 ’ = 1061, so the damage distribution curve of the northwest facade in vertical direction could be drawn as shown in Fig. 8 according to method in Fig. 7. It can be seen from Fig. 8 that the damage on southeast facade mainly occurs at level of 2 m and 9 m above the ground surface. Among them, the sum of damage reaches

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(a) southeast facade

(b) northwest facade

Fig. 6. Damage conditions of two facades

(a) Mark the damage area

(b) Divided into horizontal strips

(c)

Damage distribution curve

Fig. 7. Calculation method of damage distribution curve in vertical direction

Fig. 8. Damage distribution curve of the southeast facade in vertical direction

26.42 m at level of 2 m, including 14.62 m for saltpetering, 7.54 m for peeling, 2.22 m for dampness, and 2.04 m for mildew. Since this height belongs to the bottom part of the facade (0–4 m), so the reason for damage in this height is mainly related to capillary water rise process and the next saltpetering damage. The sum of damage reaches 29.18 m at level of 9 m, including 16.28 m for saltpetering, 0 m for peeling, 10.52 m for dampness, and 2.38 m for mildew. Since this part is near to the eaves of the second floor (height h = 8 m), so the reason for damage in this height is mainly related to the standing water

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phenomenon of the eaves and the subsequent damp and saltpetering damage under the eaves. Comparatively speaking, the damage length x within the height range of 2–9 m is smaller, this is mainly due to the longer absorption path in this part, so water content needs to be maintained at a relatively lower level to improve the potential gradient, so as to maintain the dynamic balance between water absorption and vapor effect. Therefore, the facade damage caused by capillary water at this part is relatively small.

Fig. 9. Damage distribution curve of the northwest facade in vertical direction

It can be obtained from Fig. 9 that the damage to the northwest facade mainly occurs at level of 2 m above the ground surface. The sum of damage reaches 27.02 m at this height, including 12.89 m for saltpetering, 9.54 m for peeling, 3.89 m for dampness, and 0.70 m for mildew. Since this height belongs to the bottom part of the facade (0–4 m), so the reason for damage in this height is mainly related to capillary water rise process and the subsequent saltpetering damage. In addition, it can also be found that the damage length x at height of 9 m is 0 m, which is obviously lower than that of the southeast facade of 29.18 m, indicating that the damage degree near the second-floor eaves of the northwest facade is significantly lower than that of the southeast facade, which is mainly related to the difference in structural form of these two facades, the monsoon wind direction and climate factors in Shanghai. To sum up, the damage distribution curves of the southeast and northwest facades in vertical direction have the similar characteristics, both show that the sum of damage length reaches the maximum at level of 2 m, and then decreases slightly with the increase of height. This is consistent with the water storage area and distribution characteristics of capillary water in vertical direction. Therefore, it is reasonable to believe that capillary water is one of the main reasons resulting to the damage conditions of masonry. In addition, the sum of damage length of the southeast facade obviously increases at level of 9 m above the ground surface, while that of the northwest facade is zero, indicating that in addition to the capillary water, factors such as structural differences and climatic characteristics also affect the distribution characteristics of dampness content and damage conditions in vertical direction.

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6 Conclusion Research works of statistics, classification and analysis have been carried out based on the damage conditions of a historical building in Shanghai. The distribution characteristics of damage conditions in vertical direction have been further studied, then the integrity assessment of the damage degree of two facades has been conducted. 1) the damage proportions of the southeast and northwest facade are 8.71% and 8.06% respectively. Damages of dampness, saltpetering and peeling are three main forms of both facades. By comparison, the damaged problem caused by mildew factor is relatively small. 2) the damage distribution curves of the southeast facade and the northwest facade in vertical direction have the similar characteristics, both show that the sum of damage length reaches the maximum at level of 2 m above the ground surface, and then decreases slightly with the increase of height. 3) in southeast facade, the sum of damage length obviously increases at level of 9 m above the ground surface, while that of the northwest facade is zero, indicating that in addition to the capillary water, factors such as structural differences and climatic characteristics also affect the distribution characteristics of dampness content and damage conditions in vertical direction.

Acknowledgements. This research is financially funded by National Natural Science Foundation of China (No. 52078373). The authors also gratelfully acknowledge financial support from China Scholarship Council (CSC).

References Burton, C., Visintin, P., Griffith, M.: Field testing of vintage masonry: Mechanical properties and anchorage strengths. Structure 28(12), 1900–1914 (2020) Qin, H.Y., Tang, Y.J., Shao, Z.D., et al.: Weathering effect of melt-crystallization cycle of soluble salt on dry wall. Structural Engineers 37(04), 58–64 (2021). (In Chinese) Song, W.Q.: Longmen temple of Pingshun investigation with history evolution. Cultrual Relics 18(3), 52–57 (2010) Tang, Y.J., Lu, X.B.: Crack evolvement of ancient brick masonry under uniaxial compression. J. Hunan Univ. 46(5), 45–53 (2019). (In Chinese) Tang, Y.J., Zhao, H., Ye, Z.H., et al.: Ancient brick masonry behavior and weathering degree evaluation. J. Civil Environ. Eng. 39(03), 67–74 (2017) Tang, Y., Shao, Z., Xu, T.: Pore structure of ancient Chinese bricks under environmental vicissitudes. KSCE J. Civ. Eng. 20(5), 1895–1902 (2016). https://doi.org/10.1007/s12205-0150652-1 Tang, Y.J., Shao, Z.D.: Ancient brick pore structure and saturation coefficient based on environmental variation. J. Tongji Univ. 43(11), 1662–1669 (2015). (In Chinese)

Multi-view Target-Free Video Structural Motion Estimation: A Self-adaptive Co-calibration Model Yi Zhang(B) and Enjian Cai Department of Civil Engineering, Tsinghua University, Beijing 100084, China [email protected]

Abstract. Target-free magnification-based vibration measurements can be used to compute the full-filed dynamic response of structures, which alleviate the need for structural surface preparation and can be implemented in an efficient and autonomous manner. However, up until now, such methods have limitations in the measurement range of motion that can be estimated, which fundamentally restricts their applicability. Moreover, they are only for one-dimensional (1D) or two-dimensional (2D) measurement. A rapid and accurate multi-view video estimation method is highly demanded. This paper presents a novel multi-view target-free video structural motion estimation method based on a self-adaptive co-calibration model. The model is derived from the maximum likelihood formulation with sparsity priors. Fast cosine transform with extension to phase correction operation across the levels of multi-scale pyramid is introduced. To apply it to three-dimensional (3D) video estimations, an iteratively reweighted method is employed to handle the l q -norm multi-view minimization problem. The proposed method is demonstrated in case studies considering analyses of video motion estimates for structural health monitoring (SHM). Compared to conventional methods, the proposed method provides more accurate measurement of structural motions in both time and frequency domains. Keywords: Structural health monitoring · Video processing · Structural motion estimation · Multi-view · Phase inference

1 Introduction Conventional structural displacement measurement requires attached wired or wireless sensors affixed to the structures (Walsh et al. 2013; Park et al. 2015; Poozesh et al. 2017a, b). While these sensors are reliable, instrumentation for lightweight structures results in mass-loading effects and would make unwanted changes to the dynamics of the structure. Their installation on larger structures is also a costly, time and labor-consuming process. For long-term structural health monitoring (SHM) applications, significant maintenance is needed for cabling or to assure adequate battery power (wireless sensors). More importantly, current contact sensors are only able to measure the responses at discrete locations therefore cannot provide full-field measurement, which is essential for correlating and updating highly detailed finite element models (Hang and Wang 2003). © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 739–757, 2023. https://doi.org/10.1007/978-981-19-7331-4_61

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Non-contact methods for vibration displacement measurement including scanning laser doppler vibrometry (Reu et al. 2017), holographic interferometry (Vest and Ma Cb Ain 1966), and electronic speckle pattern interferometry (Lekberg 1980), can provide data with high resolution while avoiding the installation of sensors and mass-loading effect. However, these methods usually require expensive devices and are performed sequentially which could be quite time and labor consuming for large structures. Compared to the aforementioned methods, digital video cameras are relatively agile, low-cost, easy to implement, and could simultaneously provide non-contact measurements with high spatial resolution (Baqersad et al. 2015; Ye et al. 2016; Yang et al. 2017). The tracking method is one of the most widely used vision methods. It relies on object recognition, pattern matching, edge detection, or digital image correlation to extract features in each image, and measures the displacements by counting the motions of these features in pixels over time (Baqersad et al. 2015; Ye et al. 2016; Ji et al. 2020). However, the target installation and surface preparation may be required, which can be quite difficult for large structures. Compared to the tracking method, target-free methods including feature point matching (Khuc and Catbas 2017; Li et al. 2020), particle image velocimetry (Arif and Potgieter 2016), deep learning-based object tracking (Kristan et al. 2019; Li et al. 2019), optical flow analysis (Ilg et al. 2017; Chen et al. 2018), and so on, can be implemented in a relatively autonomous and efficient manner with even higher accuracy. However, the accuracy of these methods may be restricted by nonstationary errors, and the detection of small motions of large structures is challenging. To offset these drawbacks, the phase-based method (Wadhwa et al. 2013) based on complex-valued steerable pyramids, has been proposed by the former researchers (Wu et al. 2012). This method can reveal the small movements with sub-pixel amplitudes and identify nonstationary motions in videos. Many works applied this method in real applications such as material properties prediction (Poozesh et al. 2017a, b; Wadhwa et al. 2017), system dynamics identification, and structural motion estimation (Dong et al. 2018; Mao and Sarrafi 2018; Sarrafi et al. 2018). However, problems have arisen since that: 1) The calculated motions are highly limited due to the spatial support of the pyramid filters (Meyer et al. 2015); 2) Even a small noise in raw video can drastically change the estimation because of the ill-posed problem (Katkovnik et al. 2018); 3) Most importantly, its precise measurement is practically challenging because structures contain both in-plane and out-of-plane vibration. This requires the measurement to consider three-dimensional (3D) motion instead of one-dimensional (1D) or two-dimensional (2D) motion only. To overcome the above three issues, this paper proposed two novel methods. The first method described in Sect. 2 is aimed at problems in 1D and 2D domains, the second method in Sect. 3 focuses on the improvement of multi-view estimations.

2 Proposed Multi-frequency Phase Inference The phase information is essential in motion estimation (Wadhwa et al. 2013), the relationship between them can be expressed as:   ∂φ0 (x, y, t) −1 ∂φ0 (x, y, t) , (1) u=− ∂x ∂t

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and   ∂φπ/2 (x, y, t) −1 ∂φπ/2 (x, y, t) . v=− ∂y ∂t

(2)

where u and v are image motions respectively in the x and y directions, t is time with the unit of the frame number, φ 0 and φ π /2 are local phases respectively in the x and y directions. Without considering the image distortion, the motions (e.g. pixels) can be converted to displacements (e.g. millimeters) by using the ratio of the length of an object to the number of pixels it spans in the scene. To capture the phase information φ accurately and adaptively, this section proposed a novel method of multi-frequency phase inference. The proposed method can be divided into two main parts: 1) multi-frequency phase retrieval, and 2) robust 2D phase unwrapping. Multi-frequency phase retrieval is to overcome the ill-posed problem in phase estimation, the phase information is estimated and adjusted using a maximum likelihood formulation with sparsity priors, accomplishing both denoising for Gaussian measurements and the object phase (absolute phase) retrieval. This step is to generate the estimated wrapped phase ϕ. Following the robust 2D phase unwrapping used to calculate the estimated unwrapped phase φ, which can expand the upper bound of applicable motion range, the transport of intensity equation is introduced to remove phase jumps simply and robustly. Meanwhile, an extension to phase estimation using a phase correction operation could lead to smoother estimation. These steps can increase the accuracy of motion estimation even for very noisy data and a high dynamic range of the motions. 2.1 Multi-frequency Phase Retrieval This section considers the problem of image from the multi-frequency observations (Katkovnik and Egiazarian 2018). The multi-frequency complex-valued model can be expressed as: uo,λ = bo,λ exp(juλ ϕ), λ ∈ Λ,

(3)

where uo,λ ∈ C N×N , bo,λ is the amplitude, uλ (> 0) are phase factors, basically dimensionless relative frequencies in noisy observations, ϕ represents the object absolute phase, and Λ = [λ0 , λ1 , …, λn−1 ] are a series of periods of the multi-frequency observations. In what follows ϕ, bo,λ and other variables are functions of x given on a regular 2D grid, X ⊂ Z 2 . uλ are provided but bo,λ and ϕ should be inferred from intensity observations for noisy zo,λ and noiseless yo,λ cases. For a set of experiments S,  2 us,λ = Ps,λ uo,λ , ys,λ = us,λ   2  zs,λ = G us,λ  , λ ∈ Λ, s = 1, . . . , S,

(4)

where G{.} is an operator of random noisy observations, Ps,λ is the image formation operator. Inference of uo,λ ∈ C N×N from {zs,λ } is challenging due to the periodicity of the likelihood function with respect to the non-linearity and ϕ of the observation model. For

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a stochastic noise model with independent samples, the basic criterion generated by the maximum likelihood can be expressed as: S     2 (5) l zs,λ (x), us,λ (x) L0 = λ∈

s=1

x

where l(z, |u|2 ) represents the minus log-likelihood of a candidate solution for uo,λ given through the noisy outcome z and observed true powers |u|2 . For the case of Gaussian 2  random variables, l(z, |u|2 ) = 2σ1 2 |u|2 − z  , where σ 2 is the noise variance. Considering Eqs. (3)–(5), the following likelihood function with quadratic residual penalty conditions, which includes the complex-valued exponent modeling of the multifrequency object uo,λ and the image formation model Ps,λ for us,λ is used:   2  

l zs,λ , us,λ (x) L us,λ , uo,λ , bo , ϕ, δλ = λ,s,x

1  us,λ − Ps,λ uo,λ 2 + 2 λ,s γ1  1 bo.λ exp(j(μλ ϕ + δλ )) − uo,λ 2 + 2 λ γ2

(6)

where .22 is the Frobenius norm, and γ 1 , γ 2 > 0 are parameters, and δ λ are disturbance parameters to model the unknown phase shifts. 2.2 Robust 2D Phase Unwrapping Although the motion information can be estimated successfully using the maximum likelihood formulation processes described in the previous section, the direct estimation of small values generate strong artifacts (Cai et al. 2020). In the context of the image alignment problem especially with magnification, magnified large displacements corresponding to a phase difference of more than π leads to phase ambiguity. The phase differences are only interferometric when they are defined between [−π, π ] due to the periodicity of the phase. On the other hand, if a false phase wrap appears in the analytical map, or a single phase wrap operation between two neighboring pixels is missed because of noise, an unavoidable error will occur in the unwrapping of both pixels. Eventually, this type of error propagates over the residual of the image. The accumulative nature of the phase process imposes notably stringent requirements on the algorithms that are constructed to overcome the above issues. Generally, the phase unwrapping problem can be described as follows: φ(x, y) = ϕ(x, y) + 2π · g

(7)

where ϕ(x, y) denotes the magnified wrapped phase, φ(x, y) denotes the magnified unwrapped phase, and g is the integer to be solved. Many methods have been proposed such as least square methods (Zhao et al. 2015), path- following methods (Shi 2007), region-growing methods (Baldi 2001), and the regularized phase tracker method (Servin et al. 1998). Least square solutions are mainly

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discussed in this paper. These methods seek to find an unwrapped phase by solving the Poisson equation: ∂ 2 φ(x, y) ∂ 2 φ(x, y) + = ∇ 2 ϕ(x, y) ∂x2 ∂y2

(8)

where ∇ 2 represents the Laplacian operator. However, least square methods are sensitive to noise and only work well when the noise variance is low in magnitude. The transport of intensity equation has been suitably managed using a phase unwrapping method (Pandey et al. 2016), which obtains the absolute phase directly from the intensity information. The right-hand side of Eq. (8) is substituted by the axial derivative of the intensity in two defocus planes giving: 2π I (x, y, z + z) − I (x, y, z − z) ∂ 2 φ(x, y) ∂ 2 φ(x, y) + =− 2 2 ∂x ∂y λ 2 z

(9)

where I(x, y, z + z) and I(x, y, z − z) represent the defocus intensities on the planes, respectively (Zhao et al. 2019).

3 Proposed Reweighted Multi-view Estimation The step in Sect. 2 is to measure the 2D displacements more accurately in single camera view. In this section, the iteratively reweighted algorithm is proposed to find a robust and accurate solution of the outlier removal problem in multi-view estimation, which transforms the 2D displacement data to 3D data. The traditional multi-view estimation will be firstly described. 3.1 Multi-view Estimation In a multi-view optical system, each view can be defined by a perspective projection between the 3D coordinates of a point U = {X, Y, Z}T and its mapping u = {x, y}T in a 2D image of Euclidean space. To facilitate this projective transformation, homogeneous space is introduced, thus points U and u are expressed as: U = {X , Y , Z, 1}T u = {x, y, 1}T ,

(10)

The relationship between them can be expressed as: τ u = PU,

(11)

where P is a linear projective mapping from 3D to 2D, τ is the scale factor, which can be calculated by dividing the result of Eq. (11): τ = P3 U,

(12)

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where P3 is the third row of P. The perspective transformation is non-linear in the Euclidean space (Amir-Khalili et al. 2014) since τ is dependent on U. The projection matrix P can be further decomposed as: P = K[R|t],

(13)

where K is a 3 × 3 matrix containing the camera’s intrinsic parameters, such as the focal length and the optical center. [R | t] is a 3 × 4 matrix containing extrinsic parameters including a 3 × 3 rotation matrix R and a 3 × 1 translation vector t, which are used to describe the camera’s position in a chosen reference camera. For the pinhole camera model, Eq. (11) can be written as: τ u = K[R|t]U ↓ ⎧ ⎫ ⎧ ⎫ ⎡ ⎤⎡ ⎤⎪ X ⎪ k k r r t r τ x k ⎨ ⎪ ⎨ ⎬ ⎬ 1,1 1,2 1,3 1,1 1,2 1,3 1 ⎪ Y ⎦ ⎣ ⎦ ⎣ , 0 k2,2 k2,3 r2,1 r2,2 r2,3 t2 τy = ⎪Z ⎪ ⎩ ⎭ ⎩ ⎪ ⎭ 0 0 k3,3 r3,1 r3,2 r3,3 t3 ⎪ τ 1

(14)

During the multi-view estimation, the relationships among measured positions for reference images in each distinct view are firstly matched by speeded-up robust features (SURF). Then the elements of intrinsic and extrinsic matrices are automatically determined by solving the perspective-n-point problem (Lepetit et al. 2009), which minimizes the reprojection error to solve the parameters of a camera by matching points. 3.2 Proposed Iteratively Reweighted Method However, a large number of outliers still exist since they cannot be thoroughly removed among local views in long point tracks. Traditional multi-view estimation will be significantly degraded by outliers (Olsson et al. 2008), thus outlier removal is essential to mitigate the deterioration caused by mismatch. The following reweighted lq minimization of multi-view estimation is proposed for efficient outlier removal. The squared reprojection error in multi-view estimation is Olsson et al. (2010):   2 R1 U + t1 R2 U + t2 i i , γi (U, R, t) = U1 − ,U − (15) R3 U + t3 2 R3 U + t3 where superscript i is the measurement order in the i-th camera, U j , Rj and t j are the j-th row of U, R and t respectively. The outlier removal aims to find a solution for with all errors γ i (x) ≤ δ 1 , where δ 1 is the inlier threshold, x contains the parameters of the 3D points and the camera translations (Kahl and Hartley 2008). The least-squares solution is applied to solve the residual error problem: min max γi (x), x

i

(16)

Equation (16) can be written in compact matrix form as a feasibility problem (Olsson et al. 2010): does there exist x such that Hx ≤ d, where d is a 2D × 1 vector and H is

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a 2D × F matrix. It is worth mentioning that D is the number of cameras, and F is the dimension of x. The reason for minimizing the maximum residual error is that it contains useful convexity properties (Kahl and Hartley 2008). Therefore, convex optimization are further utilized, and Eq. (16) is expressed using the constrained l0 minimization: min s0

x,s⊆

subject to Hx ≤ d + s ⊗ 1κ×1 , s ≥ 0

(17)

where s is a vector containing the slack variables, the notation s0 is l 0 -norm of s which measures the count of the nonzero entries in s, κ = 2, 1κ×1 is a κ-dimensional vector with all elements being 1, ⊗ is the Kronecker product and  is the index set. To obtain the minimization solution, deterministic approximate methods have been proposed in literature (Sturm 1998; Le et al. 2017), in which the consensus maximization problem with linear complementarity was reformulated. The Frank-Wolfe optimization scheme and alternating direction method of multipliers (ADMM) are possible algorithms to efficiently solve these reformulations. However, these methods can only handle lowdimensional problems. For large-scale multi-view estimation problems, they might not be efficient. l1 minimization (Olsson et al. 2010) is a popular method that could be used to solve the convex relaxed formulations. A convex relaxation of Eq. (17) is to replace the l 0 -norm by its convex envelope l1 -norm as: min s1

x,s⊆

subject to Hx ≤ d + s ⊗ 1κ×1 , s ≥ 0

(18)

where the notation s1 is l1 -norm of s which measures the sum of the absolute values in s. The l 1 minimization is good for its convexity, however, its performance may be degraded by convex relaxation. It has been demonstrated in the sparse recovery researches (Wen et al. 2017), the l 0 or l q (0 < q < 1) norm (Purkait et al. 2018) can usually yield a sparser solution than the l 1 -norm. Therefore l 0 or l q norm penalties can be expected to reduce the possibility of removing true outliers. In this regard, reweighted lq minimization is adopted in the multi-view estimation. The l0 norm is first approximated by the lq norm with a small value of q (e.g. q = 0.1 in the experiments). Then, at the (it + 1)-th iteration, the lq norm is approximated by first-order expansion at sit as: Algorithm 1 Iteratively reweighted multi-view estimation Input: The inlier threshold δ 1 > 0, δ 2 > 0, q ∈ (0,1), set of measurements , an initialization ω1 = 1D×1 , maximum iteration number IT. Begin: Construct H and d from the measurements . For it = 1, 2, · · · , IT Solve Eq. (22) with ωit to obtain sit . Update ωit+1 by Eq. (20) based on sit .

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End for Let s = s IT and remove the residuals for which si > 0. End Output: A subset x ⊆  of the measurements such that γ i (x) ≤ δ 1 .

q

sq,δ2 ≈

q−1 D   |si |, siit  + δ2 i=1

where δ 2 is the inlier threshold. Let   q−1 q−1     it   it  it+1 , =  s 1  + δ2 , · · ·  s D  + δ2 ω

(19)

(20)

The parameters at the (it + 1) -th iteration are updated by the iteratively reweighted algorithm as: min ωit+1 s x,s⊆

1

subject to Hx ≤ d + s ⊗ 1κ×1 , s ≥ 0

(21)

where is the Hadamard product. The Eq. (21) can be solved by the duality approach as given by: max −dT y y,μ

subject to HT y = 0 ωk+1 − Jy − μ = 0 y ≥ 0, μ ≥ 0.

(22)

where y and μ are the dual variables, J = ID ⊗ 1κ×1 , and ID is an identity matrix of size D. The proposed iteratively reweighted multi-view estimation is summarized in Algorithm 1.

4 Results and Discussion 4.1 2D Motion Estimation The proposed method was demonstrated in the modal analysis for the left span of a suspension bridge, detailed information and two measurement points can be found in (Wadhwa et al. 2017). Acceleration data were doubly integrated to measure the displacement of the structure for comparison. The displacements estimated from the bridge vibration video are qualitatively compared in Fig. 1 A–D. The sensitivity of the phasebased method and optimization-based method to noise is also compared. It can be seen from the figure, the estimated displacements from the proposed method match the measured data very well. Furthermore, the errors increase rapidly in the regions of large

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displacement using the optimization-based method and phase-based method especially the latter. This is because motion estimation is usually bounded by the spatial support of the specific pyramid filters in conventional methods (Wadhwa et al. 2013; Cai et al. 2020). Thus, exceeding the bounds will be manifested as blurring or artifacts (Wadhwa et al. 2013; Cai et al. 2020). The maximum error of the estimated displacements is used to check the performance in different methods.

Fig. 1. Qualitative comparison of estimated mode displacement time history corresponding to (a) 1st Mode (Point 1); (b) 1st Mode (Point 2); (c) 2nd Mode (Point 1) and (d) 2nd Mode (Point 2) in bridge example.

The maximum error result and quantitative comparisons are shown in Table 1 and Fig. 2. Note the mode can be estimated from different measurement points. Figure 2 shows that the displacement time history estimated by the proposed method agree very well with the measured data in 1st Mode of two points, its performance in 2nd Mode is also better than conventional methods (Wadhwa et al. 2013; Cai et al. 2020). As further observed in Table 1, the maximum error using the optimization-based method is 0.8055 mm and the value of proposed method is 0.5420 mm in 2nd Mode (Point 2), which

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Fig. 1. (continued)

may be close to some extent. This suggests that the performance of the optimizationbased method may be relatively considerable in high mode when estimating displacement time history of the bridge vibration. In general, the optimization-based method performs obviously better than the phase- based method except the close deviations of them shown in 1st Mode (Point 1). Similar result can be seen in Table 1, the maximum error using the phase-based method is 1.7455 mm and the value of the optimization-based method is 1.3226 mm in 1st Mode (Point 1). This further suggests that these two methods are limited by the spatial support of the specific pyramid filters. Therefore, errors are more likely to be generated in 1st Mode due to the largest modal motions existed in this mode. Furthermore, the power spectral densities (PSDs) are computed based on the estimated displacements, see Fig. 3. It qualitatively shows that the 1st , 2nd , 3rd and 4th modal frequencies from the measured data and the proposed method have close agreement while deviate quite a lot from other methods. The error of the estimated frequency result and comparisons are shown in Table 1, Fig. 3. The errors associated with the proposed method are range from 0.1430 Hz to 1.1740 Hz, whereas these with the optimizationbased method are range from 0.1430 Hz to 3.0300 Hz, and with the phase-based method

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Table 1. Statistics describing deviations between estimated and measured data in bridge example. Maximum error of displacement time history (mm) Mode (point) Phase

Optimization Proposed

1st (1)

1.7455 1.3226

0.1935

1st (2)

1.5079 0.6049

0.1969

2nd (1)

7.2875 1.4981

0.4070

2nd (2)

2.1117 0.8055

0.5420

Error of estimated frequency (Hz) Mode

Phase

Optimization

Proposed

1st 2nd

1.3031

0.1430

0.1430

0.8060

0.1220

0.1220

3rd

0.8350

2.2570

0.3240

4th

3.0300

3.0300

1.1740

are range from 1.3031 Hz to 3.0300 Hz. It can be seen the proposed method has the best performance. Notably, the errors of the proposed method in 1st and 2nd Mode are the same as the optimization-based method, which are 0.1430 Hz and 0.1220 Hz. This suggests the frequency estimation ability of optimization-based method is also considerable in low modes from the bridge video. However, its error increases rapidly in 3rd Mode which is 2.2570 Hz and even larger than the error of the phase-based method. Furthermore, the error of both phase-based and optimization-based method in 4th Mode are 3.0300 Hz, and the proposed method is just 1.1740 Hz. This further suggests the proposed method has an advantage of estimating modal frequency in video signals especially in highest mode order. 4.2 3D Motion Estimation The proposed method was applied in shaking table tests of a 3-storey reinforced concrete (RC) building structure. The global layout of the test specimen and cameras can be seen in Fig. 4. The test specimen had a plan dimension of 5140 mm (x direction) by 4300 mm (y direction), and a total height of 7340 mm. Its lengths in the shaking table had a plan dimension of 6000 mm by 6000 mm. Three cameras were used to measure the dynamic response of the structure. The types of cameras 1, 2, and 3 are Canon EOS 5D Mark IV, SONY a6400, and SONY FDR-AX700, respectively. A sampling frequency of 50 Hz and resolution of 1920 × 1080 were selected in the cameras. The shooting direction of camera 1 is perpendicular to x direction, cameras 2 and 3 are on the right and left sides of camera 1 and their directions are at an angle of 45 degrees with x direction. The distances of three cameras from the shaking table are all 4000 mm in both the x and y directions. In the tests, the strong motion records motions named JMA Kobe (Watabe), which was recorded in Kobe city in Great Hanshin Earthquake on Jan 17, 1995, was

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Fig. 2. Comparison between estimated and measured displacement time history corresponding to (a) 1st Mode (Point 1); (b) 1st Mode (Point 2); (c) 2nd Mode (Point 1) and (d) 2nd Mode (Point 2) in bridge example.

loaded. The peak acceleration was selected to be 0.07 g and loaded successively in the x and y directions. Based on the camera measurement, the displacement responses of the test specimen strong motion records were estimated by both the proposed and conventional methods. It is worth mentioning that the conventional method applied the phase-based motion estimation (Wadhwa et al. 2013) in each single camera view. The measurement points used to locate floors are shown at the top of Fig. 4. For comparison purpose, displacement meters were installed and used to measure the floor displacement of the structure. Comparisons of inter-storey drift response history are shown in Fig. 5. The drift responses estimated by the proposed method and the conventional method are basically close to the reference data. The estimated peak drift ratios using these two methods in all cases are compared in Fig. 6. It shows that the drift ratios using the conventional method are 0.28%, 0.11%, 0.26% in x direction and 0.25%, 0.41%, 0.33% in y direction. While the estimated ratios using the proposed method are 0.16%, 0.22%, 0.14%, and 0.18%, 0.26%, 0.28% in x and y direction. The ratios using the reference data are 0.24%, 0.27%,

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Fig. 3. PSD estimated by (a) phase-based method, (b) optimization-based method, (c) measured data, (d) proposed method in bridge example.

0.17%, and 0.17%, 0.31%, 0.24% in x and y direction. Although the data estimated by the conventional method may be relatively reasonable in y direction, there are large deviations in x direction. To quantitatively compare the errors between the estimated

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Fig. 4. Layout of the shaking table experiment.

and reference displacements, comparisons in the form of a scatter diagram are shown in Fig. 7, the red line indicates the case where the estimated data coincides exactly with the reference data. The performance of the proposed method is obviously better, since its estimated displacements fit the red lines very well, while the conventional method does not. For further demonstration, the measured displacement responses were compared in frequency domain. The deviation between the estimated value and the reference value

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in the frequency domain is measured by the coherence function (Harichandran and Vanmarcke 1986; Luco and Wong 1986; Na 1993). The value of the coherence function is from 0 to 1. Higher values indicate more similarities between two groups of data in their frequency domains. The results are shown in Fig. 8. It can be recognized that the proposed method achieves higher values.

Fig. 5. Inter-storey drift responses of 3-storey RC structure: (a) x direction in the 3rd storey, (b) x direction in the 2nd storey, (c) x direction in the 1st storey, (d) y direction in the 3rd storey, (e) y direction in the 2nd storey, (f) y direction in the 1st storey.

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Fig. 6. Comparison of peak inter-storey drift ratio in (a) x direction, (b) y direction.

Fig. 7. Comparison between estimated and measured displacements time history.

5 Conclusions This study proposed a multi-view video measurement method for estimating small and nonstationary structural motions. The proposed method does not require structural surface preparation and can be performed in an autonomous manner. The proposed method uses multi- frequency absolute phase retrieval and fast cosine transform with extension to phase correction operation across the levels of a multi-scale pyramid. To address the outlier removal problem in multi-view estimation, an iteratively reweighted method is

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Fig. 8. Comparison between estimated and reference data in frequency domain.

introduced. The experimental examples demonstrate that structural displacements can be reasonably estimated by the proposed method. Furthermore, the proposed method is shown to be more reliable in the frequency domain. Acknowledgements. The authors gratefully acknowledge the financial support from National Natural Science Foundation of China under project number of Grand No. 51908324&52111540161. The support from Tsinghua University Initiative Scientific Research Program (20213080003) is also greatly appreciated.

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Poozesh, P., Baqersad, J., Niezrecki, C., Avitabile, P., Harvey, E., Yarala, R.: Large-area photogrammetry based testing of wind turbine blades. Mech. Syst. Signal Process. 86, 98–115 (2017a) Poozesh, P., Sarrafi, A., Mao, Z., Avitabile, P., Niezrecki, C.: Feasibility of extracting operating shapes using phase-based motion magnification technique and stereo-photogrammetry. J. Sound Vibr. 407, 350–366 (2017b) Purkait, P., Zach, C., Eriksson, A.: Maximum consensus parameter estimation by reweighted L1 methods (2018) Reu, P.L., Rohe, D.P., Jacobs, L.D.: Comparison of DIC and LDV for practical vibration and modal measurements. Mech. Syst. Signal Process. 86, 2–16 (2017) Sarrafi, A., Mao, Z., Niezrecki, C., Poozesh, P.: Vibration-based damage detection in wind turbine blades using phase-based motion estimation and motion magnification. J. Sound Vibr. 421 (2018) Servin, M., Marroquin, J.L., Malacara, D., Cuevas, F.J.: Phase unwrapping with a regularized phase-tracking system. Appl. Opt. 37(10), 1917–1923 (1998) Shi, Y.: Robust phase unwrapping by spinning iteration. Opt. Express 15(13), 8059–8064 (2007) Sturm, J.: Using Sedumi 1.02, a Matlab toolbox for optimization over symmetric cones. Optim. Methods Softw. 11 (1998) Vest, C.M., Ma Cb Ain, J.C.J.O.A.I.J.o.O.: Holographic interferometry 37(2), 642–649 (1966) Wadhwa, N., et al.: Motion microscopy for visualizing and quantifying small motions. Proc. Natl. Acad. Sci. U.S.A. 114(44), 11639–11644 (2017) Wadhwa, N., Rubinstein, M., Durand, F., Freeman, W.T.: Phase-based video motion processing. ACM Trans. Graph. 32(4), 1–10 (2013) Walsh, S., Borello, D., Güldür Erkal, B., Hajjar, J.: Data processing of point clouds for object detection for structural engineering applications. Comput. Aided Civ. Infrastruct. Eng. 28 (2013) Watabe, M.: Kobe earthquake. In: 2nd International Conference on Earthquake Resistant Engineering Structures (ERES 99), Univ. Catania, Catania, Italy, pp. 779–783 Wen, F., Liu, P., Liu, Y., Qiu, R.C., Yu, W.: Robust sparse recovery in impulsive noise via L(P)-L(1) optimization. IEEE Trans. Signal Process. 65(1), 105–118 (2017) Wu, H.Y., Rubinstein, M., Shih, E., Guttag, J., Durand, F., Freeman, W.: Eulerian video magnification for revealing subtle changes in the World. ACM Trans. Graph. 31(4), 8 (2012) Yang, Y., et al.: Blind identification of full-field vibration modes from video measurements with phase-based video motion magnification. Mech. Syst. Signal Process. 85, 567–590 (2017) Ye, X.W., Dong, C.Z., Liu, T.: Image-based structural dynamic displacement measurement using different multi-object tracking algorithms. Smart Struct. Syst. 17(6), 935–956 (2016) Zhao, Z., Zhang, H., Xiao, Z., Du, H., Zhuang, Y., Fan, C., Zhao, H.: Robust 2d phase unwrapping algorithm based on the transport of intensity equation. Meas. Sci. Technol. 30(1) (2019) Zhao, Z., Zhao, H., Zhang, L., Gao, F., Qin, Y., Du, H.: 2d Phase unwrapping algorithm for interferometric applications based on derivative Zernike polynomial fitting technique. Meas. Sci. Technol. 26(1) (2015)

A Robust Bayesian Sensor Placement Scheme with Enhanced Sparsity and Useful Information for Structural Health Monitoring Mujib Olamide Adeagbo1(B) and Heung-Fai Lam1,2 1 Department of Architecture and Civil Engineering, City University of Hong Kong, HKSAR,

China {moadeagbo2,paullam}@cityu.edu.hk 2 School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, China

Abstract. For the application of structural health monitoring in civil engineering structures, one common bane is the need for sensors. Optimizing the type of sensors, the number of sensors, and the location of sensors is therefore important in ensuring that the most optimal amount of information is obtained from measurement data while making the monitoring systems (including the sensors) economical. In this study, the issue of sensor placement is addressed by developing a simple Bayesian scheme based on information entropy and progressive increment or decrement in the number of available sensors. Compared to other conventional placement schemes available in the literature, the proposed scheme offers a simple yet robust configuration optimization, with results almost always the same as a full one-by-one search through all possible configuration candidates. The proposed scheme also provides enhanced sparsity of sensors by incorporating a spatially correlated covariance matrix for the measured data. The enhanced sparsity ensures that more “useful” information is contained in the measured data. To verify the proposed scheme’s acclaimed improvement, especially for damage detection purposes, the analysis results for configurations selected by conventional algorithms and those selected by the proposed scheme are compared for a ballasted track system. Results clearly show significant improvement in configurations’ optimality, with minimal computational cost. Keywords: Sensor placement · Bayesian analysis · Information entropy · Structural health monitoring · Time-domain analysis

1 Introduction State-of-the-art structural health monitoring schemes involve the deployment of sensors, either of a single type of multi-type networks. However, given the high cost of sensors and the size of most civil engineering structures, there often arises the need to search for locations where the limited number of available sensors can be placed to obtain the maximum amount and highest quality of information about the structure for health © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 758–770, 2023. https://doi.org/10.1007/978-981-19-7331-4_62

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monitoring purposes. Optimal sensor placement (OSP) methodologies are techniques developed to approach this sensor allocation problem in a scientific way to achieve the set goals (Ostachowicz et al. 2019; Papadimitriou and Papadimitriou 2015). In the literature, for OSP algorithms, the categories of criterion used to appraise sensor configurations or to estimate the quality of information (uncertainties) involved include modal parameters-based (Reynier and Abou-Kandil 1999), response reconstruction-based (Zhang and Xu 2016), energy-based (Li et al. 2007); and information-based (Papadimitriou et al. 2000; Udwadia 1994). Notably, the informationbased criterion appears to be the most popular for OSP, with the information entropy (IE) and Fisher Information Matrix (FIM) being the most prominent indices. The IE measures the uncertainty in the model parameter estimates (Papadimitriou et al. 2000), and so the most optimal configurations with the highest information correspond to the minimal IE (Papadimitriou and Lombaert 2012). For real structural systems, the intuitive way to optimize configuration is an exhaustive search. However, it is computationally prohibitive to consider all possible locations and configurations in sensor placement, even if the structure is simple (Papadimitriou 2004). Aside from more complex algorithms like genetic algorithms (Papadimitriou et al. 2000), Papadimitriou (2004) proposed the sequential sensor placement (SSP) algorithms (i.e., the forward SSP and backward SSP), to ease the OSP in terms of computational demand. However, the accuracy of the SSP algorithms in identifying the optimal configuration relies on the assumption that the optimal sensor positions for l sensors must be a subset of the optimal sensor positions for (l + 1) sensors for all values of l. Often, this assumption cannot be met, most notably for high values of N s . Hence, the SSP may yield optimal results different from that of the full search algorithm, though with a lesser computational expense. A robust Bayesian heuristic-based enhancement of the SSP (ESSP) proposed by the authors (Lam and Adeagbo 2022) is utilized instead to address the issues in the conventional SSP algorithms. The proposed algorithm improves the ill-condition nature of the FIM involved during the calculation of the IE by drawing on additional information from the prior PDF. Also, the ESSP algorithm can select more than one optimal sensor at each optimization level, thereby solving the subset dependency problem and allowing for alternative configurations to the most optimal, for field applications. In other to reduce the sensor redundancy/clustering and improve the useful information contained in measured data, a model of the prediction error variance involving spatial correlations of different types and parameters are implemented. The applicability of the proposed algorithm is proven by considering a rail-sleeper-ballast system; and a comparison of the results with those obtained from other conventional algorithms is then made to demonstrate the accuracy and robustness of the ESSP.

2 Basic Formulations and Modelling 2.1 Information Entropy (IE) For a model class M parameterized by a set of uncertain parameters θ ∈ R1×Nθ , where N θ is the number of uncertain parameters, the posterior PDF of the uncertain parameters θ given the model class M and measured data D (where measurements are collected

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at locations specified in a vector δ ∈ RNs ×1 ) can be evaluated following the Bayesian theory (Beck and Katafygiotis 1998): p(θ|D,δ, M ) =

p(D|θ, δ, M )p(θ|M ) p(D|θ, δ, M )p(θ|M ) = p(D|M ) p(D|θ, δ, M )p(θ|M )dθ

(1)

where p(D|θ, δ, M ) is the likelihood PDF, p(θ|M ) is the prior PDF, and the denominator p(D|M ) is termed the evidence, and serves as a normalizing constant to ensure that the posterior PDF integrates to unity over the parameter space. A common way to quantify the uncertainties involved in the estimation of θ is the calculation of the information entropy (IE) (Papadimitriou et al. 2000), which can be expressed as (Papadimitriou 2004; Papadimitriou and Lombaert 2012):   H(δ|D, M ) = E − ln p(θ|D,δ, M ) (2) where E[·] is the mathematical expectation. Substituting for p(θ|D,δ, M ) yields:     H(δ|D, M ) = E ln(p(D|θ, δ, M )p(θ|M ))dθ − E ln p(D|θ, δ, M )p(θ|M )

(3)

Assuming a large D, by Laplace method of asymptotic approximation (Papadimitriou et al. 1997) and further evaluation:  1 Nθ ln(2π ) − (4) H(δ|D, M ) = ln|h(θ|D,δ, M )|p(θ|M )dθ 2 2

  

ˇ ˇ δ, M p(θ|M ) and |·| is M ∈ RNθ ×Nθ is the Hessian of − ln p D|θ, where h θ D,δ, the determinant of a matrix. By sampling the prior PDF p(θ|M ): ⎞ ⎛ Nps

Nθ 1 ⎝ 1   (i) ⎠ (5) H(δ|D, M ) ≈ ln(2π ) − ln h θ |D,δ, M 2 2 Nps i=1

where N ps is the number of samples from p(θ|M ) and θ(i) is the ith sample of θ. 2.2 Probabilistic Model of the Prediction Error For the system and model class M considered earlier, assume an additive model of the prediction error at the t th timestep and all N d measured locations, such that: 

ξ(t; θ, δ) = Z(t) − Z(t; θ, δ) 

(6)

where ξ(t; θ, δ) is the prediction error vector, Z(t) is the measured response vector, and Z(t; θ, δ) is the model-predicted response vector. Assuming that ξ(t; θ, δ) is modeled to have a zero-mean Gaussian distribution, the likelihood PDF in Eq. (1) is thus:  

 1 Nd Nt (all) J (θ |D,δ, M) exp − p(D|θ, δ, M ) ≡ p ξ |θ, δ, M =  2 (2π )Nd Nt ||Nt (7)

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  where ξ(all) = ξ(1), . . . , ξ(Nt ) and J (θ |D,δ, M) =

Nt   T 1  ˆ − Z(t; θ, δ) Z(t) − Z(t; θ, δ)  −1 Z(t) Nd Nt 

(8)

t=1

where  ∈ RNt ×Nt is the covariance matrix for each ξ(t; θ, δ). It is assumed that the covariance matrix is the same at all N t time steps, and that by assuming stationarity, its (i, j) entry can be expressed as:    i,j = Ci,j di,j , l · η2 (9) 2 Nt ×Nt is the correlation matrix, where  η is the prediction error variance, C ∈ R Ci,j di,j , l is the (i, j) entry of the spatial correlation matrix which is a function of di,j the spatial distance between two observed locations i and j, and l the correlation range. In this paper, to study the change in optimal configuration with the prediction error model, 3 different correlation functions are investigated to form the matrix C. Equations (10)–(12) are expressions for the spherical, exponential, and uncorrelated functions, respectively (Sherman 2011):

  Ci,j di,j , l =





 3 d d 1 − 1.5 li,j + 0.5 li,j if di,j < l 0

    di,j Ci,j di,j , l = exp − l    1 if i = j Ci,j di,j = 0 if i = j

if di,j ≥ l

(10)

(11) (12)

With the expression of the likelihood PDF obtained in Eq. (7), one can further evaluate  ˇ Eq. (5), by simplifying the hessian matrix h θ D,δ, M ∈ RNθ ×Nθ . The (j, k) entries

 ˇ M is defined by (Papadimitriou 2004; Papadimitriou of the Hessian matrix h θ D,δ, et al. 1997): hj,k (θ|D,δ, M ) ≈

  Nt  ∂ ∂ ∂2 ln p(θ|M ) [Z(n; θ, δ)]T  −1 [Z(t; θ, δ)]+ − ∂θj ∂θk ∂θj ∂θk n=1

(13) In Eq. (13), the second derivative of − ln p(θ|M ) vanishes if the prior is independent of θ. In other to utilize the extra information from the prior, a slowly varying Gaussian PDF with covariance  is taken as the prior PDF in this paper. Thus, the information entropy in Eq. (5) can then be written as: H(δ|D, M ) ≈

Nθ ln(2π ) 2

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⎞ N Nps t   1 ∂ ∂ −⎝ ln [Z(n; θ, δ)]T  −1 [Z(n; θ, δ)] +  −1 ⎠ 2Nps ∂θj ∂θk ⎛

u=1

(14)

n=1

where samples of θ, and samples of parameters in matrices  and  based on the expected range of values are required for the evaluations of Eq. (14), since experimental data are not available during this configuration design stage. The objective of sensor optimization is thus to obtain configurations with relatively smaller (minimal) IE values. 2.3 Structural System Model For full modeling of the model class M, not only the model of the prediction error is required but also the structural system model. In this paper, the system to be considered is a ballasted track section. The transverse section of the rail-sleeper-ballast system is modeled as a non-uniform Timoshenko beam supported by nonlinear distributed springs (Lam et al. 2020), while the 2 rails and their fasteners are modeled as spring-mass elements with only vertical DOFs. The sleeper of length 2.42 m is divided into 48 equal elements for optimal refinement. The system is as depicted in Fig. 1. The stress-strain relationship of ballast stiffness (i.e., the distributed spring) is modeled by the modified Ludwik model (Adeagbo et al. 2021a, 2021b), and given as follows. Following the derivations in (Adeagbo et al. 2021a), the stiffness of the ballast k B is expressed as:  L kB = E bh   for ε ≤ εy n σ  kB = (15) b kBN = n εy εεy h for ε > εy where kBL , kBN , E, n, σy , εy , ε and h are the stiffness in the linear zone, stiffness in the nonlinear zone, modulus of elasticity, the strain hardening exponent, the yield stress, the yield strain, the total strain, and the thickness respectively, of the ballast; while b is the sleeper’s bottom dimension. With the 2 models defining model class M fully discussed, the uncertain parameter θ can then be expressed as consisting of:      (16) θ = θs , θξ = θεy , θn , θc , θMr , θMl , θkp , θkB1 , θkB2 , θkB3 , {θl } where θs and θξ are the uncertain parameters for the structural model and the prediction error, respectively. θεy , θn , θc , θMr , θMl , θkp , θkB1 , θkB2 and θkB3 calibrate the ballast yield strain, the ballast strain hardening exponent, the damping coefficient, the right rail mass, the left rail mass, the rail pad-fastener stiffness, the ballast stiffness in the left region, the ballast stiffness in the middle region and the ballast stiffness in the right region; while θl calibrates the correlation length for matrix C. The nominal values of the ballast yield strain, strain hardening exponent, damping coefficient, rail mass, the rail pad-fastener stiffness, and ballast stiffness are 1 × 10–4 , 0.5, 18%, 60.21 kg/m, 50 MN/m, and 150 kN/m2 , respectively (Adeagbo et al. 2022).

A Robust Bayesian Sensor Placement Scheme with Enhanced Rail

Mr

Ml

763

Rail pad and fasteners

kp

Sleeper x

h

kB2

kB1

kB3

Ballast Subgrade

z

Fig. 1. The model of the rail-sleeper-ballast system.

3 Sensor Placement Algorithms and Configurations In this paper, three different algorithms are considered. The full search and sequential sensor placement algorithms (Papadimitriou 2004) are popular in the literature. For enhanced results in terms of sparsity and useful information, an enhanced sequential sensor placement algorithm proposed in (Lam and Adeagbo 2022) is also considered. 3.1 Full Search (FS) The full search (FS) method involves the utilization of all possible combinations of placing Nd sensors given No observable locations. This method is very inefficient and requires more computational efforts than all other algorithms. 3.2 Sequential Sensor Placement (SSP) The sequential sensor placement (SSP) algorithm was proposed by Papadimitriou (2004), and involves the gradual addition (or removal) of one sensor to (or from) a base configuration following the forward (or backward) direction. Both the forward SSP (FSSP) and the backward SSP (BSSP) are more optimal than the FS algorithm. The FSSP algorithm can be written as:

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3.3 Enhanced Sequential Sensor Placement (SSP) The enhanced sequential sensor placement (ESSP) algorithm was proposed by Lam and Adeagbo (2022), and it is a heuristics-based enhancement of the SSPs. For both the forward and backward ESSP (termed EFSSP and EBSSP, respectively), the optimal configuration for l sensors does not need to be a subset of the optimal configuration for (l + 1) sensors for all values of l, as is necessary for the SSP algorithms. Also, unlike the SSPs, the proposed ESSP algorithms can select more than one optimal configuration at each placement level using a threshold pruning factor to remove only non-promising candidates. The relative optimality index (ROI) provides a scalar assessment for the performance of candidate sensor configurations, given N s available sensors. The ROIi of the ith candidate configuration δi within the candidate set C for l sensors is expressed as:      H δi,l − min H(δ1 ), . . . , H δNc       for i = 1, . . . , Nc ROIi = max H(δ1 ), . . . , H δNc − min H(δ1 ), . . . , H δNc (17) where Nc is the number of candidate configurations. The maximum ROI value for accepting candidate configuration is then denoted as ROI (taken as 3% throughout this paper). Thus, the ESSPs are more robust than the SSPs, with a little increase in computation. The EFSSP algorithm can be written as:

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3.4 Sensor Placement Results To evaluate Eq. (14), N ps = 100 MCMC samples were drawn from the prior PDF of θ. The prior PDF for θs is assumed as a truncated Gaussian distribution with identity covariance, and the generated samples are presented in Fig. 2. To create the covariance matrix  for each set of θs sample, the prediction error variance is sampled according to η2 ∼ U (0.01, 0.035). To study the effect of the correlation length in the optimal configurations, 2 different values of l = 1.0le , and 2.0le , where l e = 0.0504 m is the length of the sleeper element, were considered.

Fig. 2. Distribution of the samples of uncertain structural parameters θs

In the considered rail-sleeper-ballast system, sensors would be installed on the sleeper plan surface along the centerline. Since sensors cannot be installed at the two rail-seat areas, the number of possible locations reduces from 49 finite element nodes to just 35 locations. The system is excited near the left rail-seat area (see nodal position 6 on Fig. 3) with a simulated triangular impulse of ~ 1.4 kN, to obtain the responses conditional on the sampled θ values. In this paper, the configuration of SSP is taken as the FSSP or BSSP configuration with the least information entropy. In the same vein, the ESSP results are obtained by finding the configurations with the least entropy among the combined EFSSP and EBSSP configurations. The optimal sensor configurations obtained from the ESSP, SSP, and the FS algorithms are plotted in Fig. 3(a)–(d) for all correlation functions and ranges considered. The FS algorithm is only run for when N d ≤ 4 due to computational issues. As it has been proven that the optimal sensor configuration from SSP is one of the elements in the set of selected configurations in ESSP, the results from ESSP can be considered as the correct optimal sensor configuration for values of N d where the FS evaluations are absent. In all algorithms, the priority of sensor placement moves from the left to right, pointing to

A Robust Bayesian Sensor Placement Scheme with Enhanced

767

the effect of excitation location on the optimal configuration. However, the node at the impact location (nodal position 6) is not involved in optimal configurations across all correlation cases until N d ≥ 3 (in Fig. 3(c)). For the uncorrelated case (Fig. 3(a)), sensors are placed close to each other at the two ends of the sleeper in all methods, for N d < 7. When the correlation effect is considered, i.e., l > 0 (Fig. 3(b)–(d)), the algorithms then place sensors farther apart even for low values of N d . However, the exponential correlation function does a better job in sensor sparsity (and more useful information since sensor redundancy is mitigated) as compared to the spherical function, regardless of the value of l. The difference in the optimal configuration between the ESSP and SSP is also observed to follow the same trend as the sensor sparsity. With more sparsity, the SSP algorithm becomes less and less optimal compared to the ESSP.

(a) Uncorrelated

(c) Exponential [2.0]

(b) Exponential [1.0]

(d) Spherical [2.0]

Fig. 3. Optimal sensor configurations from different algorithms

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The comparison of the IE values for all values of N d = 1 to 15 obtained at the optimal SSP configurations and the most optimal ESSP configurations for the considered correlation cases is presented in Table 1. For the uncorrelated case, the optimum configurations can be reasonably obtained by SSP at almost all values of N d ; hence the use of ESSP with higher computational demand will be discouraged. However, since measured data are innately correlated in space or time, this case will be rare. For the correlated cases with l > 0, the performance of the ESSP over the SSP then becomes prominent. The trend in the table is an exact replication of Fig. 3, as SSP is not optimal only at N d sensor numbers where the configurations for ESSP and SSP differ in Fig. 3. Table 1. IE of the optimal sensor configuration for the SSP and ESSP algorithms using different correlation functions and correlation ranges Exponential (r = 1.0 le)

Exponential (r = 2.0 le)

ESSP

SSP

ESSP

SSP

ESSP

SSP

ESSP

SSP

1

-7.5384

-7.5384

-7.5384

-7.5384

-7.5384

-7.5384

-7.5384

-7.5384

2

-10.7837

-10.7837

-10.7837

-10.7837

-10.7837

-10.7837

-10.7837

-10.7837

3

-12.2079

-12.2079

-11.8620

-11.8620

-11.6224

-11.6224

-12.0824

-12.0824

4

-13.021

-13.021

-12.5393

-12.5393

-12.3038

-12.3038

-12.7721

-12.7721

5

-13.7404

-13.7404

-13.0225

-13.0225

-12.6686

-12.6604

-13.4286

-13.4286

6

-14.2711

-14.2711

-13.4672

-13.4672

-13.0138

-13.0076

-13.9370

-13.9370

7

-14.7158

-14.7158

-13.7787

-13.7730

-13.2727

-13.2714

-14.2520

-14.2520

8

-15.0906

-15.0905

-14.0371

-14.0296

-13.4927

-13.4927

-14.5376

-14.5375

9

-15.4469

-15.4469

-14.2722

-14.2669

-13.6752

-13.6752

-14.7608

-14.7592

10

-15.7229

-15.7229

-14.4823

-14.4754

-13.8201

-13.8201

-14.9603

-14.9579

11

-15.9765

-15.9765

-14.6754

-14.6754

-13.9300

-13.9300

-15.1468

-15.1468

12

-16.1946

-16.1946

-14.8305

-14.8260

-14.0278

-14.0278

-15.3094

-15.3094

13

-16.3749

-16.3749

-14.9557

-14.9508

-14.0880

-14.0880

-15.4580

-15.4573

14

-16.5411

-16.5411

-15.0753

-15.0731

-14.1587

-14.1411

-15.5696

-15.5911

15

-16.6812

-16.6812

-15.1879

-15.1846

-14.1937

-14.1882

-15.7156

-15.7156

S/N

Uncorrelated (r = 0)

Spherical (r = 2.0 le)

[most optimal (min.) values are shaded]

4 Conclusion In this study, an enhanced sequential sensor optimization scheme is proposed based on heuristic techniques. The proposed methodology is more robust in that the optimal configuration with a number of sensors does not necessarily have to be a subset of the optimal configuration with 1 more sensor. To implement the proposed methodology, a rail-sleeper-ballast system is considered, which was modeled as a beam on elastoplastic springs. Although it is observed that the general trend of sensor allocation favors the region of the sleeper where the excitation point is located, the investigated algorithms give other locations priority over the excitation location in several N d cases, which implies that

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information distribution may not be prominent at that location as it may be assumed. Sensor clustering was dominant for the uncorrelated case, and this is the only case where the SSP algorithm can satisfactorily estimate the optimal configurations. It was demonstrated that the utilization of spatial correlation in the model of the prediction error covariance could help minimize sensor redundancy and increase the amount of useful information. However, with the implementation of correlation, the conventional SSP becomes less efficient in identifying the optimal sensor configuration. In contrast, the ESSP algorithm is observed to match the results of the more expensive FS method for all the correlation cases considered. The proposed algorithm thus shows huge potential for application in structural health monitoring schemes in the field. Acknowledgements. The work described in this article was fully supported by two grants from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 11242716 (GRF 9042336) and R5020-18 (RIF 8799008)].

References Adeagbo, M.O., Lam, H.F., Ni, Y.Q.: A Bayesian methodology for detection of railway ballast damage using the modified Ludwik nonlinear model. Eng. Struct. 236, 112047 (2021). Elsevier, https://doi.org/10.1016/J.ENGSTRUCT.2021.112047 Adeagbo, M.O., Lam, H.-F., Hu, Q.: On the selection of the most plausible non-linear axial stress– strain model for railway ballast under different impulse magnitudes. Struct. Health Monit. 0(0) (2021). SAGE Publications, Sage UK: London, England. 147592172110339, https://doi.org/ 10.1177/14759217211033968 Adeagbo, M.O., Lam, H.-F., Chu, Y.-J.: Bayesian system identification of rail–sleeper–ballast system in time and modal domains: comparative study. ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A Civil Eng. 8(3), 04022020 (2022). American Society of Civil Engineers, https:// doi.org/10.1061/AJRUA6.0001242 Beck, J.L., Katafygiotis, L.S.: Updating models and their uncertainties I: Bayesian statistical framework. J. Eng. Mech. 124(4), 455–461 (1998). https://doi.org/10.1061/(asce)0733-939 9(1998)124:4(455) Lam, H.-F., Adeagbo, M.O.: An enhanced sequential sensor optimization scheme and its application in the system identification of a rail-sleeper-ballast system. Mech. Syst. Sig. Process. 163, 108188 (2022). https://doi.org/10.1016/J.YMSSP.2021.108188 Lam, H.-F., Adeagbo, M.O., Yang, Y.-B.: Time-domain Markov chain Monte Carlo–based Bayesian damage detection of ballasted tracks using nonlinear ballast stiffness model. Struct. Health Monit. (2020). SAGE Publications Ltd: 147592172096695.https://doi.org/10.1177/147 5921720966950 Li, D.S., Li, H.N., Fritzen, C.P.: The connection between effective independence and modal kinetic energy methods for sensor placement. J. Sound Vibr. 305(4–5), 945–955 (2007). Academic Press, https://doi.org/10.1016/j.jsv.2007.05.004 Ostachowicz, W., Soman, R., Malinowski, P.: Optimization of sensor placement for structural health monitoring: a review. Struct. Health Monit. 18(3), 963–988 (2019). SAGE Publications Ltd, https://doi.org/10.1177/1475921719825601 Papadimitriou, C.: Optimal sensor placement methodology for parametric identification of structural systems. J. Sound Vib. 278, 923–947 (2004). https://doi.org/10.1016/j.jsv.2003. 10.063

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Papadimitriou, C., Lombaert, G.: The effect of prediction error correlation on optimal sensor placement in structural dynamics. Mech. Syst. Sig. Process. 28, 105–127 (2012). Elsevier, https://doi.org/10.1016/j.ymssp.2011.05.019 Papadimitriou, C., Beck, J.L., Katafygiotis, L.S.: Asymptotic expansions for reliability and moments of uncertain systems. J. Eng. Mech. 123(12), 1219–1229 (1997). https://doi.org/10. 1061/(ASCE)0733-9399(1997)123:12(1219) Papadimitriou, C., Beck, J.L., Au, S.K.: Entropy-based optimal sensor location for structural model updating. J. Vib. Control 6, 781–800 (2000). https://doi.org/10.1177/107754630000600508 Papadimitriou, D.I., Papadimitriou, C.: Optimal sensor placement for the estimation of turbulence model parameters in CFD. Int. J. Uncertain. Quantif. 5(6), 545–568 (2015). https://doi.org/10. 1615/Int.J.UncertaintyQuantification.2015015239 Reynier, M., Abou-Kandil, H.: Sensors location for updating problems. Mech. Syst. Sig. Process. 13(2), 297–314 (1999). Academic Press Ltd, https://doi.org/10.1006/mssp.1998.1213 Sherman, M.: Spatial Statistics and Spatio-Temporal Data: Covariance Functions and Directional Properties. Wiley (2011) Udwadia, F.E.: Methodology for optimum sensor locations for parameter identofocation in dynamic systems. J. Eng. Mech. 120(2), 368–390 (1994) Zhang, C.D., Xu, Y.L.: Optimal multi-type sensor placement for response and excitation reconstruction. J. Sound Vib. 360, 112–128 (2016). https://doi.org/10.1016/j.jsv.2015.09.018

Investigation of the Performance of a Bioinspired Two-Fold Blades Wind Turbine with Airfoil Blade Sections by Using QBlade Yung-Jeh Chu1(B) , Heung-Fai Lam1,2 , and Hua-Yi Peng2 1 Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee

Avenue, Kowloon, Hong Kong, China [email protected], [email protected] 2 School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, China [email protected]

Abstract. The current study focuses on the investigation of the power and thrust performance of a new two-fold blades wind turbine design by using blade element momentum (BEM) based wind turbine analytical software, namely the QBlade. The two-fold blades wind turbine is a downwind, 3-bladed airfoiled wind turbine that consists of a root fold axis and a mid-span fold axis. The blade sections are shaped by using the SD8000 airfoil. The idea of folding the straight blade wind turbine was inspired by the winged seed of the Borneo Camphor tree (Dryobalanops aromatica), which consists of wings that are folded. It was presumed that the folding of the wind turbine blades would alter the pitch and cone angles of the blade sections, which consequently affect the angle of attack, changing its power and thrust performance. Fixed fold axis angles and two levels of fold angles were applied to the root and mid-span fold axis. The unfolded wind turbine blade was also the benchmark wind turbine adopted from the study conducted by a previous researcher. This unfolded wind turbine blade was with the size of one meter in diameter and with a constant chord length of 90 mm throughout the span. The fold at the root made the blade tilt towards the downstream direction, while the mid-span fold tilts the blade tip towards the upstream direction in an attempt to mimic the folding pattern of the wings of Borneo Camphor seed. The analytical results show that under the wind speed of 10 m/s, the proposed two-fold blades wind turbine outperformed the benchmark (unfolded) wind turbine at low tip speed ratios. Thus, this confirms the potential application of the two-fold blade wind turbine design in the wind energy industry, where it can be used in power regulation through folding mechanisms. Keywords: QBlade · Folding blades · Airfoil · Wind turbine · BEM method

1 Introduction The conventional horizontal axis wind turbine geometry consists of the tapered and twisted airfoil blade sections. This type of wind turbine geometry exhibits high aerodynamic power output due to the whole blade span being involved in generating torque © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 771–782, 2023. https://doi.org/10.1007/978-981-19-7331-4_63

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induced by the incoming wind. The tapering of the wind turbine blade reduces the drag forces at the tip blade sections, while the twisting of the blade optimizes the angle of attack for each blade sections throughout the span. Thus, the tapered and twisted blade wind turbine geometry is practical and was the focus of many studies, such as these references (Giguere and Selig 1999) and (Migliaccio et al. 2020). However, the mentioned geometry is not perfect as when the wind conditions change, the angle of attack at the blade sections also changes. Thus, in order to optimize the angle of attack at all wind speeds, the pitching mechanism was introduced, which consists of a rotating machine installed at the hub, varying the pitch of the blades by rotation about the pitch axis along the blade span. This pitching mechanism complicates the blade root joint at the hub and will certainly increase the fabrication and maintenance costs. Therefore, alternative blade geometry and pitching mechanism were introduced, which is known as the forward-folding blades wind turbine. The forward-folding blade wind turbines operate by folding the wind turbine blade in an oblique manner. The oblique fold axis, which can be situated at the root or midspan of the wind turbine blade, allows the alteration of cone and pitch angles in one rotating motion about the fold axis, subsequently altering the lift and drag properties of the blade sections. For example, the study conducted by Meng et al. as based on this reference (Meng et al. 2020) shows the forward-folding blade design has the ability to reduce the rotor size and pitch angle of the blade simultaneously, subsequently reducing the power output at extreme wind speed. This makes the power control mechanisms simpler, and more reliable as the speed of power adjustment is expected to be quicker than the conventional pitching mechanism. The folding of the blade also controls the rotor size. The ability to control the rotor size means that the power output and thrust forces can be controlled easily. This is very beneficial for extreme weather conditions such as typhoons as the thrust force can be reduced quickly, causing the drop-in blade root bending moment, which ensures the safety of the wind turbine blades. Therefore, the folding of the wind turbine blade warrants attention from the research community to discover its potential in the wind power industry. There are existing analytical theories which was used in wind turbine blade design and simulation. Among those theories, the most popular is the Blade Element Momentum (BEM) theory which dissects the wind turbine blades into discrete sections and applies the 2D airfoil properties in the prediction of thrust and torque. Together with the analytical method in airfoil analysis software such as the famous XFOIL (Drela 1989), the BEM methodology is a quick solution that gives a preliminary prediction of a particular wind turbine design. This is very convenient for the purpose of introducing new wind turbine geometry such as the previously mentioned folding wind turbine blades. One good example of the software that adopts both the XFOIL and BEM methodology in wind turbine simulation is the QBlade (Marten and Wendler 2013). Thus, the QBlade was used in the current study to predict the performance of folding wind turbine blades. The biomimicry of nature in wind turbine research was a unique trend in the latest wind turbine research. This is because the bioinspired wind turbine can be described as utilizing the knowledge from the reverse engineering of natural objects or process in the effort of improving the wind turbine product. For example, previous works related to the biomimicry of the Borneo Camphor seed in marine current turbine and wind turbine

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research were done by the researchers as shown in these references (Chu 2016, 2018; Chu and Chong 2017, 2018; Chu and Lam 2020; Chu et al. 2021). In the mentioned studies, it was shown that the bioinspired wind turbine exhibits certain benefits such as high torque and power at a low tip speed ratio. However, the proposal of a bioinspired wind turbine that consists of two-fold axes and airfoiled blade sections was not investigated. Thus, the objective of this study is to investigate a proposed airfoiled two-fold blades wind turbine that was inspired by the folding nature of the Borneo Camphor seed by using an analytical model.

2 Analytical Model Setup 2.1 Airfoil Properties and XFOIL Analysis The type of airfoil used in this study was named the SD8000 airfoil (Selig et al. 1995). The airfoil 2D surface plot is as shown in Fig. 1. This airfoil has a conventional shape that resembles a teardrop. The maximum thickness of this airfoil is located at 8.9% chord at 29.4% chord in the chordwise direction, while the maximum camber is 1.5% chord at 54% chord (Tools 2021). It can be observed that this airfoil has a round leading edge and a sharp trailing edge which is similar to most conventional airfoils such as the NACA series. This type of airfoil has been used as the wind turbine blade sections and produces comparative power performances, as shown in these references (Chu et al. 2021; Lee et al. 2016). Thus, it was proposed that this airfoil be adopted in this study as the blade section of the benchmark and the two-fold blades wind turbine models.

Camber-wise, Y/c

0.08 0.06 0.04 0.02 0

-0.02 -0.04 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Chordwise, X/c Fig. 1. The SD8000 airfoil profile with normalized chordwise and camber-wise 2D surface position

The XFOIL, which was a built-in analysis module with the QBlade software, was used to analyze the SD8000 airfoil profile. The XFOIL module can be used to analyze airfoils performance in subsonic airflow conditions. The viscous formulation was used to calculate the lift and drag forces generated by the airfoil profile. More details regarding the viscous formulations used in the XFOIL module can be referred to this reference (Drela and Giles 1987). The lift coefficients of the SD8000 airfoil at various Reynolds number was calculated and plotted in Fig. 2. The range of angle of attack, α, is from

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−20° to 25°. This range of angle of attack was set to capture the operating pitch angles of the wind turbine blade sections adopted in the benchmark and the two-fold blades wind turbine as shown in the later sections. From the lift coefficient, C l versus α plot, it can be observed that the lift coefficient peaks at a 9.0° angle of attack for the 60000 Reynolds number case while it peaks at an 11.5° angle of attack for the 420000 Reynolds number case. The peak lift coefficient for the 420000 Reynolds number case is 1.28, while it is 1.03 for the 60000 Reynolds number case. This result shows that the SD8000 airfoil exhibit a higher peak lift coefficient and optimum angle of attack when operating at a higher Reynolds number. The dips of the C l versus α curves, however, is not pronounced, and all the cases have similar dip location except the 60000 and 132000 Reynolds number cases, which have higher dips compared to that of the rest. There are some irregularities observed in the curves at the linear region with ranges approximated from −5° to 8° or 10°, where the upper limit depends on the Reynolds number. These irregularities are expected as the XFOIL code is not foolproof, as mentioned in its user guide (Drela et al. 2001). Since only the 60000 Reynolds number cases have significant irregularities, it was presumed that the XFOIL analysis was successful given the high linearity of the curves of the rest of the Reynolds number cases.

2.50 2.00

60000 204000 348000

132000 276000 420000

1.50 Cl

1.00 0.50 0.00 -0.50 -1.00 -30 -20 -10

0 10 α (°)

20

30

Fig. 2. Cl versus angle of attack graph of the SD8000 airfoil at various Reynolds number

The lift coefficient, C l versus the drag coefficient, C d of the mentioned Reynold number cases, was plotted as shown in Fig. 3. It can be observed that the curves of the C l versus the C d of SD8000 airfoil exhibit the mirrored “C” shape where at the most value of C d, there are two values of C l . This pattern of curves is expected as the angle of attack is at the positive value, the C l will exhibit a positive value, while when it is at the negative value, the C l will exhibit a negative value. However, since the drag force

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only acted in one direction, which is parallel to the incoming airflow, the drag force only has a positive value regardless of the sign of the angle of attack. Thus, this explains why there are two C l values for a particular C d . It can be observed that at the same C d value, the C l magnitude for the 60000 Reynolds number case is lower than that of the 420000 Reynolds number case. For example, the C d within the range of 0.03 to 0.25 shows a lower C l upper limit for the 60000 Reynolds number case compared with other higher Reynolds number cases. This difference means that the Reynolds number has a significant effect on the performance of the airfoil, confirming the claim in the previous paragraph. It can be observed that the drag bucket, where a large range of C l values lies on approximately the lowest C d values, are wide for all of the Reynolds number cases where the widest belong to the highest Reynolds number case and the lowest belong to the lowest Reynolds number case. The drag bucket feature in the drag polar usually does not exist or is narrow in certain types of airfoil shape, such as the NACA series. Having a wide drag bucket means that the is a higher probability that the airfoil orientates toward a high lift and low drag configuration. Thus, this indicates that the current airfoil will have better performance than that of another conventional airfoil. The lift to drag coefficients ratio, C l /C d versus angle of attack graph of the SD8000 airfoil at various Reynolds numbers, was plotted in Fig. 4. This C l /C d ratio is an important measure in determining the efficiency of the airfoil. Thus, a high C l /C d ratio correlates with high efficiency. Based on the C l /C d versus α graph, it can be observed that the C l /C d peaks at approximately 4.9° for all the Reynolds number cases. These properties of the C l /C d peaks at almost the same angle of attack is beneficial for the wind turbine blade section design as the same angle of attack can be applied in a wide range of Reynolds numbers, either in local or global wind properties, making it easy to achieve high-efficiency blade sections configurations throughout the span of wind turbine blades. On the other hand, the dips for all the Reynolds number cases do not share the same angle of attack. Despite the dips feature being different, it was not an issue for the wind turbine as the angle of attacks in the negative region was not used in the wind turbine blades simulations. 2.2 Wind Turbine Blade Properties The concept of the two-fold blades is based on the folding properties of the Borneo camphor seed. It was observed that the wings of the Borneo camphor seed have a fold at the wing root, which pitches the wings accordingly (Chu et al. 2021). This fold-pitching mechanism allows the wind turbine to change its rotor size and blade section angle of attack at the same time in one folding motion. Thus, two-fold axes were introduced onto a 0.5 m radius, 90 mm constant chord length, and constant 0° pitch angle benchmark wind turbine blade retrieved from this reference (Lee et al. 2016). A fold axis was set at the blade root where its middle is located at a radial distance of 0.1 m, while another fold axis was set at mid-span where its middle is located at a radial distance of 0.3 m. The pitch angle of each of the blade sections was measured by using Computer-Aided Design (CAD) software. The blade root fold axis folds the blade towards the downstream direction, while the mid-span fold axis folds the blade towards the upstream direction. The countering fold directions cause the pitch angles to vary depending on the segments of the blades. The tip segments will possess lower pitch angle while the root segment will possess a higher pitch angle, which these configurations will favor in wind turbine

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132000 276000 420000

1.50 Cl

1.00 0.50 0.00 -0.50 -1.00 -0.05

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0.15 Cd

0.25

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Fig. 3. Cl versus Cd graph of the SD8000 airfoil at various Reynolds number

130 110 90

60000 204000 348000

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-5

25

Cl/Cd

70 50 30 10 -10 -30 -50 -25 -15

5 15 α (°)

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Fig. 4. Cl /Cd versus angle of attack graph of the SD8000 airfoil at various Reynolds number

performances. These pitch angles value of the blade sections along the blade span were input into the wind turbine Blade Element Momentum (BEM) analysis. To simplify the comparative work, all the root and mid-span fold axis possess incline angles of 50° and 30° respectively. After folding, the wind turbine models exhibit smaller rotor radius

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which are 0.4855, 0.4887, 0.4541, and 0.4633 in meters for the two-fold blades cases with notations of a30b10, a30b20, a50b10 and a50b20 respectively as shown in Fig. 5. The notation of a30b10 means root fold angle of 30° with mid-span fold angle of 10°.

Fig. 5. The wind turbine models of (a) 0° (benchmark), and two-fold blades, (b) a30b10, (c) a30b20, (d) a50b10 and (e) a50b20 cases.

2.3 Wind Properties and Model Setting The incoming wind speed was 10 m/s with a turbulence intensity of 0.35%. The Standard Sea Level (SSL) condition, according to this reference (Corda 2017), was applied onto the air properties input, which consists of a density of 1.225 kg/m3 and kinematic viscosity of 1.46 × 10–05 m2 /s. The Prantl tip and root loss were considered in the modeling to consider the performance drop due to the loss of lift forces at the tip and root part of the blades. Forty numbers discretized elements were applied onto each blade. Furthermore, corrections like the 3-dimensional effect and Reynolds drag effect were considered as well. It was observed that these corrections would reduce the values of the predicted power coefficients based on the mentioned effects and thus make the predictions more accurate.

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3 Results and Discussions 3.1 Validation Results, C P and C T The power coefficients, C P and thrust coefficients, C T of the benchmark, and two-fold blades wind turbine models were presented in graphical form as shown in Figs. 6 and 7, respectively. For the validation part of this study, the benchmark wind turbine blade model C P predictions were compared with the experimental data obtained from the wind tunnel study of this reference (Lee et al. 2016). The results show that the current model has more accuracy when the tip speed ratio, TSR, exceeds five while the accuracy drops when the TSR is lower. Despite the lower accuracies at low TSRs, the model is still able to predict the C P versus TSR trend, which resembles an inverted “U” shape curve. In addition, the current study focuses on the comparison between the benchmark and the two-fold blades wind turbine model. Thus, it was presumed that the current model is valid and the predictions are reliable with respect to the objective of this study. The C P versus TSR curves of the two-fold blades model also exhibits the mentioned “U” shape curve trend. However, the C P of the two-fold blades models peaks at lower TSR values compared to that of the benchmark wind turbine, denoted with 0° in Fig. 6. This means that after folding the benchmark wind turbine blade into the shape of two-folds blades, the wind turbine models become low TSRs operation wind turbines. This feature of the two-fold blade is good for controlling the power output of the wind turbine with respect to the weather conditions as well as the electrical grid condition, which means the two-fold blades can be very flexible in terms of power control. It was observed that the a30b20 two-fold blade case produces the highest peak C P of 0.308, which is slightly higher than that of the benchmark wind turbine. The second highest is achieved by the a30b10 configuration. The difference of the peak C P between a30b10 and a30b20 is smaller than that of the difference between the a50b10 and a30b20. This means that a power control in moderate quantity can be achieved by adjusting only the mid-span fold angles while reducing the power output drastically can be achieved by adjusting only the root fold angles. Based on the C T versus TSR graph, it can be observed that the C T values of the two-fold blade cases are significantly lower than that of the benchmark case. This shows that the folding properties of the two-fold blades wind turbine will exhibit lower blade root stresses. A low blade root stress is beneficial to the wind turbine manufacturer as it will reduce the cost of structural components such as the supporting tower. These degrees of freedom in fold angles in two-fold blades also have the potential to enable quick responses from the wind turbines both in calm and adverse weather conditions such as typhoons. 3.2 Maximum C P and Their Corresponding C T The maximum C P versus fold angle graph was plotted for all the two-fold blades wind turbine cases, as shown in Fig. 8. From the plot, it can be observed that the general trend for maximum C P versus fold angle curves is increasing. This means that the increase in fold angles will result in the increase of maximum C P . However, it also shows that the 30° root fold curve exhibits a higher gradient compared with that of the 50° root fold curve. This means that the lower root fold will exhibit a higher maximum C P . The

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0.45 0.40 0.35

Exp. a30b10 a50b10

0° a30b20 a50b20

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0.30 CP

0.25 0.20 0.15 0.10 0.05 0.00 0

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4 5 TSR

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Fig. 6. CP versus TSR graph of the wind turbine models

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a30b10 a50b10

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1.5 CT

1.2 0.9 0.6 0.3 0.0 0

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Fig. 7. CT versus TSR graph of the wind turbine models

30° root fold curve is higher than that of the 50° root fold curve. This means that the 30° root fold configuration is superior to that of the 50° root fold configuration in terms of maximum C P . The ratio of maximum C P to its corresponding C T was plotted as shown in Fig. 9. The 50° root fold case shows an increasing trend, while the 30° root fold case shows a decreasing trend. The 50° root fold case exhibit a higher maximum

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C P to corresponding C T ratio. This ratio shows the efficiency in terms of power to thrust ratio, which the higher the value indicates more power output and less material cost on supporting structure. A summary of all the main results in the current study is shown in Table 1.

0.45 50° Root fold 30° Root fold

0.40 0.35 Max. CP

0.30 0.25 0.20 0.15 0.10 0.05 0.00 5

10 15 20 Fold angle (°)

25

Fig. 8. Maximum CP versus fold angle graph of the wind turbine models

4 Conclusions The results in this study show that the proposed two-fold blades have several advantages over the conventional constant chord wind turbine blades. The findings of the current study are listed as the following: 1. The QBlade prediction results show that the current model has more accuracy when the tip speed ratio, TSR, exceeds five while the accuracy drops when the TSR is lower. Despite the lower accuracies at low TSRs, the model is still able to predict the C P versus TSR trend, which resembles an inverted “U” shape curve. 2. The a30b20 two-fold blade case produces the highest peak C P of 0.308, which is slightly higher than that of the benchmark wind turbine. 3. The C T values of the two-fold blade cases are significantly lower than that of the benchmark case. This shows that the folding properties of the two-fold blades wind turbine will exhibit lower blade root stresses. 4. The 50° root fold case exhibit a higher maximum C P to corresponding C T ratio. This ratio shows the efficiency in terms of power to thrust ratio, which the higher the value indicates more power output and less material cost on supporting structure.

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0.74 50° Root fold 0.73

30° Root fold

Max. CP / CT

0.72 0.71 0.70 0.69 0.68 0.67 5

10 15 20 Fold angle (°)

25

Fig. 9. Maximum CP to corresponding CT ratio versus fold angle graph of the wind turbine models Table 1. Summary of the results for benchmark (0°-fold angle) and two-fold blades wind turbine models. Root fold axis angle (°)

Mid-span fold axis angle (°)

Root fold angle (°)

Mid-span fold angle (°)

Max. C P

C T at Max. CP

Max. C P /C P

50

30

30

10

0.242

0.344

0.704

30

20

0.308

0.451

0.682

50

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0.106

0.148

0.711

50

20

0.132

0.186

0.714

0

0

0.306

1.125

0.272

0

0

Acknowledgements. The study presented in the paper was fully funded by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. R5020-18 (RIF 8799008)].

References Chu, Y.J.: A new biomimicry marine current turbine: Study of hydrodynamic performance and wake using software OpenFOAM. J. Hydrodyn. 28(1), 125–141 (2016). https://doi.org/10. 1016/S1001-6058(16)60614-5

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Chu, Y.J.: Conceptual Design and Performance Analysis of a Biomimetic Wind Turbine Inspired by the Dryobalanops Aromatica Seed. Master Dissertation, University of Malaya (2018) Chu, Y.J., Chong, W.T.: A biomimetic wind turbine inspired by Dryobalanops aromatica seed: numerical prediction of rigid rotor blade performance with OpenFOAM®. Comput. Fluids 159, 295–315 (2017). https://doi.org/10.1016/j.compfluid.2017.10.012 Chu, Y.J., Chong, W.T.: Numerical study of conventional and biomimetic marine current turbines in tandem by using OpenFOAM®. J. Mech. 34(5), 679–693 (2018). https://doi.org/10.1017/ jmech.2017.46 Chu, Y.J., Lam, H.F.: Comparative study of the performances of a bio-inspired flexible-bladed wind turbine and a rigid-bladed wind turbine in centimeter-scale. Energy 213, 118835 (2020). https://doi.org/10.1016/j.energy.2020.118835 Chu, Y.J., Lam, H.F., Peng, H.Y.: Numerical investigation of the power and self-start performance of a folding-blade horizontal axis wind turbine with a downwind configuration. Int. J. Green Energy (2021). https://doi.org/10.1080/15435075.2021.1930003 Corda, S.: Introduction to Aerospace Engineering with a Flight Test Perspective. Wiley, West Sussex, UK (2017) Drela, M.: XFOIL: an analysis and design system for low Reynolds number airfoils. In: Mueller, T.J. (ed.) Low Reynolds Number Aerodynamics. Lecture Notes in Engineering, vol. 54, pp. 1–12 (1989). https://doi.org/10.1007/978-3-642-84010-4_1 Drela, M., Aero, M., Youngren, A.H.: XFOIL 6.94 UserGuide. Aerocraft, Inc., Massachusetts (2001) Drela, M., Giles, M.B.: Viscous-inviscid analysis of transonic and low Reynolds number airfoils. AIAA J. 25(10) (1987). https://doi.org/10.2514/3.9789 Giguere, P., Selig, M.S.: Design of a Tapered and Twisted Blade for the NREL Combined Experiment Rotor. Nrel/Sr, 500 (April) (1999) Lee, M.H., Shiah, Y.C., Bai, C.J.: Experiments and numerical simulations of the rotor-blade performance for a small-scale horizontal axis wind turbine. J. Wind Eng. Ind. Aerodyn. 149, 17–29 (2016). https://doi.org/10.1016/j.jweia.2015.12.002 Marten, D., Wendler, J.: QBLADE: an open source tool for design and simulation of horizontal and vertical axis wind turbines. Int. J. Emerging Technol. Adv. Eng. (2013) Meng, H., Ma, Z., Dou, B., Zeng, P., Lei, L.: Investigation on the performance of a novel forwardfolding rotor used in a downwind horizontal-axis turbine. Energy 190, 116384 (2020). https:// doi.org/10.1016/j.energy.2019.116384 Migliaccio, G., Ruta, G., Bennati, S., Barsotti, R.: Beamlike models for the analyses of curved, twisted and tapered horizontal-axis wind turbine (HAWT) blades undergoing large displacements. Wind Energy Sci. 5(2) (2020). https://doi.org/10.5194/wes-5-685-2020 Selig, M.S., Guglielmo, J.J., Broeren, A.P., Giguere, P.: Summary of Low-Speed Airfoil Data. SoarTech Publications, Virginia Beach (1995) Tools, A.: Airfoil Tools. Retrieved 9 Dec 2021 (2021). http://airfoiltools.com/

A Bayesian Adaptive Resize-Residual Deep Learning Network for Fault Diagnosis of Rotating Machinery L. Zou1 , K. J. Zhuang1 , and J. Hu2(B) 1 School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan,

China 2 Laboratory of Roadway Bridge and Structure Engineering, Wuhan University of Technology,

Wuhan, China [email protected]

Abstract. Due to the high accuracy achieved in data-driven fault diagnosis, timefrequency images generated by Continuous Wavelet Transform (CWT) are widely used as the input of deep learning methods. However, the image data require huge amount of data memories. An adaptive resize technique provides a reliable way for deducing the scale of image and achieving good effect. In this study, a novel Bayesian adaptive resize-residual network was proposed to resize the input data scale and extract the image feature for mechanical fault diagnosis. The CWT and Histogram Equalization (HE) algorithm were used to generate enhanced timefrequency images. The newly developed adaptive resize-residual network was applied for feature extraction, in which the adaptive resize block can adaptively resize input image by self-learning, and the residual block was used for classification. The Bayesian optimization was introduced to optimize the model hyper parameters and obtain an effective model. A testbeds of rolling element bearings are introduced to support the experiments. The experimental results indicate that the proposed Bayesian adaptive resize-residual network obtains superior recognition accuracy and outperforms many state-of-the-art methods. This method is conducive to improving the capabilities of rotating machinery fault diagnosis, and reduces the repair time of fault. Keywords: Bayesian optimization · Deep learning · Continuous wavelet transform (CWT) · Adaptive resize-residual network · Fault diagnosis

1 Introduction Rotating machineries are core components in mechanical equipment. Typical rotating machineries (e.g., bearings and gears) have been widely used in the complex equipment in industrial field, including electric motors, aero engines, water turbines and wind turbines, etc. [1–3]. The rotating equipment are operated in an extremely poor environment, where there are heavy-load, high speed and long running time working conditions [4, 5]. Therefore, the rotating machineries are prone to be damaged. Once the damage © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 783–801, 2023. https://doi.org/10.1007/978-981-19-7331-4_64

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has occurred and not been maintained by workers, the deterioration process expands and causes negative impact on other machineries, which will lead to the breakdown of whole equipment and even result in casualty [6–8]. Therefore, developing an effective fault diagnosis technology is of great significance to the safety operation of mechanical equipment. Many researches have been conducted on fault diagnosis of rotating machineries. Such as Xiao et al. [9] combined low-pass filtering technology and empirical wavelet transform to extract the sensitive features of wind turbines for fault diagnosis. Zhou et al. [10] introduced the parameter-adaptive vibrational mode decomposition to reconstruct the vibration signals of rolling bearings, and then used the multi-point optimal minimum entropy deconvolution to extract periodic pulse signals for better fault characteristics represent. Xu et al. [11] obtained the optimal Hankel matrix and grouped the sub-signals by singular value decomposition, and applied squared envelope spectrum for fault detection. Wang et al. [12] proposed a new information interval spectrum to extract the fluctuation features and defined the fault interval by threshold processing, which can effectively identify faults in spectrum. These methods process signals for achieving better feature expression, but they rely on prior knowledge and expert experience. Furthermore, it is hard to obtain the right features which is variable for different signals, and is lack of efficiency. Machine learning (ML), as one of the hottest research areas, has shown promising application on fault diagnosis of rotating machinery in recent years [13, 14]. For example, Sun et al. [15] improved AlexNet through combining the AlexNet with network in network (NIN) module, and replacing fully connected layer with global average pooling for realizing accurate fault diagnosis. Wu et al. [16] proposed a novel deep learning method for simultaneous-fault diagnosis by combining class learning and Bayesian deep learning, which can recognize simultaneous-fault class without corresponding training samples. An extreme learning machine was introduced as the classifier in the structure of residual network by Wei et al. [17], and it achieves outstanding results on bearing dataset. Wang et al. [18] generated multiple feature subsets to train multi-classifiers using different criteria feature selection, and constructed heterogeneous ensemble learning classification for fault diagnosis of planetary gearbox. By self-training mechanism to update model parameters for extracting sensitive features, almost all ML-based fault diagnosis technologies can be free from prior knowledge and expert experience. However, there are two major premises of obtaining powerful ML-based models [19, 20]. One is using lots of data to train model for extracting effective features. And the process of data processing consumes huge memories. In reality, the input data containing more representative characteristics can improve the result of fault diagnosis, but they usually have high dimension format (e.g., time-frequency image data show more details than one-dimension time series data) [21]. Lots of scholars used complex data generated by data pre-processing for better performance without considering the impact of data volumes. At present, only a few scholars have studied the effect of data volume on the performance of model. For example, Li et al. [22] proposed a hybrid method combining deep belief network and convolutional neural network for fault diagnosis, in which deep belief network was used to deduce the dimension of input data for improving training efficiency. He et al. [23] deduced the dimension of raw signals by

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sparse autoencoder to solve the problem of hardly dealing with high dimension time series data. Another premise is the optimal hyper-parameters which determines the performance of ML-based models. The ML-based models involve amounts of hyper-parameters, and their performances depend heavily on the selection of these parameters. An improper parameter setting may cause model underfitting or overfitting [24]. Therefore, optimizing the setting of hyper-parameters for constructing better model is significant. Lots of scholars have developed different methods to optimize the hyper-parameters. Such as Wang et al. [25] proposed an enhanced particle swarm optimization algorithm to obtain the optimum hyper-parameters of the newly designed convolutional gated recurrent network for fault diagnosis. Xu et al. [26] used the optimized support vector machine to discriminate fault-types from the constructed feature subset, in which the parameters were selected through marine predator algorithm. He et al. [27] applied the reverse cognitive fruit-fly optimization algorithm to optimize extreme learning machine for rolling bearing fault diagnosis. Above mentioned optimization algorithms are belonging to heuristic algorithm, which need lots of iteration to update object values and easily fall into local optimal values [28, 29]. Most importantly, the ML-based model, especial the deep-learning-based model, has the characteristic of uncertainty. Therefore, the heuristic algorithm cannot effectively solve the optimization issues [30]. This paper mainly focuses on the data memory in data processing and the hyperparameters optimization of ML-based model. In this method, the acquired vibration signals are firstly converted into time-frequency images via continuous wavelet transform (CWT) [31], and then the Histogram Equalization (HE) algorithm is applied to enhance the contrast of the time-frequency images [32]. After that, the adaptive resize network is used to adaptive resize input data into abstract maps by self-learning, and the resized maps are fed into the residual network for fault diagnosis. In the model training process, the Bayesian optimization was introduced to optimize the model hyper parameters and obtain an effective model. A experimental case are selected to evaluate the performance of proposed method. The experimental results indicate that the proposed adaptive resizeresidual network obtains superior recognition accuracy and outperforms some state-ofthe-art methods. The rest of this paper is organized as follows: Sect. 2 introduces the basic theories of adaptive resize-residual network, Bayesian optimization scheme and the Proposed diagnostic framework. In Sect. 3, two cases are conducted to verify the performance of the proposed method. Finally, according to the analysis for the experiment result, the conclusion is summarized in Sect. 4.

2 Methodology This section introduced the newly proposed approach in detail, including the diagnostic frame of the proposed method, the principle of adaptive resize-residual network and Bayesian optimization scheme.

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2.1 Proposed Diagnostic Framework To focus on the data memory in data processing and the hyper-parameters optimization of model for fault diagnosis, a Bayesian adaptive resize-residual deep learning network is proposed. The related technologies mainly consist of CWT, HE, adaptive resize-residual network and Bayesian optimization. Figure 1 shows the flowchart of proposed diagnostic framework.

Fig. 1. The flowchart of proposed diagnostic framework.

The detailed procedure is summarized as follows: 1. Data acquisition: The vibration signal of rotating machinery (e.g., bearing) is collected. The raw dataset is then split into the training set and the test set according to the ratio of 4:1. In this framework, 20% of training set is randomly selected as the validation set.

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2. Data pre-processing: The time-domain (1-dimension) signal is converged into the time-frequency-domain spectrum through CWT (2-dimension). HE is then used to enhance the contrast of the time-frequency image. To avoid generated noise signals in enhanced image, the processed B-channel data are used to replace the R-channel data, and no change on the data of the other two channels. The results in Sect. 2.2.2 show the features in enhanced images are represented more clearly (lower level of noise), which means the improved HE is conductive for feature extraction. 3. Model training: The labeled training, validation and test sets are feed into the adaptive resize-residual network, and the resize blocks are jointly trained with the residual blocks through the gradient descent algorithm. 4. Hyper-parameter optimization: Treating the hyper-parameters of network as the parameter to be optimized by Bayesian optimization, and the corresponding classification accuracy as the objective function. Using Bayesian optimization algorithm to optimize the network hyper-parameters for the best fault diagnosis performance. 5. Model evaluation: A series of experiments were designed to analyse the performance of the trained model, such as to validate the rationality of the proposed structure, to visualize the feature extraction process, and to compare with some state-of-the-art methods. 2.2 Data Pre-processing 2.2.1 Continuous Wavelet Transform (CWT) Generally, the frequency domain signal of mechanical system is believed to be more representative to its health condition than the time domain signal. Furthermore, the changes in frequency characteristics at different time periods certainly provide valuable information on the damage status of the target mechanical system. CWT is the suitable technique for extracting the frequency characteristics from the signal in different time periods through dilation and translation. The resultant two-dimensional time-frequency spectrum provide a valuable means in exposing the frequency and time domain information of the signal [33]. In this paper, a square-integrable function is selected as the mother wavelet or basic wavelet function, i.e., ψ(t) ∈ L2 (R). The family of wavelets functions can be defined as:   t−b 1 (1) ψa,b (t) = √ ψ a a where a and b are the dilation factor and translation factor, respectively. From Eq. (1), it is clear that different ψa,b (t) function can be acquired with different values of a and b. For square integrable signal s, i.e., s(t) ∈ L2 (R), the definition of Continuous Wavelet Transform of signal s(t) can be expressed as:   t−b 1 dt (2) Ws (a, b) = s(t), ψa,b (t) = √ ∫ s(t)ψ a a where a and b are continuous variables, so it is also named continuous wavelet transform. Ws is the wavelet coefficient based on signal s.

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2.2.2 Histogram Equalization (HE) In the time-frequency image, considerable parts of the representation color of frequency features are dark, and these parts of features are key in distinguishing different fault types. As all dark color are very similar from the computer viewpoint, it affects the performance of feature extraction. To solve the problem, HE is employed in this paper to enhance the image contrast and to highlight the image features. The specific principle is [34]: L Q(DA ) = A0

DA HA (D)d D

(3)

0

where HA (D) is histogram distribution of image A, D is pixel value of image generated by the wavelet coefficients Ws in Eq. (2), For two-dimension RGB image (time-frequencydomain spectrum) which consists of R-channel (red), G-channel (green) and B-channel (blue), the grey value of each channel is processed by HE, and the resultant spectrum will have stronger contrast. The specific flowchart and example result are shown in Fig. 2. Note that the timefrequency features are more obvious in subfigure (b) than in subfigure (a), this certainly has a positive effect on the process of feature extraction. Based on the experience of the authors (after many numerical and experimental case studies), not all channels of HE have the positive effects on feature extraction. As the enhancement is not only restricted on the fault-sensitive features but also on the noise from the signal. From Fig. 2, the timefrequency image has stronger contrast after operated by HE, but it also produces more obvious noise. The main reason is that the R-channel data generate noise signals after processed by HE. Therefore, the enhanced color image shown in subfigure (c) contains noise signals (the bright areas indicate frequency contents, and the irregular and blurred edges of bright area mean the noises.). The noise signals will certainly have negative influence on feature extraction. Although the G-channel data achieve great change in the enhanced image, it is very similar to the B-channel data. Moreover, the B-channel data basically do not change after processed by HE. It is proposed in this paper that the processed B-channel data are used to replace the R-channel data, and the data of the other two channels do not change. Finally, the improved image is generated as shown in Fig. 2c. 2.3 Adaptive Resize-Residual Network Researches show that the time-frequency spectrum of the vibration signal contains more detailed information than the time-domain only or frequency-domain only methods [35]. The image generated by CWT can achieve better diagnosis result, but it also greatly increases the computational power needed to train the model. The existing methods of reducing image dimensions by losing information are obviously not desirable. To obtain low-dimensional image without losing information, an adaptive resize-residual network is proposed, in which the adaptive resize block reduces the size of image through self-learning and the residual block recognizes fault types. The diagnosis flowchart of proposed adaptive resize-residual network is shown in Fig. 3.

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Fig. 2. The enhanced time-frequency spectrum of vibration signal: (a) the time-frequency spectrum via. Continuous Wavelet Transform, (b) the time-frequency spectrum via. Histogram Equalization, (c) the improved time-frequency spectrum.

Fig. 3. The diagnosis flowchart of adaptive resize-residual network.

It is clear from Fig. 3 that the adaptive resize block and the residual block play the roles of down sampling and feature extraction, respectively. For an RGB image training

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dataset Z = {z1 , z2 , . . . , za }, zi ∈ Rn×m×k generated by HE, the proposed network deduces the images scales through the adaptive resize block. Then, the resized abstract maps are fed into the residual network for feature extraction and pattern recognition. It is formulated as follows:     (4) p(z) = pR pS z, θS , θR where pS (·) and pR (·) represent the output of the adaptive resize block and residual block, respectively, θS and θR are the learnable parameters of resize and residual blocks, respectively. For classification task, the output layer of the proposed network uses Soft-max as the active function. The output result of last layer of the proposed resize-residual network is expressed as:     exp θi u i P y = i|u; θ = v (5)  j  (i = 1, 2, . . . , v) j=1 exp θ u where y is the corresponding category for data u. v is the number θi are   of category. i the parameters corresponding to ith category of output layer. P y = i|u; θ notes the probability that data u is of the ith category. During the training process, the adaptive resize network are jointly trained with the residual network. Under supervised learning, network training (or learning) can be treated as the minimization of the loss function, which measured the discrepancy between the network outputs and the labeled outputs. It is defined as the cross-entropy function in the proposed network as: J =−

T     1  yn log yˆ n + (1 − yn ) log 1 − yˆ n T

(6)

n=1

where T is the number of samples, yn and yˆ n are real and predict labels corresponding to nth sample, respectively. Based on the presented formulations, the proposed adaptive resize-residual network can auto-resize the input image by self-learning and achieve fault classification. The main idea is to jointly train the resize block and residual block. To obtain effective model, the networks need to learn the abstract features from labeled datasets through learnable parameters. The gradient descent algorithm is employed to update the model parameters according to the loss value obtained in Eq. (6). In the proposed model, the adaptive moment estimation (Adam) is employed to design the independent learning rate for different parameters. 2.4 Bayesian Optimization Scheme The applied Bayesian optimization algorithm can obtain the optimum values after limited iteration, and has been widely used in the field of hyper-parameter of deep learning network. In this paper, the mapping relationships of the network hyper-parameter of the

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proposed method and classification accuracy is confusing (the black box model). The designed optimization scheme uses the hyper-parameter as the variable value, and the classification accuracy as the objective function, as shown in follows: a∗ = argmaxf (a)(a = a1 , a2 , ..., an )

(7)

where a represents the group of hyper-parameters a1 , a2 , ..., an , f (a) represents the objective value correspond to variable a. argmax indicates maximum the objective function. a∗ is the predicted optimum variable value based on the bayes theorem, which is lustrated as follows: p(f |D1:t ) =

p(D1:t |f )p(f ) p(D1:t )

(8)

where D1:t = {(a1 , f (a1 )), (a2 , f (a2 )), ..., (at , f (at ))} is the set of observation samples. f is the unknow objective function. p(f ) and p(D1:t ) are the prior probability distributions of f and D1:t , respectively. p(D1:t |f ) is the probability of objective values D1:t contained in f . p(f |D1:t ) is the posterior probability distribution of f . Then, constructing acquisition function to obtain the extreme point of the objective function f as the next variable group. The pseudo code is described as Table 1. Table 1. Pseudo code of the hyper-parameter optimization based on Bayesian optimization. Step 1: Initializing hyper-parameters of the proposed method, and obtaining corresponding classification accuracy for the dataset {(a1 , f (a1 )}, where the accuracy is generated following Fig. 1 Step 2: Using the hyper-parameter group as the variable, and the corresponding result as the objective function. Defining the max iteration number M (default 20), and set the iteration number from 0 to M Step 3: Optimizing the network hyper-parameter via Bayesian optimization For t = 1,2,…,M: Obtain the dataset D1:t = {(a1 , f (a1 )), (a2 , f (a2 )), ..., (at , f (at ))}; Compute and update the posterior probability distribution of p(f |D1:t ); Select the optimum variables a∗ in current probability distribution of objective function as next hyper-parameter at+1 , where a∗ = argmaxf (a) defined in Eq. (7) and at+1 = a∗   Compute the objective function value f at+1 corresponding to variables at+1 

  Update the dataset D1:t+1 = D1:t ∪ at+1 , f at+1 End for

3 Experiment Results In this part, a serious of comparative test approaches are designed to illustrate the performance of the proposed Bayesian adaptive resize-residual network. In addition, the testbed of rolling element bearings are introduced to support these experiments. In the case study,

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the failure of bearings are caused by accelerated degradation. Raw vibration signals are acquired from experimental bearings and are used to generate the dataset. Then, multiple metrics are introduced to estimate the model. Finally, the proposed method is validated through the generated dataset. 3.1 Experimental Test Rig and Data Description The accelerated degradation testbed of rolling element bearing is introduced to verify the proposed method, where the bearing failures are caused by accelerated wear [36]. The bearing testbed mainly includes an alternating current (AC) motor, a hydraulic loading system, tested bearings and two accelerometers. The model of tested bearings is LDKUER204. Five fault types of bearings are generated by accelerating wear under three operating conditions. The failure types include single failures (e.g., inner race wear (IR), outer race wear (OR) and cage fracture (Ca)) and compound failures (e.g., inner race wear + outer race wear (IR + OR), inner race wear + ball wear + cage fracture + outer race wear (IR + Ba + Ca + OR)). A horizontal force is loaded on the tested bearing by the hydraulic loading system. Hence, data from horizontal sensor are more sensitive and are used as the tested data. In the experiments, the sample frequency is set to 25.6 kHz, and the sampling time is 1.28 s in each min. In the whole life period of tested bearing, the fault data are acquired from early abnormal stage. For the collected data, the first step is to segment them into uniform format samples. In this paper, each sample contains 1024 points according to experience. Each fault type includes 250 samples, and five fault types totally contain 250 × 5 = 1250 samples. Considering the normal type (No) data are abundant, 400 samples are generated in start operating stage. For above generated dataset, a proper split ratio is necessary for better diagnosis performance. Hence, a series of partition ratios of training set and test set are set in the experiment, which range from 0.5 to 0.9 with an interval of 0.1. In light of the key structure of adaptive resize-residual network is convolution layer, a basic CNN model is used in experiment. The detail results are shown in Fig. 4. It suggests that higher partition ratio can achieve better recognition accuracy. Correspondingly, the training time increases rapidly. When the split ratio is greater than 0.8, the accuracy increases very tiny. It is because the training process of the model is over fitted. To trade-off accuracy and training time, the optimum segment ratio is set to 0.8. According to the experimental results, dataset is split into training set and test set, and 20% of the samples from the training set are selected as the validation set. In the experiments, five datasets are described as follows: dataset-1 is the original dataset in which each sample is one-dimensional data with 1024 points. Dataset-2 is the time-frequency image generated by dataset-1 through CWT and bilinear resize algorithm, each image has format [64, 64]. Dataset-3 is the image set generated from dataset2 through HE algorithm. Dataset_4 is the image generated by dataset-1 via CWT and adaptive resize network (ad-resize). Dataset-5 is the spectrum generated from dataset-4 through HE algorithm.

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Fig. 4. Experimental results under different segmentation ratios.

3.2 Evaluation Metrics In this part, the fault diagnosis performance of proposed method is evaluated quantitatively through metrics of Accuracy, Precision, Recall and F1-score, which can be defined as follows: (1) Accuracy: The metric of accuracy in this paper is used to evaluate the performance of proposed method. The definition is expressed as follows: acc =

numright numall

(9)

where numright refers to the number of samples predicted to be right, numall is the total number of samples. (2) (2) Precision, Recall and F1-score: In classification tasks, sample deviation often occurs. In the case where one type of samples are classified poorly, but others are classified well, the accuracy index is inadequate. Therefore, precision, recall and F1-score are used to evaluate the model. Precision represents the rate of real positive samples in predicted positive samples. Recall is the rate of predicted positive samples in real positive samples. F1-score is the Harmonic mean of precision and recall. The formulas are as follows: precision = recall = F1 − score = 2 ×

TP TP + FP

(10)

TP TP + FN

(11)

precision × recall precision + recall

(12)

where FP is number of samples predicted as true in real negative samples. FN is number of samples predicted as false in real positive samples. TP represents number

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of samples predicted as true in real positive samples. It notes that the higher the three metric values are, the better the performance of the classifier. 3.3 Experimental Results and Analysis (1) Verify the effect of Bayesian optimization, CWT, HE and adaptive resize network. The proposed method consists of two main blocks, one is the adaptive resize block and another is classification block. The first block determines the performance of the second block. In the first block, CWT, HE, and adaptive resize network are introduced to achieve data pre-processing. To verify the effectiveness of these algorithms, a series of experiments are designed to test. The second block is the proposed residual network based on classic LeNet-5 model. Before conducting the comparative experiments, the number of neurons in the residual network needs to be defined at first. To finish the task, the Bayesian algorithm is used to optimize the hyper-parameters [37]. Considering the experimental cumbersome process, original one-dimension signal is used as the input of the residual network. The optimized results in each iteration are shown in Fig. 5. From Fig. 5, the optimum value is generated at 9th iteration, and corresponding optimization parameters are [20, 28, 41, 512]. The first three parameters represent the kernel number of three convolutional layers respectively and the value 512 is the number of neurons of full connection.

Fig. 5. The optimized results of Bayesian algorithm.

In this case, comparative experiments are designed to verify the performance of CWT, HE and adaptive resize network. Five different tested datasets are generated following Sect. 64.1. The classifier is the optimized residual network. Then, each dataset is fed into the classifier for fault diagnosis. The experiments are conducted five times to avoid outliers. Figure 6 describes the detailed results. It indicates that using dataset-5 as the input can achieve the best performance. The accuracies of five experiments are all greater than 99%. The performances of other datasets are slightly inferior to dataset-5. But the dataset with the operation of HE (e.g., dataset-3 and dataset-5) have better performance

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than those without the operation (e.g., dataset-2 and dataset-4). The results of dataset-1 are obviously the worst among other datasets because two dimension data have stronger feature expression than vibration signal. Table 2 represents the average results of five times experiments under multiple indexes. From Table 2, the values of precision, recall rate, F1-score and accuracy have the same order as the results in Fig. 6. For the standards deviation, dataset-5 has minimum value of 0.4438%, which means the proposed model has the best stability. From above analysis, the proposed method with CWT, HE and adaptive resize network has excellent fault diagnosis effect.

Fig. 6. Detail result of under different dataset

Table 2. Pre-processing algorithm verification with different datasets. Dataset types Precision (%) Recall (%) F1-score (%) Accuracy (%) Standard deviation (%) Dataset-1

92.59

92.33

91.52

92.73

0.8835

Dataset-2

97.84

97.70

97.88

97.86

0.6718

Dataset-3

98.18

98.08

98.24

98.11

0.5980

Dataset-4

98.79

98.83

98.81

98.84

0.5568

Dataset-5

99.03

99.00

99.02

99.68

0.4438

(2) Visualization of the feature extraction of adaptive resize residual network. Figure 7 shows visualization performances of typical bilinear method and proposed resize network. The high dimension spectrum is deduced to low dimension map. Subfigure (b) is the resized result of traditional bilinear algorithm. Although the dimension is effectively deduced, the resized map is fuzzy, which has an adverse effect on feature extraction. Subfigure (c) is the result of proposed adaptive resize network. It shows the feature distribution has no visual connection with the original map, but improves performance for fault diagnosis.

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Fig. 7. The visualization of different resize methods. (a) the original map with dimension of 328 × 436. (b) the resized map with dimension of 64 × 64 via bilinear algorithm. (c) the resized map with dimension of 64 × 64 via adaptive resize network.

To visualize the process of feature extraction of the proposed method, Fig. 8 shows the clustering effect of output results of each layer: Fig. 8a represents the scatter diagram of original data and (b) is the resize data via adaptive resize network. The visualization results indicate that the original data has no regular distribution, but the resize data have good clustering effect. It can be concluded the adaptive resize network has a positive influence on feature extraction. (c)–(e) are the scatter diagrams of the output of three residual layers respectively. The results show that the same type of data has no visual quality, but the six types of data have certain regular distributions. These distributions are conducive to the feature extraction of the model. (f) represents the distribution of full connection layer and shows better visual performance than (b). It proves deeper network layers can extract more fault features. From (a)–(f), the visualization results of different layers are different. The change makes similar data more aggregated and different data dispersed from each other. It needs note that although the distributions from medial layers output may have poor visual quality, but improve the performance of pattern recognition. (3) Comparative analysis of different algorithms. To further evaluate the proposed method, four different classic algorithms and two state-of-the-art fault diagnosis methods are selected as the comparative methods, i.e., Sparse Auto-Encoder (SAE), Deep Neural Network (DNN), One Dimensional Convolutional Neural Network (1D-CNN), Two Dimensional Convolutional Neural Network (2D-CNN) [38] and Deep Residual Network (DRN) [39]. The first three methods and DRN all use the original time domain data as the input. For the 2D-CNN, two different datasets are generated as its input, respectively: (1) the one-dimensional signal is directly reshaped into two-dimensional input data. (2) One dimensional signal is processed by CWT to generate two-dimensional time-frequency spectrum. To ensure the comparison methods all have proper parameters, the Bayesian algorithm is used to optimize the parameters of these models. The optimized parameters of different methods are shown in Table 3. Figure 9 indicates the specific results of ten times experiments. In the diagram, the experimental results of SAE and DNN are the worst among all. The fault diagnosis accuracies of DRN are nearly 90%. The remaining four tested methods can obtain more

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Fig. 8. Scatter diagram via dimension reduction of t-SNE. (a) the distribution of original signal. (b) the distribution of adaptive resized network output. (c–e) Corresponding to the first to third convolution output distribution. (f) the distribution of full connection layer output.

Table 3. Configuration of comparison methods. Model

Main structure parameters

SAE

Four layers structure: 1024-408-197-10

DNN

Four layers structure: 1024-511-248-10

Other methods

Conv1: 54 × 14 × 20. Conv2: 54 × 14 × 28. Conv3: 54 × 14 × 41. Full connection layer: n-512 *where n equals the dimension of last convolutional layer

than 90% accuracy. Among them, the proposed method achieves the best performance and has the accuracy of 100% in three of the five experiments. Table 4 shows the detailed scores of seven tested methods under different evaluation metrics. From Table 4, the results indicate that the evaluation scores of SAE and DNN are lower than other methods. Their standard deviations are relatively high. Further analysis shows that these methods obtaining better effect all have convolution structure. The results prove convolution structure can improve effect of feature extraction. Comparing the results of 2D-CNN(raw) and 2D-CNN(CWT), it can be summarized that the timefrequency images generated by CWT contain more information than raw signals. In all tested results, the proposed method can obtain the best evaluation score and the lowest standard deviation. The result proves that the proposed method has good performance for fault diagnosis.

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Fig. 9. Five experimental results of different methods.

Table 4. Average results of different methods under multiple evaluation metrics. Model

Precision (%)

Recall (%)

F1-score (%)

Accuracy (%)

Standard deviation (%)

SAE

77.43

77.08

77.54

77.52

1.1009

DNN

63.59

63.62

63.58

63.64

0.9296

1D-CNN

94.31

94.27

94.33

94.36

0.7298

2D-CNN (raw)

94.87

94.57

94.79

94.89

1.1829

2D-CNN (CWT)

97.84

97.70

97.88

97.86

0.6718

DRN (raw)

92.59

92.33

91.52

92.73

0.8835

The proposed method

99.03

99.00

99.02

99.68

0.4438

4 Conclusion In this paper, a new adaptive resize-residual deep learning network for fault diagnosis of rotating machinery is proposed. First, the acquired vibration signals are converted into time-frequency images via CWT. Then, the HE algorithm is introduced to improve the visual effect of the features in these images. In this step, B-channel data of the generated images are used to replace the R-channel data, and the data of the other channels do not change. After that, the enhanced images are fed into the proposed adaptive resize-residual network for fault diagnosis, in which the adaptive resize network block can deduce input data dimension by self-learning and the residual network block can extract abstract features for pattern recognition. Meanwhile, the Bayesian optimization algorithm is introduced to optimize the hyper-parameter of the proposed method. To validate the

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performance of the proposed method, bearing datasets are used from XJTU-SY bearing dataset, and some state-of-the-art diagnostic methods are conducted as the comparative approaches. From the experimental results, it can be summarized that the proposed method can obtain superior recognition accuracy than other fault diagnosis methods. There are three notable advantages of the proposed adaptive resize-residual network. The first advantage is the proposed method uses enhanced time-frequency spectrum as the input data. For data pre-processing, the time-frequency spectrum generated by CWT contains abundant information, but much darker area is easily covered up which also contain useful information. Using HE can effectively enhance the information, and also introduces noise information like (b) in Fig. 2. Through analysing each channel result, the ideal enhancement effect can be obtained by replacing channel R with channel B after HE processing. The second advantage is an adaptive resize network is designed to deduce high dimension data by self-learning. In fact, the widely used resize algorithms are bilinear and bi-cubic and so on, which is developed before deep learning. Although these algorithms can obtain great visual quality, they are not well compatible with deep learning. The proposed adaptive resize network can be jointly trained with classification model. This means it can adaptive resize high dimension data and the resized result has a positive effect for feature extraction. The third advantage is the designed scheme of hyper-parameter optimization based on the Bayesian optimization algorithm. The MLbased model, especial the proposed deep-learning-based model, has the characteristic of uncertainty. The heuristic algorithm can not effectively solve the optimization issues. The designed Bayesian optimization scheme can obtain the optimum values after limited iteration, and search the global optimum value through acquisition function based on the bayes theorem.

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28. Hang, J., et al.: Integration of interturn fault diagnosis and torque ripple minimization control for direct-torque-controlled SPMSM drive system. IEEE Trans. Power Electron. 36(10), 11124–11134 (2021) 29. Huang, T., Zhang, Q., Tang, X., Zhao, S., Lu, X.: A novel fault diagnosis method based on CNN and LSTM and its application in fault diagnosis for complex systems. Artif. Intell. Rev. (2021).https://doi.org/10.1007/s10462-021-09993-z 30. Lee, C.-K., Shin, Y.-J.: Detection and assessment of I&C cable faults using time-frequency R-CNN-based reflectometry. IEEE Trans. Industr. Electron. 68(2), 1581–1590 (2021) 31. Zhang, K., Jiang, B., Chen, F.: Multiple-model-based diagnosis of multiple faults with highspeed train applications using second-level adaptation. IEEE Trans. Industr. Electron. 68(7), 6257–6266 (2021) 32. Han, J.H., Yang, S., Lee, B.U.: A novel 3-D color histogram equalization method with uniform 1-D gray scale histogram. IEEE Trans. Image Proc. 20(2), 506–512 (2011) 33. Sha, G., Radzienski, M., Soman, R., Wandowski, T., Cao, M., Ostachowicz, W.: Delamination imaging in laminated composite plates using 2D wavelet analysis of guided wavefields. Smart Mater. Struct. 30(1) (2021) 34. Sbert, M., Ancuti, C., Ancuti, C.O., Poch, J., Chen, S., Vila, M.: Histogram ordering. IEEE Access 9, 28785–28796 (2021) 35. Cheng, Y., Lin, M., Wu, J., Zhu, H., Shao, X.: Intelligent fault diagnosis of rotating machinery based on continuous wavelet transform-local binary convolutional neural network. Knowl.Based Syst. 216 (2021) 36. Wang, B., Lei, Y., Li, N., Li, N.: A hybrid prognostics approach for estimating remaining useful life of rolling element bearings. IEEE Trans. Reliab. 69(1), 401–412 (2020) 37. Snoek, J., Larochelle, H., Adams, R.P.: Practical bayesian optimization of machine learning algorithms. Adv. Neural Inf. Proc. Syst. 25 (2012) 38. Zhou, Q., Li, Y.,Tian, Y., Jiang, L.: A novel method based on nonlinear auto-regression neural network and convolutional neural network for imbalanced fault diagnosis of rotating machinery. Measurement 161 (2020) 39. Chen, Z., Chen, Y., Wu, L., Cheng, S., Lin, P.: Deep residual network based fault detection and diagnosis of photovoltaic arrays using current-voltage curves and ambient conditions. Energy Convers. Manage. 198 (2019)

Mechanics of Materials and Structures with Generalized Continua: Flexible Structures, Composite Materials, Optimizations, and Applications

Nonlinear Vibrations of Deepwater Catenary Riser Subjected to Wave Excitation Nutwadee Lertchanchaikun1 , Karun Klaycham1(B) , Chainarong Athisakul2 , and Somchai Chucheepsakul2 1 Research Center for Sustainable Infrastructure Engineering, (RSIE), Department of Civil Engineering, Faculty of Engineering at Kamphaeng Saen, Kasetsart University, Bangkok 73140, Thailand [email protected], [email protected] 2 Department of Civil Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand

Abstract. The purpose of this research is to present the mathematical model for the nonlinear vibration analysis of a deepwater catenary riser subjected to a wave excitation. The mathematical model of the catenary riser is derived from the work-energy principle, including the geometrical nonlinearity and nonlinear loading from a square drag term of hydrodynamic force. The finite element method is used to form the equation of motion for solving the numerical solution. The nonlinear equation of motion can be written in the appropriate form, which is convenient to perform the numerical integration. The Newmark time integration incorporated direct iteration is used to solve the nonlinear vibration response of the catenary riser. The nonlinear forced vibration analysis is carried out for both small and large vibration amplitudes. From numerical investigation, it was found that the vibration response of the riser due to wave force is a harmonic motion and the vibration amplitude increases as the increasing in wave amplitude. In addition, the effect of nonlinear geometry has a significant influence on the vibration amplitude of the riser. Keywords: Catenary riser · Finite element method · Hydrodynamic wave · Large amplitude vibration · Nonlinear vibration

1 Introduction The facilities used in exploration and production petroleum in the offshore oil field have faced many challenging problems, especially in the ultradeep sea operations. A marine riser, which is a very long slender pipe considered as a major subsea structural component used for conveying crude oil from seabed to production platform on the sea surface, could face complex and severe environmental loadings. Understanding dynamic behaviour of the deepwater marine riser would help improve the design process. A basic principle and simplified analysis on the mechanics of marine risers can be found in the book by Sparks (2007). Recent research works on the deepwater marine risers

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 805–818, 2023. https://doi.org/10.1007/978-981-19-7331-4_65

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including the internal fluid flow (Zhang et al. 2015; Montoya-Hernández et al. 2014), the hydrodynamic current and wave forces (Lei et al. 2014: Duanmu et al. 2018), the vibration induced by floating platform motion (Mazzilli et al. 2016; Wang et al. 2016) have been found and mentioned herein. Because the riser is subjected to severe and complex dynamic loadings, especially in deep water (Cheng et al. 2018; Meng et al., 2018), the linearized vibration theory representing small amplitude vibration behavior may be insufficient (Takafuji and Martins 2012). There have been few research studies regarding large amplitude vibration of the riser, such as Kaewunruen et al. (2005) and Punjarat and Chucheepsakul (2021) but the studies were limited only to free vibration analysis of a riser in shallow water (water depth of 400 m). The solution for large amplitude forced vibration of a deepwater riser has not been reported. In addition, the previous literature has not clearly explained the effect of nonlinear geometric on the forced vibration response of the riser. This research aims to study the large amplitude vibration of a deepwater catenary riser subjected to a hydrodynamic wave. The mathematical model of the riser is derived from the work-energy principle. The geometrical nonlinearity and nonlinear loading from a square drag term of hydrodynamic force are taken into account. The finite element method is used to form the equation of motion. The nonlinear equation of motion can be written in the appropriate form, convenient for performing the numerical integration. The Newmark time integration incorporated direct iteration is used to solve the nonlinear vibration response of the catenary riser. The nonlinear forced vibration analysis is carried out for both small and large vibration amplitudes. The nonlinear dynamic responses are presented and discussed on the large amplitude vibration characteristics of the catenary riser subjected to wave force.

2 Model Formulation This research emphasizes on the dynamic analysis regarding large amplitude vibration characteristics of the catenary riser. Firstly, it needs to find an initial static configuration when it is induced by the time-independent load (i.e., self-weight, buoyancy force, the quasi-static force of the current, and the internal transporting fluid). The static configuration is used as an initial position for riser vibration, which is excited and vibrated to the dynamic equilibrium position at any instant of time, t. The theoretical model for static analysis used in this study is based on the variational formulation proposed by Chucheepsakul et al. (2003), which can capture the large displacement analysis. The axial stretching and the bending are taken into account for the strain energy. The static loads concerned in this work are the riser weight, the buoyancy force, the drag force caused by the hydrodynamic current, and the centrifugal force induced by transported fluid motion. The static configuration may be a large sag like a classical catenary curve. At this stage, the position of the riser is defined by the  vector, r Ps = xs ˆi + ys ˆj, in which xs and ys are the coordinates in horizontal and vertical directions, respectively; ˆi and ˆj represent the unit vector in the 2-dimensional rectangular coordinate system. The static equilibrium configuration is evaluated by using the finite element method, which more details are given in Athisakul et al. (2014).

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For dynamic analysis, the riser is vibrated around the static configuration, which may be a large sag curve. The nonlinear equation of motion is derived by using the virtual work principle. The nonlinear response of the riser subjected to wave force is obtained by applying the Newmark time integration method incorporated direct iteration to the equation of motion. These details for large amplitude vibration analysis are described in the following subsections. 2.1 Kinematics of Riser 

As shown in Fig. 1, the vector r Ps (ss ) represents the position vector of the riser at the static equilibrium state. In this formulation, the dynamic displacements of the riser are ˆ which represent the unit vectors in the tangential defined by the local coordinates ˆt and n, and normal directions, respectively. The parameters vnd and utd represent the components of the displacement vec tor u d (ss , t) in the normal and tangential directions, respectively. Consequently, the 

dynamic position of the riser r P (ss , t) can be defined in the global coordinate (x, y), as shown below. 







r P (ss , t) = r Ps (ss ) + u d (ss , t) = r Ps (ss ) + vnd nˆ + utd ˆt

Fig. 1. Kinematics and configurations of the riser

(1)

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Based on the differential geometry of a plane curve, the relations between the displacements, curvature, and axial strain provided by Chucheepsakul and Huang (1989) are expressed as dκs d2 vnd + κs2 vnd + utd dss2 dss  2  2  dutd 1 dvnd + − κs vnd + + κs utd 2 dss dss

κ = κs + εt = εs +

dutd − κs vnd dss

(2a)

(2b)

where κ and εt are the curvature and the total axial strain at the dynamic state, respec  tively; κs = xs ys − xs ys is the initial or static curvature at any points of the riser, which can be determined from the static analysis as described in the previous section; and εs = Nas /EAP is the static axial strain. As shown in Eq. (2b), the nonlinear terms of vnd and utd are included in the expression of axial strain. According to these nonlinear terms, the nonlinear stiffness of the riser system will be derived in the following section. 2.2 Element Strain Energy The expression of strain energy due to the axial stretching and bending of the riser element is given by 1 Ue = 2

l   EAP εt2 + EIP (κ − κs )2 dss

(3)

0

where l is an element length measured along the arc-length (ss ) of the riser. By utilizing Eqs. (2a) and (2b), the element strain energy of the riser is given by the following equation. Ue =

1 EA 2 P

l 2 1  2 2  1  εs + utd − κs vnd + u − κs vnd + v + κs utd dss 2 td 2 nd 0

+

1 EI 2 P

l 

 2

 + κ 2 v + u κ vnd td s s nd

dss

(4)

0

 It has to be noted that the superscript  in the dynamic analysis represents the derivative of the parameters with respect to the arc-length coordinate ss .

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2.3 Element Kinetic Energy The kinetic energy of the riser element caused by the riser motion and the motion of the transported fluid inside the riser (Paidoussis, 1998) can be written as follows. ⎧ ⎫ ⎪ ⎪ l ⎪  ⎬





⎪ 1 ⎨   2 2 2 2 2 Te = (mP + mi ) v˙ nd + u˙ td + 2mi Vi v˙ nd vnd + u˙ td utd + mi Vi vnd + utd dss 2 ⎪ ⎪ ⎪        ⎪ ⎭ 0 ⎩ Inertial term

Gyroscopic term

Centrifugal term

(5) As shown in Eq. (5), each term will contribute to the mass matrix (first term), the gyroscopic matrix (second term), and the centrifugal force matrix (last term), respectively, in the equation of motion. The variable mP is the mass per unit length of the riser; mi is the mass per unit length of transported fluid; Vi is the relative velocity of internal fluid with respect to the riser velocity; and the superscript (·) represents the derivative of the parameter with respect to time (t). 2.4 Element External Virtual Work The expression for the element external virtual work induced by current and wave forces can be written as l {fHn δvnd + fHt δutd }dss

δWe =

(6)

0

where fHn and fHt are the hydrodynamic current and wave forces in normal and tangential directions, respectively, which are calculated based on the Morison model (Morison et al., 1950). The extended equation can be expressed as follows.    ∗  ∗ 2 ∗ ∗ V ˙ Hn Ceqn 0 fHn v˙ nd Ca 0 v¨ nd CDn VHn + CM =− − + (7) ∗ V 2 + C∗ V ∗ ˙ 0 Ceqt fHt u¨ td u˙ td CDt 0 Ca∗ Ht M Ht          Added mass force

Hydrodynamic damping force

Hydrodynamic excitation

As shown in Eq. (7), each term will contribute to the mass matrix (first term), the hydrodynamic damping matrix (second term), and the force vector (last term), respec∗ , tively, in the equation of motion. The coefficients of equivalent normal damping Ceqn ∗ ∗ ∗ normal drag force CDn , tangential damping Ceqt , tangential drag force CDt , and the ∗ are equivalent coefficients of added mass Ca∗ and inertia forces CM ∗ ∗ ∗ Ceqn = CDn = 0.5ρe De CDn · sgn(γn ) [2VHn − v˙ nd ], CDn

(8a, b)

∗ ∗ ∗ = CDt = 0.5ρe De π CDt · sgn(γt ) Ceqt [2VHt − u˙ td ], CDt

(8c, d)

∗ = ρe Ae CM Ca∗ = ρe Ae Ca , CM

(8e, f)

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in which Ca is the added mass coefficient, and CM = Ca + 1 is the inertia coefficient. The symbol VHx is the velocity of hydrodynamic in the horizontal direction, which is composed of the current velocity Vc and the wave velocity Vw . VHx = Vc + Vw

(9)

The profile of the current velocity (Chucheepsakul and Monprapussorn, 2001) may be expressed in the power function as   ys + yb n Vc = VcH (10) yH + yb The symbol VcH is the current velocity at mean sea level, while yb and yH are defined in Fig. 1. The index n can be varied from 0 to1 depending on the current profile, for example, n = 0 for constant current velocity, and n = 1 for linear profile varying along the vertical coordinate with the maximum velocity at the sea surface of VcH . In this study, for the tidal current profile, = 1/7, which is recommended by DNV-RP-C205—Rules and standards (Vásquez and Avila 2019) is employed in the numerical investigations. For the wave velocity, it is the function of the vertical coordinate and the time, which can be expressed as Vw = Vwa cos ωw t

(11)

where t is time and ωw is the wave frequency. The velocity amplitude of wave-particle, Vwa is varied exponentially along vertical coordinate, which can be expressed as Vwa = ζa ωw ek [(ys +yb )−(yH +yb )]

(12)

 where ζa = H /2 is the wave amplitude; H is the wave height; and k = ωw2 /g is the wave number. 2.5 Nonlinear Equation of Motion The dynamic displacements vnd and utd at any points of the riser element are approximated using the cubic polynomials shape function in terms of the arc-length coordinate (ss ). By separating variables, the displacement vector {ud } can be expressed in terms of the nodal degree of freedom of the element {d d } through the matrix of shape functions [N d ] as follows.  T ∼ {ud } = vnd utd = [N d (ss )]{d d (t)} where the shape function matrix [N d ] defined above is   N31 N32 0 0 N33 N34 0 0 [N d ] = 0 0 N31 N32 0 0 N33 N34

(13)

(14)

where N3i is the components of the cubic polynomial shape function used for the standard beam element (Cook et al., 2002). The nodal degree of freedom vector {d d } of the riser

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element consists of the nodal displacements and their derivative, which can be written as  T     {d d } = v1nd v1nd u1td u1td v2nd v2nd u2td u2td (15) Subscripts 1 and 2 represent the node on the left and right ends of the riser element, respectively. By substituting Eq. (13) into Eqs. (4), (5), and (6) and preforming the variation, the expressions of the element virtual strain energy, the element virtual kinetic energy, and the element external virtual work can be rearranged into the matrix forms as given in Eqs. (16), (17) and (18), respectively.   1 1 (16) δUe = δ{d d }T [kL ] + [kN 1 ] + [kN 2 ] {d d } 2 3   T      δTe = δ d˙ d (17) [m] d˙ d + g {d d } + δ{d d }T [ki ]{d d }       δWe = δ{d d }T −[ma ] d¨ d − [c] d˙ d + {f }

(18)

in which [kL ], [kN 1 ], and [kN 2 ] are the linear element stiffness matrix, the first-order nonlinear element stiffness   matrix, and the second-order nonlinear element stiffness matrix, respectively; [m], g , and [ki ] in Eq. (17) are the element mass matrix, the element gyroscopic matrix, and the element centrifugal force matrix, respectively; [ma ], [c], and {f } in Eq. (18) are the element added mass matrix, the element hydrodynamic damping matrix, and the element hydrodynamic excitation vector, respectively. Theexpressions    of these element matrices are given in Appendix A. The vectors d˙ d and d¨ d are the element nodal velocity and the element nodal acceleration vectors, respectively, which are obtained from differentiation of the nodal displacement in Eq. (15) with respect to time t. After the element Eqs. (16), (17) and (18) are assembled to obtain the total virtual work of the riser system, the nonlinear equation of motion is derived by using the stationary condition.       1 1 ˙ ¨ (19) [M] Dd + [[C] + [G]] Dd + [K L ] + [K N 1 ] + [K N 2 ] {Dd } = {F} 2 3 where {Dd } =

    ˙ d , and D ¨ d are the nodal displacement, nodal velocity, and {d d }, D

nelem i=1

nodal acceleration vectors of the global system, respectively; [M] =

nelem

{[m] + [ma ]}

i=1

is the total mass matrix; [C] = [G] =

nelem

[c] is the total hydrodynamic damping matrix; i=1

nelem

nelem  {[kL ] − [ki ]} is the total linear g is the total gyroscopic matrix; [K L ] =

i=1

stiffness matrix; [K N 1 ] =

i=1 nelem

[kN 1 ] is the total first-order nonlinear stiffness matrix; i=1

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[K N 2 ] =

nelem

nelem

i=1

i=1

[kN 2 ] is the total second-order nonlinear stiffness matrix; {F} =

{f } is

the total hydrodynamic excitation force vector, where nelem is the number of discretized elements. This subsection presents the nonlinear forced vibration analysis procedure for obtaining the large amplitude response of the riser subjected to excitation forces of hydrodynamic current and wave, as well as an unsteady flow of transported fluid. The equation of motion Eq. (19) established by the finite element procedure yields the nonlinear initial value problem arising from time-dependent terms of the damping matrix and the stiffness matrix, thus the numerical integration based on time domain approach is convenient to solve such equation. The Newmark method (Newmark 1959), which is probably most extensively used as an algorithm for integrating the equation of structural dynamic, is utilized.

3 Numerical Result This section presents the numerical validations to check the result accuracy. Then the effect of hydrodynamic wave force on the large amplitude vibration of a deepwater catenary riser is investigated. 3.1 Numerical Validations To verify the mathematical model and finite element solution of a deepwater catenary riser, the numerical solutions obtained in this study are compared with those results from another riser model proposed by Klaycham et al. (2020). The riser properties and environmental loadings used in this simulation are shown in Table 1 (No. 1). The comparative results of the vibration amplitude caused by hydrodynamic waves are shown in Figs. 2(a) and 2(b) for tangential and normal directions, respectively. It can be seen that the present results are in good agreement with those results presented by Klaycham et al. (2020). Therefore, the developed riser model is efficient and reliable enough for simulating the vibration analysis of the catenary riser, focusing on hydrodynamic wave excitation. 3.2 Small and Large Amplitude Vibrations Analysis This subsection presents the large amplitude vibration of the catenary riser subjected to hydrodynamic wave excitation. The riser’s properties are given in Table 1 (No. 2). The wave amplitude is varied from 2.5–10 m, while the wave frequency is specified to be 0.2492 rad/s. Figures 3(a) and 3(b) graphically show the time history response of normal tangential displacements, respectively. For this example, the riser position at the arc-length coordinate of ss = 773 m is attended based on the simulation from wave amplitude of 10 m. The abbreviation “SAV” represents the solution of small amplitude vibration, the nonlinear stiffness is not considered in the simulation. Instead, the nonlinear stiffness is

Nonlinear Vibrations of Deepwater Catenary Riser Table 1. Parameters of riser and environment loadings Properties

Values No. 1

No. 2

Outside diameter, De (m)

0.26

0.26

Inside diameter, Di (m)

0.20

0.20

Riser length, st (m)

1057.198

1325

Young’s modulus, E (N/m2 )

2.07×1011

2.07×1011

Sea depth, yH (m)

300

1000

Horizontal top end offset, xH (m)

45

800

Height of the bottom support above seabed, yb (m)

0

0

Top tension, NaH (kN)

600

2333.5

Density of riser, ρP (kg/m3 )

7850

7850

Density of sea water, ρe (kg/m3 )

1025

1025

Density of internal fluid, ρi (kg/m3 )

998

998

Internal flow speed, Vis (m/s)

0.0

5

Current velocity at mean sea level, VcH (m/s)

0.5

1.0

Normal drag coefficient,CDn

0.70

0.70

Tangential drag coefficient,CDt

0.03

0.03

Add mass coefficient,Ca

1.0

1.0

Wave amplitude, ζa (m)

10.0

10.0

Wave frequency, ωw (rad/s)

(≈ ωL1 )

0.2492

(a) Normal displacement amplitudes

(b) Tangential displacement amplitudes

Fig. 2. Comparison of distribution of displacement amplitude along vertical coordinate.

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taken into account for the solution of large amplitude vibration, which is noted by the abbreviation “LAV”. From Figs. 3(a) and 3(b), it can be seen that the hydrodynamic wave induces the riser to vibrate as the harmonic motion, corresponding to the wave characteristic. The riser takes a time about 50 s to reach the steady-state response. Figure 3(a) shows that the normal displacement amplitude for SAV is greater than LAV. On the other hand, the tangential displacement for SAV is less than LAV, as shown in Fig. 3(b).

(a) Normal vibration displacement

(b) Tangential vibration displacement

Fig. 3. Time history of riser displacement at arc-length coordinate at ss = 773 m.

(a) Normal displacement contour

(b) Tangential displacement contour

Fig. 4. Time history of displacement contour for LAV analysis of the riser.

In addition, Figs. 4(a) and 4(b) present the time history of displacement contour for LAV analysis. From Fig. 6(a), the maximum vibration amplitude for normal displacement is occurred at the arc-length coordinate of 1100 m, approximately. However, the maximum amplitude for tangential displacement is approximately at the arc-length coordinate of 600 m.

Nonlinear Vibrations of Deepwater Catenary Riser

(a) Normal direction

815

(b) Tangential direction

Fig. 5. Time history of phase space of the riser at arc-length coordinate ss = 773 m.

Figure 5 shows the time history of phase space of the riser in normal and tangential directions. Since the phase space forms an elliptical shape, this figure also represents the periodic motion of the riser due to the hydrodynamic wave excitation. Figures 6(a) and 6(b) present the distribution of vibration amplitude along the riser length in the normal and tangential direction, respectively, investigating from different wave amplitude. It can be seen that higher wave amplitude produces the higher wave force, which causes to increase in the vibration amplitude of the riser. However, the wave amplitude has an insignificant effect on the envelope curve of vibration. On the effect of nonlinear geometry, the supplementary nonlinear stiffness increases the normal vibration amplitude of the riser at the coordinate 0 < ss ≥ 550 m, however the vibration amplitude is reduced at the coordinate 550 < ss ≥ 1325 m. For tangential vibration, supplementary nonlinear stiffness reduces the axial stiffness of the riser, which increases the vibration amplitude.

4 Conclusion The large amplitude forced vibration analysis of deepwater catenary riser subjected to a hydrodynamic wave is presented in this paper. The mathematical model of the riser is derived from the work-energy principle. The geometrical nonlinearity and nonlinear loading from a square drag term of hydrodynamic force are concerned. The hydrodynamic current and wave forces are performed by using the Morison equation. The finite element method is used to evaluate the riser’s motion. The nonlinear vibration response of the catenary riser is solved by the Newmark time integration scheme. The nonlinear forced vibration analysis is carried out based on the effect of wave force for both small and large vibration amplitudes. The results show that the wave force induces the harmonic vibration response and the increase in wave amplitude resulted in increasing the nonlinear vibration amplitude of the riser. The nonlinear geometric contributes a significant effect on the vibration amplitude of the riser. It can be concluded that the increase in nonlinear stiffness resulted in reducing the axial stiffness of the riser, thus the vibration amplitude increases.

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(a) Normal displacement amplitudes

(b) Tangential displacement amplitudes

Fig. 6. Comparing displacement amplitude of SAV and LAV obtained from different wave amplitude.

Acknowledgements. The authors gratefully acknowledge the funding provided by the Department of Civil Engineering, Faculty of Engineering at Kamphaeng Saen, Kasetsart University, and the support from Thailand Research and Innovation under Fundamental Fund 2022 (Advanced Construction Towards Thailand 4.0 Project) to the Construction Innovations and Future Infrastructures Research Center at the King Mongkut’s University of Technology Thonburi.

Appendix A According to Eq. (16), the linear element stiffness matrix [kL ] can be calculated by [kL ] = [b kL ] + [a kL ] where the linear element bending stiffness matrix  stiffness matrix a kL are



b kL

(A.1) 

and the linear element axial

 4 2   2 ! "  κs κs κs T T κs 0 N d dss [N d ] + [N d ]   2 b kL = EIP ∫ [N d ] 2 κ 0 κs κs κs 0 s   !  "T  1 0 !  " l !  "T κ 2 κ  s s [N ] + N + EIP ∫ N d N d dss d d 00 0 0 0  2   2    l κs 0 κs 0 T Nas + EAP [N d ] dss a kL = ∫ [N d ] 0 κs2 0 0 0     l 0 −κs 0 −κs !  " + EAP N d dss + ∫ [N d ]T Nas κs 0 0 0 0     l !  "T 0 κs 0 0 Nas + EAP + ∫ Nd [N d ] dss −κs 0 −κs 0 0





l

(A.2)

Nonlinear Vibrations of Deepwater Catenary Riser

! "      T 10 00 ! " Nas + ∫ Nd + EAP N d dss 01 01 0

817

l

(A.3)

The first-order nonlinear element stiffness matrix [kN 1 ] resulting from the nonlinear geometric is  2   ! " 2 l 3  T 2κs α −κs β T −κs β −2κs α N d dss [kN 1 ] = EAP ∫ [N d ] [N d ] + [N d ] 2β 0 β −κ 0 κ 2 s 0 s   !  "T  0 β !  " l !  "T −κ β 0 3 s + EAP ∫ N d (A.4) N d dss [N d ] + N d −2κs α κs β β 2α 2 0 and the second-order nonlinear element stiffness matrix [kN 2 ] is  2 2    2 !  " l 3 κs α −κs2 αβ T T −κs αβ −κs α N d dss [kN 2 ] = EAP ∫ [N d ] [N d ] + [N d ] κs β 2 κs αβ −κs2 αβ κs2 β 2 2 0   !  "T  β 2 αβ !  " l !  "T −κ αβ κ β 2 3 s s N d dss (A.5) + EAP ∫ N d + Nd ] [N d −κs α 2 κs αβ αβ α 2 2 0 The parameters α and β in Eqs. (A.4) and (A.5) are defined as follows. 

α = utd − κs vnd

(A.6)



β = vnd + κs utd

(A.7)   The matrices [m], g , and [ki ] in Eq. (17) are the element mass matrix, element gyroscopic matrix, and element centrifugal force matrix, respectively. These matrices can be expressed as follows. l

[m] = ∫[N d ]T (mP + mi )[N d ]dss

(A8)

  l !  "T g = ∫ N d 2mi Vis [N d ]dss

(A.9)

! " l !  "T [ki ] = ∫ N d mi Vis2 N d dss

(A.10)

0

0

0

The matrices [ma ], [c], and {f } in Eq. (18) are the element added mass matrix, the element hydrodynamic damping matrix, and the element hydrodynamic excitation vector, respectively. These matrices can be expressed as follows. l

[ma ] = ∫[N d ]T Ca∗ [N d ]dss 0

 ∗ Ceqn 0 [c] = ∫[N d ] [N d ]dss ∗ 0 Ceqt 0 ∗ 2 ∗ V l ˙ Hn CDn VHn + CM {f } = ∫[N d ]T dss ∗ V 2 + C∗ V ˙ CDt 0 Ht M Ht l

T

(A.11)



(A.12) (A.13)

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References Athisakul, C., Klaycham, K., Chucheepsakul, S.: Critical top tension for static equilibrium configuration of a steel catenary riser. China Ocean Eng. 28(6), 829–842 (2014). https://doi.org/ 10.1007/s13344-014-0064-x Cheng, Y., Ji, C., Zhai, G., Oleg, G.: Nonlinear analysis for ship-generated waves interaction with mooring line/riser systems. Mar. Struct. 59, 1–24 (2018) Chucheepsakul, S., Monprapussorn, T.: Nonlinear buckling of marine elastica pipes transporting fluid. Int. J. Struct. Stab. Dyn. 1(3), 333–365 (2001) Chucheepsakul, S., Monprapussorn, T., Huang, T.: Large strain formulations of extensible flexible marine pipes transporting fluid. J. Fluids Struct. 17(2), 185–224 (2003) Chucheepsakul, S., Huang T.: Natural frequencies of a marine riser in three-dimensions. In: Proceedings of the 7th International Offshore Mechanics and Arctic Engineering Symposium, pp. 651–658 (1989) Cook, R.D., Malkus, D.S., Plesha, M.E.: Concept and Applications of Finite Element Analysis, 4th edn. Wiley, New York, USA (2002) Duanmu, Y., Zou, L., Wan, D.: Numerical analysis of multi-modal vibrations of a vertical riser in step currents. Ocean Eng. 152, 428–442 (2018) Kaewunruen, S., Chiravatchradej, J., Chucheepsakul, S.: Nonlinear free vibrations of marine risers/pipes transporting fluid. Ocean Eng. 32(3–4), 417–440 (2005) Klaycham, K., Athisakul, C., Chucheepsakul, S.: Large amplitude vibration of a deepwater riser conveying oscillatory internal fluid flow. Ocean Eng. 217, 107966-1–108015 (2020) Lei, S., Zhang, W., Lin, J., Yue, Q., Kennedy, D., Williams, F.W.: Frequency domain response of a parametrically excited riser under random wave forces. J. Sound Vib. 333(2), 485–498 (2014) Mazzilli, C.E.N., Rizza, F., Dias, T.: Heave-imposed motion in vertical risers: A reduced-order modelling based on Bessel-like modes. Procedia IUTAM 19, 136–143 (2016) Meng, S., Song, S., Che, C., Zhang, W.: Internal flow effect on the parametric instability of deepwater drilling risers. Ocean Eng. 149, 305–312 (2018) Montoya-Hernández, D.J., Vázquez-Hernández, A.O., Cuamatzi, R., Hernandez, M.A.: Natural frequency analysis of a marine riser considering multiphase internal flow behavior. Ocean Eng. 92, 103–113 (2014) Morison, J.R., O’Brien, M.P., Johnson, J.W., Schaaf, S.A.: The force exerted by surface waves on piles. Petrol. Trans. Am. Inst. Min. Eng. 189, 149–154 (1950) Newmark, N.M.: A method of computation for structural dynamics. J. Eng. Mech. Div. ASCE 85(3), 67–94 (1959) Paidoussis, M.P.: Fluid Structure Interaction: Slender Structure and Axial Flow, vol. 1. Academic, London (1998) Punjarat, O., Chucheepsakul, C.: Nonlinear formulation and free vibration of a large-sag extensible catenary riser. Ocean Syst. Eng. 11(1), 59–81 (2021) Sparks, C.P.: Fundamentals of Marine Riser Mechanics: Basic Principles and Simplified Analyses. Pennwell Corporation, Oklahoma, USA (2007) Takafuji, F.C.M., Martins, C.A.: Comparison between frequency domain and time domain riser analysis. J. Offshore Mech. Arct. Eng. 134(4), 041301–041309 (2012) Vásquez, J.A.M., Avila, J.P.J.: A parametric analysis of the influence of the internal slug flow on the dynamic response of flexible marine risers. Ocean Eng. 174, 169–185 (2019) Wang, J., Xiang, S., Fu, S., Cao, P., Yang, J., He, J.: Experimental investigation on the dynamic responses of a free-hanging water intake riser under vessel motion. Mar. Struct. 50, 1–19 (2016) Zhang, L., et al.: Axial and transverse coupled vibration characteristics of deep-water riser with internal flow. Procedia Eng. 126, 260–264 (2015)

Effects of High Turbulence Intensity on Dynamic Characteristics of Membrane Structure in Typhoon Dong Li(B) , Yiteng Lin, and Hongwei Huang Department of Civil Engineering, Fuzhou University, College Road 2, Fuzhou 350108, China [email protected]

Abstract. To investigate the effects of high turbulence in typhoon on the aerodynamic characteristics of membrane structure, wind tunnel tests of an umbrellashaped tensioned membrane structure were carried out in both typhoon and traditional atmospheric boundary layer in terrain B field (B-type). Dynamic identification of the aeroelastic model in these two wind fields are discussed in terms of frequency, modal shape and damping ratio. Results show that the influences of high-level turbulence intensity are (i) the fluid-structure interaction in typhoon becomes more severe with larger damping ratio, resulting in the reduction of displacement response and frequency, (ii) the frequencies in different order distribute closely in some narrow bands and perform localization, and (iii) the non-Gaussian distribution of displacement response appears more obvious in typhoon condition, which should be considered in reliability design of membrane structure. This study can address the deficiency of current studies for dynamic characteristics of membrane structure in typhoon. Keywords: High turbulence intensity · Membrane structure · Typhoon · Aerodynamic characteristics · Wind engineering

1 Introduction Membrane structures have been widely used in long-span spatial structures due to their aesthetic features of beauty and thinness (Liu et al. 2020). Umbrella-shaped tensioned membrane structure is a typical membrane structure used in public facilities such as stadiums, expo centers, and airports. Membrane structures are susceptible to wind loads due to their lightweight and flexible nature. This leads to many aero-elastic phenomena such as dynamic buffeting, galloping, flutter, and even collapse of the structure (Michalski et al. 2011; Yin et al. 2021). Therefore, it is essential to for membrane structures, especially in coastal areas prone to typhoons. Different from the normal wind that has been widely studied, the typhoon is one of the extreme winds (abnormal load) with high wind velocity and turbulence intensity, which may lead to the differences in dynamic characteristics and more damages to membrane structure. Furthermore, some engineering accidents of membrane structures have already occurred under typhoon attack (Yang et al. 2018). However, the dynamic © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 819–828, 2023. https://doi.org/10.1007/978-981-19-7331-4_66

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response problem of membrane structure in typhoon representing high turbulence flow has not been paid much attention and fully investigated. Some researchers have conducted deep research of the dynamic response of membrane structure in low turbulent flow, which can provide the meaningful reference for this study. The hyperbolic-parabolic shaped suspended roof in turbulent flow is found to be quite similar to vortex excited oscillation (Uematsu and Uchiyama 1986). The wind tunnel test for long-span roof was performed in terrain B wind flow, and the significant effects of higher mode vibrations on displacement and stress were found (Yasui et al. 1999). The added mass and aerodynamic damping were studied quantitatively by testing a saddle-shaped cable membrane in the terrain B wind field experimentally (Yang et al. 2010). With the particle-image-velocimetry (PIV) and high-speed digital-imagecorrelation (DIC) techniques developed, the interaction between a turbulent fluid low and a flexible membrane structure model was investigated in wind tunnel, and the effects of turbulent fluctuations on the deformed membrane can be obtained in detail (Wood et al. 2018). The wind tunnel tests on both enclosed and open models of oval-shaped arch-supported membrane structure was carried out in the terrain B wind environment, and the peak response of structure was identified (Kandel et al. 2021). In this paper, the scaled model of umbrella-shaped membrane structure is designed and fabricated firstly. Then, a series of wind tunnel tests in both typhoon and terrain B wind environment (B-type) simulated are performed to identify the dynamic characteristics in terms of frequency, modal shape and damping ratio. Finally, the influences of large wind velocity and high-level turbulence in typhoon on dynamic behavior of membrane structure are discussed.

2 Experimental Study 2.1 Model Design and Fabrication The plane dimension of scaled model is 1.2 m × 1.2 m, and its height is 0.44 m shown in Fig. 1. With the consideration of steel support structure height, the absolute height of experimental model above floor surface is 1.0 m, which is defined as the reference height z1 . After the form-finding analysis, the required pretension at every corner point should be 8.74 kN. The polyvinyl chloride (PVC) membrane material commonly used in engineering was selected, i.e. XYD brand made in China. The mechanical characteristics can be identified based on the strip method. The riggings and fixtures at four corner positions and the pillar at central position were processed using low-alloy steel material. The properties of steel material were identified by testing steel coupons. The three-wire steel strand was selected as the boundary cable and tested. The material parameters identified are listed in Table 1. 2.2 Wind Environment Simulation The aerodynamic model experiments were carried out at Fujian’s Key Laboratory of Wind Disaster and Engineering in Xiamen University of Technology. The wind tunnel

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Fig. 1. Photograph of fabricated model.

Table 1. Technical parameters of materials. Technical parameter

Membrane

Steel

Steel strand

Elastic modulus (GPa)

1.72 (warp)/1.49 (weft)

207

202

Yield strength (MPa)

NA

272

NA

Tensile strength (MPa)

110 (warp)/105 (weft)

413

1760

is a closed-circuit type tunnel with a low-velocity test section of 6 m in width and 3.6 m in height, and upstream fetch of 25 m. The maximum wind velocity is 32 m/s. The wind tunnel floor is lined with automatic roughness elements, whose plane dimension is of 50 mm × 50 mm. The trips and spires are used to generate additional turbulence. These setups are regulated comprehensively to achieve the desired boundary layer profiles and turbulence levels. Due to the simplicity and efficiency, the empirical power law has been widely adopted to express the wind velocity profile in structural design codes expressed as: U = U1 (z/z1 )α

(1)

where U is the wind velocity at height z, U 1 is the wind velocity at reference height z1 , and α is the power law coefficient, which is the key parameter to describe the terrain roughness and atmospheric stability. For membrane structure generally established in suburban regions, the coefficient α = 0.15 is recommended for terrain B. However, the coefficient α in typhoon increased to α = 0.19 after their in-field observation of the Super Typhoon Mangkhut (He et al. 2020). For both extratropical wind and typhoon, the wind velocity profiles (marked by separate points) in wind tunnel can be measured by cobra probes located in different height, and furtherly validated after comparison with the theoretical curve in Fig. 2(a). The reference height z1 is 1.0 m and the corresponding wind velocity is U 1 .

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The turbulence profile is expressed with the general form of power function as: γ = c(z/10)d

(2)

where γ is turbulence intensities, c is the corresponding value at 10 m, and d is the power coefficient affecting the shape of the profile. It is stipulated that d = −0.15 (used in this study) for terrain B. However, the in-field records in the Super Typhoon Mangkhut revealed that the turbulence intensities were obviously larger, and d = −0.23 were given (He et al. 2020). The wind turbulence intensities in wind tunnel are compared with the theoretical curve in Fig. 2(b). The turbulence intensities at the top height of membrane structure (z1 = 1.0 m) are 14% for B-type extratropical wind and 20.5% for typhoon, respectively. It can be viewed that the wind velocity and turbulence intensity profiles match well with the reference theoretical profiles.

(a) Wind velocity profile

(b) Turbulence intensity profile

Fig. 2. Wind parameters of B-type and typhoon simulated in wind tunnel.

2.3 Wind Tunnel Tests Three levels of mean wind velocity at top roof are designed as 11 m/s, 15 m/s and 19 m/s. In order to compare the structural dynamic characteristics in typhoon and Btype extratropical wind, these two types of wind flows were simulated in wind tunnel. The photograph of the model in wind tunnel is shown in Fig. 3. In summary, two types of wind flows including B-type wind and typhoon were simulated, and three levels of wind velocity (i.e., 11 m/s, 15 m/s and 19 m/s) were designed for each type. For each wind condition, seven wind directions were scheduled including 0°, 30°, 60°, 90°. A total of 24 test cases were summarized as shown in Table 2. Each test case was measured for 180 s after the wind field became steady. The test cases were identified using wind type, wind velocity and attack angle. For example, the test case T-11-30 means: (i) the wind type is belonged to typhoon, (ii) the wind velocity is 11 m/s, (iii) the attack angle is 30°. The displacement response was measured by two types of laser sensors, namely LK-G150 and LK-G400 with the Keyence brand made in Japan. The largest sampling

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Fig. 3. Photograph of model in wind tunnel. Table 2. Summary of the test cases. Attack angle

Wind type

Wind velocity 11 m/s

15 m/s

19 m/s

B-11-0

B-15-0

B-19-0

0°

B-type Typhoon

T-11-0

T-15-0

T-19-0

30°

B-type

B-11-30

B-15-30

B-19-30

Typhoon

T-11-30

T-15-30

T-19-30

B-type

B-11-60

B-15-60

B-19-60

Typhoon

T-11-60

T-15-60

T-19-60

B-type

B-11-90

B-15-90

B-19-90

Typhoon

B-11-90

B-15-90

B-19-90

60° 90°

rate is 50 kHz (2 kHz used in this study), and the measurement error is 0.05%. Eight measurement points of displacement were located at the membrane surface, shown in Fig. 4.

3 Test Results and Analysis 3.1 Displacement Analysis As is shown in Fig. 5, the time history analysis of displacement at Point 3 and Point 7 were performed quantitatively to identify some significant parameters when the average wind

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Fig. 4. Schematic diagram and photograph of measurement.

velocity is 19 m/s. It is noted that the positive value of displacement results mean that the membrane experienced the upward motion. The displacement-time history results can be analyzed using some significant parameters, namely time average deformation d , root mean square (RMS) deformation σ and peak to peak value d et al. The time average deformation d represents the new equilibrium position during vibration, and the RMS deformation σ describes the amplitude above the time average deformation, representing the level of kinetic energy of membrane structure. The peak-to-peak value d reveals the difference between maximal displacement d max and minimum displacement d min . It can be found that the vibration is belonged to the stationary type, with its time average deformation d remaining constant. In particular, the time average deformations of B-type wind at Point 3 and Point 7 are 3.99 and −4.23 mm, respectively. However, the corresponding value for typhoon condition reduces to 1.98 and −1.73 mm, respectively. The similar phenomena occur in RMS deformation and peak to peak value analysis as well. For B-type wind condition, the RMS deformation results at Point 3 and Point 7 are 2.04 and 1.62 mm, respectively. However, the RMS value in typhoon condition decreases to 1.62 and 0.69 mm, respectively. The peak-to-peak value at Point 3 reduces from 17.56 mm to 14.93 mm for the B-type wind and typhoon condition. The reason why the displacement response in typhoon is less than the value in B-type wind is that the fluid-structure interaction (FSI) in typhoon (larger turbulence density) is much more obvious than the B-type wind condition, resulting in the more energy dissipation and larger damping in FSI process in typhoon. 3.2 Frequency Analysis Based on the measured displacement response, the structural modal parameters (e.g., frequencies, damping ratios and mode shapes) can be identified using the Bayesian FFT method. The root power spectra density (PSD) and single value (SV) spectrum of displacement is shown in Fig. 6. The SV spectrum plots the eigenvalues of the PSD

Effects of High Turbulence Intensity on Dynamic Characteristics

(a) B-type (Point 3)

(b) B-type (Point 7)

(c) Typhoon (Point 3)

(d) Typhoon (Point 7)

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Fig. 5. Displacement response-time results in the case of 19 m/s average wind flow.

results, and gives the natural frequencies clearly. Due to the flexible characteristics and symmetric shape of membrane structure, multiple closely-space frequencies and can be observed. For example, the first six frequencies in typhoon vary within 50 Hz and distribute closely, including the 1st band with two frequencies (i.e., 20.76 Hz and 22.02 Hz), the 2nd band with three frequencies (i.e., 31.36 Hz, 34.66 Hz and 36.18 Hz), and the 3rd band with single frequency (i.e., 44.93 Hz). The similar trend occurs in B-type wind condition but with little difference in value. 3.3 Damping Ratio Analysis As is shown in Fig. 7, the damping ratio results in B-type wind and typhoon are extracted for the first six frequency orders and three levels of wind velocity. For B-type wind, the damping ratio in the 1st frequency (i.e., 5.63%) is much larger than others when the wind velocity is 11 m/s. However, the largest damping ratio (i.e., 3.29% and 4.88%) appears in the 3rd and 4th frequency with wind velocity increasing to 15 m/s and 19 m/s. However, this trend is not suitable to typhoon. The damping ratio in the 1st frequency always makes the most contribution to the damping effects in different wind velocity cases, with its damping ratio 3 times averagely than others, which indicates the 1st frequency makes the most contribution to the energy dissipation in typhoon.

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(a) B-type wind

(b) Typhoon Fig. 6. PSD and SV spectrum.

(a) B-type wind

(b) Typhoon

Fig. 7. Identified damping ratio for the first six modes.

3.4 Distribution Characteristics of Displacement The distribution characteristics of displacement at Point 3 and Point 7 are shown in Fig. 8 for both B-type wind and typhoon when the wind flow is 19 m/s on average. The

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test results are expressed in histogram, and the generalized extreme value distribution (GEV) and Gaussian distribution curves are applied to fit the test data histogram. It is obvious to find that the GEV distribution is much better to fit test data histogram than the Gaussian distribution, indicating the displacement response follows the nonGaussian distribution with significant tail characteristics. Moreover, the statistical results including skewness and kurtosis are given and analyzed. For point 7, the skewness (S = 0.66) and kurtosis (K = 3.91) in typhoon is larger than those data (S = 0.40 and K = 3.34) in B-type wind. The same trend occurs at Point 7. These differences indicate that with larger turbulence intensity, the correlation between the non-Gaussian distribution characteristics of displacement and turbulence level in wind field is strengthened.

(a) B-type (Point 3)

(b) B-type (Point 7)

(c) Typhoon (Point 3)

(d) Typhoon (Point 7)

Fig. 8. Probability density function of displacement in the case of 19 m/s average wind flow.

4 Conclusions Wind tunnel tests of an umbrella-shaped membrane structure were conducted under Btype wind and typhoon field. The influences of high turbulence intensity in typhoon

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on aerodynamic characteristics of structure were analyzed in terms of displacement response, frequency, damping ratio and distribution characteristics. The main conclusions can be summarized as follows. (1) Due to the large turbulence intensity, the fluid-structure interaction in typhoon is much more severe than the B-type wind condition with larger damping ratio (especially in the 1st mode), leading to the reduction of displacement response and frequency. (2) Many natural frequencies are very close to each other within some narrow bands, and perform localization. (3) The non-Gaussian characteristics of displacement in typhoon are significantly more obvious than B-type wind case, with both skewness and kurtosis increasing.

Acknowledgements. This study has been financially supported by the National Natural Science Foundation of China (Grant No. 52108121), the Natural Science Foundation of Fujian Province, China (2020J05127).

References He, J.Y., et al.: Observational study of wind characteristics, wind speed and turbulence profiles during Super Typhoon Mangkhut. J. Wind Eng. Ind. Aerodyn. 206, 104362 (2020) Kandel, A., Sun, X.Y., Wu, Y.: Wind-induced response and equivalent static design method of oval-shaped arch-supported membrane structure. J. Wind Eng. Ind. Aerodyn. 213, 104620 (2021) Liu, C.J., Deng, X.W., Liu, J., Yang, S.P., Zheng, Z.L.: Dynamic response of saddle membrane structure under hail impact. Eng. Struct. 214, 110597 (2020) Michalski, A., et al.: Validation of the computational fluid-structure interaction simulation at realscale tests of a flexible 29 m umbrella in natural wind flow. J. Wind Eng. Ind. Aerodyn. 99(4), 400–413 (2011) Uematsu, Y., Uchiyama, K.: Aeroelastic behavior of an H.P. shaped suspended roof. In: Proceedings of IASS Symposium: Shells, Membrane and Space Frames, vol. 2. Elsevier, Osaka (1986) Wood, J.N., Breuer, M., Nayer, G.D.: Experimental studies on the instantaneous fluid-structure interaction of an air-inflated flexible membrane in turbulent flow. J. Fluids Struct. 80, 405–440 (2018) Yang, Q.S., Gao, R., Bai, F., Li, T., Tamura, Y.: Damage to buildings and structures due to recent devastating wind hazards in East Asia. Nat. Hazards. 92, 1321–1353 (2018) Yang, Q.S., Wu, Y., Zhu, W.L.: Experimental study on interaction between membrane structures and wind environment. Earthq. Eng. Eng. Vib. 9(4), 523–532 (2010) Yasui, H., Marukawa, H., Katagiri, J., Katsumura, A., Tamura, Y., Watanabe, K.: Study of windinduced response of long-span structure. J. Wind Eng. Ind. Aerodyn. 83(1), 277–288 (1999) Yin, Y., Chen, W.J., Hu, J.H., Zhao, B., Wang, Q.: In-situ measurement of structural performance of large-span air-supported dome under wind loads. Thin- Walled Struct. 169, 108476 (2021)

Effects of Discretization Schemes on Free Vibration Analysis of Planar Beam Structures Using Isogeometric Timoshenko-Ehrenfest Beam Formulations Duc Van Nguyen1 , Duy Vo2 , and Pruettha Nanakorn1(B) 1 School of Civil Engineering and Technology, Sirindhorn International Institute of Technology,

Thammasat University, Pathumthani, Thailand [email protected], [email protected] 2 Center of Excellence in Applied Mechanics and Structures, Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand [email protected]

Abstract. Several Timoshenko-Ehrenfest beam formulations have been presented in the literature for analysis of planar beam structures. In general, the displacements of the beam axis and the cross-sectional rotation are taken as kinematic unknowns. Two discretization schemes are available, namely discretization of local displacements and discretization of global displacements. In the case of linear static analysis, it has been shown that discretization of local displacements fails to accurately represent rigid transformations, whereas discretization of global displacements does not. Consequently, numerical instability is observed in analysis using discretization of local displacements. This paper investigates the effects of the two discretization schemes on free vibration analysis of planar beam structures using isogeometric Timoshenko-Ehrenfest beam formulations. Several numerical experiments on a free-form cubic beam are used for the investigation. In terms of accuracy, better performance from a formulation that employs discretization of global displacements is noticed. Keywords: Isogeometric analysis (IGA) · Free vibration analysis · Planar Timoshenko-Ehrenfest beam formulations · Discretization schemes · Convergence tests

1 Introduction Isogeometric analysis (IGA) (Hughes et al. 2005) is a relatively new numerical approach employed in many disciplines of computational mechanics. In this approach, computeraided design basis functions, e.g., rational B-spline functions and T-spline functions, are used for both the geometric description and the approximation of unknown variable fields. The approach enables the direct use of representative geometry in analysis and offers high-continuity approximations of unknown variable fields.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 829–836, 2023. https://doi.org/10.1007/978-981-19-7331-4_67

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In the framework of IGA, several Timoshenko-Ehrenfest beam formulations have been successfully developed for analysis of planar beam structures. Examples include linear static analysis (Adam et al. 2014; Bouclier et al. 2012; Cazzani et al. 2014; Vo et al. 2021), geometrically nonlinear analysis (Hosseini et al. 2018; Luu and Lee 2016; Vo and Nanakorn 2020), and free vibration analysis (Luu et al. 2015). In those formulations, the displacements of the beam axis and the cross-sectional rotation are commonly considered kinematic unknowns. Regarding discretization, two schemes, i.e., discretization of local displacements (Adam et al. 2014; Bouclier et al. 2012; Cazzani et al. 2014; Hosseini et al. 2018; Luu and Lee 2016) and discretization of global displacements (Vo et al. 2021; Vo and Nanakorn 2020), are possible. In the case of linear static analysis, although the discretization scheme for local displacements is widely used, this scheme fails to describe rigid transformations properly (Choi and Cho 2016) and consequently undermines the numerical performance of beam formulations. On the contrary, the performance can be improved considerably when global displacements are discretized as rigid transformations can be exactly represented. This paper aims to investigate further the effects of the two discretization schemes with regard to free vibration analysis of planar beam structures using isogeometric Timoshenko-Ehrenfest beam formulations. A free-form cubic beam is examined through several numerical experiments, i.e., modal analysis and convergence tests. The obtained results highlight the superior performance of discretization of global displacements.

2 Strain Measures of Planar Curved Timoshenko-Ehrenfest Beams For expressions of vectorial quantities, two Cartesian coordinate frames are considered, i.e., global and local coordinate frames. The global coordinate frame is a stationary frame spanned by two orthonormal vectors, while the local one is a moving frame attached to the beam axis. The unit tangent vector A1 and the normal vector A2 of the beam axis are used as the base vectors of the local coordinate frame, i.e., dR0 (S)  = R0 (S) A2 = A1 . (1) dS Here, R0 (S) is the position vector of an arbitrary point on the beam axis parameterized by the arc-length parameter S. In addition,  denotes a rotation matrix expressed as   0 −1 = . (2) 1 0 A1 =

Note that primes denote derivatives with respect to S. The displacement vector of the beam axis can be expressed in the local coordinate frame as u0 (S) = u01 A1 + u02 A2 .

(3)

Here, u01 and u02 are, respectively, the displacement components along vectors A1 and A2 . The strain measures can be derived as follows (Adam et al. 2014; Choi and Cho 2016): 



ε = u01 − κu02 γ = κu01 + u02 − θ χ = θ 

(4)

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where ε, γ , and χ are, respectively, the membrane, shear, and bending strain measures. In addition, θ represents the cross-sectional rotation, and κ denotes the curvature of the undeformed beam axis. For planar Timoshenko-Ehrenfest beams, u0 (S) and θ are considered as kinematic unknowns. The derivatives of the base vectors of the local coordinate frame can be expressed as 



A1 = κA2 A2 = −κA1 .

(5)

By using Eqs. (3)–(5), the strain measures can be alternatively expressed as (Choi and Cho 2016) 



ε = u0 · A1 γ = u0 · A2 − θ χ = θ  .

(6)

Once the strain measures are determined, the cross-sectional stress resultants can be computed as n = EAε q = GAγ m = EI χ

(7)

where n, q, and m are the axial force, shear force, and bending moment, respectively. Here, A and I denote the cross-sectional area and moment of inertia, while E and G represent Young’s modulus and the shear modulus of an isotropic linear elastic material.

3 Virtual Work Principle In this study, only free vibration analysis is considered. Therefore, the external virtual work is omitted. The inertia and internal virtual work can be written as L δiner =

  ρAu¨ 0 · δu0 + ρI θ¨ δθ dS

(8)

0

L δint =

(nδε + qδγ + mδχ )dS.

(9)

0

Here, ρ denotes the mass density, L is the length of the beam, and the double dots represent the second derivatives with respect to time. The virtual work principle is then stated as δ = δiner + δint = 0.

(10)

By substituting the discretization of the kinematic unknowns into the virtual work equation, the system equations can be obtained in the following form as Md¨ + Kd = 0

(11)

with M being the mass matrix, K being the stiffness matrix, and d being the vector of discrete unknowns. By assuming harmonic solutions, the system equations in Eq. (11) are reduced into a generalized eigenvalue problem as   M − ω2 K d = 0. (12)

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Here, ω is a natural frequency, and d is a normalized natural mode shape. In the subsequent section, the two discretization schemes to be investigated are presented.

4 Discretization Schemes In several studies (Adam et al. 2014; Bouclier et al. 2012; Cazzani et al. 2014; Hosseini et al. 2018; Luu and Lee 2016), the components of u0 in the local coordinate frame and the cross-sectional rotation θ are discretized as u01 (ξ ) =

r

Ri,p (ξ )u01i u02 (ξ ) =

i=1

r

Ri,p (ξ )u02i

(13)

i=1

θ=

r

Ri,p (ξ )θi

(14)

i=1

where Ri,p (ξ ) is a rational B-spline basis function parameterized by a knot parameter ξ , and r is the number of basis functions. More details of rational B-spline basis functions are available in many textbooks (Piegl and Tiller 1997). By using Eqs. (4), (13), and (14) in the virtual work equation, a beam formulation is obtained. In this study, this formulation is referred to as formulation D#1. In the case of linear static analysis, formulation D#1 cannot properly describe rigid transformations, and consequently, its performance suffers from severe numerical instability (Choi and Cho 2016). This shortcoming can be overcome by using the following discretization of the displacement vector u0 as u0 (ξ ) =

r

Ri,p (ξ )u0i .

(15)

i=1

Substituting Eqs. (6), (14), and (15) into the virtual work equation yields an alternative beam formulation in terms of u0 , which is referred to as formulation D#2. This formulation eliminates the numerical instability due to the failure in representing rigid transformations.

5 Numerical Results This section investigates the performance of formulations D#1 and D#2 for free vibration analysis. A free-form cubic beam in Fig. 1 is analyzed. The beam axis is represented by a cubic B-spline curve whose control points are given in Fig. 1. Regarding the crosssectional and material properties, the following values are used, i.e., A = 0.12 , I = 0.14 /12, E = 3 × 1010 , G = 1.2 × 1010 , and ρ = 2.5 × 103 .

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Fig. 1. A free-form cubic beam with a fixed support.

5.1 Accuracy Verification The first experiment is devoted to verifying the accuracy of formulations D#1 and D#2. Since the analytical solutions of the natural frequencies do not exist, the cubic beam is also simulated in Marc Mentat, a commercial finite element package, using 799 B98 twonoded beam elements. The B98 two-noded beam element employs linear interpolation for all kinematic unknowns. The results obtained by Marc Mentat are used as reference results. In this study, the cubic beam is analyzed using a sextic B-spline curve consisting of 800 control points. With this implementation, the numbers of degrees of freedom utilized by Marc Mentat and the present study are equivalent. The first five natural frequencies are reported in Table 1, revealing good agreement between Marc Mentat and formulations D#1 and D#2. This good agreement verifies the accuracy of formulations D#1 and D#2. Table 1. Comparison of the first five natural frequencies. Natural frequency 1

Marc Mentat 1.793

Formulation D#1 1.793

Formulation D#2 1.793

2

8.674

8.674

8.674

3

11.659

11.658

11.658

4

29.382

29.379

29.379

5

59.878

59.863

59.863

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5.2 Convergence Tests Convergence tests are performed to assess further the performance of formulations D#1 and D#2. In this numerical experiment, the results obtained using sextic B-spline curves and 800 control points are considered as the converged results. The relative errors of frequencies are computed by



ω



(16) relativeError =

− 1

ωref where ωref is the converged natural frequency, and ω is the natural frequency obtained using B-spline curves of degrees p = 3, 4, and 5. Here, the relative errors are considered functions of the number of degrees of freedom N .

Fig. 2. Convergence tests for different B-spline degrees.

The obtained results are depicted in Fig. 2. At first glance, one can easily observe that the results obtained by formulation D#1 are less accurate than those obtained by formulation D#2. However, a closer inspection reveals that, for formulation D#1, higher

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frequencies have higher levels of accuracy. In other words, the accuracy is improved with the frequency index. In contrast, the accuracy of formulation D#2 is reduced with the frequency index. However, formulation D#1 offers higher orders of convergence than formulation D#2 for all the degrees p considered.

6 Conclusions This paper considers free vibration analysis of planar beam structures using isogeometric Timoshenko-Ehrenfest beam formulations with two different displacement discretization schemes. The investigated discretization schemes are formulation D#1, where the local displacements are discretized, and formulation D#2, where the global displacements are discretized. A free-form cubic beam is examined to assess the effects of the two discretization schemes. For modal analysis, excellent agreement between the results obtained by Marc Mentat and the two formulations confirms the accuracy of the two formulations. However, from the performed convergence tests, it is found that formulation D#1 offers lower accuracy but higher orders of convergence in comparison with formulation D#2. Acknowledgements. The scholarships from the ASEAN University Network/Southeast Asia Engineering Education Development Network (AUN/SEED-Net) and Sirindhorn International Institute of Technology (SIIT), Thailand, for the first author are greatly appreciated. The second author acknowledges the Postdoctoral Fellowship awarded by the Second Century Fund (C2F) from Chulalongkorn University, Thailand. The authors appreciate the support from the Alumni Support Program for Research (Grant number: SIIT ASP-R 2101) from AUN/SEED-Net for this study.

References Adam, C., Bouabdallah, S., Zarroug, M., Maitournam, H.: Improved numerical integration for locking treatment in isogeometric structural elements, part I: beams. Comput. Methods Appl. Mech. Eng. 279, 1–28 (2014) Bouclier, R., Elguedj, T., Combescure, A.: Locking free isogeometric formulations of curved thick beams. Comput. Methods Appl. Mech. Eng. 245–246, 144–162 (2012) Cazzani, A., Malagù, M., Turco, E.: Isogeometric analysis of plane-curved beams. Math. Mech. Solids 21(5), 562–577 (2014) Choi, M.-J., Cho, S.: Elimination of self-straining in isogeometric formulations of curved Timoshenko beams in curvilinear coordinates. Comput. Methods Appl. Mech. Eng. 309, 680–692 (2016) Hosseini, S.F., Hashemian, A., Moetakef-Imani, B., Hadidimoud, S.: Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations. Acta. Mech. Sin. 34(4), 728–743 (2018). https://doi.org/10.1007/s10409-018-0753-4 Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194(39–41), 4135– 4195 (2005) Luu, A.-T., Kim, N.-I., Lee, J.: Isogeometric vibration analysis of free-form Timoshenko curved beams. Meccanica 50(1), 169–187 (2014). https://doi.org/10.1007/s11012-014-0062-3

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Luu, A.-T., Lee, J.: Non-linear buckling of elliptical curved beams. Int. J. Non-Linear Mech. 82, 132–143 (2016) Piegl, L., Tiller, W.: The NURBS Book. Springer, New York (1997) Vo, D., Li, X., Nanakorn, P., Bui, T.Q.: An efficient isogeometric beam formulation for analysis of 2D non-prismatic beams. Eur. J. Mech. A. Solids 89, 104280 (2021) Vo, D., Nanakorn, P.: A total Lagrangian Timoshenko beam formulation for geometrically nonlinear isogeometric analysis of planar curved beams. Acta Mech. 231(7), 2827–2847 (2020). https://doi.org/10.1007/s00707-020-02675-x

Geometrically Nonlinear Behavior of L-Shaped Frames Under Forces Applied at Different Positions Nghi Huu Duong1 , Duy Vo2 , and Pruettha Nanakorn1(B) 1 School of Civil Engineering and Technology, Sirindhorn International Institute of Technology,

Thammasat University, Pathumthani, Thailand [email protected], [email protected] 2 Center of Excellence in Applied Mechanics and Structures, Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand [email protected]

Abstract. L-shaped frames are widely encountered in engineering applications, and the most notable examples are perhaps cranes at container ports and construction sites. In these applications, L-shaped frames are designed to support vertical and horizontal movements of heavy loads. For their safe and efficient designs, thorough insights into the nonlinear behavior of such frames are crucial. Although several studies on geometrically nonlinear responses of L-shaped frames exist, a single force applied at a specific position is commonly considered. For a comprehensive reflection of practical operations of L-shaped frames, this paper presents a numerical investigation of the geometrically nonlinear behavior of L-shaped frames under a concentrated force applied at different positions. The frames are analyzed by using an isogeometric Timoshenko-Ehrenfest beam formulation. The load-displacement curves of the frames with different force positions are exhibited. The influence of the ratio between the lengths of the two members is also discussed. Keywords: L-shaped frames · Geometrically nonlinear analysis · Isogeometric analysis · Timoshenko-Ehrenfest beam formulation · Length-to-length ratio

1 Introduction L-shaped frames have many engineering applications (Morales 2010), e.g., cranes, antenna reflectors, and building entrances. Some of the most encountered L-shaped frames are cranes devised to support heavy loads’ movements. Knowledge of the nonlinear behavior of these structures is essential for their safe and efficient designs. Several studies that consider the geometrically nonlinear analysis of L-shaped frames subjected to a concentrated force have been carried out (Lee et al. 1968; Vo et al. 2021; Vo and Nanakorn 2020). In these studies, structural instability of L-shaped frames involving severe snap-through and snap-back phenomena has been demonstrated. From these studies, two remarks can be made. First, only one load position is generally considered. Since © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 837–842, 2023. https://doi.org/10.1007/978-981-19-7331-4_68

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L-shaped frames are often used to carry slow-moving heavy loads, studies of L-shaped frames under various load positions should be done. Second, only one ratio between the lengths of the two members is typically considered, and the members are commonly set to have the same length. In practice, L-shaped frames with different combinations of the member lengths exist. This study addresses the shortcomings mentioned above by performing the geometrically nonlinear analysis of L-shaped frames under a concentrated force applied at different positions. In addition, the influence of the ratio between the lengths of the two members is also investigated.

2 Problem Descriptions and Numerical Analysis

Fig. 1. L-shaped frames and their loading and boundary conditions: (a) Pinned-pinned supports. (b) Fixed-pinned supports.

Figure 1 shows L-shaped frames whose geometrically nonlinear analysis is of interest. Regarding geometry, each frame consists of vertical and horizontal members, whose lengths are, respectively, denoted by L1 and L2 . A concentrated downward force P is applied on the horizontal member. The position of the force P is characterized by the distance d measured from the left end of the horizontal member. Two different boundary conditions are specified, i.e., pinned-pinned and fixed-pinned supports (see Fig. 1). The nonlinear responses of the frames are illustrated using the vertical displacement v at the force P. The numerical analysis is performed using the beam formulation proposed by Chorn et al. (2021). The mentioned beam formulation is developed with the kinematic assumptions of the Timoshenko-Ehrenfest beam theory. The displacements of the beam axis and the cross-sectional rotation are treated as kinematic unknowns. The basic concept of the isogeometric approach (Hughes et al. 2005) is adopted. More precisely, B-spline basis functions are used for the discretization of the kinematic unknowns, as well as the geometric descriptions.

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In the following tests, the position of the force P is varied by setting d /L2 = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.8. In addition, to represent a certain number of L-shaped frames, several values of L1 /L2 are considered. 2.1 L-Shaped Frames with Pinned-Pinned Supports The numerical results of the L-shaped frames with pinned-pinned supports are depicted in Fig. 2. Six values of L1 /L2 are considered, i.e., L1 /L2 = 0.1, 0.3, 0.6, 0.7, 0.8, and 1.0. From the results, transition behavior is observed. Generally, no snap phenomenon occurs for d /L2 ≥ 0.6. For d /L2 < 0.6, only the snap-through behavior is observed with L1 /L2 ≤ 0.6 while the frames exhibit both snap-through and snap-back behavior with L1 /L2 > 0.6. Therefore, the snap-back behavior can be avoided by setting L1 /L2 ≤ 0.6. Furthermore, the snap behavior can be entirely avoided by setting d /L2 ≥ 0.6. 2.2 L-Shaped Frames with Fixed-Pinned Supports Figure 3 visualizes the results of the L-shaped frames with fixed-pinned supports for six values of L1 /L2 , i.e., L1 /L2 = 0.1, 0.5, 1.0, 1.2, 1.3, and 1.5. Generally, no snap phenomenon occurs with L1 /L2 ≤ 0.1 or d /L2 ≥ 0.4. For d /L2 < 0.4, only the snapthrough phenomenon occurs with 0.1 < L1 /L2 ≤ 1.2 while both snap-through and snap-back phenomena occur with L1 /L2 > 1.2. Therefore, a fixed-pinned L-shaped frame should have L1 /L2 ≤ 1.2 to avoid the snap-back behavior or d /L2 ≥ 0.4 to completely eliminate the snap behavior. As expected, the obtained solutions show that the fixed-pinned L-shaped frames are stabler than the pinned-pinned L-shaped frames. The fixed-pinned L-shaped frames have larger prospects of not having the snap behavior than the pinned-pinned L-shaped frames, i.e., L1 /L2 ≤ 1.2 versus L1 /L2 ≤ 0.6 for no snap-back behavior, and d /L2 ≥ 0.4 versus d /L2 ≥ 0.6 for no snap behavior.

3 Conclusions This study performs the geometrically nonlinear analysis of L-shaped frames subjected to a concentrated force. Different from the existing studies, the analysis is carried out for different positions of the force. Furthermore, the ratio between the lengths of the vertical and horizontal members is also varied. These considerations provide a better understanding of optimal designs of L-shaped frames. It is found that the considered frames exhibit transition behavior regarding their stability robustness. The types of severe instability observed are the well-known snap-through and snap-back phenomena. In general, the prospect of the occurrence of these phenomena is reduced when the distance between the force and the vertical member is increased. As expected, the fixed-pinned L-shaped frames are proved to be stabler than the pinned-pinned L-shaped frames.

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Fig. 2. Normalized load-displacement curves of the L-shaped frames with pinned-pinned supports.

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Fig. 3. Normalized load-displacement curves of the L-shaped frames with fixed-pinned supports.

Acknowledgements. The first author acknowledges the scholarships from the ASEAN University Network/Southeast Asia Engineering Education Development Network (AUN/SEED-Net) and Sirindhorn International Institute of Technology (SIIT), Thailand. The second author acknowledges the Postdoctoral Fellowship awarded by the Second Century Fund (C2F) from Chulalongkorn University, Thailand. The authors appreciate the support from the Alumni Support Program for Research (Grant number: SIIT ASP-R 2101) from AUN/SEED-Net for this study.

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References Chorn, V., Vo, D., Nanakorn, P.: A total lagrangian isogeometric timoshenko beam formulation for large displacement analysis of 2D frames. Springer (2021) Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194(39–41), 4135– 4195 (2005) Lee, S.-L., Manuel, F.S., Rossow, E.C.: Large deflections and stability of elastic frame. J .Eng. Mech. Div. 94(2), 521–548 (1968) Morales, C.: L-shaped structure mass and stiffness matrices by substructure synthesis. Meccanica 45(2), 279–282 (2010) Vo, D., Duong, N.H., Rungamornrat, J., Nanakorn, P.: A 2D field-consistent beam element for large displacement analysis using a rational Bézier representation with varying weights. Appl. Math. Model. (2021) Vo, D., Nanakorn, P.: Geometrically nonlinear multi-patch isogeometric analysis of planar curved Euler-Bernoulli beams. Comput. Methods Appl. Mech. Eng. 366, 113078 (2020)

Interfacial Displacement Discontinuity in Coated Substrate with Couple-Stress Effects W. Wongviboonsin1 , P. A. Gourgiotis2 , and J. Rungamornrat1(B) 1 Center of Excellence in Applied Mechanics and Structures, Department of Civil Engineering,

Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand [email protected] 2 Department of Civil Engineering, University of Thessaly, Pedion Areos, GR-38334 Volos, Greece [email protected]

Abstract. A size-dependent elastic response of a thin-layer-coated substrate induced by a finite-length interfacial displacement discontinuity is fully investigated in the present work. The material microstructures responsible for the size effects are simulated within a continuum-based framework via the couple stress elasticity theory. A method of Fourier transform is adopted first to derive the general solution of an elastic field for both coating layer and coated substrate. The boundary conditions on the free surface, the continuity and discontinuity conditions along the coating interface, and the remote conditions are subsequently enforced together with the established general solution to solve for all key unknowns. Results are collected to demonstrate the effect of material contrast between coating layer and coated substrate and the crucial role of material microstructures on predicted response as the length of displacement discontinuity and the thickness of coating layer becomes comparable to the material length scale. Keyword: Couple stress theory · Interfacial displacement discontinuity · Layered media · Microstructures · Size-dependent effects

1 Introductions Micro-scale and microstructured materials have been increasingly encountered in a wide range of applications including fabrications of electronic components and devices. The mechanical responses of those tiny objects are observed to be very different from those in the macroscopic scale. Such difference becomes more pronounced when the external length scales of a body are comparable to the length scales of microstructures of the constituting material (e.g., Zisis 2018; Wongviboonsin et al. 2021, 2022). To take such material microstructural effects into account in the modeling, various generalized (high-order) continuum mechanics theories have been adopted to remedy the failure of conventional linear elasticity to capture the size dependent behavior. Among those existing theories, the couple stress elasticity theory has been found relatively simple

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 843–851, 2023. https://doi.org/10.1007/978-981-19-7331-4_69

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in integrating the size effect and employed to successfully tackle various problems in mechanics and structures (e.g., Georgiadis and Velgaki 2003; Gourgiotis and Georgiadis 2011; Le et al. 2022). A multi-layered arrangement of micro-structured materials is commonly found in both surface coating applications and fabrications of composite components. The presence of interfaces between any two dissimilar materials renders multi-layered systems susceptible to interfacial damages and delamination (e.g., Wiklund et al. 1999; Wieci´nski et al. 2014). To be capable of taking such failure mechanism into account in the design of micro-layered systems, understanding of their fundamental behavior with induced defects and consideration of material microstructural effects is clearly essential. While various studies were carried out, within the framework of couple stress elasticity, to investigate the size-dependent mechanical response of defects and flaws in homogeneous media (e.g., Gourgiotis and Georgiadis 2007, 2008; Georgiadis and Gourgiotis 2010, Homayounfard et al. 2018), those focusing on interfacial damages are relatively few and limited to simple settings (e.g., Gharahi et al. 2017a, 2017b). To the best of the authors’ knowledge, the modeling of interfacial defects in a micro-layered system in terms of the general displacement discontinuity is still missing in the literature and, therefore, deserves a thorough investigation. The present study aims primarily to establish a size-dependent elastic solution of a coated substrate containing an interfacial defect of a finite length. The size effect is simulated via the couple stress elasticity theory and the defect is modeled as a line of opening displacement discontinuity with the prescribed jump. Obtained results provide not only a means to investigate the influence of the material microstructural effects on the predicted elastic field in the neighborhood of the defects but also the fundamental solutions essential for the development of a solution scheme to tackle interfacial cracks in layered systems.

2 Problem Formulation Consider a two-dimensional, semi-infinite substrate coated with a thin material layer of thickness h as illustrated in Fig. 1. Both the substrate and the layer are made of homogeneous, isotropic, linearly elastic materials with or without the presence of material microstructures. The coated substrate is free of the body force and remote loading but subjected to the prescribed opening displacement along the layer-substrate interface of length 2a. Hereafter, such a line of discontinuity is termed the interfacial opening displacement discontinuity. In the present study, the attention is restricted only to the plane-strain case and a reference Cartesian coordinate system {x, y, z; O} is introduced as shown in the figure. By following the indeterminate couple stress theory proposed by Toupin (1962), Mindlin and Tiersten (1962), and Kolter (1964) and the plane-strain assumptions (i.e., ux = ux (x, y), uy = uy (x, y), uz = 0), governing equations of the elastic field for both layer and substrate can be readily established. The equilibrium equations, constitutive laws, and kinematics relating all field quantities, in the absence of body force and body couple, can be summarized as ∂σyx ∂σxx + = 0, ∂x ∂y

∂σxy ∂σyy + = 0, ∂x ∂y

∂myz ∂mxz + + σxy − σyx = 0 ∂x ∂y

(1)

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Fig. 1. Two-dimensional, semi-infinite, elastic substrate coated by thin layer of elastic material and containing interfacial opening displacement discontinuity of length 2a.

σxx =

2μ 2μ [(1 − ν)εxx + νεyy ], σyy = [νεxx + (1 − ν)εyy ] 1 − 2ν 1 − 2ν σxy = 2μεxy − 2ηωz , σyx = 2μεxy + 2ηωz

(2a) (2b)

∂ωz ∂ωz , myz = 4η (2c) ∂x ∂y     ∂uy ∂uy ∂ux 1 ∂ux 1 ∂uy + , εyy = , ωz = − = 2 ∂y ∂x ∂y 2 ∂x ∂y (3) mxz = 4η

εxx =

∂ux , εxy = εyx ∂x

where {ux , uy }, ωz , {εxx , εxy , εyx , εyy }, {σxx , σyy , σxy , σyx }, and {mxz , myz } denote nonzero components of the displacement, rotation, strain, force stress, and couple stress, respectively;  is the two-dimensional Laplace operator; μ and ν are the shear modulus and Poisson’s ratio, respectively; and η = μ 2 denotes the curvature modulus with being introduced to represent the length scale of material microstructures. Note that all field equations degenerate to the case of classical linear elasticity by taking → 0. Combining Eqs. (1)–(3) yields Navier-type equations governing the non-zero displacement components:     ∂ 2 uy ∂ 2 uy ∂ 2 ux ∂ 2 ux ∂ 2 ux 2 μ α 2 + + (α − 1) − − μ  =0 (4) ∂x ∂y2 ∂x∂y ∂y2 ∂x∂y     2u 2u ∂ 2 uy ∂ ∂ 2 uy ∂ ∂ 2 ux y x +α 2 + − + μ 2  =0 (5) μ (α − 1) ∂x∂y ∂y ∂x2 ∂x∂y ∂x2 where α = 2(1 − ν)/(1 − 2ν).

3 Solution Procedure General solutions of Eqs. (4)–(5) for both layer and substrate can be readily obtained using the method Fourier transform (e.g., Sneddon 1951) and details of derivation can

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be found in the work of Wongviboonsin et al. (2021) and Wongviboonsin et al. (2022). For brevity, the final displacement general solutions are summarized below. Layer: −|ξ |(h−y) u(l) C1 − i(κ (l) + |ξ |y)e−|ξ |(h−y) C2 + i|ξ |e−|ξ |y C3 x = −i|ξ |e

− i(κ (l) − |ξ |y)e−|ξ |y C4 −

iζ (l) −ζ (l) (h−y)/ (l) iζ (l) (l) (l) e C5 + (l) e−ζ y/ C6 (l)

(6)

−|ξ |(h−y) u(l) C1 + ξ ye−|ξ |(h−y) C2 + ξ e−|ξ |y C3 y = ξe

+ ξ ye−|ξ |y C4 + ξ e−ζ

(l) (h−y)/ (l)

C5 + ξ e−ζ

(l) y/ (l)

C6

(7)

Substrate: ∗

∗

ux(s) = i|ξ |e−|ξ |y C7 − i(κ (s) − |ξ |y∗ )e−|ξ |y C8 + ∗

∗

uy(s) = ξ e−|ξ |y C7 + ξ y∗ e−|ξ |y C8 + ξ e−ζ

iζ (s) −ζ (s) y∗ / (s) e C9 (s) (s) y ∗ / (s)

C9

(8) (9)

where overbar is used to designate Fourier transform of associated quantities; the superscript “(l)” and “(s)” are used to designate quantities of the layer and substrate, respec √ tively; ξ isthe transform parameter; i = −1 is an imaginary unit; ζ (l) = 1 + (ξ (l) )2 ; 1 + (ξ (s) )2 ; κ (l) = 3 − 4ν (l) ; κ (s) = 3 − 4ν (s) ; y∗ = y − h; and ζ (s) = Cm (m = 1, 2, . . . , 9) are independent unknown coefficients. By using the results in Eqs. (6)–(9) together with Eqs. (2)–(3), the general solutions of the rotation, force stress, and couple stress of the layer and substrate in the transform space can be readily established. The explicit expressions of those quantities can also be found in Wongviboonsin et al. (2021) and Wongviboonsin et al. (2022). (l) (l) (l) (l) (l) T (l) (l) T = {σ (l) = By defining P 0 = {σ (l) yx , σ yy , myz }y=0 , P 1 yx , σ yy , myz }y=h , U 0 (l)

(s)

(s)

(l) (l) T (l) (l) (l) T (s) (s) (s) T {u(l) x , uy , ωz }y=0 , U 1 = {ux , uy , ωz }y=h , P 0 = {σ yx , σ yy , myz }y∗ =0 , and U 0 = (s)

(s)

(s)

{ux , uy , ωz }Ty∗ =0 , we obtain 

(l)





P0 (l) P1 (s)

(l) (l)

=N C ,

(l)

U0 (l) U1 (s)

 = M (l) C (l)

P 0 = N (s) C (s) , U 0 = M (s) C (s)

(10) (11)

where C (l) = {C1 , C2 , . . . , C6 }T , C (s) = {C7 , C8 , C9 }T , and matrices N (l) , N (s) , M (l) , M (s) can be obtained explicitly from the general solutions of the displacements, rotations, force stresses, and couple stresses. By further eliminating the unknown coefficients C (l) and C (s) in Eqs. (10)–(11), it leads to the flexibility equations for the layer and substrate  (l)   (l) 

 (l)  (l) (l) U0 P F P0 F tt 0 tb = F(l) = (12) (l) (l) (l) (l) (l) F F U1 P1 P1 bt bb

Interfacial Displacement Discontinuity in Coated Substrate (s)

(s)

U 0 = F(s) P 0

847

(13)

where F(l) = M (l) (N (l) )−1 and F(s) = M (s) (N (s) )−1 are the flexibility matrices of (l) (l) (l) (l) the layer and substrate, respectively, and Ftt , Ftb , Fbt , Fbb are sub-matrices of F(l) . The traction-free conditions on the surface of the layer and the conditions on the layersubstrate interface can be expressed as (l)

P0 = 0 (l)

(s)

I

(s)

(14) (l)

P 1 = P 0 ≡ P , U 0 − U 1 = U

(15)

where 0 is a zero vector and U = {0, uy , 0}T with uy denotes the prescribed opening displacement along the interface over the interval [−a, a]. Combining Eqs. (12)–(13) together with the boundary and interface conditions given by Eqs. (14)–(15), it yields

    (l) (l) (l) 0 Ftt Ftb U0 = (16) I (l) (l) P Fbt Fbb − F(s) −U (l)

I

The unknown vectors P and U 0 can be determined first by solving the system of linear algebraic equations Eq. (16) and the unknown coefficients C (l) and C (s) are, subsequently, computed from Eqs. (10)–(11). Finally, the elastic fields of the layer and substrate are obtained by Fourier transform inversion and Gaussian-Legendre Quadrature.

4 Results and Discussion In the numerical study, three different types of the opening displacement along the interfacial displacement discontinuity (i.e., the interval [−a, a]) are considered:  Type-I : uy = b0 1 − (x/a)2 , x ∈ [−a, a] (17) Type-II :

uy = b0 [1 − (x/a)2 ], x ∈ [−a, a]

(18)

Type-III :

uy = b0 [1 − (x/a)2 ]2 , x ∈ [−a, a]

(20)

where b0 denotes the opening displacement at the center of the displacement discontinuity. Note that the opening displacements of Type-I, Type-II, Type-III are chosen to represent the crack-like discontinuity with infinite, finite, and zero gradients at the tips, respectively. To verify the proposed scheme, computed results are compared with those for the case of a straight opening displacement discontinuity of Type-II buried in a full plane of a classical homogeneous, isotropic, linear elastic material. To simulate this particular

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case, the layer thickness h is chosen to be sufficiently large (i.e., h/a = 1000) to resemble the full plane; material properties of the layer and substrate are taken to be identical; and the length scales (l) , (s) → 0 are considered. The normalized normal traction along the upper face of the displacement discontinuity and the normalized vertical stress along the layer-substrate interface are reported in Fig. 2 for ν = 0.3 and b0 /a = 1. It is seen that the computed results exhibit an excellent agreement with the exact solutions; in particular, the difference is nearly indistinguishable in the plots. 0.8

0.4 Exact solution

0.6 0.3

0.2

σyy / 2 μ

t (x,h +) / 2 μ

0.4

0.0

0.2

0.1

-0.2 0.0 -0.4 Exact solution -0.6 -1.0

-0.1 -0.5

0.0 x/a (a)

0.5

1.0

-5 -4 -3 -2 -1

0 1 x/a (b)

2

3

4

5

Fig. 2. Results for (a) normalized normal traction t(x, h+ )/2μ on the upper face of displacement discontinuity and (b) normalized vertical stress σyy /2μ along layer-substrate interface for ν = 0.3 and b0 /a = 1.

Consider, next, the displacement discontinuity buried in a homogeneous half-plane. To simulate such case, the material properties and length scales of the layer and substrate are taken to be identical, i.e., μ(l) = μ(s) = μ, ν (l) = ν (s) = ν, and (l) = (s) = . The normalized vertical stresses induced in the neighborhood of the right tip of the discontinuity for all three types of the opening displacement are illustrated in Fig. 3 for ν = 0.3, b0 /a = 1, h/a = 1, and both the classical case ( /a → 0) and couple stress elasticity ( /a = 1). It is evident that the couple stress theory predicts the significantly higher vertical stress ahead of the tips of the discontinuity tip and this emphasizes the significant role of the material microstructures. It is worth noting that the presence of couple stresses does not alter the singularity characteristic of the stress field at the tip of the displacement discontinuity from the classical case; in particular, the couple stress theory still predicts the singular stress at the tip if the opening displacement possesses a non-zero gradient at that tip. Finally, the case of opening displacement discontinuity embedded along the interface of the coating layer the substrate is investigated. In the numerical study, the shear modulus of the coating layer is chosen to be twice of that of the substrate (i.e., μ(l) /μ(s) = 2), Poisson’s ratio and material length scale are taken to be the same (i.e., ν (l) = ν (s) = ν, (l) = (s) = ); and the aspect ratio h/a = 1 is considered. The normalized vertical

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2.8 Type I Type II Type III Classical elasticity Couple stress elasticity

2.3

σyy / 2 μ

1.8 1.3 0.8 0.3 -0.2 1.0

1.2

1.4

1.6

1.8

2.0

x/a Fig. 3. Normalized vertical stress σyy /2μ along the line of opening displacement discontinuity embedded in a homogeneous half-plane. Results are reported for ν = 0.3, b0 /a = 1, h/a = 1, and both classical case ( /a → 0) and couple stress elasticity ( /a = 1).

stresses along the line of the discontinuity are reported in Fig. 4 for both classical ( /a → 0) and couple stress ( /a = 1) cases. Evidently, similar trend to the case of displacement discontinuities buried in a homogeneous half plane is observed. While the presence of couple stresses (or, equivalently, the material microstructures) does not change the singularity behavior, it clearly renders the material stiffer from the classical case. Specifically, larger forces are generally required to produce the same opening displacement.

5 Conclusion The elastic field induced by an interfacial opening displacement discontinuity in a thinlayer-coated substrate is investigated within the framework of couple stress elasticity theory. A simple procedure based on Fourier transform and flexibility equation methods is implemented to construct the solution of the layer-substrate system for arbitrary opening displacement profiles. Results from an extensive numerical study not only confirms the validity of the proposed solution scheme but also demonstrate the significant role of couple stresses on the predicted elastic field. While, in the prediction, the couple stress theory does not alter the singular characteristic of the stress at the tip of the displacement discontinuity from the classical case, the stiffening effect is clearly pronounced. More in-depth investigations on this aspect and the size dependent behavior are still required. It is worth noting that fundamental results established in the present study form the essential basis for the development of a solution scheme for tackling interfacial cracks in layered media with consideration of material microstructures.

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2.8 Type I Type II Type III Classical elasticity Couple stress elasticity

2.3

σyy / 2 μ (s)

1.8 1.3 0.8 0.3 -0.2 1.0

1.2

1.4

1.6

1.8

2.0

x/a Fig. 4. Normalized vertical stress σyy /2μ(s) along the interface induced by interfacial opening displacement discontinuity in a layer-substrate system. Results are reported for μ(l) /μ(s) = 2, ν = 0.3, b0 /a = 1, h/a = 1, and both classical ( /a → 0) and couple stress ( /a = 1) cases. Acknowledgements. The research project is supported by the Second Century Fund (C2F), Chulalongkorn University; and the National Research Council of Thailand [grant number NRCT5-RSA63001-17].

References Georgiadis, H.G., Velgaki, E.G.: High-frequency Rayleigh waves in materials with micro-structure and couple-stress effects. Int. J. Solids Struct. 40(10), 2501–2520 (2003) Georgiadis, H.G., Gourgiotis, P.A.: An approach based on integral equations for crack problems in standard couple-stress elasticity. In: Maugin, G.A., Metrikine, A.V. (eds.) Mechanics of Generalized Continua: One Hundred Years After the Cosserats, pp. 253–262. Springer New York, New York, NY (2010) Gharahi, A., Dai, M., Schiavone, P.: Screw dislocation in a thin film–substrate in couple stress elasticity. Zeitschrift für angewandte Mathematik und Physik 68(2), 1–23 (2017). https://doi. org/10.1007/s00033-017-0774-z Gharahi, A., Dai, M., Wang, G.-F., Schiavone, P.: Interaction of a screw dislocation with a bimaterial interface in anti-plane couple stress elasticity. Math. Mech. Solids 23(4), 651–666 (2017) Gourgiotis, P.A., Georgiadis, H.G.: Distributed dislocation approach for cracks in couple-stress elasticity: shear modes. Int. J. Fract. 147(1), 83–102 (2007) Gourgiotis, P.A., Georgiadis, H.G.: An approach based on distributed dislocations and disclinations for crack problems in couple-stress elasticity. Int. J. Solids Struct. 45(21), 5521–5539 (2008) Gourgiotis, P.A., Georgiadis, H.G.: The problem of sharp notch in couple-stress elasticity. Int. J. Solids Struct. 48(19), 2630–2641 (2011)

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Homayounfard, M., Daneshmehr, A., Salari, A.: A finite element formulation for crack problem in couple-stress elasticity. Int. J. Appl. Mech. 10(02) Koiter, W.: Couple stresses in the theory of elasticity. Proc. Koninklijke Nederl. Akaad. van Wetensch 67 (1964) Le, T.M., Wongviboonsin, W., Lawongkerd, J., Bui, T.Q., Rungamornrat, J.: Influence of surface and couple stresses on response of elastic substrate under tilted flat indenter. Appl. Math. Model. 104, 644–665 (2022) Mindlin, R.D., Tiersten, H.F.: Effects of couple-stresses in linear elasticity. Arch. Ration. Mech. Anal. 11(1), 415–448 (1962) Sneddon, I.N.: Fourier Transforms, 1st edn. McGraw-Hill, New York (1951) Toupin, R.A.: Elastic materials with couple-stresses. Arch. Ration. Mech. Anal. 11(1), 385–414 (1962) Wieci´nski, P., Smolik, J., Garbacz, H., Kurzydłowski, K.J.: Failure and deformation mechanisms during indentation in nanostructured Cr/CrN multilayer coatings. Surf. Coat. Technol. 240, 23–31 (2014) Wiklund, U., Gunnars, J., Hogmark, S.: Influence of residual stresses on fracture and delamination of thin hard coatings. Wear 232(2), 262–269 (1999) Wongviboonsin, W., Gourgiotis, P.A., Van, C.N., Limkatanyu, S., Rungamornrat, J.: Size effects in two-dimensional layered materials modeled by couple stress elasticity. Front. Struct. Civ. Eng. 15(2), 425–443 (2021). https://doi.org/10.1007/s11709-021-0707-y Wongviboonsin, W., Le, T.M., Lawongkerd, J., Gourgiotis, P.A., Rungamornrat, J.: Microstructural effects on the response of a multi-layered elastic substrate. Int. J. Solids Struct. 241 (2022) Zisis, T.: Burmister’s problem extended to a microstructured layer. J. Mech. Mater. Struct. 13(2), 203–223 (2018)

Mechanical Properties of Lattice Specimens Having a Triangular Pattern with Different Relative Densities Itthidet Thawon1 , Pana Suttakul2(B) , Thongchai Fongsamootr2 , and Yuttana Mona2 1 Master’s Degree Program in Mechanical Engineering, Faculty of Engineering, Chiang Mai

University, Chiang Mai 50200, Thailand [email protected] 2 Department of Mechanical Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai 50200, Thailand {pana.s,thongchai.f,yuttana.mona}@cmu.ac.th

Abstract. This study experimentally investigates the mechanical properties of lattice specimens with triangular unit cells using a tensile test, including Young’s modulus and yield strength. The lattice specimens made of 316L stainless steel are fabricated by a metal 3D printer. The mechanical properties of the lattice specimens with different relative densities are studied. Formulas of the normalized Young’s modulus and normalized yield strength of the lattice structure obtained from the literature are used to validate the experimental results. The discrepancies between the normalized results obtained from the experiment and the formulas are also discussed. Keywords: 316L stainless steel · Lattice structure · Triangular unit cell · Young’s modulus · Tensile test

1 Introduction Lightweight lattice structures have many applications because of their easily alterable mechanical properties, which are directly dependent upon the topologies and sizes of their unit cells. Many researchers have explored the mechanical properties of lattice structures (Sam et al. 2016; Suttakul et al. 2019; Wang and McDowell 2004). For 2D lattices, some unit-cell topologies, such as triangular, hexagonal, and square unit cells, have been widely used in real practice. A triangular unit cell is a popular pattern for lattice structures among various unit-cell topologies. It yields 2D orthotropic material properties, which help design match specific applications, especially aircraft and spacecraft. Experimental and numerical studies on the mechanical behavior of triangular lattice structures have been done by Gu et al. (2018), Li et al. (2020), Limpitipanich et al. (2021), Liu and Liang (2012), and Suttakul et al. (2021a). Nowadays, additive manufacturing (AM) or 3D printing is widely used for fabricating complex parts. An AM part is fabricated additively layer-by-layer to form the shape designed by a digital file. Thus, AM technologies can help reduce consuming raw © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 852–859, 2023. https://doi.org/10.1007/978-981-19-7331-4_70

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materials and manufacturing time. These technologies can produce parts with different densities for desired lightweight parts. The density of an AM part can be set through the parameters of its infill pattern. Triangular, square, and hexagonal patterns are widely used as infill patterns in 3D printing. Recently, extrusion-based metal additive manufacturing (MAM) technologies have played a greater role in improving metal manufacturing processes, enabling low volume production and economical metal parts. Since MAM is new for manufacturing sectors, only small to medium parts can be fabricated by these technologies. For this reason, MAM technologies are suitable for home or small workshops, in which most parts manufactured exclude engineering considerations. This study aims to investigate the mechanical properties of the MAM parts with different infill densities. The mechanical properties of MAM parts having a triangular infill pattern, including Young’s modulus and yield strength, are investigated using tensile tests. According to the ASTM standard, the MAM parts are fabricated as specimens made of 316L stainless steel. The specimens having a triangular infill pattern with different densities are considered. Finally, the normalized values of Young’s modulus proposed in the literature (Gu et al. 2018; Sam et al. 2016; Wang and McDowell 2004) are used to compare the experimental results in this study. The normalized yield strength of the specimens with different infill densities is also reported and discussed.

2 Effective Elastic Properties An inhomogeneous solid in which the inhomogeneities are distributed periodically can be considered as a lattice structure. In artificial lattice structures, such periodic patterns are used to help reduce the amounts of materials used compared to making original solids while retaining the desired properties of the original solids. If a lattice structure consists of a substantial number of unit cells, then the effective properties of the structure can be determined. Since an infill pattern of MAM parts is periodic, the specimens in this study can be treated as lattice structures. The elastic properties of triangular infill specimens can be obtained by considering the effective elastic properties of lattice structures with the triangular unit cells. Figure 1 shows the lattice structure with triangular unit cells, in which l denotes the characteristic length of the unit cells while b×t denotes cross-sections of the unit-cell struts. Many studies have proposed methods to determine the effective properties of lattice structures. Analytical forms of the effective Young’s modulus of the lattice structure with the triangular pattern were derived by Wang and McDowell (2004). The normalized effective Young’s modulus is written as E∗ = 0.33 Eρ

(1)

where E ∗ and E are the effective Young’s modulus of the infill specimens and Young’s modulus of the base material. In addition, ρ denotes√the relative density of the lattice structure with the triangular pattern that is equal to 2 3b/l.

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Fig. 1. Triangular unit cell.

Similarly, the normalized yield strength of the infill specimens can be expressed as σy∗ σy ρ

= 0.5

(2)

where σy∗ denotes the yield strength of the infill specimens while σy denotes the yield strength of the base material. In a study by Sam et al. (2016), a generic symbolic finite element program is used to derive closed-form effective Young’s modulus of lattice structures with triangular unit cells using the strain-energy-based homogenization method. The normalized effective Young’s modulus is expressed as l 2 + b2 E∗ = 2 Eρ 3l + b2

(3)

3 Experimental Study 3.1 Specimen Fabrication The 316L stainless steel specimens were fabricated using MAM technology by Studio System Desktop Metal 3D printer. The geometry and dimension of the specimens were considered according to ASTM E8/E8M standard, sheet type with a thickness of 3 mm. The MAM full-solid and infill parts were created as specimens with the same geometry and dimension. The infill specimens with a triangular pattern, as shown in Fig. 2, were fabricated by varied infill densities. The infill densities of 16, 20, and 24% were set via the printer setting, in which the characteristic length l is 3.0 mm, 2.4 mm, and 2.0 mm, respectively. The cross-sections of all struts in the lattice structures are rectangular sections of 0.5 × 3.0 mm. The infill specimens were created without sides and top/bottom

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wall thicknesses for solely determining the mechanical properties of the triangular lattice structures. A ratio between the weight of infill specimens and the full-solid one was defined as the relative densities. Table 1 shows the average relative densities of the infill specimens.

16%

20%

24%

Fig. 2. The 316L stainless steel specimens with different infill densities.

Table 1. Relative density of specimens. Infill density (%)

Weight (g)

Relative density (%) Mean

SD

16

38.49

50.45

0.05

20

47.22

61.89

0.09

24

55.58

72.85

0.15

Full-solid counterpart

76.29

100 equivalent

Note that the percentage of infill density is a printing parameter feature in the printer setting, while the relative density is computed by the actual weight of a specimen per its full-solid counterpart 3.2 Tensile Test According to the ASTM E8/E8M standard, a tensile test was carried out by Instron 8802 universal testing machine to obtain Young’s modulus and yield strength of the 316L stainless steel specimens. The tensile tests were operated in displacement control with 1.0 mm/min speed before the yield point and 5.0 mm/min speed after the yield point. Extensometer was used to measure strain during the elastic region, as shown in Fig. 3, and then removed after the yield point. In the plastic region, the strain was measured by crosshead displacement. Three sets of full-solid and infill specimens were tested to achieve sufficiently correct data for each relative density. Note that the full-solid

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specimens, considered 100% relative density equivalent, were tested to determine the mechanical properties of the base material.

Fig. 3. Testing setup and strain measurement.

4 Results and Discussion In this study, 316L stainless steel is used as the base material of the specimens. Young’s modulus and yield strength of the base material are obtained from the tensile test of the full-solid specimens. The average values of Young’s modulus and yield strength are 169.00 and 157.30 MPa, with standard deviation values of 4.00 and 4.41, respectively. Figure 4 illustrates the stress-strain relationship of selected triangular infill specimens of each relative density. As expected, the specimen with higher density yields higher Young’s modulus and yield strength. The average Young’s modulus of the specimens with the relative densities of 50.45, 61.89, and 72.85% is 28.57, 48.42, and 60.70 GPa, with standard deviation values of 2.71, 4.14, and 2.05, respectively. Additionally, the average yield strength of the specimens with relative densities of 50.45, 61.89, and 72.85% is 41.80, 52.22, and 64.24 MPa, with standard deviation values of 1.62, 1.05, and 1.20, respectively. Table 2 shows the normalized Young’s modulus of the specimens with different relative densities obtained from the experiment in this study and the literature. The normalized Young’s modulus values from Sam et al. (2016), and Wang and McDowell (2004) have been obtained from the closed-form effective Young’s modulus of lattice structures with triangular unit cells. The normalized Young’s modulus values from Gu et al. (2018) have been obtained from an experimental study. It can be seen that at the relative density with low values, the experimental results show good agreement with the results from the closed forms, i.e., ρ = 50.45% in this

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Fig. 4. Stress-strain relationship of the infill specimens.

Table 2. Comparison of the normalized Young’s modulus of the infill specimens. Relative density, ρ (%)

Normalized young’s modulus, E ∗ /(Eρ) This study Mean

SD

50.45

0.33

0.03

61.89

0.46

0.04

72.85

0.49

0.04

Gu et al. (2018)

Wang and McDowell (2004)

Sam et al. (2016)

0.35 (ρ = 34.64%)

0.33

0.34

0.33

0.34

0.33

0.35

study and ρ = 34.65% in the study by Gu et al. (2018). In contrast, the discrepancy between the results from the experiment and closed forms is considerable because the closed forms were derived excluding consideration of the shear deformation effect of the unit-cell struts, which is more significant when the ratio between l/b increases or the relative density in a considered volume and dimension increases (Suttakul et al. 2021b). Table 3 shows the normalized yield strength of the specimens with different relative densities obtained from the experiment in this study and the literature. The normalized yield strength values from Wang and McDowell (2004) were obtained from the closed form, while the normalized yield strength values from Gu et al. (2018) were obtained from an experimental study. The normalized yield strength values obtained from this study present larger values than those from the literature, which increases related to the relative density. Nevertheless, good agreement between both results is observed.

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Relative density, ρ (%)

  Normalized yield strength, σy∗ / σy ρ This study Mean

SD

50.45

0.53

0.02

61.89

0.54

0.01

72.85

0.56

0.02

Gu et al. (2018)

Wang and McDowell (2004)

0.48 (ρ = 34.64%)

0.50

0.50 0.50

5 Conclusions In this study, Young’s modulus and yield strength of MAM specimens with a triangular pattern were investigated by tensile tests. The triangular infill specimens made of 316L stainless steel were fabricated by a metal 3D printer. The material behavior of the specimens with different infill densities was studied. Young’s modulus and yield strength vary depending on the relative density. The experimental results in this study are compared to results from the literature obtained from closed forms and experiments using the normalized Young’s modulus and normalized yield strength. The normalized Young’s modulus of the infill specimens with low relative density values shows good agreement between the results from experiments and closed forms. The discrepancy between both results is more significant when the relative density increases. This study’s normalized yield strength values show larger values than those from the literature, showing good agreement between both results. The closed forms obtained from the literature can be used to predict Young’s modulus and yield strength of the infill specimens approximately, while the closed forms can be used to accurately predict Young’s modulus of the specimens with a low relative density. Acknowledgements. The first author has received the TA/RA scholarship from the Graduate School, Chiang Mai University. This work was supported by the Faculty of Engineering, Chiang Mai University.

References ASTM E8/E8M-16a: Standard Test Methods for Tension Testing of Metallic Materials. ASTM International, West Conshohocken, PA, USA Gu, H., Pavier, M., Shterenlikht, A.: Experimental study of modulus, strength and toughness of 2D triangular lattices. Int. J. Solids Struct. 152–153, 207–216 (2018) Li, Y., Pavier, M.J., Coules, H.: Fatigue properties of aluminium triangular lattice plates. Procedia Struct. Integrity 28, 1148–1159 (2020) Limpitipanich, P., Suttakul, P., Mona, Y., Fongsamootr, T.: Material behavior of 2D steel lattices with different unit-cell patterns. Mater. Sci. Forum 1046, 15–21 (2021) Liu, X., Liang, N.: Effective elastic moduli of triangular lattice material with defects. J. Mech. Phys. Solids 60, 1722–1739 (2012)

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Sam, P., Nanakorn, P., Theerakittayakorn, K., Suttakul, P.: Closed-form effective elastic constants of frame-like periodic cellular solids by a symbolic object-oriented finite element program. Int. J. Mech. Mater. Des. 13(3), 363–383 (2016). https://doi.org/10.1007/s10999-016-9342-5 Suttakul, P., Chaichanasiri, E., Nanakorn, P.: Design of 2D-lattice plates by weight efficiency. Eng. J. 25, 13–31 (2021) Suttakul, P., Fongsamootr, T., Vo, D., Nanakorn, P.: Effects of shear deformation of struts in hexagonal lattices on their effective in-plane material properties. Mater. Sci. Forum, 2021b. Trans Tech Publ, 193–198 Suttakul, P., Nanakorn, P., Vo, D.: Effective out-of-plane rigidities of 2D lattices with different unit cell topologies. Arch. Appl. Mech. 89(9), 1837–1860 (2019). https://doi.org/10.1007/s00 419-019-01547-8 Wang, A.J., Mcdowell, D.L.: In-plane stiffness and yield strength of periodic metal honeycombs. J. Eng. Mater. Technol. 126, 137–156 (2004)

Analytical Solution for Circular Microbeams with Strain Gradient Elasticity Zwe Yan Aung, Duy Vo, Toan Minh Le, and Jaroon Rungamornrat(B) Center of Excellence in Applied Mechanics and Structures, Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand [email protected]

Abstract. In the analysis of skeletal structures, circular beams are widely studied since their simple geometry allows the derivation of analytical solutions which are useful tools to assess the accuracy and efficiency of numerical ones. With such feature, the present study aims mainly to establish the key governing equations, boundary conditions, and corresponding analytical solutions of circular microbeams within the framework of strain gradient elasticity and TimoshenkoEhrenfest beam theories. It is worth highlighting that the curviness is also included in the formulation, and its influence on the predicted responses is explored. A solution procedure is implemented to establish the analytical solutions for general loading and boundary conditions. A representative semi-circular beam is subsequently analyzed with the adopted procedure, and a selected set of results is reported to illustrate the effects of the curviness. Keywords: Circular microbeams · Strain gradient elasticity · Timoshenko-Ehrenfest beam theory · Analytical solutions · Influence of curviness

1 Introduction Experimental investigations reveal the size-dependent behavior of objects at micron scale (Lam et al. 2003), and the classical Cauchy’s continuum theory fails to describe such behavior. This shortcoming necessitates the development of alternative continuum theories for the better prediction of responses of micro-sized objects. Recently, Mindlin’s strain gradient theory (Mindlin 1964) and its variants (Altan and Aifantis 1997; Lam et al. 2003) have gained a huge attention. Amongst these theories, the simplified strain gradient (SSG) (Altan and Aifantis 1997) theory is prevalent since it involves only one additional material parameter. The SSG theory has been used for the analysis of solids (Niiranen et al. 2016; Hosseini and Niiranen 2022), microplates (Niiranen et al. 2017), microshells (Balobanov et al. 2019), and microbeams (Balobanov and Niiranen 2018; Niiranen et al. 2019; Tran and Niiranen 2020). Such proposed formulations are proved to be able to simulate the size-dependent responses. To authors’ best observations, the analysis of curved microbeams having general geometry is not yet performed within the framework of the SSG theory. The present study © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 860–872, 2023. https://doi.org/10.1007/978-981-19-7331-4_71

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aims mainly to address this deficiency for circular microbeams. Concretely, the governing equations and boundary conditions are derived by using SSG and Timoshenko-Ehrenfest beam theories. The derivation fully includes the curviness to define the cross-sectional characteristics. A procedure is presented for determining the analytical solutions with arbitrary loading and boundary conditions. A semi-circular microbeam is analyzed to demonstrate the size-dependent response and effect of the curviness.

2 Kinematic Descriptions of Circular Beams with Timoshenko-Ehrenfest Beam Theory The configuration of a representative circular beam having a rectangular cross section of width b and height h is depicted in Fig. 1.The beam axis is parameterized by the arc 1 length parameter  1S , and the position vector of an arbitrary point Q0 on the beam axis is denoted by R0 S . The unit tangent vector A1 and normal vector A2 of the beam axis at the point Q0 are identified as     dR0 S 1 0 −1 A1 = A2 = (1) A1 = A1 . 1 0 dS 1 In subsequent derivations, primes denote derivatives with respect to the arc length S 1 . One should note the orthonormality between A1 and A2 , and thus, these vectors are used as base vectors of a local Cartesian coordinate system.

Fig. 1. Configuration of a typical circular beam.

On the same cross section containing the point Q0 , a generic point Q is identified with the position vector as     (2) R S 1 , S 2 = R0 S 1 + S 2 A2 .

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Here, S 2 denotes the parameter along the vector A2 , i.e., −0.5h ≤ S 2 ≤ 0.5h. Differentiations of Eq. (2) yield the covariant vectors at the point Q as     ∂R S 1 , S 2 ∂R S 1 , S 2 2  = A1 + S A2 G2 = = A2 . (3) G1 = ∂S 1 ∂S 2 Since the beam axis is a planar curve, the following relations are valid, i.e., A1 = κA2 A2 = −κA1

(4)

where κ can be referred to as the curvature of the beam axis. By substituting Eq. (4) into Eq. (3), the alternative expression of G1 is derived as   G1 = 1 − S 2 κ A1 . (5) The contravariant vectors at the point Q can be defined as (Vo and Nanakorn 2020) G1 =

G1 1 A1 G2 = G2 = A2 . = G1 · G1 1 − S 2κ

(6)

Consequently, the gradient of an arbitrary quantity w at the point Q is written as (Lebedev et al. 2010) ∂w ∂w 1 ∂w ∂w A1 ⊗ 1 + A2 ⊗ 2 . + G2 ⊗ 2 = (7) 1 2 ∂S ∂S 1−S κ ∂S ∂S   The displacement vector of the point Q0 is denoted by u0 S 1 . The component form   of u0 S 1 in the local coordinate system is expressed as       u0 S 1 = u01 S 1 A1 + u02 S 1 A2 . (8) ∇ ⊗ w = G1 ⊗

The displacement vector of the point Q is determined as (Vo et al. 2021)     u S 1 , S 2 = u0 − S 2 φA1 = u01 − S 2 φ A1 + u02 A2

(9)

with φ being the cross-sectional rotation. In the Timoshenko-Ehrenfest beam theory, the cross-sectional rotation φ is independent of the deformation of the beam axis. Consequently, the displacement of the beam axis u0 and the cross-sectional rotation φ are commonly considered as kinematic unknowns in Timoshenko-Ehrenfest beam formulations.

3 Simplified Strain Gradient Elasticity for Circular Microbeams 3.1 Expression of Strain Energy Density By simplifying the Form II of Mindlin’s strain gradient theory (Mindlin 1964), the strain energy density of an isotropic linear elastic body can be expressed as (Altan and Aifantis 1997) W=

. 1 . 1 1 1 σ : ε + τ..γ = σ : ε + g 2 ∇ ⊗ σ..∇ ⊗ ε. 2 2 2 2

(10)

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Here, deformations of the body are characterized by the conventional infinitesimal strain tensor ε and micro-deformation gradient tensor γ, i.e., ε=

1 ∇ ⊗ u + (∇ ⊗ u)T γ = ∇ ⊗ ε. 2

(11)

The energy conjugates of ε and γ are, respectively, the classical Cauchy stress tensor σ and double stress tensor τ. These tensorial quantities are obtained as σ=

∂W ∂W = 2με + λtr(ε)I τ = = g 2 ∇ ⊗ σ. ∂ε ∂γ

(12)

For material parameters, μ and λ are so-called Lamé’s constants, whereas g is referred to as the gradient parameter. 3.2 Strain and Stress Measures The component form of the tensors ε and γ in the local coordinate system can be written as ε = εαβ Aα ⊗ Aβ γ = γijk Ai ⊗ Aj ⊗ Ak .

(13)

By substituting Eqs. (4), (7), and (9) into Eq. (11), non-zero components of ε and γ are derived as 11 − S 2 K11 12  ε12 = ε21 =  (14) 1 − S 2κ 2 1 − S 2κ  2  2 X111 + S 2 Y111 + S 2 Z111 X112 + S 2 Y112 + S 2 Z112 = γ112 = γ121 =   3 3 1 − S 2κ 1 − S 2κ (15) ε11 =

γ111

γ122 =

X122 + S 2 Y122 X211 + S 2 Y211 γ211 =   3 3 1 − S 2κ 1 − S 2κ γ212 = γ221 =

X212 + S 2 Y212  3 . 1 − S 2κ

(16)

(17)

In above definitions, the generalized strain measures are expressed in terms of kinematic unknowns as   11 = u01 − κu02 K11 = φ  12 = κu01 + u02 −φ

(18)

    X111 = 11 − κ12 Y111 = −K11 − κ11 + κ 2 12 Z111 = κK11

(19)

1  1  X112 = κ11 + 12 Y112 = −κK11 − κ 2 11 − κ12 Z112 = κ 2 K11 2 2

(20)

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X122 = κ12 Y122 = −κ 2 12 X211 = κ11 − K11 Y211 = −κ 2 11 + κK11 X212 =

1 1 κ12 Y212 = − κ 2 12 . 2 2

(21) (22)

Since the curvature of circular microbeams is constant, its derivatives vanish in the expressions of generalized strain measures. Regarding the tensors σ and τ, their corresponding components with the non-zero ones of ε and γ can be determined by considering Eqs. (12), and (14)–(17). The cross-sectional stress resultants are defined by the following integrations over the cross section as



C C C = σ11 dA M11 = − σ11 S 2 dA N12 = σ12 dA (23) N11 A

A

Q111 = g 2 A

P111 = g 2 A

τ111

 1 − S 2κ

W112 = g

A

A

Q211 = g 2 A

Q212 = g 2 A

A

τ111 S 2

 2 dA 1 − S 2κ

(24)

(25)

 2 τ112 S 2  2 dA 1 − S 2κ

(26)

τ122 S 2 2 dA  1 − S 2κ

(27)

τ211 S 2  2 dA 1 − S 2κ

(28)

τ212 S 2  2 dA 1 − S 2κ

(29)

A



τ112 S 2

 2 dA P112 = g 1 − S 2κ

Q122 = g 2

2 2 dA W111 = g

 2

τ111 S 2 τ112 2   2 dA Q112 = g 2 dA 2 1−S κ 1 − S 2κ

2

A



τ122

 1 − S 2κ

2 A

2 2 dA W122 = g

τ211 2  2 dA W211 = g 2 1−S κ τ212 2  2 dA W212 = g 2 1−S κ

A

A

A

Here, dA = bdS 2 represents the differential area of the cross section, A denotes the area of the cross section, and b is the cross-sectional width. 3.3 Virtual Work Principle The internal virtual work can be expressed as δint = δW =



 . σ : δε + g 2 ∇ ⊗ σ..∇ ⊗ δε dV . V

(30)

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  where dV = 1 − S 2 κ dAdS 1 denotes the differential volume. With the aid of Eqs. (13)– (29), the expression in terms of generalized strain measures and cross-sectional stress resultants can be easily obtained. For the sake of conciseness, the lengthy expression is omitted. The external virtual work for beams can be specifically defined as

L δext =

(f1 δu01 + f2 δu02 + mδφ)dS1 0

     L + F1 δu01 + F2 δu02 + M δφ + D1 δu01 + D2 δu02 + T δφ . 0

(31)

Here, f1 and f2 are the components of the distributed force vector, i.e., f = f1 A1 + f2 A2 , whereas m represents the distributed moment. In analogous, F1 and F2 are the components of the concentrated force vector, i.e., F = F1 A1 + F2 A2 , whereas M is the concentrated moment prescribed at the ends of the beam. The concentrated loads associated with the derivatives of kinematic unknowns are denoted by D1 , D2 , and T . Eventually, the virtual work principle is stated as δint − δext = 0.

(32)

4 Governing Equations and Boundary Conditions The virtual work principle serves as a means to derive the governing equations and boundary conditions. Firstly, the integration by parts is performed, then the corresponding terms with the common virtual kinematic unknowns are grouped. Finally, the fundamental theorem of the variational calculus is employed to yield the governing equations and boundary conditions. 4.1 Governing Equations Governing equations of circular microbeams are derived as • Equation corresponding to δu01 :    − [(λ + 2μ)AC + g 2 λκ 2 AH + κ 2 I H g 2 (λ + 2μ)(AH − 2κH H + κ 2 I H )u01       2 4  H + 5g μκ A + κ 2 I H + 15g 2 μκ 2 AH + κ 2 I H − 30g 2 μκ 3 H H − 2g 2 λκ 3 H H u01       − 10g 2 μκ 5 H H + μκ 2 AC u01 − g 2 λκ AH + κ 2 I H + 7g 2 μκ AH + κ 2 I H      − 14g 2 μκ 2 H H − 2g 2 λκ 2 H H u02 + λκAC + 3μκAC + g 2 λκ 3 AH + κ 2 I H      2 + 15g 2 μκ 3 AH + κ 2 I H − 30g 2 μκ 4 H H − 2g 2 λκ 4 H H u02 + 2g (λ + 2μ)κI H   − g 2 (λ + 2μ)H H − g 2 (λ + 2μ)κ 2 J H φ  + (λ + 2μ)H C + 7g 2 μκAH   − 9g 2 μκ 3 I H + g 2 λκ AH + κ 2 I H − 6g 2 μκ 2 H H − 2g 2 λκ 2 H H + 8g 2 μκ 4 J H ]φ     − 5g 2 μκ 3 AH + κ 2 I H − 10g 2 μκ 4 H H + μκAC φ = f1 .

(33)

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• Equation corresponding to δu02 :      g 2 λκ AH + κ 2 I H + 7g 2 μκ AH + κ 2 I H − 14g 2 μκ 2 H H − 2g 2 λκ 2 H H u01     − [λκAC + 3μκAC + 15g 2 μκ 3 AH + κ 2 I H + g 2 λκ 3 AH + κ 2 I H − 30g 2 μκ 4 H H      + g 2 μ AH + κ 2 I H − 2g 2 μκH H u − μAC − 2g 2 λκ 4 H H u01 02      + g 2 λκ 2 AH + κ 2 I H + 15g 2 μκ 2 AH + κ 2 I H − 30g 2 μκ 3 H H − 2g 2 λκ 3 H H ]u02     + [6g 2 μκ 4 AH + κ 2 I H + g 2 λκ 4 AH + κ 2 I H − 12g 2 μκ 5 H H − 2g 2 λκ 5 H H   + (λ + 2μ)κ 2 AC u02 − g 2 μAH − 2g 2 λκ 2 I H − 11g 2 μκ 2 I H + g 2 λκH H   + g 2 λκ 3 J H + 4g 2 μκH H + 6g 2 μκ 3 J H φ  + (λ + 2μ)κH C + 11g 2 μκ 2 AH   + 3g 2 μκ 4 I H + g 2 λκ 2 AH + κ 2 I H − 18g 2 μκ 3 H H − 2g 2 λκ 3 H H + 4g 2 μκ 5 J H



+ μAC ]φ  = f2 .

(34)

• Equation corresponding to δφ: 

 2g 2 (λ + 2μ)κI H − g 2 (λ + 2μ)H H − g 2 (λ + 2μ)κ 2 J H u01   + [g 2 λκ AH + κ 2 I H + 7g 2 μκAH − 9g 2 μκ 3 I H − 2g 2 λκ 2 H H − 6g 2 μκ 2 H H    − [5g 2 μκ 3 AH + κ 2 I H − 10g 2 μκ 4 H H + 8g 2 μκ 4 J H + (λ + 2μ)H C ]u01 + μκAC ]u01 + [−2g 2 λκ 2 I H − 11g 2 μκ 2 I H + g 2 μAH + g 2 λκH H + 4g 2 μκH H    − [g 2 λκ 2 AH + κ 2 I H + 11g 2 μκ 2 AH + 3g 2 μκ 4 I H + g 2 λκ 3 J H + 6g 2 μκ 3 J H ]u02  − 2g 2 λκ 3 H H − 18g 2 μκ 3 H H + 4g 2 μκ 5 J H + (λ + 2μ)κH C + μAC ]u02  + g 2 (λ + 2μ)I H − 2g 2 (λ + 2μ)κJ H + g 2 (λ + 2μ)κ 2 LH φ  − [g 2 λ(AH

+ κ 2 I H ) + 3g 2 μAH − 9g 2 μκ 2 I H − 2g 2 λκH H + 2g 2 μκH H + 4g 2 μκ 4 LH   + (λ + 2μ)I C ]φ  + [5g 2 μκ 2 AH + κ 2 I H − 10g 2 μκ 3 H H + μAC ]φ = m.

(35)

In above expressions, cross-sectional characteristics are defined as

1 dA H C = 1 − S 2κ

A = C

A

A = H

A



1

 5 dA H 1 − S 2κ

JH = A

H

=

 2 3 S

A

A



S2 dA I C = 1 − S 2κ S2

 5 dA I 1 − S 2κ

H  5 dA L = 1 − S 2κ

A



A

H

=

 2 4 S

A

 2 2 S dA 1 − S 2κ  2 2 S

 5 dA 1 − S 2κ

 5 dA. 1 − S 2κ

(36)

(37)

(38)

Here, it should be noted that the term S 2 κ is commonly neglected, especially for shallow thin beams. However, it is shown that (Qatu 1993; Hajianmaleki and Qatu 2012) this term should be included for more accurate predictions in the analysis of thick beams. In later discussions, the influence of including S 2 κ in the context of the SSG theory is examined.

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4.2 Boundary Conditions Boundary conditions of circular microbeams are given by • Boundary condition corresponding to δu01 :       − g 2 (λ + 2μ) AH + κ 2 I H − 2g 2 (λ + 2μ)κH H u01 + [13g 2 μκ 2 AH + κ 2 I H    + g 2 λκ 2 AH + κ 2 I H − 26g 2 μκ 3 H H − 2g 2 λκ 3 H H + (λ + 2μ)AC ]u01       + g 2 λκ AH + κ 2 I H + 7g 2 μκ AH + κ 2 I H − 2g 2 λκ 2 H H − 14g 2 μκ 2 H H u02     − [8g 2 μκ 3 AH + κ 2 I H + g 2 λκ 3 AH + κ 2 I H − 2g 2 λκ 4 H H − 16g 2 μκ 4 H H + (λ + 2μ)κAC ]u02 − [2g 2 (λ + 2μ)κI H − g 2 (λ + 2μ)H H     − g 2 (λ + 2μ)κ 2 J H φ  − 7g 2 μκAH − 5g 2 μκ 3 I H + g 2 λκ AH + κ 2 I H − 8g 2 μκ 2 H H − 2g 2 λκ 2 H H + 6g 2 μκ 4 J H + (λ + 2μ)H C ]φ  = F1 or u01 = u01 . (39) • Boundary condition corresponding to δu02 :       − g 2 λκ AH + κ 2 I H + 7g 2 μκ AH + κ 2 I H − 2g 2 λκ 2 H H − 14g 2 μκ 2 H H u01      + 7g 2 μκ 3 AH + κ 2 I H − 14g 2 μκ 4 H H + μκAC u01 − [g 2 μ AH + κ 2 I H      − 2g 2 μκH H ]u02 + [g 2 λκ 2 AH + κ 2 I H + 13g 2 μκ 2 AH + κ 2 I H − 26g 2 μκ 3 H H  − 2g 2 λκ 3 H H + μAC ]u02 + [g 2 μAH − 2g 2 λκ 2 I H − 11g 2 μκ 2 I H + g 2 λκH H   + 4g 2 μκH H + g 2 λκ 3 J H + 6g 2 μκ 3 J H ]φ  − [7g 2 μκ 2 AH + κ 2 I H − 14g 2 μκ 3 H H

+ μAC ]φ = F2 or u02 = u02 .

(40)

• Boundary condition corresponding to δφ:   − 2g 2 (λ + 2μ)κI H − g 2 (λ + 2μ)H H − g 2 (λ + 2μ)κ 2 J H u01 − [−11g 2 μκ 3 I H + 5g 2 μκAH + g 2 λκAH − 2g 2 μκ 2 H H + 8g 2 μκ 4 J H − 2g 2 λκ 2 H H + g 2 λκ 3 I H  + (λ + 2μ)H C ]u01 + [11g 2 μκ 2 I H + 2g 2 λκ 2 I H − g 2 μAH − g 2 λκH H − 4g 2 μκH H      − g 2 λκ 3 J H − 6g 2 μκ 3 J H ]u02 + [4g 2 μκ 2 AH − κ 2 I H + g 2 λκ 2 AH + κ 2 I H

− 4g 2 μκ 3 H H + 4g 2 μκ 5 J H − 2g 2 λκ 3 H H + (λ + 2μ)κH C ]u02 −[g 2 (λ + 2μ)I H − 2g 2 (λ + 2μ)κJ H + g 2 (λ + 2μ)κ 2 LH ]φ  + [g 2 λAH + 3g 2 μAH − 5g 2 μκ 2 I H − 2g 2 μκ 3 J H + 4g 2 μκ 4 LH − 2g 2 λκH H + g 2 λκ 2 I H + (λ + 2μ)I C ]φ  = M or φ = φ. (41)

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 : • Boundary condition corresponding to δu01       g 2 (λ + 2μ) AH + κ 2 I H − 2g 2 (λ + 2μ)κH H u01 − [2g 2 μκ 2 AH + κ 2 I H     − 4g 2 μκ 3 H H ]u01 − [g 2 λκ AH + κ 2 I H + 4g 2 μκ AH + κ 2 I H − 8g 2 μκ 2 H H  − 2g 2 λκ 2 H H ]u02 + [−g 2 (λ + 2μ)H H + 2g 2 (λ + 2μ)κI H − g 2 (λ + 2μ)     κ 2 J H ]φ  + 2g 2 μκ AH + κ 2 I H − 4g 2 μκ 2 H H φ = D1 or u01 = u01 .

(42)

 : • Boundary condition corresponding to δu02         3g 2 μκ AH + κ 2 I H − 6g 2 μκ 2 H H u01 + g 2 μ AH + κ 2 I H − 2g 2 μκH H u02    − 2g 2 μκ 2 AH + κ 2 I H − 4g 2 μκ 3 H H u02 − (g 2 μAH − 3g 2 μκ 2 I H  + 2g 2 μκ 3 J H )φ  = D2 or u02 = u02 .

(43)

• Boundary condition corresponding to δφ  :   2g 2 (λ + 2μ)κI H − g 2 (λ + 2μ)H H − g 2 (λ + 2μ)κ 2 J H u01   − 4g 2 μκ 3 I H − 2g 2 μκ 2 H H − 2g 2 μκ 4 J H u01 − [2g 2 λκ 2 I H + 8g 2 μκ 2 I H  g 2 λκH H − 4g 2 μκH H − g 2 λκ 3 J H − 4g 2 μκ 3 J H ]u02 + [g 2 (λ + 2μ)I H

− 2g 2 (λ + 2μ)κJ H + g 2 (λ + 2μ)κ 2 LH ]φ  − (2g 2 μκH H + 2g 2 μκ 3 J H − 4g 2 μκ 2 I H )φ = T or φ  = φ¯  (44) Here, the prescribed values of kinematic unknowns are signified by overbars.

5 Procedure for Analytical Solutions A close inspection of Eqs. (33)–(35) indicates that the set of derived governing equations is in fact a system of linear ordinary differential equations with constant coefficients. In this scenario, solutions of the homogeneous part can be assumed as h u01 = AeαS

1

h u02 = BeαS

1

φ h = CeαS

1

(45)

where A, B, C, and α are unknown constants. By inserting Eq. (45) into Eqs. (33)–(35) with the vanishing of f1 , f2 , and m, it leads to a system of linear algebraic equations as ⎡ ⎤⎡ ⎤ ⎡ ⎤ T11 T12 T13 A 0 ⎣ T21 T22 T23 ⎦⎣ B ⎦ = ⎣ 0 ⎦ (46) T31 T32 T33 C 0 where all entries of the coefficient matrix are given in terms of α. To obtain non-trivial solutions of A, B, and C, the determinant of the coefficient matrix in above system must vanish. This condition leads to the characteristic equation in terms of α as   (47) α 2 (α − κi)2 (α + κi)2 c6 α 6 + c4 α 4 + c2 α 2 + c0 = 0

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with i2 = −1 being the imaginary unit. One can easily observe that the characteristic equation has three repeated roots of multiplicity of 2, i.e., α1 = α2 = 0, α3 = α4 = κi, and α5 = α6 = −κi. In addition, the last term can be reduced to a cubic equation whose roots can be determined by using Cardano’s formula. Eventually, the substitution of twelve characteristic roots into Eq. (46) results in twelve relations between the unknown constants A, B, and C as ⎡ ⎤ Aj ⎣ Bj ⎦ = Ej Dj , (j = 1, 2, . . . , 12). (48) Cj Here, Ej can be referred to as the characteristic vectors of the homogeneous part. p p To determine particular solutions u01 , u02 , and φ p associated with loads prescribed in terms of elementary functions, the method of undetermined coefficients is adapted. Once the homogeneous and particular solutions are constructed, the general solutions of the governing equations can read as p

p

h h + u01 u02 = u02 + u02 φ = φ h + φ p . u01 = u01

(49)

To this end, only twelve constants Dj remain unknown. These constants can be sought by considering the boundary conditions at both ends of the beam, i.e., either six natural or essential boundary conditions in Eqs. (39)–(44) should be prescribed at each end. As a result, these boundary conditions yield a system of twelve linear equations with respect to Dj , and the determination of these unknowns completes the forms of the general solutions of the governing equations with given loading and boundary conditions.

6 Discussions on a Semi-circular Microbeam This section is devoted to the analysis of a particular semi-circular microbeam. The analytical solutions are obtained by following the procedure presented in the previous section. Boundary and loading conditions of the semi-circular microbeam are depicted in Fig. 2. The left  end is fixed while the right end is pinned. A sinusoidal moment m = 2EI (2π/L)2 sin 2π S 1 /L is prescribed, where I represents the conventional moment of inertia of the cross section. In following tests, square cross sections are considered. The material parameters are chosen as: Young’s modulus E = 1.44GPa, Poisson’s ratio ν = 0.3, and the gradient parameter g = 17.6 μm. The Lamé’s constants can be computed as: λ = Eν/[(1 + ν)(1 − 2ν)] and μ = E/[2(1 + ν)]. The size-dependent responses are firstly illustrated by means of displacements of the beam axis and the cross-sectional rotation. Figure 3a–b, respectively, show the results with h = 10g and h = g. In this test, κh is set as 0.2. For the SSG theory, one can easily observe a reduction in magnitude of quantities of interest as h decreases. This implies the increase in the stiffness with decreasing h. On the other hand, the larger values of h, the closer the results obtained by the classical and SSG theories. These observations are analogous to those reported for straight microbeams in the literature (Tran and Niiranen 2020).

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Fig. 2. A semi-circular microbeam—Geometry and boundary conditions.

To study the influence of the curviness on predicted responses, the relative difference in the displacements of the beam axis is considered, i.e.,     L  nc c 2 1  0 u0 − u0 dS  × 100. (50) =  L  c 2 1 0 u0 dS Here, u0nc denotes the displacements of the beam axis with no curviness, i.e., the term S 2 κ is neglected in Eqs. (36)–(38). On the other hand, u0c represents the displacements of the beam axis with curviness. It should be recalled that −0.5h ≤ S 2 ≤ 0.5h, and thus, the relative difference  is considered as a function of κh. Figure 4 plots the results obtained from the classical theory and SSG theory with three values of h, i.e., 10g, 5g, and g. A same tendency is noticed for both theories, i.e., the relative difference increases with increasing κh. However, the relative differences of the SSG theory are higher than those of the classical one, especially for κh > 0.5. More importantly, the size effect is also observed in this test, i.e., the smaller values of h, the higher magnitudes of the relative difference. The size effect is more pronounced for higher values of κh. With those observations, it may be concluded that the influence of the curviness is more significant in the SSG theory than the classical one.

7 Conclusions In the present study, the governing equations and boundary conditions of circular microbeams within the framework of the simplified strain gradient theory are derived. In the derivation, the curviness is fully considered. A procedure to obtain analytical solutions for circular microbeams under arbitrary loading and boundary conditions is presented. Then, this procedure is utilized in the analysis of a particular semi-circular microbeam. Several tests are performed to demonstrate the size-dependent behavior and

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Fig. 3. Displacements of the beam axis and the cross-sectional rotation with κh = 0.2: (a) h = 10g. (b) h = g.

Fig. 4. Relative difference in the displacements of the beam axis.

the influence of the curviness. It is worth highlighting that the influence of the curviness is more pronounced in the simplified strain gradient theory than the classical one, and this deserves more intensive examinations. Acknowledgements. The first author gratefully acknowledges the support from the Graduate Scholarship Programme for ASEAN or Non-ASEAN Countries from Chulalongkorn University, Thailand. The Postdoctoral Fellowship and PhD scholarship awarded, respectively, to the second and third authors from the Second Century Fund (C2F), Chulalongkorn University are acknowledged.

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References Altan, B.S., Aifantis, E.C.: On some aspects in the special theory of gradient elasticity. J. Mech. Behav. Mater. 8(3), 231–282 (1997) Balobanov, V., Kiendl, J., Khakalo, S., Niiranen, J.: Kirchhoff-Love shells within strain gradient elasticity: weak and strong formulations and an H3-conforming isogeometric implementation. Comput. Methods Appl. Mech. Eng. 344, 837–857 (2019) Balobanov, V., Niiranen, J.: Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity. Comput. Methods Appl. Mech. Eng. 339, 137–159 (2018) Hajianmaleki, M., Qatu, M.S.: Static and vibration analyses of thick, generally laminated deep curved beams with different boundary conditions. Compos. B Eng. 43(4), 1767–1775 (2012) Hosseini, S.B., Niiranen, J.: 3D strain gradient elasticity: variational formulations, isogeometric analysis and model peculiarities. Comput. Methods Appl. Mech. Eng. 389, 114324 (2022) Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51(8), 1477–1508 (2003) Lebedev, L.P., Cloud, M.J., Eremeyev, V.A.: Tensor Analysis with Applications in Mechanics. World Scientific (2010) Mindlin, R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16(1), 51–78 (1964) Niiranen, J., Balobanov, V., Kiendl, J., Hosseini, S.: Variational formulations, model comparisons and numerical methods for Euler-Bernoulli micro- and nano-beam models. Math. Mech. Solids 24(1), 312–335 (2019) Niiranen, J., Khakalo, S., Balobanov, V., Niemi, A.H.: Variational formulation and isogeometric analysis for fourth-order boundary value problems of gradient-elastic bar and plane strain/stress problems. Comput. Methods Appl. Mech. Eng. 308, 182–211 (2016) Niiranen, J., Kiendl, J., Niemi, A.H., Reali, A.: Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates. Comput. Methods Appl. Mech. Eng. 316, 328–348 (2017) Qatu, M.S.: Theories and analyses of thin and moderately thick laminated composite curved beams. Int. J. Solids Struct. 30(20), 2743–2756 (1993) Tran, L.V., Niiranen, J.: A geometrically nonlinear Euler-Bernoulli beam model within strain gradient elasticity with isogeometric analysis and lattice structure applications. Math. Mech. Complex Syst. 8(4), 345–371 (2020) Vo, D., Li, X., Nanakorn, P., Bui, T.Q.: An efficient isogeometric beam formulation for analysis of 2D non-prismatic beams. Eur. J. Mech. A/Solids 89 (2021) Vo, D., Nanakorn, P.: A total Lagrangian Timoshenko beam formulation for geometrically nonlinear isogeometric analysis of planar curved beams. Acta Mech. 231(7), 2827–2847 (2020). https://doi.org/10.1007/s00707-020-02675-x

Free Vibration Analysis of Toroidal Shell Segments with Novel Four-Unknown Refined Theory Van-Loi Nguyen1,3 , Suchart Limkatanyu2 , and Jaroon Rungamornrat1(B) 1 Center of Excellence in Applied Mechanics and Structures, Department of Civil Engineering,

Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand [email protected], [email protected] 2 Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University, Songkhla 90112, Thailand [email protected] 3 Department of Strength of Materials, Hanoi University of Civil Engineering, Hanoi 10000, Vietnam

Abstract. This study presents an analytical solution for the free vibration response of toroidal shell segments subjected to different boundary conditions. The shell segments are made of a functionally graded graphene platelet reinforced composite (FG-GPLRC). The modified Halpin-Tsai model together with the rule of the mixture is adopted to derive the effective material properties of the nanocomposites. The governing equation of motion for the shell is formulated within the framework of the novel four-unknown refined shell theory. The positive feature of such adopted shell theory results directly from the reduction of the number of key unknowns, without using the shear correction factor. The Rayleigh–Ritz procedure is subsequently implemented to determine the natural frequencies of the shell with different boundary conditions. Finally, numerical results and useful remarks on the free vibration of the shells are provided. Keywords: Free vibration · Toroidal shell segments · Four-unknown refined shell theory · Rayleigh–Ritz method

1 Introduction As a new family of advanced materials, an increase in applications of graphene-based composite materials is apparent and strongly due to its outstanding advantages compared with conventional materials in terms of mechanical, thermal, and electrical properties (Scarpa et al. 2009; Lau and Hui 2002). Recently, studies on both static and dynamic responses of shell structures made of advanced nanocomposites have been increasingly conducted (Shen et al. 2017; Liu et al. 2018; Barati and Zenkour 2019; Wang et al. 2019; Ghabussi et al. 2019; Afshari 2020; Dong et al. 2020; Li and Han 2020; Heydarpour et al. 2020; Eyvazian et al. 2021; Khayat et al. 2021; Ninh et al. 2021). While most of those existing investigations have been carried out in the context of cylindrical and conical © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 873–883, 2023. https://doi.org/10.1007/978-981-19-7331-4_72

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shells, the free vibration analysis of advanced nanocomposite toroidal shell segments subjected to different boundary conditions has not been well established and is the main focus of the present study. Another key aspect of the current work is that the novel four-unknown refined shell theory (RT4) is adopted in the formulation of governing equations. Until now, various shell theories have been developed and employed in the modeling, such as the classical shell theories (CSTs), first-order shear deformation shell theory (FSDT), and higherorder shear deformation shell theories (HSDTs), etc. In general, the HSDTs have been found to not only better represent kinematics across the shell thickness without the need of shear correction factors, but also provide more accurate stress distributions (Reddy 2003). Among those HSDTs, the four-unknown refined theory (RT4) has been proved computationally efficient and relatively simple (Shimpi and Patel 2006; Thai and Choi 2011; Thai and Kim 2013). In particular, the RT4 involves only four unknowns but is capable of describing the parabolic distribution of the shear deformation across the shell thickness without the shear correction factors. Many recent studies on mechanical behaviors of plate structures using the RT4 have been documented (Shimpi and Patel 2006; Thai and Choi 2011; Thai and Kim 2013; Thai and Vo 2013; Han et al. 2015; Rouzegar and Abad 2015; Nguyen et al. 2021; Vu et al. 2021). However, investigations of shell structures within the framework of this theory are still limited, and only a few studies related to shell panels using different variants of the RT4 can be found in the literature (Zine et al. 2018; Sobhy and Zenkour 2019; Allam et al. 2020; Quoc et al. 2021; Tran et al. 2021). In the present study, the performance of the RT4 used in the simulation is fully explored in the context of toroidal shell segments. The governing equations of motion of FG-GPLRC toroidal shell segments are derived and subsequently solved by the Rayleigh-Ritz method. A selected set of results illustrating the influence of material properties and boundary conditions is provided.

2 FG-GPLRC Toroidal Shell Segment and Material Model Consider a toroidal shell segment with a radius of the equator R2 ; longitudinal curvature radius R1 ; length L; and thickness h, as illustrated in Fig. 1. The shell configuration is defined in a local coordinate system (x, y, z) where x- and y-axes are chosen to align with the axial and circumferential directions, respectively, and the z-axis is directed outward and perpendicular to the shell surface. The geometric relation of the shell is given by r = R2 − R1 (1 − sin ϕ),

(1)

in which ϕ denotes the angle between the symmetric axis and the normal to the middle surface of the shell. In the region of the equator of the torus, when R1 is sufficiently large, the approximation ϕ ≈ π/2 is commonly adopted, and thus, r = R2 . The form of the governing equations of the shell is simplified by setting dx = R1 d ϕ and dy = R2 d θ (Ninh et al. 2021; Vuong and Duc 2020). The FG-GPLRC toroidal shell segment consists of NL layers with the same thickness for each layer. To form the layer-wise variation, the GPL weight fraction of the k-th layer is defined as follows: (k)

∗ ; for UD type, gGPL = gGPL

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875

Fig. 1. The geometry of toroidal shell segments (k)

1 (NL + 1 − |NL + 1 − 2k|); for FG − O type, NL + 2 1 ∗ = 2gGPL (1 + |NL + 1 − 2k|); for FG − X type, NL + 2

∗ gGPL = 2gGPL (k)

gGPL

(2)

∗ is the GPL weight fraction and NL is the number of layers of the composite. where gGPL The material properties (i.e., Young’s modulus E (k) , Poisson ratio ν (k) , mass density ρ (k) ) of the k-th layer of the shell structure can be determined according to the modified Halpin–Tsai model and the rule of mixture as presented in the work of (Ninh et al. 2021).

3 Model Kinematics and Material Laws Based on the RT4 (Shimpi and Patel 2006; Thai and Choi 2011; Tran et al. 2021), the displacement field of the shell is expressed as follows: u = u0 + z(u0 /R1 − wb,x ) − f (z)ws,x ; v = v0 + z(v0 /R2 − wb,y ) − f (z)ws,y ; w = wb + ws ;

(3)

where (u0 , v0 ) are displacement components in the (x, y) directions; (wb , ws ) are bending and shear components of the transverse displacement at the middle surface of the shell; and f (z) = −z/4 + 5z 3 /3h2 is a function related to the distribution of the shear strain through the thickness of the shell. The strain field of the shell can be determined by ⎧ ⎫ ⎧ s⎫ ⎧ ⎫ ⎧ 0⎫ ⎪ ⎪ εx ⎪ κb ⎪

s

⎪ ⎪ ⎪ ⎨ x ⎪ ⎨ κx ⎪ ⎬ ⎬ ⎬ ⎪ ⎨ ⎪ ⎬ ⎨ εx ⎪ γyz γyz s 0 b εy = εy + z κy + f (z) κy and = g(z) , (4) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ γxz γxzs ⎪ ⎩ ⎪ ⎪ ⎭ ⎪ ⎪ ⎭ ⎩ ⎪ s ⎩ ⎭ ⎭ ⎩ 0 γxy κxy γxy κb xy

in which ⎧ ⎫ ⎧ ⎫ ⎧ b⎫ ⎧ ⎫ ⎪ κx ⎪ ⎪ εx0 ⎪ u + (w + w )/R ⎪ ⎪ ⎪ ⎪ ⎪ 0,x s 1 b ⎨ u0,x /R1 − wb,xx ⎨ ⎪ ⎨ ⎬ ⎨ ⎬ ⎪ ⎬ ⎪ ⎬ εy0 = v0,y + (wb + ws )/R2 ; κyb = v0,y /R2 − wb,yy ; ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ ⎪ ⎩ κb ⎪ ⎩γ0⎪ ⎭ ⎩ u0,y + v0,x ⎭ ⎩ u0,y /R1 + v0,x /R2 − 2wb,xy ⎭ xy

xy

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⎧ s⎫ ⎧ ⎫

⎪ ⎨ κx ⎪ ⎬ ⎪ ⎨ −ws,xx ⎪ ⎬ γs ws,y df (z) yz s κy = −ws,yy ; = ; g(z) = 1 − . s ⎪ ⎪ dz ws,x ⎩ s⎪ ⎭ ⎪ ⎩ ⎭ γxz −2ws,xy κxy

(5)

The stress–strain relations of the shell are given by ⎧ (k) ⎫ ⎡ σx ⎪ ⎪ 1 ⎪ ⎪ ⎪ ⎪ ⎢ ν (k) ⎪ σ (k) ⎪ ⎪ ⎬ ⎢ ⎨ y ⎪ (k) E (z) ⎢ (k) = σxy

⎢ 0 ⎪ (k) 2 ⎢ ⎪ ⎪ (k) ⎪ 1 − ν ⎪ ⎪ ⎣ 0 σ ⎪ yz ⎪ ⎪ ⎭ ⎩ (k) ⎪ 0 σxz

ν (k) 1 0 0 0

⎧ ⎫ ⎤⎪ ε ⎪ x ⎪ ⎪ ⎪ ⎪ 0 0 0 ⎪ ⎪ ⎪ εy ⎪ ⎪ ⎪ ⎥ ⎪ 0 0 0 ⎬ ⎥⎨ ⎪ ⎥ γ (k) 0 0 (1 − ν )/2 ⎥ xy . ⎥⎪ ⎪ ⎪ ⎪ ⎦⎪ 0 0 (1 − ν (k) )/2 ⎪ ⎪ γyz ⎪ ⎪ ⎪ ⎪ ⎪ 0 0 (1 − ν (k) )/2 ⎪ ⎩γ ⎪ ⎭ xz (6)

4 Energy Expressions The force and moment resultants of the FG-GPLRC toroidal shell segment can be determined as follows (Thai and Choi 2011; Dong and Van Dung 2017): (Nx , Mx , Px ) = (A11 , B11 , E11 )εx0 + (A12 , B12 , E12 )εy0 + (B11 , D11 , F11 )κxb + (B12 , D12 , F12 )κyb + (E11 , F11 , H11 )κxs + (E12 , F12 , H12 )κys ;



Ny , My , Py = (A12 , B12 , E12 )εx0 + (A22 , B22 , E22 )εy0 + (B12 , D12 , F12 )κxb

+(B22 , D22 , F22 )κyb + (E12 , F12 , H12 )κxs + (E22 , F22 , H22 )κys ;

0 b s Nxy , Mxy , Pxy = (A66 , B66 , E66 )γxy + (B66 , D66 , F66 )κxy + (E66 , F66 , H66 )κxy ; Qyz = A44 γyzs ; Qxz = A55 γxzs .

(7)

where z NL k+1      Aij , Bij , Dij , Eij , Fij , Hij = Qij(k) 1, z, z 2 , f , zf , f 2 dz; i, j = 1, 2, 6; k=1 zk z NL k+1  (k) Aij = Qij g 2 dz; i, j = 4, 5

; (8)

k=1 zk

with (k) (k) = Q22 = Q11

E (k) E (k) (k) (k) (k) (k) (k) (k) .

2 ; Q12 = ν Q11 ; Q44 = Q55 = Q66 =  2 1 + ν (k) 1 − ν (k) (9)

Free Vibration Analysis of Toroidal Shell Segments

The strain energy of the shell is given by    0 b Nx εx0 + Ny εy0 + Nxy γxy + Mx κxb + My κyb + Mxy κxy 1 U = dS. s 2 + Px κxs + Py κys + Pxy κxy + Qyz γyzs + Qxz γxzs

877

(10)

S

The kinetic energy of the shell is expressed by 1 T= 2 NL

zk+1 

k=1 zk

ρ

(k)

S



2 u˙ 0 + z(˙u0 /R1 − w˙ b,x ) − f w˙ s,x dzdS; 2  + v˙ 0 + z(˙v0 /R2 − w˙ b,y ) − f w˙ s,y +(w˙ b + w˙ s )2 (11)

5 Solution Procedure In the present study, the Rayleigh–Ritz procedure is adopted to determine the natural frequencies and corresponding mode shapes of the FG-GPLRC toroidal shell segments. Specifically, the displacement components of the shell are assumed to be in the following form: u0 = U (x)cos(nθ )cos(ωt) v0 = V (x)sin(nθ )cos(ωt) wb = Wb (x)cos(nθ )cos(ωt) ws =Ws (x)cos(nθ )cos(ωt)

(12)

where n is the circumferential wave number; ω is the natural angular frequency of the shell; t is the time variable; and θ = y/R2 . The longitudinal modal functions of the shell are represented by U (x) =

M 

Um φmu (x); V (x) =

m=1 M 

Wb (x) =

m=1

M 

Vm φmv (x);

m=1

Wbm φmwb (x); Ws (x) =

M 

Wsm φmws (x);

(13)

m=1

in which Um ,Vm ,Wbm , Wsm are unknown coefficients; functions φmu (x), φmv (x), φmwb (x), φmws (x) are normalized members of characteristic orthogonal polynomials that satisfy the geometric boundary conditions at the ends of the shell; and M denotes the truncated number of terms used in the representation. Such functions can be generated using the Gram-Schmidt procedure (Bhat 1985) with the first members of the orthogonal polynomials given in Table 1 for different types of end conditions. Note that the clamped– clamped immovable (CC-IM), clamped–simply supported (CS), and simply supported– simply supported (SS) boundary conditions are considered in this study.

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By substituting Eq. (12) into Eqs. (10)−(11) and applying Rayleigh–Ritz method, the equations of motion of the FG-GPLRC toroidal shell segment for the free vibration problem, can be obtained as   (14) K − ω2 M = 0.  T where = U1 , U2 , . . . , UM , . . . , WsM and K, M are the stiffness and mass matrices of the shell structure, respectively. By solving Eq. (14), the natural frequency and vibrational mode of the shell can be obtained. Table 1. The first members of characteristic orthogonal polynomials (η = x/L) Boundary conditions CC-IM

Geometric boundary conditions η = 0 : u0 = v0 = wb = wb,x =ws = ws,x = 0; η = 1 : u0 = v0 = wb = wb,x =ws = ws,x = 0;

CS

η = 0 : u0 = v0 = wb = wb,x =ws = ws,x = 0;

SS

η = 1 : v0 = wb = ws = 0; η = 0 : v0 = wb = ws = 0; η = 1 : v0 = wb = ws = 0;

First members ϕ1u = η(η − 1); ϕ1v = η(η − 1); ϕ1wb = η4 − 2η3 + η2 ; ϕ1ws = η4 − 2η3 + η2 ; ϕ1u = η; ϕ1v = η(η − 1); ϕ1wb = η3 − η2 ; ϕ1ws = η3 − η2 ; ϕ1u = 1; ϕ1v = η(η − 1); ϕ1wb = η(η − 1); ϕ1ws = η(η − 1);

6 Numerical Results Unless otherwise stated, the material properties used in the numerical study are given as follows: EM = 3.0 GPa, νM = 0.34, ρM = 1200 kg/m3 , EGPL = 1.01 TPa, νGPL = 0.186, ρGPL = 1060 kg/m3 , lGPL = 2.5 µm, hGPL = 1.5 nm, wGPL = 1.5 µm, ∗ = 1.5%, and NL = 20. Computed natural frequencies are normalized by gGPL  2 )ρ /E ω = ωR2 (1 − νM M M and each mode of vibration is denoted by (k, n) where k is the wave number in the x-direction and n is the circumferential wave number. 6.1 Convergence Studies In this section, the convergence of the proposed solution as the truncated number M is increased is confirmed. In Table 2, the normalized natural frequencies ω of simply supported FG-GPLRC toroidal shell segments with different GPL distributions (UD, FG-X, and FG-O types) are presented for various values of M . In the analysis, the

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geometric parameters of the shell are taken as L/R2 = 2, h/R2 = 0.1, and R1 → ∞ (i.e., cylindrical shell). It is evident from this set of results that the use of the truncated number M = 15 in the computation is sufficient to ensure the convergence of the computed natural frequencies. Table 2. Convergence of normalized natural frequencies ω of simply supported FG-GPLRC toroidal shell segments Patterns

Mode

Truncated number M=3

M=5

M=8

M = 10

M = 12

M = 15

UD

(1, 3)

0.84201

0.82554

0.82549

0.82549

0.82549

0.82549

FG-X

(1, 2)

0.90626

0.88383

0.88376

0.88376

0.88376

0.88376

FG-O

(1, 3)

0.73425

0.71599

0.71594

0.71594

0.71594

0.71594

6.2 Comparison Studies Two examples are considered, in this section, to verify the results of shell structures with different boundary conditions and those made of FG-GPLRC materials. Firstly, for shell structures subjected to different boundary conditions (i.e., SS, CS, and CC-IM), a comparison of current results (ω) with those of Loy et al. (1997), who used the CST, is reported in Table 3 for isotropic cylindrical shell structures. It is seen that the present model yields results of good agreement with those of Loy et al. (1997). Secondly,√a comparison of the first three normalized natural frequencies, ω1 = ω(R2 − h/2) ρM /EM , obtained from the present model and those of Liu et al. (2018) and Abedini Baghbadorani and Kiani (2021) is provided in Table 4 for the case of a simply supported FG-GPLRC cylindrical shell. It is evident that the present results are nearly identical to those of Liu et al. (2018), in which the three-dimensional theory of elasticity (3D theory) was employed in their formulation. It is worth emphasizing that the accuracy of the proposed model with RT4 is better than that of the model based on the FSDT. 6.3 FG-GPLRC Shell Structures Finally, the effects of material properties and different boundary conditions on the natural frequencies of FG-GPLRC toroidal shell segments are demonstrated. The computed natural frequencies, ω, from the proposed model for UD, FG-X, and FG-O types and SS, CS, and CC-IM boundary conditions are presented in Table 5. The geometric and physical parameters used in the simulations are as follows: L/R2 = 20, h/R2 = 0.01, and R1 = 500R2 . Based on the obtained results, it is seen that the FG-X shell structure is stiffer than the UD and FG-O shell structures and, as a result, the best material profile among the three cases considered. In addition, the shell segment with the CC-IM boundary condition possesses the highest natural frequencies, whereas the SS shell segment yields the lowest values among the three types of boundary conditions treated.

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Table 3. Comparison of normalized natural frequencies ω of SS, CS, and CC isotropic cylindrical shells with L/R2 = 20, h/R2 = 0.01, νM = 0.3, and k = 1 n Boundary conditions SS

CS

CST (Loy Present et al. 1997)

CC-IM

Diff. CST (Loy Present (%) et al. 1997)

Diff. CST (Loy Present (%) et al. 1997)

Diff. (%)

1 0.016101

0.016102 0.01 0.023974

0.023970 0.02 0.032885

0.032875 0.03

2 0.009382

0.009387 0.05 0.011225

0.011229 0.04 0.013932

0.013930 0.01

3 0.022105

0.022105 0.00 0.022310

0.022310 0.00 0.022672

0.022670 0.01

4 0.042095

0.042085 0.02 0.042139

0.042129 0.02 0.042208

0.042198 0.02

Table 4. Comparison of the first three normalized natural frequencies, ω1 , of simply supported FG-GPLRC toroidal shell segments (α = kπ a/L = 2) Patterns

3D theory (Liu et al. 2018)

FSDT (Abedini Baghbadorani and Kiani 2021)

Present

Diff. [FSDT-3D] (%)

Diff. [Present-3D] (%)

UD

0.3743

0.3726

0.3746

0.45

0.08

0.3891

0.3865

0.3894

0.67

0.08

0.4239

0.4228

0.4242

0.26

0.07

0.4129

0.4073

0.4132

1.36

0.07

0.4085

0.4139

0.4088

1.32

0.07

0.4838

0.4867

0.4841

0.60

0.06

0.3311

0.3262

0.3313

1.48

0.06

0.3537

0.3473

0.3539

1.81

0.06

0.3688

0.3646

0.3689

1.14

0.03

FG-X

FG-O

7 Conclusion Some key points and findings from the present study are briefly summarized as follows: (i)

Free vibration of advanced nanocomposite (FG-GPLRC) toroidal shell segments are considered. Three GPL distribution patterns, including FG-X, FG-O, and UD types, are investigated. (ii) Performance of the novel four-unknown shell theory (RT4) used in the simulation of the toroidal shell segments is assessed. Such theory can capture the smooth profile of the shear deformation through the shell thickness without shear correction factors, and generally yields better results than the FSDT-based model but requires less number of unknowns.

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Table 5. Normalized natural frequencies ω of FG-GPLRC toroidal shell segments (k = 1) n Boundary conditions SS UD

CS FG-X

FG-O

UD

CC-IM FG-X

FG-O

UD

FG-X

FG-O

1 0.04202 0.04203 0.04202 0.06010 0.06010 0.06010 0.08076 0.08076 0.08076 2 0.02537 0.02792 0.02252 0.02964 0.03185 0.02724 0.03574 0.03760 0.03378 3 0.05475 0.06385 0.04376 0.05530 0.06432 0.04443 0.05617 0.06508 0.04551 4 0.10326 0.12090 0.08182 0.10338 0.12101 0.08196 0.10356 0.12116 0.08218

(iii) The RT4 is successfully adopted for the first time to study the free vibration of FG-GPLRC toroidal shell segments. A novel set of solutions is derived for the shell subjected to various types of boundary conditions.

Acknowledgements. This research is funded by Thailand Science Research and Innovation Fund Chulalongkorn University (Grant No. CU_FRB65_ind(11)_159_21_25). The authors also gratefully acknowledge the support provided by the CU Scholarship for ASEAN or Non-ASEAN Countries 2019 awarded to Van-Loi Nguyen and the Thailand Research Fund (Grant No. RTA6280012).

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Ghabussi, A., Ashrafi, N., Shavalipour, A., Hosseinpour, A., Habibi, M., Moayedi, H., Babaei, B., Safarpour, H.: Free vibration analysis of an electro-elastic GPLRC cylindrical shell surrounded by viscoelastic foundation using modified length-couple stress parameter. In: Mechanics Based Design of Structures and Machines, pp. 1–25 (2019) Han, S.-C., Park, W.-T., Jung, W.-Y.: A four-variable refined plate theory for dynamic stability analysis of S-FGM plates based on physical neutral surface. Compos. Struct. 131, 1081–1089 (2015) Heydarpour, Y., Malekzadeh, P., Dimitri, R., Tornabene, F.: Thermoelastic analysis of rotating multilayer FG-GPLRC truncated conical shells based on a coupled TDQM-NURBS scheme. Compos. Struct. 235, 111707 (2020) Khayat, M., Baghlani, A., Najafgholipour, M.A.: The propagation of uncertainty in the geometrically nonlinear responses of smart sandwich porous cylindrical shells reinforced with graphene platelets. Compos. Struct. 258, 113209 (2021) Lau, A.K.-T., Hui, D.: The revolutionary creation of new advanced materials—carbon nanotube composites. Compos. B Eng. 33, 263–277 (2002) Li, C., Han, Q.: Semi-analytical wave characteristics analysis of graphene-reinforced piezoelectric polymer nanocomposite cylindrical shells. Int. J. Mech. Sci. 186, 105890 (2020) Liu, D., Kitipornchai, S., Chen, W., Yang, J.: Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell. Compos. Struct. 189, 560–569 (2018) Loy, C.T., Lam, K.Y., Shu, C.: Analysis of cylindrical shells using generalized differential quadrature. Shock. Vib. 4, 538754 (1997) Nguyen, V.-L., Tran, M.-T., Nguyen, V.-L., Le, Q.-H.: Static behaviour of functionally graded plates resting on elastic foundations using neutral surface concept. Arch. Mech. Eng. 68, 5–22 (2021) Ninh, D.G., Eslami, H., Viet Hoang, V.N.: Dynamical behaviors of conveying-fluid nanocomposite toroidal shell segments with piezoelectric layer in thermal environment using the Reddy’s third-order shear deformation shell theory. Thin-Walled Struct. 159, 107204 (2021) Quoc, T.H., Van Tham, V., Tu, T.M.: Active vibration control of a piezoelectric functionally graded carbon nanotube-reinforced spherical shell panel. Acta Mech. 232(3), 1005–1023 (2021). https://doi.org/10.1007/s00707-020-02899-x Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press (2003) Rouzegar, J., Abad, F.: Free vibration analysis of FG plate with piezoelectric layers using fourvariable refined plate theory. Thin-Walled Struct. 89, 76–83 (2015) Scarpa, F., Adhikari, S., Srikantha Phani, A.: Effective elastic mechanical properties of single layer graphene sheets. Nanotechnology 20, 065709 (2009) Shen, H.-S., Xiang, Y., Fan, Y.: Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical shells in thermal environments. Compos. Struct. 182, 447–456 (2017) Shimpi, R.P., Patel, H.G.: Free vibrations of plate using two variable refined plate theory. J. Sound Vib. 296, 979–999 (2006) Sobhy, M., Zenkour, A.M.: Vibration analysis of functionally graded graphene platelet-reinforced composite doubly-curved shallow shells on elastic foundations. Steel Compos. Struct. 33, 195– 208 (2019) Thai, H.-T., Choi, D.-H.: A refined plate theory for functionally graded plates resting on elastic foundation. Compos. Sci. Technol. 71, 1850–1858 (2011) Thai, H.-T., Kim, S.-E.: A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates. Compos. Struct. 96, 165–173 (2013) Thai, H.-T., Vo, T.P.: A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates. Appl. Math. Model. 37, 3269–3281 (2013)

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Tran, T.T., Tran, V.K., Pham, Q.-H., Zenkour, A.M.: Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation. Compos. Struct. 264, 113737 (2021) Vu, T.-V., Nguyen-Van, H., Nguyen, C. H., Nguyen, T.-P., Curiel-Sosa, J. L.: Meshfree analysis of functionally graded plates with a novel four-unknown arctangent exponential shear deformation theory. In: Mechanics Based Design of Structures and Machines, pp. 1–33 (2021) Vuong, P.M., Duc, N.D.: Nonlinear static and dynamic stability of functionally graded toroidal shell segments under axial compression. Thin-Walled Struct. 155, 106973 (2020) Wang, Y.Q., Ye, C., Zu, J.W.: Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets. Aerosp. Sci. Technol. 85, 359–370 (2019) Zine, A., Tounsi, A., Draiche, K., Sekkal, M., Mahmoud, S.R.: A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells. Steel Compos. Struct. 26, 125–137 (2018)

Linear Analysis of Planar Curved Bi-directional Functionally Graded Microbeams Using the Modified Couple Stress Theory Duy Vo1 , Pana Suttakul2 , Jaroon Rungamornrat1 , and Pruettha Nanakorn3(B) 1 Center of Excellence in Applied Mechanics and Structures, Department of Civil Engineering,

Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand [email protected], [email protected] 2 Department of Mechanical Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand [email protected] 3 School of Civil Engineering and Technology, Sirindhorn International Institute of Technology, Thammasat University, Pathumthani, Thailand [email protected]

Abstract. This paper presents an efficient formulation for linear analysis of planar curved microbeams made of bi-directional functionally graded materials. The formulation is derived using the modified couple stress theory in conjunction with the kinematic assumptions of the Euler-Bernoulli beam theory. Univariate non-uniform rational B-spline (NURBS) basis functions are used to discretize the kinematic unknowns. In addition, the volume fraction of materials is described by a NURBS surface to enable the consideration of arbitrary variations of material properties in two directions, i.e., the directions of the beam axis and cross-sectional height. To validate the presented formulation, linear static and vibration analyses of a semi-circular microbeam are performed. Since the exact solutions of the considered problems do not exist, the reference solutions are obtained with significantly many isogeometric plane elements, and the accuracy and efficiency of the proposed formulation are assessed. Keywords: Modified couple stress elasticity · Planar curved microbeams · Bi-directional functionally graded beams · Isogeometric analysis · Euler-Bernoulli beam theory

1 Introduction Microbeams are among key structural components of micro-electro-mechanical systems (MEMS) such as sensors and actuators. Due to the increasing importance of MEMS to today’s industrial products, comprehensive understandings of microbeams become crucial to designs of MEMS. In practice, cross-sectional dimensions of microbeams are generally in the order of microns, and the size-dependent behavior at this scale has

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 884–893, 2023. https://doi.org/10.1007/978-981-19-7331-4_73

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been experimentally observed (Lam et al. 2003). However, the conventional Cauchy’s continuum theory cannot predict such behavior, and thus, several alternatives have been proposed. Recently, the modified couple stress (MCS) theory (Yang et al. 2002) has been extensively considered for the analysis of microbeams (Kong et al. 2008; Ma et al. 2008; Park and Gao 2006; Vo et al. 2022a). In these cited publications, each microbeam is assumed to be made of a single material, e.g., metals, polymers, and silicon-based materials. However, MEMS devices usually function under simultaneous impacts of mechanical, electrical, and thermal loads. In these scenarios, the use of a single material is not an appropriate choice. Instead, composite materials are widely used to enhance the performance of MEMS devices. Among different types of composite materials, functionally graded (FG) materials are preferable since they exhibit smooth and continuous variations of material parameters. Therefore, the literature on FG microbeams is constantly expanding (Kong 2022). To the authors’ best knowledge, research efforts of FG microbeams are, to date, limited to those having straight axes and simple rules of material distributions. In practice, the geometry of microbeams is generally complex (Lobontiu and Garcia 2004). In addition, some material optimization problems of FG beams, not particularly microbeams, show resulting material distributions that are complex (Truong et al. 2020). As the first step to address those limitations and challenges, this paper presents a formulation for analyzing planar arbitrarily curved FG microbeams in the context of the MCS theory. The kinematic assumptions of the Euler-Bernoulli beam theory are considered. The material parameters vary in two directions, i.e., the directions of the beam axis and cross-sectional height. NURBS surfaces are used to allow the descriptions of complex material distributions to be described conveniently. Some numerical tests of a semi-circular microbeam are performed to assess the accuracy and efficiency of the presented formulation.

2 Modified Couple Stress Theory for Planar Curved Microbeams This section summarizes the use of the MCS theory for the analysis of planar curved microbeams. For detailed derivations, readers should consult relevant studies (Park and Gao 2008; Vo et al. 2022b; Yang et al. 2002). The beam axis is a planar curve parameterized by the arc length parameter S (1) , i.e., 0 ≤ S (1) ≤ L, with L being the length of the beam axis. The unit tangent vector of the beam axis is represented by A1 , and the unit normal vector to the beam axis A2 is determined by rotating A1 by an angle of 90o in the counterclockwise direction. Clearly, A1 and A2 are orthonormal, and thus, they are used as the base vectors of a local Cartesian coordinate system. The generalized strain measures are given by (Vo et al. 2022b)      X13 = −K11 (1) Γ11 = u01 − κu02 K11 = − κ  u01 + κu01 + u02 where Γ11 is the generalized membrane strain describing longitudinal actions, and K11 is the generalized bending strain measuring the change in the curvature of the beam axis

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due to bending actions. In the above expressions, u01 and  u02 are the components in the local coordinate system of the displacement vector u0 S 1 of the beam axis, i.e.,       (2) u0 S (1) = u01 S (1) A1 + u02 S (1) A2 . The primes denote derivatives with respect to S (1) . The cross-sectional stress resultants are computed as N11 = EAΓ11 + EH K11

M11 = EH Γ11 + EI K11

Q13 = lGAX13

(3)

where the generalized cross-sectional characteristics are defined as 0.5h EA = b −0.5h

0.5h EI = b −0.5h

E dS (2) 1 − S (2) κ 

 (2) 2

E S dS (2) 1 − S (2) κ

0.5h EH = b −0.5h

0.5h lGA = b −0.5h

ES (2) dS (2) 1 − S (2) κ

(4)

l2G dS (2) . 1 − S (2) κ

(5)

Here, S (2) is the parameter along the vector A2 , h is the cross-sectional height, b is the cross-sectional width, and κ is the curvature of the undeformed beam axis. Regarding the material parameters, E represents Young’s modulus, G is the shear modulus, and l is the material length scale. The inertia virtual work δWine is determined as ⎤ ⎡   L ρAu¨ 0 · δu0 − ρH u¨  · A2 (A1 · δu0 ) 0  ⎦ dS (1) . (6)  δWine = ⎣     −ρH (u¨ 0 · A1 ) A2 · δu0 + ρI u¨ 0 · A2 A2 · δu0 0

Here, a double dot represents a second derivative with respect to time. In addition, the quantities ρA, ρH , and ρI are defined as    0.5h  0.5h ρA = b ∫ ρ 1 − S (2) κ dS (2) ρH = b ∫ ρS (2) 1 − S (2) κ dS (2) (7) −0.5h

−0.5h

2   1 − S (2) κ dS (2) ρI = b ∫ ρ S (2) 0.5h



−0.5h

(8)

where ρ is the mass density. With the aid of the generalized strain measures and cross-sectional stress resultants in Eqs. (1) and (3), the internal virtual work is expressed as L

δWint = ∫(N11 δΓ11 + M11 δK11 + Q13 δX13 )dS (1) .

(9)

0

The expression of the external virtual work δWext can be found elsewhere (Vo et al. 2022b). Eventually, the virtual work principle is stated as δWine + δWint = δWext .

(10)

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3 NURBS Interpolations of Material Parameters This study considers microbeams made of a mixture of two materials. The volume fraction of the first constituent is interpolated using a NURBS surface, i.e., V1 =

m n

    Ni ξ (1) Nj ξ (2) Vfij

(11)

i=1 j=1

    where Ni ξ (1) and Nj ξ (2) are univariate NURBS basis functions parameterized by the knot parameters ξ (1) and ξ (2) , respectively. In addition, Vfij denotes a volume fraction coefficient. As a common practice, ξ (1) and ξ (2) are set to vary between 0 and 1. More details of the properties of NURBS basis functions can be found in several reference books (Piegl and Tiller 1997). Once the volume fraction of the first constituent is determined, the volume fraction of the second material can be straightforwardly computed as V2 = 1 − V1 .

(12)

For the sake of simplicity, the effective material parameters are calculated by using Voigt’s model (Voigt 1889) as P = P1 V1 + P2 V2

(13)

where P can be any material parameter of interest, such as Young’s modulus, Poisson’s ratio, material length scale, and mass density.

Fig. 1. A semi-circular microbeam–Geometry, loading, and boundary conditions.

For microbeams exhibiting material variations along the beam axis and crosssectional height, the knot parameters of NURBS basis functions can be determined

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as ξ (1) =

S (1) L

ξ (2) =

S (2) + 0.5. h

(14)

4 Analysis of a Semi-Circular Microbeam This section validates the accuracy and efficiency of the presented MCS beam formulation. The numerical implementation is performed using the isogeometric approach (Hughes et al. 2005; Vo et al. 2020; Vo et al. 2022b). Due to the absence of the analytical solutions, the numerical results produced by dense meshes of an isogeometric MCS plane formulation (Vo et al. 2022b) are considered as reference results.

Fig. 2. Distribution of volume fraction.

For the tests, the material parameters of the two materials are given by: E2 = 400 GPa, E2 = 110 GPa, ν1 = 0.28, ν2 = 0.34, ρ1 = 19, 300 kg/m3 , and ρ2 = 8, 960 kg/m3 . Here, ν represents Poisson’s ratio. Regarding the material length scales, l1 = l2 = 15 μm are assumed. Figure 1 shows the geometry of the semi-circular microbeam together with the loading and boundary conditions. The beam is fixed at both ends and subjected to uniformly distributed forces on the outer surface. The magnitudes of the tangential and radial forces are prescribed as t1 = 5

E1 I κ bl1 L2

t2 = 0.5

E1 A bl1 L

(15)

where A and I are, respectively, the cross-sectional area and moment of inertia. The radius R of the beam is chosen as R = 40l1 , and the cross-sectional dimensions are specified as h = 2l1 and b = 0.5h. The distribution of the volume fraction is visualized in Fig. 2. The NURBS surface is constructed by quadratic basis functions with uniform knot vectors having 4 knot intervals. The values of the volume fraction coefficient Vfij are given in Table 1. Here,

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Table 1. Volume fraction coefficients Vfij of the first constituent. i

1

2

3

4

5

6

7

8

9

10

1

1.00

1.00

1.00

0.00

0.00

0.33

0.00

1.00

1.00

1.00

2

1.00

1.00

1.00

0.00

0.00

0.00

0.00

1.00

1.00

1.00

3

1.00

1.00

1.00

0.00

0.00

0.00

0.00

1.00

1.00

1.00

4

1.00

1.00

0.00

0.00

0.00

0.00

0.00

0.00

1.00

1.00

5

1.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

1.00

6

1.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

1.00

7

1.00

1.00

0.00

1.00

0.00

0.00

1.00

0.00

1.00

1.00

8

1.00

1.00

1.00

1.00

0.00

0.00

1.00

1.00

1.00

1.00

9

1.00

1.00

1.00

1.00

0.00

0.00

1.00

1.00

1.00

1.00

10

1.00

1.00

1.00

1.00

0.00

0.00

1.00

1.00

1.00

1.00

j

Fig. 3. Displacements of the beam axis obtained with plane and beam formulations.

it is worth highlighting that this distribution cannot be represented by conventional

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D. Vo et al.

mathematical functions, such as exponential, polynomial, and trigonometric functions, which are commonly considered in the literature. This observation demonstrates the superiority of NURBS basis functions in describing complex variations of material parameters.

Fig. 4. Contour plots of the total displacement (a scale factor of 5 is applied to the deformed shapes).

Fig. 5. Convergence results for the total displacement of the central point of the beam axis.

The accuracy of the presented beam formulation is first examined. The reference results are produced using a mesh of isogeometric MCS plane elements with 100 elements along the beam axis and 10 elements along the cross-sectional height. The elements use different interpolations between the directions of the beam axis and cross-sectional

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height. The interpolation in the direction of the beam axis is cubic, while that in the direction of the cross-sectional height is quadratic. For the results of the beam formulation, 100 cubic elements are used. Figure 3 plots the displacement components of the beam axis, and Fig. 4 exhibits the contour plots of the total displacement. Although slight discrepancies can be noticed, the observed good agreement validates the accuracy of the presented beam formulation. The convergence tests are performed for the total displacement ||u0c || of the central point of the beam axis. The plane formulation is implemented with different numbers of elements along the cross-sectional height, i.e., 2, 4, and 8 elements. The results are shown in Fig. 5. The fast convergence to the reference result demonstrates the efficiency of the beam formulation. With a difference of approximately 2%, the presented beam formulation is computationally efficient and reliable.

Fig. 6. Contour plots of the total displacement for the first vibration mode (a scale factor of 10−2 is applied to the deformed shapes, and the mass normalization is performed).

Table 2. The first three natural frequencies. Vibration mode

Plane formulation

Beam formulation

Difference (%)

1

720.94

734.36

1.86

2

1521.03

1552.65

2.08

3

2656.66

2721.48

2.44

Lastly, the accuracy of the presented beam formulation is further verified for free vibration analysis. Contour plots of the total displacement for the first vibration mode are portrayed in Fig. 6. Again, an excellent match is observed. The values of the first three natural frequencies are reported in Table 2. The accuracy of the beam formulation is again validated with differences of less than 2.5%.

5 Conclusions This contribution presents a beam formulation for linear analysis of planar curved microbeams made of bi-directional functionally graded materials. The modified couple stress and Euler-Bernoulli beam theories are considered. The material parameters

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are set to vary in the directions of the beam axis and cross-sectional height. NURBS surfaces are conveniently used to describe any complex variations of the material parameters. Several tests are performed using a semi-circular microbeam. The accuracy and efficiency of the presented beam formulation are validated as good results are obtained with smaller numbers of degrees of freedom compared to those of the plane formulation. This quality of the presented formulation is advantageous, and the use of the formulation for material optimization problems is expected to be beneficial since the computational costs can be significantly reduced. Moreover, better-optimized material distributions can also be expected due to the capability of NURBS basis functions to describe complex variations of material distributions. Acknowledgements. This study is supported by the Alumni Support Program for Research (Grant number: SIIT ASP-R 2101) of the ASEAN University Network/Southeast Asia Engineering Education Development Network (AUN/SEED-Net). The first author acknowledges the Postdoctoral Fellowship awarded by the Second Century Fund (C2F) from Chulalongkorn University, Thailand.

References Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194(39–41), 4135– 4195 (2005) Kong, S.: A review on the size-dependent models of micro-beam and micro-plate based on the modified couple stress theory. Arch. Comput. Methods Eng. 29(1), 1–31 (2022) Kong, S., Zhou, S., Nie, Z., Wang, K.: The size-dependent natural frequency of Bernoulli-Euler micro-beams. Int. J. Eng. Sci. 46(5), 427–437 (2008) Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51(8), 1477–1508 (2003) Lobontiu, N., Garcia, E.: Mechanics of microelectromechanical systems. Springer Science & Business Media (2004) Ma, H.M., Gao, X.L., Reddy, J.N.: A microstructure-dependent Timoshenko beam model based on a modified couple stress theory. J. Mech. Phys. Solids 56(12), 3379–3391 (2008) Park, S.K., Gao, X.L.: Bernoulli-Euler beam model based on a modified couple stress theory. J. Micromech. Microeng. 16(11), 2355–2359 (2006) Park, S.K., Gao, X.L.: Variational formulation of a modified couple stress theory and its application to a simple shear problem. Z. Angew. Math. Phys. 59(5), 904–917 (2008) Piegl, L., Tiller, W.: The NURBS Book. Springer, New York (1997) Truong, T.T., Lee, S., Lee, J.: An artificial neural network-differential evolution approach for optimization of bidirectional functionally graded beams. Compos. Struct. 233, 111517 (2020) Vo, D., Borkovi´c, A., Nanakorn, P., Bui, T.Q.: Dynamic multi-patch isogeometric analysis of planar Euler-Bernoulli beams. Comput. Methods Appl. Mech. Eng. 372, 113435 (2020) Vo, D., Nanakorn, P., Rungamornrat, J., Bui, T.Q.: Spatial arbitrarily curved microbeams with the modified couple stress theory: Formulation of equations of motion. Eur. J. Mech. A/Solids (2022a) Vo, D., Suttakul, P., Rungamornrat, J., Nanakorn, P.: Static analysis of planar arbitrarily curved microbeams with the modified couple stress theory. Part I: Euler-Bernoulli beam formulation. Appl. Math. Model. (In revision) (2022b)

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Voigt, W.: Ueber die beziehung zwischen den beiden elasticitätsconstanten isotroper körper. Ann. Phys. 274(12), 573–587 (1889) Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39(10), 2731–2743 (2002)

Steel Braces Optimization Design of Steel Tall Building Based on Stiffness Performance Sensitivity Data Yuzhou Hou1,2 and Xin Zhao1,2(B) 1 Department of Structural Engineering, Tongji University, Shanghai, China

[email protected] 2 Tongji Architectural Design (Group) Co., Ltd., Shanghai, China

Abstract. Complex high-rise steel structures have many design variables. Through sensitivity analysis of grouping of different types of components, it can be determined that optimizing the form, quantity and arrangement of steel braces can effectively reduce the maximum inter-story drift, which is the controlling wind response of the structure, so as to save the time cost of optimization. Adjusting the form, quantity and arrangement of steel braces to achieve the ideal steel consumption on the premise of satisfying the limit of maximum inter-story drift is a process of re-analyzing the modified results and guiding the next modification until the results converge. An effective re-analysis method can also reduce the calculation times and save the time cost of optimization. In the optimization process, sensitivity analysis and reanalysis are indispensable. In this paper, high-rise braced steel frame structure is taken as the research object and the steel braces are divided into groups according to different vertical zones and different plane positions, to analyze the sensitivity of maximum inter-story drift under wind load to different groups of steel braces, and to study the reanalysis method of specific steel structure system, specific design constraints, and specific optimization variables, so as to achieve rapid and efficient optimization design. Finally, a 150 m high-rise steel structure residence is taken as an engineering case to verify the correctness of sensitivity analysis results of high-rise steel structure for wind vibration stiffness performance control, and the effectiveness and practicability of re-analysis method in optimization design. Keywords: Braced steel frame structure · Steel braces optimization design · Sensitivity analysis of stiffness performance · Re-analysis method

1 Introduction In recent years, China has vigorously promoted energy-efficient buildings, and braced steel frame structure, as one of the excellent alternative structural systems for prefabricated buildings, has been more and more applied in the structural design of high-rise residential buildings. Although the designer chose to use the braced steel frame structure, it can be seen from many design results that the designer is still designing the steel structure with the design concept of concrete structure. Different structural systems have © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 894–904, 2023. https://doi.org/10.1007/978-981-19-7331-4_74

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different controlling design constraints, and the primary high-sensitivity components corresponding to the design constraints are also different. Strengthening low-sensitivity components in order to meet the requirements of structural design constraints will only waste the cost of the project. Since the end of the 20th century, a large number of engineers and researchers have been committed to discovering and improving structural optimization design methods of buildings to make full use of the properties of structural materials and reduce engineering costs. Among these researches, sensitivity analysis and reanalysis is one of the most important achievements. Sensitivity indices can be computed by establishing and simplifying mathematical expressions between structural component size and structural control design constraints. It is more direct and effective to optimize the component size according to the sensitivity index than to optimize the component size according to the engineer’s subjective engineering experience. Kirsch et al. (2007) summarized optimization methods based on sensitivity reanalysis for linear and nonlinear, static and dynamic situations. Dong (2015) derived sensitivity indices of story drift and period. Qin (2017) classified design constraints according to structural performance and derived sensitivity indices systematically and comprehensively according to the classification of dynamic characteristics, stiffness, strength and stability. Ma (2018) summarized and classified sensitivity analysis methods, and summarized the characteristics, advantages and disadvantages of virtual work principle based sensitivity index analysis method, constant incremental sensitivity analysis method and total sensitivity index analysis method through experimental cases. Wang et al. (2021) verified the effectiveness of sensitivity analysis through the outrigger optimization of a 623 m super high-rise building, and successfully applied the method to the outrigger optimization of a 428 m super high-rise building. For high-rise braced steel frame structures, the stiffness performance is usually corresponding to the controlling design constraints of the structure. In this paper, based on the previous research results, sensitivity analysis and reanalysis methods are used to study how to effectively optimize and improve the stiffness of high-rise braced steel frame structure under wind load.

2 Stiffness Sensitivity Analysis of High-Rise Braced Steel Frame Structure 2.1 Stiffness Design Criteria for High-Rise Braced Steel Frame Structures In this paper, the load-stiffness performance matrix of high-rise braced steel frame structure system with support is sorted out on the basis of predecessors, and the loads are distinguished according to different design conditions. For steel structures with light weight and high flexibility, the story drift under wind load is often the controlling design constraint of the structure (Table 1). 2.2 Sensitivity Analysis of Story Drift Under Wind Load The story drift under wind load is used to limit the horizontal displacement of structures under serviceability states, in order to avoid the poor comfort at higher floors of buildings and the cracking damage of non-structural elements caused by excessive displacement.

896

Y. Hou and X. Zhao Table 1. Load-stiffness performance matrix.

Design criteria

Gravity load design condition

Seismic design condition Wind resistant design conditions

Entirety

–

–

–

Components

–

Maximum story drift under frequent earthquake ≤1/300, GBT 51232-2016, 5.2.8 Maximum story drift under rare occurrence earthquake ≤1/50, 50011-2010(V2016), 5.5.5 Lateral stiffness ratio, JGJ 99-2015, 3.3.10

Maximum story drift ≤1/300, GBT 51232-2016, 5.2.8

Members

Steel beam deformation control, GB 50017-2017, Appendix B Serviceability limit state, GB 50009-2012, 3.2.2

Story drift ratio, JGJ 3-2010, 3.4.5 –

–

Dong (2015) used the virtual work principle to derive the sensitivity index calculation formula of component size and story drift under wind load, and simplified the expression of sensitivity index to reduce the workload of reanalysis. δ=

N 

eδi

(1)

eδi = Fi i

(2)

i=1

where, δ is the maximum story drift of the structure; N is the number of components; eδi is the virtual work of component i under external load and virtual load; Fi is the nodal force vector of component i under external loads; i is the nodal displacement vector of component i under external loads. According to the principle of energy conservation, the external work of a component is equal to the internal energy of a component. Equation (2) of beam and column components can be expressed as Eq. (3): Lbi eδi = 0

FX fX FY fY FZ fZ MX mX MY mY MZ mZ + + + + + EA GAY GAZ GIX EIY EIZ

 dx

(3)

i

It is assumed that the model to be optimized is a statically determinate structure, and when the size of the optimization variable changes, the internal force of the component

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remains constant, and the internal work of the beam and column components can be expressed as Eq. (4):   ebδ2 ebδ1 ebδ3 ebδ4 ebδ5 ebδ6 + + + + + (4) eδi = EA GAY GAZ GIX EIY EIZ i In these formulations, Lbi is the length of the for the ist beam or column component, FX , FY , FZ , MX , MY and MZ is the internal force of the component under external loads, fX , fY , fZ , mX , mY and mZ is the internal force of the component under virtual loads, A is the cross-sectional area of the beam or column component, AY and AZ is the shear area of the beam or column component, IX , IY and IZ is the torsion and bending moment of inertia of the beam or column component under the inertial force, ebδ is a constant. Beam and column components usually have a rectangular section, assuming that the aspect ratio of the rectangular section is k. The cross-section attributes of beam and column components AY , AZ , IX , IY and IZ can be mathematically expressed with component volume vo. Formula (5) can be obtained by substituting the relation between section attributes of beam and column components and component volume vo into Formula (4):   ebδ1 L 6ebδ2 L 6ebδ3 L ebδ4 kL2 12ebδ5 kL2 12ebδ3 L2 + + + eδi = + + (5) Evo 5Gvo 5Gvo 0.2Gvo2 Evo2 Ekvo2 i For the optimization work where the story drift of a certain layer of the structure is the constraint condition, the component volume is the optimization variable, and the minimum total volume of the component is the optimization objective, the following Lagrange function can be established: L=

N 

voi + λδ (

i=1

N 

eδi − [δ])

(6)

i=1

voL ≤ voi ≤ voU

i = 1, 2, · · · , N

(7)

where, δ is the story drift of the structure, [δ] is the story drift limit of the structure, st voi is the volume of the ist component, voU i is the upper limit of the i optimization variable, voLi is the lower limit of the ist optimization variable, and N is the number of components to be optimized. By taking the derivative of Eq. (7) with respect to voi , the expression of sensitivity index of story drift SIδi can be expressed as Eq. (8): SIδi =

deδi 1 =− dvoi λδ

(8)

where, λδ is the Lagrange multiplier of the story drift constraint optimization work. In order to reduce the times of reanalysis and improve the calculation efficiency, the simplified sensitivity index of story drift SSIδ can be adopted, which is expressed in Eq. (9): SSIδi =

eδi voi

(9)

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By dividing Eq. (5) by voi , the simplified sensitivity index of story drift SSIδi can be expressed as Eq. (10):   ebδ1 L 6ebδ2 L 6ebδ3 L ebδ4 kL2 12ebδ5 kL2 12ebδ3 L2 + + + + + (10) SSIδi = Evo2 5Gvo2 5Gvo2 0.2Gvo3 Evo3 Ekvo3 i For any two beam or column components i and j, if SIδi > SIδj , then SSIδi > SSIδj , the sensitivity index of story drift SIδi of each beam and column component can be determined by referring to the simplified sensitivity indices of story drift. By dividing Eq. (2) by the volume of component i, the simplified sensitivity index of components i under the constraint of story drift SSIδi can be expressed as Eq. (11): SSIδi =

Fi i voi

(11)

By comparing Eqs. (8) and (9), it can be seen that Eq. (8) is the tangent line of the curve of the relation between component volume and story drift, and the most accurate sensitivity index can be obtained by using it. Equation (9) is the slope of the corresponding point on the curve of the relation between component volume and story drift, and the sensitivity index obtained is of low accuracy. However, it can be seen from Eqs. (5) and (10) that the two sensitivity indices have the same trend with the change of component volume and have consistent relative relationship. In this paper, a simplified sensitivity index expression with an accuracy between Eq. (8) and Eq. (9) is adopted, that is, the secant of the curve of the relationship between component volume and story drift, which can be expressed as Eq. (12): SSIδi =

eδi voi

(12)

3 Optimization Design of Brace Based on Sensitivity Reanalysis 3.1 Overview of Study Case In this section, a 150 m high-rise steel structure residence is taken as an example to verify the applicability and convenience of the sensitivity reanalysis method mentioned in Sect. 2 in brace optimal design of braced steel frame structure. The building height of the tower is 149.85 m, with a total of 44 floors, of which the 1st floor is the lobby, the 15th floor and the 30th floor are refuge floors, and the other standard floors are residential. The two refuge floors divide the tower vertically into three zones: low, middle and high. The tower adopts a braced steel frame structure consisting of concrete-filled rectangular steel tubular columns, composite floors of steel beams and concrete slabs, and steel braces. The building, located in Shanghai, has a reference wind pressure of 0.55 kN/m2 during the 50-year return period, which is used for the stiffness design of the tower, and the corresponding damping ratio is 2%. The length-width ratio of the building plane is about 3.2, the structural shape factor of wind load is 1.2 in the X direction and 1.4 in the Y direction, and the terrain roughness is class D (Fig. 1).

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Fig. 1. 3D model and vertical partition diagram of the tower.

Fig. 2. Standard layer of middle and high zone of the tower.

When the structure is arranged as shown in Fig. 2, the story drift under wind load is 1/300, which is equal to the limit value. After preliminary design analysis, the sensitivity index of steel braces to the story drift under wind load is higher than that of columns. In order to ensure that the stiffness of the tower has appropriate redundancy, and to strengthen the stiffness while saving the amount of material as much as possible, the sensitivity reanalysis method is adopted to optimize brace design of this project. 3.2 Grouping of Potential Brace Strengthen Positions Firstly, according to the architectural function of each floor plan in the building drawings, the possible positions to strengthen braces are figured out, so the design variables are screened once to reduce the computational workload. For the residential standard floor, the baseline condition has been as full as possible to lay out braces, so the strengthening method is to change the original unidirectional brace to x-type bidirectional brace. For refuge floors as 15 and 30 F, there are two ways of strengthening, one is adding unidirectional braces, the other is replacing the original unidirectional brace with x-type bidirectional brace.

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Fig. 3. Story drift of Benchmark solution structure under wind load.

Secondly, vertical groups are made for the positions to strengthen braces of the whole building. As can be seen from the curve in Fig. 3, the areas where the story drift is close to the limit are the middle and high zones, which can further exclude the potential positions to strengthen braces in the range of low zone. Compared with the baseline condition, condition 1 (replacing the original unidirectional braces with x-type bidirectional braces in the stairwells on 20–29 F) and condition 2 (replacing the original unidirectional braces with x-type bidirectional braces in the stairwells on 35–44 F) are added (shown in Fig. 4). Thirdly, the potential positions to strengthen braces are divided into three groups in the standard floor plan. According to different building functions of the potential positions to strengthen braces, condition 3 (replacing the original unidirectional braces with x-type bidirectional braces at external walls on 20–29 F) and condition 4 (replacing the original unidirectional braces with x-type bidirectional braces at internal partitions on 20–29 F) are added (shown in Fig. 5). Finally, the potential positions to strengthen braces at asylum floors are divided into four groups, and condition 5 (replacing the original unidirectional braces with x-type bidirectional braces on 15 F), condition 6 (replacing the original unidirectional braces with x-type bidirectional braces on 30 F), condition 7 (adding unidirectional braces on 15 F), and condition 8 (adding unidirectional braces on 30 F) are added (shown in Fig. 6). 3.3 Sensitivity Analysis of Braces First of all, sensitivity analysis of the baseline condition and condition 1 and condition 2 is carried out, and the results are shown in Table 2. As can be seen from Table 2, strengthening high-zone braces does not contribute to the redundancy of structural overall stiffness. Therefore, the potential positions to

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Fig. 4. Schematic diagram of baseline condition, condition 1 and condition 2.

Fig. 5. Schematic diagram of condition 3 and condition 4.

strengthen braces in the high zone can be excluded to further reduce the computational workload. Thus, condition 3 and condition 4 can just be used for 20–29 F in the middle zone. Sensitivity analysis results of the baseline condition and condition 1, 3 and 4 are compared, and the results are shown in Table 3. It can be seen from Table 3 that strengthening the three groups of braces in the middle zone all contributes to the redundancy of structural overall stiffness, and its contribution degree can be ranked from large to small according to the absolute value of sensitivity index: condition 1 > condition 3 > condition 4. Finally, sensitivity analysis of conditions 5–8 is carried out, and the result comparison between conditions 5–8 and the baseline condition is shown in Table 4. According to Table 4, only strengthening the two groups of braces on 30 F contributes to the redundancy of structural overall stiffness, and their contributions can be ranked from large to small according to the absolute value of sensitivity index: condition 8 > condition 6. According to the above analysis, only strengthening braces in the middle zone of the tower has an effect on the improvement of structural stiffness performance. The order of improvement efficiency is condition 8 > condition 1 > condition 3 > condition 6

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Fig. 6. Schematic diagram of condition 5, condition 6, condition 7 and condition 8. Table 2. Sensitivity data between brace strengthen conditions grouping by vertical position. Condition 2

Condition 1

Baseline condition

value

1/767

1/779

1/766

Percentage

100%

98%

100%

Value

1/300

1/306

1/300

Percentage

100%

98%

100%

Difference (1/1000)

0

−0.065

0

Incremental steel use per m2 (kg/m2 )

0.46

0.46

0

Sensitivity index of y-direction story drift under wind load ((1/1000)/kg)

–

−0.141

–

Story drift under wind load

X direction Y direction

> condition 4 in descending order, and the order of improvement effect is condition 1 > condition 3 > condition 4 > condition 6 and condition 8 in descending order. Considering the efficiency and effect of stiffness performance improvement, the above five conditions are finally all adopted as a comprehensive condition. Finally, the story drift of the structure under wind load is 1/309, the story drift difference is −0.097 (1/1000), and the increment of steel quantity per m2 is 0.6 kg/m2 . The sensitivity index of the y-direction story drift under wind load is −0.162 (1/1000)/kg.

4 Conclusions In this paper, based on the previous research results of sensitivity analysis and structural optimization, the incremental sensitivity analysis method is used to study the sensitivity

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Table 3. Sensitivity data between brace strengthen conditions grouping by plane position.

Story drift under wind load

X direction Y direction

Condition 4

Condition 3

Condition 1

Baseline condition

Value

1/766

1/767

1/779

1/766

Percentage

100%

100%

98%

100%

Value

1/302

1/305

1/306

1/300

Percentage

99%

98%

98%

100%

Difference (1/1000)

−0.022

−0.055

−0.065

0

Incremental steel use per m2 (kg/m2 )

0.51

0.62

0.46

0

Sensitivity index of y-direction story drift under wind load ((1/1000)/kg)

−0.044

−0.088

−0.141

–

Table 4. Sensitivity data between brace strengthen conditions at refuge floors.

Story drift under wind load

Condition 8

Condition 7

Condition 6

Condition 5

Baseline condition

X direction

Value

1/769

1/766

1/769

1/766

1/766

Percentage

100%

98%

100%

98%

100%

Y direction

Value

1/302

1/300

1/301

1/300

1/300

Percentage

99%

100%

100%

100%

100%

Difference (1/1000)

−0.022

0

−0.011

0

0

Incremental steel use per m2 (kg/m2 )

0.08

0.06

0.19

0.21

0

Sensitivity index of y-direction story drift under wind load ((1/1000)/kg)

−0.278

–

−0.057

–

–

between the brace design and the stiffness constraint of braced steel frame structure. In the process of structural optimization, the potential positions to strengthen braces are grouped according to the building function, and the sensitivity index of braces to the story drift under wind load was obtained, which successfully guided the optimization design of structural braces and improved the structural stiffness with minimal cost. The applicability of the incremental sensitivity analysis method is verified by the optimization of a practical engineering case. The conclusions are as follows: 1. The method of strengthening braces aims to reduce the maximum story drift to improve the stiffness performance of the structure, and it can only be effective in floors where the story drift is close to the limit.

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2. The brace positions at external walls of the building is more sensitive to the story drift than those at internal partitions of the building, and the addition of braces is more sensitive to the story drift than the strengthening of original braces. 3. When several groups of brace reinforcement conditions with different sensitivity indices are combined, the sensitivity index of the comprehensive condition is no greater than that of the most efficient condition before combination, nor less than that of the least efficient condition before combination. 4. Sensitivity analysis results of different components obtained by incremental sensitivity analysis method and reasonable reanalysis of the results can effectively reduce the computational workload of optimization design, and the analysis results have good guiding significance and practical value for practical engineering. Thus, Incremental sensitivity analysis method has good practicability.

Acknowledgements. Sensitivity Data Driven Multilevel Design Optimization of Super Tall Building Structures—Theory and Methodology, Sponsored by Natural Science Foundation of Shanghai, Project No.: 21ZR1469200.

References Bogomolni, M., Kirsch, U., Sheinman, I.: Efficient design sensitivities of structures subjected to dynamic loading. Int. J. Solids Struct. 43, 5485–5500 (2006) Dong, Y.M.: Optimal design for structural lateral system of super tall buildings under multiple constraints. Tongji University (2015) Kirsch, U.: Reanalysis and sensitivity reanalysis by combined approximations. Struct. Multidisc. Optim. 40, 1–15 (2010) Kirsch, U., Bogomolni, M., Sheinman, I.: Efficient structural optimization using reanalysis and sensitivity reanalysis. Eng. Comput. 23, 229–239 (2007) Ma, Z.: Descending order reversely constrained optimal design for super tall structure. Tongji University (2018) Manickarajaha, D., Xie, Y.M., Steven, G.P.: Optimum design of frames with multiple constraints using an evolutionary method. Comput. Struct. 74, 731–741 (2000) Ministry of Housing and Urban-Rural Development of the People’s Republic of China: Technical specification for steel structure of tall building, JGJ 99-2015, Beijing, China Architecture & Building Press (2015) Ministry of Housing and Urban-Rural Development of the People’s Republic of China: Technical standard for assembled buildings with steel-structure, GB/T 51232-2016, Beijing, China Architecture & Building Press (2017) Qin L.: Constraints sensitivity and multi-constraint optimal structural design of super tall building. Tongji University (2017) Wang, L.L., Zhao, X.: Fast optimization of outriggers for super-tall buildings using a sensitivity vector algorithm. J. Build. Eng. 43, 102531 (2021) Zuo, W., Huang, K., Bai, J., Guo, G.: Sensitivity reanalysis of vibration problem using combined approximations method. Struct. Multidiscip. Optim. 55(4), 1399–1405 (2016). https://doi.org/ 10.1007/s00158-016-1586-z

Sensitivity Data Driven Composite Floor Structural Optimization for Tall Office Buildings Morn Chornay1 and Xin Zhao1,2(B) 1 Department of Structural Engineering, Tongji University, Shanghai, China

[email protected] 2 Tongji Architectural Design (Group) Co., Ltd., Shanghai, China

Abstract. In tall office buildings, steel beam composite floor system is a popular solution for floor systems as it is known for requiring less construction time and having good weight-to-strength ratio. However, despite being a relatively lightweight floor system, steel beams in composite floor systems are still accountable for a large percentage of buildings’ self-weight. Therefore, optimization of this floor system design is still required, especially for tall buildings, and it can be achieved by reducing the weight of steel beam supporting the composite deck. In this paper, optimization methods, Multiple Decomposition Method and Sensitivity Data Driven Algorithm, are employed to design and optimize a large span steel beams supporting deck floor of a tall office building. Based on Multiple Decomposition Method, the composite floor’s beams are divided into three substructure levels. To global structural performance, the 1st level which consists of the entire composite deck floor aims to achieve floor the serviceability performance. Subsequently, the 2nd level involves serviceability requirement of composite beams within the floor. Lastly, the 3rd level consists of structural elements such as the composite deck, steel beams, and shear studs, and the optimization problem is related to sizing the cross-section dimensions of each beam to meet the design requirements from both the 2nd level and 3rd level. In addition, Sensitivity Data Driven Algorithm is also used to further determine design constraint sensitivity coefficients to design variables as guidance to examine optimum beam sizing proportion. Keywords: Tall office building · Composite floor steel beam · Sensitivity data driven algorithm · Multiple decomposition method

1 Introduction Tall buildings have been selected in urban-planning strategy as a solution to increasing demands in housing, office, and commercial space in limited land for development. Moreover, in recent decades, the importance of building sustainability is being realized and emphasized in many fields, and structural engineers also play an important role in providing well-engineered buildings by minimizing material consumption (minimum structural weight), reducing building carbon footprint, and reducing maintenance and retrofit cost throughout building service life. As a result, to improve practicality, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 905–916, 2023. https://doi.org/10.1007/978-981-19-7331-4_75

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efficiency, and accuracy in structural optimization design problems, many optimization algorithms such as multilevel decomposition (Sobieszczanski-Sobieski et al. 1987), and reanalysis and sensitivity reanalysis (Kirsch 2010), have been developed. This paper presents a procedure to optimize structural beam members (I-shaped steel beams supporting decked slab) for minimum weight by using a combination of two optimization methods which are Multi-Decomposition Method and Sensitivity Data Driven Algorithm. Details and a framework of optimization methods are introduced in Sect. 2. Implementation of optimization methods on steel beam design is given in Sects. 3 and 4 are related to results and conclusion respectively.

2 Optimization Methods Introduction and a detailed framework of optimization methods are given here. Multiple decomposition method is described in Sect. 75.1, and Sensitivity data driven algorithm is described in Sect. 75.2. 2.1 Multilevel Decomposition Method Multilevel decomposition method is an optimization procedure that decomposes a large intractable problem (entire system) into small tractable subproblems (subsystems), solves each subproblem independently and optimally, preserves coupling between among subproblems and entire problem, and iterates the problem to a converged point (Sobieszczanski-Sobieski et al. 1985). This approach also reduces computational costs which increase nonlinearly to problem size and complexity (Yates et al. 1994). Furthermore, in structural design applications, this procedure aligns nicely to engineer design workflow since engineers often work in teams which each individual works simultaneously on different parts of a project (Sobieszczanski-Sobieski et al. 1987), and the decomposition process is natural and can be easily visualized since a structure is always seen physically as a composition of different aspects in term of materials, structural elements, or floors. However, Sobieszczanski-Sobieski et al. (1987) mentioned that coupling between levels would introduce a costly computation due to two-way coupling effect caused by reoptimization of elements affected by the change in design variables, and this limitation is solved by the introduction of optimum sensitivity analysis which will be explained in detail in Sect. 75.2. In structural design application, a system (an entire structure) is seen as a hierarchical system and is decomposed into several levels. Generally, 1st level is always the entire system (a whole structure) while the lower levels (subsystems) are arranged hierarchically (which can be based on physical or field perspective). 1st level (entire system) is often subjected to global constraints such as lateral displacement, story drift, or frequencies which are affected by global variables such as cross-section area, and planar and polar moment of inertia while the objective function such as minimum structural weight is also controlled at the 1st level. At lower levels (subsystems), it is often related to subsystem constraints such as relative constraints, member stress, member stability, local stress, or local stability which are controlled by subsystem design variables (which

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can be cross-section dimensions) while objective functions (also known as the cumulative constraint) measuring the degree of constraint violation is to be minimized. The optimization is achieved by minimizing or maximizing objective functions and minimizing cumulative constraint through the process of iterating back and forth between the solution of the system and subsystems until convergence is reached. This method has been adopted in many works such as optimization of prestressed concrete via two-level optimization (Kirsch 1997), steel frame optimization (Li et al. 1999), and space truss optimization (Yates et al. 1994). A composite floor system shown in Fig. 1 is used to demonstrate a framework on how multilevel decomposition optimization method can be used to optimize a large-scale problem of a structural floor design for minimum weight. Figure 2 shows the hierarchical system of the whole floor which is decomposed into three levels, and level 1, level 2, and level 3 is the entire floor systems; composite beams; and steel beam, slab, and shear studs respectively.

Fig. 1. Composite floor system of a tall building

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Level 1 110

Entire Composite Floor 110

Level 2 2n1

Composite beam 211

Composite beam 221

Composite beam 2n1

Level 3 3jn

Steel beam 3j2

composite floor deck 3j2

Headed shear stud 3j2

Fig. 2. The hierarchical system of the composite floor

Once the hierarchical system is determined, optimization and flow of information are summarized in Table 1. Table 1. Optimization and flow of information Level 01: Entire composite floor Objective

Minimum composite beam material mass

Design variables

Beam sections

Design constraints

Natural frequency of the floor

Level 02: Composite beams Design variables

Beam sections

Constraints

Deflection of single beam

Level 03: Design limit states of each composite beam Design variables

Height of the beam

Constraints

Strength utilization of single composite beam

Full optimization problem of the whole floor is not illustrated in this paper. However, in the view of the fact that the nature and process of composite beam optimization is the same, a detailed framework of an optimum design for minimum mass of one structural composite beam would be able to provide useful insight in the large portion of optimization problem, and optimum composite beam design can be effectively achieved by using sensitivity data driven algorithm which is presented in the following section. 2.2 Sensitivity Data Driven Algorithm Sensitivity analysis has been an important involving area in engineering research, and it has been applied to various disciplines (eg. Chemical kinetics, aerodynamics, structural analysis, etc.) (Adelman et al. 1984). Sensitivity analysis is used to evaluate how sensitive

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response is to the change of its design parameter, and this involves the derivations of the response to its design parameter to determine the sensitivity coefficient, which provides useful insights on how each design parameter affects the direction and magnitude of the response (Kirsch 2009). Related multilevel decomposition optimization method, sensitivity analysis has also been a useful tool to bypass the costly computation of subsystem reoptimization since sensitivity analysis is used to quantify subsystem’s parent effects on the change of subsystem’s minimized constraint violation measure and subsystem design variable (Sobieszczanski-Sobieski et al. 1985). Sensitivity data driven algorithm is used to find the most effective design variables to satisfy design constraints or requirements in Level 2 and Level 3, and, in optimization of a composite beam, it is translated into detailed composite beam dimensions which result in minimum beam cross-section area and minimum cumulative constraint or, in other words, satisfy design requirements with minimum beam cross-section area. In addition, it should be noticed that shear studs and slabs are not input parameters that are to be optimized in composite beam design since the minimum area of steel beam will result in minimum numbers of shear studs, shear studs are relatively light compared to other structural members, and composite steel deck profile and overall thickness are generally designed and optimized based on structural beam layout rather than composite beam strength or stiffness requirement. Hence, composite steel beam optimization can be done as follows. • • • •

Determining design objective (minimum structural weight or cross-section) Identifying design requirements (serviceability at level 2, and strength in level 3) Defining design variables (height and width of a beam) Computing sensitivity coefficients (cross-section, deflection, and design strength sensitivity coefficients to design variables in different beam width-to-height ratio cases).  ∂F  xi,o · (1) Sensitivity Coefficient = F(xo ) ∂xi x0

Once sensitivity coefficients are calculated, the optimum detailed composite beam dimension is chosen based on a width-to-height ratio case which the cross-section area is less sensitive to change in beam height, and deflection and design strength have the highest sensitivity coefficient to change in beam height.

3 Case Study At level 02 in the hierarchical system of the composite floor, a large-span composite Ishaped steel beam shown in Fig. 3 is selected for a case study and is designed according to an international building code, ANSI/AISC 360-16 Specification for Structural Steel Buildings (Fig. 4 and Table 2). Sensitivity coefficient of design constraints to design variables in different beam width-to-height ratio cases is shown in Tables 3 and 4, and derivatives are computed by using forward finite difference (1st order accurate).

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135

64 140

76

140

76

64

Beff

141

Tf

Tw

H

305

164

B

(a) Composite Deck Section

(b) Composite Steel Beam

Fig. 3. (a) Composite deck section, (b) composite steel beam section

Table 2. Input data of composite beam Material input Steel specification 

Concrete strength, F c

ASTM A36 (Fy = 245 MPa) 30.00 MPa

Geometry input Beam span, L

L = 11.80 m

Boundary condition

Simply supported beam (finned plate connection)

Load distribution width

2.90 m

Composite deck total height

140 mm (concrete topped up of 64mm)

Design assumptions Composite action percentage

100%

Steel section classification

Compact flange, compact web

Construction method

Shoring provided during construction

Design load Composite beam self-weight

Varies

Composite deck

2.51 kPa (data from manufacturer’s specifications)

Superimposed dead load, SDL

3.00 kPa

Floor live load, LL

2.40 kPa

From sensitivity coefficient, it can be said that steel beam moment of inertia (Ix ), design strength (flexural strength, φMn and shear strength, φVn ), and beam deflection () are more sensitive to change in height than that in width since coefficients predict that quantities (such as Ix , φMn , and φVn ) increase quadratically, and beam deflection () also decrease quadratically with change in height. Moreover, it is also seen that the

Sensitivity Data Driven Composite Floor Structural Optimization

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Uniform Distributed Load, W (kN/m)

L = 11.80m

Fig. 4. Composite beam model for structural analysis

Table 3. Sensitivity coefficients to height change (H) in different width-to-height ratio cases Width-to-height ratio

Constraints at level 02

Constraints at level 03

Area, As

Moment of Inertia, Ix

Deflection, 

φMn

φVn

0.20

1.482a

2.972

−2.721b

2.109

2.035

0.25

1.287

2.755

−2.538

1.916

2.045

0.30

1.107

2.596

−2.378

1.737

2.055

0.35

0.949

2.480

−2.246

1.581

2.064

0.40

0.813

2.396

−2.139

1.448

2.074

0.45

0.699

2.334

−2.054

1.337

2.084

0.50

0.603

2.288

−1.987

1.245

2.094

a Positive sign indicates increases in value as beam height increases b Negative sign indicates decreases in value as beam height increases

relation between increase in cross-section to that in height is almost a linear relation when the range of beam width-to-height ratio is between 0.3 and 0.35. Tables 5 and 6 shows steel composite beam design outputs in different beam widthto-height ratio cases, and the results are based on targeted minimum utilization of 0.95 of allowable deflection or controlling design strength. Compared to width-to-height ratio of 0.20, width-to-height ratio of 50 not only requires larger steel cross-section area (34% larger), but also produces less desirable structural performance in term of beam deflection () and shear strength (φVn ). Generally, it can be seen the smaller the beam width-to-height ratio is, the smaller the steel cross-section section is required to satisfy design requirements/constraints, and the better the cross-section performance is. In addition, computation of sensitivity coefficients of composite beam studied above does not account for the change in beam internal forces due to change in beam stiffness, and it is acceptable due to assumed boundary condition which is simply supported beam. However, sensitivity coefficients of composite beam with support condition rather than simply supported beam (e.g. composite beam with moment connection at its ends) shall consider internal forces redistribution due to change in beam stiffness. Moreover, despite

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Table 4. Sensitivity coefficients to beam change (B) in different width-to-height ratio cases Width-to-height ratio

Constraints at level 02

Constraints at level 03

Area, As

Moment of Inertia, Ix

Deflection, 

φMn

φVn

0.20

0.516 a

1.020

−0.567b

0.508

−0.038

0.25

0.711

1.238

−0.753

0.699

−0.047

0.30

0.891

1.398

−0.911

0.874

−0.057

0.35

1.049

1.514

−1.038

1.026

−0.067

0.40

1.185

1.599

−1.135

1.154

−0.077

0.45

1.299

1.661

−1.207

1.259

−0.086

0.50

1.395

1.707

−1.259

1.345

−0.097

a Positive sign indicates increases in value as beam height increases b Negative sign indicates decreases in value as beam height increases

Table 5. Steel cross-section detailed dimensions in different width-to-height ratio cases Width-to-height ratio

H (cm)

B (cm)

Tf (cm)

Tw (cm)

Area, As (cm2 )

Moment of Inertia, Ix (cm4 )

0.20

67.90

13.58

0.63

0.68

62.47

36,057

0.25

64.60

16.15

0.74

0.65

64.81

38,028

0.30

61.30

18.39

0.85

0.61

67.53

39,232

0.35

58.00

20.30

0.93

0.57

70.22

39,373

0.40

54.90

21.96

1.01

0.54

73.05

38,921

0.45

52.00

23.40

1.08

0.51

75.87

37,966

0.50

51.00

25.50

1.17

0.50

84.13

41,959

there are some conditions (eq. AISC G2-1a, AISC G2-3, and G2-4 in Appendix A) in shear strength calculation, the sensitivity coefficient of composite beam shear strength is still a good prediction in the change in shear strength due to constant steel beam depth to steel beam web thickness ratio and constant steel beam depth to steel beam flange thickness ratio (Figs. 5 and 6).

4 Conclusion Multilevel decomposition method is a practical optimization algorithm since decomposition of a large optimization problem into smaller subproblems makes the nature of

Sensitivity Data Driven Composite Floor Structural Optimization

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Table 6. Constraints and utilization ratio in different width-to-height ratio cases Width-to-height Constraints at level 02 Constraints at level 03 ratio Deflection, allow / φMn (kN.m) φVn (kN.m) Mu /φMn  (mm)

Vu /φVn

0.20

23.3

0.465

646

407

0.952

0.504

0.25

23.7

0.474

646

365

0.953

0.563

0.30

24.3

0.486

648

325

0.951

0.632

0.35

25.1

0.503

648

289

0.953

0.713

0.40

26.1

0.522

648

256

0.953

0.804

0.45

27.2

0.544

648

228

0.954

0.906

0.50

25.5

0.511

707

217

0.877

0.953

Steel cross-section Area (cm2)

90 85 84.13

80 75

75.87 73.05

70 70.22 65 60

67.53 62.47

64.81

55 50

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Beam width-to-height ratio Fig. 5. Steel cross-section area (cm2 ) according to beam width-to-height ratio

optimization more manageable and trackable while it also enables optimization of subproblems to be done independently with the application of optimum sensitivity derivatives. In addition, by providing useful insights in behavior and direction of design outputs to change in inputs, sensitivity data driven algorithm serves as an efficient process in exploring for optimum design variables and optimum cumulative constraints in multilevel decomposition method. A composite deck floor from an office building on plot 4 of Hongqi Village was optimized for the minimum structural weight of composite beams. Based on multilevel level decomposition, the entire floor was decomposed into three levels which 1st, 2nd,

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Ultilization

0.70 0.60 0.50 0.40 0.30 Δallow/Δ

0.20

Vu/ϕVn

0.10

Mu/ϕMn

0.00 0.2

0.25

0.3

0.35

0.4

0.45

0.5

Beam width-to-height ratio Fig. 6. Limit state utilization according to beam width-to-height ratio

3rd level are the entire floor; composite beams; and the slab, shear studs, and steel beam respectively, and, to efficiently determine the sizing proportion of composition steel beam for minimum structural weight and maximum structural performance, sensitivity coefficients from sensitivity data driven algorithm is employed. Numerical results have shown that sensitivity coefficients provide a reliable and convenient path to search for optimum design variables for each subproblem, and it is also worth mentioning that minimizing design variables within each design constraint shall be implemented in order to reduce laborious efforts required for computation of derivatives for sensitivity coefficient determination.

Appendix A This appendix provides necessary detailed formulations for composite steel beam analysis. Limiting width-thickness ratios for flanges of doubly I-shaped built-up sections  Es Compact web : (H − 2Tf )/Tw ≤ λp = 3.76 (AISC Table B4.1b) Fy  Es (AISC Table B4.1b) Compact flange : (0.5B)/Tf ≤ λp = 0.38 Fy Notice: In this study case, Tf chosen for design is 10% larger than Tf required by AISC specifications.

Sensitivity Data Driven Composite Floor Structural Optimization

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Steel beam section properties As = BTf + (H − 2Tf )Tw Is.x = (1/12)(BH3 ) − (1/12)(B − Tw ).(H − 2 Tf )3 Zx = (1/4)BH2 Transformed concrete section properties Beff = min (min beam spacing. 2 the smallest distance to the nearest slab edge, L/4) (AISC Sec I3.1a) Beff.Tr = αBeff α = Ec /Es Ac.tr = Beff.tr Hcon Ic.tr.x = (1/12)Beff.tr H3con Full composite beam section properties Y = (Ac.tr (Hcon /2) + As .(Hdeck.total + H/2))/(Beff.tr Hcon + As ) Ifull.com.x = Isx + As ((Hdeck.total + 0.5 H) − Y)2 + Ic.tr.x + Ac.tr .((0.5 Hcon ) − Y)2 Total deflection after composite action Ieff.x = Ifull.com.x (100% composite action and shoring during construction) max.mid =

5 (Mdead + Msuper-dead + Mliveload )L2 48 E Ieff.x allowable =

L 240

Design composite plastic moment capacity for positive bending Assuming shear studs provide 100% composite action. C = min(As Fy , 0.85 fc Hcon Beff ) C 0.85 fc Beff   H a Mn = C + Hdeck.total − 2 2 a=

(AISC C-I3-6, C-I3-7) (AISC C-I3-6, C-I3-9) (AISC C-I3-10)

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φMn = φbcpp Mn = 0.9 Mn

(AISC Sec. I3.2)

Design shear strength in the major direction For I-shaped section, φv Vn = φv 0.6Aw Fy Cv1  φv = 1.0 if(H − 2Tf )/tw ≤ 2.24  0.9 if(H − 2Tf )/tw > 2.24  Cv1 = 1.0 if(H − 2Tf )/tw ≤ 1.10

(AISC G2-1)

Es Fy

Es Fy

(AISC G2-1a)

5.34 Es Fy

  1.1 5.34 Es /Fy 5.34 Es if(H − 2Tf )/tw > 2.24 (H − 2Tf )/tw Fy Aw = HTw

(AISC G2-3, G2-4) (AISC G2-1)

References Adelman, et al.: Structural sensivity analysis: methods, applications and needs. Recent Experiences in Multidisciplinary Analysis and Optimization, Part 1 (1984) ANSI/AISC 360-16: Specification for structural steel buildings. American Institute of Steel Construction, Chicago, Illinois (2016) ASCE/SEI 7-16: Minimum design loads and associated criteria for buildings and other structures. American Society of Civil Engineers. Reston, Virginia (2017) Building code requirement for structural concrete (ACI 318-19) and commentary, ACU 318R-19. American Concrete Institute, Farmington Hills, MI (2019) Krish, U.: Two-level optimization of prestressed structures. Eng. Struct. 19(04), 309–317 (1997) Krish, U.: Reanalysis and sensitivity reanalysis by combined approximations. Struct. Multidisc. Optm. 40(03), 01–15 (2009) Krish, U.: Reanalysis and sensitivity reanalysis by combined approximations. Struct. Multidisc. Optm. 40(1-6), 01–15 (2010) Li, et al.: Multiobjective and multilevel optimization for steel frames. Eng. Struct. 21(06), 519–529 (1999) Sobieszczanski-Sobieski, et al.: Structural optimization by multilevel decomposition. AIAA J. 23(11), 1775–1782 (1985) Sobieszczanski-Sobieski, et al.: Structural sizing by generalized, multilevel optimization. AIAA J. 25(01), 139–145 (1987) Yates, K., Gürdal, S., Thangjitham, S.: Multilevel optimization of space trusses using continuum modelling. Struct. Optim. 7(03), 176–183 (1994)

Load-Resistant Mechanism and Failure Behaviour of RC Flat Plate Slab-Column Joints Under Concentric and Eccentric Loading Mengzhu Diao1 , Hong Guan1(B) , Huizhong Xue2 , Yi Li3 , and Xinzheng Lu4 1 School of Engineering and Built Environment, Griffith University, Queensland, QLD 4222,

Australia [email protected], [email protected] 2 Shandong Jianzhu University, Jinan 250101, China [email protected] 3 Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China [email protected] 4 Key Laboratory of Civil Engineering Safety and Durability of Ministry of Education, Tsinghua University, Beijing 100084, China [email protected]

Abstract. Progressive collapse, usually caused by accidental or abnormal loading, is a structural failure disproportionate to its original cause. Reinforced concrete (RC) flat plate structures are vulnerable to brittle punching shear failure in the vicinity of slab-column joints, which may initiate disastrous progressive collapse causing significant economic, social, and psychological consequences. This paper presents a series of experimental investigations of twenty-one 1/3-scaled slab-column joint specimens with in-plane restraints, under opposite punching shear directions, and subject to concentric and eccentric loading conditions. Three design parameters (slab thickness, reinforcement ratio, and flexural reinforcement extension) and three strengthening methods (embedded beams, stirrups in punching area, and ring beams) were considered. The load-resisting and deformation capacities of the joints, as well as their punching shear and post-punching failure behaviours were examined in detail. In addition to the experimental studies, numerical modelling techniques were also developed to simulate the physical tests with emphasis on their load-displacement responses, punching shear and post-punching capacities and crack development. Results demonstrate that (1) the punching shear capacity is mainly governed by the geometrical dimensions of the slab; (2) the post-punching strength is primarily regulated by the integrity rebars going through the column. The continuous integrity rebars are imperative for activating tensile membrane action thereby enhancing post-punching capacity in progressive collapse events. Keywords: RC flat plate systems · Slab-column joints · Punching shear failure · Post-punching failure · Load resistance

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 917–928, 2023. https://doi.org/10.1007/978-981-19-7331-4_76

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1 Introduction An RC flat plate is one of the most popular structural systems used for the construction of high-rise commercial/residential buildings and carparks in Australia and worldwide. Flat plate construction is however prone to brittle punching shear failure in the vicinity of slab-column joints which may trigger a catastrophic progressive collapse of the entire structure. The most recent partial collapse of a 40-year-old reinforced concrete (RC) flat plate building in Surfside, Florida was the most severe incident initiated by punching shear failure, which claimed 98 lives (Lu et al. 2021). Similar collapses have continued to occur worldwide at an alarming rate, exemplified by the underground carpark collapse in Spain in 2020 (Euro Weekly 2021) and more than ten similar collapses in China since 2014 (ABCNews 2021) with estimated US$20 million direct economic losses. Given that a progressive collapse is an event with low probability, adequate postpunching strength and deformation capacity are considered as an effective and low-cost secondary defence for preventing the propagation of progressive collapse. Tests carried out by Melo and Regan (1998), Habibi et al. (2012), Ruiz et al. (2013) and Peng (2015) show that the post-punching strength of a slab with both flexural and integrity reinforcements could reach up to 70% of the punching shear strength. Therefore, properly detailed continuous integrity reinforcement in the slab may arrest catastrophic progressive collapse of flat plate structures. In addition, existing studies on the slab-column joints show that the development of the secondary defence mechanism (tensile membrane action, TMA) in the post-punching stage can be fully activated with properly anchored reinforcement and well-restrained boundary conditions (Hawkins and Mitchell 1979; Regan et al. 1979; Mitchell and Cook 1984; Keyvani et al. 2014). Nevertheless, existing tests regarding punching and post-punching failure behaviours are mostly made on isolated slab-column joints with simple supports. Note that progressive collapse is a complex mechanical process in structural systems where, after the initial failure occurred, subsequent UPS (upward punching shear) and DPS (downward punching shear) failure may occur at the adjacent slab-column joints due to load redistributions. Currently, most studies have focused on the behaviour of slab-column joints under UPS failure modes (Ruiz et al. 2010; Carvalho et al. 2011), with few research being conducted considering DPS failure modes. Existing experimental work on eccentrically loaded slab-column joints (Elgabry and Ghali 1996; Kruger et al. 2000; Binici and Bayrak 2005) show that the unbalanced moments, caused by unsymmetrical loading and/or boundary conditions, and unequal spans etc., could cause the reduction of the punching shear capacity of the slabcolumn joints. However, experimental investigations on the post-punching mechanism of eccentrically loaded (EL) joints are still lacking. To gain an in-depth understanding of the load-resistant mechanism, and punching shear and post-punching failure behaviours, this paper presents experimental and numerical studies of laterally-restrained slab-column joints under opposite punching shear directions, and subjected to concentric and eccentric loading.

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2 Slab-Column Joints Under Concentric Loading 2.1 Experimental Tests To investigate the punching and post-punching shear behaviours of interior slab-column joints, a total of fourteen 1/3-scaled RC slab-column joint specimens were tested under concentric loading, representing a high shear force and balanced moment condition (Diao et al. 2018; Yang et al. 2018) (see Fig. 1a). The specimens were divided into the UPS and DPS failure cases (Fig. 1b). The slab reinforcements are similar in these two cases except that the top and bottom reinforcements were swapped in position. The overall dimension of each specimen was 2000 mm × 2000 mm with the slab being monolithically casted with a strong boundary beam of 300 mm × 380 mm to represent the actual in-plane restraints likely provided by the surrounding slab. A column stub with a 150mm × 150mm cross-section, and 90 mm and 120 mm extrusions from the top surface and soffit of the slab, respectively, was built. The slab reinforcing bars of 8mm diameter were of HRB400-grade and C30-grade concrete was used (with the mean concrete cylinder compressive strengths f cm given in Table 1 for the UPS series). Four steel columns bolted and welded to the four corners of the boundary beam provided adequate fixity of the specimens. A quasi-static pushdown loading method was used and a downward displacement was applied to the top of the column stub. Three design parameters given in Table 1 were examined including the slab thickness h, the slab top and bottom reinforcement ratios ρ T and ρ B , and the anchorage length of flexural reinforcement lb . Three strengthening methods were also investigated covering embedded beams, stirrups in punching area, and ring beams (Fig. 1c). The structural parameters of the DPS series were the same as those of the UPS counterparts, with different values of f cm (27 MPa, 25 MPa, 25 MPa, 27 MPa, 24 MPa, 25 MPa and 32 MPa for DPS-1 to DPS-7, respectively).

(a) Test setup

(b) Specimens

(c) Strengthening methods showing top reinforcement arrangement

Fig. 1. Slab-column joint specimens under concentric loading.

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M. Diao et al. Table 1. Design parameters in UPS series.

Specimen

f cm (MPa)

h (mm)

ρ T (%)

ρ B (%)

Column strip

Middle strip

l b (mm) Column strip

Middle strip

UPS-1

27

90

0.60

0.33

0.30

1260

890

UPS-2

24

70

0.81

0.45

0.40

1260

890

UPS-3

21

90

0.86

0.40

0.43

1260

890

UPS-4

17

90

0.60

0.33

0.30

2560

2560

UPS-5

24

90

0.60

0.33

0.30

1260

890

UPS-6

24

90

0.60

0.33

0.30

1260

890

UPS-7

23

90

0.60

0.33

0.30

1260

890

Load-displacement responses of the fourteen specimens under concentric load are shown in Fig. 2. Two typical load-resistant mechanisms, namely compressive membrane and tensile membrane actions, were observed. In general, UPS series with varied design parameters had higher punching shear strengths (V p ) than the DPS equivalence; this is vice versa for the post-punching strengths (V pp ). Note that V pp is considered as the secondary defence to resist a progress collapse. Reduction of the slab thickness by 20 mm resulted in a 39% decrease in the V p . However, there was only a 5% variation in V p when the reinforcement ratio was increased by 30%. While being largely regulated by the through-column rebars, the level of V pp were similar for the UPS and DPS series. It can be concluded from the experimental results that the punching shear strength is mainly governed by the geometrical dimensions of the slab, while the continuous integrity rebars are imperative for activating tensile membrane action thereby enhancing post-punching capacity in progressive collapse events. For specimens with different strengthening methods, punching shear failure occurred twice in the ring beam specimens UPS/DPS-7, thereby the deformation and strength improvements were not as remarkable as those in the embedded beam and stirrup specimens UPS/DPS-5 & 6. At the post-punching stage, the addition of the embedded beams facilitated higher deformation and load capacities in the suspension stage, causing the corresponding displacement delayed by 37% and the punching shear resistance increased by 97% in UPS-5, compared with those in UPS-1. Whereas the post-punching displacements in UPS/DPS-5 and UPS/DPS-6 were delayed by 25% and 32% on average, along with the average capacity improvements of 64% and 50%, respectively. 2.2 Numerical Studies The quarter-symmetric finite element model of UPS-1 (control specimen) is shown in Fig. 3 where the concrete was modelled using eight-node 3D solid Lagrangian elements and the reinforcing bars were modelled using two-node Hughes-Liu integration beam elements. The key features of the modelling approach are: (a) the solid and beam

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Fig. 2. Experimental load-displacement responses of specimens under concentric load.

elements were rigidly coupled; (b) an automatic general contact was set to the beam elements to ensure that the upper and lower rebar elements just “touch” each other without initial element penetrations; (c) the material behaviours of the concrete and the rebars were simulated by the continuous surface cap model and the multi-linear elasto-plastic material model, respectively; and (d) the calibrated element failure criteria were used to regulate the punching shear occurrence (by the maximum effective strain of concrete) and the rebar fracture (by the maximum effective plastic strain of steel). The analysis was performed using LS-DYNA finite element software.

Fig. 3. Finite element model of UPS-1.

Figure 4 compares the experimental and numerical load-displacement responses illustrating the punching shear capacity (V p ), the abrupt drop and the re-ascending trend (suspension stage) of the applied load up until the post-punching capacity (V pp ) for all the seven UPS specimens. The experimental and numerical load-resistants for the UPS series are compared in Table 2. The mean ratio of the experimental and numerical capacities V p,e /V p,s is 1.00 with a COV of 0.08 and that of V pp,e /V pp,s is 0.97 with a COV of 0.11. The measured capacities influenced by three design parameters and strengthening methods were also well replicated: (1) reduced slab thickness h in UPS-2 weakened its V p

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than that of UPS-1, which is not conductive to punching shear resistance; (2) increased reinforcement ratios in UPS-3 had little effect on the V p and V pp , compared to UPS-1. However, over-reinforcement accelerated the punching shear failure at a smaller deformation; (3) increased flexural reinforcement anchorage length lb in UPS-4 enhanced the deformation capacity than UPS-1; (4) the addition of embedded beams and stirrups facilitated higher deformation and load capacities in the post-punching stage.

Fig. 4. Experimental and numerical load-displacement responses of UPS specimens.

Table 2. Experimental and numerical load-resistant comparison for UPS specimens. Specimen

Punching shear strength V p (kN) Experiment

V p,e /V p,s

Simulation

Post-punching strength V pp (kN) Experiment

V pp,e /V pp,s

Simulation

UPS-1

144

150

0.96

92

122

0.75

UPS-2

83

86

0.97

96

104

0.92

UPS-3

138

145

0.95

99

98

1.01

UPS-4

140

119

1.18

103

110

0.94

UPS-5

165

170

0.97

199

177

1.12

UPS-6

167

159

1.05

170

163

1.04

UPS-7

127

139

0.91

141

135

1.04

Average

1.00

0.97

C.O.V

0.08

0.11

The experimental and numerical load-resistants for the DPS series are also compared. The punching shear and the post-punching capacities are satisfactorily simulated. The mean ratio of the experimental and numerical capacities V p,e /V p,s is 0.96 with a COV of 0.07 and that of V pp,e /V pp,s is 1.04 with a COV of 0.12. The in-plane restraint facilitated

Load-Resistant Mechanism and Failure Behaviour

923

a full development of the post-punching capacity, in some cases even exceeding the corresponding punching shear capacity. The results further indicate that the V pp is critically important as being the secondary defence to resist a progress collapse. Figure 5 compares favourably the observed and simulated crack patterns of DPS-1 showing circumferential and radial cracks on the slab top and bottom surfaces, respectively. Radial flexural cracks

Lower bottom bars Lower bottom bars

Upper bottom bars

Upper bottom bars

Slab peripheral cracks Slab peripheral cracks

Column punching through

Column punching through

(a) Top surface

(b) Bottom surface

Fig. 5. Experimental and numerical damage mode and crack patterns of DPS-1.

3 Slab-Column Joints Under Eccentric Loading In a flat plate structure, transfer of unbalanced moments from the slab to the columns is almost unavoidable. These unbalanced moments may be generated due to unsymmetrical loading, unequal span lengths or horizontal forces such as wind or earthquake. The existence of unbalanced moments could increase the vulnerability of a flat plate structure to punching shear failure. In addition, the load originally resisted by a potentially damaged column will be transferred to the adjacent joints, at which a large additional shear forces and unbalanced bending moments will be produced, eventually leading to more complex mechanical performance and failure mechanism of the joints. Limited collapse-resistant design guidelines are available for slab-column joints under the action of unbalanced moments. Moreover, their punching shear and post-punching failure mechanisms in the context of a progressive collapse are still in need of an in-depth study. 3.1 Experimental Tests A quasi-static test program was conducted on seven joint specimens, including one concentrically loaded (CL) joint and six eccentrically loaded (EL) ones. The effects of eccentricity, slab thickness and reinforcement ratio on the structural performances were investigated. The CL joint, equivalent to UPS-3, denotes a repeat test. The EL joints were subjected to two levels of eccentricity, namely 405 mm and 780 mm, representing 2.7 and 5.2 times the column width, respectively. These seven specimens plus the previously tested UPS-1 & 2 specimens (CL joints) were divided into three series with eccentricities of 0 mm, 405 mm and 780 mm: SE series covering the control specimens, TE and RE series, respectively, representing the slab thickness variations (reduced by 20 mm) and reinforcement ratio variations (increased by 30%). The average compressive strengths of concrete for SE/TE/RE405, SE/TE/RE780 and RE0 are 28 MPa, 27 MPa, 27 MPa, 27 MPa, 28 MPa, 37 MPa, 29 MPa, respectively.

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A main difference between the seven specimens and those UPS series presented in Sect. 2 is that the loading scheme was changed from downward loading to upward loading, because the eccentric loading device (see Fig. 6) would likely be in contact with the slab under large deformations if a downward loading was applied. Compared with the UPS specimens, the integrity reinforcement (IR) and flexural reinforcement (FR) of the seven joint specimens were reversed accordingly to facilitate an upward punching shear failure. Other than the loading direction, the design parameters of the seven joint specimens were mostly consistent with those of the UPS series (Fig. 7).

Concentric loading device

Eccentric loading device

Steel column

(a) Test setup

(b) Specimens

Fig. 6. Slab-column joint specimens under eccentric loading.

SE0 SE405 SE780

120 100

Fpp

Fp

120

80 60 40

180 TE0 TE405 TE780

Fpp

100

Applied load (kN)

Applied load (kN)

140

80

Fp

60 40

Pre-punching

Post-punching

50

100

Fp

90 60

Pre-punching Post-punching

Pre-punching Post-punching

0 0

Fpp

120

30

20

20

RE0 RE405 RE780

150

Applied load (kN)

160

150

200

Column displacement (mm)

250

0

0 0

50

100

150

Column displacement (mm)

200

250

0

50

100

150

200

250

Column displacement (mm)

Fig. 7. Experimental load-displacement responses of specimens under eccentric load.

The test results indicate that a large eccentricity can result in a reduction in peak punching shear capacity of up to 62%, while it has little effect on the post-punching capacity. Specifically, compared with the CL joint specimens, the average reductions of the punching shear capacity are about 36% and 62% for joints with eccentricities of 405 mm and 780 mm, respectively. The reduction of the measured punching shear capacity was similar (around 5%) for the EL specimens with the same eccentricity regardless of varied slab thicknesses and reinforcement ratios in different specimens. Experimental results also show that locations of the fractured rebars were mainly on the eccentric loading side of the slab due to combined action of the unbalanced moment and shear force.

Load-Resistant Mechanism and Failure Behaviour

925

3.2 Numerical Studies 3D numerical models were established to further evaluate the effect of different levels of in-plane restraints on slab-column joints and the effect of unbalanced moments on their punching shear and post-punching capacities. Based on the UPS models, the proposed models of the EL specimens were established with different concrete element types, different failure criteria, and additional bond-slip relationship. Specifically, eightpoint integration solid elements were used within the critical punching areas to capture complicated stress patterns; the maximum principal strain was adopted as the criterion for concrete element erosion; and bond slip, taking place after punching at the critical punching area, was considered by adopting the FIB Model Code. In addition, the material model *MAT_ELASTIC_PLASTIC_THERMAL (*MAT_004) was employed to simulate the uplifting process (retraction of the jack rod) of the hydraulic jack in the EL joint test, because the thermoelastic material enabled the jack rod to deform linearly when subjected to temperature gradients. Figure 8 presents the experimental and numerical load-displacement responses of SE405 and SE780, demonstrating a reasonably good agreement. It can be seen from Fig. 9 that asymmetrical punching shear crack patterns at both the top and bottom surfaces were well reproduced. 140

120

Applied load (kN)

Experiment

SE780:

Simulation

Experiment

Simulation

120 Fpp,e Fpp,s

Applied load (kN)

SE405:

100 Fp,e Fp,s 80 60 40 20

Fpp,s

100 Fp,e

80

Fpp,e

Fp,s

60 40 20 0

0 0

30

60 90 120 150 Column displacement (mm)

180

210

0

30

60 90 120 Column displacement (mm)

150

180

Fig. 8. Experimental and numerical load-displacement responses of SE specimens.

(a) Top surface

(b) Bottom surface

Fig. 9. Experimental and numerical crack patterns of SE405 at the onset of punching.

The punching shear capacities of all the EL joint specimens and RE0, denoted as V p,e and V p,s for the test and numerical values, respectively, together with their postpunching shear capacities (denoted as V pp,e and V pp,s , respectively), are summarised in

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Table 3. The numerical models produced excellent predictions in terms of the average test-to-simulation ratios, being 1.04 (4%) and 1.07 (7%) for the punching shear and post-punching capacities with the coefficients of variation (COV in Table 3) being 5% and 10%, respectively. Table 3. Experimental and numerical load-resistant comparison. Specimen

Punching shear strength V p (kN)

Experiment

Simulation

SE405

94

93

1.01

80

81

0.99

SE780

70

61

1.15

90

70

1.28

TE405

61

60

1.02

98

92

1.05

TE780

38

38

1.00

86

81

1.06

RE0

160

158

1.01

108

111

0.98

RE405

99

94

1.05

106

98

1.09

RE780

58

56

1.04

111

110

1.01

Experiment

V p,e /V p,s

Simulation

Post-punching strength V pp (kN)

V pp,e /V pp,s

Average

1.04

1.07

C.O.V

0.05

0.10

4 Conclusions To investigate the load-carrying capacities, crack development and failure modes, as well as load re-distribution characteristics at large-deformations of RC flat plate systems, a total of twenty-one slab-column joint specimens were tested. To cover different loading and failure scenarios, the tests were conducted considering opposite punching shear failure directions as well as concentric and eccentric loading conditions. The influences of three design parameters and three strengthening methods on the punching and post-punching shear capacities and the deformation capacities were discussed. A numerical modelling approach was developed that features well-defined material properties and calibrated element failure criteria. Numerical validations on selected joint specimens confirmed the applicability and reliability of the modelling approach in replicating punching and post-punching shear capacities. Major findings are given below: 1. The experimental results showed that the punching shear strength is mainly governed by the geometrical dimensions of the slab. Reducing the slab thickness by 20 mm, the punching shear capacity decreased by 39%, while the capacity varied within 5% with a 30% increase in the reinforcement ratio. The post-punching strength is mainly regulated by the through-column rebars. Given that the amount and cross-sectional area of these rebars were consistent for different specimens with varying structural

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parameters (UPS/DPS-1 to 4), the post-punching strengths of the UPS and DPS series had maximum deviations of 11% and 9%, respectively. 2. For specimens with different strengthening methods, the deformation and load capacity improvements in the ring beam specimens UPS/DPS-7 were not as significant as those in the embedded beam and stirrup specimens UPS/DPS-5 & 6, since punching shear failure occurred twice in UPS/DPS-7. The addition of the embedded beams and stirrups in UPS/DPS-5 & 6 facilitated higher deformation and load capacities in the post-punching stage, causing the corresponding displacements in UPS/DPS-5 and UPS/DPS-6 delayed by 25% and 32% on average, with the average capacity improvements of 64% and 50%, respectively. 3. The punching shear capacity of the joints decreased with increased eccentricities. Compared with the CL joint specimens, the average reduction of the punching shear capacity could reach up to 62% for the EL joints, regardless of the various parameters (slab thickness and reinforcement ratio) in different specimens. In addition, asymmetrical punching failure mode could be observed on the slab in the EL joint specimens, the greater the eccentricity, the more obvious the asymmetry. 4. In the post-punching stage, the eccentricity has little effect on the post-punching capacities. Before the rupture of the first rebar, similar post-punching capacities were observed in all three series (SE, TE and RE) with average reductions of around 5% for specimens with eccentricities of 405 mm and 780 mm. The rupture locations of rebars were mainly on the eccentric loading side of the slab due to combined action of the unbalanced moment and shear force. The proposed joint models can provide detailed slab in-plane, flexure and shear actions, as well as their interactions. These can facilitate the development of a simplified numerical model capable of simulating multi-story multi-bay flat plate structures, thereby enabling the assessment of the system behaviour of actual buildings for progressive collapse prevention and mitigation. Acknowledgements. The authors are grateful for the financial support received from the Australian Research Council through an ARC Discovery Project (DP150100606), the National Key Research and Development Program of China (No. 2019YFC1511000), and the National Natural Science Foundation of China (No. 52178094).

References Lu, X.Z., et al.: A preliminary analysis and discussion of the condominium building collapse in Surfside, Florida, US, June 24. Front. Struct. Civ. Eng. 15(5), 1097–1110 (2021) Euro Weekly: WATCH: Dramatic images of collapsed car park in Spain. https://www.euroweekl ynews.com/2020/01/13/watch-dramatic-images-of-collapsed-car-park-in-spain/. Accessed 25 Jan 2021 ABCNews: Chinese underground construction site collapses, killing 8. https://abcnews.go.com/ International/wireStory/chinese-underground-construction-site-collapses-killing-66606520. Accessed 25 Jan 2021 Melo, G.S., Regan, P.E.: Post-punching resistance of connections between flat slabs and interior columns. Mag. Concr. Res. 50(4), 319–327 (1998)

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Habibi, F.: Post-Punching Shear Response of Two-Way Slabs, Ph.D Thesis, McGill University (2012) Ruiz, M.F., Mirzaei, Y., Muttoni, A.: Post-punching behavior of flat slabs. ACI Struct. J. 110, 801–812 (2013) Peng, Z., Orton, S.L., Liu, J., Tian, Y.: Effects of in-Plane Restraint on Progression of Collapse in Flat-Plate Structures, Ph.D Thesis (2015) Hawkins, N.M., Mitchell, D.: Progressive collapse of flat plate structures. J. Proc. 76, 775–808 (1979) Regan, P.E., Walker, P.R., Zakaria, K.A.A.: Tests of Reinforced Concrete Flat Slabs. CIRIA Project RP, 220 (1979) Mitchell, D., Cook, W.D.: Preventing progressive collapse of slab structures. J. Struct. Eng. 110(7), 1513–1532 (1984) Keyvani, L., Sasani, M., Mirzaei, Y.: Compressive membrane action in progressive collapse resistance of RC flat plates. Eng. Struct. 59, 554–564 (2014) Ruiz, M.F., Muttoni, A., Kunz, J.: Strengthening of flat slabs against punching shear using postinstalled shear reinforcement. ACI Struct. J. 107(4), 434–442 (2010) Carvalho, A.L., Melo, G.S., Gomes, R.B., Regan, P.E.: Punching shear in post-tensioned flat slabs with stud rail shear reinforcement. ACI Struct. J. 108(5), 523–531 (2011) Elgabry, A.A., Ghali, A.: Moment transfer by shear in slab-column connections. ACI Struct. J. 93, 187–196 (1996) Kruger, G., Burdet, O., Favre, R.: Punching strength of RC flat slabs with moment transfer. In: International Workshop on Punching Shear, Royal Institute of Technology, TRITA-BKN Bulletin 57, Stockholm (2000) Binici, B., Bayrak, O.: Upgrading of slab–column connections using fiber reinforced polymers. Eng. Struct. 27(1), 97–107 (2005) Diao, M.Z., Li, Y., Lu, X.Z., Guan, H., Liu, F.F.: Post-punching mechanism of slab-column joints subjected upward and downward punching shear actions. In: Structures Conference 2018, Apr 19–21, Fort Worth, Texas, USA, pp. 246–254 (2018) Yang, Y.Z., Diao, M.Z., Li, Y., Guan, H., Lu, X.Z.: Experimental investigation on post-punching mechanism of slab-column joints. In: 15th International Symposium on Structural Engineering (ISSE-15), Oct 24–27, Hangzhou, China (2018)

Numerical Simulation for Parallel-To-Grain Withdrawal Failure of Self-tapping Screws in Glulam Lijing Fang(B) , Wenjun Qu, and Shengdong Zhang Department of Structural Engineering, Tongji University, Shanghai 200092, China {lijing-fang,quwenjun.tj,zhangsh_d}@tongji.edu.cn

Abstract. The exploration of connection technology is an important topic in the field of modern timber structure. Tapping in manufacturing is the process of cutting threads inside a hole, and self-tapping screw, as the name implies, is a mechanical fastener that can enter the matrix material (wood) and cut threads on the internal surface of a pre-drilled hole by itself. Compared with the glued-in steel rod used as the axially-loaded fastener in timber connection, the self-tapping screw can be applied as a kind of new axially-loaded fastener without applying adhesive in assembly. The mechanical interlocking through the tight fit of the thread pair between the screw and the wood promises a method of realizing the strong and stiff connection in timber structure. In order to take full advantage of this fastener in axial load transfer, the withdrawal failure mechanism of self-tapping screws in wood needs to be researched to avoid the withdrawal failure at first. A numerical model containing contact analysis and considering the material damage of failure surface is constructed to simulate the parallel-to-grain withdrawal failure of the self-tapping screw in glulam by the finite element method program ABAQUS/Explicit. The steel-wood friction coefficient in contact analysis and the self-defined parameters aimed to reflect the stiffness in the bi-linear tractionseparation law are used as trial parameters in simulation. The model results for the parallel-to-grain withdrawal capacity of the screw are found to be in a good agreement with the experimental results. The trial calculations imply that the steel-wood friction coefficient in contact analysis has no obvious influence on the withdrawal capacity/stiffness of the screw; however, the ratios of initiation displacement and failure displacement in the traction-separation law have negligible influence on the withdrawal capacity but significant influence on the withdrawal stiffness of the screw. Keywords: Glulam structure · Connection technology · Self-tapping screw · Withdrawal failure · Numerical simulation

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 929–939, 2023. https://doi.org/10.1007/978-981-19-7331-4_77

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1 Introduction As a kind of bio-based material, timber attracts a new attention in the field of AEC (architecture, engineering and construction), due to the global carbon-neutral goal in coping with the growing climate crisis. In order to encourage a broad application of timber structure in practice, the technical support of modern timber connection with high mechanical performance is indispensable. Currently the improving screw manufacturing process can supply the mechanical fasteners with sufficient lengths and optimized threads to the market, which provides a promising technical solution to realize the timber connections with high strength and stiffness (Ellingsbø and Malo 2010; Kasal et al. 2014; Fang et al. 2022). Distinguished from the common dowel-type metal fasteners such as the dowel, bolt and traditional screw in timber engineering, the self-tapping screw or threaded rod can be regarded as a kind of threaded fastener capable of load transfer along the direction of the axis. To make a full use of axial load-carrying capacity, the withdrawal failure of self-tapping screw or threaded rod is expected to avoid at first. Considering that the withdrawal failure of self-tapping screws in wood adversely affect the mechanical performance of timber connection, the stress behavior and failure mechanism of self-tapping screws in wood should be researched in depth before promoting the application of axially-loaded threaded fastener in timber connection. Therefore, based on the universal finite element method program ABAQUS/Explicit, a numerical model containing contact analysis and considering the material damage of failure surface is constructed to simulate the parallel-to-grain withdrawal failure of the self-tapping screw in glulam. In this model, the interaction between the screw thread and the wood is concerned in contact analysis; and to reflect the whole withdrawal process (especially the descent stage of withdrawal load-displacement curve), the bi-linear traction-separation law as the constitutive response is introduced into the material property of withdrawal failure surface composed by a layer of inserted cohesive elements. The steel-wood friction coefficient in contact analysis and the self-defined parameters aimed to reflect the stiffness in the bi-linear traction-separation law are used as trial parameters in numerical calculation.

2 Model Description 2.1 Embedment and Withdrawal Failure of Self-tapping Screws in Glulam Self-tapping screw is a kind of metal fastener whose thread is produced and hardened by rolling or forging a wire rod around its shank. Most screws are manufactured with a continuous thread over the whole length, which leads to a more uniform load transfer between the screw and the wood. Figure 1 shows a cut open specimen of the self-tapping screw without withdrawal failure. A tight fit without clearance between the thread of the screw and the wood filled in the screw pitch can be seen in Fig. 1a. After the embedded screw is removed manually, the internal thread formed in the wood can be clearly observed in Fig. 1b. Figure 2 shows the typical withdrawal failure phenomena of a self-tapping screw in glulam. It could be considered that, during the external axial load applying on the screw, cracks appear and expand from the root of the internal thread in

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the wood, and a withdrawal failure surface around the screw is cut out from the wood by the screw thread. Finally, the screw is pulled out, with failure wood filled in the screw pitch (Fig. 2b).

Fig. 1. A cut open specimen of the self-tapping screw without withdrawal failure: (a) a tight fit without clearance between the thread of the screw and the wood filled in the screw pitch; (b) the internal thread formed in the wood.

Fig. 2. Typical withdrawal failure phenomena of a self-tapping screw in wood: (a) the longitudinally and radially cut wood; (b) the screw surrounded with failure wood; (c) wood fragments with a length of the screw pitch.

Based on the tight fit between the screw thread and the wood, and the typical withdrawal failure phenomena, a reasonable numerical model should not ignore the following: (1) the load transfer between the screw and the wood, which involves contact analysis in the view of numerical simulation; (2) the initiation and evolution of cracks on the withdrawal failure surface, which requires the modeling method and the damage theory. 2.2 Numerical Model Containing Contact Definition With reference to the modeling method of screw thread pair in mechanical engineering, the geometry model is created in the Part and Assembly modules together with the mesh model in the Mesh module, as shown in Fig. 3. Please note that the wood around the screw is treated as a wood nut, with the same length as the screw, in order to embody the internal thread formed in the wood and the tight fit without clearance between the screw thread and the wood.

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Fig. 3. Numerical model: (a) the wood net; (b) the tight fit between the screw and the wood net; (c) the local refined mesh; (d) the inserted cohesive elements (dark green orphan mesh); (e) different mesh density in the whole model; (f) the withdrawal failure surface composed by a layer of inserted cohesive elements.

The contact pairs and the mechanical contact properties for contact pairs are defined in the Interaction module of ABAQUS/Explicit. The contact pair algorithm is a kind of surface-based contact-definition approach (SIMULIA User Assistance 2017, abbr. SUA2017). Before defining individual contact pair containing two surfaces, the terms of screw thread are necessary to be illustrated in Fig. 4. The whole contact surface between the screw thread and the wood nut thread are divided into four contact pairs containing two surfaces, respectively shown from Fig. 5a–d: the upper flank of screw thread and the lower flank of wood nut thread (Fig. 5a); the lower flank of screw thread and the upper flank of wood nut thread (Fig. 5b); the root of screw thread and the crest of wood nut thread (Fig. 5c), the crest of screw thread and the root of wood nut thread (Fig. 5d). Among these contact pairs, the surfaces of the screw are defined as the master surfaces and the surfaces of the wood nut as the slave surfaces. The four contact pairs respectively adopt the “penalty contact algorithm” in the contact constraint enforcement method and the “finite sliding” in contact sliding formulation (SUA2017).

Fig. 4. The terms of screw thread

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Fig. 5. The definition of contact pairs between the screw and the wood

Assigning contact properties for contact pairs is required. Contact properties define the mechanical surface interaction models that govern the behavior of surfaces when they are in contact (SUA2017). The contents of contact properties usually include the normal behavior, tangential behavior and so on. “Hard contact” is adopted in the normal behavior of the contact properties, which implies that the surfaces transmit no contact pressure unless the nodes of the slave surface contact the master surface and there is no limit to the magnitude of contact pressure that can be transmitted when the surfaces are in contact (SUA2017). “Penalty” in friction formulation based on the Coulomb friction model is adopted in the tangential behavior of the contact properties, and the coefficient of friction in Coulomb friction model is tried by the steel-wood friction coefficient in the range of 0.1–0.3. 2.3 Cohesive Element with Constitutive Response of Bi-linear Traction-Separation Law In the Property module of ABAQUS/Explicit, the screw, the wood and the withdrawal failure surface are respectively assigned with three kinds of materials, namely materialscrew, material-wood and material-cohesive. Material-screw is assumed to be isotropic elastic material with a density of 7.85 × 10–9 ton/mm3 , an elastic modulus of 2.00 × 105 MPa and a Poisson’s ratio of 0.3. Material-wood is assumed to be orthotropic material with Hill criterion adopted to control the material plastic yielding. The physical and mechanical properties of Douglas fir glulam used in withdrawal experiment for numerical model validation are tested in a laboratory and listed in Table 1. The detailed material parameters associated with elastic and plastic properties are respectively listed in Tables 2 and 3. In order to simulate the cracks which appear and expand from the root of wood nut thread, a layer of cohesive elements assigned with the bi-linear traction-separation law is inserted around the screw thread diameter and along the screw length to construct the so-called cohesive zone model. Therefore, the fundamental knowledge of fracture mode, cohesive element and traction-separation law will be briefly introduced below. According to crack stress situation, the basic modes of fracture include Mode I (opening), Mode II (slipping) and Mode III (tearing), as illustrated in Fig. 6. To analyze interface fracture mechanism in the field of composite materials, some advanced fracture theories have been developed. Dugdale (1960) and Barenblatt (1962) originally proposed the cohesive zone conception near the crack tip which describes discrete fracture as the material separation across the surface. In the cohesive zone model, cohesive elements

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Category

Average value

Moisture (%)

Standard deviation

Coefficient of variation (%)

11.60

0.26

Air-dry density (kg/m3 )

2.26

462.01

15.67

3.39

Compressive strength parallel to grain (MPa)

31.23

5.58

17.86

MOE of compression parallel to grain (MPa)

12370.78

4347.75

35.15

Compressive strength perpendicular to grain (MPa)

2.47

0.15

5.90

MOE of compression perpendicular to grain (MPa)

365.35

51.96

14.22

Tensile strength parallel to grain (MPa)

88.32

18.49

20.94

Tensile strength perpendicular to grain (MPa)

2.22

0.43

19.51

Shear strength parallel to grain (MPa)

4.75

0.55

11.57

Note MOE stands for modulus of elasticity

Table 2. Elastic parameters of material-wood E1 (MPa)

E2 (MPa)

E3 (MPa)

Nu12

Nu13

Nu23

G12 (MPa)

G13 (MPa)

G23 (MPa)

12370.78

365.35

365.35

0.37

0.37

0.38

775.89

775.89

132.37

Table 3. Plastic parameters of material-wood σ 0 (MPa)

R11

R22

R33

R12

R13

R23

31.23

1

0.08

0.08

0.26

0.26

0.26

can emulate the traction-separation relationship between two adjacent surfaces, where a gradual softening behavior represents the material properties degradation caused by the damage process (Oliveira and Donadon 2020). The three-dimensional cohesive element COH3D8 making up the withdrawal failure surface is shown in Fig. 7a. The relative motion of the bottom and top faces measured along the thickness direction (local 3-direction for 3D cohesive elements) represents

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Fig. 6. Basic modes of fracture: (a) opening; (b) slipping; (c) tearing.

opening or closing of the interface. The relative change in position of the bottom and top faces measured in the plane orthogonal to the thickness direction quantifies the transverse shear behavior of the cohesive element (SUA2017). The available traction-separation law in ABAQUS assumes initially linear elastic behavior followed by the initiation and evolution of damage (SUA2017). The bi-linear triangle model shown in Fig. 7b can represent the fracture of Mode I, Mode II and Mode III. Here n represents the normal and s, t the two shear directions for the 3D cohesive elements; t n 0 , t s 0 and t t 0 represent the peak values of the nominal stress when the deformation is either purely normal to the interface or purely in the first or the second shear direction, respectively. In consideration of both normal and shear stress actually existing on the failure surface, the damage evolution under a combination of normal and shear deformation across the interface will be discussed later (see Fig. 7c).

Fig. 7. The cohesive element COH3D8 (a) and the bi-linear traction-separation law in the pure (b) and the mixed (c) modes

Before damage initiation, the linear elastic behavior is written as Eq. (1), in terms of an elastic constitutive matrix that relates the nominal stresses to the nominal strains across the interface. The nominal stresses are the force components divided by the original area at each integration point, while the nominal strains are the displacements (namely separations) divided by the original thickness at each integration point. ⎧ ⎫ ⎡ ⎤⎧ ⎫ Knn Kns Knt ⎨ εn ⎬ ⎨ tn ⎬ (1) t = ts = ⎣ Ksn Kss Kst ⎦ εs = K × ε ⎩ ⎭ ⎩ ⎭ tt Ktn Kts Ktt εt The nominal traction stress vector t consists of three components: t n , t s and t t , which represent the normal (along the local 3-direction) and the two shear tractions (along the

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local 1- and 2-directions), respectively. The corresponding displacements are denoted by d n , d s and d t , and the three components of the nominal strain vector ε can be defined as Eq. (2), with T 0 (the value of 1.00 mm in the model) denoting the original thickness of the cohesive element: εn =

dn ds dt , εs = , εt = T0 T0 T0

(2)

Once a damage initiation criterion is met, material damage can occur according to a damage evolution law. Post damage-initiation response is defined as Eq. (3), where K dam is the stiffness matrix after introducing the damage variable D. K dam = (1 − D)K

(3)

Generally, material damage model usually consists of two parts: damage initiation criterion and damage evolution criterion. Damage initiation refers to the beginning of degradation of the response of a material point. The process of degradation begins when the stresses and/or strains satisfy certain damage initiation criteria available in ABAQUS. The maximum nominal stress criterion as the damage initiation given by Eq. (4) is adopted in the model:

tn  ts tt (4) max 0 , 0 , 0 = 1 tn ts tt Damage evolution definition is mainly based on energy or displacement in ABAQUS. Damage evolution can be defined based on the energy that is dissipated as a result of the damage process, also called the fracture energy. The fracture energy denoted by Gn c /Gs c /Gt c is equal to the area under the traction-separation curve (see Fig. 7b). The damage variable D in energy-based damage evolution can be defined as a function of the mode mix using the analytical BK (Benzeggagh and Kenane 1996) fracture criterion: D=

(GI + GII + GIII ) β  II +GIII GIC + (GIIC − GIC ) GIG+G II +GIII

(5)

where the GI , GII and GIII are the energy release rates respectively corresponding to the fracture of Mode I, Mode II and Mode III; the GIC , GIIC and GIIIC are the critical energy release rates respectively corresponding to the fracture of Mode I, Mode II and Mode III; the semi-empirical material parameter β is between 0.5 and 2.5. When the cohesive elements COH3D8 assigned with constitutive response of bilinear traction-separation law are adopted in the model, the differences between GIIC and GIIIC are ignored. To obtain the stiffness in the bi-linear traction-separation law, namely the E nn , E ss and E tt in material-cohesive, the self-defined parameters η1 for Mode I and η2 for Mode II, namely the ratios of initiation displacement and failure displacement in the bi-linear traction-separation law, are respectively introduced as follow: fail

dn

=

2 × GIC ini ft,90 fail , dn = η1 × dn , Enn = ini ft,90 dn /T0

(6)

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fail

2 × GIIC ini fv,0 fail , ds = η2 × ds , Ess = ini fv,0 ds /T0

=

ds

937

(7)

with f t,90 denoting the tensile strength perpendicular to grain and f v,0 the shear strength parallel to grain of wood; GIC = 0.25 N/mm (Moura and Dourado 2018) and GIIC = 0.7 N/mm (Jensen et al. 2012) in the model. The values of E nn , E ss and E tt in materialcohesive according to the trial parameters η1 and η2 are listed in Table 4. Table 4. E nn , E ss , E tt in material-cohesive E nn (MPa)

E ss (MPa)

E tt (MPa)

η1 = η2 = 0.2 η1 = η2 = 0.5

40

80.58

80.58

16

32.23

32.23

η1 = η2 = 0.8

10

20.15

20.15

3 Model Results 3.1 Withdrawal Failure Load The numerical model is verified by withdrawal tests of five specimens with the screw embedment length of 65 mm. The average withdrawal failure load is 11.595 kN. The trial parameters in the model are the steel-wood friction coefficient μ (0.1, 0.2, 0.3) in contact analysis; and the ratios of initiation displacement and failure displacement in bi-linear traction-separation law: η1 and η2 (0.2, 0.5, 0.8). Therefore, nine cases are calculated and each calculation is compared with the average withdrawal failure load, as shown in Table 5. The error between the model result and the average failure load in each case is controlled at about 6%, which implies the parallel-to-grain withdrawal failure load of the self-tapping screw in glulam can be well predicted by the model. Table 5. Simulations of parallel-to-grain withdrawal failure load μ

η1 = η2 = 0.2 0.1

0.2

η1 = η2 = 0.5 0.3

0.1

0.2

η1 = η2 = 0.8 0.3

0.1

0.2

0.3

Simulation 10.870 10.937 10.985 10.824 10.896 10.949 10.803 10.859 10.884 Error (%)

6.25

5.68

5.27

6.65

6.03

5.57

6.83

6.35

6.14

3.2 Stiffness Degradation of Cohesive Elements Taking the case of μ = 0.1, η1 = η2 = 0.5 as an example, Fig. 8 shows the stiffness degradation of cohesive elements on the withdrawal failure surface. Step Time = 0.7 corresponds to the position of the maximum withdrawal load on the withdrawal loaddisplacement curve.

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Fig. 8. Stiffness degradation of cohesive elements on the withdrawal failure surface

3.3 Withdrawal Load-Displacement Curve The withdrawal load and withdrawal displacement of the reference point fixed on the self-tapping screw along the loading direction in each case are extracted to plot the withdrawal load-displacement curve during the whole loading process. Nine cases are divided into two groups according to the steel-wood friction coefficient μ (0.1, 0.2, 0.3) and the ratios of initiation displacement and failure displacement in the bi-linear traction-separation law η1 and η2 (0.2, 0.5, 0.8), as shown in Figs. 9 and 10, respectively.

Fig. 9. The effect of the friction coefficient μ on the withdrawal load-displacement curve

4 Conclusions A numerical model containing contact analysis and considering the material damage of failure surface is constructed to simulate the parallel-to-grain withdrawal failure of the self-tapping screw in glulam by the universal finite element method program ABAQUS/Explicit. In this model, the interaction between the screw thread and the wood is concerned in contact analysis; and the bi-linear traction-separation law as the constitutive response is introduced into the material property of withdrawal failure surface composed by a layer of cohesive elements. In order to reasonably specify the algorithm and related parameters in contact analysis, as well as the parameters of the bi-linear traction-separation law, plenty of references are consulted. The steel-wood friction coefficient in contact analysis and the self-defined parameters aimed to reflect the

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Fig. 10. The effect of the ratios η1 and η2 on the withdrawal load-displacement curve

stiffness in the bi-linear traction-separation law are used as trial parameters in numerical calculation. The model results for the parallel-to-grain withdrawal capacity of the screw are found to be in a good agreement with the experimental results. The trial calculations of the model also imply that the steel-wood friction coefficient in contact analysis has no obvious influence on the withdrawal capacity/stiffness of the screw; however, the ratios of initiation displacement and failure displacement in the bi-linear traction-separation law has negligible influence on the withdrawal capacity but significant influence on the withdrawal stiffness of the screw. In the future, the self-defined parameters in the bilinear traction-separation law can be adjusted and corrected through the further research on the withdrawal stiffness of self-tapping screws in glulam.

References Barenblatt, G.I.: The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55–129 (1962) Benzeggagh, M.L., Kenane, M.: Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Compos. Sci. Technol. 56(4), 439–449 (1996) Dugdale, D.S.: Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8(2), 100–104 (1960) Ellingsbø, P., Malo, K.A.: Cantilever glulam beam fastened with long threaded steel rods. In: Presented at the Proceedings of WCTE 2010 – World Conference on Timber Engineering. Trentino, Italy (2010) Fang, L., Qu, W., Zhang, S.: Rotational behavior of glulam moment-resisting connections with long self-tapping screws. Constr. Build. Mater. 324, 126604 (2022) Jensen, J.L., Nakatani, M., Quenneville, P., et al.: A simplified model for withdrawal of screws from end-grain of timber. Constr. Build. Mater. 29, 557–563 (2012) Kasal, B., Guindos, P., Polocoser, T., et al.: Heavy laminated timber frames with rigid threedimensional beam-to-column connections. J. Perform. Constr. Facil. 28(6), A4014014 (2014) Moura, M., Dourado, N.: Mode I fracture characterization of wood using the TDCB test. Theoret. Appl. Fract. Mech. 94, 40–45 (2018) Oliveira, L.A., Donadon, M.V.: Delamination analysis using cohesive zone model: a discussion on traction-separation law and mixed-mode criteria. Eng. Fract. Mech. 228, 106922 (2020) SIMULIA User Assistance: Information on https://abaqus-docs.mit.edu/2017/English/DSSIMU LIA_Established.htm (2017)

Advances in Design and Intelligent Optimization of Large-Span Bridge

A Study on Time Synchronization Method for Creating a Cable Surface Image of Cable-Stayed Bridge Using Image Processing Z. Wei1(B) , K. Kawamura1 , T. Nakamura2 , and M. Shiozaki2 1 Department of Information Science and Engineering, Faculty of Engineering, Yamaguchi

University, Tokiwadai 2-16-1, Ube City 755-8611, Yamaguchi Prefecture, Japan {c114vgw,kay}@yamaguchi-u.ac.jp 2 Sumitomo Mitsui Construction Co., Ltd., Tsukuda 2-1-6, Chuoku 104-0051, Tokyo, Japan {t-nakamura,MasandoShiozaki}@smcon.co.jp

Abstract. The authors have developed a cable-stayed bridge (CSB) cable inspection robot to improve the efficiency of cable inspection of CSB. Six cameras were mounted on the robot, which takes a video of the whole circumference of the cable surface as it moves up and down the cable. The method is characterized by making an image development diagram from the taken video. In this paper, the red LEDs on the green base plate are installed in the CSB cable inspection robot in order to synchronize the cameras. Then, a time synchronization method using image processing is proposed to automatically detect the red LEDs from the taken video. Finally, this paper discusses the results of automatically detecting the detection accuracy of red LEDs lighting from the actual videos of the inclined cables, which demonstrate the robot’s ability to improve work efficiency and reduce workplace hazards. Keywords: Cable-stayed bridges · Robot · Image processing · Inspection · Time synchronization

1 Introduction As of March 2019, the CSB has constructed 318 bridges in Japan and the need for maintenance is increasing. Cable inspection of cable-stayed bridge is either conducted visually on aerial work platforms or carried out by inspectors with special altitude technology. However, these inspection methods are problematic in that there is a limit to the inspection height, and there is a problem that the work must be carried out at the height which is dangerous for the inspector. Consequently, research on improving CSB cable inspection robot is being done in Japan. In terms of existing research, cable inspection robots have been developed by Nagasaki University and Nishimatsu Construction Corporation in addition to the robot used in this study. The inspection robot developed by the study authors photographed the entire circumference of the CSB cable surface with several cameras while moving up and down along the cable, and then creating an image development diagram of the CSB © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 943–958, 2023. https://doi.org/10.1007/978-981-19-7331-4_78

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cable surface from the video. By utilizing an image development diagram, it is possible to confirm the position and the shape of damage to the cable, which can be difficult to grasp using video only. Furthermore, it is necessary to automatically synchronize the start time of each mounted camera to avoid timing errors. This study employs a method to automatically synchronize each camera with the ultimate goal of making an image development diagram. Specifically, by making a majority of red LEDs set in the inspection robot flash synchronously in time with each camera, the flicker can be confirmed to be within the processing range of the image development diagram of the inspection robot. In addition, the initial illumination of the red LED is automatically detected within the photographic image, and the photographic image synchronization of each camera is executed. However, due to the existence of pixels similar in red color to that of the LEDs, it is possible to perform a false identification, leading to unwanted synchronizations. Therefore, a method was proposed to install the red LEDs on green base plates in order to perform the detection with fewer similar color pixels in the shooting area. In addition, Camshift, a dynamic image processing tool used for object discovery and tracking, was used in the automatic detection. This paper also outlines a method to automatically detect the start of red LED flashing and applies this method to the actual video footage to verify whether the red LEDs can be detected.

2 Inspection Method of CSB Inspection Robot 2.1 Introduction This chapter describes existing CSB cable inspection robots and compares them to the CSB cable inspection robot used in this study. The inspection method of this study’s CSB inspection robot is to photograph the cable surface with the robot and make the image development diagram of the cable surface from the produced video. Figures 1 and 2 show a diagram of the CSB and a photo of the robot installed on a cable. At point A in Fig. 1, video photography is started manually. After the CSB cable inspection robot rises to point B, the red LEDs flashes and returns to point A. The image development diagram is made using the video taken during the descent from location B to A. 2.2 Existing Cable-Stayed Bridge Cable Inspection Robots In Japan, the development of inspection devices using robots is proceeding rapidly. Nagasaki University has constructed robots which are driven by four propellers running off of electric motors, moving along the cable through guide rollers and taking photos of the cable with equipped cameras. The inspection can be carried out quickly and safely without inspectors having to climb to dangerous heights. The robot built by the Nishimatsu Construction is equipped with cameras and runs along the cable in a similar manner to the robot in this study. A control box lets the inspector operate the device wirelessly. Due to its small size, if enough installation space can be ensured, the investigation can be carried out without traffic control. On the other hand, the inspection robot developed by the author takes video of the entire cable surface, and creates an image development diagram of the cable surface

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Fig. 1. Schematic image of a bridge by the cable-stayed bridge cable inspection robot

Fig. 2. Photograph of cable-stayed bridge cable inspection robot

using the footage. This method of image development diagram making has not been employed in other inspection robots as of now. However, in the method of making an image development diagram proposed by the study authors, the image development diagram was automatically developed after the time synchronization of each camera was manually adjusted. Consequently, we propose an automatic time synchronization method for further improvement of inspection efficiency. 2.3 Construction of the Cable-Stayed Bridge Cable Inspection Robot As shown in Fig. 2, CSB cable inspection robot is composed of three units: a photography unit, an elevation unit (UAV), and the image development diagram software. The elevation unit is used to raise the photography unit, detaching from the photography unit after reaching the destination so as not to interfere with photography. Inside the photography unit, six cameras are mounted so that the entire surface of a cable can be photographed at a single elevation. In addition, the descent speed mechanism keeps the

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descent speed of the photography unit stable, while a separate device records the distance (mm) in which the photography unit has moved in relation to the cable as well as the angle (°) of rotation. The amount of movement recorded by this measuring device is then used when creating an image development diagram. 2.4 Image Deployment Diagram Production The processing of image development diagram software can be divided into six steps. STEP 1: Video Capture. PNG files are generated for each video frame from the video taken by the photography unit. STEP 2: Lens distortion correction. Lens distortion correction is then performed on all captured images generated in STEP 1. STEP 3: Trimming. After lens distortion correction, the area where the cable is projected is cropped off. The crop range is specified using the first captured image and applied uniformly to the remaining images. STEP 4: Planarization. Next, the image conversion formula suitable for visualizing the surface of the cable is adopted to make a planarized image. STEP 5: Synthesis. Using the movement data recorded during photography, the images made in STEP 4 are then combined into a single synthesized image of the cable surface. STEP 6: Image combination between cameras. Since STEPS 1–5 occur for all six cameras on the photography unit, a detailed image of the entire circumference of the cable surface can be generated by further combining all of the continuous images made during STEP 5. 2.5 Necessity of LED Detection

Fig. 3. Interior of cable-stayed bridge cable inspection robot

During STEP 5 of the image development process, it is necessary to synchronize the start time of the image development diagram making process for each of the six

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Fig. 4. Enlarged image of a green base

cameras mounted on the CSB cable inspection robot. Therefore, a number of green bases equipped with red LEDs are installed inside the CSB cable inspection robot. Figures 3 and 4 respectively show photos taken inside the CSB cable inspection robot and the enlarged area of the green bases equipped with red LEDs. The configuration condition is that all cameras can detect any kind of red LEDs, which are set to light up at the same time as the start of the image development diagram. Thus, in order to grasp the start time of the image development diagram process, it is necessary to correctly obtain the frame number for when the red LEDs begin flashing. Although this frame number is obtained visually in previous studies, in order to improve the efficiency of the image development diagram, it was necessary to develop a more reliable method for obtaining the initial frame number automatically when the red LEDs begin flashing.

3 Method of Detection 3.1 Introduction This section describes the existing time synchronization method for making an image development diagram utilized in the other studies mentioned in the previous section. Specifically, a method for automatically detecting the flash of the red LEDs from captured video in order to synchronize six cameras installed on a CSB cable inspection robot was adopted for this study. 3.2 Method of LED Detection Umehara et. al. have conducted research on the time synchronization of multiple cameras for the purpose of obtaining measurements at construction sites. In their research, a screen displaying an alternating color image every five seconds in order of red, blue, yellow and green is photographed with multiple video cameras. Cameras in this method detect a change in RGB (Red, Green, Blue) value at the center of dynamic graph and synchronize the frame number. In this study, the CSB cable inspection robot unifies the start time of image development by detecting whether the red LEDs on the green bases are lit at the same time. The goal is to automatically detect the lighting of red LED from the video taken by the cameras mounted on the robot; however, due to the internal lighting of the robot and

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environment lighting similar in color to the red LEDs, false detection may occur. This study differs from previous research in that the illumination of the red LEDs is detected only after the green base with fewer similar pixels is detected in the captured image, thereby reducing the possibility of false detection. In addition, the CSB cable inspection robot will experience vibration during lifting and lowering, resulting in the position of green bases and red LEDs on an image not being set correctly. For this reason, the Camshift algorithm proposed in 1998 was employed to accurately track the detection of green bases in video. The specific detection methods of green bases and red LEDs will be described in the next section. 3.3 LED Detection Process Processing of the red LEDs lighting detection algorithm that is performed on every camera is divided into five steps. Below, Fig. 5 shows the flow of the detection algorithm and summarizes the details of each step. STEP 1: The video is read frame by frame, and the color representation of the image pixels value is converted from RGB format to HSV (Hue, Saturation, Value) format, also referred to as Hexcone Model. The color parameters in this model are hue, saturation and brightness respectively. RGB format is typically used for pixel values, but because it is difficult to specify the range of specific colors with RGB, this study used HSV format instead to intuitively show the brightness, hue, and saturation of visualized images. STEP 2: After the image is converted from RGB to HSV format, it is then binarized according to the following Formula 1. Specifically, the candidate pixels of the green bases are treated as white, while other pixels not falling into the predefined range are treated as black.  255, (35, 43, 46) ≤ h(x, y) ≤ (77, 255, 255) I (x, y) = (1) 0, otherwise Here, the pixel value in coordinate (x, y) is expressed as I (x, y), and the pixel value of (H,S,V) in HSV format is expressed as h(x, y). A threshold for separating the green bases candidates and other candidates is set within an established range of HSV values. If the pixel is within the range set by Formula 1, a binary image with a pixel value of 255 (white) will be generated. If it is outside the range, it is set to 0 (black). The range of HSV values utilized in Formula 1 for identifying the color green was set beforehand by the study authors after careful image analysis. STEP 3: Through Camshift processing of the binary image obtained in STEP 2, an exploration rectangle containing the green bases can be obtained. This contains the xy coordinates of the upper-left corner of the rectangle, as well as its length and width. Camshift processing is described in the next section in more detail. STEP 4: This step involves detecting the illumination of red LEDs within the search rectangle obtained in STEP 3. First, the pixel value (HSV) of the rectangular frame’s xy coordinates are binarized according to the following Formula 2:  255, (0, 43, 46) ≤ h(x, y) ≤ (10, 255, 255) (2) I (x, y) = 0, otherwise

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Fig. 5. LED detection algorithm flow chart

As with Step 2, a threshold for separating red LED light from other pixel values within a predetermined HSV range is set, with pixels falling within this range designated as 255 (white) and those outside the range as 0 (black). In this way, targeted sections of the image are converted into 255 pixels by Formula 2 and identified as red. The range of red HSV values used in Formula was determined in advance by the authors through image

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analysis of the red LED lights. If the sum of pixel values in the exploration rectangular for the binary image is more than 1, it is assumed that the red LEDs are lit and the algorithm proceeds to STEP 5. When a pixel is determined as red by Formula 2 its pixel value will be 255, and the sum of pixel values in the search rectangular box is 255. In other words, if there is even one red pixel in the exploration rectangular, it treats the red LEDs as lit. On the other hand, if the sum of pixel values in the exploration rectangle is 0, it is judged that the red LEDs are not lit and will return to STEP 1. STEP 5: In the event STEP 4 determines that the red LEDs are lit, the frame number of the image is obtained and the algorithm terminates. 3.4 Camshift Camshift is a video analysis tool that uses a function known as Meanshift to process a series of frames in a video and track target places of high pixel density in a video. The difference between Camshift and Meanshift is that the parameters of Camshift exploration rectangle is variable, while the exploration rectangle for object detection and tracking is fixed in Meanshift. Though Camshift is mainly used for object detection in video, Meanshift is used for image object detection. The basic idea of Camshift is to determine the initial position of the exploration rectangle used in the proceeding frame through Meanshift processing. In addition, the size of the search rectangle box is iteravely updated according to the density of target pixels determined by Meanshift processing, which is subsequently used for the next frame. In addition, the initial parameters of the search rectangle box for the first frame need to be set in advance. The processing sequence of Meanshift and Camshift are described in Fig. 6. STEP 2–1: The center of gravity for the target pixel in the search rectangle box set in STEP 1 of Fig. 6 is calculated using Formulas 3, 4, and 5. Since the processing image is a binary image, the target pixel is a white pixel (pixel value: 255).  I (x, y) (3) M00 = x

M10 =

 x

y

xI (x, y), M01 =

y

xc =

 x

M10 M01 , yc = M00 M00

yI (x, y)

(4)

y

(5)

Here, I (x, y) is the pixel value at the coordinate (x, y), and the coordinate (xc , yc ) is the center-of-gravity coordinate. STEP 2–2: The center of gravity calculated in STEP 2–1 is used as the center of the new search rectangle box to determine the position of the next search rectangle box. STEP 2–3: Until the movement of the search Rectangle box “converges” and the moving distance of the center of the search rectangle is less than the threshold—or the number of repetitions reaches the set value—STEPS 2–1 and 2–2 will repeat. In addition, the threshold of center movement is 1 pixel, while the repetition limit is 20 times.

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Fig. 6. Flow chart of Camshift

Next, the processing of Camshift shown in STEPS 1 and 3 of Fig. 6 will be described.

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STEP 1: First, the size and position of the search rectangle box need to be set. The initial value which was input in advance is used is used for the first frame, while the size and position of the search rectangle box obtained in the processing of the previous frame are used for the subsequent frames. When establishing the size and position for the next frame, if no white pixels are detected within the box (i.e. there is no green base) the algorithm will increase the size of the search rectangle box and return to STEP 1 of Fig. 5. Therefore, if a green base is not detected within the box for a repeated number of times, the size of the search rectangle box will become the same as that of the full frame. On the other hand, if white pixels are detected, Camshift will proceed to STEP 2 and execute Meanshift. At this point, if the sum of all pixel values in the search rectangle box is greater than 200,000, the program determines there to be white pixels present. This threshold was set after prior investigation of the green base photographed by the six cameras consistently resulted in a pixel value sum of roughly ~ 200,000. STEP 3: The final coordinates of the search rectangle box of the processing object frame are then obtained through the Meanshift of STEP 2 by taking the initial coordinates of the search rectangle box in the following frame. Camshift automatically adjusts the size of the search rectangle box according to the parameters of the detected object using Formula 6. The transverse width of the exploration box, s, is equal to the box’s height multiplied by 1.2, resulting in the size of the search rectangle box for the next frame. According to research where Camshift is used, the search box width is set to 1.2 times the height due to its original purpose as facial detection software and the fact that faces are usually in a 6:5 proportion. As the shape of the green base is also rectangular, the width (s) is set at 1.2 times the height.  M00 (6) s=2∗ 256 In Formula 6, M00 is obtained by Formula 3. After STEP 3 concludes, the algorithm then returns to STEP 4 in Fig. 5.

4 Experimental Verification 4.1 Introduction This chapter applies the proposed method described in Chap. 3 to the actual captured images to verify the accuracy of the red LED lighting detection. 4.2 Experimental Methods and Results In this experiment, the CSB cable inspection robot was used to take videos through six cameras of a test cable with a frame rate of 30 (FPS) and image resolution at 1280 × 720. Photographic images taken from each camera and the initial point of the corresponding search rectangle box are shown in Figs. 7, 8, 9, 10, 11 and 12. After the robot rises to the inspection starting point, the white LED is lit to take photos of the cable, causing the interior of the robot to become bright. Figures 8 and 11 show the inside of the robot before white LED lighting, while the other Figures. Show the same area after lighting. In order

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Fig. 7. Camera 1

Fig. 8. Camera 2

Fig. 9. Camera 3

to study the influence of a search box’s start position on red LED detection, the authors set nine red dots labelled A ~ I within the image as the initial search coordinates of the search rectangle box. The values on the right side of the red dot are the XY coordinate values of the initial point in the image, while the symbols under the coordinates in the

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Fig. 10. Camera 4

Fig. 11. Camera 5

Fig. 12. Camera 6

figure indicate the LED detection result,「〇」being successful and「 × 」failure to detect. Table 1 compares the frame numbers of red LED lighting confirmed via visual inspection and the frame numbers of red LED lighting detected using the method of this

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Table 1. Frame number of red LED illumination detected. Data#

Visual

Automatic

Data#

Visual

Automatic

1

213

213

4

753

753

2

751

751

5

823

823

3

761

562

6

816

622

Table 2-1. Experimental results of each initial point. Search initial point Camera #1

Camera #2

Camera #3

Green base Red LED Green base Red LED Green base Red LED A

◯

◯

◯

◯

×

×

B

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×

×

C

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×

×

D

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×

E

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×

F

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◯

◯

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×

×

G

◯

◯

◯

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×

×

H

◯

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◯

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×

×

I

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×

Table 2-2. Experimental results of each initial point. Search initial point Camera #4

Camera #5

Camera #6

Green base Red LED Green base Green base Red LED Green base A

◯

◯

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B

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×

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×

C

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×

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×

D

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◯

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E

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×

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×

F

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×

×

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×

×

G

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H

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I

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×

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×

proposal for the photographic data of the six cameras, with the data number of the table corresponding to the camera number. The results show that when the green base was

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detected in cameras 1, 2, 4 and 5, the red LEDs was also detected at the same frame. Next, Tables 2-1 and 2-2 shows the photographic detection results for each initial search point of the green base and the red LEDs lighting. In addition, “〇” indicates that the green base or red LEDs was successfully detected, while “×” indicates a false detection of the green bases or red LEDs. 4.3 Investigation of Results Based on Table 1, the results for cameras 1, 2, 4 and 5 are consistent with the frame number of red LEDs lighting detected by this study’s method. However, in cameras 3 and 6 the frame numbers of red LEDs lighting detected by this method were inconsistent with the frame numbers confirmed by visual inspection. The source of this inconsistency was determined to be that the red wires connected to the green base were included in the scope of the search box, causing the algorithm to confuse them for a red LEDs flash and resulting in false detection. From this result, it can be seen that automatic red LEDs lighting detection can be carried out accurately in environments other than cameras 3 and 6 using the proposed method. Next, the influence of varying initial search points of the search rectangle box on detection results will be discussed. According to the results in Figs. 7 and 8 along with Table 2-1, cameras 1 and 2 detected the green base at all initial search points as well as successfully detecting the lighting of the red LEDs. According to the results for camera 3, the green base was not detected accurately in the search initial points A, B, C, F, G, H and I. The primary reason is that green is often mistakenly detected as part of the electronic component in the upper part of the image. In addition, there are also cases such as in Fig. 9 where another green base beneath the target green base is erroneously detected. For the search points D and E, the green base was correctly detected, but the illumination of red LEDs was not. This is thought to be because the bottom of a green base is included near the red wire in the search rectangle. Looking at the results for camera 4, the green base at the upper or lower edges of the image was detected at all initial search points. However, the lighting of red LEDs could not be detected for search points F and I. The reason is that although a portion of the base plate was detected in the search box, there was no red LEDs within the image. According to Fig. 11 and Table 2-2, camera #5 did not detect the correct green base in the search points B, C, E, F and I during the first scan. The reason is that these initial points were set under the assumption that the green base would be at the lower half of the image and the presence of another green base in the upper part of the image was detected instead, producing the error. In addition, since only a part of another green base on the screen was photographed, the red LEDs themselves were not captured, so the illumination of the red LEDs was not detected. Based on the results of Fig. 12 and Table 2-2, the green base could be detected at all initial search points, but the illumination of red LEDs was not detected, the reason being red wires near the green base in the search box. To summarize the causes of the above error detection, green base error detection arose from the detection of a green base different from the expected one and detection of other unrelated electronic components. The reason for red LEDs error detection is

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that red wires near a green base commonly enter the image frame and even though the expected green base was detected, no actual red LEDs were present in the image. During the production of the image development diagram, it is necessary to determine whether or not a red LED detection error has occurred. A determination that a false detection has occurred can be made visually by the researcher when the length of the assimilated images taken by all six cameras is different. In addition, when the position of the cable connector in one image is different from the assimilated images of other cameras, it can also be deduced as a false detection. Another instance is when certain identifying markers such as a connection port which was pasted on the circumferential direction of the cable is not visible on the cable surface, which can indicate a detection error.

5 Conclusion In this study, Camshift was proposed as a method to automate the time synchronization of video taken by multiple cameras in order to make image development diagram. In addition, an experiment involving the use of actual images to detect the red LED lighting from varying initial points of search was carried out. The results suggest that when the initial position is set properly and the pixels around the green base inside the robot are not similar in color to the red LEDs, it can accurately detect the presence of red LED light. However, there were cases when the green base was detected but because the red LEDs were not present in the search rectangle box the flash of the red LEDs could not be detected. This can be corrected to a certain extent by adjusting the threshold for judging the existence of the green base according to the size of the green base. Furthermore, the false detections resulting from red wiring can be prevented by wrapping the wire with black tape to conceal them or using different colored wiring. Further experiments incorporating these corrections could further validate the accuracy of the image development diagram. Acknowledgements. We would like to express our gratitude to Kenji Mochida and Kenji Honda of TechnoFlash Corporation for their assistance on this research.

References Bradski, G.R.: Computer vision face tracking for use in a perceptual user interface. In: Proceedings of the Fourth IEEE Workshop on Applications of Computer Vision (WACV’98). IEEE (1998) Fukunaga, K.: Introduction to Statistical Pattern Recognition. Academic Press, Boston (1990) Hideaki, S., Takashi, O.: Development and operation of non destructive inspection equipment for inspection of the cable. Concrete Eng. 55(8), 651–656 (2017) Kawamura, K., Hasegawa, T., Shiozaki, M.: Basic study of an inspection record system for cablestayed bridge cable inspection robot. J. Jpn. Soc. Civ. Eng. Ser. F3 (Civ. Eng. Inf.) 72(2), I_83–I_92 (2016) Kawamura, K., Hasegawa, E., Shiozaki, M.: Development of inspection record system mounted on a cable inspection robot for cable-stayed bridges. J. Jpn. Soc. Civ. Eng. Ser. F3 (Civ. Eng. Inf.) 73(2), I_201–I_210 (2017)

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Kawamura, K., Hashimoto, Y., Shiozaki, M., Nakamura, T.: A geometric transformation method of a cable surface image for cable-stayed bridge inspection. J. Jpn. Soc. Civ. Eng. Ser. F3 (Civ. Eng. Inf.) 77(2), I_51–I_57 (2021) Ministry of Land, Infrastructure, Transport and Tourism: Annual report of road statistics and present state of bridges in 2020. https://www.mlit.go.jp/road/ir/ir-data/tokei-nen/2020/nen po03.html Nagasaki University: the Cable-Stayed bridge cable inspection robot VESPINAE. https://www. chodai.co.jp/vespinae/ Nishimatsu Construction: the cable protection pipe inspection robot of the Cable-Stayed bridge coroner checker. https://www.nishimatsu.co.jp/assets/upload/solution/1455769046_0 74527800.pdf Okutomi, M.: Digital image processing, pp. 80–81 (2015) Yoshimasa, U., Yuhei, Y., Jang, W., Toshio, T., Tanaka, S., Sato, M.: Basic research on time synchronization of human measuring instruments. J. Civ. Eng. Inf. 45, 221–224 (2020) Yun, H., Kim, S., Wu., L., Lee, J.: Development of inspection robots for bridge cables. Sci. World J. 2013 (2013)

Assembly Fault-Tolerant Interval Inversion Method for Cable-Stayed Bridge Based on Bilayer Surrogate Model Fan Wang(B) , Jianling Zhao, Xiaoming Wang, Pengfei Li, and Pei Tao Highway School, Chang’an University, Xi’an 710064, China {2020121071,wxm}@chd.edu.cn, [email protected], [email protected]

Abstract. Focusing on the assembly accuracy control problem of practical engineering and installation tolerance ability under uncertain interference, this paper presents an interval inversion method derived from reliability-based optimization design (RBDO) scheme. The proposed method is applied to the tolerance planning of cable tensioning process of an example cable-stayed bridge. In this paper, the midpoint and radius of the controllable parameters are taken as the optimization variables, and a decoupling evaluation framework based on bilayer surrogate model is established to quantify uncertainty, and then the maximum tolerance range is efficiently extracted from the highly coupled design objectives. The results illustrates that the proposed method not only effectively saves calculation resources, but also ensures high accuracy. The application of tolerance interval to guide engineering decision-making process has shown better inclusiveness to the error accumulation during construction, which improves the construction resilience under the influence of manufacturing and assembly errors. Keywords: Interval inversion · Tolerance capacity · Reliability optimization · Surrogate model · Cable force optimization

1 Introduction The direct and indirect loss of environmental impacts and mobility disruptions resulting from the urban bridge constructions can exceed the actual cost of the structure itself (Wang et al. 2022). In order to shorten the construction period, the industrialized construction technology of factory prefabrication and on-site assembly is widely used in engineering practice. However, because the components are prefabricated before installation, it is impossible to use the measured data to correct the inevitable manufacturing deviation and assembly error, which may lead to assembly failure. Therefore, the assembly tolerance capacity of structures which suppresses multi-source uncertain interference is particularly important, which has become the main approach to improve its error tolerance. For practical engineering, the above uncertainty mainly comes from two aspects: first, the approximate error caused by the simplified mathematical modeling of the objective

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 959–974, 2023. https://doi.org/10.1007/978-981-19-7331-4_79

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structure. For this, Wei et al. (2012) fully considered the unmodeled dynamics for nonlinear system of the vehicle suspension and proposed the strategy combining neural network and sliding mode control, which effectively reduced the vehicle vibration and enhanced driving comfort; Second, the ubiquitous variation of internal parameters of the structure itself and the interference from external environment. For modern cable-stayed bridges with complex spatial configuration, in order to accelerate the construction progress, parallel wire finished cables are often used, which requires the manufacturing length of cables to be given before tensioning operation. Once the fabrication length is given by design, it will become a constant physical quantity. Therefore, the manufacturing error cannot be corrected according to actual measured information; In addition, because both ends of the cable are anchored in the anchor box inside the girder and tower respectively as a concealed project, which leads to the problem of insufficient spatial lofting accuracy (Kang et al. 2018; Wei et al. 2020). Therefore, when the construction control of engineering structures is limited by cognition, time, technology and investment, the assembly tolerance capacity can enhance the constructability of the construction process at the cost of moderately sacrificing the assembly accuracy. In order to control uncertain parameters, suppress interference and realize comprehensive trade-off under multi criteria and constraints, reliability based design optimization (RBDO) method is proposed and developed: Nan et al. (2018) introduced fault-tolerant planning into the design of high false work, where uncertain variables are treated with probability distribution to achieve the design objectives of safety, applicability and economy; Yuning et al. (2016) applied interval method to quantify the uncertainty of material parameters and external load, described the shear buckling reliability with an interval possibility index, and finally established the interval reliability optimization model of composite corrugated plate. However, the optimization result of the above research is a set of determined values, which can only provide the nominal parameters of structural design or construction control for decision-makers, thus the adaptive error range is unknown and may cause serious damage to the optimality of design objectives and structural reliability in the direction with strongest error interference. In order to solve the above problems, the interval inversion theory is developed: Jiang et al. (2015) proposed an interval optimization method based on tolerant design, which taking the design optimality and interval economy as the optimization objectives at the same time; Liu et al. (2016) established a new adaptive surrogate model framework under interval uncertainty and combined it with multi-objective solver, in which the interval width is regarded as an independent design variable. This provides a feasible idea for the fault-tolerant interval inversion of stay cables. The previous research on construction control of cable-stayed bridges (Xiu-dao et al. 2019, Mingzhi et al. 2013; Sun et al. 2016) can only give the nominal parameters of assembly components, which requires high-leveled on-site assembly accuracy control. In this paper, the worst-case influence of uncertain interference is fully considered, and a new inversion method of assembly fault-tolerance interval for stay cables is proposed to extract the maximum tolerance range from multiple structural performance indexes which are highly coupled. Aiming at the bottleneck of calculation accuracy and efficiency for reliability index under random-interval hybrid uncertainty, a bilayer surrogate model

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framework is developed to substitute for the traditional nested search method, which directly maps the lower bound of reliability interval, namely, the worst-case reliability index. By using interval rather than deterministic parameters to guide the assembly process, the structure obtains the ability of restraining interference, which makes the cumulative effect of assembly error more inclusive and adaptive. The calculation accuracy and efficiency of the proposed method are verified by a numerical example and an engineering example.

2 Interval Inversion Framework of Assembly Fault-Tolerance for Stay Cables In the traditional RBDO framework, the reliability of structural performance, the optimality of design objectives and the constructability of assembly process can be described as multiple objectives or constraint functions, and the result is a deterministic optimal value. In order to invert the maximum tolerance of design variables, the interval method is applied in this paper to describe uncertainty, where the midpoint and radius of the interval are regarded as optimization variables at the same time; Besides, the nonnegative dimensionless index W proposed by Jiang Chao et al. (2015) is used to reflect the total uncertainty of all design variables, and it is integrated into the inversion model as an independent optimization target, so as to maximize the multi performance optimality and fault-tolerant capacity under the constraint of interval reliability. The mathematical format is:     find DI = d1I , · · · , diI , · · · , dnID , diI ∈ dic − diw , dic + diw   min fj X, Y I , DI , j = 1, 2, · · · , l

s.t.

−W   β L X, Y I , DI ≥ β T

(1)

DL ≤ DI ≤ DU where DI is nD -dimensional design vector, DU and DL represent the upper and lower of each dimension of bounds of the design domain; dic and diw is the midpoint and  radius the design variable, so its dimension is extended to 2nD ; fj DI , j = 1, 2, · · · , l describes l’s design goals, and W reflects the fault-tolerant capacity; Obviously, under the joint action of random variable X , interval random variable Y I and interval design variable DI , the reliability index β It is not a definite value, but an interval of [β L , β R ]. In this paper, the lower bound β L is used to establish the worst-case reliability constraint, which should be no greater than the given value β T . The dimensionless index W is expressed as follows:

n D d w k nD W = (2) k=1 d c k Then, the multi-objective optimizer NSGA-II proposed by Deb et al. (2002) is applied to drive the above inversion model to quickly locate the Pareto front in the

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high-dimensional nonlinear design domain. This process is realized by the “gamultiobj” function in global optimization toolbox of MATLAB.

3 Evaluation Method of Error Extreme Interference Based on Bilayer Surrogate Model 3.1 Decoupling Evaluation Framework of Error Extreme Disturbance After introducing the interval characteristics of optimization variables, the extreme interference of uncertain factors can be quantified and solving the maximum tolerance range is regarded as an interval reliability optimization problem under multiple objectives and constraints. The biggest difficulty lies in the efficient prediction of the worst-case reliability index β L under random-interval hybrid uncertainty. The traditional hybrid reliability analysis method based on Monte-Carlo simulation (MCS) is characterized by a doubleloop nested search process, that is, in the inner layer, extreme response of the structure is located through optimization algorithm, and in the outer layer, failure probability is calculated by probabilistic reliability analysis (Yang et al. 2015). However, when the above procedure is integrated into the process of interval inversion, an even more complex three-loop nested optimization scheme is formed, with multi-objective optimization in the outer loop, reliability analysis in the center and extreme response calculation in the inner loop. Even if the computational burden of finite element analysis (FEA) in the inner loop can be significantly reduced by using surrogate models which can explicitly express the performance function, frequent optimization process is still unavoidable in center and outer loop. In order to break through the efficiency bottleneck of the nested evaluation framework, this paper proposes the worst-case reliability prediction method assisted by a bilayer surrogate model, that is, firstly, the limit-state function is surrogated by Active-learning Kriging (AK) model, and then the worst-case reliability is directly mapped by BP neural network (BPNN), which realizes the complete decoupling of the three-loop nested problem. The process is shown in Fig. 1, including four main steps as follows: (1) The limit-state function G = R − S is built based on the relationship between resistance R and effect S, and the finite element model of structural analysis is established; (2) The AK model is established to locally approximate the limit-state function at region of interest (G(X , Y , D) = 0); (3) The interval characteristic of design variable DI is introduced, which is expressed as midpoint d c and radius d w ; For each group of design variables, the hybrid reliability analysis method based on MCS is applied to obtain the corresponding lower bound β L of reliability index; (4) Finally, taking the results obtained in step (3) as training samples, BPNN is established to directly map β L . The constraint function is converted to:   βˆ L X, Y I , DI ≥ β T (3) where β L is the worst-case reliability index predicted by the surrogate model.

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Generation of Monte Carlo population for AK model Generation of input samples in design space, (D)

Well-trained BPNN for βL-surrogate

Input: introducing the intervals of design variables dI=[dc-dw, dc+dw]

Mapping relation of design variables and reliability index

Query strategy

MCS-based hybrid reliability analysis β [βL, βR]

Output: the worst-case reliability βL

Well-trained AK model for G-surrogate

Explicit limit-state function G(X,Y,D)

Direct worst-case reliability prediction βL(X,YI,DI)

Input: all variables, (X, Y, D) FEM Calculation Output: structural response

Build-up of initial AK model

Fig. 1. Decoupling evaluation framework of extreme error interference based on bilayer surrogate model

3.2 AK Model for Limit-State Function Approximation The real industrial construction of cable-stayed bridge is a dynamic process with nonlinear time-delay characteristics. To quickly build a surrogate model for its complex structural response, it is necessary to ensure the quality of training samples. This requires not only to predict the dynamics and trend of unknown points according to the existing information, but also to obtain the prediction error to evaluate the value of samples, so as to improve sampling efficiency. Therefore, this paper combines Kriging model with Pool Based Active-learning (AL) strategy, constructs the “step-by-step approximation” mechanism with efficient query strategy, and forms a Kriging surrogate model based on learning function U which can replace the real limit-state function. The main steps are as follows: (1) Determine the initial Design of Experiment (DoE): Latin hypercube sampling (LHS) method is used to generate initial samples in the uncertain space and the corresponding value of limit-state function is calculated by FEA; (2) Generate alternative Monte Carlo (MC) sample set: for random variables, sample according to their probability distribution; For interval variables, uniformly sample between the upper and lower boundaries; The number of alternative samples n should be large enough to cover the entire uncertainty space; (3) Kriging model is established according to DoE; (4) Use Kriging model to predict and identify high-value samples: calculate the predicted value and variance of all points in the alternative MC sample set, calculate value of U and locate the minimum U at x∗ according to the following formula (Echard et al. 2011): μ ˆ (x) G U (x) = (4) σGˆ (x) x∗ = arg min U (x) x

(5)

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where x is the input value of the unknown point, μGˆ (x) and σGˆ (x) are the predicted value and prediction variance of Kriging model at this point. (5) Convergence condition: when Umin ≥ 2 is satisfied, that is, for all sample points, there are [U (x)] ≥ 0.977, ensuring that the prediction accuracy of the sign of the limit-state function is higher than 97.7%. The model’s accuracy is enough and the iteration stops; Otherwise, proceed to the next step; (6) Update DoE: calculate the value of the limit-state function at the point x∗ , then add it to DoE, and return to step (3); (7) Update the alternative MC sample set: in order to ensure the diversity of training samples and avoid redundant information (Kumar et al. 2020), the standard Euclidean distance between the new sample x∗ and each point in the alternative set is calculate according to the following formula, and redundant points that do not meet the distance constraint are eliminated from the set.

 n  (xi − yi )2 dis =  ≥ disT (6) 2 s i i=1 where, n is the dimension of variables, xi , yi represents the ith-dimensional value of two samples respectively, si is the standard deviation of the ith dimension, and disT is the distance limit. 3.3 GA-BPNN Approach to the Worst-Case Reliability Surrogation The well-trained AK model realizes the accurate prediction of complex structural response during construction, thus repeated call of time-demanding implicit finite element analysis in the whole process is avoided. Even so, the boundary prediction of reliability index under hybrid uncertainty is still a double-loop nested search procedure (Yang et al. 2015), and it is still inevitably faced with the problems of high computational burden and huge time cost. Therefore, considering the strong nonlinear fitting ability of BPNN, this paper establishes the direct mapping relationship between design variables and the worst-case reliability index, so as to realize the complete decoupling of the above nested problems. At the same time, in order to reduce the fitting deviation caused by improper definition of network parameters (Chatterjee et al. 2012), genetic algorithm (GA) is applied to assist the network’s construction process, forming the GA-BPNN framework which optimizes the best network parameters. The steps are as follows: (1) Obtain training samples: After replacing the real limit-state function with AK model, the samples of design variables are randomly selected in the design domain, and the corresponding worst-case reliability index is calculated using the hybrid reliability analysis method based on MCS (Yang et al. 2015), so as to train BPNN. (2) Network initialization: A three-layer neural network is established in this paper. The hidden layer neurons are S-type transferring function and the output layer neurons are linear

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transferring function. Other network hyperparameters, such as the number of hidden neurons and learning rate, are first determined by experience, and then adjusted through subsequent trial calculation. (3) Network parameters optimization by GA: Each individual in the genetic population corresponds to a set of network parameters, and the sum of squares of network prediction error Esum is taken as the individual’s fitness to complete the optimization process described in the following formula through selection, crossover, variation and other operations: find min

W; θ Esum =

k   2 yˆ i − yi

(7)

i=1

s.t.

W ∈ [−3, 3]; θ ∈ [−3, 3]

where W and θ are the network threshold and weight matrix respectively, yˆ i and yi are the predicted value and real value of the ith test point, and k is the total number of test points. (4) Train and test the network: The optimal parameters are assigned to the initial network, then the new network is trained and tested. In this paper, the maximum relative prediction error and goodness of fit are taken as the measurement indexes of network performance, which are expressed as follows:   yˆ i − yi (8) Emax = max yˆ i 2 k  i=1 yˆ i − yi 2 R = 1 − k (9) 2 i=1 (y − yi ) where yi is the mean value of the test set. The closer R2 is to 1, the better the fitting performance of the network.

4 Case Study 4.1 Numerical Case Figure 2 shows the cantilever tube structure under external uncertain load F1 , F2 , P and T . The statistical parameters and limit-state function expression are detailed in literature (Du et al. 2007). As a typical problem, this structure is frequently studied with different reliability analysis method in literature (Liu et al. 2016; Yang et al. 2015; Zhang et al. 2021). Based on the method proposed in this paper, the design variables are extended as the tube’s thickness t, diameter d and its tolerance range, which are described by the midpoint t c , d c and radius t w , d w of the interval. Obviously, when the radius is 0, it

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degenerates into the traditional RBDO problem. In addition, taking the tube’s volume V and fault-tolerant index W as the objective functions and worst-case reliability index as constraint function, an interval inversion model is constructed. According to the idea of this paper, first AK model is built to replace the real limitstate function of the structure: as shown in Fig. 2, the initial DoE contains 13 training samples, and an AK model that meets the accuracy requirements can be obtained after only 32 iterations. Obviously, the new training points selected by the query strategy are mostly near limit state (G = 0), and adding these points to DoE can significantly improve the accuracy of the model, Thus, the sampling efficiency is greatly improved. Then, the worst-case reliability index is directly mapped by GA-BPNN framework. Figure 3 shows the prediction performance of the surrogate model. Its goodness of fit reaches R2 = 0.99966, and the maximum error is only 4.38%, showing high prediction accuracy. The interval inversion process is efficiently conducted with the help of the above surrogate models. Partial inversion results are listed in Table 1. It can be seen that with the increase of fault-tolerant capacity, the volume of cantilever tube slightly increases. Surely there is a certain conflict between them. At the same time, it should be noted that the inversion result is no longer a definite value, but an interval.

Value of Limit-state Function G /MPa

Initial DoE Added Samples G=0

13 Samples

32 Samples

Iteration

Fig. 2. DoE of the AK model

2

R =0.99966

Relative Error

Worst-case Reliability

1.00 0.95

MCS BPNN Relative Error

Test Point No.

Fig. 3. Accuracy verification of GA-BPNN surrogating worst-case reliability β L

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Table 1. Partial Pareto solutions of the cantilever tube No

Thickness t/mm

Diameter d /mm

Volume V /mm3

Fault-tolerant index W

1

4.220 ± 0.500

45.036 ± 1.993

64929.6

−0.072

2

3.949 ± 0.289

45.158 ± 1.737

61350.3

−0.053

3

3.888 ± 0.256

45.234 ± 1.627

60610.1

−0.049

4

4.084 ± 0.409

45.211 ± 1.867

63316.1

−0.064

5

4.090 ± 0.429

45.225 ± 1.882

63431.9

−0.066

6

4.135 ± 0.427

45.155 ± 1.977

63943.5

−0.067

Table 2 compares the worst-case reliability index at design point [5, 0, 42, 0], , using method in this paper and methods in literature (Liu et al. 2016; Du et al. 2007). The result shows that the proposed method can achieve high prediction accuracy with fewer calls of the real performance function. Table 2. Comparison of calculation accuracy for worst-case reliability β L Method

Maximum failure rate Pfmax

worst-case reliability β L

Calls of real limit-state function Ncall

This paper

1.71 × 10–4

3.5812

45

Liu et al. (2016)

1.63 × 10–4

3.5937

1092

Du et al. (2007)

1.63 × 10–4

3.5937

147

Note Design point [5, 0, 42, 0] as example

Taking the second result in Table 1 as optimal solution, Table 3 compares the optimization results between the proposed method and the traditional tolerance-free multiloop nested RBDO method. It clearly shows that although the volume of the optimal solution increases by 4.73%, it provides a large safety margin for the manufacturing deviation. It can be seen that the interval inversion method quantifies the maximum fault-tolerant capacity of components on the premise of ensuring structural reliability and design optimality. In terms of time consumption, the traditional RBDO process takes up to 4479 min, which is unacceptable for complex engineering problems that require a large number of calls for finite element calculation; In contrast, method in this paper only requires 174 min, which makes it applicable to the industrial construction process of complex cable-stayed bridges. 4.2 Engineering Case Figure 4 shows a single pylon cable-stayed bridge with a span combination of 151.1 + 91.1m and bridge width of 46m. Its structural characteristics are as follows: (1) SteelUHPC composite box girder is used in the main span, and concrete box girder in the

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Method

Thickness t/mm

Diameter d /mm

Volume V /mm3

Time cost /min

This paper

[3.66,4.24]

[43.42,46.90]

61350.3

174

RBDO

3.99

42.97

58579.8

4479

side span, with ratio of the side to main span 0.6; (2) Steel bridge tower is used, in which the left tower is 105.12 m high and the right tower 120.12 m; (3) 34 pairs of stay cables are arranged asymmetrically in a spatial form. The main beam is constructed on temporary supports, then the stay cables are symmetrically stretched, and finally the supports are removed to complete system transformation. Figure 5 shows the finite element model in ABAQUS for structural response analysis. During construction, the cable is tensioned for two rounds. The first round of tensioning is required to reach about 70% of the designed cable force, and then the second round aims to adjust cable force to the target completion state. However, under uncertain interference, the actual completed state of the structure is difficult to fully match the target state, so the second round of cable force adjustment needs to provide additional fault-tolerant interval. In addition, the tower column deformation under the combined action of natural environment and construction load puts forward higher requirements for the positioning control of anchor box and the measurement accuracy of cable force and length, which requires engineers to consider tolerance redundancy when giving the manufacturing length of cable.

B17 B16 B15

Tower Top Long Cables

Z17 Z16 Z15

Long Cables

Fig. 4. Structural description

Because the long cable are arranged in the sensitive area of bridge tower deformation control, its cable force deviation will significantly affect the tower top displacement, and then hinder the realization of reasonable finished state of the bridge; In addition, limited by the existing detection technology, the cable force of long cables with large sag are difficult to measure accurately (Xiao et al. 2014); Besides, long cables under high stress condition are more sensitive to the geometric deformation of the structure. Any small error in tensioning operation or measurement process may lead to a wide range of cable

Assembly Fault-Tolerant Interval Inversion Method Tower Top Cable

Material：Strand 1860 Elastic Modulus：E=1.95×105MPa Section characteristics： A=0.0042~0.0063m2 Element Type：T3D2

Long Cable Tower

B15 B16 B17

Material：Steel Q390 Elastic Modulus：E=2.06×105MPa Section characteristics： A=0.304~1.677m2 Iyy=0.439~9.374m4 Element Type：B31

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Z17 Z16 Z15

Long Cable

Material：Steel Q345 Elastic Modulus：E=2.06×105MPa Section characteristics： A=2.047m2，Iyy=3.199m4 Element Type：B31

Material：Concrete C50 Elastic Modulus：E=3.45×104MPa Concrete Section characteristics：A=36.809m2 Iyy=40.700m4 Element Type：B31

Girder

Steel Girder

Fig. 5. FEA model in ABAQUS

force fluctuation. Therefore, the demand for interval inversion of long cables is more urgent. Of course, the interval inversion framework proposed in this paper also allows decision makers to further consider the fault-tolerant capacity of other cables, but this will increase the dimensions of design domain and bring more computational burden. Here the midpoint and radius of cable forces interval are regarded as optimization variables, and multiple objectives and constraint functions are designed to fully consider the trade-off between different design criteria. Besides, the fault-tolerant capacity is integrated into the inversion process as an independent optimization objective. The results can not only provide the optimal cable force under uncertain interference for the regulation of long cable tension, but also offers maximum tolerant range for on-site construction operations. The inversion model is as follows: find obj.

T    DI = d1I , d2I , · · · , d6I , diI ∈ dic − diw , dic + diw , i = 1, 2, · · · , 6 fˆ1 = min{max(Z)}    6  c d − d ∗ + max d c − d w − d ∗ |, |d c + d w − d ∗ f2 = min i i i i i i i i i=1

s. t.

f3 = min{−W }   βˆ L X , DI ≥ β T     dic ∈ 95%di∗ , 105%di∗ ; diw ∈ 0, 10%di∗ (10)

The cable force of long cables (Z15, Z16, Z17, B15, B16 and B17) are shown in Table 4. Considering that the variability of material parameters has little effect on the structural response, it is ignored in the inversion process, and only the cable tensions X are taken as random variables. di∗ is the design tension of the i th cable to be optimized, max(Z) is the maximum deflection of the main beam under uncertainty. Objective fˆ1 reflects the influence of cable force optimization on the main beam, which is surrogated by GA-BPNN. Objective f2 is designed to achieve minimum deviation between the optimal

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tensions and the designed tensions, that is, it ensures the best reasonable finished stage possible. Objective f3 aims to maximize fault-tolerant capability. Table 4. Design domain of design variables Design variables

Description

Lower bound of design domain/kN

Upper bound of design domain/kN

d1c

Midpoint of Z15

2322.8

2567.3

d1w

Radius of Z15

0

244.5

d2c d2w d3c d3w d4c d4w d5c d5w d6c d6w

Midpoint of Z16

2324.7

2569.4

Radius of Z16

0

244.7

Midpoint of Z17

2339.9

2586.2

Radius of Z17

0

246.3

Midpoint of B15

2806.3

3101.7

Radius of B15

0

295.4

Midpoint of B16

2825.3

3122.7

Radius of B16

0

297.4

Midpoint of B17

2834.8

3133.2

Radius of B17

0

298.4

In terms of constraint function, the horizontal deviation of the tower top during construction is taken as the evaluation index which reflects the mechanical performance of tower to establish the limit-state function as follow:     G X, DI = aT − a X, DI (11) where aT is the maximum allowable deviation of thetower top, which can be taken as 30 mm according to the specification requirements; a X , DI is the actual displacement  of the tower top under uncertainty. When it exceeds the allowable value a X , DI , it is considered as structural failure, which is not allowed during construction. Constrained reliability index β T is taken as 2.5, that is, the failure rate of bridge tower shall be less than 0.62%. Then, GA-BPNN is established to surrogate the above objective and constraint functions that have no explicit form. For fˆ1 , finite element model in ABAQUS is called to obtain the maximum deflection max(Z) of the main beam. Figure 6 shows the prediction accuracy: the maximum prediction error is only 0.027%, and the goodness of fit reaches R2 = 0.99999; In terms of the worst-case reliability constraints, based on the method proposed in Chap. 3, the inner AK model is established to express the limitstate function explicitly and outer GA-BPNN for direct mapping worst-case reliability index. As shown in Fig. 7, the maximum prediction error is 4.82%, and goodness of fit is R2 = 0.99949, meaning the model’s accuracy fully meets engineering requirements.

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2

R =0.99999

1.00

0.95

Fig. 6. BPNN surrogate of objective fˆ1

2

R =0.99949

1.00

0.95

Fig. 7. BPNN surrogate of constrain βˆ L

With the assistance of fˆ1 and βˆ L surrogate models, multi-objective optimizer NSGAII is used to drive the interval inversion problem described in Eq. (10). Algorithm parameters are as follows: population number is 400, maximum generation 200, crossover probability 0.8 and mutation rate 0.01. And maximum generation is taken as the convergence condition. The Pareto fronts are shown in Fig. 8, and Partial Pareto solutions are shown in Table 5. The above results fully show the conflict characteristics of different design objectives, that is, with the improvement of fault-tolerant capacity (f3 ), design optimality (fˆ1 and f3 ) slightly decrease. Therefore, decision-makers should reasonably judge according to specific engineering scenario. Here, the eighth result with maximum W in Table 5 is selected as the optimal one, and the corresponding inversion results are listed in Table 6. Different from traditional RBDO, the cable tension is given in the form of interval, which is no longer a deterministic value. The maximum deviation between the inversion result and the designed cable force d ∗ increases 7.3–13.0%. The enlarged fault-tolerant range are easier to realize in the process of on-site cable force regulation. As long as the construction tensioning force is within this range, it can ensure good structural performance and optimal finished state of the bridge, which undoubtedly greatly reduces the difficulty of tensioning operation. Table 6 also shows the corresponding manufacturing length interval of stay cables. In the parallel prefabrication stage, considering the extreme interference of assembly error, the above fault-tolerant interval can be used

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-W

-W

to guide the manufacturing process, which provides stronger interference suppression ability and better inclusiveness to the error accumulation during construction.

f1 /m

(a) Pareto Fronts

and

-W

f2 /kN

(b) Trade-off between

f2 /kN

(c) Trade-off between

f1 /m

and

(d) Trade-off between

and

Fig. 8. Interval inversion result for cable force optimization

Table 5. Partial optimal solutions No

fˆ1 /m

f2 /kN

−W

βˆ L

1

0.0107

1.5150

−0.0427

2.5349

2

0.0105

0.8618

−0.0194

2.5007

3

0.0108

1.3322

−0.0389

2.5137

4

0.0108

1.7943

−0.0488

2.5134

5

0.0107

1.0590

−0.0294

2.5040

6

0.0104

1.1476

−0.0273

2.5104

7

0.0108

1.8663

−0.0496

2.5006

8

0.0109

1.8535

−0.0510

2.5007

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Table 6. Optimization result of design variables Cable No

Tensions interval   d L , d R /kN

Maximum deviation form d ∗ /%

Designed manufacturing length/m

Manufacturing length interval/m

Z15

[2365.2,2762.3]

12.976

145.086

145.068 ± 0.030

Z16

[2452.2,2670.9]

9.150

153.309

153.291 ± 0.018

Z17

[2453.2,2705.3]

9.838

161.565

161.545 ± 0.022

B15

[2692.6,2967.9]

8.851

110.223

110.234 ± 0.012

B16

[2732.3,3016.9]

8.126

114.917

114.926 ± 0.013

B17

[2766.6,3030.3]

7.287

119.621   Note Maximum deviation form d ∗ = max d ∗ − d L |, |d ∗ − d R /d ∗

119.629 ± 0.013

5 Conclusions In this paper, focusing on the problem of assembly accuracy control in practical engineering under uncertain interference, a fault-tolerant interval inversion framework based on RBDO is proposed and applied to the fault-tolerant planning of cable tensioning process of a real-scale cable-stayed bridge. By taking the midpoint and radius of uncertain interval as optimization variables at the same time, and with the help of bilayer surrogate model which quantifies assembly error, the decoupling of the triple-loop nested optimization process of interval reliability calculation is realized, and then the maximum fault-tolerant range of controllable parameters is effectively extracted from the highly coupled design objectives. The robustness of the above method is verified by two examples. The results show that: (1) The interval inversion method reasonably considers the uncertainty of design variables. On the premise of ensuring design optimality and constraint reliability, the obtained inversion results can not only provide the optimal control value under uncertain interference for engineering decision-making, but also offer the largest fault-tolerant interval possible to deal with potential risks and reduce control costs. (2) In order to break through the efficiency bottleneck of the traditional nested assembly error evaluation framework, an error extreme interference evaluation framework based on bilayer surrogate model is proposed, which not only effectively saves computing resources, but also ensures high solution accuracy. (3) The proposed method provides a feasible idea for solving similar problems, which can be transplanted to the construction fault-tolerant design of all kinds of accelerated construction structures, concurrent engineering, and the fault-tolerant design of complex structural systems.

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References Chatterjee, S., Bandopadhyay, S.: Reliability estimation using a genetic algorithm-based artificial neural network: An application to a load-haul-dump machine. Expert Syst. Appl. 39(12), 10943– 10951 (2012) Deb, K., Pratap, A., Agarwal, S., et al.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002) Du, X.: In interval reliability analysis. In: ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 1103–1109 (2007) Echard, B., Gayton, N., Lemaire, M.: AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation. Struct. Saf. 33(2), 145–154 (2011) Jiang, C., Xie, H., Zhang, Z., et al.: A new interval optimization method considering tolerance design. Eng. Optim. 47(12), 1637–1650 (2015) Kang, L., Wei-dong, X., Yuan, Z., et al.: Techniques for installation, measuring and positioning control of steel anchor boxes in Pylons of Jialingjiang river bridge in Hongyan Village. World Bridges 46(4), 6 (2018) Kumar, P., Gupta, A.: Active learning query strategies for classification, regression, and clustering: A survey. J. Comput. Sci. Technol. 35(4), 913–945 (2020). https://doi.org/10.1007/s11390-0209487-4 Liu, Y., Jeong, H.K., Collette, M.: Efficient optimization of reliability-constrained structural design problems including interval uncertainty. Comput. Struct. 177(dec.), 1–11 (2016) Mingzhi, X., Yizhi, B., Ran, W., et al.: Unstressed cable length and geometric linear control of hybrid girder cable-stayed bridge with 1000 m sale span. J. Chongqing Jiaotong Univ. (Nat. Sci.) (3), 5 (2013) Nan, X., Kai, Z., Hang, H., et al.: Error-tolerant optimization design of high false work. Eng. Mech. 35(A01), 6 (2018) Sun, Y., Zhu, H.P, Xu, D.: A specific rod model based efficient analysis and design of hanger installation for self-anchored suspension bridges with 3D curved cables. Eng. Struct. 110(Mar.1), 184–208 (2016) Wang, X., Wang, H., Sun, Y., et al.: Fault-tolerant interval inversion for accelerated bridge construction based on geometric nonlinear redundancy of cable system. Autom. Constr. 134, 104093 (2022) Wei, W., Yuling, S., Tichun, W., et al.: Intelligent control of automotive semi-active suspension with uncertain factors. Eng. Mech. 29(9), 337–342 (2012) Wei, C, Xin-jun, F, Xiang, C, et al.: Positioning and measuring techniques for steel anchor beams in Pylon at Pier No.2 of Wuhu Changjiang River Rail-cum-Road Bridge on Shangqiu-HefeiHangzhou Railway. Bridge Constr. 50(2):6 (2020) Xiao, W., Ru-cheng, X.: Tension force estimation for cable-stayed bridge under both Sag and Bending stiffness effects. J. Huazhong Univ. Sci. Technol. (Nat. Sci. Edition) 000(003), 92–95 (2014) Xiu-dao, M., Yi-yan, L.: Construction control calculation method for long-span cable-stayed bridge based on cable length and application. Bridge Constr. 49(6), 6 (2019) Yang, X., Liu, Y., Gao, Y., Zhang, Y., Gao, Z.: An active learning kriging model for hybrid reliability analysis with both random and interval variables. Struct. Multidiscip. Optim. 51(5), 1003–1016 (2015). https://doi.org/10.1007/s00158-014-1189-5 Yu-ning, Z., Zhi-ping, Q., Kai-hua, Y.: Buckling performance analysis and reliability optimization of composite corrugated plates under shear loading. J. Vibr. Shock 35(19), 9 (2016) Zhang, X., Wu, Z., Ma, H., et al.: An effective Kriging-based approximation for structural reliability analysis with random and interval variables. Struct. Multi. Optim. 10 (2021)

Dimensionless Continuum Model of Vertical Free Vibration of Spatial Self-anchored Suspension Bridge Jianling Zhao(B) , Fan Wang, Xiaoming Wang, Pei Tao, and Pengfei Li School of Highway, Chang’an University, Xi’an 710064, China [email protected], [email protected]

Abstract. Due to the spatial coupling of main cable-hanger and the internal selfbalance between subsystems, the free vibration continuum model of spatial selfanchored suspension bridge is difficult to establish, which limits the acquisition and identification of its dynamic characteristics. In this paper, the vertical free vibration continuum model considering hanger tension is established by integrating the vibration form deflection theory and the deformation and compatibility equation of main cable-hanger-beam, which is dimensionless to identify the characteristic parameters controlling dynamic characteristics; The shape function of main cable and girder satisfying the geometric and mechanical boundary is constructed, and the model is transformed into matrix form by Galerkin method to solve the modal frequency and vibration mode; Numerical examples and finite element models are used to verify the universality and accuracy of the continuum model, and the sensitivity of key stiffness characteristic parameters is analyzed. The results show that the relative elastic bending stiffness of the main girder significantly affects the modal frequency, and the elastic stiffness of the main cable only slightly affects the symmetrical modal frequency; The elastic axial stiffness of the hanger is sensitive to the relative elastic bending stiffness of the main girder. Whether the hanger tension is considered or not will significantly affect the highorder modal frequency, especially the antisymmetric mode. In conclusion, the continuum model considering hanger tension is more accurate, which can provide an effective reference for the preliminary design of the project and the real-time planning of dynamic disaster prevention and control scheme. Keywords: Continuum model · Dimensionless · Vertical free vibration · Spatial self-anchored suspension bridge · Galerkin method

1 Introduction The static and dynamic analysis models of self-anchored suspension bridges are usually divided into two categories: discrete model and continuum model. Discrete models based on finite element method are mostly used to calculate the accurate numerical solution of structural mechanical response (Xuhong et al. 2006; Juntao et al. 2013), but complex initial equilibrium state analysis is required in the process of finite element © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 975–991, 2023. https://doi.org/10.1007/978-981-19-7331-4_80

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model modeling (Xiaoming et al. 2011; Chuanxi et al. 2010), and a lot of time will be consumed in the process of form finding analysis; The continuum model based on the analytical method does not need to analyze the initial equilibrium state, and the structural mechanical behavior can be identified by solving the differential equation (Li et al. 2021; Han et al. 2021). As the basis of dynamic problems such as bridge wind resistance, earthquake resistance and vehicle bridge coupling, the continuum model of free vibration characteristics has attracted extensive attention. The vibration system of self-anchored suspension bridge includes two subsystems: main cable-hanger-beam and tower-pier. Its analytical methods can be divided into two categories: approximate method and classical analytical method. Most of the approximate methods are based on the principle of energy conservation, and the Rayleigh-Ritz method is used to solve the vibration system. By introducing the vibration shape function, the direct solution of complex differential equations can be avoided, and the contribution of two kinds of subsystems to the vibration system can be considered at the same time to obtain a relatively concise approximate solution (Jun et al. 2019; Xiaoyu et al. 2017), but the accuracy of the approximate method depends too much on the adaptability of the vibration shape function, Only relatively accurate low-order natural frequencies can be obtained, which can’t be extended to the study of high-order vibration characteristics. The classical analytical methods are mostly based on the deflection theory and Hamilton principle to derive the differential equation of the cable cable beam subsystem and solve it directly. Bleich et al. (1950) took the lead in extending the linear deflection theory to the vibration form and established the cablebeam vertical free vibration continuum model. Abdel Ghaffar (1982) Research shows that the vertical bending-torsional vibration can be decoupled under small amplitude vibration, Hayashikawa and Watanabe (1984) and Kim et al. (2000) showed that the shear deformation and the moment of inertia of the main beam have limited influence on the vertical vibration characteristics. Luco et al. (2010) systematically reviewed the classical theories such as Bleich et al. (1950), and studied the influence of the relative stiffness of the cable and beam on the vertical vibration. However, the above studies are aimed at the earth-anchored suspension bridge, and the continuum model research on the vibration characteristics of the self-anchored suspension bridge is rare; Based on the deflection theory, Chinese scholars Shi et al. (2004) and Liu et al. (2005) established the large displacement incomplete generalized potential energy functional, and derived the vertical bending vibration differential equation and analytical solution of self-anchored suspension bridge through constrained variational method. The results show that ignoring the shear strain energy of the beam, the vertical bending can be decoupled from the three modes of longitudinal floating, transverse bending and torsion. In order to reduce the difficulty of solving the vibration differential equation, the above classical analytical methods ignore the contribution of the elastic stiffness of the hanger in the main cable-hanger-beam subsystem, that is, the cable-beam displacement is consistent. Considering the extensible of the hanger, Turmo et al. (2010) deduce the main cable-hanger-beam vibration equation again with dimensionless treatment. The research shows that when the main beam of the earth-anchored suspension bridge has greater elastic bending stiffness, the elastic stiffness of the hanger has a great influence on the higher-order modal frequency. On this basis, Gwon and Choi (2018a, 2018b) studied

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the structural response of the continuum model of earth-anchored suspension bridge with parallel cable plane and spatial cable plane under static, dynamic and temperature loads, and compared with the finite element model. Compared with earth-anchored suspension bridge, self-anchored suspension bridge has more significant nonlinear problems and more complex dynamic characteristics due to its “self-balancing” characteristics, which makes the solution of nonlinear vibration equation more complex, which has not been intensively studied in the existing literature. The spatial self-anchored suspension bridge is often used as a landmark building because of its elegant and flexible shape and tension structure. However, the existing literature mostly focuses on the system transformation in the construction process (Xiaoming et al. 2016), and the research on its free vibration characteristics needs to be carried out urgently. In this context, in order to explore the vertical free vibration characteristics of spatial self-anchored suspension bridge, in the first part of this paper, based on the deflection theory, the differential equations of main cable-hanger-beam free vibration considering the extensible of hanger are derived, and the dimensionless continuum model including six dimensionless characteristic parameters and the inclination angle of spatial cable plane is obtained; In the second part, the governing equations are transformed into matrix form by Galerkin algorithm, and the frequencies and mode shapes of dimensionless continuum model are solved; In the third part, the finite element model of spatial self-anchored suspension bridge are used to verify the universality and accuracy of the dimensionless continuum model; In the fourth part, the parameter sensitivity analysis of dimensionless characteristic parameters affecting free vibration characteristics is carried out to identify the influence of parameters on dynamic characteristics.

2 Dimensionless Continuum Model of Spatial Self-anchored Suspension Bridge 2.1 Basic Assumptions and Vibration Differential Equations 2.1.1 Basic Assumptions The continuum model of spatial self-anchored suspension bridge follows the following assumptions: (1) the dead load is evenly distributed along the whole bridge, and only the main cable bears it, and there is no vertical displacement under the dead load of the main beam; (2) Under the action of dead load, the main cable shape is parabola; (3) The hanger has no mass and evenly distributed along the whole bridge. It remains vertical and extensible during vibration; (4) The additional horizontal force of the main cable caused by vibration is far less than the initial dead load horizontal force, and the additional horizontal force of each span is equal; (5) In the process of vibration, the displacement of main cable-beam is different, but they all follow the assumption of small displacement; (6) The inclination angle of spatial cable plane is consistent along the whole bridge, and the variation of inclination angle in vibration can be ignored. Figure 1 shows the schematic diagram of spatial self-anchored suspension bridge, where mc and mg are the mass of main cable and main beam per unit length respectively; E c , I c and Ac are respectively the elastic modulus, moment of inertia and area of the main cable; E g , I g and Ag are the elastic modulus, moment of inertia and area of the

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main beam respectively; E h and Ah are elastic modulus and area of hanger respectively; L hz and L hy are the length components from the main cable IP point to the bridge deck side in the vertical plane and horizontal plane respectively; d h is the distance between hangers; θ Is the inclination angle of spatial cable plane; L j is the length of each span; f zj , f yj and f oj are the main cable sag in the vertical plane, horizontal plane and inclined plane of each span respectively; zcj , ycj and ocj are the coordinates of the main cable of each span in the vertical plane, horizontal plane and inclined plane under the initial equilibrium state. The vertical coordinates of the parabola shape of the space main cable can be expressed as (Jose Turmo et al. 2010): ⎧ Lhz 4fz1 ⎪ zc1 (x1 ) = Lhz − x1 − 2 x1 (x1 − L1 ) ⎪ ⎪ ⎪ L1 L1 ⎪ ⎪ ⎪ ⎨ 4fz2 zc2 (x2 ) = 2 x2 (L2 − x2 ) (1) ⎪ L2 ⎪ ⎪ ⎪ ⎪ 4fz3 L ⎪ ⎪ ⎩ zc3 (x3 ) = hz x3 − 2 x3 (x3 + L3 ) L3 L3 The other two plane main cable shapes can be obtained from assumption (6): ycj (x) =

zcj tan θ , ocj (x)

=

zcj sin θ

j = 1, 2, 3

xj (a) Lhz

Vertical plane

x y

Inclined plane Horizontal plane

xj (b) Lhy

z

(2)

zcj

fzj

Eg Ig Eg Ag mg sym. fyj

dh ycj

xj dh ocj

foj

(c) Lho θ

dh

Ec Ac mc Eh Ah

Lj

Fig. 1. Structural parameters of spatial self-anchored suspension bridge in (a) vertical, (b) horizontal and (c) inclined plane.

2.1.2 Spatial Cable Beam Deformation Equation For a single span, H w is the initial horizontal force of the main cable in the initial equilibrium state, and H p is the additional horizontal force of the main cable caused by vibration. According to assumption (1) and (2), the equilibrium equations of vertical plane and horizontal plane under the initial equilibrium state of main cable are (Jung et al. 2015): Hw

d 2 zc + (mc g + hz ) = 0 dx2

(3a)

Dimensionless Continuum Model of Vertical Free Vibration

d 2 yc + hy = 0 dx2

Hw

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(3b)

where hz and hy are the vertical and horizontal components of the hanger. In the initial equilibrium state, hz = mg g/2, hy = mg g/(2 tan θ ). Then the initial horizontal force of the main cable:  m  mc + 2g gL2 (4a) Hw = 8fz  mg  2 gL Hw = 2 tan θ (4b) 8fy The initial equilibrium state and vibration variation state of the hanger are shown in Fig. 2. During the vibration process, the hanger equations of the vertical plane and horizontal plane are as follows: mg g + hp sin θ 2 mg g hy = + hp cos θ 2 tan θ hz =

mgg/2

mgg/(2tanθ) mgg/(2sinθ)

mgg/2 +hpsinθ

(5a) (5b)

mgg/(2tanθ)+hpcosθ mgg/(2sinθ)+hp

mcg

mcg

θ

θ mgg/(2sinθ) mgg/(2tanθ) mgg/2

mgg/(2tanθ) mgg/(2sinθ)+hp +hpcosθ

hpsinθ

(a)

mgg/2 +hpsinθ (b)

Fig. 2. Load conditions of hanger in cross-sectional view (a) initial shape (b) deformed shape under vibration.

where hp is the additional cable force of the sling caused by vibration, which can be expressed as: hp = kho δho

(6)

The axial elastic stiffness of the hanger k ho can be obtained from assumption (3): kho =

Eh Ah lho dh

where lho is the inclined length of the hanger, lho = L hz /sinθ-oc .

(7)

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The elongation of hanger caused by vibration δ ho , which can be expressed as (Gwon et al. 2018):   (8) δho = wg − wc sin θ − vc cos θ where wc and vc are the vertical and horizontal displacement of main cable caused by vibration, and wg is the vertical displacement of main beam caused by vibration, as shown in Fig. 3. y zc Main cable

z o oc yc wc

x y z

sym. Main beam

lho lhz

vc Hanger

θ θ

Centerline of main beam

(a)

Lhz

lhy

wg

Lhy (b)

Fig. 3. (a) Cable-hanger-girder system (b) cross-sectional view of its initial shape and deformed shape under vibration.

2.1.3 Vibration Differential Equation According to the theory of vibration form deflection, the vibration differential equation of main cable can be expressed as (Jung et al. 2015): mc

∂ 2 wc ∂ 2 (zc + wc ) − (H + H ) − (mc g + hz ) = 0 w p ∂t 2 ∂x2

(9a)

∂ 2 vc ∂ 2 (yc + vc ) − (H + H ) − hy = 0 w p ∂t 2 ∂x2

(9b)

mc

The vibration differential equation of beam can be expressed as:  ∂ 2 wg  mg g mg ∂ 2 wg Eg Ig ∂ 4 wg  − h + + H + H − w p z =0 2 ∂t 2 2 ∂x4 ∂x2 2

(10)

According to assumption (4), H w + H p ≈ H w ; Eqs. (6)–(8) are substituted into Eqs. (9)–(10) to simplify, rearrange and expand to multiple spans, and the coupled vibration differential equations of main cable-hanger-beam system can be obtained:   ∂ 2 wcj ∂ 2 wcj d 2 zcj Dcj xj , t = mc − H − H w p ∂t 2 ∂xj2 dxj2

Dimensionless Continuum Model of Vertical Free Vibration

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  − khoj sinθ wgj − wcj sin θ − vcj cos θ = 0

(11a)

  mg ∂ 2 wgj ∂ 2 wgj Eg Ig ∂ 4 wgj + + H Dgj xj , t = w 2 ∂t 2 2 ∂xj4 ∂xj2 

  +khoj sinθ wgj − wcj sin θ − vcj cos θ = 0.

(11b)

  ∂ 2 vcj ∂ 2 vcj d 2 ycj Drj xj , t = mc 2 − Hw 2 − Hp 2 ∂t ∂xj dxj 

  − khoj cosθ wgj − wcj sin θ − vcj cos θ = 0

(11c)

Among them, the unknown variables of the equation are the vertical displacement wcj of the main cable, the transverse displacement vcj of the main cable, the vertical displacement wgj of the main beam and the additional horizontal force H p of the main cable. 2.1.4 Deformation Compatibility Equation Deformation coordination is a supplementary condition for solving coupled vibration differential equations. According to the condition that the horizontal component of the main cable elongation under load is consistent with the compression of the main beam, the self-anchored suspension bridge compatibility equation can be expressed as: ⎞  3   Lj  Hp Lj docj 2 2 Hp ⎝ ⎠ dxj + 1+ Ec Ac 0 dxj Eg Ag j=1     3 fy2 Lj fz2 Lj = vcj dcj +8 2 wcj dcj 8 2 L2 0 L2 0 j=1

3

⎛

(12)

Simplifying Eq. (12), the additional horizontal force of the main cable caused by vibration can be expressed as:   3 L  f L 8 Ly22 0 j vcj dxcj +8 fLz22 0 j wcj dxcj Hp =

where, LE =

  3  Lj  j=1

0

2

j=1

1+

2

LE Ec Ac



docj 2 dxj

+



3 2

dxj

(13)

Lb Eg Ag

Lb =

3 

Lj .

j=1

2.2 Dimensionless Equation In order to better identify the control parameters of dynamic characteristics, Eq. (11) is dimensionless, and the dimensionless transformation of basic variables can be expressed

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as:      wcj xj , t = 8fz2 wcj xj , t xj = L2 xj t = 8fgz2 t         wgj xj , t = 8fz2 wgj xj , t vcj xj , t = 8fz2 vcj xj , t

(14)

where, xj and t refers to dimensionless coordinate and dimensionless time; wcj (xj , t), v cj (xj , t) and wgj (xj , t) refers to dimensionless vertical displacement of main cable, lateral displacement and dimensionless vertical displacement of main beam respectively. Replace Eq. (14) with Eq. (11) to obtain the dimensionless vibration differential equations:    Lj 3 Lj   ∂ 2 wcj ∂ 2 wcj 1 Dcj xj , t = (1 − m) 2 − − λ2 wcj d xj + v cj d xj tan θ 0 ∂x2j 0 ∂t j=1

   8f − κ 2 sinθ wgj − wcj sin θ − v cj cos θ = 0 l hj

(15a)

4   ∂ 2 wgj ∂ 2 wgj 2 ∂ w gj + α + Dgj xj , t = m 2 ∂x4j ∂x2j ∂t

+κ 2

8f l hj



  sinθ wgj − wcj sin θ − v cj cos θ = 0

(15b)

   Lj 3 Lj   ∂ 2 v cj ∂ 2 vcj λ2 1 Drj xj , t = (1 − m) 2 − − wcj d xj + v cj d xj tan θ tan θ 0 ∂x2j 0 ∂t j=1 − κ2

8f l hj



  cosθ wgj − wcj sin θ − v cj cos θ = 0

(15c)

The dimensionless parameters in the formula are: mg 2

Lj Eg Ig fz2 f = α2 = L L 2Hw L22 mc + 2 hz ⎛ ⎞   L2 Ah 8fz2 2 ⎝ 2 ⎠ κ 2 =  Eh m λ =  H L H L w w E b L2 mc + 2g gdh Ec Ac + Eg Ag m=

mg 2

Lj =

The corresponding dimensionless length of each span hanger:   ⎧   1 x1 ⎪ ⎪ l h1 = + 4f x1 − L1 ⎪ ⎪ sin θ L1 ⎪ ⎪ ⎨   1  1 + 4f · x2 x2 − L2 l h2 = ⎪ sin θ  ⎪  ⎪ ⎪   ⎪ x3 1 ⎪ ⎩ l h3 = 1− + 4f · x3 x3 − L3 sin θ L3

(16)

(17)

Dimensionless Continuum Model of Vertical Free Vibration

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Equation (15) shows that the vertical free vibration characteristics are determined by the six dimensionless characteristic parameters and the inclination angle of spatial cable θ in Eq. (16). Where, m is the relative mass of the main beam; Lj is the relative length of side span; f is the relative sag of the main cable. λ2 is Irvine stiffness coefficient, which is the ratio of geometric stiffness and elastic stiffness of main cable, that is, the relative elastic axial stiffness of main cable; α 2 is Steinman stiffness coefficient, which is the ratio of elastic bending stiffness of main beam to gravity stiffness, that is, the relative elastic bending stiffness of main beam; κ 2 is the relative elastic axial stiffness of the hanger.

3 Galerkin Method 3.1 Boundary and Shape Function In Eq. (15), the unknown variables are the dimensionless vertical displacement wcj (xj , t), lateral displacement v cj (xj , t) of the main cable and dimensionless vertical displacement wgj (xj , t) of the main beam respectively, the shape function satisfying the geometric and mechanical boundary is constructed, and the approximate solution is calculated by Galerkin method. There are 12 boundary conditions for the main cable, that is, the vertical and horizontal displacement at both ends of each span are zero:         (18) wcj 0, t = 0 wcj Lj , t = 0 vcj 0, t = 0 v cj Lj , t = 0 The main beam is a three span continuous beam with 12 boundary conditions, that is, the displacement at each fulcrum is zero, the rotation and bending moments at both ends of the fulcrum in the span are equal, and the bending moment of the side fulcrum is zero:     wgj 0, t  = 0 wgj Lj , t = 0 wg1 0, t = 0 w L3 , t = 0      g3    (19)    0, t wg1 L1 , t = wg2 0, t wg2 L2 , t = wg3          0, t w  L , t = w  0, t wg1 L1 , t = wg2 g2 2 g3 The dimensionless displacement of main cable and main beam is set as: ⎧ N ⎪      ⎪ ⎪ w x , t = cjn t × Cjn xj ⎪ cj j ⎪ ⎪ ⎪ n=1 ⎪ ⎪ ⎪ ⎪ N ⎨      wgj xj , t = gn t × Gjn xj ⎪ ⎪ n=1 ⎪ ⎪ ⎪ ⎪ N ⎪ ⎪      ⎪ ⎪ v x , t = rjn t × Cjn xj ⎪ cj j ⎩

(20)

n=1

where, N is the order of shape function; cjn (t), gn (t) and rjn (t) is the undetermined coefficient; Cjn (xj ) is the shape function of main cable vibration satisfying the geometric

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and mechanical boundary of Eq. (18), which can be expressed as:      nπ xj  Cjn xj = sin 0 ≤ xj ≤ Lj Lj

(21)

Gjn (xj ) is the vibration shape function of the main beam satisfying the geometric and mechanical boundary of Eq. (19), and the specific form is shown in the appendix (Konstantakopoulos et al. 2012). 3.2 Solution Procedure After substituting Eq. (20) into Eq. (15), multiply the corresponding shape functions of main cable and main beam and integrate them to 7N equations and 7N unknowns (cj1 , …, cjN , gj1 , …, gjN 和r j1 , …, r jN ). The format can be expressed as: ⎧ L j ⎪ ⎪ ⎪ Cjm Dcj d xj = 0 ⎪ ⎪ ⎪ 0 ⎪ ⎪ ⎪ 3  Lj ⎨ Gjm Dgj d xj = 0 ⎪ 0 ⎪ j=1 ⎪ ⎪ ⎪ ⎪  Lj ⎪ ⎪ ⎪ ⎩ Cjm Drj d xj = 0

(22)

0

Simplify Eq. (22) and rearrange it into matrix form, which can be expressed as:     (23) [M ]7N ×7N U¨ t + [K]7N ×7N U t = {0}7N ×1 where,  U (t) ⎧ ⎪ ⎪ ⎨ c(t) g(t) ⎪ ⎪ ⎩ r(t)

T 3N ×1

T

N ×1

T

3N ×1

7N ×1

=

!

c(t)

T 3N ×1

 , g(t)

T N ×1

 , r(t)

T

"

3N ×1

 = c11 (t) · · · c1N (t), c21 (t) · · · c2N (t), c31 (t) · · · c3N (t)  = g1 (t) · · · gN (t)  = r11 (t) · · · r1N (t), r21 (t) · · · r2N (t), r31 (t) · · · r3N (t)

(24)

(25)

In Eq. (23), the dimensionless mass matrix [M ]7N ×7N is a diagonal matrix, which can be expressed as: $ #   

g c c , M N ×N , Mj [M ]7N ×7N = diag Mj (26) N ×N N ×N j = 1, 2, 3 where,

⎤ ⎤ ⎡ g Mj1c 0 0 M1 0 0 ⎥ g ⎢ ⎥ ⎢ . . ⎥ =⎢ ⎣ 0 . . 0 ⎦ M N ×N = ⎣ 0 . . 0 ⎦ g c 0 0 MjN 0 0 MN ⎡

  Mjc

N ×N

(27)

Dimensionless Continuum Model of Vertical Free Vibration

Mjnc = (1 − m)

 Lj 0

g

2 dx M = m Cjn j n

3 L  j i=1

0

2 dx Gjn j

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(28)

The dimensionless stiffness matrix [K]7N ×7N in Eq. (23) can be expressed as:    



(29) [K]7N ×7N = K cg 7N ×7N + K ce 7N ×7N + K ge 7N ×7N + K he 7N ×7N

 where, K cg 7N ×7N is the dimensionless geometric stiffness matrix of the main cable;

ce  

K 7N ×7N dimensionless elastic axial stiffness matrix of main cable; K ge 7N ×7N is 

the dimensionless compression bending stiffness matrix of the main beam; K he 7N ×7N is the dimensionless elastic axial stiffness matrix of the hanger. 

The dimensionless geometric stiffness matrix of the main cable K cg 7N ×7N is a diagonal matrix, which can be expressed as: $ #   

cg  cg cg K 7N ×7N = diag Kj , [0]N ×N , Kj (30) N ×N N ×N j = 1, 2, 3 where,

⎤ cg Kj1 0 0   ⎥ ⎢ cg .. ⎥ Kj =⎢ . 0 0 ⎦ ⎣ N ×N cg 0 0 KjN  Lj cg  Kjn = − Cjn Cjn d xj ⎡

(31)

(32)

0

 Dimensionless elastic axial stiffness matrix of main cable K ce 7N ×7N , which can be expressed as: ⎡



⎤ K cen 0 tan1 θ K cen

ce  ⎢ ⎥ K 7N ×7N = ⎣ (33)

0 cen  0 1 0 cen  ⎦ 1 K 0 K tan θ tan2 θ where,

cen  K 3N ×3N

⎡  ce K11 ⎢ ce T = ⎣ K21

ce T K31

⎤ ⎡

ce  ⎤ ce · · · K ce Kji11 K13 ji1N ⎥ ⎢ . .

ce  ⎥  ce  . . ... ⎥ =⎢ K ⎦ Kji ⎦ ⎣ ..

23  N ×N ce ce · · · K ce K33 KjiN 1 jiNN  Lj  Li = λ2 Cjn d xj Cin d xi

ce  K

12  ce K22

ce T K32

ce Kjimn

0

(34)

(35)

0

geThe  dimensionless compression bending stiffness matrix of the main beam K 7N ×7N is a diagonal matrix, which can be expressed as: " ! 

ge  (36) K 7N ×7N = diag [0]3N ×3N , K ge N ×N , [0]3N ×3N

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where,

ge

Kn

⎤ ⎡ ge K1 0 0

ge  ⎥ ⎢ K N ×N = ⎣ 0 . . . 0 ⎦ ge 0 0 KN 3  Lj 3  Lj   = α2 Gjn Gjn d xj + Gjn Gjn d xj i=1

0

i=1

(37)

(38)

0

 Dimensionless elastic axial stiffness matrix of hanger K he 7N ×7N , which can be expressed as: ⎤ ⎡ − sin2 θ sin2 # θ sin θ cos θ # $ # $⎥ $T    ⎢  ⎥ ⎢ hecg hecc hecc K K diag diag ⎥ ⎢ Kj j j N ×N N ×N ⎥ ⎢ N ×N ⎥ ⎢ ⎢ − sin θ cos θ $ ⎥ 2θ

he  # sin ⎥ ⎢  

hegg  K 7N ×7N = ⎢ ⎥ hecg T ⎥ ⎢ K K j N ×N ⎥ ⎢ N ×N ⎥ ⎢ 2 ⎥ ⎢ cos #θ ⎢ $⎥   ⎦ ⎣ sym. diag Kjhecc N ×N

j = 1, 2, 3 (39) where,

⎤ hecc · · · K hecc Kj11 j1N   ⎥ ⎢ . . .. . . ... ⎥ Kjhecc =⎢ ⎦ ⎣ N ×N hecc · · · K hecc KjN 1 jNN ⎤ ⎤ ⎡ hecg ⎡ hecg hegg hegg Kj11 · · · Kj1N · · · K K 11 1N   ⎥ hegg  ⎥ ⎢ . . ⎢ . . hecg .. . . ... ⎥ .. . . ... ⎥ Kj K =⎢ =⎢ N ×N ⎦ ⎦ ⎣ ⎣ N ×N hecg hecg hegg hegg KjN 1 · · · KjNN KN 1 · · · KNN  Lj Cjm Cjn hecc = κ 2 · 8f d xj Kjmn l hj 0  Lj 3  Lj Cjm Gjn Gjm Gjn hecg hegg 2 2 Kjmn = κ · 8f d xj Kjmn = κ · 8f d xj l hj l hj 0 i=1 0 ⎡

(40)

(41)

Finally, the natural frequency and undetermined eigenvector of dimensionless continuum model can be obtained by the following formula:     (42) [K] − ω2n [M ] U t = {0}

Dimensionless Continuum Model of Vertical Free Vibration

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4 Finite Element Model Verification 4.1 Numerical Example Midas civil is used to establish the finite element model for eigenvalue analysis. As shown in Fig. 4, the bridge tower and main beam are simulated by beam element, and the main cable and hanger are simulated by cable element; The hanger-beam is rigidly connected, the main cable-beam end is rigidly connected, the main beam is continuous throughout the bridge, and the bottom of the bridge tower is consolidated. See Table 1 for structural parameters.

y

z

x

Fig. 4. Finite element model of spatial cable self-anchored suspension bridge.

Table 1. Model parameters of spatial self-anchored suspension bridge. Bridge layout

Main beam Main cable

L 1 /(m)

L 2 /(m)

L 3 /(m)

d h /(m)

L hz /(m)

L hy /(m)

L t /(m)

190

400

190

10

85

14.5

45

f z1 /(m)

f z2 /(m)

f z3 /(m)

f y1 /(m)

f y2 /(m)

f y3 /(m)

18.05

80

13.65

3.08

18.65

3.08

mg /(t/m)

E g /(Gpa)

Ag /(m2 )

I g /(m4 )

Tower

14.858

206

1.2784

1.331

mc /(t/m)

E c /(Gpa)

Ac /(m2 )

Hanger

0.225

200

0.0256

E t /(Gpa)

I t /(m4)

34.5

54.401

E h /(Gpa)

Ah /(m2 )

200

0.0013

The order of shape function of continuum model is set as N = 24, and the natural frequency are solved. The natural frequencies of the first eight symmetric and antisymmetric modes are extracted and compared with the natural frequency results of the finite element model, shown in Tables 2 and 3. The natural frequency error of the first-order antisymmetric mode is −6.47%, the natural frequency error of the second-order antisymmetric mode is −7.89%, and the natural frequency errors of the other modes are less than ± 5%. The results of the continuum model are basically consistent with those of the finite element model, and the parameter analysis used for subsequent dynamic characteristics is reliable and accurate.

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Table 2. Comparison of natural frequency of symmetric mode between continuum model and finite element model. Mode order

Natural frequency of symmetric mode/Hz Continuum model CM-Ext

CM-InExt

1st

0.1396

0.1403

2nd

0.3546

3rd

0.4996

4th

FEM

Comparison of results/% CM-Ext

CM-InExt

0.1434

−2.66

−2.16

0.3582

0.3538

0.22

1.24

0.5050

0.5002

−0.13

0.95

0.8173

0.8179

0.8039

1.66

1.75

5th

1.1631

1.1641

1.1282

3.09

3.18

6th

1.7707

1.7713

1.6976

4.31

4.34

7th

2.2193

2.2200

2.1945

1.13

1.16

8th

3.0807

3.0810

2.9664

3.85

3.86

Table 3. Comparison of natural frequency of antisymmetric mode between continuum model and finite element model Mode order

Natural frequency of antisymmetric mode/Hz Continuum model CM-Ext

FEM

CM-InExt

Comparison of results/% CM-Ext

CM-InExt

1st

0.1727

0.1728

0.1846

−6.47

−6.40

2nd

0.2733

0.2735

0.2967

−7.89

−7.81

3rd

0.6922

0.6927

0.6861

0.88

0.96

4th

0.8916

0.8924

0.8746

1.95

2.04

5th

1.5543

1.5548

1.5011

3.54

3.57

6th

1.8687

1.8696

1.7699

5.58

5.63

7th

2.7564

2.7566

2.7022

2.01

2.01

8th

3.2066

3.2078

3.0527

5.04

5.08

Note CM-Ext is the continuum model considering hanger extensible, CM-InExt is the continuum model considering hanger inextensible, and FEM is the finite element model

4.2 Sensitivity Analysis of Characteristic Parameters In order to study the sensitivity of the modal frequency to the relative elastic bending stiffness of the main beam α 2 , the relative elastic axial stiffness of the main cable λ2 and the relative elastic axial stiffness of the hanger κ 2 , α 2 and λ2 of the original model of the spatial self-anchored suspension bridge are expanded and reduced by 5 times and 2 times respectively, and the parameter analysis is carried out considering whether the hanger is extensible or not.

Dimensionless Continuum Model of Vertical Free Vibration

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When the relative elastic bending stiffness of the main beam α 2 changes, the trend of modal frequency is shown in Fig. 5. The increase of α 2 will significantly improve the overall stiffness of the structure, and the modal frequencies of each order will increase with the increase of α 2 . Compared with the relatively gentle growth range of lower order (1-4th order) modal frequencies, the influence of higher order (5-8th order) modal frequencies is more significant.

Fig. 5. Natural frequencies versus the relative elastic bending stiffness of the girder α 2 (a) symmetric modes (b) antisymmetric modes

When the relative elastic stiffness of the main cable λ2 changes, the trend of modal frequency is shown in Fig. 6. Compared with α 2 , λ2 has a limited impact on each order frequency, but the difference is that with the increase of λ2 , it has a more significant impact on the low order (1-3rd order) symmetrical modal frequency, and the higher order (4-8th order) modal frequency has less impact, indicating that the increase of λ2 is conducive to improving the overall stiffness of the structure, but the improvement effect is very limited. However, the antisymmetric modal frequency is not affected by the change of λ2 , because the integral result of the term associated with λ2 in Eqs. 15 (a) and 15 (c) in antisymmetric mode is zero, indicating that the main cable cannot provide relative elastic axial stiffness in antisymmetric mode. The relative elastic stiffness of the hanger κ 2 and the relative elastic stiffness of the main cable λ2 are less sensitive, and the relative elastic bending stiffness of the main beam α 2 is more sensitive. For the case of small α 2 , whether the hanger extensible is considered or not has little effect on the modal frequency, which is basically consistent with the results of the finite element model; However, for the case of large α 2 , especially the high-order antisymmetric mode, the modal frequency will be significantly increased without considering the hanger extensible. The results of the continuum model considering the hanger extensible are more consistent with the finite element model, closer to the engineering practice, and the results are more reliable and accurate.

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Fig. 6. Natural frequencies versus the relative elastic axial stiffness of the cable λ2 (a) symmetric modes (b) antisymmetric modes

5 Conclusions Based on the vibration form deflection theory, combined with the main cable-hangerbeam coupling deformation equation and compatibility equation, this paper establishes the continuum model of spatial self-anchored suspension bridge considering the extensible of the hanger. In order to identify its dynamic characteristics, the dimensionless continuum model including six dimensionless characteristic parameters and inclination angle of spatial cable is obtained through dimensionless processing. The modal frequency is solved by Galerkin method, and its accuracy is verified by numerical examples and finite element model. The sensitivity analysis of characteristic parameters is carried out, and the following conclusions are drawn: (a) The increase of the relative elastic bending stiffness of the main beam α 2 will significantly increase the modal frequency and have a stronger impact on the higher-order frequency; The relative elastic axial stiffness of the main cable λ2 only slightly increases the low-order symmetric modal frequency and has no effect on the antisymmetric modal frequency. (b) The relative elastic axial stiffness of hanger κ 2 has no obvious correlation with λ2 , but has a higher correlation with α 2 ; When α 2 is large, whether to consider the hanger extensible will significantly affect the accuracy of higher-order modal frequencies. Considering the hanger extensible makes the continuum model more reliable and accurate. (c) Compared with the finite element model, the continuum model considering hanger extensible proposed in this paper can efficiently and accurately calculate the vertical free vibration natural frequency of self-anchored suspension bridge, which can provide an effective reference for the preliminary design of the project.

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References Abdel-Ghaffar, A.M.: Suspension bridge vibration: continuum formulation. J. Eng. Mech. Div. 108(6), 1215–1232 (1982) Bleich, F., McCullough, C.B., Rosecrans, R., et al.: The Mathematical Theory of Vibration in Suspension Bridges. US Government Printing Office, Washington (1950) Chuanxi, L., Hongjun, K., Haibo, L., et al.: Determination of finished bridge state of self-anchored suspension Brjdge with spatial cables. Eng. Mech. 27(5), 137–146 (2010) Chuncheng, L., Zhe, Z., Lei, S., et al.: Theoretical study of vertical free vibrations of concrete self-anchored suspension bridges. Eng. Mech. 22(4), 126–130 (2005) Enrique Luco, J., Turmo, J.: Linear vertical vibrations of suspension bridges: a review of continuum models and some new results. Soil Dyn. Earthq. Eng. 30(9), 769–781 (2010) Fei, H., Deng, Z., Dan, D.: Vertical vibrations of suspension bridges: a review and a new method. Arch. Comput. Methods Eng. 28(3), 1591–1610 (2020). https://doi.org/10.1007/s11831-02009430-4 Gwon, S.-G., Choi, D.-H.: Static and dynamic analyses of a suspension bridge with threedimensionally curved main cables using a continuum model. Eng. Struct. 161, 250–264 (2018) Gwon, S.-G., Choi, D.-H.: Continuum model for static and dynamic analysis of suspension bridges with a floating girder. J. Bridge Eng. 23(10), 04018079.1–04018079.13 (2018) Hayashikawa, T., Watanabe, N.: Vertical vibration in Timoshenko beam suspension bridges. J. Eng. Mech. 110(3), 341–356 (1984) Jose Turmo, J., Luco, E.: Effect of hanger flexibility on dynamic response of suspension bridges. J. Eng. Mech. 136(12), 1444–1459 (2010) Jun, G., Shenghong, L., Song, G., et al.: Estimation formula of vertical bending vibration fundamental frequency of self-anchored single tower suspension bridge. J. Chongqing Jiaotong Univ. (Natural Sciences) 38(5), 27–32 (2019) Jung, M.-R., Shin, S.-U., Mario, M., Attard, et al.: Deflection theory for self-anchored suspension bridges under live load. J. Bridge Eng. 20(7), 04014093 (2015) Juntao, K., Min, Y., Tongmin, W.: Parametric analysis of dynamic performance of completion state of long span self-anchored suspension bridge. Bridge Constr. 43(6), 64–70 (2013) Kim, M.Y., Kwon, S.D., Kim, N.I.: Analytical and numerical study on free vertical vibration of shear-flexible suspension bridges. J. Sound Vib. 238(1), 65–84 (2000) Konstantakopoulos, T.G., Raftoyiannis, I.G., Michaltsos, G.T.: Reduced formulae for vibration of continuous beams with application on moving loads. Open Mech. J. 6(1), 1–7 (2012) Lei, S., Chuncheng, L., Zhe, Z.: Basic differential equation deductive of the self-anchored suspension bridge. J. Harbin Inst. Technol. 36(12), 1733–1735 (2004) Li, T., Liu, Z.: An improved continuum model for determining the behavior of suspension bridges during construction. Autom. Constr. 127, 103715 (2021) Xiaoming, W., Xianwu, H., Ruifang, D.: Initial equilibrium state analysis of suspension bridge with spatial cables based on Steffens-Newton algorithm. Chin. J. Comput. Mech. 28(5), 717–722 (2011) Xiaoming, W., Shuanhai, H., Ruifang, D.: Hanger tensioning process analysis of self-anchored suspension bridge with spatial cables. Eng. Mech. 33(10), 164–172 (2016) Xiaoyu, Z., Laijun, L., Tao, S., et al.: Frequency estimation formulas of vertical vibration for selfanchored suspension bridge with double-tower considering tower stiffness. J. Jiangsu Univ. (Natural Science Edition) 38(3), 355–360 (2017) Xuhong, Z., Jun, W., Jin, D.: Mechanical analysis for long-span self-anchored suspension bridges. China Civil Eng. J. 39(2), 42–45, 65 (2006)

Dynamic Modal Parameters of an Extremely Lightweight Structure Using a Gyroid Core for Bridge Bearings P. Sengsri(B) and S. Kaewunruen Laboratory for Track Engineering and Operations for Future Uncertainties (TOFU Lab), School of Engineering, The University of Birmingham, Edgbaston, Birmingham B15 2TT, UK [email protected]

Abstract. This article reports an extremely lightweight structure used as a sandwich core for bridge bearings due to their superior mechanical properties, such as sound and vibration attenuation, rigidity, and energy absorption. The structure is based on triply periodic minimal surfaces (TPMS) conceived by observing the scales of butterflies’ wings. The vibration behaviours of this innovative structure used in these bearings are not well-known and have never been fully investigated. Therefore, it is important to comprehend their vibration behaviours and also to identify dynamic modal parameters of these bridge bearings. Two gyroid sandwich panel finite element models with different unit cell sizes used as bridge bearings are examined with a computational method. The numerical investigation shows the vibration mechanisms and provides the dynamic modal parameters important in establishing relationships between its mechanical performance and geometry. Finite element predictions of the vibration behaviours of the two models with different unit cell sizes under free vibration provide good results. These results can be implemented to better generate informed lightweight structure designs for bridge bearings, which are subjected to different vibration conditions. Keywords: Bridge bearings · Triply periodic minimal surfaces (TPMS) · Gyroid · Vibration behaviours

1 Introduction In contemporary bridge system, base isolation with elastomeric bearings also wellknown as laminated rubber bearings (LRB) has been widely employed for attenuating the influence of seismic loads (vibrations) by reducing the loads transferred to the substructure [1–3]. These seismic loads can lead to the failure of a bridge and its components due to natural frequency resonance. The key functions of these bearings are not only to experience the compressive loads, transmitted from the deck, but also to facilitate deformations in horizontal and rotational direction. On the other hand, in some cases, LRBs, which are fixed between the superstructure and the substructure via bolted connections, are likely to face tensile displacements (uplift) induced by the rotation of a

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 992–1000, 2023. https://doi.org/10.1007/978-981-19-7331-4_81

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pier cap during earthquakes [4–6]. This results in internal local failures in the rubber as a well-known cavitation phenomenon [7–10]. In term of materials used in LRBs, they are a combination of rubber layers and steel shim plates which are laminated together alternately. Steel shim plate is a solid material that provides high vertical stiffness. Unlike rubber layer, it is a mainly incompressible material which offers high horizontal flexibility [11, 12]. Thus, LRBs possess an extremely high vertical stiffness, whilst remaining high horizontal flexibility which is needed to extend the period of a structure under seismic loading condition. This response is required for isolation of a civil engineering structure. Nevertheless, there is an optional structure like a lattice structure which is possible to be used in an elastomeric bearing as a sandwich-structured composite, in order to show better mechanical properties than common structures provide currently, due to their high-performance and weight ratio. Lattice sandwich structures do not only offer benefits in lightweight, but also vibration attenuation, superior energy absorption, as well as thermal dissipation when compared to general structures (foam and honeycomb sandwich structures) [13–18]. Therefore, the lattice structures could potentially be the ideal core of sandwich structures for bridge bearing applications. A common sandwich plate consists of a lightweight core connected to two relatively thin, dense, high-strength and stiffness face sheets. In this work, the idea of a novel extremely lightweight structure called a porous structure is inspired by butterfly wings due to their specific design with several features [19, 20]. The wings consist of a lightweight structure core with an infinitely connected triply periodic minimal surface (TPMS) geometry called gyroid and reinforced on their outer areas with a series of ribs. Thus, the architecture of the porous structure used in butterfly wings can lead to a wellknown porous structure (gyroid), which is a member of a TPMS family [21]. TPMSs are minimal surfaces with mean curvature of zero and periodic structures in three coordinate directions [22]. In term of great benefits of using a TMPS structure, a TMPS can locally minimise its region (uniform stress distribution) and free it of self-intersections [23]. Additionally, it possesses high manufacturability of additive manufacturing (AM) process because of its geometrical characteristics [24–26]. Gyroid structures can be designed, but it is difficult to produce them until the advantages of AM technologies [27]. The main advantage of AM is that it allows the design and fabrication of more complex components by their features than conventional manufacturing processes [28, 29], with a certain benefit in enhancing performances of components [30, 31]. As aforementioned, bridge bearings can fail in resonance when the frequency of a periodically applied load is close or equal to a natural frequency of a bridge system on which it behaves. Hence, it is crucial to comprehend the dynamic modal parameters of bridge bearings for designing and predicting their vibration responses. Lots of research works have been performed on the stability of laminated rubber bearings imposed to vertical and horizontal loading [32–34], the buckling load capacity of LRBs [35], and also the instability of LRBs influenced by cavitation [36]. There are our previous works on the development of a common bridge bearing using lattice structures, which focus on their compressive and modal behaviour under compression and vibration, respectively [37–42].

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On the other hand, to the best of our knowledge, there is no existing research on identifying dynamic modal parameters of an extremely lightweight structure with a gyroid core for bridge bearing applications. As these parameters obtained, an effective seismic base isolation system can be designed. In this paper, we aim to determine the dynamic modal parameters of the gyroid sandwich panel used as a bridge bearing (BB) subjected to free vibration, in terms of natural frequencies, mode shapes through numerical modal analysis.

2 Materials and Methods 2.1 Design of an Extremely Lightweight Structure A computer-aided design (CAD) model of the gyroid structure is created by using Rhino 6 software. The software allows users to design a gyroid structure by plotting an implicit function presented in the following Eq. (1). This function reproduces a structure closely similar to the three-dimensional pattern of the gyroid topology. sin x∗ cos y + sin y∗ cos z + sin z∗ cos x = 0.

(1)

The unit cell is 10 mm in size and the gyroid cell is patterned on the 3D space to the desired core shape (3 × 3 × 2 unit cells) with a width of 30 mm, a length of 30 mm, and a height of 20 mm. As presented in Fig. 1, it illustrates the gyroid structure with a unit cell size of 10 mm and a thickness of 0.75 mm created with Rhino 6 software. The unit cell size is one of the parameters investigated in this paper.

Fig. 1. A gyroid core with a unit cell size of 10 mm. (a) 10 mm gyroid unit cell (b) 30 × 30 × 20 mm array.

The two metallic facets with a thickness of 1.5 mm are connected to the upper and lower surface of the gyroid core, illustrated in Fig. 2. The connections are designed by employing Siemens NX 12.0 software. 2.2 Numerical Modal Analysis Modal analysis is a tool which is one of the most widely used methods to characterise and identify the properties of systems in the frequency domain. In this paper, we aim to

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Fig. 2. Gyroid sandwich panel used as a bridge bearing.

determine the dynamic modal parameters of extremely lightweight structure components with a gyroid core, in terms of fundamental frequencies and mode shapes via finite element (FE) modal analysis. The dynamic equation under free vibration for a single degree of freedom system without damping can be described as [43].  (2) [m] s¨ + [k]{s} = {0}. Free vibration solution is mathematically considered as a non-trivial solution. It should take the form as: {s} = {S} sin ωt.

(3)

By substituting Eq. (3) into Eq. (2), the equation becomes a simple algebraic matrix equation:   (4) [K] − ω2 [M] {S} = {0}. As {S} cannot be zero in Eq. (4), therefore:     det [K] − ω2 [M] = {0}.

(5)

where, ω2 represents the eigenvalue which identifies the natural frequency of the system and {S} denotes the eigenvector which identifies the mode shape of the system. Two gyroid sandwich panel finite element models with different unit cell sizes are generated and analysed using Siemens NX 12.0 software. Modal analysis is proposed as the mode of analysis employed to investigate these panels. For gyroid core, TPU which is used in the core for the simulations is a rubber-like material (hyperplastic) with very high bulk modulus but having low shear modulus. Whilst two thin steel facets are assigned to be linear elastic materials. Their properties are shown in Table 1. Also, the materials are meshed using 238,813 and 210,819 tetra10 elements with 0.5 and 1 mesh size for 10 and 20 mm unit cell size presented in Fig. 3, respectively. Simulations are employed to reveal the dynamic modal behaviours and to conduct a parametric study. It is important to mention that the two gyroid sandwich panels in this paper are modelled with a small scale to reduce computational time.

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P. Sengsri and S. Kaewunruen Table 1. Engineering properties of a gyroid sandwich core and two steel facets.

Properties

TPU

Steel

Unit

Density

1235

7829

kg/m3

Poisson’s ratio

0.39

0.29

–

Young’s modulus

2491

206,940

MPa

Yield strength

21.00

137.90

MPa

Ultimate tensile strength

38.40

276.00

MPa

Table 2 Results of modal analysis for both gyroid sandwich panels. Mode No.

FE model with 10 mm cell size Mode shape Frequency (Hz)

FE model with 20 mm cell size Mode shape Frequency (Hz)

∆%

behaviour

1

421.17

292.48

30.56

Torsion

2

603.25

407.86

32.90

Rollover

3

613.60

415.07

32.35

Rollover

4

649.63

446.71

31.24

Uplift

3 Results and Discussion The dynamic modal parameters of a gyroid sandwich panel for bridge bearing applications are well-known as natural frequencies and mode shapes without damping. These

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Fig. 3. Finite element model of a gyroid sandwich panel for modal analysis.

parameters are obtained from finite element modal analysis. A comparison of dynamic modal parameters of both gyroid sandwich panels with two different unit cell sizes (10 and 20 mm) extracted from the numerical modal analysis is presented in Table 2. The natural frequencies and mode shapes from both analyses are compared for the first four modes. The results show that, for both panels, the first torsional deformation pattern is generated in the first mode, whilst the first and the second rollover deformation patterns are produced in the second and third mode, as well as the first uplift deformation occurred in the fourth mode. It is obvious that the difference of natural frequencies of FE models of gyroid sandwich panels with different unit cell sizes exhibits quite large discrepancies. On the other hand, the natural frequencies of the gyroid sandwich panel made of 10 mm unit cells are approximately 1.4 times the other ones of the gyroid sandwich panel with 20 mm unit cell size. This is because natural frequencies depend on geometry property and mass of a material.

4 Conclusions Modal analysis is completely conducted to examine the dynamic behaviours of two gyroid sandwich panels with different unit cell sizes for bridge bearing applications. These panels consist of a gyroid core confined between two thin steel facets which provide higher stiffness of their structure. The results show that the first natural torsion mode obviously controls the first resonant mode of vibration for both panels. Also, the gyroid sandwich panel with a smaller unit cell size can better experience vibrations than a one with a bigger one as the increasing natural frequencies of all the modes. These insights will be useful to the performance benchmarking of bridge bearings as well as the development of the vibration-based design approach to predict their modal dynamic characteristics. Further work of model validation should be performed for practical use in reality. Acknowledgements. The first author wishes to thank Royal Thai Government for his PhD Scholarship at the University of Birmingham. The last author wishes to gratefully acknowledge the Japan Society for Promotion of Science (JSPS) for his JSPS Invitation Research Fellowship (Long-term), Grant No L15701, at the Track Dynamics Laboratory, Railway Technical Research Institute and at Concrete Laboratory, the University of Tokyo, Tokyo, Japan. The JSPS financially supports this work as part of the research project, entitled “Smart and reliable railway infrastructure.” Special thanks to European Commission for H2020-MSCA-RISE Project No. 691135 “RIS-EN: Rail

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Infrastructure Systems Engineering Net-work” (www.risen2rail.eu). Partial support from H2020 Shift2Rail Project No 730849 (S-Code) is acknowledged. In addition, the sponsorships and assistance from LORAM, Network Rail, RSSB (Rail Safety and Standard Board, UK) are highly appreciated.

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21. Michielsen, K., Stavenga, D.G.: Gyroid cuticular structures in butterfly wing scales: biological photonic crystals. J. R. Soc. Interface 5, 85–94 (2007) 22. Rajagopalan, S., Robb, R.A.: Schwarz meets Schwann: design and fabrication of biomorphic and durataxic tissue engineering scaffolds. Med. Image Anal. 10(5), 693–712 (2006) 23. Schoen, A.H.: Infinite Periodic Minimal Surfaces without Self-Intersections. NASA Electronics Research Center, Cambridge, MA, USA (1970) 24. Yan, C., Hao, L., Hussein, A., Bubb, S.L., Young, P., Raymont, D.: Evaluation of lightweight AlSi10Mg periodic cellular lattice structures fabricated via direct metal laser sintering. J. Mater. Process. Technol. 214(4), 856–864 (2014) 25. Yan, C., Hao, L., Hussein, A., Young, P.: Ti-6Al-4V triply periodic minimal surface structures for bone implants fabricated via selective laser melting. J. Mech. Behav. Biomed. Mater. 51, 61–73 (2015) 26. Yang, L., Yan, C. and Shi, Y.: Fracture Mechanism Analysis of Schoen gyroid Cellular Structures Manufactured by Selective Laser Melting. In: Solid Freeform Fabrication Symposium, pp. 2319–2325 (2017) 27. Marco, P., Alberto, O.: Nature-inspired, ultra-lightweight structures with gyroid cores produced by additive manufacturing and reinforced by unidirectional carbon fiber ribs. Materials 12, 4134 (2019) 28. Wang, S.X.X., et al.: Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: a review. Biomaterials 83, 127–141 (2016) 29. Pelanconi, M., Barbato, M., Zavattoni, S., Vignoles, G.L., Ortona, A.; Thermal design, optimization and additive manufacturing of ceramic regular structures to maximize the radiative heat transfer. Mater. Des. 163 (2019) 30. Klahn, B.L.C., Meboldt, M.: Design strategies for the process of additive manufacturing. Procedia CIRP 36, 230–235 (2015) 31. Yang, S., Zhao, Y.F.: Additive manufacturing-enabled design theory and methodology: a critical review. Int. J. Adv. Manuf. Technol. 80, 327–342 (2015) 32. Pinarbasi, S., Akyuz, U.: Investigation of compressive stiffness of elastomeric bearings. In: 6th International Congress on Advances in Civil Engineering, Bogazici University, Istanbul, Turkey, October 6–8 (2004) 33. Kumar, M.: Analysis of elastomeric bearings in compression. Unpublish Doctoral Dissertation, University at Buffalo, United State (2012) 34. Osgooei, P.M., Tait, M.J., Konstantinidis, D.: Three dimensional finite element analysis of circular fiber reinforced elastomeric bearings under compression. Compos. Struct. 108, 191– 204 (2014) 35. Chang, C.H.: Modeling of laminated rubber bearings using an analytical stiffness matrix. Int. J. Solids Struct. 39(24), 6055–6078 (2002) 36. Kelly, J.M., Marsico, M.R.: Tension buckling in rubber bearings affected by cavitation. Eng. Struct. 56, 656–663 (2013) 37. Sengsri, P., Kaewunruen, S.: Local failure modes and critical buckling loads of a metafunctional auxetic sandwich core for composite bridge bearing applications. Appl. Sci. 11, 10844 (2021). https://doi.org/10.3390/app112210844 38. Sengsri, P., Kaewunruen, S.: Additive manufacturing meta-functional composites for engineered bridge bearings: a review. Constr. Build. Mater. 262, 120535 (2020) 39. Sengsri, P., Fu, H., Kaewunruen, S.: Mechanical properties and energy-absorption capability of a 3D-printed tpms sandwich lattice model for meta-functional composite bridge bearing applications. J. Compos. Sci. 6(3), 71 (2022). https://doi.org/10.3390/jcs6030071 40. Sengsri, P., Marsico, R.M., Kaewunruen, S.: IOP Conf. Ser.: Mater. Sci. Eng. 603, 02206 41. Sengsri, P., Baniotopoulos, C., Kaewunruen, S.: Engineered model for the numerical investigation into vibration characteristics of a novel bridge bearing under free-free and fixed

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boundary condition. In: EURODYN 2020 XI International Conference on Structural Dynamics: EURODYN 2020. European Association for Structural Dynamics, EURODYN 2020 XI International Conference on Structural Dynamics, Athens, Greece, 23/11/20 (2020) 42. Sengsri, P., Kaewunruen, S.: Compression behaviour of an extremely lightweight structure with a gyroid core used for bridge bearings. Mater. Today: Proc. pp. 2214–7853 (2022). https://doi.org/10.1016/j.matpr.2022.04.703 43. He, J., Fu, Z.F.: Modal Analysis. 1st edn. Butterworth Heinemann (2001)

Exploring Patterns in Municipal Bridge Management Issues and Their Relationship with Municipal Conditions in Hokkaido, Japan Michael Henry(B) Department of Civil Engineering, Shibaura Institute of Technology, Toyosu 3-7-5, Koto-ku, Tokyo 135-8548, Japan [email protected]

Abstract. Following legislation passed in 2013, the Japanese government now requires the visual inspection of road bridges every five years. Over 700,000 bridges have been inspected as of 2021, of which nearly two-thirds are under the management of municipal governments. Results have shown that the number of municipal bridges in need of early or urgent repair is much greater than that at other management levels; however, many municipalities lack the necessary financial and human resources to realize maintenance of their bridge infrastructure. As a result, bridge management at the municipal level is becoming a critical issue for ensuring the safety of road infrastructure in Japan, but there are notable disparities in the challenges facing bridge management even within the municipal level. In this research, cluster analysis is adopted to explore patterns in the bridge management issues faced by local municipalities in Hokkaido, the prefecture with the most municipalities in Japan. Publicly available bridge inspection data and socioeconomic data were collected at the municipal level, and a set of descriptive features was constructed. Cluster analysis was then carried out twice – once to identify patterns in municipal bridge management issues, and once to identify patterns in municipal conditions – and the relationship between these results was examined. It was found that, while there are a few highly unique municipalities, most municipalities possess fairly similar bridge management issues and municipal characteristics, which could be judged as the “average” conditions in Hokkaido. Furthermore, there was generally an overlap between the “average” bridge management conditions and “average” municipal conditions, although some municipalities with “average” conditions did exhibit unique bridge management issues. Keywords: Bridge management · Cluster analysis · Inspection data · Local government · Japan

1 Introduction As reported by the Ministry of Land, Infrastructure, Transport and Tourism (MLIT), by 2030 more than half of road bridges over 15 m long in Japan will have been in service for more than 50 years (MLIT 2018). This aging of bridge infrastructure has contributed

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1001–1014, 2023. https://doi.org/10.1007/978-981-19-7331-4_82

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to increased awareness of the need for strategic maintenance and, following legislation passed in 2013, it is now required that visual inspection of road infrastructure – including bridges – be carried out at least once every five years. In the years since the legislation was passed, visual inspection and condition assessment has been carried out for more than 700,000 road bridges (two meters or longer), the results of which have been made publicly available on the MLIT website. More than 60% of these road bridges are managed at the municipal (local government) level. Data from the inspection reports show that the function of approximately 8% of these municipal bridges may be impaired and require early or urgent countermeasures (classification level III or IV; definitions provided later in Table 2). While this percentage is not notably different than that at other management levels (Fig. 1), the sheer number of municipal bridges means that the scale of countermeasures necessary at the municipal level is far beyond that of other levels. This can be seen most clearly when focusing just on bridges that require urgent countermeasures (classification level IV), as 93.8% (534 of 569) of these bridges are under the management of municipal governments. I Total (705,927)

III

IV

31%

59%

Municipal (465,073)

20%

8% 0.11%

48%

44% 0%

10% 0.01%

52%

38%

40%

10% 0.05% 12% 0.00%

74%

14%

Prefectural (181,926)

9% 0.08%

49%

42%

National (36,908) Expressway (22,020)

II

60%

80%

100%

Fig. 1. Distribution of road bridges by classification level (data source: MLIT 2021)

Municipal governments are also lagging behind other management levels in initiating repairs for deteriorated bridge infrastructure. As shown in Table 1, repairs have begun for only 20% of municipal bridges that require urgent countermeasures, compared to 94% of prefectural bridges and 100% of national bridges in the same condition. Furthermore, almost no countermeasures have been initiated by municipalities for bridges needing preventive maintenance. The major issues underlying this lack of progress among local municipalities are insufficient financial power, lack of specialized knowledge, and shortage of civil engineers in municipal public works departments (MLIT 2021). Even among municipal governments, however, there is a large disparity in the challenges facing bridge management. For example, 57% of villages (the smallest unit of municipal government) have no civil engineering staff, compared to just 23% of towns and 6% of cities and wards (Fig. 2). While this is a small improvement compared to 2014, when 63% of villages

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Table 1. Initiation rate of bridge repair by management level (data source: JSCE 2020). Bridge condition

National (%) Prefectural (%) Municipal (%) Expressway

Preferable to take countermeasures for preventive maintenance

26

2

2

2%

Early countermeasures should be taken

53

24

18

32%

Urgent countermeasures should 100 be taken

94

20

n/a

reported having no civil engineering staff, there clearly remains a need to explore the diversity of conditions faced by municipalities in Japan. None City, Ward (795)

30%

42%

57% 0%

2%

75%

23%

Village (183)

6 or more

64%

6%

Town (743)

1 to 5

20%

40%

60%

80%

1% 100%

Fig. 2. Distribution of municipal governments by number of civil engineering staff (data source: MLIT 2020)

In this research, the similarities and differences between municipalities is examined from two perspectives: the challenges facing road bridge management at the municipal level, and the socio-economic conditions at the municipal level. To make the analysis manageable, this research focuses just on Hokkaido, the largest prefecture in Japan, which also has the most municipalities (179) among Japan’s 47 prefectures. Agglomerative hierarchical cluster analysis, an unsupervised machine learning technique that groups observations together based on their similarities, is applied to identify the patterns in bridge management conditions and municipal conditions in Hokkaido using two sets of features constructed from road bridge inspection data and statistical data at the municipal level, respectively. From these analyses, two sets of clusters are extracted, which contain municipal governments with similar bridge management and municipal conditions. The clusters found from the bridge management data and the clusters found from the municipal conditions data are then compared to understand the relationship between challenges in bridge management and municipal conditions in Hokkaido.

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2 Research Methodology 2.1 Bridge Inspection Data Data on road bridges at the municipal level in Hokkaido were collected from the aforementioned annual road maintenance reports published by the Ministry of Land, Infrastructure, Transport and Tourism. These reports include the following items: bridge name, route name, year of construction (if known), bridge length and width, managing agency, and classification of the bridge condition. The classification spans four levels (Table 2) and is judged based on the results of the periodic inspection. Table 2. Description of bridge classification levels (MLIT 2020). Classification level

Description

I

Good (sound)

The function of the bridge is not impaired

II

Preventive maintenance

The function of the bridge is not impaired, but it is preferable to take measures for preventive maintenance

III

Corrective maintenance

The function of the bridge may be impaired, and early measures should be taken

IV

Emergency rehabilitation

The function of the bridge is impaired, or extremely likely to become impaired, and urgent measures should be taken

A total of 18,080 municipal road bridges in Hokkaido were identified in the MLIT database, and their distributions by condition classification, length, and age at time of inspection (which was calculated from the year of inspection and year of construction) are shown in Fig. 3. While 32.7% of these bridges have been in service for 40 years or longer (or for an unknown period), only 17.4% have or may have impaired function requiring corrective maintenance or rehabilitation (classification III or IV). Furthermore, 61.6% of the municipal road bridges are between 2 and 15 m in length, but a small percentage (2.9%) is 100 m or longer. 2.2 Municipal Conditions Five types of statistical data were collected to explore the similarities and differences between municipal conditions in Hokkaido (Table 3). Area and population characterize the geographic and demographic size of each municipality, respectively, and the percentage of the municipal population residing in densely inhabited districts (DID) is a measure of the degree of urbanization. The financial capability index is a unitless index that assesses the financial power of municipalities as a ratio of their financial income to financial demand, with higher values indicating greater financial resources. Finally, bridge maintenance budget represents the economic resources available for maintaining

Exploring Patterns in Municipal Bridge Management Issues 70%

70%

50% 40%

32.0%

30% 17.1%

20% 10% II

III

50% 40% 29.2%

30% 20%

6.2%

10%

0.3%

0% I

61.6%

60%

50.6%

Ratio of bridges

Ratio of bridges

60%

1005

0%

IV

0.0% 0 (16) The collated Eqs. (15) or (16) is turned into a transcendental equation without analytical solution. In order to obtain the numerical solution of the equation and realize the whole assembly process, this procedural calculation can be written into a loop program

Mechanical Model for Parallel-to-Grain Withdrawal Failure

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in C language. N is the loop control variable in the program and also associated with the required number of assembly units when an integrated screw subjected to axial load P is pulled out. Note that the last assembly unit is not included due to the occurrence of compressive force, the effective embedment length of parallel-to-grain withdrawal P corresponding to axial load P is failure of self-tapping screw in wood denoted as lem given by: P lem = [(N − 1) × s]

(17)

P . More genThe goal of the model is to calculate the effective embedment length lem erally, the relationship curve between withdrawal failure load and embedment length can be obtained by entering the information about geometry, material and axial load into the model. Among the input values, the axial load starts from 0 and gradually increases to the ultimate tensile capacity of the screw, which means each axial load corresponds to an embedment length and the withdrawal failure occurs prior to the tensile failure of the screw. For the system of screw and timber capable of vertical force transferring, there exists an anchorage length (namely the withdrawal failure will be avoided if the embedment length exceeds the anchorage length) limited by the geometrical characteristics and material properties.

3 Verification and Discussion 3.1 Model Verification Douglas-fir glulam and the WRT-type self-tapping screws produced by SFS intec were used in withdrawal experiments conducted by our research group. A total of 120 specimens were divided into 24 groups with 5 replicates in each group, according to the 4 different embedment lengths (65 mm, 130 mm, 195 mm, 260 mm) and 6 different screwto-grain angles (0°, 15°, 30°, 45°, 60°, 90°). The pull-push loading configuration was adopted in withdrawal test, with the purpose-made steel shelf for specimen installment and type SHT4106D electro-hydraulic servo universal testing machine for withdrawal test (Fang et al. 2022). In addition, this paper also uses the test data of parallel-tograin withdrawal failure of threaded rods by Stamatopoulos and Malo (2015) for model verification. Considering that the withdrawal experiments by our research group are similar to the verification experiments by Jensen (2012), theoretical results based on the theory of Jensen are also presented in Fig. 9a. It should be pointed out that the mode II fracture energy of wood adopts the same value provided by Jensen (2012), and the initial shear stress as an empirical fitting parameter is tried in two cases, 0 and 1. Since the theory of Jensen does not clearly suggest the calculation method for the compressive area of the wood involved in formulas, the calculation for theoretical failure loads based on the full cross section area of 200 × 200 mm2 similar to Jensen (2012), may lead to conservative results. However, the basic shape of the relationship curves between failure load and embedment length will not be changed.

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Fig. 9. Experimental and theoretical relationship curves between failure load and embedment length

3.2 Discussion In general, an acceptable agreement has been achieved between experimental results and theoretical predictions from the current model. A nearly linear relationship between withdrawal failure load and embedment length is predicted by the model. The main reasons affecting the accuracy of the model are summarized as follows: (I) The solution of the governing differential equation of assembly unit contains a lot of assumptions, among which the friction between the wood tube and screw rod is simplified to be proportional to the shear stress on shear failure surface; however, the influence of the simplification on the deformation and stress of the wood tube and screw rod is hard to evaluate. (II) The role of stress function or displacement function on an assembly unit is similar to the role of shape function on an element in the finite element method. Just as the calculation precision lies on the authenticity of the shape function, the stress function or displacement function will affect the availability of the assembly unit, and then the final precision of the whole model. (III) Now that the wood between threads is simplified into separate thin-walled wood tube, the stress state at the moment of withdrawal failure which relates to the assumption of failure criterion for the whole model is very necessary to be further researched. At present, the model adopts the maximum shear stress criterion for each assembly unit. When the number of assembly units is large; namely the embedment length is long, a rough assumption of failure criterion will inevitably lead to the inaccuracy of prediction. (IV) If the shear strength of wood under combined shear-compressive stresses is not concerned in the model, the theoretical prediction may not be accurate enough.

4 Conclusions Through the introduction of assembly unit, a new mechanical model for parallel-tograin withdrawal failure of self-tapping screws in wood is presented in this paper. The local deformation and compression of wood, and the discontinuous transfer of shear stress on the shear failure surface, as the distinctive mechanical behaviors caused by the

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thread of the screw, are reflected and investigated in the aspects of model simplification, formula derivation and algorithm design. In general, an acceptable agreement is achieved between theoretical predictions and experimental results, and a nearly linear relationship between withdrawal failure load and embedment length is predicted by the model. At last, the reasons affecting the accuracy of the model are discussed in detail for further improvement in the follow-up research.

References Blaß, H.J., Bejtka, I., Uibel, T.: Tragfähigkeit von Verbindungen mit selbstbohrenden Holzschrauben mit Vollgewinde. Universitätsverlag Karlsruhe (2006). https://doi.org/10.5445/ KSP/1000004810 CEN: European Committee for Standardization, EN 1995-1-1:2004: Design of timber structures. Part 1–1: General—Common rules and rules for buildings, Brussels, Belgium (2004) Fang, L.J., Qu, W.J., Zhang, S.D.: Mechanical model for withdrawal failure of self-tapping screws in glulam. Eng. Mech. 39(6), 212–225 (2022). https://doi.org/10.6052/j.issn.1000-4750.2021. 11.0866 Jensen, J.L., Koizumi, A., Sasaki, T., et al.: Axially loaded glued-in hardwood dowels. Wood Sci. Technol. 35, 73–83 (2001) Jensen, J.L., Nakatani, M., Quenneville, P., et al.: A simple unified model for withdrawal of lag screws and glued-in rods. Eur. J. Wood Wood Products 69, 537–544 (2011) Jensen, J.L., Nakatani, M., Quenneville, P., et al.: A simplified model for withdrawal of screws from end-grain of timber. Constr. Build. Mater. 29, 557–563 (2012) Stamatopoulos, H., Malo, K.A.: Withdrawal capacity of threaded rods embedded in timber elements. Constr. Build. Mater. 94, 387–397 (2015) Nakatani, M., Komatsu, K.: Development and verification of theory on pull-out properties of lagscrewbolted timber joints. In: Proceedings of the 8th world conference on timber engineering (WCTE), pp. 95–99 (2004) Ellingsbø, P., Malo, K.A.: Withdrawal capacity of long self-tapping screws parallel to grain direction. In: Proceedings of the 12th world conference on timber engineering (WCTE), pp. 228–237 (2012) Volkersen, O.: Die nietkraftverteilung in zugbeanspruchten nietverbindungen mit konstanten laschenquerschnitten (the rivet load distribution in lap-joints with members of constant thickness subjected to tension). Luftfahrtforschung 15, 41–47 (1938)

Practice of Sustainable Urban Development

A Study on Estimation Method of Curing Influence Area for Prediction of Remaining Life on Real Concrete Structures T. Iyoda(B) , A. Sugiyama, and M. Miyawaki Department of Civil Engineering, Shibaura Institute of Technology, 3-7-5 Toyosu Koto-Ku , Tokyo 1358548, Japan {iyoda,ah18052,mh21021}@shibaura-it.ac.jp

Abstract. The life cycle of concrete structures is known to be highly dependent on the manufacturing, construction and the environment of the structure’s location. In order to keep the durability of concrete, it is necessary (1) determination of materials and mix proportion on design, (2) keeping the enough compaction and curing period on construction and (3) understanding the environmental effects such as supply of carbon dioxide, chloride ions and water. Therefore, it is important to implement the design with the required performance to satisfy the design service life. On the other hand, in maintenance management, it is necessary to predict the remaining life based on the supplying period and the state of deterioration at that time. In this case, the information at the time of design and construction is often unknown, and it is difficult to estimation. In this study, as a first step to sort out these issues, concrete specimens were prepared using various types of cement, varying the water cement ratio and also varying the curing period. The accelerated carbonation test and vacuum water absorption test were combined to represent the penetration of carbon dioxide and water in the specimens. The area of influence of curing was organized in terms of material and mix proportion conditions. Porosity was also measured to evaluate the relationship between the penetration properties. In addition, wall specimens were also prepared to measure the effect of curing by non-destructive test. As a result, it was confirmed that the larger the water cement ratio, the greater the effect of curing on the surface layer, but the depth of curing effect was about 20 mm. It was also confirmed that the effect of curing and curing area were larger for Low heat Portland cement and high replacement blast furnace slag cement, where the hydration would slower. Keywords: Life cycle · Curing period · Curing effective area · Carbonation · Vacuum water absorption test

1 Introduction Curing is known to be very important in the construction for concrete structures. Curing is meaning for accelerating the hydration reaction of cement and contributing to the development of concrete strength. If curing is neglected, it is assumed that moisture in the concrete will evaporate from concrete, resulting in a lack of moisture in the concrete. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1031–1039, 2023. https://doi.org/10.1007/978-981-19-7331-4_84

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It is known that if the moisture inside the concrete is insufficient, hydration cannot continue, and strength and durability will decrease. Therefore, it is required to establish a standard for the wet curing period and to construct the concrete to satisfy days. However, it is not considered difficult to ensure the concrete strength of the actual structure, since the moisture does not easily dissipate, considering the thickness of the concrete and other factors. On the other hand, the covered concrete, which is considered to be the surface concrete, is easily affected by the curing process, causing hydration to cease and leaving a large number of voids. It can be imagined that the movement of materials will be facilitated. If the cover concrete, which was installed to protect against corrosion of the reinforcing steel bars, has many voids and is prone to mass movement, it will be difficult to protect it from corrosion. In other words, it can be imagined that ensuring the denseness of the cover concrete and ensuring its resistance to mass movement is an important factor in ensuring the durability of the RC structure. On the other hand, considering the life cycle of concrete structures, it is also necessary to estimate the remaining service life during maintenance. In the diagnosis of structures, it is necessary to accurately determine the current condition and future service life, and repair and reinforcement should be carried out. However, the origin of the structure, concrete materials, and construction information are often unknown at the time of maintenance. In particular, considering the need to ensure the durability of concrete and extend its service life, we believe that understanding the material, construction, and environmental conditions are very important factor. In this study, the first step is to organize basic information to understand the resistance to mass transfer of surface concrete as a function of the number of curing days using concrete with different types of cement and water-cement ratios. We also decided to organize the relationship between the mass transfer resistance of concrete and curing using nondestructive testing based on surface measurements.

2 Outline of Experiment 2.1 Outline of Specimen Ordinary Portland cement (hereafter OPC), blast furnace cement class B (50% replacement of ground granulated blast furnace slag, hereafter BB), and low heat Portland cement (hereafter LPC) and high volumes blast furnace slag containing as 70% replacement cement (hereafter ECM) were used for the concrete. Table 1 shows the listed for kind of cements using in this research. Crushed sand with a density of 2.65 g/cm3 and water absorption of 1.35% was used as fine aggregate and crushed stone with a density of 2.70 g/cm3 and water absorption of 0.26% was used as coarse aggregate. The planned concrete mixes for this study are shown in Table 2. The water-cement ratio was varied from 35%, 45%, 55%, and 65% for the mixes using OPC and BB, and all mixes were deformed the day after placing and cured by seal curing. The curing periods were 1, 3, 5, 7, 10, and 28 days, and in addition to these, specimens cured for 12 and 14 days were prepared only for the formulations using LPC in consideration of the delay in hydration.

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Table 1. Cement physical properties Cement

Density (g/cm3 )

Blaine (cm2 /g)

Replacement (%)

OPC

3.16

3080

–

BB

3.02

3500

50

LPC

3.24

3780

–

ECM

2.96

3920

70

Table 2. Mix proportion on this research (different kinds of cements) No

Kinds of cement

W/C (%)

s/a (%)

Unit (kg/m3 ) W

C

S

G

N35

OPC

35

44

170

486

788

886

N45

45

46

378

830

934

N55

55

48

309

858

965

N65

65

50

262

876

986

35

44

486

780

877

BB45

45

46

378

824

927

BB55

55

48

310

852

959

BB65

65

50

262

872

981

BB35

BB

L55

LPC

55

48

309

861

969

E55

ECM

55

48

309

850

956

2.2 Accelerated Carbonation Test The test was conducted on a prismatic specimen (100 × 100 × 400 mm). After the setting curing period, the specimen was sealed with aluminum tape excepted two sides of the specimen and placed in an accelerating carbonation environment. In this research, we focus on the carbonation ratio effect on curing condition, so that we conducted the pretreatment for curing period not based on JIS testing method. Carbonation acceleration conditions were 20 °C, 60% relative humidity, and 5.0% carbon dioxide concentration based on JIS A 1153:2012. The specimens were split at 50mm intervals during the specified acceleration periods (2 days, 1, 4, 8, and 13 weeks), the cross sections were sprayed with phenolphthalein solution, and the distance to the discoloration boundary was measured at 6 points per surface, 12 points in total, and the average of these measurements was used as the carbonation depth. 2.3 Vacuum Water Absorption Test The vacuum water absorption test currently proposed by the author’s group is a simple method for evaluating the mass transfer resistance of concrete and for continuously

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determining the mass transfer resistance of concrete in the depth direction. A cylindrical specimen (100 × 200 mm) was used in this study. The pretreatment method for this test is shown Fig. 1. After the prescribed curing was completed, the sides were sealed with aluminum tape as shown in Fig. 1, and the specimens were put in an environment of 20 °C and 60% relative humidity for 28 days with both ends released to simulate the drying associated with de-framing after curing in the actual construction of the structure. The aluminum tape was then removed and dried in a drying oven at 40 °C for 5 days.

Fig. 1. Testing methodology for vacuum absorption test

After pretreatment, the bottom of the cylinder, the casting surface, and part of the side surfaces were sealed with aluminum tape as shown in Fig. 1 to prevent water from entering through the side surfaces of the specimen. Next, the butt was filled with water so that the cylindrical specimen was immersed in 26 mm of water and placed in a desiccator. The inside of the desiccator was then vacuumed with a vacuum pump for 1 h, and the vacuum was kept for 2 h before the test was conducted. After that, the specimen was split and the height at which water was sucked up was measured at 10 mm intervals in the depth direction for a total of 21 points. 2.4 Surface Water Absorption Test (SWAT) The surface water absorption rate after 10 min of water injection was calculated using SWAT, one of the methods to evaluate the surface quality of concrete structures. The test specimens of 150 × 150 × 260 mm were prepared and demolded the day after casting, and the excepting test surfaces were covered with aluminum tape to prevent water loss except for the test surface. The curing sheets were sealed and cured with commercially available curing sheets with water retention properties. After curing, the specimens were dried in the same environment for a specified period (7, 14, 28, 56 days), and then measured. Equations are left-justified and numbered in Arabic numerals.

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1035

150mm

SWAT Testing area

φ80mm Testing area

Curing sheet

260mm

Aluminum tape

150mm

Fig. 2 System for SWAT and outline of specimen

3 Results of Tests 3.1 Accelerated Carbonation Test 1. Relationship between curing periods and coefficient of carbonation rate Figure 3 shows the relationship between the curing periods and the coefficient of carbonation rate, based on the results of the accelerated carbonation test for the mix proportions using OPC and BB and LPC and ECM. Regardless of the watercement ratio and cement type, the longer the curing period, the lower the coefficient of carbonation rate, but the BB and LPC and ECM mix proportions show a greater decrease in the coefficient of carbonation rate with extended curing. Therefore, it can be said that a longer curing period is necessary to obtain the original mass transfer resistance of concrete when using slow-hydrating cement, and this is also the reason why BB has a longer curing period than OPC in the standard wet curing period described in the JSCE Standard Specifications for Construction [Construction Edition]. In addition, it was confirmed that the decrease in the depth of carbonation tends to reach a ceiling after a certain period of curing. In the case of compressive strength, it is known that the strength continues to increase with wet curing up to about 28 days, but the decrease in the coefficient of carbonation rate stagnates after curing up to about 7 days for the OPC-based mix proportion and up to about 10 days for the BB-based mix proportion, indicating that the decrease in the coefficient of carbonation rate is not significant at the initial stage of curing. It is considered that the voids that contribute to mass transport resistance are filled by the progress of hydration reactions at the age of the hydration products. Therefore, it is considered that the majority of the mass transfer resistance potential of the concrete mix can be realized if the initial curing period is conducted properly.

2. Effects of insufficient curing Figure 4 shows the results of accelerated carbonation tests for B55 at 1, 3, and 28 days of curing. This figure shows that the depth of carbonation is proportional to the square root of the curing period for the 28day curing period, but not for the 1day and 3day

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16

N35 N55

14

Coefficient of carbonation rate (mm/√week)

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Fig. 3. The results for coefficient of carbonation rate on different cements and W/C

Carbonation Depth (mm)

for curing periods. This can be attributed to the stagnation of hydration of the surface concrete due to water dissipation caused by insufficient curing. Compared to the latter half of the acceleration period, the speed of increase in carbonation depth with respect to the acceleration period is almost the same regardless of the number of curing days, indicating that the interior concrete, which is not affected by curing, has almost the same resistance to mass transfer regardless of the curing period. Therefore, the usual fitting is done by the root t rule, but to see the effect of curing, an approximate line passing through the origin was created, and a two-line approximation was considered. 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 10.0 5.0 0.0

BB55-1d BB55-3d BB55-28d

0

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4

Fig. 4. Carbonation depth on accelerated carbonation periods on different curing period

A Study on Estimation Method of Curing Influence Area

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3.2 Vacuum Water Absorption Test The test results of N55, BB55, L55, and E55 are shown in Fig. 5 as representative mixes. The bottom surface is shown on the left, and the casting surface is on the right. Both graphs show a large suction uplift on the casting side, which may be due to moisture loss in the 24 h before demolding and bleeding effects. On the other hand, the bottom side is considered to be unaffected by these factors and thus reflects only the effects of curing. Therefore, this study focused on the bottom side. The results of the vacuum water absorption test also showed that, as in the carbonation acceleration test, the effect of the test tended to reach a ceiling after a certain curing period, and that the mix proportions using BB and LPC were susceptible to insufficient curing due to the slow rate of hydration and required a longer curing period. In addition, the short curing period of L55 also resulted in a greater water absorption depth in the interior concrete, which is considered to be unaffected by curing, indicating that more attention should be paid to curing. N55-1d N55-5d N55-10d

80.0

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Fig. 5. The results for water absorption test in vacuum conditions

3.3 Surface Water Absorption Test Results Figure 6 shows the surface water absorption rate of concrete with different cement types after 56 days of curing for each of the different curing days. For all cements, the water absorption rate decreased as the curing period increased. The improvement in surface quality was N 0.0085 where, εps = strain of prestressing strands in tension (variable) f ps = stress of prestressing strands corresponding to εps E ps = modulus of elasticity of prestressing strands.

Fig. 5. (a) Stress-strain diagram of strand; (b) stress-strain diagram of steel

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For nonprestressed steel, Grade 60 steel was selected in this study. The stress-strain diagram is shown in Fig. 5(b). Similarly, the curve can be expressed using Eq. (5).  Es εs , εs ≤ εsy (5) fs = fy , εs > εsy where, εs = strain of reinforcing bars (variable) εsy = yield strain of reinforcing bars f s = stress of reinforcing bars corresponding to εs f y = specified yield strength of reinforcing bars E s = modulus of elasticity of reinforcing bars. 3.2 Interactions Between Reinforcement and Concrete Two types of interaction models, embedment model and friction model, were applied to the surfaces of steel-concrete and strand-concrete. 3.2.1 Embedment Model The embedment technique states that an element or element group is embedded in “host” elements. In this study, the mild steel was assumed fully bonded to surrounding concrete, which was perfectly applied to embedment model (Yan 2019). Therefore, all mild steel and surrounding concrete were modeled to be embedded and host elements, respectively. Translational degree of freedom in steel element is constrained to concrete element. The embedment technique is able to significantly improve the numerical efficiency by getting a set of elements embedded into concrete element instead of defining contact surface properties between slave and master elements. 3.2.2 Friction Model To simulate the bond mechanism between strands and surrounding concrete, the friction model was employed. This model includes two components which are tangential behavior and normal behavior (Arab et al. 2011; Kang et al. 2015). Once strands and concrete are interacted, both normal and shear stress would be transmitted based on tangential behavior. The tangential behavior is described as Coulomb friction model shown in Fig. 6. The friction model will govern the maximum allowable shear and normal stress on contact surface. If equivalent shear stress exceeds the critical shear stress, strand sliding occurs. The critical shear stress is related to contact pressure between strand and surrounding concrete. It is described as coefficient of friction in Abaqus. This coefficient was calibrated by a series of parametric studies. For the fully bonded prestressed concrete beam, a coefficient of friction of 1.4 is good enough to provide the interface interactions (Arab et al. 2011). In order to prevent strands from overlapping with concrete during the process of loading, the “hard” contact pressure-overclosure relationship was used to simulate the normal behavior between strands and concrete. Based on the stiffness of materials, the strand and concrete surfaces were selected as the master and slave surfaces, respectively.

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Fig. 6. Coulomb friction model (ABAQUS 6.16)

3.3 Boundary Conditions and Element Types 3.3.1 Boundary Conditions Due to the doubly symmetric characteristics of the model, only a quarter of the girderdeck system was modeled with the consideration of running time reduction. Using the z-direction symmetry, the girder-deck system was divided into two parts with a plane parallel to x-y plane. The displacement in z-direction and the rotation around x, ydirections were constrained by a roller supports (U3 = UR1 = UR2 = 0). Similarly, using the x-direction symmetry, the girder-deck system was cut with a plane parallel to y-z plane. The displacement of x-direction and the rotation around y, z-direction were constrained by a roller supports (U1 = UR2 = UR3 = 0). Additionally, the girder-deck system was supported with roller supports constraining the displacement in y-direction at the support (U2 = 0). The boundary conditions for the models are shown in Fig. 7. 3.3.2 Concrete Element The first order linear brick element with reduced integration and hourglass control (C3D8R) was employed to simulate concrete element. C3D8R elements are more suitable to both linear and nonlinear analysis regarding stress/displacement analysis (ABAQUS 2016). The reduced integration of the element has two significant advantages compared with full integration elements (C3D8): 1) Reduced integration element takes less time to simulate. 2) Reduced integration element is more likely to avoid shear and volumetric locking whereas it may occur in full integration element. In addition to first order elements, second order elements, such as C3D20R, are also available to choose, and they provide smoother deformed shape in bending. However, the computational time will dramatically increase. Therefore considering the computational efficiency, the first order was employed in this study.

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Fig. 7. Boundary conditions: (a) a quarter of the girder (b) x-direction symmetry (c) z-direction symmetry

3.3.3 Strand and Steel Elements The simplified circular cross-section was modeled for a strand. The area of cross-section is equivalent to real seven-wire strand. 3-D linear triangular prism elements (C3D6) were assigned to strand. 3-D linear truss elements (T3D2) were used for the reinforcing steel. 3.4 Failure Modes in FEA Model Prestressed girder-deck systems have two types of flexural failure mechanisms, which are concrete crushing (CC) and strand rupture (SR). The CC failure is identified that the

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concrete strain in compression exceeds the failure strain of 0.0038 (Yan 2019). The SR failure occurred if the stress in strand exceeds the tensile strength.

4 FEA Model Verification Against Experimental Data In order to validate the accuracy of finite element model, the FE models were compared against the experimental test data. EISafty et al. performed a study for the laterally damaged prestressed concrete girders by over-height vehicle collisions. The thirteen tested half-scale prestressed concrete girders were 20 ft long and had cross-sectional dimensions set at exactly half-scale of an AASHTO type II girder. Additionally, a deck with 4 in. Thickness was cast on top to simulate a bridge deck composite. The crosssection information is shown in Fig. 8(a). Five low-relaxation grade 270 seven-wire prestressing strands and three non-prestressed steel bars were used to reinforce the girder. In addition, to ensure full composite action, half of the stirrups extended vertically from the girder to the deck while the other half remained entirely in the girder. The FEA results showed good agreement with the experimental test, as seen in Fig. 8(b). Therefore, the FEA model is able to predict flexural response of the girder-deck system.

5 Effects of Reinforcement Ratio and Span-to-depth Ratio Figure 9(a), (b) and (c) show the result comparison with different prestressing reinforcement ratios under the same span-to depth ratio. Figure 10(a), (b) and (c) describe the load versus deflection behaviors with the different span-to-depth ratios under the same reinforcement ratio. 5.1 Effect of Reinforcement Raito Figure 11 shows the effect of reinforcement ratio on the ultimate load with different span-to-depth ratios. The three curves in Fig. 10 have prestressing reinforcement ratios of 0.101, 0.126 and 0.151%. Ultimate load decreases with a higher span-to-depth ratio. The reductions of ultimate load of girder-deck system with prestressing reinforcement ratios of 0.101, 0.126 and 0.151% are 47.7, 48.7 and 50.1% as span-to-depth ratio increases. The difference of reduction between these three prestressing reinforcement ratios is 2.4%, which is a very small value. Additionally, the prestressing reinforcement ratio has a larger effect on the ultimate load of girder-deck system with a relatively lower span-to-depth ratio. The increase of ultimate load of girder-deck system with L/d of 10 is twice more than the girder-deck system with L/d of 20. 5.2 Effect of Span-to-depth Ratio Figure 12 describes the influence of span-to-depth ratio on the impact of reinforcement ratio on ultimate load. The impact of span-to-depth ratio on the increment of ultimate load decreases with an increasing reinforcement ratio. As span-to-depth ratio increases from 10 to 20, the increment of ultimate load drops from 30.1 to 23.3% under the ranges of prestressing reinforcement ratio from 0.101 to 0.151%. The difference is almost 7%. Thus, the span-to-depth ratio has an significant effect on ultimate load compared with reinforcement ratio.

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6 Conclusions FEA models for predicting flexural behavior of prestressed Type III girder-deck system were developed and presented. Based on the research results, the following conclusions could be drawn:

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1. By verifying the accuracy of FEA model against experimental data, it was demonstrated that the proposed FEA models can be used to estimate the flexural behavior of a prestressed concrete girder-deck system with good accuracy. 2. The reinforcement ratio has a larger effect on the ultimate load of girder-deck system with a relatively lower span-to-depth ratio than on girder-deck system with a higher span-to-depth ratio. The increase of ultimate load of girder-deck system with L/d of 10 is twice higher than the girder-deck system with L/d of 20. However, reinforcement ratio has an insignificant impact on the reduction of ultimate load as the span-to-depth ratio increases. For the girder-deck systems with different reinforcement ratios, the reductions of ultimate load only have a difference of 3%. 3. Span-to-depth ratio has a significant influence on the increment of ultimate load as reinforcement ratio increases. For the girder-deck system with L/d of 10, the ultimate load improves by 30.1% as the increase of reinforcement ratio from 0.101 to 0.151%, which is almost 7% more than the girder-deck system with L/d of 20. 4. The ductility is affected by both reinforcement ratio and span-to-depth ratio. Under the same span-to-depth ratio, the larger reinforcement ratio results in a lower ductility. But the larger the span-to-depth ratio is, the higher the ductility is, if the reinforcement ratio remains the same.

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Fig. 11. Effect of reinforcement ratio

5. The stiffness slightly improves as the increasing of reinforcement ratio under the unchanged span-to-depth ratio. However, the stiffness decreases with the increase of span-to-depth ratio, with the same reinforcement ratio. 6. The yielding strength of the girder-deck system with higher stiffness and lower ductility is always larger than those with relatively lower stiffness and higher ductility.

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References AASHTO LRFD: Design of highway bridges based on AASHTO LRFD bridge design specifications (2012) ABAQUS, A.S. and User’s Manual, V.: Dassaults Systemes Inc., 2015 (2016) Arab, A.A., Badie, S.S., Manzari, M.T.: A methodological approach for finite element modeling of pretensioned concrete members at the release of pretensioning. Eng. Struct. 33(6), 1918–1929 (2011) Ataei, H., Mamaghani, M.: Finite Element Analysis: Applications and Solved Problems Using Abaqus® (2018) Bai, T., Yan, B., Ataei, H., Aboutaha, R.: Strength and ductility of CFRP strengthened highway PC girders: an fem investigation. In: 8th International Conference on Fibre-Reinforced Polymer (FRP) Composites in Civil Engineering, CICE 2016, pp. 307–312. Department of Civil and Environmental Engineering and Research Institute for Sustainable Urban Development, The Hong Kong Polytechnic University (2016) ElSafty, A., Graeff, M.K., Fallaha, S.: Behavior of laterally damaged prestressed concrete bridge girders repaired with CFRP laminates under static and fatigue loading. Int. J. Concr. Struct. Mater. 8(1), 43–59 (2014) Kaklauskas, G., Ghaboussi, J.: Stress-strain relations for cracked tensile concrete from RC beam tests. J. Struct. Eng. 127(1), 64–73 (2001) Kang, T., Huang, Y.: Computer modeling of post-tensioned structures. In: 4th international conference on computer modeling and simulation, vol. 22, pp. 41–45 (2012) Mercan, B., Schultz, A.E., Stolarski, H.K.: Finite element modeling of prestressed concrete spandrel beams. Eng. Struct. 32(9), 2804–2813 (2010) PCI Concrete Handbook Committee: PCI Handbook Precast Prestressed Concrete (2010) Yapar, O., Basu, P.K., Nordendale, N.: Accurate finite element modeling of pretensioned prestressed concrete beams. Eng. Struct. 101, 163–178 (2015) Yan, B.: Residual flexural strength of corroded AASHTO Type II pretensioned concrete girderdeck system. Doctoral dissertation, Syracuse University (2019) Yang, K.H., Mun, J.H., Cho, M.S., Kang, T.H.: Stress-strain model for various unconfined concretes in compression. ACI Struct. J. 111(4), 819 (2014)

Disaster Mitigation

Flexural Performance of Mill Cut Steel Fiber Reinforced Concrete Beam Degraded by Mild Corrosion Khanh Minh Vo1(B) , Withit Pansuk1 , Thi Nguyen Cao2 , and Hai Yen Thi Nguyen3 1 Department of Civil Engineering, Faculty of Engineering, Chulalongkorn University,

Bangkok 10330, Thailand [email protected], [email protected] 2 Faculty of Technology Engineering, Tien Giang University, My Tho 84100, Vietnam [email protected] 3 Faculty of Civil Engineering, Industrial University of Ho Chi Minh City, Ho Chi Minh City 727010, Vietnam [email protected]

Abstract. Corrosion of steel occurred in the reinforced concrete structures is one of the most significant causes of deterioration and reduction of the loading capacity of the reinforced concrete structures. Applying fiber extended the initiation stage and postponded the crack propagation stage of corrosion process in RC structure. Therefore, this research aims to evaluate the effectiveness of utilizing steel fiber reinforced concrete (SFRC) for its application in a chloride environment. To investigate the flexural behavior of the corroded SFRC beam under static loads, the concrete with the water-to-cement ratio of 0.4 containing steel fibers of 0, 0.5%, 1.0%, and 1.5% were used. The impressed current method was applied to accelerate the corrosion of steel to reach 5% by applying the constant current of 250 μA/cm2 within 38 days. The flexural strength of eight beams having an identical section of 150 × 200 mm and a length of 1400 mm were examined under a four-point bending test. The experimental results showed that the presentation of mill cut steel fibers significantly influenced the flexural performance of the corroded SFRC beams. Corrosion of steel led to a more significant reduction of load capacity of the RC beams, whereas the beam containing the steel fiber remained the ultimate or yield load capacity. Fibers take account for compensating the flexural strength of the structure due to the loss of cross-section of the steel bar by corrosion effect and limit the propagation of the width crack. Keywords: SFRC · Steel corrosion · Flexural behaviors · Load capacity · Deflection

1 Introduction The reinforced concrete (RC) structure is one of the most used materials for various construction such as buildings, underground structures, highways, tunnels, harbors, dams, bridges… Nevertheless, corrosion of steel rebar in RC structures appears to be a critical © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1403–1412, 2023. https://doi.org/10.1007/978-981-19-7331-4_112

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worldwide issue. It shortens the structure’s service life and concerns the budget for repair, rehabilitation, or reconstruction. Concrete with high alkalinity is assumed to be an excellent material to protect steel reinforcement and prevent it from corrosion (Broomfield 2003). The alkaline condition leads to the form of a dense ‘passive’ layer; this impenetrable film entirely prevents further corrosion on the steel surface. However, the invasion of aggressive ions from exposing environment incorporating the reduction of alkalinity in concrete can induce the corrosion of steel reinforcement in reinforced concrete (Poursaee 2016). The formation of corrosion products, which have a volume of about 2.5–5 times higher than the original steel, resulted in a reduction in cross-section and strength of corroded steel bar (Almusallam 2001; Ou et al. 2016), subsequently degrading the bonding strength between steel rebar and concrete (Fang et al. 2004, Tondolo 2015). In addition to decreasing the effective cross-section of steel bar, the corrosion products also degrade the performance of RC by making concrete crack due to high expansive stress. This deterioration leads to a change in the structure’s performance, considerably increases the brittleness of the structure (Du et al. 2013; Yu et al. 2015; Zhang et al. 2018; Yalciner et al. 2020). The economic loss and damage caused by steel corrosion in concrete make it arguably the enormous single infrastructure problem facing industrialized countries. Therefore, it is a potential market for those responsible for dealing with structures suffering from corrosion. In recent decades, several methods have been applied to reduce or prevent the corrosion of reinforcement, such as corrosion inhibitors, surface reinforcement bars treatment, or utilizing the alternative reinforced material with high corrosion resistance such as stainless steel or fiber-reinforced polymer (FRP) (Bicer et al. 2018; MarcosMeson et al. 2018). However, the additional chemical compounds into the concrete mixture, coating epoxy on the steel bar surface, or using the alternative materials face drawbacks such as equipment requirement, loss of mechanical properties, and prohibitive cost. Recently, a method is preventing the mitigated corrosion effectively and provides a mechanism to improve the structural behaviors by using fiber-reinforced concrete since the degradation process of reinforced concrete is affected by the transport mechanism relative to the crack, which is regarded as potentially harmful to the corrosion process, as they provide preferential paths for external agents to penetrate the reinforced location (Berrocal et al. 2017; Berrocal et al. 2018; Hou et al. 2021). Fiber-reinforced concrete (FRC) has been studied and applied for decades for various construction due to its advantage of providing the toughness and more ductile behavior that are commonly considered the disadvantages of plain concrete (Micelli et al. 2020). With appropriate volume content of steel, fiber can increase crack resistance, ductility (Sahin ¸ and Köksal 2011), cyclic loading capacity (Boulekbache et al. 2016), impact, and fatigue resistance for concrete (Yoo et al. 2015a). Fibers are more effective in improving the post-cracking behavior of concrete, thanks to fiber-bridging mechanisms across the crack surface, it inhibits cracking and limits the high brittleness of conventional concrete (Lee et al. 2017; Abbass et al. 2018; El-Sayed 2019; Nassani 2020). It consequently increases the ductility and capacity of absorbing energy and durability of concrete (Yoo et al. 2015b). Since the FRC could be applied in structures such as bridges, harbor piers due to its limit the crack, using FRC exposed to the chloride environment has become

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a controversial issue. There is a lack of relation to the durability of SFRC structural elements exposed to chloride. Thanks to these aforementioned problems, this research aims to investigate the correlation between the loading capacity of SFRC beams with the degree of corrosion. The mill cut steel fiber is utilized in this study due to its advantages, such as no fiber balling while mixing, non-subsidence, and non-outcrop. Three values of volume contents of fiber 0.5, 1.0, and 1.5 percent were used, and the level of corrosion was considered as 5 percent mass loss of the steel. The corrosion of steel reinforcement is accelerated by applying the impressed current method utilizing current densities of 250μA/cm2 (Caré and Raharinaivo 2007; Ahmad 2009).

2 Materials and Experimental Methods 2.1 Materials and Mixture Proportion Materials were used in this study consisting of ordinary Portland cement type 1, fine aggregates as.river sand, coarse aggregates with a maximum size of 20mm, chemical admixture as the superplasticizers (SP), and the addition vary volume fractions of steel fibers. The RC beam was reinforced by round and deformed bars with yield strengths were 240 MPa and 390 MPa, respectively. The hook-end steel fiber has a rough surface, twisted along the length, and tensile strength is more than 700 MPa. The physical property of mill cut steel fiber is illustrated in Fig. 1, and other properties are listed in Table 1. Table 1. Properties of mill cut steel fibers Average length (mm)

Diameter (mm)

Tensile strength (MPa)

Young modulus (GPa)

Density (kg/m3 )

32.0 ± 2.0

2.6 ± 1.2

≥700

200

7850

Fig. 1. The geometry of mill cut steel fibers

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The concrete was designed to achieve a compressive strength of 40 MPa at 28 days having the water/cement ratio of 0.4 with a slump of 14 ± 2 cm, which was cast on both the plain and SFRC beams. The mixture proportion of materials is shown in Table 2. In total, 24 cylinders with 100 mm in diameter and 200 mm in height, six specimens for each mixture with three different volume fractions of 0.5%, 1.0%, and 1.5% of fiber equivalent to 39 kg, 78 kg, and 117 kg were cast for the compressive test at 7 and 28 days. Table 2. Mixture proportions of RC beams Mix design

Cement (kg)

Water (L)

Sand (kg)

Gravel (kg)

Plain

445

178

666

1126

2.2 Fabrication of the Beam Specimens Eight beams including RC and SFRC were of identical dimensions with a rectangular section of 150 × 200 mm and a length of 1400 mm was cast to study the flexural behavior of corrosive SFRC beam. The beam was designated as C5F10, where C and F denote the degree of corrosion and fiber volume content, respectively. The configuration of the specimens was demonstrated in Fig. 2 with the same tensile reinforcement ratio. These specimens were reinforced with four longitudinal deformed steel bars diameter of 12 (two placed in the compression zone and two in the tensile zone) and transverse round steel bars with 6 mm diameter equally spaced 100 mm arranged within a span. To avoid local pitting corrosion causing the shear failure, known as the brittle failure, the stirrup, and the anchor bars was coated with epoxy to prevent the formation of corrosive products. All beams were cast into the steel molds. For steel fiber reinforced concrete, extra time was inquired to improve the higher volume fraction and well dispersion rheology. The specimens were demoulded after the first 24 h and cured under humidity conditions and temperature for 28 days by covering and watering 2–3 times daily.

Fig. 2. Detail of the section of the beam’s elements

The impressed current technique was applied to accelerate corrosion of the primary reinforcement embedded in the SFRC beam within a short period. These beams were

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submerged into the 3% sodium chloride environment with the solution depth were equivalent to concrete cover thickness to allow the entrance of both humidity and oxygen. After the first 24 h, these specimens were ensured in a saturated condition, and a constant direct density was applied. Figure 3 shows the detail of the impressed current technique; a water tank was built for the facility for the technique. The steel bars were connected to the positive terminal of the DC power source, while the negative terminal was connected to a stainless-steel plate placed along the length of the beam. In order to obtain the degree of corrosion of steel bar equal to 5 percent, a constant current density of 250 μA/cm2 was set for all specimens for approximately 38 days. t=

zFm MiS

(1)

The corrosion times can be determined based on the Faraday laws where F is Faraday’s constant (96500 C/mol), z is the ionic charge number (z = 2) of iron, m is the mass loss of corroded reinforcement (g), M is the molar mass of iron (56 g/mol), i is the corrosion current density (A/cm2 ), and S is the superficial area of rebar within the corrosion region (cm2 ).

Fig. 3. Accelerated corrosion setup.

Fig. 4. Four-point bending test setup.

2.3 Test Method Eight beams had been tested under four points bending up to failure. Figure 4 demonstrates the flexural strength test setup for the specimens with 1200 mm effective span and 400 mm shear span. A load cell with a maximum capacity of 200 kN was used as a

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monitor with a rated load of 0.2 mm/min. Three linear variable differential transducers were attached at the mid-span and support to measure the vertical deflection corresponding to load capacity. Moreover, A strain gauge was attached to the surface concrete at the middle top of the beams to measure the strain at the compressive zone. Another two strain gauges were set in the tensile zone and shear zone. All of the measurements were connected to the data logger, transferred to the computer, recording all of the data during the test. The original and damaged weight of steel rebars were recorded to measure the degree of corrosion. The corroded steel bars were extracted from concrete and immersed into a 3,5 g hexamethylenetetramine solution diluted in 500ml of hydrochloric acid and 500 ml of reagent water for at least ten minutes to remove the rust according to the procedures of ASTM G1-03. The bars were taken out of the solution, washed with clean water, and then measured the mass to determine the level of corrosion following the equation. Where ρ = percentage loss due to corrosion (%), Wi mass of reinforcing steel before corrosion (g), Wf mass of reinforcing steel under corrosion (g).   wi − wf × 100 (2) ρi = wi

3 Result and Discussion 3.1 Effect of Volume Content SF on the Flexural Strength of RC Beams The load capacity of the SFRC beams under four-point loading is indicated in Table 3. The test result showed that the load capacity of the SFRC beams improved proportionally to the volume content fibers utilized. The addition of volume fraction steel fiber from 0.5% to 1.5% increased both the RC beam’s yield and ultimate load capacity. The ultimate failure load of beam C0F0 is 120.85 kN, whereas the SFRC beams had higher failure loads ranging from 123.08 kN to 133.11 kN. After the yield strength was reached, the load capacity was strongly dependent on the volume fraction of steel fiber which transferred the load through the crack by the bridge mechanism. Furthermore, fiber presentation increases the steel cross-section area playing an essential role in resisting tensile stress. Nevertheless, this increase was insignificantly for plain RC beam since the improvement is only 10% or even a negligible effect for the case of lesser fiber content. While the ultimate load capacity of SFRC beams was slightly enhanced compared to the RC beam, the load-deflection curve was noticeable, as shown in Fig. 5. The ascending part clearly showed that the deflection of SFRC beams was lower than the RC beam under the same load stage, particularly those containing a higher quantity of SF. 3.2 Effect of Corrosion on the Flexural Strength of RC Beams The corrosion of steel is accelerated by the impressed current method was achieved. The average degree of corrosion determined by Eq. 2 is equal to 5.1% compared to the 5% theoretical evaluation. Despite the difference between natural corrosion and artificial corrosion, the technique still is reliable to generate corrosion considering a lost mass

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40 20 0 0

5

10 15 Deflection (mm)

20

25

Fig. 5. Load deflection curve of SFRC beam

140

140

120

120

100

100

80 60

C0F0

Load (kN)

Load (kN)

of steel. Figure 6 illustrates the correlation between the load capacity and deflection of the corroded RC beams under static load. The load-deflection curve exhibited the reduction load capacity of the corroded RC beam. Due to corrosion, the loss of crosssectional tensile reinforcement, subsequently loss of mechanical properties of corroded steel bar degraded the performance of structural element contemporaneously. As a result, beam C5F0 experienced a decrease in ultimate load and yield load capacity by 21.3% and 24.6%, respectively. In addition, the ultimate deflection of the beam C5F0 is dramatically higher at 41% than the non-corrosive RC beams.

80 C5F0

60

C5F5

40

40 C5F0

20 0

C5F10

20

C5F15

0 0

5

10 15 Deflection (mm)

20

25

0

5

10 15 Deflection (mm)

20

25

Fig. 6. Load-deflection curve of corroded RC and SFRC beams

3.3 Load-Deflection Curve of Corroded SFRC Beams Figure 6 illustrates the relationship between the deflection and load capacity of the corroded SFRC concrete beams. Those corrosive SFRC beams were observed to have a tendency similar to non-corrosive SFRC beams; yield and ultimate load capacity improved linearly according to the volume contents of steel fiber. However, the corrosive RC beams experienced a more significant reduction of ultimate load capacity. Nevertheless,

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the corroded SFRC beams showed considerably maintained load capacity; for instance, the ultimate failure load of beam C5F5 was reduced by 10% or even unchanged in the case of beam C5F10. In general, the corroded RC shows a loss of performance due to the loss of cross-section of the tensile bar. With sufficient volume fraction of steel fiber still maintains the performance of RC beams. Due to steel fiber serving as compensation for the loss of reinforced and rising the amount of reinforcing steel to the beam cross-section then, the flexural strength was improved better than the non-fiber corroded beams. There was a growth ultimate deflection of the corroded SFRC beams. Figure 7 demonstrated that the rising both deflection and load capacity of corroded SFRC was more significant than the non-corrosive SFRC. The steel fiber not only compensated the load capacity of corrosive RC but also provide more deflection since beam C5F15 showed the ultimate deflection reached 22 m whereas this number was 14.58 mm for beam C5F0. Table 3. Experimental program test result Specimen

Yield Load fy (kN)

Ultimate Load fu (kN)

Deflection y (mm)

Deflection u (mm)

120.85

2.91

10.34

C0F0

80.88

C0F5

107.79

123.08

4.41

9.96

C0F10

115.27

129.73

5.36

10.56

C0F15

110.43

133.11

4.69

9.94

C5F0

60.98

95.05

2.64

14.58

C5F5

96.17

111.77

7.84

11.45

C5F10

109.38

122.28

6.55

12.64

C5F15

102.22

132.63

3.49

22.02

25

140

Ultimate deflection mm

120

Ultimate Load kN

100 80 60 40 20

20 15 10 5 0

0 C0F0 C0F5 C0F10C0F15 C5F0 C5F5 C5F10C5F15

C0F0 C0F5 C0F10 C0F15 C5F0 C5F5 C5F10 C5F15

Fig. 7. Ultimate load capacity and deflection of the specimen

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4 Conclusion This study investigated the flexural strength of corroded SFRC beams containing different volume fractions of fiber. The load-bearing capacity of artificial corroded SFRC beams under static load was presented. Based on the result obtained from the experimental program, the following conclusion can be drawn: 1. Using mill cut steel fiber combined with the steel-reinforced slightly improved both yield and ultimate strength of the SFRC beams, nevertheless SF provides greater stiffness for RC beams to reach lower deflection under the same load stage. 2. The load capacity of corroded RC beams decreased dramatically with the corrosion of a couple of tensile bars. At corrosion ratios of about 5%, ultimate load capacity was reduced by 21.3% compared to the RC beams. 3. The sufficient amount of steel fiber perfectly enhanced some limits of the mechanical behavior of the corroded RC beam. The steel fiber maintained the load capacity by transferring the stress through the cracks such as the beam C5F15 reached the ultimate strength equally to C0F15. Currently, there are few studies carried out on the durability of corroded SFRC, the controversial problem is still unclear. Therefore further experimental study or simulation work with various degrees of corrosion is still required for fully understanding the behavior of corroded SFRC elements. Acknowledgements. This research was carried out at the Laboratory for Concrete and Material Testing, Department of Civil Engineering, Chulalongkorn University. It was funded by The Asahi Glass Foundation.

References Abbass, W., Khan, M.I., Mourad, S.: Evaluation of mechanical properties of steel fiber reinforced concrete with different strengths of concrete. Constr. Build. Mater. 168, 556–569 (2018) Ahmad, S.: Techniques for inducing accelerated corrosion of steel in concrete. Arab. J. Sci. Eng. 34, 95 (2009) Almusallam, A.A.: Effect of degree of corrosion on the properties of reinforcing steel bars. Constr. Build. Mater. 15, 361–368 (2001) Berrocal, C.G., Fernandez, I., Lundgren, K., Löfgren, I.: Corrosion-induced cracking and bond behaviour of corroded reinforcement bars in SFRC. Compos. B Eng. 113, 123–137 (2017) Berrocal, C.G., Löfgren, I., Lundgren, K.: The effect of fibres on steel bar corrosion and flexural behaviour of corroded RC beams. Eng. Struct. 163, 409–425 (2018) Bicer, K., Yalciner, H., Balkıs, A.P., Kumbasaroglu, A.: Effect of corrosion on flexural strength of reinforced concrete beams with polypropylene fibers. Constr. Build. Mater. 185, 574–588 (2018) Boulekbache, B., Hamrat, M., Chemrouk, M., Amziane, S.: Flexural behaviour of steel fibrereinforced concrete under cyclic loading. Constr. Build. Mater. 126, 253–262 (2016) Broomfield, J.: Corrosion of Steel in Concrete: Understanding, Investigation and Repair. CRC Press (2003)

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Caré, S., Raharinaivo, A.: Influence of impressed current on the initiation of damage in reinforced mortar due to corrosion of embedded steel. Cem. Concr. Res. 37, 1598–1612 (2007) Du, Y., Cullen, M., Li, C.: Structural performance of RC beams under simultaneous loading and reinforcement corrosion. Constr. Build. Mater. 38, 472–481 (2013) El-Sayed, T.A.: Flexural behavior of RC beams containing recycled industrial wastes as steel fibers. Constr. Build. Mater. 212, 27–38 (2019) Fang, C., Lundgren, K., Chen, L., Zhu, C.: Corrosion influence on bond in reinforced concrete. Cem. Concr. Res. 34, 2159–2167 (2004) Hou, L., Peng, Y., Xu, R., Zhang, X., Huang, T., Chen, D.: Corrosion behavior and flexural performance of reinforced SFRC beams under sustained loading and chloride attack. Eng. Struct. 242, 112553 (2021) Lee, J.-H., Cho, B., Choi, E.: Flexural capacity of fiber reinforced concrete with a consideration of concrete strength and fiber content. Constr. Build. Mater. 138, 222–231 (2017) Marcos-Meson, V., Michel, A., Solgaard, A., Fischer, G., Edvardsen, C., Skovhus, T.L.: Corrosion resistance of steel fibre reinforced concrete—a literature review. Cem. Concr. Res. 103, 1–20 (2018) Micelli, F., Renni, A., Kandalaft, A.G., Moro, S.: Fiber-reinforced concrete and ultrahighperformance fiber-reinforced concrete materials. In: New Materials in Civil Engineering. Elsevier (2020) Nassani, D.E.: Experimental and analytical study of the mechanical and flexural behavior of hybrid fiber concretes. In: Structures, pp. 1746–1755. Elsevier (2020) Ou, Y.-C., Susanto, Y.T.T., Roh, H.: Tensile behavior of naturally and artificially corroded steel bars. Constr. Build. Mater. 103, 93–104 (2016) Poursaee, A.: Corrosion of steel in concrete structures. In: Corrosion of Steel in Concrete Structures. Elsevier (2016) Sahin, ¸ Y., Köksal, F.: The influences of matrix and steel fibre tensile strengths on the fracture energy of high-strength concrete. Constr. Build. Mater. 25, 1801–1806 (2011) Tondolo, F.: Bond behaviour with reinforcement corrosion. Constr. Build. Mater. 93, 926–932 (2015) Yalciner, H., Kumbasaroglu, A., El-Sayed, A., Balkıs, A.P., Dogru, E., Turan, A., Karimi, A., Kohistani, R., Mermit, M., Bicer, K.: Flexural strength of corroded reinforced concrete beams. ACI Struct. J. 117 (2020) Yoo, D.-Y., Yoon, Y.-S., Banthia, N.: Flexural response of steel-fiber-reinforced concrete beams: effects of strength, fiber content, and strain-rate. Cem. Concr. Compos. 64, 84–92 (2015) Yoo, D.-Y., Yoon, Y.-S., Banthia, N.: Predicting the post-cracking behavior of normal-and highstrength steel-fiber-reinforced concrete beams. Constr. Build. Mater. 93, 477–485 (2015) Yu, L., François, R., Dang, V.H., L’Hostis, V., Gagné, R.: Structural performance of RC beams damaged by natural corrosion under sustained loading in a chloride environment. Eng. Struct. 96, 30–40 (2015) Zhang, W., Zhang, H., Gu, X., Liu, W.: Structural behavior of corroded reinforced concrete beams under sustained loading. Constr. Build. Mater. 174, 675–683 (2018)

Structures Under Blast Loads from Academic Research into Engineering Applications: Advances and Limitations Tin V. Do(B) and Asher Gehl Karagozian & Case (K&C) Australia, Bondi Junction, NSW 2022, Australia {van,gehl}@kcse.com.au

Abstract. Recent increases in terrorist activities and accidental explosions, e.g., the 2020 Beirut blast or gas explosion event in the North-eastern city of Shenyang, China in 2021, have caused devastating consequences and imposed significant threats to public safety and economic development. Together with direct primary effects from explosive events, i.e., primary shock pressure and/or secondary fragments, the indirect secondary effects caused by blast events such as the progressive collapse of structures are also critical when resulting in more widespread significant losses. Therefore, critical infrastructure, e.g., government buildings, public transport infrastructure, petrochemical, and hazardous material storage facilities, need to be carefully considered under these extreme loading events in their design and operations. In current engineering practices, Single-Degreeof-Freedom (SDOF) is typically utilised to design structures under far-field blast events, whilst finite element (FE) analysis is adopted when considering close-in or contact blast scenarios. With the recent developments of material models under high loading rates, e.g., K&C concrete material release III or Continuous Surface Cap concrete model (CSCM), and fluid-structure interaction simulation technique, e.g., Arbitrary Lagrangian-Eulerian (ALE), the capability and application of FE analysis in the blast effect analysis of structures under close-in blast events have increased considerably. Although FE and SDOF analyses developed in previous studies contribute to providing reasonable predictions on the blast performance of structures, there are several limitations that need to be resolved in order to increase the reliability of the analysis techniques employed to ensure accurate prediction of structural behaviour to these complex response modes. Typical studies normally focus on the structural member responses, i.e., flexural or shear responses, while connection forces between structural members have not been fully investigated. The accuracy of the FE model and SDOF in predicting the reaction at structural supports is still unknown. Moreover, the failure of concrete structures under closein blast events, e.g., concrete spalling and breaching or fragment velocity, is not considered to be accurately predicted by the abovementioned methods. Advances and limitations of those analysis methodologies are to be discussed in this study. Keywords: Blast effect analysis · Dynamic responses · Close-in blast · Finite element modelling · Dynamic reactions

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1413–1431, 2023. https://doi.org/10.1007/978-981-19-7331-4_113

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1 Literature Review In recent decades, government/political headquarters and critical infrastructure, i.e., bridges, metro stations, airports, stadiums have been the targets of terrorist attacks around the world as they are in critical locations of the city/country or present high concentrations of population. Terrorist activities have generally caused catastrophic consequences including number of fatalities, immense social disruption, and economic loss. For instance, with the series of 12 terrorist bombings, the 1993 Bombay bombings in India resulted in 257 fatalities and 1400 injuries (Dua et al. 2019). The detonation of 1818 kg trinitrotoluene (TNT) equivalent explosive at 4.5 m standoff distance in front of the Alfred P. Murrah Federal Building in Oklahoma City in 1995 caused 168 losses and hundreds of injuries (Longinow and Mniszewski 1996; Ngo et al. 2007). The blast event also resulted in the progressive collapse of a third of the building which was later demolished. The 7/7 attacks on the London transit system in 2005 caused the largest mass casualty event in the UK since World War 2 with the loss of 56 people and 775 casualties (Aylwin et al. 2006). On July 11, 2006, a series of terrorist bombs in Mumbai’s commuter train system in India resulted in 209 deaths and 714 injuries (Dua et al. 2019). In addition to terrorism events, numbers of accidental explosions within high-rise buildings or warehouses have also increased noticeably in recent years. For example, the explosions that occurred at a container storage station in Tianjin, China on August 12, 2015, killed 173 people and injured more than 700 (Yu et al. 2016). The explosion produced an enormous crater of more than 100m in diameter and damaged 304 buildings and 12,428 cars. On 4 August 2020, the accidental explosion of approximately 2750 tons of ammonium nitrate, i.e. 1.1 kilotons of TNT equivalent, stored at the Port of Beirut in the capital city of Lebanon, resulted in 218 deaths and over 7000 non-fatal injuries (Rigby et al. 2020; Valsamos et al. 2021). The explosion also created a blast crater approximately 43 m in depth and 124 m in diameter and caused damage to houses10 km away. In 2021, a gas explosion in the city of Shenyang in North-eastern China caused 4 deaths, 47 injures, and also resulted in substantial damage to buildings in the area. Accidental explosions have raised the necessity of appropriate risk and blast vulnerability assessments of locations including but not limited to petrochemical and explosive storage facilities, gas and electrical transformers at densely populated locations. Together with direct effects from explosion events, i.e., primary shock pressure and/or secondary fragments, the indirect secondary consequences caused by explosive events, i.e. the loss of critical structural elements leading to disproportionate collapse, are known to be more critical. Studies of structures under high magnitude but extremely short duration loading resulting from such an explosive event have therefore attracted a lot of attention from scientific groups all over the world (Do et al. 2020; Dua et al. 2019; Hao et al. 2016; Ngo et al. 2007; Yuan et al. 2017). Various types of structural and non-structural elements including RC slabs, beams, columns, steel structures, glass, and blockwork walls have been experimentally, numerically, and analytically studied under blast loads to develop an understanding of their blast performance and damage mechanism from which to adopt an appropriate design approach for each type of structure (Fischer and Häring 2009; Hao et al. 2016; Krauthammer et al. 1986; Ngo et al. 2007). In the practical design analysis of structures under blast loads, empirical calculation tools,

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i.e. Conventional Weapons (CONWEP), and Single-Degree-of-Freedom (SDOF) analysis methodology are widely adopted to derive the peak blast pressure and impulse on structures and to predict the structural performance, respectively. It is worth noting that the CONWEP algorithm which is developed based on the empirical data from Kingery and Bulmash (1984) is considered to be able to model a surface blast, i.e., hemispherical charge, and a free-air blast, i.e., a spherical charge, whilst the SDOF analysis is considered an effective tool to determine the dynamic responses and performances of structures under a far-field blast event when the flexural response is predicted to govern the structural performance (Hao et al. 2016). However, there are some limitations associated with CONWEP and SDOF analysis that requires then to be used carefully. CONWEP is not considered to provide accurate predictions of the blast parameters under the close-in blast event or within a confined or partially confined space. Additionally, the shock wave propagation and interaction with surrounding structures cannot be reliably predicted by using CONWEP. In terms of SDOF analysis which idealises the structural element as an equivalent mass and stiffness, the load factor on the equivalent system is determined by the assumed deflected shape of the structure under uniform or concentrated loading conditions. Thus, when the loading condition is non-uniform, i.e., resulting from a closein blast event, or the performance of structures is governed by other response modes, i.e., diagonal or direct shear response, SDOF analysis is not able to accurately predict the structural performance. Moreover, when the ratio of the blast duration to the natural vibration period of the member is small, the structural performance is considered to be dominated by stress wave propagation resulting in concrete spall or breach failure, whilst the global performance of the member has not been activated in that short duration. In that condition, the use of SDOF analysis is not considered appropriate. To account for the localised effects of a close-in blast event or the confinement effects when the detonation is located in a confined environment, finite element (FE) analysis via commercially available software such as ANSYS/LS-DYNA, AUTODYN is generally adopted (Do and Nguyen 2021; Do et al. 2020; Hao et al. 2016; Li et al. 2019; Yan et al. 2015; Yuan et al. 2017). The applicability of the FE analysis in predicting the structural performance under close-in blasts has been proven and reported in the previous studies (Dua et al. 2019; Dua et al. 2020; Yuan et al. 2017). In this study, recent developments in the material models, dynamic increase factors, and fluid-structure interaction simulation methodology via LS-DYNA, which can be utilised to predict the close-in/contact blast performance of structures, will be introduced. These advances will then be adopted to develop High-Fidelity Physics-Based (HFPB) FE models of a reinforced concrete (RC) and composite columns under close-in and contact blast events. Comparisons between numerical simulation results and experimental results are also undertaken to demonstrate accuracy as well as the applicability of the simulation technique presented. The applications of these advances in practical blast design applications are then discussed in the later section. Limitations of the FE analysis observed during the design analysis are also presented in this study for future consideration.

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2 FE Simulation Techniques for Close-In Blast 2.1 Arbitrary Lagrangian-Eulerian Simulations The LS-DYNA ALE/FSI (Arbitrary Lagrangian-Eulerian/Fluid-Structure Interaction) package is one of the most common techniques that has been used in recent studies to investigate the blast response of structures under close-in and contact blast (Do et al. 2020; Dua et al. 2020; Wu et al. 2011; Yuan et al. 2017). Although this simulation technique is generally time-consuming and requires a large amount of computational resources due to the simulation of Eulerian materials, i.e. structured mesh of the air domain, the ALE solver offers a feasible solution to simulate the shock wave-structure interaction and predict local failures of structures under close-in blast effects, i.e. shear failure, concrete crushing. The application and accuracy of the ALE simulation technique in predicting the responses of RC and steel structures under close-in blast loads have been reported in recent studies (Dua et al. 2019; Dua et al. 2020; Yuan et al. 2017). In this section, advances from the previous studies including material models, equations of state, and dynamic increase factors that were developed and proposed for concrete, reinforcement, air domain, TNT material and reinforcement for the ALE simulation in LS-DYNA are summarized and briefly introduced. The detailed input parameters for each material can be obtained from the previous studies (Do et al. 2020; Dua et al. 2019; Dua et al. 2020; Yuan et al. 2017) and they are not presented here to prevent repetition. Various concrete models available in LS-DYNA can accurately predict the dynamic responses of concrete structures under high loading rates as reported in the previous studies, e.g. *MAT_CSCM_CONCRETE (Mat_159) (Dua et al. 2020; Fan et al. 2019; Li et al. 2019), *MAT_WINFRITH_CONCRETE (Mat_0.84-0.85) (Thai and Kim 2016; Wu et al. 2012). Among the available material models, the K&C concrete model, i.e. *MAT_072_REL3, is one of the most efficient models to simulate the dynamic responses of reinforced concrete (RC) structures which have been widely adopted in recent studies (Liu et al. 2020; Liu et al. 2018; Yan et al. 2015). The K&C concrete material model includes three independent strength surfaces; namely yield strength, maximum strength, and residual strength surfaces (Magallanes et al. 2010; Wu et al. 2014; Wu et al. 2012). The strength surfaces can be determined in a generalised form as follows. Fi (p) = aoi +

p a1i + a2i p

(1)

where i stands for y, m, r, which are the yield strength surface, the maximum strength surface, and the residual strength surface, respectively, p is the pressure; and aji (j = 0, 1, 2) are the calibrated parameters (Magallanes et al. 2010; Wu et al. 2012). The failure surface of the material model is interpolated between either the yield or residual strength surfaces and the maximum strength surface. This material model can accurately predict both local failures, i.e. concrete crushing, direct shear failure, and global response of RC structures, i.e. flexural cracks under blast loads (Do et al. 2018; Li and Hao 2014). It is noted that by validating the calibrated parameters, i.e., aji , and the shape of the hardening and softening regions of the stress-strain relationship, the K&C concrete material has been currently adopted for the analysis of steel fibre reinforced concrete (SFRC) or ultra-high performance concrete (UHPC) under impact and blast loads (Lee

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et al. 2021; Su et al. 2022). The material model shows its capacities in predicting the dynamic responses of various types of concrete structures under blast and impact loads. This material model also allows dynamic increase factor (DIF) to be incorporated in the simulation (Hallquist 2007). In this study, the compressive DIF and tensile DIF at different strain rates proposed by Hao and Hao (2014), are used. Furthermore, the LS-DYNA keyword *EOS_TUBULATED_COMPACTION was used to define the equation of state (EOS) of concrete under close-in blast in this study. It is worth mentioning that this EOS is the compulsory keyword for the simulation of concrete under extreme loading events when intensive pressure is applied to structural surfaces in a short duration of time (Hallquist, 2007). The compaction model used for concrete is defined as follows: p = C(εv ) + γ T (εv )E

(2)

where p is the pressure; E is the internal energy per initial volume; γ is the ratio of specific heat; εv is the volumetric strain which is given by the natural logarithm of the relative volume, V. The relationship between pressure and volumetric strain can be obtained from (Magallanes et al. 2010). The LS-DYNA keyword *MAT_NULL (*Mat_009) was used to model the air domain in the simulation. The EOS of the air domain is defined by using the keyword *EOS_LINEAR_POLYNOMIAL, with the pressure related to the energy, and can be expressed as follows: p = Co + C1 μ + C2 μ2 + C3 μ3 + (C4 + C5 μ + C6 μ2 )E

(3)

where Co ~C6 are the constant input parameters; μ = ρ/ρo − 1, ρ/ρo is the ratio of the current density to the initial density; and E is the energy per initial unit volume. The input values of these parameters can be obtained from Yuan et al. (2017). The TNT charge was modelled by using *MAT_HIGH_EXPLOSIVE_BURN (MAT_008) material model, while the EOS for TNT was defined by the *EOS_JWL keyword with the pressure, and is defined as follows:     ω ωE ω e−R1 V + B 1 − e−R2 V + (4) p=A 1− R1 V R2 V V where p is hydrostatic pressure; A, B, R1 , R2 and ω are the material parameters; E is the energy per initial unit volume; and V is the relative volume or the expansion of the explosive. The LS-DYNA material model namely *MAT_PIECEWISE_LINEAR_PLASTICITY (*MAT_024) was utilised to simulate longitudinal and transverse reinforcements (if applicable). The DIF of steel reinforcements at different strain rates, ε˙ d , was obtained from Malvar and Crawford (1998) and presented below:  DIF =

ε˙ d 10−4

0.074− 0.04fy

where f y is the yield strength of steel in MPa.

414

(5)

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In the simulation, a lagrangian constant stress solid element type (ELFORM 1) is used for concrete material, while a 1-point ALE multi-material element type (ELFORM 11) is used for the air elements and TNT material. Beam elements are used for steel reinforcement. The location and geometry of the TNT charge are defined through the INITIAL_DETONATION card and INITIAL_VOLUME_FRACTION_GEOMETRY. The interaction between the air domain and structures is defined by using the CONSTRAINED_LAGRANGE_IN_SOLID keyword in LS-DYNA. 2.2 ALE Simulations Versus Contact/Close-In Blast Testing Results In this study, the experimental tests of a circular RC column under contact blast conducted by Yuan, et al. [3] are used to validate the blast simulation technique and localised responses of concrete under contact blast effects (see Fig. 1a). The diameter and the length of the column were 400 mm and 3700 mm, respectively. The compressive strength of concrete was 38.5 MPa. The column was reinforced by 10N12 longitudinal reinforcement, N8a100 stirrups near the column ends (600 mm at the two ends) and N8a150 in the middle part of the columns, see Fig. 1b. The nominal yield strength of the longitudinal and transverse reinforcement was 400 MPa and 300 MPa, respectively. The column was connected to a strong concrete footing which was buried underground, while the column top was constrained by a steel frame fixed to a reaction wall. The columns were tested under 1 kg TNT attached to the column surface at the height of 330 mm above the ground level. The accelerometers were installed on the back face of the column to record the column accelerations during the blast test. A comparison between the experimental and numerical results is presented in Figs. 2 and 3 in which the damage to the concrete close to the blast location, i.e., concrete crushing, and the acceleration of the column at 330 m above the ground is reasonably predicted by the ALE simulation. Figure 4 shows the experimental setup of a concrete-filled double steel tube column (CFDST) under close-in blast events conducted by Li et al. (2021). In the experiment, the outer diameter of the column was 325 mm, whilst the inner diameter of the steel tube was 159 mm. The thickness and the yield strength of the steel tubes were 6 mm and 345 MPa, respectively. Concrete with the compressive strength of 40MPa was filled in the gap between the two steel tubes. The column which was 2.5 m high was fixed at the base through the heavy footing that was buried underground, whilst the pinned connection to the header beam was used at the top of the column. To represent the gravity load of the superstructure, the column was axially loaded with 500 kN through the high-strength threaded steel bear as noted in the figure. The column was considered under two close-in blast conditions in that study, i.e. 5 kg TNT and 8 kg TNT at 200 mm standoff distance. The height of the TNT charges was considered at 500 mm from the ground level. After the blast tests, the columns were brought to the laboratory and then axially loaded until failure to capture their residual capacity. From the ALE simulation technique presented in the previous sections, the High-Fidelity Physics-Based (HFPB) Finite Element (FE) model of the CFDST column has been developed in LS-DYNA. The HFPB FE simulation process consists of three continuous phases, i.e., preload the column with 500 kN, ALE blast simulation phase, and residual capacity after the blast phase. It is worth mentioning that the residual capacity of the column is determined by applying the axial displacement at the top of the blast damage column until failure. The

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N8a100 670

400

10N12

COLUMN CROSS-SECTION

500

N8a100 630

Acceleromete

400 1000

3700

N8a125 2400

1000

1000

(a) The column testing setup

(b) Reinforcement details

60 cm

64 cm

Fig. 1. Experimental test setup of the columns under contact blast (Yuan et al., 2017)

Front view

Left side view

Right side view

Back view

Fig. 2. Comparisons of damage to concrete under contact blast. Experimental data obtained from Yuan et al. (2017)

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Max: 15,000 m/s2

Acceleration (m/s2)

13,000

Max: 13,000 m/s2

6,500

Experiment Simulation

0 -6,500 Min: -13,000 m/s2

-13,000

Min: -14,500 m/s2

-19,500

0

2

4 Time (ms)

6

8

Fig. 3. Comparisons of acceleration of the column under contact blast. Experimental data obtained from Yuan et al. (2017)

peak value from the axial force—axial displacement curve from the compression test is called the residual capacity of the column. Figure 5 compares the local performance of the columns, i.e., local denting at the height of the TNT charge, under two different load cases between the experimental test and ALE simulation. The ALE simulation presented in this study can accurately predict the local deformation of the CFDST column along its length with the difference between the simulation and the testing results being under 10%. The axial force-displacement curves of the columns after the close-in events predicted by the experiment and ALE simulations are shown in Fig. 6. The residual capacities of the columns were 4760 kN under 5 kg TNT and 3700 kN under 8 kg TNT, whilst those in the simulation are 5030 kN and 3936 kN, respectively. The difference between the test and the simulation is under 10%, which is far above the expectation from the FE numerical simulation when considering the difficulty and the complexity of the close-in blast events. The comparisons between the numerical results and experimental blast testing results demonstrated that with the current developments and the advances in the ALE simulation technique, the dynamic performance and failure of different types of structures, e.g., RC column or composite column such as CFDST, under the close-in/contact blast events can be reasonably predicted. The use of the ALE simulation thus significantly enhances the level of accuracy in the design analysis of structures under blast loads and contributes to reducing project costs in comparison to undertaking experimental blast tests. Additionally, these advances contribute toward effective and reliable design processes for protective structures and safeguard the community from accidental explosions or terrorist attacks.

3 Engineering Applications and Limitations This section presents the application of the ALE simulation technique in LS-DYNA in contributing to solving actual engineering problems such as blast design of RC columns and connections, blast effect analysis of RC structures in the confined area, undertaken

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(a) Overview of the blast test setup

5kg TNT@200mm

8kg TNT@200mm

(b) Two different blast loading conditions considered to be simulated in this study Fig. 4. Concrete filled double steel tube columns under close-in blasts (Li et al. 2021)

by K&C Australia. Challenging issues observed in the design analysis of structures under blast loads including designing connections to resist peak dynamic reactions, predicting concrete spalling and breaching or fragment velocity under close-in events, will be presented and discussed. Figure 7a shows the blast performance of a 600mm diameter RC column under a close-in blast event, i.e., the scaled distance of 0.116 m/kg1/3 . The column was heavily

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Local denting: 29.5

(a) Under 5kg TNT

Local denting: 70.0

Fig. 5. Local deformation of the column under the blast load. Experimental data obtained from (Li et al. 2021) 6,000

5030kN

Axial force (kN)

4760kN 4,500 3700kN 3,000

3936kN

1,500

0

ALE - 5kg TNT ALE - 8kg TNT Test - 5kg TNT Test - 8kg TNT

0

5

10 15 20 Axial displacement (mm)

25

Fig. 6. Residual capacity of the column after the close-in blast loads. Experimental data obtained from (Li et al. 2021)

reinforced with vertical reinforcement ratio of 2% and shear reinforcement ratio of 1.5%. Due to the close-in effect of the blast event, severe damage to the concrete cover

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is predicted by the ALE simulation. However, with heavy shear reinforcement provided, no breaching or direct shear failure to the column base is predicted under the blast event. Thus, the damaged column was still able to support the vertical load after the blast event. The residual capacity of the column was predicted at approximately 30.1% of its initial capacity. The numerical results indicate that the ALE simulation can provide a feasible tool to predict the performance of the structures under close-in blast events where SDOF analysis is not considered appropriate for such events. It is also worth highlighting that at K&C we have developed an empirical technique named CBARD that is able to predict the performance of columns under close-in blasts including the damage level, the dynamic reaction time histories at the column base, and residual capacity index, but is not widely used in industry (Gehl et al. 2019). Figure 7b presents the reaction time histories predicted at the base of the column during the blast event in which the peak shear reaction is predicted at 5236.5 kN. It is noted that to reduce the computational time and resource, the base of the column is typically assumed with the fixed boundary condition in the ALE simulation and there is no substructure or footing considered. Therefore, in the design analysis of the structure, the peak dynamic shear reaction obtained from the FE analysis then needs to be considered in the design of the column-substructure connection. However, the predicted peak shear reaction is generally higher than the static/dynamic direct shear capacity of the structure. In this case, the peak dynamic shear force is 5236.5 kN, whilst the dynamic direct shear capacity is 4490 kN. It is noted that the dynamic direct shear capacity of RC structures under blast load can be determined according to the recommendation from UFC-3-340-02 (2008) as follows: Vd = 0.16fdc bd

(6)

where f dc is the dynamic compressive strength of concrete (MPa), bd is the effective area of RC concrete structure (mm2 ). Hawkins (1982) proposed an empirical equation to predict the direct shear capacity of RC structure under blast load by utilising a piecewise linear approach to relate direct shear strength and the corresponding shear slip values. Krauthammer et al. (1986) then modified the equation to consider the dynamic enhancement factor of 1.4 as follows:  6.895A   (N ) (7) Vd = 1.4 8 145fc + 0.8ρv 145fy 1000 where f c is the compressive strength of concrete (MPa), ρv is the geometrical reinforcement ratio; A is the cross-section area of RC structure; f y is the yield strength of shear reinforcement. Another empirical equation that can be considered in the design of RC structures under the shear reaction caused by blast load is using an effective coefficient of friction from PCI recommendation (Tanner 2008) as follows: Vn = Avf fy μλ

(8)

where Avf (mm2 ) and f y (MPa) are an area of shear-friction and yield strength of reinforcement, respectively; μ is coefficient of friction: 1.4λ, 1.0λ, 0.6λ or 0.7λ for monolithic concrete, concrete to hardened concrete contact with roughened contact, concrete

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to concrete contact, or concrete to steel contact, respectively; λ is the modification factor related to the density of concrete: 1.0 for normal concrete; 0.85 for sand-lightweight concrete, and 0.75 for all other lightweight concrete.

Localised damage of concrete cover

Explosive t = 5 ms

t = 30 ms

(a) Damage to the column

(b) Shear reaction time histories at the column base Fig. 7. Example of a circular RC column subjected to a close-in blast event

It is worth mentioning that the peak shear reaction at the base of the 400mm diameter column considered in the contact blast test by Yuan et al. (2017) presented in Sect. 2 is predicted at approximately 1630kN by the ALE simulation. By using Eqs. (6), (7) and (8), the dynamic direct shear capacity of the column can be predicted at 851.5 kN, 884.2 kN, 791.7 kN respectively, which is smaller than the peak direct shear reaction

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predicted by the ALE model. However, there is no direct shear failure at the column base observed in the blast test and the ALE simulation with the footing being considered in the analysis. These results have presented two main concerns that need to be considered in the blast effect analysis: 1. The accuracy of the ALE simulation in predicting the dynamic shear reaction. 2. The accuracy of the presented empirical equations in predicting the dynamic shear capacity of RC structures. It should be noted that although the accuracy of the ALE simulation has been widely validated against the experimental results in terms of pressure time histories, structural performance, damage to concrete, and failure mechanism as presented in the previous sections, the validation of the reaction time histories at the structure supports is still questionable when there is limited experimental testing data for the reaction under closein/contact blast due to the complexity of the blast test and the capacity of the testing instrument. It is suggested that the reaction time histories at the structural support should be taken into consideration in future studies of structures under blast loads to develop a better understanding of the requirements for the connection design. More research works on the dynamic shear capacity of RC structures are also necessary. For the 600mm diameter column considered in the analysis presented in Fig. 7, a significant amount of longitudinal and shear reinforcement was nominated in the column to resist various failure modes susceptible to the blast load and to accommodate the blast shear reaction of 5236.5 kN at the column base. Figure 8 shows the blast performance of a 1200 mm × 1000 mm rectangular column under a close-in blast event, in which the detailed connection at the column base, i.e., bolt connection between the base plates, and the connection between the starter bars and the base plates, was considered in the analysis. Since the precast concrete column was considered in the study, the connection between the structural elements is a critical location under the blast load; however, there is no empirical equation or analytical solution to predict the shear reaction at the base of the column for the connection design. In this study, K&C Australia have developed and followed a rigorous design process in order to provide an accurate and reliable design for precast structures under close-in blast events as presented below: (1) Step 1: Developing a detailed FE model of the precast column under the close-in blast event by using ALE simulation with the fixed boundary condition at the base. (2) Step 2: From the reaction time histories predicted by the ALE simulation in Step 1, the base connection was then designed statically to accommodate the peak dynamic shear reaction force. In this case, 80 mm thick base plates and 28M36 bolts were used to accommodate the peak dynamic shear reaction of approximately 12,000 kN from the close-in blast event. (3) Step 3: The detailed connection at the column base determined in Step 2 was then incorporated into the ALE simulation to investigate the actual blast performance of the proposed connection.

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Starter bars threaded to the base plates

Precast column

Bolts between base plates

Base plates See through base plates

RC wall under

(a) Connection between the precast column and substructure

TNT Charge

Detailed base connection (refer to Figure 8a)

Side view

Front view

Rear view

Middle section

(b) Performance of the column under close-in blast

Fig. 8. Precast RC column with a detailed base connection under close-in blast

Another challenging issue for structural engineers is reliably predicting the performance of structures when subject to blast within a confined space. The reflected surfaces from the surrounding objects/structures may substantially increase the blast impulse on the structures resulting in more deformation and damage to considered structural elements. Additionally, the shape of the reflecting surface, i.e. curved tunnels, has been demonstrated to sufficiently influence the load parameters in confined spaces. To account for the confinement effect, two design approaches are normally adopted as follows: 1. Using Computational Fluid Dynamic (CFD) simulations using solvers such as blastFoam (2019) or ArunaCFD (2015) to predict the blast pressure time histories on structural surfaces. The predicted blast time histories are then utilised as an input loading condition in the FE model of the structural elements.

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2. Using ALE simulation in LS-DYNA in which the air domain, TNT charge, and the detailed simulation of structures are considered. Each analysis approach has its pros and cons. The CFD simulation can significantly save the computing times but typically ignores the deformation of structures and the local damage of structure when predicting the pressure time histories on the structure surfaces, whilst the ALE simulation uses the coupled analysis but consumes more computational time and resources. An example of the blast assessment of structures within a confined space is presented in Fig. 9. In this example, the height of the column and walls was 6 m, and the length of the beams was 10 m. The scaled distances to the RC slab and columns were 0.27 m/kg1/3 and 0.43 m/kg1/3 , respectively. The second analysis approach, i.e., ALE simulation, was chosen for this example to accurately capture the influence of the blast load interaction with the local structural response of the considered slabs and walls. Heavy reinforcement was developed in the structural elements as shown in Fig. 9b to resist the high magnitude blast pressure. The blast performance of the structural elements is presented in Fig. 9c and 9d where severe flexural cracks occurred on both the front and back faces of the walls, and the top and bottom faces of the slab. Large deformation to the slab directly below the charge was also observed in the simulation, see Fig. 9c. It is worth highlighting that by adopting the recommendation in Section 4.55—UFC-3-340-02 (2008), a breach failure is predicted in the slab considered in this analysis; however, no concrete spalling failure of concrete was predicted by the simulation. It is worth noting that to prevent the concrete spalling and to reduce the hazard caused by high-velocity hazardous debris to the population in the protected level below and behind the walls, a standard UFC specified (UFC-3-340-02, 2008) single leg stirrup with 200 mm × 200 mm spacing was introduced in all structural elements in the analysis. Although no concrete spalling was predicted in the FE analysis, its applicability is still questionable when limited validation against testing results has been performed previously. It is considered challenging to accurately predict the concrete damage area, fragment sizes, and fragment velocities by using the presented material models and simulation techniques. Therefore, this secondary effect from the blast event is typically considered a residual risk/hazard in the design that needs to be appropriately communicated to the asset owner to ensure the simulation limitations are understood and accepted. Recently, Shi et al. (2020) have experimentally examined the fragment mass, fragment sizes, and splash distribution of an RC wall resulted from a close-in blast event, see Fig. 10. In the test, a 120mm RC wall was subjected to 2, 4, and 6 kg TNT at a 400 mm standoff distance. The slab was reinforced by N12@100 mm spacing in the primary direction and N12@200mm in the secondary direction. No shear tie was provided in the wall under these blast tests. The concrete spalling damage from the test is presented in Fig. 10. As reported, the maximum mass of the fragment was approximately 6 kg, whilst the maximum debris throw distance was recorded at 38m. The relationship between the fragment velocity and scaled distance is shown in Fig. 10c (Shi et al., 2020). In the figure, VHS is the ejecting velocity of the fragment determined using a high-speed camera, whilst Vcal is defined by using an analytical method based on the debris throw distance. It can be found that the maximum velocity of the fragment can

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RC Beams

RC slab RC walls

Air domain

(a) 3D view of structures within the confined space

(b) Detailed reinforcement within the RC members

Large deformation

(c) Damage to concrete after blast (front view)

(d) Damage to concrete after blast (back view)

Fig. 9. Example of blast performance of RC structure within the confined space

reach 100 m/s in the blast tests. The concrete damage with such high ejecting velocity may cause a major hazard to the population and critical equipment behind/ under the RC structures. Additionally, such high velocity debris may result in additional impact load that may induce secondary risks to structures. In design practice, an appropriate design spall catching system or steel plate can be used at the rear surface of the structure to reduce the above-mentioned secondary effect of the blast event. However, there is no analytical method available in the open literature that can be used to accurately predict fragment sizes and fragment velocities under close-in blast events.

4 Conclusions This study summarises the recent developments in the finite element analysis of structures under close-in blast events by using the ALE simulation technique available in LS-DYNA. The material models and equation of state for concrete, reinforcement, air domain, and TNT proposed and presented in previous studies are briefly reproduced in this study. The comparisons between the ALE simulations and experimental blast testing results in terms of concrete damage, dynamic performance, and residual capacity are undertaken to demonstrate the applicability and accuracy of the ALE simulation in predicting the blast performance of various types of structures under contact/close-in blast events. The applications of the ALE simulation in resolving a selection of actual engineering problems are then presented in Sect. 3 of this paper. From the lessons learned in

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(b) Fragments far field behind the wall

(c) Relation between fragment velocities and scaled distance

Fig. 10. Concrete damage under close-in blast event (Shi et al. 2020)

the blast analysis of RC structures, two main concerns have been raised in this work, i.e., the accuracy of the ALE technique in predicting the dynamic shear reaction at the structural support, and the accuracy of the empirical equations recommended in the design guidelines in estimating the dynamic shear capacity of RC structures. The limitation of the ALE simulation in predicting concrete spalling damage under close-in blast is also discussed in this study. It is suggested that further research to investigate the close-in blast responses of structures is deemed necessary to enhance the accuracy and the applicability of the ALE simulation in predicting the shear reaction time histories as well as predicting the spall damage of concrete structures. K&C are working closely with various groups to develop new blast-loaded connection design guidelines in addition

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to developing a novel computational code that is capable of simulating the debris flow under close-in blast events.

References Aruna, C.F.D.: K&C’s efficient computation fluid dynamics (CFD) solver for multi-phase and chemically reactive flow problems (2015). Retrieved from https://www.kcse.com/arunacfd/ Aylwin, C.J., et al.: Reduction in critical mortality in urban mass casualty incidents: analysis of triage, surge, and resource use after the London bombings on July 7, 2005. The Lancet 368(9554), 2219–2225 (2006) blastFoam.: blastFoam: an OpenFOAM solver for compressible multi-fluid flow with application to high-explosive detonation: Synthetik Applied Technologies, LLC (2019) Do, T.V., Nguyen, T.P.: Response of concrete-filled double skin tube segmental columns under blast loads. In: Bui T.Q., Cuong L.T., Khatir S. (eds.) Structural Health Monitoring and Engineering Structures. Lecture Notes in Civil Engineering, vol. 148, pp. 207–218 (2021) Do, T.V., Pham, T.M., Hao, H.: Dynamic responses and failure modes of bridge columns under vehicle collision. Eng. Struct. 156, 243–259 (2018) Do, T.V., Pham, T.M., Hao, H.: Stress wave propagation and structural response of precast concrete segmental columns under simulated blast loads. Int. J. Impact Eng 143, 103595 (2020) Dua, A., Braimah, A., Kumar, M.: Contact explosion response of RC columns: experimental and numerical investigation. Struct. Build., pp. 1–22 (2019) Dua, A., Braimah, A., Kumar, M. J.: Experimental and numerical investigation of rectangular reinforced concrete columns under contact explosion effects. Eng. Struct. 205, 109891 (2020) Fan, W., Shen, D., Yang, T., Shao, X.: Experimental and numerical study on low-velocity lateral impact behaviors of RC, UHPFRC and UHPFRC-strengthened columns. Eng. Struct. 191, 509–525 (2019) Fischer, K., Häring, I.: SDOF response model parameters from dynamic blast loading experiments. Eng. Struct. 31(8), 1677–1686 (2009) Gehl, A., Weaver, M., Smith, Z., Crawford, J.E.: Development and validation of criteria used to assess the blast resistance of RC columns. Paper presented at the 11th International Conference of the IFHS on Extreme Engineering, Singapore (2019) Hallquist, J.O.: LS-DYNA keyword user’s manual, vol. 970, pp. 299–800 (2007) Hao, H., Hao, Y., Li, J., Chen, W.: Review of the current practices in blast-resistant analysis and design of concrete structures. Adv. Struct. Eng. 19(8), 1193–1223 (2016) Hao, Y., Hao, H.: Influence of the concrete DIF model on the numerical predictions of RC wall responses to blast loadings. Eng. Struct. 73, 24–38 (2014) Hawkins, N.: Direct shear resistance. Letter Report to US Navy 5 (1982). Kingery, C.N., Bulmash, G.: Airblast parameters from TNT spherical air burst and hemispherical surface burst: US Army Armament and Development Center, Ballistic Research Laboratory (1984) Krauthammer, T., Bazeos, N., Holmquist, T.: Modified SDOF analysis of RC box-type structures. J. Struct. Eng. 112(4), 726–744 (1986) Lee, M., Kwak, H.-G., Park, G.-K.: An improved calibration method of the K&C model for modeling steel-fiber reinforced concrete. Compos. Struct. 269, 114010 (2021) Li, J., Hao, H.: Numerical study of concrete spall damage to blast loads. Int. J. Impact Eng 68, 41–55 (2014) Li, M., Zong, Z., Du, M., Pan, Y., Zhang, X.: Experimental investigation on the residual axial capacity of close-in blast damaged CFDST columns. Thin-Walled Struct. 165, 107976 (2021)

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Li, R., Zhou, D., Wu, H.: Experimental and numerical study on impact resistance of RC bridge piers under lateral impact loading. Eng. Fail. Anal., p. 104319 (2019) Liu, L., Zong, Z., Gao, C., Yuan, S., Lou, F.: Experimental and numerical study of CFRP protective RC piers under contact explosion. Compos. Struct. 234, 111658 (2020) Liu, L., Zong, Z., Li, M.: Numerical study of damage modes and assessment of circular RC pier under noncontact explosions. J. Bridg. Eng. 23(9), 04018061 (2018) Longinow, A., Mniszewski, K.R.: Protecting buildings against vehicle bomb attacks. Pract. Periodical Struct. Des. Constr. 1(1), 51–54 (1996) Magallanes, J.M., Wu, Y., Malvar, L.J., Crawford, J.E.: Recent improvements to release III of the K&C concrete model. Paper presented at the 11th international LS-DYNA Users conference (2010) Malvar, L.J., Crawford, J.E.: Dynamic increase factors for steel reinforcing bars. Paper presented at the The Twenty-Eighth DoD Explosives Safety Seminar Held, Orlando, USA (1998) Ngo, T., Mendis, P., Gupta, A., Ramsay, J.: Blast loading and blast effects on structures–an overview. Electron. J. Struct. Eng. 7, 76–91 (2007) Rigby, S.E., et al.: Preliminary yield estimation of the 2020 Beirut explosion using video footage from social media. Shock Waves 30(6), 671–675 (2020). https://doi.org/10.1007/s00193-02000970-z Shi, Y., Wang, J., Cui, J.: Experimental studies on fragments of reinforced concrete slabs under close-in explosions. Int. J. Impact Eng 144, 103630 (2020) Su, Q., Wu, H., Fang, Q.: Calibration of KCC model for UHPC under impact and blast loadings. Cem. Concr. Compos. 127, 104401 (2022) Tanner, J.A.: Calculating shear friction using an effective coefficient of friction. PCI J. (2008) Thai, D.-K., Kim, S.-E.: Prediction of UHPFRC panels thickness subjected to aircraft engine impact. Case Stud. Struct. Eng. 5, 38–53 (2016) DoD.: UFC 3-340-02: structures to resist the effects of accidental explosions. US DoD, Washington, DC, USA (2008) Valsamos, G., Larcher, M., Casadei, F.: Beirut explosion 2020: a case study for a large-scale urban blast simulation. Saf. Sci. 137, 105190 (2021) Wu, K.-C., Li, B., Tsai, K.-C.: Residual axial compression capacity of localized blast-damaged RC columns. Int. J. Impact Eng. 38(1), 29–40 (2011) Wu, Y., Crawford, J.., Lan, S., Magallanes, J.M.: Validation studies for concrete constitutive models with blast test data. Paper presented at the 13th International LS-DYNA User’s Conference, Dearborn, MI (2014) Wu, Y., Crawford, J.E., Magallanes, J.M.: Performance of LS-DYNA concrete constitutive models. Paper presented at the 12th International LS-DYNA users conference (2012) Yan, B., Liu, F., Song, D., Jiang, Z.: Numerical study on damage mechanism of RC beams under close-in blast loading. Eng. Fail.Anal. 51, 9–19 (2015) Yu, M., Lv, Q., Ding, H., Zeng, X., Cao, J., Liu, J., Fan, H., Hou, S.: Evaluation of blast injury patients from the 2015 Tianjin explosions in China. Burns 42(5), 1133–1140 (2016) Yuan, S., Hao, H., Zong, Z., Li, J.: A study of RC bridge columns under contact explosion. Int. J. Impact Eng 109, 378–390 (2017)

Free and Forced Vibration Characteristics of Functionally Graded Sandwich Beam with GPL-Reinforced Porous Core Tran Quang Hung1 , Do Minh Duc1(B) , and Tran Minh Tu2 1 Faculty of Civil Engineering, The University of Da Nang - University of Science and

Technology, 54 Nguyen Luong Bang, Da Nang, Vietnam {tqhung,dmduc}@dut.udn.vn 2 Hanoi University of Civil Engineering, Ha Noi, Vietnam [email protected]

Abstract. In this report, the dynamic response of a functionally graded graphene platelets porous (FGP-GPL) sandwich beam composed of two functionally graded material (FGM) face sheets and an FG porous core reinforced with graphene platelets is investigated. Uniform/non-uniform distribution patterns of internal pores and GPLs along the thickness direction are considered. The governing equations are derived from Lagrange’s equations in the framework of quasi-3D beam theory. Ritz method based on polynomial trial functions is utilized to discretize the equilibrium equations into a matrix form and then solved by Newmark’s constant average acceleration method to obtain the time-dependent response. The accuracy of the presented methodology is confirmed by comparison with analytical solution and with results available in the open literature. Parametric studies are conducted to highlight the effect of porosity coefficient, porosity and GPL distribution patterns, volume fraction index, GPL weight fraction, boundary supports on the dynamic characteristics of the sandwich beam. Keywords: Graphene platelets · Free and forced vibration · Functionally graded porous sandwich beam · Ritz method

1 Introduction Functionally graded materials (FGMs) belong to a novel class of advanced composite materials. They were first introduced by Japanese scientists in 1984 as a means of preparing thermal barrier materials (Koizumi 1997). FGMs are typically made of a mixture of two distinct materials so that their physical properties vary smoothly in the desired direction(s). Thus, the delamination and cracking phenomena due to the sudden change in the physical properties at the interface between the two different materials can be avoided. Furthermore, the variation of properties can be tailored properly so that FGMs achieve the best structural performances. FGMs have had a great potential application in

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1432–1452, 2023. https://doi.org/10.1007/978-981-19-7331-4_114

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a lot of engineering areas, including space structures, structural and machine elements, nuclear reactors, gears, thermal barrier systems, turbine rotors, etc. (Sayyad and Ghugal 2019). Metal foam, a special type of functionally graded porous material, is a cellular structure constructed of solid metal with pores inside. It offers many beneficial features, such as low self-weight, effective capacity of damping and energy dissipation, good thermal and acoustic insulation, so on. This material is therefore attractive for the development of multifunctional lightweight structures and promises a wide range of applications, such as automotive industry, lightweight construction, crash energy absorption, noise control, aerospace, biomedical industry, civil engineering, etc. (Banhart 2001; Banhart and Seeliger 2008; Smith et al. 2012; Gokhale et al. 2019). Sandwich beams in which a metal foam core is inserted into two FGM face sheet layers, shortened as P-FGM sandwich beams, is a form of efficient lightweight structures. This beam type exhibits many beneficial purposes, such as reducing self-weight, absorbing energy, withstanding high temperature, so on. Therefore, researches on these beams have been received concerns by authors. For example, Wang et al. (2019) examined the dynamic response of P-FGM sandwich beam under a non-uniformly distributed moving mass by Chebyshev–Ritz approach. Mu and Zhao (2016) focused on the natural frequency of P-FGM sandwich beams using the extended Galerkin method. Hung and Truong (2018) analyzed the free vibration behavior of P-FGM sandwich beam resting on Winkler elastic foundation by Navier’s solution. Chinh et al. (2020) developed a meshfree method for static analysis of P-FGM sandwich beam. Using Ritz method based on simple polynomial trial functions, Hung et al. (2021) presented the fundamental natural frequency of P-FGM sandwich beam embedded into two piezoelectric layers and lying on Pasternak elastic foundation. Hung et al. (2022) reported the static response of P-FGM sandwich beams considering effect of the liquid phase in the pores by the analytical solution. The review of studies in Refs. (Wang et al. 2019; Mu and Zhao 2016; Hung and Truong 2018; Chinh et al. 2020; Hung and Tu 2021; Hung et al. 2022) and the literature show that the internal pores in the metal foam significantly reduce the structural stiffness, which results in reducing the load-carrying capacity of the structures. To overcome the shortcoming, an innovative solution has been introduced by adding nanofiller such as carbon nanotubes (CNTs), graphene platelets (GPLs) (Rafiee et al. 2009; García-Macías et al. 2018; Zhao et al. 2020) with extremely high strength and Young’s modulus into the metal matrix to enhance the mechanical properties of the metal foam. Studies show that if the metal foam is reinforced with only a small amount of GPLs, its stiffness can be improved remarkably while its lightweight ability is maintained. Various mechanical problems have been examined by great efforts of researchers for metal foam structures reinforced with GPLs, such as beams (Barati and Zenkour 2019; Reza Barati and Zenkour 2017; Gao et al. 2020; Anirudh et al. 2019; Kitipornchai et al. 2017; Priyanka et al. 2021), plates (Nguyen et al. 2020; Li et al. 2018), shells (Rahimi et al. 2020; Li and Zheng 2020, Zhou et al. 2019; Shahgholian et al. 2020). However, investigation on the mechanical behavior of FGP-GPL sandwich beams has not been conducted yet. To fill the research gap, this study presents the dynamic behavior of an FGP-GPL sandwich beam. Uniform/non-uniform distribution patterns of internal pores and GPLs

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along the thickness direction are considered. The governing equations of the sandwich beam are derived from the Lagrange’s equations in the framework of quasi-3D beam theory. Ritz method based on polynomial trial functions is utilized to discretize the equilibrium equations into a matrix form and then solved by Newmark’s constant average acceleration method to obtain the time-dependent response. The accuracy of proposed approach is validated. The effect of porosity coefficient, porosity and GPL distribution patterns, volume fraction index of FGM, GPL weight fraction, boundary supports are investigated through various numerical examples. The obtained results could help identify effective ways in design of the proposed sandwich beam.

2 Theories and Basic Formulations 2.1 FGP-GPL Sandwich Beam and Material Properties Considering an FGP-GPL sandwich beam with width b, length L, and height h as depicted in Fig. 1a. The z-axis of Cartesian coordinate system O(x, y, z) coincides with the geometric mid-surface of the beam. hc and hf are the thickness of the core and the face layers, respectively; h = (hc + 2 × hf ). It is assumed that the face layers are perfectly bonded to the porous core. The faces are made of FGM which is a mixture of metal and ceramic, and the core is made of GPLreinforced metal foam (FGP-GPL). The effective mechanical properties of the materials of each layer, i.e., Young’s modulus E, mass density ρ, vary in the z-direction and are defined by the following laws ⎧ k ⎪ ⎨ E(z) = (Em − Ec )[(h − 2z)/(h − hc )] + Ec , z ∈ [hc /2, h/2] E(z) = E1 [1 − eo χ (z)] , z ∈ [−hc /2, hc /2] (1) ⎪ ⎩ k E(z) = (Em − Ec )[(h + 2z)/(h − hc )] + Ec , z ∈ [−h/2, −hc /2] ⎧ k ⎪ ⎨ ρ(z) = (ρm − ρc )[(h − 2z)/(h − hc )] + ρc , z ∈ [hc /2, h/2] ρ(z) = ρ1 1 − ep χ (z) , z ∈ [−hc /2, hc /2] (2) ⎪ ⎩ k ρ(z) = (ρm − ρc )[(h + 2z)/(h − hc )] + ρc , z ∈ [−h/2, −hc /2] in which function χ (z) refers to the porosity distribution patterns, which are selected here as either uniform variation, namely Poro-A, or non-uniform symmetric variation, namely Poro-B (see Fig. 1b), as follows  χ (z) = χo z ∈ [−hc /2, hc /2] Poro - A (3) χ (z) = cos(π z/hc ) z ∈ [−hc /2, hc /2] Poro - B and the subscripts m and c denote the metal and ceramic constituents of FGM, respectively; k is the volume fraction index, which indicates the inhomogeneity of FGM; eo , ep are the coefficients of porosity and mass density, respectively; E 1 , ρ 1 are, respectively, Young’s modulus and mass density of GPL-reinforced core without internal pores.

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z

FGM

x

hf hc

o FGM

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porous core

h

hf

L

(a) Geometry parameters and coordinate system

(b) Porosity distributions

(c) GPL dispersion patterns Fig. 1. FGP-GPL sandwich beam and parameters.

Shear modulus G can be calculated through Young’s modulus E and Poisson’s ratioν by the equation of the linear elasticity theory G(z) = E(z)/(2 + 2ν). The coefficient of mass density ep can be determined through the coefficient of porosity eo by the following relationship (Kitipornchai et al. 2017)   √ 1.121 1 − 2.3 1 − eo χ (z) ep = (4) χ (z) For Poro-A with a uniform porosity distribution, the function χ (z) = χo is constant. It is assumed that the total mass of the porous core with two porosity distributions, i.e.,

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Poro-A and Poro-B, is the same for a fair comparison later. Thus,χo can be obtained as follows (Anirudh et al. 2019) ⎡ ⎤2.3  hc /2 1 1 1 ⎣ ρ1 hc −hc /2 ρ(z)dz − 1 − (5) χo = + 1⎦ eo eo 1.121 Young’s modulus E 1 of GPL-reinforced core without internal pores can be evaluated based on Halpin-Tsai data model (Tjong 2013) as     1 + ξL ηL VGPL 1 + ξW ηW VGPL E1 = 0.375 × × Emf + 0.625 × × Emf (6) 1 − ηL VGPL 1 − ηW VGPL where ξL =

EGPL /Emf − 1 EGPL /Emf − 1 2lGPL 2wGPL ; ηL = ; ξW = ; ηW = tGPL EGPL /Emf + ξL tGPL EGPL /Emf + ξW

(7)

Mass density ρ 1 and Poisson’s ratioν 1 of GPL-reinforced core without internal pores can be computed employing the rule of mixture as (Zhao et al. 2020)  ρ1 = ρGPL VGPL + ρmf (1 − VGPL ) (8) ν1 = νGPL VGPL + νmf (1 − VGPL ) In Eqs. (6–8), E mf , ρ mf and ν mf refer to the elastic modulus, mass density, and Poisson’s ratio of the metal matrix, respectively, whereas E GPL , ρ GPL and ν GPL are those of GPLs; V GPL is the volume fractions of GPLs of the core; lGPL , t GPL , wGPL are the average length, thickness and width of GPLs in the metal core, respectively. Equations (6) and (8) points out that E 1 , ρ 1 and ν 1 , can be determined based on the volume fraction of GPLs, V GPL . In this study, it is assumed that the volume fraction of GPLs varies along the core thickness with three dispersion patterns, i.e., uniform, symmetric, and asymmetric dispersions, which are defined as ⎧ (1) ⎪ V (z) = VGPL uniform dispersion (GPL - 1) ⎪ ⎪ GPL ⎪ ⎪ ⎨ V (z) = V (2) [1 − cos(π z/h )] symmetric dispersion (GPL - 2) GPL c GPL (3) ⎪ ⎪ VGPL (z) = VGPL [1 − cos(π z/(2hc ) + π/4)] asymmetric dispersion (GPL - 3) ⎪ ⎪ ⎪ ⎩ , z ∈ [−hc /2, hc /2] (9) (1)

(2)

(3)

where VGPL , VGPL and VGPL are the peak volume fraction values of GPLs corresponding to the patterns GPL-1, GPL-2, and GPL-3 (see Fig. 1c). Each of them also depends on the cases of porosity distribution, i.e., Poro-A and Poro-B. They are determined through the weight fraction of GPLs, W GPL , by the following equation (Kitipornchai et al. 2017) WGPL   WGPL + ρGPL /ρmf (1 − WGPL )

hc /2  −hc /2

  1 − ep χ (z) dz =

hc /2 

  1 − ep χ (z) VGPL (z)dz

−hc /2

(10)

Free and Forced Vibration Characteristics of Functionally

1437

Poisson’s ratio of GPL-reinforced metal foam is also estimated as (Kitipornchai et al. 2017)   ν(z) = 0.221ζ + ν1 0.342ζ 2 − 1.21ζ + 1 (11) where

   ζ = 1 − ρ(z)/ρ1 = 1.121 1 − 2.3 1 − eo χ (z)

(12)

2.2 Displacement Field, Strain Field and Hook’ Law For one-dimensional (1D) beam modelling, beam theories are usually employed to establish formulations and predict the response of beams. Euler–Bernoulli beam theory is simple because it needs a minimum number of variables. However, neglecting the shear strain and rotary inertia in this theory leads to over predict the load-carrying capacity of beams. Timoshenko beam theory takes the effects of shear strain and rotary inertia into account; thus, the predictions are more actual than Euler–Bernoulli theory. However, Timoshenko theory requires the use of a shear correction factor and does not capture the actual shear stress over the cross section due to the assumption of constant shear strain. To overcome the shortcomings of Timoshenko theory, higher-order beam theories (HOBTs) without requiring the shear correction factor have been proposed. They have been widely used in 1D beam analysis. Recently, quasi-3D theory, which is extended from HOBTs with taking into consideration the thickness stretching effect, has been developed. It helps predict the response of beams more realistically than HOBTs. Different beam theories and their application for FGM sandwich beam modelling were reviewed in detail by Sayyad and Ghugal (2019). In this work, quasi-3D theory is adopted. The displacement field, in which both the shear strain and thickness stretching effect are taken into account, can be expressed as (Sayyad and Ghugal 2019)   u(x, z, t) (13) d= = θ1 B1 w(x, z, t) where

 θ1 =

1 0 −z f (z) 0 0 1 0 0 ∂f∂z(z)



  BT1 = uo (x, t) wo (x, t) wo (x, t) φo (x, t) woz (x, t)

(14) (15)

in which uo , wo , φ o , and woz are four unknown displacements on the mid-surface of the beam. t stands for time. The superscript T implies the matrix transpose operation.f (z) is the shape function which characterizes the shear strain and shear stress distributions over the cross-section. Various shape functions have been proposed by the authors. They were

1438

T. Q. Hung et al.

reviewed in detail by Sayyad and Ghugal (2019). Among them, the third-order function f (z) = z − 4z 3 / 3h2 (Sayyad and Ghugal 2019) is widely used in the literature. This function is adopted to model the beams in the present study. The strain field relating to the displacement field can be expressed as follows T  ε = εx εz γxz = θ2 B2 where

⎡

1 −z f (z)

⎢ θ2 = ⎣ 0 0 0 0 

BT2 = uo (x, t)

wo (x, t)

0 0

0

0

∂ 2 f (z) ∂z 2

0

0

(16)

0

⎤

⎥ 0 ⎦

∂f (z) ∂f (z) ∂z ∂z

 φo (x, t) woz (x, t) φo (x, t) woz (x, t)

(17) 

(18)

The stress field and strain field are related by Hook’ law. This relationship based on the plane stress condition for quasi-3D beam theory can be written as ⎧ ⎫ ⎡ ⎤⎧ ⎫ Q11 Q12 0 ⎨ εx ⎬ ⎨ σx ⎬ (19) σ = σz = ⎣ Q21 Q22 0 ⎦ εz = Ed ε ⎩ ⎭ ⎩ ⎭ τxz γxz 0 0 Q33 # $% & Ed

where Qij (i, j = 1, 2, 3) are the stiffness coefficients which are defined as Q11 = Q22 =

E E ; Q12 = Q21 = νQ11 ; Q33 = G = 1 − ν2 2 + 2ν

(20)

In Eqs. (15) and (18), the single and double prime symbols denote the first and second derivatives with respect to variable x. 2.3 Energy Functions The internal energy S e due to the strain of the beam is calculated as   1 1 T Se = σ εdV = εT Ed εdV 2 2 V

(21)

V

Substituting Eq. (16) into Eq. (21), the strain energy is then expressed as 1 Se = 2

L BT2 DE B2 dx

(22)

0

in which DE is the 6 × 6 square matrix of stiffnesses given by  DE(6×6) = θT2 Ed θ2 dA A

(23)

Free and Forced Vibration Characteristics of Functionally

The kinetic energy K e of the beam is calculated by    2   ∂u 2 1 ∂w ρ(z) + Ke = dV 2 ∂t ∂t

1439

(24)

V

Substituting Eq. (13) into Eq. (24), the kinetic energy is then expressed as 1 Ke = 2

L 0

∂BT1 ∂B1 DR dx ∂t ∂t

where DR is the 5 × 5 square matrix of the inertial coefficients given by  θT1 ρ(z)θ1 dA DR(5×5) =

(25)

(26)

A

The potential energy V e due to the distributed dynamic loading q(x, t) can be written as L Ve = −

q(x, t)wo (x, t)dx

(27)

0

In the above formulations, L, A and V are, respectively, the length, cross-section area, and volume of the studied beam. Lagrangian functional of the problem is given as  = Ke − Se − Ve

(28)

2.4 Ritz Solution In this study, Ritz method is employed to obtain the approximate solution of dynamic parameters of the beam. Based on the concept of Ritz method, the unknown displacement functions uo , wo , φ o , and woz can be expanded in a series of admissible functions as follows ⎧ M M ' ' ⎪ ⎪ (i) (i) (i) ⎪ u U Wo(i) (t)Swo t) = ; w t) = (x, (t)S (x) (x, (x) ⎪ o o o uo ⎪ ⎨ i=1 i=1 (29) M M ⎪ ' ' ⎪ ⎪ (i) (i) (i) (i) ⎪ o (t)Sφo (x) ; woz (x, t) = Woz (t)Swoz (x) ⎪ ⎩ φo (x, t) = i=1 (i)

(i)

(i)

i=1 (i)

where Uo , Wo , o , and Woz are the time-dependent unknown coefficients. M is the number of terms in the series, which is set here the same for the four approximate functions for convenience. M is determined in the analysis so that the obtained results achieve

1440

T. Q. Hung et al. (i)

(i)

(i)

(i)

the desired accuracy.Suo , Swo , Sφo , and Swoz are admissible functions that should satisfy the essential boundary conditions. There are several types of admissible function which can be chosen in the analysis. Because it is simple to satisfy different kinds of the boundary condition (BC) as well as effective in mathematical calculations, polynomial functions are selected in this study. They can be expressed as  (i) (i) Suo (x) = xpu (x − L)qu xi−1 ; Swo (x) = xpw (x − L)qw xi−1 (30) (i) (i) Sφo (x) = xpφ (x − L)qφ xi−1 ; Swoz (x) = xpwz (x − L)qwz xi−1 , i = 1, 2, ..., M in which p(·) and q(·) , (·) represents u, w, φ, and wz, are the exponents depending on BCs. They are provided in Table 1 for four kinds of BC, i.e., simply supported (SS), clamped hinged (CH), clamped clamped (CC), and clamped free (CF). Table 1. Values of exponent indices for different BCs BCs

pi

pw

SS

1

1

CH

1

2

CC

1

2

CF

1

2

Pφ

pwz

qu

qw

qφ

qwz

0

1

0

1

0

1

1

2

1

1

0

1

1

2

1

2

1

2

1

2

0

0

0

0

Inserting Eq. (29) into the energy expressions of Lagrangian functional, Eq. (28), then using Lagrange’s equations below ∂ (i) ∂Qo (i)

(i)

−

(i)

d ∂ = 0, ˙ (i) dt Q o (i)

i = 1, 2,..., M

(31)

(i)

with Qo represents Uo , Wo , o , Woz , yields the system of equilibrium equations of motion which can be expressed by a matrix form as ⎧ ⎫ ⎧ ⎫ ¨o ⎪ Uo ⎪ U ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎬ ⎨ ¨ ⎪ ⎬ Wo Wo + [M]4M ×4M = {F(t)}4M ×1 [K]4M ×4M ¨ ⎪ ⎪ o ⎪ ⎪ ⎪  ⎪ ⎪ ⎩ ⎭ ⎩ o ⎪ ⎭ ¨ oz W Woz 4M ×1 4M ×1

(32)

where K is the elastic stiffness matrix, M is the mass matrix, F(t) is the load vector generated by dynamic loading. Uo , Wo , os and Woz are the vectors collecting all the coefficients of the approximate functions of uo , wo , φ o , and woz , respectively. The dots over the variables denote the first and second derivatives with respect to time. Note that the damping is not included in Eq. (32).

Free and Forced Vibration Characteristics of Functionally

1441

When the dynamic loading is removed, F(t) = 0, Eq. (32) reduces to the free vibration equation. The displacement functions are harmonic functions. Therefore, the unknown coefficients can be assumed as sinusoidal functions below ⎧  ⎫ ⎫ ⎪ ⎧ ⎪ ⎪ ⎪ Uo ⎪ ⎪ Uo ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪  ⎬ ⎬ ⎨ ⎨ Wo Wo sin(ωt) (33) =  ⎪  ⎪ ⎪ ⎪ ⎪ o ⎪ ⎪ ⎪ ⎭ ⎪ ⎩ o ⎪ ⎪ ⎪ ⎪ ⎪ Woz ⎩ ⎭ Woz 







in which ω is the natural frequency of the sandwich beam; Uo , Wo , o , and Woz are the vectors of the coefficients of vibration amplitude. Substituting Eq. (33) back into Eq. (32) and setting F(t) to be zeros vector yield the following frequency equation ⎧  ⎫ ⎪ ⎪ ⎪ U ⎪ ⎪ ⎪ ⎪ o ⎪ ⎪ ⎬ ⎨ ⎪  Wo 2 = {0}4M ×1 (34) [K]4M ×4M − ω [M]4M ×4M  ⎪ ⎪ ⎪ o ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭ ⎩ ⎪ Woz 4M ×1 The natural frequency ω of the beam can be determined by the eigenvalue solution of Eq. (34).

3 Numerical Results This section is devoted to numerical computation and discussion. Firstly, three examples are conducted for specific cases of the studied beam. Their results are compared with analytical solution and other publications available in the open literature to confirm the correctness of the developed theories and formulations. After that, the free and forced vibration characteristics of the FGP-GPL sandwich beam are investigated in detail. The mechanical properties of materials composing FGMs, metal matrix, and GPLs, as well as the geometry parameters of GPLs, are given in Table 2. 3.1 Comparative Studies Because there has been no publication related to the FGP-GPL sandwich beam, the studied beam will be modified to become specific beams that were studied by other authors for comparison purposes. For the first comparative study, the studied beam is modified to become a solid FGM sandwich beam without GPLs. The solid hard-core is full ceramic (Al2 O3 ), whereas the faces are FGMs which are composed of ceramic (Al2 O3 ) and metal (Al). Material properties of Al2 O3 (Alumina) and Al (Aluminum) are given in Table 2. The variation of material properties across the beam thickness follows Eqs. (1) and (2); however, it must interchange the roles of ceramic (E c , ρ c ) and metal (E m , ρ m ) as well as set eo = 0

1442

T. Q. Hung et al. Table 2. Material properties and geometry parameters.

Layers Materials FGM

Core

Properties

Geometry parameters

E (GPa) ρ (kg/m3 ) ν (−)

wGPL (µm) l GPL (µm) t GPL (nm)

Ceramic (Al2 O3 ) (Vo et al. 2015)

380

3960

0.3

−

−

−

Metal (Al) (Vo et al. 2015)

70

2702

0.3

−

−

−

Metal matrix 70 (Al)

2702

0.3

−

−

−

GPLs 1010 (Kitipornchai et al. 2017)

1062.5

0.186

1.5

2.5

1.5

and W GPL = 0. The free vibration of this solid FGM sandwich beam was conducted by Nguyen et al. (Nguyen et al. 2016) and Vo et al. (Vo et al. 2015) based on the framework of quasi-3D theory. Obtained non-dimensional fundamental frequencies of solid FGM sandwich beam are listed in Table 3. For the second comparative study, the studied beam is modified to become the singlelayer GPL-reinforced porous beam by omitting the two FGM faces in the analysis (setting hf = 0). The free vibration problem of this beam type was done by Kitipornchai et al. (2017) based on Timoshenko beam theory and by Priyanka et al. (2021) based on quasi3D theory. Properties and geometries of GPLs are taken in Table 2. Metal matrix of the porous layer is copper (Cu) which has material properties as E Cu = 130 GPa, ρ Cu = 8960 kg/m3 , ν Cu = 0.34 (Priyanka et al. 2021). Obtained results are reported in Table 4. The data in Tables 3 and 4 show an excellent agreement between the present study and the studies of Vo et al. (2015), Nguyen et al. (2016), Kitipornchai et al. (2017), and Priyanka et al. (2021). A further comparative study is devoted to the free and forced vibration of an isotropic beam without pores and GPLs by setting, in Eqs. (1) and (2), E c = E m = E 1 = E, ρ c = ρ m = ρ 1 = ρ, eo = 0, and W GPL = 0. An analytical solution of this beam with SS edges based on the mode-superposition method for Euler–Bernoulli beam theory is presented. The results can be a benchmark for the comparison with those of the developed Ritz method. The analytical solution of the natural frequencies for the beam is (   bh3 i2 π 2 i2 π 2 (35) ωi = 2 EI / ρbh + ρI 2 , i = 1, 2, ..., N ; I = L L 12 Assuming zero initial conditions of the displacement and velocity, the analytical solution of the deflection for the beam subjected to harmonic transverse loading q =

Free and Forced Vibration Characteristics of Functionally

1443

√ Table 3. Non-dimensional fundamental frequency ω = ωL2 /h ρAl /EAl (Nguyen et al. 2016) of solid FGM sandwich beam without GPLs (quasi-3D theory, hc /hf = 8). )

BCs

Sources

L/h

k 0

CC

SS

0.5

1

2

5

Present

5

10.1835

9.6838

9.4153

9.1391

8.8628

Vo et al. (2015)

5

10.1851

9.6857

9.4174

9.1415

8.8653

Nguyen et al. (2016)

5

10.1790

9.6747

9.4078

9.1307

8.8536

Present

20

12.3213

11.5390

11.1323

10.7211

10.3145

Vo et al. (2015)

20

12.2660

11.4867

11.0815

10.6719

10.2669

Nguyen et al. (2016)

20

12.2756

11.4949

11.0916

10.6820

10.2771

Present

5

5.1632

4.8527

4.6901

4.5249

4.3608

Vo et al. (2015)

5

5.1618

4.8511

4.6884

4.5231

4.3589

Nguyen et al. (2016)

5

5.1620

4.8504

4.6883

4.5229

4.3587

Present

20

5.4628

5.1093

4.9260

4.7410

4.5583

Vo et al. (2015)

20

5.4610

5.1073

4.9239

4.7388

4.5560

Nguyen et al. (2016)

20

5.4611

5.1067

4.9240

4.7389

4.5561

*   2 /E (Priyanka et al. Table 4. Non-dimensional fundamental frequency ω = ωL ρCu 1 − νCu Cu 2021) of single-layer GPL-reinforced porous beam (L/h = 20, CC beam, W GPL = 1 wt.%). GPL pattern Sources GPL-1

GPL-2

GPL-3

Poro-A

Poro-B

eo = 0.2 0.4

0.6

eo = 0.2 0.4

Present

0.3732

0.3578

0.3398 0.3845

0.3834 0.3845

Priyanka et al. (2021)

0.3716

0.3565

0.3388 0.3825

0.3812 0.3820

Present

0.4161

0.3991

0.3790 0.4277

0.4250 0.4233

Priyanka et al. (2021)

0.4134

0.3967

0.3770 0.4248

0.4219 0.4201

Kitipornchai et al. − (2017)

−

−

0.4468

0.4442 0.4436

Present

0.3691

0.3538

0.3359 0.3797

0.3778 0.3775

Priyanka et al. (2021)

0.3664

0.3515

0.3340 0.3766

0.3746 0.3742

0.6

1444

T. Q. Hung et al.

qo sin(Ωt) can be presented as N '



/ωi 1     sin(ωi t) −   sin(t) w(x, z, t) = 2 − ω2 2 − ω2 i2 π 2   i i i=1, 3, 5... iπ ρbh + ρI 2 4qo



L

iπ x sin L

(36)

In Eqs. (35) and (36), ωi is the i-th natural frequency of the beam; Ω is the excitation frequency of the harmonic loading.

Fig. 2. Non-dimensional time history deflection at the centre of SS isotropic beam based on Ritz and analytical solutions.

The comparative study is then conducted for the SS thin beam with L = 1 m and h = L/50. Isotropic material is Al (E = E Al = 70 GPa, ρ = ρ Al = 2702 kg/m3 , ν = ν Al = 0.3). The excitation frequency Ω = 100 rad/s. In the result demonstration, non-dimensional quantities are used as * ωi L2 ρAl 100EAl bh3 w(x, z, t) ωi = ; w(x, z, t) = (37) h EAl qo L4 )

)

The obtained result of the non-dimensional fundamental frequency, ωˆ 1 , of Ritz method is 2.8482 whereas that of analytical solution, from Eqs. (35) and (37), is 2.8486. In addition, the time history central deflection of the beam calculated by both Ritz and analytical solutions is plotted in Fig. 2. The results show that Ritz method matches well with the analytical solution. 3.2 Comprehensive Studies In this sub-section, effects of important parameters, such as the porosity coefficient, porosity and GPL distributions, volume fraction index of FGM face-sheets, GPL weight

Free and Forced Vibration Characteristics of Functionally

1445

fraction, excitation loading, boundary supports on the free and forced vibration characteristics of the FGP-GPL sandwich beam are investigated. The thick core beam with the layer thickness ratio hc /hf = 8 is selected throughout all the examples. Material properties are provided in Table 2. The non-dimensional quantities which are defined by Eq. (37) are used. √ Table 5. Non-dimensional fundamental natural frequency ω = ωL2 /h ρAl /EAl of FGP-GPL sandwich beam (hc /hf = 8, L/h = 10, W GPL = 0.6 wt.%, eo = 0.4). )

BCs CC

Porosity distributions

GPL patterns

Poro-A (uni.)

GPL-1 (uni.)

Poro-B (sym.)

CH

Poro-A (uni.)

Poro-B (sym.)

SS

Poro-A (uni.)

Poro-B (sym.)

CF

Poro-A (uni.)

Poro-B (sym.)

k 0

0.5

1

2

5

10

6.3038

8.1038

8.7286

9.2325

9.6394

9.7970

GPL-2 (sym.)

6.4472

8.1667

8.7656

9.2491

9.6403

9.7982

GPL-3 (asym.)

6.3154

8.1088

8.7305

9.2318

9.6365

9.7933

GPL-1 (uni.)

6.4769

8.1771

8.7698

9.2484

9.6357

9.7863

GPL-2 (sym.)

6.6261

8.2468

8.8141

9.2730

9.6453

9.7996

GPL-3 (asym.)

6.4878

8.1823

8.7722

9.2483

9.6336

9.7835

GPL-1 (uni.)

4.4460

5.7941

6.2795

6.6795

7.0083

7.1366

GPL-2 (sym.)

4.5616

5.8598

6.3295

6.7171

7.0361

7.1608

GPL-3 (asym.)

4.4581

5.8019

6.2855

6.6840

7.0115

7.1393

GPL-1 (uni.)

4.5858

5.8724

6.3383

6.7229

7.0396

7.1635

GPL-2 (sym.)

4.7072

5.9438

6.3940

6.7662

7.0732

7.1935

GPL-3 (asym.)

4.5980

5.8809

6.3451

6.7282

7.0436

7.1669

GPL-1 (uni.)

2.8970

3.8216

4.1654

4.4542

4.6955

4.7903

GPL-2 (sym.)

2.9804

3.8777

4.2133

4.4958

4.7320

4.8250

GPL-3 (asym.)

2.9045

3.8281

4.1713

4.4595

4.7003

4.7949

GPL-1 (uni.)

2.9981

3.8891

4.2229

4.5039

4.7390

4.8315

GPL-2 (sym.)

3.0865

3.9497

4.2751

4.5496

4.7796

4.8702

GPL-3 (asym.)

3.0055

3.8959

4.2292

4.5097

4.7444

4.8367

GPL-1 (uni.)

1.0458

1.3857

1.5131

1.6213

1.7118

1.7474

GPL-2 (sym.)

1.0768

1.4076

1.5324

1.6385

1.7274

1.7628

GPL-3 (asym.)

1.0485

1.3880

1.5158

1.6237

1.7138

1.7497

GPL-1 (uni.)

1.0834

1.4124

1.5367

1.6422

1.7308

1.7656

GPL-2 (sym.)

1.1169

1.4356

1.5573

1.6608

1.7478

1.7819

GPL-3 (asym.)

1.0864

1.4149

1.5391

1.6448

1.7331

1.7673

1446

T. Q. Hung et al.

3.2.1 Natural Frequencies The non-dimensional fundamental natural frequencies of FGP-GPL sandwich beam for different values of volume fraction index k and four kinds of BC is reported in Table 5. Two porosity distributions, i.e., Poro-A and Poro-B, and three GPL patterns, i.e., GPL-1, GPL-2, GPL-3 are considered in this investigation. It is found out from Table 5 that when k increases, the frequency increases. This is due to the fact that increasing the values of k leads to an increase in the ceramic with a higher elastic modulus. This makes the beam become stiffer, thus increasing the value of natural frequency. In addition, for the same specific condition of k, porosity distribution, as well as GPL pattern, CC beam gives the greatest value of natural frequency and then is followed by an order as CH, SS, and CF beams. In regard to the GPL patterns as well as porosity distributions, in general, Poro-B gives higher values of natural frequency than Poro-A. Among three GPL patterns, GPL-2 gives the greatest values of natural frequency. In other words, FGP-GPL sandwich beam in which Poro-B combined with GPL-2 offers the best effectiveness to enhance the stiffness of the beam. Consequently, this type of beam will be examined in the next examples.

Fig. 3. Effect of span-to-height ratio, porosity coefficient and BCs on the non-dimensional fundamental natural frequency of the beam (k = 0.5, Poro-B, GPL-2).

Figure 3 plots the non-dimensional fundamental natural frequency of the FGP-GPL sandwich beam with various values of span-to-height ratio L/h, porosity coefficient

Free and Forced Vibration Characteristics of Functionally

1447

eo . Four kinds of BC, i.e., CF, SS, CH, and CC, are considered. The plots point out that the non-dimensional natural frequency usually increases with the increase of L/h. Furthermore, when eo increases, the non-dimensional natural frequency of SS and CF beams usually increases for all values of L/h; however, that of CC and CH beams increases for high values of L/h, but decreases for small values of L/h. This complex development of the frequency is due to the correlation effect between the stiffness and mass matrices of the system when eo increases. In general, the correlation depends on the boundary conditions and L/h ratio. In addition, the greatest non-dimensional frequency for each BC is obtained when both L/h and eo reach the maximum value in the range investigation, i.e., L/h = 20 and eo = 0.6.

Fig. 4. Effect of GPL weight fraction, porosity coefficient and BCs on the non-dimensional fundamental natural frequency of the beam (k = 0.5, L/h = 5, Poro-B, GPL-2).

Figure 4 plots the non-dimensional fundamental natural frequency of SS and CC sandwich beams for various values of GPL weight fraction W GPL , porosity coefficient eo . Parameters k = 0.5, L/h = 5 are selected for this investigation. As expected, adding a small amount of GPLs through W GPL , the stiffness of the beams increases, then the natural frequency increases. Besides, increasing eo leads to an increase in the nondimensional fundamental natural frequency of SS beam, but a reduction in that of CC beam. This effect is revealed in Fig. 3 for thick beams (small L/h ratio). Figure 5 depicts the non-dimensional fundamental frequency of SS sandwich beam with various values of GPL weight fraction W GPL , porosity coefficient eo , and volume fraction index k. As can be seen, the effect of k on the enhancement of the nondimensional frequency is much more remarkable than W GPL or eo does, especially when k varies in the range 0 ≤ k ≤ 2. 3.2.2 Forced Vibration Assuming that the beam is subjected to a sinusoidal pulse loading q = qo sin(300t) for 0.012 s. After that, the excitation loading is removed, and the beam vibrates freely. The total time in this investigation is taken to be 0.024 s. The parameters L = 1 m, L/h = 10 and SS edges beam are chosen. It is assumed that the initial conditions of the displacement

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Fig. 5. Effect of GPL weight fraction, porosity coefficient and volume fraction index on the non-dimensional fundamental natural frequency of the beam (SS, L/h = 20, Poro-B, GPL-2).

and velocity (at t = 0) are equal to zero. To obtain the time-dependent response, the equation of motion, Eq. (32), is numerically solved by the implicit Newmark’s method (Chopra 2017) with the average acceleration. A time step of 0.0001 s is used to perform the time history analysis, and the damping is not considered here. The non-dimensional time history central deflection w(L/2, h/2) of the beam with various values of porosity coefficient eo , volume fraction index k, and GPL weight fraction W GPL are illustrated in Figs. 6, 7, and 8, respectively. It is observed in these figures that for the first 0.012 s, the beam is in the forced vibration state due to the pulse loading. After that, this loading ends, the free vibration of the beam is started by the displacement and velocity at the end of the forced vibration (at t = 0.012 s). It is also found out that increasing eo or W GPL or k results in increasing the frequency of the SS beam investigating. This effect is examined and discussed in Sect. 3.2.1. Thus, the period of oscillation of the beam is shorter. Consequently, the time interval between two peaks of dynamic deflection response tends to be shorter, especially for the peaks in the free vibration phase. Finally, the peak deflection decreases with increasing of k or W GPL but increases with increasing of eo . )

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Fig. 6. Effect of porosity coefficient on the non-dimensional displacement response at the centre of the sandwich beam (SS, L/h = 10, k = 1, W GPL = 0.5 wt.%, Poro-B, GPL-2).

Fig. 7. Effect of volume fraction index on the non-dimensional displacement response at the centre of the sandwich beam (SS, L/h = 10, W GPL = 0.5 wt.%, eo = 0.5, Poro-B, GPL-2).

4 Conclusion Dynamic response of the FGP-GPL sandwich beam is performed. Both uniform/nonuniform distribution of internal pores and GPLs along the thickness direction are examined. The governing equations of motion are derived from Lagrange’s equations in conjunction with quasi-3D beam theory. Ritz method based on polynomial functions is adopted to discretize the equilibrium equations into the matrix form. These equations are then solved by Newmark’s constant average acceleration method to obtain the time-dependent response. The correctness of the presented methodology is confirmed by comparison with the results of the analytical solution and other authors. Finally, parametric studies on the free and forced vibration are conducted for various cases of the porosity coefficient, porosity and GPL distributions, GPL weight fraction, volume fraction index, boundary supports. From the numerical examples, some outstanding findings can be pointed out as follows.

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Fig. 8. Effect of GPL weight fraction on the non-dimensional displacement response at the centre of the sandwich beam (SS, L/h = 10, k = 1, eo = 0.5, Poro-B, GPL-2).

1. Ritz method based on polynomial admissible functions can be used to analyze the dynamic response of the FGP-GPL sandwich beam with arbitrary end conditions. 2. By reinforcing the foam core with a small amount of GPL, the stiffness of the beam is significantly improved, then the natural frequency increases, whereas the dynamic deflection of the beam decrease. 3. Enlargement of the porosity coefficient can lead to an increase or decrease in the frequency. This depends on the correlation effect between the stiffness and mass of the beam. 4. The symmetric porosity distribution (Poro-B) combined with the symmetric GPL dispersion (GPL-2) gives the highest stiffness among the regarded schemes of GPLreinforced foam core. It can offer a good choice for designers to enhance structural performance. 5. The natural frequency increases, whereas the dynamic deflection decrease as the volume fraction index increases. 6. Span-to-height ratio and boundary supports have important effects on the dynamic response of the beam.

Acknowledgements. This work was supported by The University of Danang, University of Science and Technology, code number of Project: T2022–02-27.

References Anirudh, B., Ganapathi, M., Anant, C., Polit, O.: A comprehensive analysis of porous graphenereinforced curved beams by finite element approach using higher-order structural theory: bending, vibration and buckling. Compos. Struct. 222, 110899 (2019) Banhart, J.: Manufacture, characterisation and application of cellular metals and metal foams. Prog. Mater Sci. 46, 559–632 (2001) Banhart, J., Seeliger, H.W.: Aluminium foam sandwich panels: manufacture, metallurgy and applications. Adv. Eng. Mater. 10, 793–802 (2008)

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Barati, M.R., Zenkour, A.M.: Analysis of postbuckling of graded porous GPL-reinforced beams with geometrical imperfection. Mech. Adv. Mater. Struct. 26, 503–511 (2019) Chinh, T.H., Tu, T.M., Duc, D.M., Hung, T.Q.: Static flexural analysis of sandwich beam with functionally graded face sheets and porous core via point interpolation meshfree method based on polynomial basic function. Arch. Appl. Mech. 91(3), 933–947 (2020). https://doi.org/10. 1007/s00419-020-01797-x Chopra, A.K.: Dynamics of structures. Theory Appl. Earthq. Eng. (2017) Gao, K., Do, D.M., Li, R., Kitipornchai, S., Yang, J.: Probabilistic stability analysis of functionally graded graphene reinforced porous beams. Aerosp. Sci. Technol. 98, 105738 (2020) García-Macías, E., Rodríguez-Tembleque, L., Sáez, A.: Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates. Compos. Struct. 186, 123–138 (2018) Gokhale, A., Prasad, N.E., Basu, B. (eds.): Light weighting for defense, aerospace, and transportation. IIMS, Springer, Singapore (2019). https://doi.org/10.1007/978-981-15-1263-6 Hung, D.X., Truong, H.Q.: Free vibration analysis of sandwich beams with FG porous core and FGM faces resting on Winkler elastic foundation by various shear deformation theories. J. Sci. Technol. Civ. Eng. NUCE 12, 23–33 (2018) Hung, T.Q., Duc, D.M., Tu, T.M.: Static Behavior of Functionally Graded Sandwich Beam with Fluid-Infiltrated Porous Core. Springer, Modern Mechanics and Applications (2022) Hung, T.Q., Tu, T.M.: Free vibration of piezoelectric FGM sandwich beam with porous core embedded in thermal environment and elastic foundation. J. Sci. Technol. Civ. Eng. (STCE)HUCE, 15, 15–28 (2021) Kitipornchai, S., Chen, D., Yang, J.: Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater. Des. 116, 656–665 (2017) Koizumi, M.: FGM activities in Japan. Compos. B Eng. 28, 1–4 (1997) Li, Q., Wu, D., Chen, X., Liu, L., Yu, Y., Gao, W.: Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler-Pasternak elastic foundation. Int. J. Mech. Sci. 148, 596–610 (2018) Li, Z., Zheng, J.: Nonlinear stability of the encased functionally graded porous cylinders reinforced by graphene nanofillers subjected to pressure loading under thermal effect. Compos. Struct. 233, 111584 (2020) Mu, L., Zhao, G.: Fundamental frequency analysis of sandwich beams with functionally graded face and metallic foam core. Shock. Vib. 2016, 3287645 (2016) Nguyen, Q.H., Nguyen, L.B., Nguyen, H.B., Nguyen-Xuan, H.: A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets. Compos. Struct. 245, 112321 (2020) Nguyen, T.-K., Vo, T.P., Nguyen, B.-D., Lee, J.: An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory. Compos. Struct. 156, 238–252 (2016) Priyanka, R., Twinkle, C. M. & Pitchaimani, J. (2021), Stability and dynamic behavior of porous FGM beam: influence of graded porosity, graphene platelets, and axially varying loads, Engineering with Computers. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.-Z., Koratkar, N.: Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 3, 3884–3890 (2009) Rahimi, A., Alibeigloo, A., Safarpour, M.: Three-dimensional static and free vibration analysis of graphene platelet–reinforced porous composite cylindrical shell. J. Vib. Control 26, 1627–1645 (2020) Reza Barati, M., Zenkour, A.M.: Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection. Compos. Struct. 181, 194–202 (2017)

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Sayyad, A.S., Ghugal, Y.M.: Modeling and analysis of functionally graded sandwich beams: a review. Mech. Adv. Mater. Struct. 26, 1776–1795 (2019) Shahgholian, D., Safarpour, M., Rahimi, A.R., Alibeigloo, A.: Buckling analyses of functionally graded graphene-reinforced porous cylindrical shell using the Rayleigh–Ritz method. Acta Mech. 1–16 (2020) Smith, B.H., Szyniszewski, S., Hajjar, J.F., Schafer, B.W., Arwade, S.R.: Steel foam for structures: a review of applications, manufacturing and material properties. J. Constr. Steel Res. 71, 1–10 (2012) Tjong, S.C.: Recent progress in the development and properties of novel metal matrix nanocomposites reinforced with carbon nanotubes and graphene nanosheets. Mater. Sci. Eng. R. Rep. 74, 281–350 (2013) Vo, T.P., Thai, H.-T., Nguyen, T.-K., Inam, F., Lee, J.: A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Compos. Struct. 119, 1–12 (2015) Wang, Y., Zhou, A., Fu, T., Zhang, W.: Transient response of a sandwich beam with functionally graded porous core traversed by a non-uniformly distributed moving mass. Int. J. Mech. Mater. Des. 16(3), 519–540 (2019). https://doi.org/10.1007/s10999-019-09483-9 Zhao, S., Zhao, Z., Yang, Z., Ke, L., Kitipornchai, S., Yang, J.: Functionally graded graphene reinforced composite structures: a review. Eng. Struct. 210, 110339 (2020) Zhou, Z., Ni, Y., Tong, Z., Zhu, S., Sun, J., Xu, X.: Accurate nonlinear buckling analysis of functionally graded porous graphene platelet reinforced composite cylindrical shells. Int. J. Mech. Sci. 151, 537–550 (2019)

Engineering Design and Dynamics Structural Response

Ballastless Track Support Deterioration Evaluation Using Machine Learning Jessada Sresakoolchai1 , Ting Li2 , and Sakdirat Kaewunruen1(B) 1 Department of Civil Engineering, University of Birmingham, Birmingham B15 2TT, UK

[email protected], [email protected] 2 School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China

[email protected]

Abstract. Ballastless tracks have been widely used for highspeed rail systems globally since their maintenance is relatively minimal. However, support deterioration right beneath the in-between slabs’ connectors has been usually reported and quite well known in the industry. Any water ingress can quickly undermine the condition of cement-stabilized soil that supports the track slabs. It is thus very crucial to very early detect the impaired condition of the slab supports since mudded support can result in poor ride quality and eventually endanger highspeed train operations. Therefore, the ability to predict the deterioration of track slab supports is highly beneficial to predictive and preventative maintenance in practice. In this study, track slab support stiffness is considered as a precursor to identify the severity of deterioration. The nonlinear FE models, which were validated by field measurements, have been used to populate data in order to develop machine learning models capable of evaluating the track support deterioration. Axle box accelerations are adopted in a form of datasets for machine learning models. Parametric studies have yielded a diverse range of datasets considering the train speed variations, train axle loads, and irregularities. The results demonstrate that the machine learning models can reasonably diagnose the condition of the track slab supports. The outcome reveals the potential of machine learning to evaluate ballastless track support deterioration in practice, which will be beneficial for railway maintenance. Keywords: Ballastless track · Deterioration · Machine learning · Finite element modeling · Condition monitoring

1 Introduction Ballastless tracks are popularly used in the high-speed rail industry due to their benefits such as lower maintenance requirements, relatively efficiency, and more stability. They are widely used in different countries such as Germany, China, Japan, and Korea (Park et al. 2020). However, common defects in ballastless tracks are settlements and cracks which affect the track stiffness. The deterioration is a result of high loads, vibrations, or water that accelerate the slab deterioration. This can lead to a more severe defect in the track structure in terms of track geometry, rail surface defects, and track infrastructure © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1455–1463, 2023. https://doi.org/10.1007/978-981-19-7331-4_115

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defects. Therefore, an ability to early evaluate the ballast track support deterioration is crucial in terms of predictive and preventive maintenances because required maintenances can be performed on time when the deterioration is not severe, the maintenance costs are not high, and the safety can be maintained in the standard criteria. In this study, track slab support stiffness is considered as the main precursor to identify the severity of ballast track deterioration. Data used in the study are generated using finite element (FE) models which are validated with field data measurement. Then, data are used to develop machine learning models to evaluate track stiffnesses. Axle box accelerations (ABA) are used to feed into machine learning models to make predictions. Different parameters are varied to create data variations such as train speed, axle loads, or track irregularities. A machine learning technique that is used to develop a predictive model is a convolutional neural network (CNN). Hyperparameter tuning is performed to ensure the performance of the machine learning model. More information is explained in Sect. 3. The expected benefits and contributions of the study are the developed machine learning model can be used to evaluate or estimate the slab track stiffness which will be beneficial to the maintenance planning. Train operators can be aware of slab track deterioration based on regular operations because ABA is mainly used to evaluate track stiffnesses. The stiffnesses are evaluated early and the maintenance can be performed in time when the deterioration is not severe. Therefore, the maintenance cost is not high compared to when the deterioration is severe, the operation is more smooth, the reliability of the system is higher, and passenger comfort is better because the track condition is always maintained in a good condition.

2 Literature Reviews Desai (2016) studied different types of ballastless track defects. The causes of defects were analyzed using a developed equation. From that study, it was found that the most common defect in slab track was the deterioration of concrete slab. The study mentioned different causes of slab deterioration consisting of low-quality material, environmental factors, poor design, and poor construction. Moreover, slabs were cast-in-situ concrete which cracks were commonly found due to construction, application, and environment which also resulted in slab deterioration. These critically affected slab durability and operational safety. Guo and Zhai (2018) tried to predict long-term track geometry degradation in the ballastless track system used in the high speed railway industry. They considered different subgrade settlements as a precursor. They applied a numerical power model to study subgrade settlement affecting track geometry degradation. Li and Berggren (2010) studied the relationship between global track stiffness and track performances which were dynamic responses. They conducted static and dynamic methods to explore the relationships. They found that dynamic responses such as sleeper acceleration, wheel-rail forces, and rail moment were related to slab stiffnesses. From the literature reviews, it can be found that studies relevant to ballastless track support stiffness measurement and evaluation are limited. In addition, there have been no studies using machine learning to evaluate ballastless track support stiffness. Therefore,

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this study aims to apply machine learning to develop a predictive model to evaluate ballastless track support stiffness.

3 Methodology 3.1 FE Model Development and Validation This study applies FE models for numerical simulation and generates numerical data. Then, results from FE simulations are used to develop the machine learning model. The FE model is developed based on Li et al. (2020). The FE model is shown in Fig. 1. The FE model is a 3D vehicle-slab model. Rolling stock is modeled using the multi-body simulation (MBS) concept. The rolling stock comprises a car body, two bogies, four wheelsets, two primary suspensions, and two secondary suspensions. The software used to develop the EF model is LS-DYNA which is a popular FE software.

Fig. 1. FE model

For the ballasted track, the track structure is a concrete slab comprising two rails that are modeled as beams (206 GPa), rail pads that are modeled as a series of springs and dampers (160 kN/mm), concrete slabs that are modeled as elastic objects (36 GPa), mortar layers (under the concrete slabs) that are models as elastic objects (0.3 GPa), and concrete bases that are models as elastic objects (32 GPa). The rails are developed using the Euler beam concepts supported by rail pads. Then, the loads are transferred to mortar layers and concrete based underneath the concrete slabs respectively which are modeled as elastic material for both of them. The detail of the ballastless track model is shown in Fig. 2. The FE model is created using different keywords available in LSDYNA. The main keyword used in the model is the keyword that is used for creating the interaction between wheels and rails which is *Rail_Track and *Rail_Train. *S01SPRING_ELASTIC and *S02-DAMPER_VISCOUS keywords are used to model the stiffness and damping properties of rail pads as mentioned. To simulate the deterioration

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Fig. 2. Detailed ballastless track model

of ballastless track support, the stiffnesses of the concrete slabs are varied as the main precursors as mentioned. Model validation is performed by comparing with the field measurement. The field measurement is conducted using the Suining-Chongqing railway as the benchmark. This railway line is originally constructed for test purposes. The rolling stock used in this line is Changbai Mountain. Therefore, the FE model is developed based on the rolling stock and railway line parameters. On-site, the operational speeds of the rolling stock range from 160 to 220 km/h. track irregularities are also measured to imitate the real situation. Moreover, track irregularities are varied to create data variation. More detail about data variation will be presented in the next section. Wheel-rail contact forces, maximum displacements of rail, and maximum displacements of sleeper are used as criteria to validate the FE model. Referred to the field measurement (Kaewunruen et al. 2019), the comparison of each value is shown in Table 1. For the comparison, it can be seen that the differences are less than 7% so it can be concluded that the FE model provides acceptably accurate results compared to the field measurement and can be used further to generate numerical data. Table 1. The comparison between the field measurement and results from the FE model Parameters

Field measurement

FE model

Wheel-rail contact force (kN)

100

98.4

Rail displacement at rail seat (mm)

2.606

2.596

Rail displacement at mid span (mm)

2.604

2.415

Sleeper displacement at rail seat (mm)

2.576

2.522

Sleeper displacement at mid span (mm)

2.511

2.352

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3.2 Data Variation and Preparation To create the data variation, different parameters in the FE models are varied. The data variation is shown in Table 2. The output from simulations used to develop the machine learning model is the vertical ABA of the front wheelset. The frequency of the simulation is 1000 Hz. The total number of simulations is 1458. The total length of the ballastless-track section is 15 m approximately. Table 2. Data variation Parameters

Range

Slab stiffness (GPa)

28.8–43.2

Speed of the rolling stock (km/h)

150–200

Size of irregularity (%)

80–120

Weight of rolling stock (tons)

35.64–43.56

In this study, raw data are used to develop the machine learning model. The raw data of vertical ABA is used in form of time-series data. That is a reason why this study applied CNN to develop the machine learning model because the CNN model is suitable for dealing with this form of data. Because the frequency of outputs from the FE model is fixed, the size of the output is varied based on the speed of rolling stock. The fasterrolling stock provides a smaller size of the output. Therefore, the padding technique is used to make the size of the data equal. It can be simply done by adding zero to the data with a smaller size to make the size or shape the same as the data with the biggest shape. An example of ABA from simulations is shown in Fig. 3. The figure demonstrates the ABA from a simulation with the following parameters; the speed of rolling stock is 150 km/h, the weight of rolling stock is 43.56 tons, the irregularity is original as shown in Fig. 4, and the slab stiffness is 43.2 GPa. 30

ABA (m/s2)

20 10 0 -10 -20 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Time (s)

Fig. 3. Example of ABA output

3.3 Machine Learning Model Development This study applies CNN to develop the machine learning model. CNN is a powerful technique used to extract the pattern in the data. This is a benefit of the feature extraction

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Irregularity (mm)

10 5 0 -5 -10 0

3

6

9

12

15

Distance (m)

Fig. 4. Original irregularity

part in the CNN architecture. Because this study uses the raw data to feed into the model, the feature extraction part is significantly useful for evaluating the slab stiffnesses. The developed model is a regression model. Outputs of the model are continuous values so the number of the output node is one. As mentioned in the previous section, the inputs of the machine learning model are time-series ABA. The total number of samples is 1458. 70% of data are used to train the machine learning model while another 30% are used to test the model. To ensure the performance of the model, hyperparameter tuning is conducted to test the models with different combinations of hyperparameters. Grid search is used for hyperparameter tuning. It is a technique used to test the performance of the model when hyperparameters are varied and when performances of every combination are recorded. Then, the model with the most suitable combination of hyperparameters is reported. The list of hyperparameters for hyperparameter tuning is shown in Table 3. Criteria used to evaluate the model performance are mean absolute error (MAE), root mean square error (RMSE), mean percentage error (MPE), and R2 . Table 3. Hyperparameter tuning list Model

Hyperparameters

CNN

Number of convolutional layers Filter Kernel size Number of pooling layers Pool size Activation function Batch size Optimizer Number of hidden layers Number of hidden nodes

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4 Results and Discussion From the machine learning model development, the relationship between true values and prediction is shown in Fig. 5. It can be seen that the prediction is significantly related to the true value. The R2 is 0.94 which demonstrates that the prediction can be used as representative of the true value. Other criteria are presented in Table 4. 45

R-Square 0.9426

Prediction (GPa)

40

35

30

25 25

30

35

40

45

True value (GPa)

Fig. 5. True value and prediction

From Table 4, it can be seen that the MAE and RMSE are 0.63 and 1.13 GPa respectively which are relatively low compared to the true value. The MPE is about 1.75% or the accuracy of the prediction is 98.25%. This indicates the developed machine learning model can be used to evaluate the ballastless track support stiffnesses with high accuracy and reliability. Table 4. Model performance Criteria

Values

MAE

0.63 GPa

RMSE

1.13 GPa

MPE

1.75%

R2

0.94

From hyperparameter tuning, the combination of hyperparameters that provides the best performance is shown in Table 5.

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Model

Hyperparameters

Tuned values

CNN

Number of convolutional layers

2

Filter

64 (conv1) and 32 (conv2)

Kernel size

3

Number of pooling layers

0

Pool size

N/A

Activation function

Linear

Batch size

8

Optimizer

Adam

Number of hidden layers

2

Number of hidden nodes

100

5 Conclusion This study aims to develop the machine learning model to evaluate the ballastless track support deterioration. The machine learning technique used in the study is CNN. Slab stiffnesses are used as the precursor to identify the ballastless track support deterioration. Numerical data is used to develop the machine learning model. Validated FE models are used to generate the numerical data. From the study, the developed machine learning model can provide a good result. The accuracy is higher than 95% and the MAE is less than 1 GPa. This indicates that the developed model can evaluate the slab stiffnesses accurately. This study demonstrates the potential of machine learning in evaluating the slab stiffnesses which there have not been previous studies studying on this aspect. The contribution of this study is the developed model can be used with railway maintenance. The slab stiffnesses can be tracked in real-time with a regular operation because the inputs used to develop the machine learning model in this study is ABA which can be measured using an accelerometer attached to an axle box. Therefore, the evaluation can be conducted immediately and does not obstruct railway operations. Then, the evaluated stiffnesses can be used to plan the maintenance responses. Early notice of ballastless track support deterioration will be beneficial in terms of management, maintenance planning, and maintenance cost. The severity of deterioration will not be too high so the damage can be minimized and managed efficiently. A limitation of this study is data used are numerical data. Using field data can guarantee the finding of the study. Additional features can be added to the machine learning model to improve the accuracy of the evaluation as well as data variation to improve the comprehensiveness of the machine learning model. Different machine learning techniques can be tried to explore their potential on ballastless track support deterioration.

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Acknowledgment. The authors also wish to thank the European Commission for the financial sponsorship of the H2020-RISE Project no.691135 “RISEN: Rail Infrastructure Systems Engineering Network”, which enables a global research network that addresses the grand challenge of railway infrastructure resilience and advanced sensing in extreme environments (www.risen2rai l.eu).

References Desai, A.: Defects in cast-in-situ ballastless track. IRJET 3(8), 130–134 (2016) Guo, Y., Zhai, W.: Long-term prediction of track geometry degradation in high-speed vehicle– ballastless track system due to differential subgrade settlement. Soil Dyn. Earthq. Eng. 113, 1–11 (2018) Kaewunruen, S., Ngamkhanong, C., Ng, J.: Influence of time-dependent material degradation on life cycle serviceability of interspersed railway tracks due to moving train loads. Eng. Struct. 199, 109625–109638 (2019) Li, M.X.D., Berggren, E.G.: A study of the effect of global track stiffness and its variations on track performance: simulation and measurement. Proc. Inst. Mech. Eng. F. J. Rail. Rapid. Transit. 224(5), 375–382 (2010) Li, T., Su, Q., Kaewunruen, S.: Influences of dynamic material properties of slab track components on the train-track vibration interactions. Eng. Fail. Anal. 115, 104633–104648 (2020) Park, S., Kim, J.Y., Kim, J., Lee, S., Cho, K.-H.: Analysis of dynamic characteristics of deformed concrete slab track on transition zone in high-speed train line according to train speeds. Appl. Sci. 10(20), 7174–7189 (2020)

Bursting Effects in Prestressed Concrete Sleepers at Different Prestressed Levels Dan Li1,2(B) , Sakdirat Kaewunruen1,2 , and Ruilin You3 1 Department of Civil Engineering, School of Engineering, University of Birmingham,

Birmingham B15 2TT, UK [email protected], [email protected] 2 TOFU Lab (Track Engineering and Operations for Future Uncertainties), School of Engineering, University of Birmingham, Birmingham B15 2TT, UK 3 China Academy of Railway Sciences, Beijing 100081, China [email protected]

Abstract. The railway sleeper is an important part of the railway track system, which distributes the wheel load to the substructure. The prestressed concrete sleeper is the most commonly used type around the world, which is usually designed for 50 years of service life. Prestressed concrete sleepers experience various environmental and loading conditions. Meanwhile, the material properties degrade with time. The premature failures of prestressed concrete sleepers could happen and result in a series of problems especially cracking. Tensile strength of prestressed concrete sleeper is much lower than compressive strength like other concrete structures. During service, impact loads could cause cracking in railseat or centre area of a prestressed concrete sleeper. Therefore, it is important to understand tensile stress at different prestressed levels. This paper presents a tensile stress assessment method for prestressed concrete sleepers. The outcomes of this paper will improve the concrete sleeper maintenance and inspection criteria. Keywords: Railway infrastructures · Prestressed concrete · Bursting effects · Tensile stress · Cracking

1 Introduction Nowadays, railway is believed the safest form of transportation for either passengers or goods, which provides the safe, economical, and comfort ride of trains (Remennikov et al. 2012). Conventional railway track (also called ‘ballasted railway track’) can be divided into two main parts: superstructure and substructure. Superstructure consists of rails, rail pads, prestressed concrete sleepers, fastening systems. Substructure includes ballast, sub-ballast, and formation (subgrade). The typical conventional railway track structure is illustrated in Fig. 1. Railway sleepers (or called ‘railroad ties’) are the main component of railway track structures (Gustavson 2004; Kaewunruen and Remennikov 2009a, 2009b; Kaewunruen et al. 2014; Remennikov and Kaewunruen 2007; Remennikov et al. 2012). Concrete

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1464–1470, 2023. https://doi.org/10.1007/978-981-19-7331-4_116

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Fig. 1. Typical conventional railway track

sleepers can be seen as concrete transverse beam laying on ballast. Railway sleepers can also be manufactured using timber and steel. However, prestressed concrete sleepers are the most commonly used type because of their high load carrying capacity, stability, and low maintenance costs. In general, the life span of prestressed concrete sleepers is designed to be 50 years. However, many prestressed concrete sleepers do not reach their expected life span due to damage or deterioration (Remennikov and Kaewunruen 2014; Thun 2006). The most critical problems related to concrete sleepers worldwide are ranked in Table 1 according to a survey conducted by Van Dyk (2012). It is obvious that cracking from dynamic loads is a significant problem in concrete sleepers. Cracking in prestressed concrete sleepers is usually caused by impact loads (Murray and Cai 1998). When trains run at high speed and with heavy haul, the rail-wheel interactions can induce much higher magnitude of loads than simple quasi-static loads (Remennikov and Kaewunruen 2008). The typical magnitude of impact loads can vary between 100 kN and 750 kN. The midspan and rail-seat section of railway sleepers are the most likely sections for cracking to occur (Montalbán Domingo et al. 2014). This paper aims to investigate the crack behaviour of prestressed concrete sleepers. The tensile stresses inside prestressed concrete sleepers at midspan is analysed. In this paper, a numerical study is rigorously executed to comprehensively assess the structural performance of prestressed concrete sleepers. The finite element sleeper model was developed and validated by the capacity experiment (Jing et al. 2021; Li et al. 2021).

2 Numerical Model 2.1 Fracture Analysis and Methods Cracks happen in a component due to imperfections. These imperfections can result from inclusions, grain boundary mismatches, differential thermal expansion or any other mechanisms. The growth of a crack throughout the volume of the structure could result in failure. In crack simulations, fracture toughness replaces the material strength in fracture calculations. The stress intensity factor (SIF) which determines the fracture toughness subject to linear-elastic fracture mechanics (LEFM) is a function of the stress on the flaw, flaw size, and structural geometry. The stress intensity factor can be calculated by: √ (1) KIC = σβ π α

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Table 1. Most critical causes of concrete sleeper failures (ranked from 1 to 8, with 8 being the most critical) Main causes

Problems

Worldwide response

Lateral load

Abrasion on rail-seat Shoulder/fastening system wear or fatigue

3.15 5.5

Vertical dynamic load

Cracking from dynamic loads Derailment damage Cracking from centre binding

5.21 4.57 5.36

Manufacturing and maintenance defects

Tamping damage Others (e.g., manufactured defects)

6.14 4.09

Environmental considerations

Cracking from environmental or chemical degradation

4.67

where σ is the applied stress; β is the dimensionless correction factor dependent on specimen geometry; and α is the crack length. 2.2 Crack Simulation Methods The extended finite element method (XFEM) is often used in fracture simulation, without updating the mesh, instead of traditional cohesive zone modelling (CZM) (Bergara et al. 2017). The extended finite element method eliminates the need for remeshing crack tip regions and it defines an extended finite element enrichment area around a crack tip and in regions where it is plausible that the crack tip might grow (Ansys 2018). In this way, a finer mesh is created by splitting existing cells instead of remeshing. However, the enrichment area usually takes a long time to compute, and so in large projects with large enrichment areas, the simulation becomes very slow. The new Unstructured Mesh Method (UMM) in Ansys mechanical was introduced to generate mesh on crack fronts. With the Unstructured Mesh Method, all-tetrahedral mesh for crack fronts can be generated automatically which reduces pre-processing time. Based on the Unstructured Mesh Method, the Separating Morphing and Adaptive Remeshing Technology (SMART) crack growth simulation was developed. This method automatically updates the mesh according to crack-geometry changes due to crack growth at each solution step instead of using the enrichment area derived from XFEM (Ansys 2018; Kulakov et al. 2021). The SMART crack simulation can be applied in large projects, unlike XFEM. 2.3 Finite Element Sleeper Model In this paper, a 2600-mm long Chinese Type III prestressed concrete sleeper with 7mm diameter tendons (Fig. 2) is utilised in the crack simulation. This type of railway sleeper, which is an integrated concrete block using pre-tensioning technology, is widely used

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in China. The material properties are shown in Table 2. Modelling is performed a model which is as close to the actual sleeper as possible.

Fig. 2. Geometrical features of the prestressed concrete sleeper

2.4 Crack Model An experimental study investigated crack propagation in the Chinese Type III prestressed concrete sleeper. The static capacity test of the railway sleeper was executed in accordance with EN 13230-2 (Standardization, 2009). Using the experimental procedure, the

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Material properties

Basic variables

Value

Concrete

Mean compressive strength

65 MPa

Modulus of elasticity

33 GPa

Prestressed wire

Yield strength

1570 MPa

Modulus of elasticity

200 GPa

Prestressing force

420 kN

crack propagation of prestressed concrete sleepers under capacity experiment is simulated. Figure 3 presents the simulation of crack propagation in the sleeper model at midspan.

Fig. 3. Simulation of crack propagation in the sleeper model at midspan

The comparison of the numerical and experimental results on crack propagation is presented in Fig. 4. Numerical model basically simulated the crack propagation in comparison with the experimental results. In the simulation, the numerical model has a good correlation with the initial crack point and ultimate crack point, with the difference being only 6.31% and 4.34% respectively.

3 Results and Discussion Using the crack model in Sect. 2, the tensile stresses of the prestressed concrete sleeper can be illustrated in Fig. 5 for crack propagation at midspan. Figure 5 presents the bursting effects of prestressed concrete sleepers at midspan.

4 Conclusions Cracking from dynamic loads at midspan is one of the most common forms of railway sleeper damage in conventional tracks. The challenge for railway engineers is to improve the performance of railway sleepers to fulfil crack resistance requirements. In this study, numerical and experimental investigations into the bursting effects of prestressed concrete sleepers were conducted. A full-scale model of Chinese Type III prestressed concrete sleepers was modelled and validated. The outcome of this paper will enhance the

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Numerical Experimental

150 140 130

Crack length (mm)

120 110 100 90 80 70 60 50 40 30 20 10 0 30

40

50

60

70

80

90

100 110 120 130 140 150

Load (kN)

Fig. 4. Comparison of the crack propagation in the numerical and experimental results 10

Tensile stresses

9

Tensile stresses (MPa)

8 7 6 5 4 3 2 1 0 0

1

2

3

4

5

6

7

8

9

10

Deflection (mm)

Fig. 5. Tensile stresses of prestressed concrete sleepers

reliability and safety of track components, and railway sleeper manufacturers could use the numerical model to assess their product designs. Acknowledgements. The authors are grateful to the Track Engineering and Operations for Future Uncertainties (TOFU) Lab, University of Birmingham for support throughout this study. The authors would like to thank the Commission for H2020-MSCA-RISE, Project No. 691135

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“RISEN: Rail Infrastructure Systems Engineering Network” (www.risen2rail.eu) [39]. In addition, the first author wishes to thank the China Academy of Railway Science (CARS) for the collaborative project.

References Bergara, A., Dorado, J., Martin-Meizoso, A., Martínez-Esnaola, J.: Fatigue crack propagation in complex stress fields: Experiments and numerical simulations using the Extended Finite Element Method (XFEM). Int. J. Fatigue 103, 112–121 (2017) Gustavson, R.: Structural Behaviour of Concrete Railway Sleepers (2004) Jing, G., Yunchang, D., You, R., Siahkouhi, M.: Comparison study of crack propagation in rubberized and conventional prestressed concrete sleepers using digital image correlation. In: Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 09544097211020595 (2021) Kaewunruen, S., Remennikov, A.M.: Impact capacity of railway prestressed concrete sleepers. Eng. Fail. Anal. 16(5), 1520–1532 (2009) Kaewunruen, S., Remennikov, A.M.: Structural safety of railway prestressed concrete sleepers. Aust. J. Struct. Eng. 9(2), 129–140 (2009) Kaewunruen, S., Remennikov, A.M., Murray, M.H.: Introducing a new limit states design concept to railway concrete sleepers: an Australian experience. Front. Mater. 1, 8 (2014) Kulakov, P., Kutlubulatov, B., Rubtsov, A., Mukhametzyanov, Z., Afanasenko, V.: The assessment of impact of the crack size on the fracture load of a cylindrical element. In: CEUR Workshop Proceedings–2021 (2021) Li, D., Kaewunruen, S., You, R.: Time-dependent behaviours of railway prestressed concrete sleepers in a track system. Eng. Fail. Anal. 127, 105500 (2021) Montalbán Domingo, L., Zamorano Martín, C., Palenzuela Avilés, C., Real Herráiz, J.I.: Analysis of the influence of cracked sleepers under static loading on ballasted railway tracks. Sci. World J. (2014) Murray, M., Cai, Z.: Literature Review on the Design of Railway Prestressed Concrete Sleeper. RSTA Research Report (1998) Remennikov, A., Kaewunruen, S.: Resistance of Railway Concrete Sleepers to Impact Loading (2007) Remennikov, A., Murray, M.H., Kaewunruen, S.: Reliability-based conversion of a structural design code for railway prestressed concrete sleepers. Pro. Inst. Mech. Eng. Part F: J. Rail Rapid Transit 226(2), 155–173 (2012) Remennikov, A.M., Kaewunruen, S.: A review of loading conditions for railway track structures due to train and track vertical interaction. Struct. Control Health Monit.: Official J. Int. Assoc. Struct. Control Monit. Eur. Assoc. Control Struct.s 15(2), 207–234 (2008) Remennikov, A.M., Kaewunruen, S.: Experimental load rating of aged railway concrete sleepers. Eng. Struct. 76, 147–162 (2014) Standardization, E.C.F.: EN 13230-2: Railway Applications-Track-Concrete Sleepers and Bearers Part 2: Prestressed Monoblock Sleepers (2009) Thun, H.: Assessment of Fatigue Resistance and Strength in Existing Concrete Structures. Luleå Tekniska Universitet (2006) Van Dyk, B.J., Dersch, M.S., Edwards, J.: International Concrete Crosstie and Fastening System Survey–Final Results. University of Illinois at Urbana-Champaign (2012)

Plate Thickness Distribution Estimation of a Belt Conveyor Support Structure Member Based on Cross-Sectional Vibration Modes Using Machine Learning Daichi Ogawa1 , Yaohua Yang1 , Tomonori Nagayama1(B) , Sou Kato2 , Kazumasa Hisazumi2 , and Tomonori Tominaga2 1 Department of Civil Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-Ku,

Tokyo 113-8656, Japan [email protected] 2 Nippon Steel Corporation, 6-1, Marunouchi, Chiyoda-Ku, Tokyo 100-8071, Japan

Abstract. Belt conveyor support structures are usually under a corrosive environment due to the dust accumulation from the belt conveyor. The corrosive damage may cause severe safety problems. Therefore, it is necessary to develop a specific health monitoring method for this kind of structure. Recently, Cross-Sectional vibration Mode (CSM)-based methods have been investigated. CSM has been shown to have sensitivity to damage to a member of a belt conveyor support structure. However, the quantitative evaluation of the damage has not yet been realized. In this paper, a machine learning method is applied to estimate the spatial distribution of plate thickness of the member. To create a large and precise CSM dataset efficiently, a new CSM indicator is proposed. To validate the method, the CSMs of multiple members are measured, and discrete plate thickness distributions of each member is estimated using a trained machine learning model. The result shows high accuracy. Keywords: Local vibration mode · Damage identification · Machine learning · Load carrying capacity estimation · Corrosion

1 Introduction A typical belt conveyor support structure is shown in Fig. 1. These structures are exposed to a highly corrosive environment because of the dust accumulation on the lower chord members from the belt conveyor’s mechanical part above. However, the hands-on inspection of the members is difficult due to the risk of entanglement accidents. Visual inspection from a remote place is also challenging because of dust accumulation. Therefore, a novel contactless inspection method for the lower chord members is necessary for the sustainable maintenance of the structure. The previous research (Rana et al. 2017) showed that the cross-sectional vibration modes (CSMs) of lower chord members with L-shaped cross-sections are localized, and © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1471–1480, 2023. https://doi.org/10.1007/978-981-19-7331-4_117

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Fig. 1. Belt conveyor support structure (Rana et al. 2017)

the properties of CSMs change only when the member has damage. The sensitivity of CSM to damages is high, e.g., the change of eigenfrequencies of CSMs is tens of Hertz when a member has a 10% cross-sectional loss (Rana et al. 2017). In addition, contactless measurements of CSM have been achieved using acoustic excitation or operational vibration (Kato et al. 2018; Yang et al. 2021). However, previous research does not realize the quantitative evaluation of corrosion damage. The target structural components of this research are lower chord members of a belt conveyor support structure. Because a tension force acts on these members, the load-carrying capacity is determined by its minimum cross-section. Therefore, the spatial distribution of plate thickness of these members is evaluated.

Fig. 2. The location of observation points and sections

In the inverse analysis of damage from dynamic characteristics, machine learning methods are getting increasing attraction (Chun et al. 2016; Wu et al. 1990). In these methods, non-linear relationship between input and output is learned using numerous forward simulation datasets. These methods are considered to have high applicability as long as the forward simulation is implementable. In this research, a stable method is proposed to estimate the plate thickness distribution of members of a belt conveyor support structure. In the method, FEM eigenvalue analysis is applied for creating dataset and a machine learning method is utilized for the thickness distribution estimation.

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2 Estimation of Spatial Distribution of Plate Thickness 2.1 Formulation In this research, the spatial distribution of plate thickness is estimated from CSM properties. From the view of measurability, the first three CSMs are utilized and their eigenfrequencies and discrete mode shapes are regarded as the input to the following machine learning model. Mode shapes are observed at three points per cross-section and the location of points are called A, B, and C as shown in Fig. 2. Here, mode shape means the amplitude with the sign at each observation point. A continuous member has infinite DOF while the number of the CSM properties to be considered is finite as described above. To estimate the thickness distribution with high stability, the state of a member needs to be expressed in lower dimension than the CSM properties. In this research, a member is divided into several “sections” and the thickness distribution of the member is expressed using average plate thickness of each section. In this research, the number of sections is set to 10. All sections have the same size, and the location of sections is as shown in Fig. 2. 2.2 Dataset Preparation Using FEM and CSM Indicator The results of the FEM eigenvalue analysis contain both CSMs and non-CSMs. To extract only CSMs, a CSM indicator (CSMI) is used. Kato et al. (2018) proposed a CSMI to extract CSMs from vibration modes identified through the acoustic excitation experiment. Typical cross-section shape of CSM features motions of points A and C in the same rotational direction, and point B’s motion with small amplitude as shown in Fig. 3. The CSMI is based on the following two functions (Kato et al. 2018).

Fig. 3. Typical vibration mode of L-shaped member: (a) CSM, (b)(c) non-CSM

G1 (f ) = 1 −

min(SA−C , SA+C ) SA+C

(1)

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G2 (f ) = 1 −

min(SB , SA+C ) SA+C

(2)

where SA+C , SA−C andSB are power spectrums of VA +VC , VA −VC , and VB , respectively. VA , VB , and VC are velocity responses at point A, B, and C, respectively. In the CSMI, only one cross-section is considered. These two functions take values between 0 and 1, and when the mode shape meets the characteristics of CSM, the functions take large value. CSMs can be extracted by thresholding G1 (f ), G2 (f )andG1 (f ) × G2 (f ). However, when a vast number of corrosion patterns are considered, finding appropriate thresholds for all patterns is very difficult, and sometimes extraction failure and mis-extraction happen. In this research, a threshold-free CSMI is proposed. The major difference lies on that the new CSMI considers all antinode cross-sections, while the previous CSMI only considers one cross-section. Firstly, antinode cross-sections are picked up considering VA + VC . Set of subscripts of antinode cross-section is expressed as I , and the following two functions are calculated at each cross-section.   min SA−C,i , SA+C,i g1 (i, f ) = 1 − (3) SA+C,i   min SB,i , SA+C,i g2 (i, f ) = 1 − (4) SA+C,i where SA+C,i , SA−C,i andSB,i are power spectrums at cross-section i ∈ I . Now, the new CSMI is defined as i∈I g1 (i, f )g2 (i, f ). If a vibration mode is CSM, the new CSMI is not 0, and otherwise the new CSMI is 0 or very close to 0. To check the performance of the proposed CSMI, CSMs are extracted from FEM eigenvalue analysis results. In this case, the FE model of the member is constructed using shell elements and has 2214 (369 × 6) DOFs in total. As mentioned above, the model is divided into ten sections which have one of four levels of thickness reduction (0, 20, 40, 60%), so the number of analyzed cases is 410 . The mode shapes are observed at 5 cross-sections. The comparison of CSM extraction using CSMIs is shown in Table 1. Using the proposed CSMI, both extraction failure and mis-extraction cases are reduced significantly. Table 1. Comparison between two CSMIs Extraction failure

Mis-extraction

Kato’s CSMI (Kato et al. 2018)

170757/410 =16.3%

50674/410 =4.8%

The proposed CSMI

61627/410 =5.9%

0

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3 Experimental Validation 3.1 Measurement Laboratory experiment of several specimens is conducted to extract the CSMs. The arrangement of the measurement is shown in Fig. 4. To consider the actual situation, tension forces of 16 kN are introduced by tension bolts on the two ends of the member. In the experiment, the specimens are excited using a hammer, and the velocity responses at 27 observation points are measured using laser doppler velocimeters (LDV). Two LDVs are used in the experiment. One measures vibration at a fixed reference point and the other measures the remaining points in sequence. The number of observation cross-sections is 9, and the measurements are conducted 26 (3x9–1) times per specimen. The setup of the measurement is shown in Fig. 5. To obtain modal frequencies and mode shapes of the CSMs, Eigensystem Realization Algorithm (ERA) (Juang and Pappa 1985) and Discrete Fourier Transform (DFT) are utilized. Firstly, modal frequencies are picked up using DFT, and then ERA calculates the amplitudes and phases at every observation point corresponding to each modal frequency.

Fig. 4. Plate thickness distribution of damaged members

Fig. 5. The abstract of measurement

In the experiment, 6 specimens are measured. They are one healthy member, one member with real corrosion, and four members with artificial damage. The four artificially damaged members are called specimens 1 to 4 in this study. Artificially damaged

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Fig. 6. The arrangement of experiment

members have uniform plate thickness in each section, while the real corroded member has spatially continuous thickness. The average thickness reductions of each member are shown in Fig. 6. The measured mode shapes are shown in Figs. 7, 8, and 9, and the eigenfrequencies are shown in Table 2. The results of the eigenvalue analysis of the FE model with the same thickness distribution are also shown. The FE model for the real corroded member is simplified by setting thickness per each section. The property of material for the FE model is adjusted so that the eigenfrequencies of the healthy member become close to the measurement result. As a result, both identified eigenfrequencies and mode shapes show good correspondence with the numerical model. As shown in Fig. 10, specimen 1 has two 2nd CSMs. However, the properties of these two modes are close to each other, and these two modes can be interpreted as the same vibration mode, which is identified as two modes because of noise. 3.2 Thickness Estimation from Measured CSM Machine learning model is trained with the FEM dataset, and average thickness reductions of 10 sections are estimated from measured CSMs. In this study, a machine learning model called LightGBM (Ke et al.2017) is used because the model is a kind of gradient boosting machine known for high accuracy and low calculation cost. The training data is created using suggested CSMI and the same FEM as 3.1. Each section has four types of damage (0, 20, 40, 60%) and the thickness of each section is uniform. For artificially damaged members, the training data contains the same thickness distribution pattern, which may lead to overestimating estimation accuracy. The section division is shifted by half-section as shown in Fig. 11, and another dataset is created. The true values of thickness reduction are the average thickness of each section. With the trained machine learning model, the average thickness reductions of the 10 sections are estimated for each specimen using the measured CSMs. True thickness reduction of each section and the estimation results are shown in Fig. 12. Additionally, to evaluate the accuracy of estimation for each specimen, the root mean square errors (RMSEs) for the 10 sections are calculated. Here, the RMSE is shown as the ratio to plate thickness of the healthy member. The results are shown in Table 3.

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Fig. 7. Comparison of measured mode shapes and FEM result: (a) healthy, (b) real corroded

Fig. 8. Two measured second CSMs of specimen 1

Fig. 9. Comparison of measured mode shape and FEM result: (a) specimen 3, (b) specimen 4

As a result, the average thickness reductions are estimated with about 10% RMSE for the real corroded member and specimen 2 to 4, but RMSE is about 15% for the healthy member and specimen 1. The result can be interpreted that the number of healthy and

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Fig. 10. Comparison of measured mode shape and FEM result: (a) specimen 1, (b) specimen 2

Fig. 11. Shifted section division for training data creation

Table 2. Comparison of measured eigenfrequencies and FEM result Measurement Freq1 (Hz) Freq2 (Hz) Healthy Real corroded

Shell FEM Freq3 (Hz) Freq1 (Hz) Freq2 (Hz) Freq3 (Hz)

107.8

221.0

342.9

106.3

218.1

343.2

97.5

163.3

273.5

93.8

166.9

258.4

Spe. 1

117.4

165.0, 172.7 324.6

115.1

171.6

314.6

Spe. 2

104.7

210.7

304.0

106.0

210.0

305.4

Spe. 3

60.6

175.5

315.7

62.6

176.8

318.9

Spe. 4

96.2

165.9

253.8

90.4

156.4

238.2

low damaged cases is small in the training data, and LightGBM cannot obtain enough information for such cases. 3.3 Training Data with Negative Damaged Cases To increase the information about low damaged cases, negative damage cases and low damage cases are added to the training data, even though negative damages do not exist in real members. Each section has one of three types of damage levels (5, −5, −15%), and therefore the number of newly analyzed cases is 310 . CSMI can extract CSMs in 34523 cases. These cases are added to the previous dataset, and LightGBM is trained

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Fig. 12. Thickness reduction estimation result: (a) healthy, (b) spe. 1, (c) spe. 2, (d) spe. 3, (e) spe. 4, (f) real corroded, (A) without negative damage, (B) with negative damage

Table 3. RMSEs of thickness estimation with two types of training data Healthy

Spe. 1

Without negative damage

15.66%

16.68%

With negative damage

10.07%

13.08%

Spe. 2

Spe. 3

Spe. 4

Real corroded

8.00%

9.70%

5.17%

9.29%

10.07%

9.32%

8.28%

9.29%

with the entire dataset. The estimation results and RMSEs for the 10 sections are shown in Fig. 12 and Table 3. RMSE is reduced for the healthy member and specimen 1 while the estimation accuracy does not degrade significantly in other cases.

4 Conclusions IN this paper, a machine learning and CSM-based method is proposed to estimate the spatial distribution of plate thickness of a belt conveyor support structure member. At first, a new CSMI is proposed to efficiently create a CSM dataset for machine learning. By using the CSMI, the number of extraction failures and mis-extractions is reduced significantly. Based on the CSM dataset, a LightGBM model is trained to estimate the thickness reductions of the member. Through experimental validations, adding negative damage cases to the training dataset is shown to improve the model’s performance. As a result, the plate thickness distribution of all specimens in the experiment is estimated at about 10% RMSE.

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References Ke, G., Meng, Q., Finley, T., Wang, T., Chen, W., Ma, W., Ye, Q., Liu, T.-Y.: LightGBM: a highly efficient gradient boosting decision tree. In: Proceedings of the 31st International Conference on Neural Information Processing Systems, pp. 3149–3157 (2017) Juang, J.-N., Pappa, R.: An Eigensystem realization algorithm for modal parameter identification and modal reduction. J. Guid. Control. Dyn. 8(5), 620–627 (1985). https://doi.org/10.2514/3. 20031 Chun, P.-J., Kuramoto, N., Kumaoka, K.: Damage identification on I-Beam member using multipoint acceleration measurement and machine learning. J. Jap. So. Civ. Engineers, A2 (Applied Mechanics (AM)), 72(2), I_623-I_631 (2016). https://doi.org/10.2208/jscejam.72.I_623 Kato, S., Nagayama, T., Di, S., Hisazumi, K., Tominaga, T.: Identification of a cross-sectional vibration mode of a belt conveyor support structure using acoustic loading. J. Struct. Eng. 064A, 354–363 (2018). https://doi.org/10.11532/structcivil.64A.354 Rana, S., Nagamaya, T., Hisazumi, K., Tominaga, T.: Damage identification of belt conveyor support structure based on cross-sectional vibration characteristics. Struct. Cont. Health Monitor. (2017). https://doi.org/10.1002/stc.2349 Wu, X., Ghaboussi, J., Garrett, J.H., Jr.: Use of neural networks in detection of structural damage. Comput. Struct. 42(4), 649–659 (1990). https://doi.org/10.1016/0045-7949(92)90132-J Yang, Y., Namayama, T., Kato, S., Hisazumi, K., Tominaga, T.: Sensitivity analysis and identification of cross-sectional modes of a belt-conveyor using operational vibration. In: Proceedings of the 76th Annual Conference of Japan Society of Civil Engineers (2021)

Simulation and Simplified Method Study on Seismic Collapse of Core-outrigger Structures Y. Liu2 , J. Huang2 , F. F. Sun1,2(B) , and G. Y. Chen2 1 State Key Laboratory for Disaster Mitigation in Civil Engineering, Tongji University,

Shanghai 200092, China [email protected] 2 Department of Building Engineering, Tongji University, Shanghai 200092, China [email protected], [email protected], [email protected]

Abstract. The seismic collapse resistance of super high-rise structures is very important. Based on the shaking table test of a core-outrigger structure, a multiscale finite element model is established for collapse simulation analysis; IDA static equivalent method is proposed to evaluate the collapse resistance of the model on the assumptions about lateral force distribution, capacity spectrum curve and collapse performance point; blind source separation method is used for datadriven damage detection to reveal the earthquake collapse mechanism and evolution process of super high-rise structures. The results show that the response time history of the multi-scale model is in good agreement with the experiment, and can simulate the lateral collapse of the structure caused by the local buckling of the column; IDA static equivalent method is efficient and accurate for evaluating the seismic collapse resistance of the core-outrigger structure; blind source separation method can extract the information of time and location of structural damage only from structural response data. Keywords: Core-outrigger structure · Collapse margin ratio · Structural damage detection · Blind source separation

1 Introduction The core-outrigger structure strengthens the connection between the central core and the perimeter columns through the outriggers, exerting the axial stiffness of the perimeter columns to resist overturning bending moment, and effectively improving the overall lateral stiffness of the structure. In order to ensure that structures do not collapse under strong earthquake, it is necessary to study the earthquake resistance and collapse mode. At present, there are few real-world cases of earthquake collapse of core-outrigger structure, and most of the existing researches are carried out by experiment and numerical simulation. Sun et al. (2017) conducted a scale shaking table test on a 56-story steel core-outrigger structure, compared the response of the structure under resonance wave and non-resonance wave, and found that the peak acceleration of the structure under resonance wave could cause the collapse of the structure only at the standard level of

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1481–1500, 2023. https://doi.org/10.1007/978-981-19-7331-4_118

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small or medium earthquake, and the collapse mode is the overturning failure caused by the buckling of the side column in the middle layer. In this paper, multi-scale finite element simulation (Tan et al. 2020; Li et al. 2009) and simplified collapse analysis are adopted to further study based on the previous test. Pushover Analysis (Krawinkler and Seneviratna 1998) and Incremental Dynamic Analysis (IDA) (Vamvatsikos and Cornell 2002) are two commonly used seismic collapse analysis methods for building structures. The former has low computational complexity and is suitable for structures controlled by first-order mode. However, this approach needs improvement when used for high-rise structures because the influence of high order modes on high-rise structures cannot be ignored. Based on a series of dynamic elastoplastic time history analysis which increasing the ground motion intensity until the structure collapses, the collapse margin ratio (CMR) is defined as the evaluation index of the collapse resistance of structures. However, this method requires considerably longer computational time (Huang et al. 2017; Samadi and Jahan 2019). Many scholars have noticed this problem and put forward various simplified methods. Vamvatsikos et al. (2006, 2007, 2010) and De Luca et al. (2013) proposed and developed the SPO2IDA method, which predicts the IDA curve of the structure through the static Pushover method, so as to obtain the collapse resistance of the structure. Hamidia et al. (2014a, 2014b, 2015) established IDA database of SDOF system based on ideal elastic-plastic model, and then simplified MDOF into SDOF according to first-order modal pushover curve; finally, obtained CMR of MDOF by using the database of SDOF. Soleimani et al. (2018) proposed a two-component energy-based pushover method for the bidirectional IDA simplification of asymmetric-plan buildings, and verified it in a three-story steel frame. Navideh et al. (2012) analyzed the difference between Pushover capacity curve and IDA curve for steel frame structure, and the results show that the collapse resistance of the structure obtained by IDA method is the strongest, while the collapse resistance curve obtained by Pushover method in the form of uniform loading is the weakest. The Pushover ability curve with inverted triangle and lateral loading mode of the first mode is located in the middle. It is concluded that these pushover-based simplified methods are mainly applicable to low-rise or multi-storey structures dominated by first-order modes. However, the influence of high-order modes in high-rise core-outrigger structures cannot be ignored, leading to the results of simplified pushover method not consistent with those of IDA method. Therefore, it is necessary to study the improved Pushover equivalent method for the case of high-rise buildings. Using the structural response monitoring data, damage identification, real-time monitoring of the overall behavior of the structure, and damage location and damage degree diagnosis are beneficial to reveal the damage evolution process and collapse mechanism of the structure. The data-driven damage identification method has obvious advantages in practical application by using appropriate algorithms to identify structural damage from sensor monitoring data without structural information, and has received increasing attention and favor. Burgos et al. (2020) summarized the current data-driven methods for damage identification in structural health monitoring research. Blind source separation (BSS) signal processing technology is one of the important methods. BSS technology can separate

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multiple source signals from observation signals when the signal transmission channel is unknown and there is only a little prior knowledge of source signals. Second order blind identification (SOBI) (Huang and Nagarajaiah 2021), independent component analysis (ICA) (Kerschen et al. 2007) and other excellent algorithms are currently widely used in speech recognition, image processing, biomedical signal processing, structural modal recognition and other fields. Yang and Nagarajaiah (2014) proposed WT-ICA method by combining wavelet transform (WT) and ICA algorithm of blind source separation. Firstly, data pre-processing is conducted in the wavelet domain, and then the selected high-frequency signal is used as the input for blind source separation to reveal the damage time and location information. The effectiveness of the method is verified by numerical experiments and multi-layer structure monitoring data. However, the applicability of this method in the damage detection of complex high-rise structures remains to be tested. In this study, the earthquake collapse of core-outrigger structure is simulated by multi-scale finite element analysis. At the same time, IDA static equivalent method for the evaluation of the seismic collapse resistance of structures are proposed and the effectiveness are verified, and the blind source separation technology is used to carry out data-driven damage identification based on the structural response.

2 Overview of Shaking Table Test 2.1 Test Model The prototype of the test modal is a 56-story steel core-outrigger structure with a constant story height of 3.6 m, a total height of 201.6 m, column spacing of 8 m, and a structure plane of 32 × 32 m. The central core is a trussed tube, and the outriggers and belt trusses are placed on the 18, 19, 37 and 38th stories. In order to facilitate model processing, the prototype structure is simplified into a two-dimensional model, as shown in Fig. 1 (a). On the premise that the overall performance is basically consistent, two adjacent layers are merged into one, as shown in Fig. 1 (b). Further, the 1:40 scale design is carried out. The section sizes of the original model, simplified model and scale test model are shown in the paper of Sun et al. (2017). The shaking table model consists of two identical planar core-outrigger structures in parallel with a connecting rod on which floor slabs are placed with a weight of 180 kg on each floor. According to the design of similarity ratio, the component material in the test is red copper. The test model is shown in Fig. 1 (c). 2.2 Test Cases Both non-resonant and resonant ground motions are applied in the experiment. The former are natural seismic waves, of which the energy distribution is not relatively concentrated at the natural frequency of the structure. On the contrary, the latter are obtained by scaling the Fourier spectra of natural seismic waves, that is, amplifying the amplitudes in the frequency range of 0.75T n ~ 1.25T n for near-field earthquakes, and the scaled seismic wave is obtained by inverse Fourier transform. For far-field earthquakes, the same operation is performed in the frequency range of 0.9T n ~ 1.1T n .

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(a) 56-layer two-dimensional model

(b) extracted layer twodimensional model

(c) test model

Fig. 1. Simplification of the shaking table test model

The natural far-field earthquake record selected in this paper is the Chi-Chi TCU117 (1999). Frequent occurrence of seismic intensity 7 of China Code for Seismic Design of Building (Chinese Standard 2016) with peak acceleration of 35 gal was chosen as the intensity of input ground motions in the test. The Chi-Chi wave is scaled to obtain the first-order resonance wave, i.e. Chi-Chi-1st of the structure. The time history of natural wave and resonance wave is shown in Fig. 2.

(a) Chi-Chi

(b) Chi-Chi-1st

Fig. 2. Time histories of Chi-Chi and its first-order resonant ground motion

The peak values of seismic acceleration under Chi-Chi natural wave case and ChiChi-1st case are both 0.07 g, and the actual values are 0.093 g and 0.103 g during the test respectively, which are slightly different from the set scheme. Measured values are used as input for the finite element analysis in the next chapter. Test cases 1 and 5 were two white noise cases, and cases 2–4 were El Centro natural wave and the first two resonant waves, respectively. The experimental phenomenon of

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the above cases was far from collapse. In case 6, the Chi-Chi natural wave was loaded, and the structural displacement response was obvious. Case 7 (Chi-Chi-1st) was loaded by Chi-Chi first-order resonance wave, and the axial deformation of the left perimeter column of the 13th floor further increased, and finally buckled, causing lateral collapse of the structure. Therefore, this study mainly conducts simulation analysis on Chi-Chi natural wave (case 6) and Chi-Chi-1st resonance wave (case 7).

3 Simulation Based on Multi-scale Model 3.1 Non-collapse Case Simulation It is found that the left perimeter column of the 13th floor of the structure has a large axial deformation, which makes the superstructure tilt to one side and eventually leads to the lateral collapse of the structure. In this chapter, ABAQUS was used to establish a multi-scale model for analysis. S4R shell element was used for the perimeter column of the 13th floor of the structure to establish the box column model, and B31 beam element was used for other components. Because the beam-column joints of the test model are strengthened, there is basically no damage in the test process, so the beam-column joints of the finite element model are set as rigid connections. That is, in the multi-scale model, the end joints of the 13th layer perimeter column are still simulated by beam element, while the middle part of the perimeter column is simulated by shell element within 150 mm. The four edges of the end section of the shell element column are connected with the end of the beam element by coupling constraints, and all the six degrees of freedom are constrained. Multiscale finite element is shown in Fig. 3 (a).

(a) Model before loading

(b) Model after the non-collapse case

Fig. 3. Multiscale model of non-collapse case

The first three natural periods of the model were obtained through modal analysis, which was very close to the results of white noise cases 1 and 5, as shown in Table 1. At

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the same time, there is little difference between the two white noise results, indicating that the overall damage of the structure is not obvious before case 6. Therefore, for the sake of space, only the simulation of Chi-Chi case is given as a representative of non-collapse case. Table 1. Periods of the multiscale model and the test model T 1 (s)

T 2 (s)

T 3 (s)

Case 1, white noise

0.530

0.159

0.082

Case 5, white noise

0.533

0.160

0.083

Multiscale model

0.539

0.161

0.084

(a) Roof acceleration

(b) Roof displacement

Fig. 4. Comparison of the top layer response of experiment and finite element analysis of Chi-Chi case

In order to consider the influence of accumulated damage and residual deformation in earlier cases, the multi-case relay calculation was carried out. Figure 4 (a) and (b) respectively show the time-history curves of acceleration and displacement at the top of the model under the action of Chi-Chi natural wave (case 6), which are in good agreement with the test results. At the end of this case, the deformation of the element part of the left perimeter column shell on the 13th floor of the structure is shown in Fig. 3 (b). It can be seen that there is local buckling of the perimeter column, but the displacement of the top layer does not shift significantly to the left. 3.2 Collapse Case Simulation In the last case of the shaking table test (Chi-Chi-1st), the left perimeter column of the 13th floor buckled severely, and the inner core column also suffered great damage, which eventually led to the collapse of the structure. In order to more accurately simulate the seismic response of the structure under this case, the finite element model was adjusted.

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Based on the original multi-scale model, the core columns on the left and right sides of the 13th floor of the structure were also changed into multi-scale members. Due to the different sectional sizes of the inner core column and the perimeter frame column, the buckling modes of both cannot be obtained simultaneously in the buckling analysis, so the initial defects need to be treated separately when introducing. In this model, the initial defect of the perimeter column is still obtained by introducing the buckling mode, while the initial defect of the inner column is obtained by importing the result file of the axial compression analysis of individual member. Finally, the adjusted multi-scale finite element model is shown in Fig. 5 (a).

(a) Model before loading

(b) Model after the collapse case

Fig. 5. Multiscale model of the collapse case

The time-history analysis was conducted on the adjusted multi-scale finite element model under Chi-Chi-1st case, and the time-history curves of the acceleration and displacement of the top layer were obtained, which were compared with the test results, as shown in Fig. 6 (a) and (b) respectively. When the earthquake affected about 6.2 s, the displacement of the top layer was very large and the calculation was difficult to converge. Therefore, the finite element curves in the figure all stopped at about 6.2 s. It can be seen that the finite element curve is in good agreement with the test curve before the calculation stops. It can be seen from Fig. 6 (b) that the displacement of the top floor of the structure began to shift to one side continuously when the seismic action was 3.3 s, indicating that lateral collapse occurred at this time, which is consistent with the test situation. In the test, when the displacement of the top floor reached about 60 mm, the structure stopped overturning and began to vibrate again, mainly because the weight on the floor had a certain thickness. After the failure of the left column on the 13th floor, the upper structure fell on the weight, so it stopped overturning and continued to vibrate. At the end of this case, the deformation of the element part of the left inner column and perimeter column shell of the 13th floor of the structure is shown in Fig. 5 (b). It can be seen that at this time, the inner column and the perimeter column have serious axial

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(a) Roof acceleration

(b) Roof displacement

Fig. 6. Comparison of the top layer response of experiment and finite element analysis of ChiChi-1st case

deformation and have buckled. Meanwhile, the superstructure of the 13th floor overturns obviously to the left.

4 IDA Static Equivalent Method 4.1 Procedure of IDA Static Equivalent Method The general idea of IDA static equivalence method is to realize IDA static equivalence through Pushover analysis. The load-deformation curve obtained from Pushover analysis is used to be equivalent to IDA curve. In the lateral force mode of Pushover analysis, mode combination method is used to introduce mode participation coefficient and seismic influence coefficient to consider the influence of dynamic response characteristics and seismic spectrum characteristics of the structure. The pushover curve was transformed into capacity spectrum curve, and then the collapse performance point on the pushover capacity curve was identified by referring to the idea of defining collapse performance point on IDA curve. On this basis, the ductility coefficient, the equivalent period and equivalent damping ratio of the equivalent elastic structure were obtained according to the energy equivalent criterion. In this study, the 5% damped elastic spectral acceleration at the first period of the structure, i.e., Sa (T1 , 5% ) is adopted as an index of ground motion intensity. According to Vamvatsikos and Cornell’s research findings (Vamvatsikos and Cornell 2002), the IDA curve obtained from the same group of seismic waves using Sa (T1 , 5% ) as a measure index of ground motion intensity was less discrete than that obtained from the peak acceleration of ground motion, i.e., PGA as the intensity index. The demand spectrum of the seismic wave is determined according to the equivalent damping ratio, and then the demand spectrum of the seismic wave is scaled to pass through the collapse performance point, and the ground motion intensity of the structure collapse corresponding to the seismic wave is obtained. Then the seismic collapse intensity of a group of seismic waves is analyzed statistically, and the vulnerability curve and CMR value are obtained. IDA static equivalence method is based on the following assumptions:

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(1) Assumption of lateral force distribution in pushover analysis. In the mode decomposition response spectrum method, the horizontal seismic action of the structure is proportional to the mode participation coefficient and the seismic influence coefficient. Therefore, when determining the lateral force distribution of Pushover analysis, the mode participation coefficient and the seismic influence coefficient are introduced to consider the dynamic characteristics of the structure and the spectrum characteristics of ground motion. It is assumed that the first and second modes have a great influence on the seismic collapse of the structure, so the combination of the two modes is used to obtain the multimodal lateral force distribution. The lateral force distribution of the jth seismic wave can be calculated according to Eq. (1): φj = ω1j γ1 φ1 + ω2j γ2 φ2

(1)

where, φj is the multimodal lateral force distribution mode corresponding to the jth seismic wave; γ1 and γ2 are respectively the mode participation coefficients of 1st mode and 2nd mode; if γ1 or γ2 is negative, its absolute value is taken. ω1j and ω2j are respectively the seismic influence coefficients corresponding to the first and second order periods of the structure of the jth seismic wave. (2) Assumption of capability spectrum curve. Firstly, the pushover curve (Qbase −U roof ) is converted into capability spectrum curve (Sa −Sd ) according to Eqs. (2) and (3):   Sd Tj , ξ = U roof /γj φjroof (2)   Sa Tj , ξ = Qbase /αj Mt

(3)

where, U roof and Qbase are the top displacement and base shear force respectively, Mt is the total mass. γj φjroof and αj are obtained by interpolation. In detail, the mode participation coefficients γ1 and γ2 of the first two modes are obtained by modal analysis, so as to obtain γ1 φ1roof and γ2 φ2roof , and at the same time, the mode mass participation coefficients α1 and α2 are obtained. The 1st-mode and 2nd-mode pushover analysis were conducted respectively, and the corresponding pushover curves and their initial stiffness Ko1 and Ko2 were obtained. For the jth ground motion, the pushover curve corresponding to the multimodal lateral force distribution is calculated, and then the initial stiffness Koj is obtained. Finally, the γj φjroof and αj corresponding to the jth ground motion are interpolated according to Eqs. (4) and (5). γj φjroof =

 Koj − Ko1  × γ2 φ2roof − γ1 φ1roof + γ1 φ1roof Ko2 − Ko1

(4)

Koj − Ko1 × (α2 − α1 ) Ko2 − Ko1

(5)

αj = α1 +

(3) Assumption of the collapse performance point. For IDA analysis methods, collapse is usually considered when the tangent stiffness of IDA capacity curve degrades to 20% of the initial stiffness or the maximum inter-story displacement angle of

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the structure exceeds 10%. In this study, a similar criterion is used to conclude that collapse occurs when the tangent stiffness of the capacity curve degrades to 10% of the initial stiffness. Due to the dynamic effect, IDA capacity curve will continue to rise in the later stage, and its stiffness will be larger than that of the corresponding pushover curve. Therefore, the set of tangent stiffness degradation degree corresponding to the collapse point of pushover analysis is smaller than that of IDA method. The basic ideas and assumptions of IDA static equivalent method are introduced above, and the calculation process is summarized as follows: (1) Wave selection. Select a set of seismic waves with the same requirements as IDA; (2) Modal analysis. The modal analysis of the structure is carried out to obtain the first two modes (φ1 and φ2 ), periods (T1 and T2 ), mode mass participation coefficients (α1 and α2 ), and the mode participation coefficients (γ1 and γ2 ). (3) Mode combination. For each earthquake record, the seismic influence coefficients of the first and second order periods (ω1j and ω2j ) were calculated and the multimodal lateral force distribution mode was obtained according to Eq. (1). (4) Pushover analysis. Based on the multimodal lateral force distribution model corresponding to the jth ground motion, the structural pushover analysis was carried out to obtain the capacity curve, which was converted into acceleration displacement response spectra (ADRS) format; take the point where the tangent stiffness degrades of 10%  stiffness   on ADRS as the collapse performance point,   to the initial total , S c T , ξ total ; next, ADRS is equivalent to an ideal elastici.e., Sdc Teq , ξeq eq eq a plastic model according to the principle of equal energy, and the ductility coefficient μ is calculated according to Eq. (6); on this basis, the secant stiffness equivalent linearization method proposed by Rosenblueth and Herrera (1964) is adopted to take the secant stiffness at the maximum deformation (collapse performance point) as the equivalent stiffness Keq . According to the principle that the hysteretic energy dissipation of the ideal elastoplastic structure is equal to the viscous damping energy dissipation of the equivalent elastic system in a vibration cycle, the equivalent period Teq and equivalent damping ratio ξeq of the equivalent elastic structure are presented in Eqs. (7) and (8). μ = Sdu /Sdy

(6)

√ Teq =T1 μ

(7)

ξeq =

2 μ−1 π μ

total ξeq = ξ + κξeq

(8) (9)

Since the equivalent damping ratio ξeq is not the whole damping of the elasticplastic structure, the total equivalent damping ratio of the structure should be obtained

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by superposition with the initial damping ratio ξ of the structure itself, as shown in Eq. (9). Considering the possible errors caused by the transformation of the structure’s inelastic deformation energy into the velocity related damping ratio, as well as the differences in the hysteretic models of elastic-plastic structures, equivalent damping adjustment coefficient κ is introduced in ATC-40 specification (Applied Technology Council 1996). (5) Response spectrum calculation. For each seismic wave, the 5% damped elastic spectral acceleration at the first period of the structure,  i.e., Sa (T1 , 5% ) and the total total are calculated. ξeq damped elastic spectral acceleration at Teq , i.e., Sa Teq , ξeq (6) Calculation of collapse ground motion intensity index Sac (T1 , 5%). The seismic wave demand spectrum is scaled the collapse performance point on ADRS.  to pass   total total , so the collapse ground Sa Teq , ξeq The scaling coefficient is Sac Teq , ξeq motion intensity index can be obtained as follows:   total Sac Teq , ξeq  Sa (T1 , 5%) Sac (T1 , 5%) =  (10) total Sa Teq , ξeq (7) Calculation of vulnerability curve and collapse margin ratio (CMR). 4.2 Verification of IDA Static Equivalent Method The two-dimensional model of the prototype structure of the shaking table test model in Fig. 1(a) was taken for analysis, and the modal analysis of the structure was carried out first. The first two vibration modes of the structure are calculated as shown in the solid black line and dotted black line in Fig. 7. The first two natural periods of the structure T1 = 4.269s and T2 = 1.358s. The 20 seismic waves given in Table 2 are selected for calculation, and the first two seismic influence coefficients ω1 and ω2 of each seismic wave with 5% damping ratio are obtained, as shown in Table 2. According to the first two modes and the mass of each layer of the structure, the mode participation coefficients can be obtained, i.e., γ1 = 1.52 and γ2 = −0.77. The absolute value of γ2 are taken according to hypothesis 1. As a consequence, the multimodal lateral force distribution can be calculated by Eq. (1) as shown in Fig. 7. Pushover analysis was conducted on the structure according to the multimodal lateral force distribution, and 20 pushover curves were obtained, as shown in Fig. 8. Note that the pushover curve corresponding to no. 6 seismic wave did not generate platform segment, which was inconsistent with the actual situation and was not shown in the figure. It can be seen that the ductility of each pushover curve is larger than that of the first and second order natural modes. This is because the plastic development position of the structure is relatively concentrated when the single natural mode is conducted, while the plastic development position is more dispersed and more difficult to destroy when the multi-mode is conducted, so the displacement of the top layer is larger than that of the single vibration mode.

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Record number

Ground motion

ω1

ω2

Equation 1

SUPERSTITION MOUNTAIN_45

0.058

0.088

Equation 2

CPC_TOPANGA CANYON_16_nor

0.061

0.579

Equation 3

LWD_DEL AMO BLVD_90_nor

0.044

0.334

Equation 4

PEL_HOLLYWOOD STORAGE_90

0.184

0.559

Equation 5

PEL_HOLLYWOOD STORAGE_180

0.103

0.188

Equation 6

ELCENTRO

0.455

0.226

Equation 7

TRI_TREASURE ISLAND_90

0.097

0.841

Equation 8

SHW1

0.211

0.633

Equation 9

SHW2

0.232

0.673

Equation 10

SHW3

0.208

0.810

Equation 11

SHW4

0.238

0.729

Equation 12

Northridge-Arleta

0.057

0.339

Equation 13

San Fernando-180deg

0.205

0.868

Equation 14

San Fernando-90deg

0.167

0.647

Equation 15

Taft Lincoln School-69deg

0.083

0.332

Equation 16

Taft Lincoln School-339deg

0.064

0.287

Equation 17

Mexico City_270

0.211

0.760

Equation 18

Loma Prieta_270

0.049

0.534

Equation 19

Hollywood Storage_270deg

0.144

0.456

Equation 20

Fsd_SANTA FELICIA DAM172

0.078

0.120

For this structure, rare occurrence of seismic intensity 7 of China Code for Seismic Design of Building (Chinese Standard 2016) with peak acceleration of 1.21 m/s2 , that is, Sa,MCE (T1 , 5%) equals to 1.21 m/s2 , note that MCE means maximum considered earthquake. The calculation results of seismic waves are shown in Table 3. For each ground motion intensity level Sa , the number of ground motions whose collapse strength index Sac (T1 , 5% ) is lower than Sa is counted as Ncollapse ; the total number of ground motions is counted as Ntotal ; therefore, the collapse probability corresponding to a certain ground motion intensity level is Ncollapse /Ntotal . According to the seismic wave calculation results, scattered points of collapse probability were statistically obtained, and the cumulative function of lognormal distribution was used for fitting to obtain the collapse vulnerability curve, as shown in Fig. 9. The collapse margin ratio of the structure can be expressed as: CMR =

Sac (T1 , 5% )50% = 4.28 Sa,MCE (T1 , 5% )

(11)

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Fig. 7. Lateral force distributions for Pushover analysis of 20 ground motions

Fig. 8. Roof displacement-base shear curves by Pushover analysis of 20 ground motions

The collapse vulnerability curve calculated by IDA is shown as the dotted line in the Fig. 9, and the corresponding CMR value is 4.92 (Ge 2012). The results obtained by the IDA static equivalence method are close to those calculated by IDA and tend to be conservative.

γ φ roof

1.44

0.98

1.03

1.25

1.39

1.00

1.26

1.26

1.18

1.25

1.08

1.16

1.18

1.17

1.15

1.20

0.96

1.24

1.43

Record No

Equation 1

Equation 2

Equation 3

Equation 4

Equation 5

Equation 7

Equation 8

Equation 9

Equation 10

Equation 11

Equation 12

Equation 13

Equation 14

Equation 15

Equation 16

Equation 17

Equation 18

Equation 19

Equation 20

0.61

0.48

0.30

0.46

0.42

0.44

0.45

0.43

0.38

0.49

0.45

0.50

0.50

0.33

0.58

0.49

0.35

0.32

0.62

ω

1.61

1.50

1.44

1.49

1.47

1.48

1.48

1.48

1.46

1.50

1.48

1.51

1.51

1.44

1.58

1.50

1.44

1.43

1.62

μ

0.17

0.16

0.15

0.15

0.15

0.15

0.15

0.15

0.15

0.16

0.15

0.16

0.16

0.15

0.17

0.16

0.15

0.15

0.17

total ξeq

4.98

3.88

2.51

3.70

3.42

3.55

3.59

3.48

3.08

3.92

3.58

4.01

4.02

2.69

4.71

3.93

2.83

2.62

5.03

Te

0.76

1.42

0.48

2.07

0.63

0.81

1.63

2.01

0.56

2.33

2.04

2.28

2.17

0.95

1.01

1.80

0.44

0.60

0.57

Sa (T1 , 5%)

4.14

5.09

7.98

5.33

5.77

5.54

5.48

5.66

6.41

5.04

5.49

4.95

4.92

7.39

4.31

5.03

7.01

7.60

4.12

  total Sa Teq , ξeq

Table 3. Summary of the calculation results

7.87

8.18

3.75

3.80

5.64

7.25

7.49

3.79

4.56

6.74

6.66

2.98

5.96

2.53

7.23

7.25

3.43

2.69

7.95

Sac (T1 , 5%)

6.50

6.76

3.10

3.14

4.66

6.00

6.19

3.13

3.77

5.57

5.51

2.46

4.92

2.09

5.97

5.99

2.83

2.22

6.57

Sac /Sa,MCE

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Fig. 9. Collapse vulnerability curve

5 Structural Damage Identification Based on Blind Source Separation 5.1 Basic Theory of Blind Source Separation for Damage Identification Blind source separation (BSS) is a signal processing technology that can extract or recover the source signal from the observed mixed signal only according to the statistical characteristics of the source signals when the characteristics of the source signals and the transmission channels are unknown. Independent component analysis (ICA) is a commonly used algorithm in BSS, which is separated by independent criterion and achieves maximum value through objective function (cost function) to eliminate high-order statistical correlation in mixed observation signals and achieve source signal separation. The relationship can be defined as x(t) = As(t) =

n 

ai si (t)

(12)

i=1

where, x(t) is the mixed observation signal, A is the mixed matrix, and s(t) is the independent source signal. The essence of ICA lies in finding an appropriate separation matrix W to recover the input signal s(t) from the observation signal x(t) through the separation matrix, that is, y(t) = Wx(t) ≈ s(t), in which y(t) is the estimated vector of the input signal s(t). Fast independent component analysis (Fast-ICA), which is based on the goal of maximization of gaussian function with negative entropy as a measure of independence between each component of the objective function, using Newton iterative algorithm for observation signals batch, a large number of sampling points of each is presented for separating each vibration signal from an independent component, isolated until all of the independent component. Yang and Nagarajaiah (2014) proposed WT-ICA method which combining discrete wavelet transform (DWT) and Fast-ICA, and achieving good performance in structural damage identification. High frequency signals with abnormal pulses were extracted by

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discrete wavelet transform, which were input into ICA algorithm as mixed signals to identify the time and location of damage. Remarkably, no structural model information is required in this method, only structural response monitoring data is required, which is a data-driven approach. The damage identification process of this method is as follows: (1) DWT pre-processing. DWT is carried out on the structural response collected by m sensors, and the signal is respectively decomposed into high frequency signal and low frequency signal, and then the low frequency signal is decomposed by repeating the previous step. The high frequency signal containing abnormal pulses can be extracted by multi-level decomposition of the low frequency signal. (2) BSS based on Fast-ICA. m high-frequency signals obtained by DWT were used as mixed signals of BSS and input into Fast-ICA algorithm to obtain m independent components (ICs), among which the ICs containing obvious pulses were judged as feature independent components (FICs). (3) Determine the time and location of damage. The number of structural damage events was determined according to the number of pulses in the FICs, and the time of damage was determined according to the time when the pulse appeared in FIC time history curves, and the location of damage was determined according to the signal distribution vectors (SDVs) corresponding to FICs. 5.2 Chi-Chi-1st Case Damage Identification Based on WT-ICA The arrangement of accelerometers in excitation direction is shown in Fig. 10. According to the above steps, the responses of 19 accelerometer points under Chi-Chi-1st case were firstly subjected to discrete wavelet transform with db10 wavelet and 4-layer decomposition, and the high-frequency signal containing the most abundant pulses was selected as the input of BSS. Figure 11 shows four FICs separated by ICA. The damage time is determined by the position of signal pulse on the time axis and the damage position is determined by SDV curve. FIC1 shows that at 3.0 s, the upper and lower adjacent weak layers of the upper outrigger are damaged first, and the damage of the lower adjacent layer is more serious than that of the upper adjacent layer. FIC2 shows that the 15th layer was damaged successively from 5.3 to 7.6 s. FIC3 contained the most pulse signals, indicating that the damage occurred several times in the perimeter column of the 13th layer from 3.3 to 8.9 s. FIC4 showed that the damage of the 14th layer occurred successively from 3.0 to 7.4 s. In conclusion, under the Chi-Chi-1st case, the damage of the model first occurred in the adjacent weak layer of the upper outrigger, and the subsequent damage signals were mainly generated near the 13th floor, that is, the buckling floor.

6 Conclusions The main conclusions of this paper are summarized as follows:

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Fig. 10. Layout of horizontal acceleration measuring points

(1) In this study, multi-scale finite element models are established to simulate the collapse of a core-outrigger structure. The buckling column adopts shell element, and the other components adopt beam element. The overturning phenomenon of the structure above 13 stories can be simulated successfully, which is consistent with the experiment, and the acceleration and displacement response of the top floor are in good agreement with the measured time history curves. (2) IDA static equivalent method is proposed, which can consider the effects of structural dynamic characteristics and seismic spectrum characteristics. The concepts and steps of this method are clear. Besides, compared with IDA, the computation is simple and the calculation precision of CMR is sufficient and conservative. It is applicable to the case that the high-order vibration modes of high-rise buildings cannot be ignored. (3) The WT-ICA method combined with discrete wavelet transform and blind source separation technology can realize data-driven damage identification and better reveal the damage process of the core-outrigger structure, which starts from the adjacent weak layer of the upper outrigger, and the damage events occur most frequently in the buckling floor. In order to simplify simulation and facilitate convergence, the spot-welded component of the experimental model is equivalent to the full-welded component in the

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(a) IC1

(b) SDV1

(c) IC2

(d) SDV2

(e) IC3

(f) SDV3

(g) IC4

(h) SDV4

Fig. 11. Damage Signals and SDV curves of Chi-Chi-1st Case

multi-scale model. The equivalent principle is that the axial compression properties remain unchanged, but the flexural and shear properties are different, which are ignored in this study. What’s more, the applicability of the proposed IDA static equivalent method needs to be verified by more examples.

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References Applied Technology Council.: Seismic evaluation and retrofit of concrete buildings. Report ATC40. Redwood City (CA). Applied Technology Council (1996) Burgos, D.A.T., Vargas, R.C.G., Pedraza, C., Agis, D., Pozo, F.: Damage identification in structural health monitoring: A brief review from its implementation to the use of data-driven applications. Sensors 20 (2020) Chinese Standard, GB, 50011–2010: Code for Seismic Design of Buildings. Chinese Building Press, Beijing, China (2016) De Luca, F., Vamvatsikos, D., Iervolino, I.: Near-optimal piecewise linear fits of static pushover capacity curves for equivalent SDOF analysis. Earthq. Eng. Struct. Dynam. 42, 523–543 (2013) Fragiadakis, M., Vamvatsikos, D.: Fast performance uncertainty estimation via pushover and approximate IDA. Earthq. Eng. Struct. Dynam. 39, 683–703 (2010) Ge, R.X.: Study on Seismic Collapse Mechanism of Core-outrigger Structures [D]. Tongji University, Shanghai (2012) Hamidia, M., Filiatrault, A., Aref, A.: Simplified seismic sidesway collapse analysis of frame buildings. Earthq. Eng. Struct. Dynam. 43, 429–448 (2014) Hamidia, M., Filiatrault, A., Aref, A.: Simplified seismic sidesway collapse capacity-based evaluation and design of frame buildings with linear viscous dampers. J. Earthq. Eng. 18, 528–552 (2014) Hamidia, M., Filiatrault, A., Aref, A.: Seismic collapse capacity-based evaluation and design of frame buildings with viscous dampers using pushover analysis. J. Struct. Eng. 141 (2015) Huang, C.J., Nagarajaiah, S.: Output only system identification using complex wavelet modified second order blind identification method—A time-frequency domain approach. Struct. Eng. Mech. 78, 369–378 (2021) Huang, T.C., Ren, X.D., Li, J.: Incremental dynamic analysis of seismic collapse of super-tall building structures. Struct. Design Tall Special Build. 26 (2017) Kerschen, G., Poncelet, F., Golinval, J.C.: Physical interpretation of independent component analysis in structural dynamics. Mech. Syst. Signal Process. 21, 1561–1575 (2007) Krawinkler, H., Seneviratna, G.: Pros and cons of a pushover analysis of seismic performance evaluation. Eng. Struct. 20, 452–464 (1998) Li, Z.X., Chan, T.H.T., Yu, Y., Sun, Z.H.: Concurrent multi-scale modeling of civil infrastructures for analyses on structural deterioration-Part I: Modeling methodology and strategy. Finite Elem. Anal. Des. 45, 782–794 (2009) Navideh, M., Hamid, R.A., Hamed, M.: A comparative study on conventional push-over analysis method and incremental dynamic analysis (IDA) approach. Sci. Res. Essays 7 (2012) Rosenblueth, E., Herrera, I.: On a kind of hysteretic damping. J .Eng. Mech. Div. 90, 37–48 (1964) Samadi, M., Jahan, N.: Determining the effective level of outrigger in preventing collapse of tall buildings by IDA with an alternative damage measure. Eng. Struct. 191, 104–116 (2019) Soleimani, S., Aziminejad, A., Moghadam, A.S.: Approximate two-component incremental dynamic analysis using a bidirectional energy-based pushover procedure. Eng. Struct. 157, 86–95 (2018) Sun, F.F., Hu, Z.B., Chen, G.Y., Xie, L.M., Sheng, L.: Shaking table test on seismic resonant behavior of core-outrigger structure. Struct. Design Tall Special Build. 26 (2017) Tan, Z., Zhong, W.H., Tian, L.M., Meng, B., Song, X.Y., Qiu, S.Z.: Research on the collapseresistant performance of composite beam-column substructures using multi-scale models. Structures 27, 86–101 (2020) Vamvatsikos, D.: Influence of parameter uncertainties on the seismic performance of oscillators via SPO2IDA. In: 10th International Conference on Application of Statistics and Probability in Civil Engineering, pp. 491–492, Jul 31–Aug 03 2007 Tokyo, Japan (2007)

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Vamvatsikos, D., Cornell, C.A.: Incremental dynamic analysis. Earthq. Eng. Struct. Dynam. 31, 491–514 (2002) Vamvatsikos, D., Cornell, C.A.: Direct estimation of the seismic demand and capacity of oscillators with multi-linear static pushovers through IDA. Earthq. Eng. Struct. Dynam. 35, 1097–1117 (2006) Yang, Y.C., Nagarajaiah, S.: Blind identification of damage in time-varying systems using independent component analysis with wavelet transform. Mech. Syst. Signal Process. 47, 3–20 (2014)

Advanced Transportation Infrastructure and System

Application of Ai-based Deformation Extract Function from a Road Surface Video to a Road Pavement Condition Assessment System Hisao Emoto1(B) , Miori Numata2 , and Atsuki Shiga3 1 Department of Civil and Environmental Engineering, National Institute of Technology,

Fukushima College, 30 Nagao, Kamiarakawa, Taira, Iwaki, Fukushima 970-8034, Japan [email protected] 2 Department of Industrial Technology and Systems Engineering, National Institute of Technology, Fukushima College, 30 Nagao, Kamiarakawa, Taira, Iwaki, Fukushima 970-8034, Japan [email protected] 3 Department of Infrastructure and Urban Society, Institute of Urban Innovation, Yokohama National University Graduate School, 79-1, Tokiwadai, Hodogaya Ward, Yokohama City, Kanagawa 240-8501, Japan [email protected]

Abstract. In Japan, there is a concern that civil infrastructure will rapidly age in the near future. This study focuses on asphalt road surfaces, which are typically renovated every 10 years depending on the amount of traffic and roadbed properties. Existing MCI (Maintenance Control Index) measurement systems come at a high cost to local governments and are not efficient in allowing engineers to detect cracks and deficiencies. New road pavement assessment systems, as developed by our research group, are needed to ensure sustainable road maintenance and management. Pavement surface evaluation system development involves the use of a video camera and a 3D motion sensor, which can be used for simple and low-cost inspections. However, 3D motion sensors can only capture acceleration. Because of this, they can only be used to illustrate the roughness of the road surface, not to detect cracks. In this study, to utilize road surface video recorded while driving, we have developed a method of automatic extraction of deformations by an AI object detection function. This function specifically serves to extract cracks, joints, manholes, and repair marks detections from the surface video. However, in using this function, the accuracy for detecting cracks was less than 40% (Shiga et al. 2020). In this study, we aim to apply this method to detect deformations and suggest annotation rules for improving the accuracy of crack detection, as well as overall accuracy. To discuss the accuracy of detecting cracks and other deformities, cracks are divided into different types and deep learning is performed. In addition, we enlarged images of the cracks. The results of this study show that the AI object detection function for cracks is made more accurate by utilizing annotation rules and making a learning data rule set divided by the crack type classification. Keywords: Road maintenance system · Artificial intelligence · Surface video · Motion sensor · Crack © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1503–1514, 2023. https://doi.org/10.1007/978-981-19-7331-4_119

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1 Introduction In Japan, much civil infrastructure was erected by the government during the economic growth period from 1954 to 1973. A large amount of civil infrastructure is now greater than 40 years old. In another10 years, many structures will reach 50 years of age (MLT 2022a). If our civil infrastructure is managed for an optimally sustainable condition, life safety will also be ensured. Otherwise, the severe condition of civil infrastructure in the future poses dangers for life, budgets, and safety. As a countermeasure, the service life of each civil infrastructure project can be expanded based on an optimized plan for repair or reinforcement. This paper focuses on asphalt pavement maintenance. For asphalt pavement, damaged conditions tend to increase under a large number of cars and heavy truck traffic. Furthermore, in Japan there are many natural disasters, such as earthquakes, flood and typhoons (MLT 2022b). Therefore, cracks, cave-ins, and collapses occur on road pavement. A maintenance strategy based on an awareness of each specific situation is needed to prevent severe conditions for safety and traffic. Implementation of sustainable maintenance needs to establish a maintenance cycle (MLT 2022c). The maintenance cycle is composed of inspection, diagnoses, repair / reinforcement, and documentation. This cycle allows for planning to maintain a longer service life for the infrastructure. Efficiency in renovation is also is important. The first step in the maintenance cycle is inspection. The method of inspection for road pavement is visual inspection and a specialty measurement car (Japan Road Association 2017). The visual inspection is mainly performed by an engineer. This method has some problems, including the lack of qualified inspectors and increasing inspection work. On the other hand, using a specialty measurement car provides high accuracy and quantification, but the initial and operation costs are higher than visual inspection. Using the above methods, these inspections pose problems of economic cost and efficiency. In other words, performing road pavement condition assessment has some problems. In the field of road condition assessment, new inspection systems using motion sensors, smart phones, and drive video recorders have been proposed. Database systems for road management are also being developed. In our research group, we have been developing a road pavement condition assessment system using a 3D-motion sensor and high vision camera (Yoshitake et al. 2012; Hugo et al. 2014). This system is called “Ippocampo”. It is low cost as it uses consumer products, and the 3D-motion sensor and high vision camera data offer efficient software analysis features. The “Ippo-campo” system is utilized by attaching a 3D-motion sensor and its equipment on a normal vehicle and simply driving the target route at an average speed. However, the “Ippo-campo” system doesn’t evaluate a road surface by the in-vehicle video camera. This means that just pavement roughness, not cracks or deficiencies, are evaluated. The road surface video is used to extract road deformation data by AI using an object detection function. In prior research by Shiga et al. 2020, crack, repairs, joints, and manholes were the target deformations. The accuracy of the extracted data averaged 70% for all deformations, more than 90% for joints and repairs, more than 80% for manholes, and less than 40% for cracks. In this case, the accuracy of extracting crack information was not so good. In this study, we aim to apply road surface video from the in-vehicle camera to extract deformation data and improve the accuracy of extracting crack conditions. Specifically,

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we focus on the quality and volume of learning data and discuss how to annotate for deformation.

2 Management of Road Surface Using the Ippo-Campo System 2.1 Outline of Road Surface Management in Japan IN Japan, pavement material is divided into asphalt and concrete types. Initial cost of asphalt pavement, because of material and construction equipment costs, is lower than for concrete pavement types. Therefore, most pavement is the asphalt type. Asphalt is also easy to repair deformation areas in a single day, and car traffic can be reopened on the same day. To keep asphalt pavement in good condition, it should be evaluated for road pavement condition. There are two types of road condition assessments normally used in Japan: MCI (Civil Engineering Research Center 2022) and IRI (International Roughness Index). Here MCI is explained because the current study subject, “Ippocampo”, is partially based on this method. MCI is the index of evaluated quantitative serviceability as concerns “cracking ratio”, “rut depth”, and “roughness”. If quantitative serviceability is evaluated for road pavement, it needs to assess these multiple types of deformations. The Public Works Research Institute, Ministry of Construction, as road administrator, developed the MCI in 1981 to be a comprehensive road assessment value. MCI is calculated based on the value of these parameters, i.e., “cracking ratio”, “rut depth”, and “roughness”, by multiple regression analysis. An MCI value to evaluate damage condition level gives a comprehensive assessment maximum of 10 points due to “cracking ratio”, “rut depth”, and “roughness”. The MCI index signifies good condition at a managed level as more than 5.0; intermediate condition in need of repair as between 5.0 and 3.0; and bad condition needing immediate repair as less than 3.0. 2.2 Development of the Ippo-Campo System The Ippo-Campo system was developed by our research group to efficiently evaluate road pavement condition. An outline of this system is shown in Fig. 1. Input data is the driving video (a road surface video), subtitle data, GPS data, and sensor data providing acceleration. The Ippp-Campo system is used to analyze these data to judge conditions. Output data is an Excel file type, a video subtitle file, and web map file, such as GIS. The Excel file outputs road condition at 3 levels, “Good”, “Intermediate” and “Bad” condition, at every 1 s. This system converts latitude/ longitude information to world geodetic system coordinates and can then create a map system or road register file for the road manager. Installed measurement equipment in the Ippo-Campo system is shown in Fig. 2. It takes 20 min to set up the equipment. The driving video (road surface video) is taken using video equipment. GPS data and sensor data, such as three-axis acceleration, is taken by a motion sensor made by XSENS products. A laptop computer is used to record the motor sensor data. Measurement coordinates illustrate that the z-axis is vertical, x-axis is forward direction, and y-axis is width direction. These data are synchronized in time by linking the video camera and the x, y, z axis motion sensor with GPS. Analysis data results are exported by excel file. The system interprets them by a map system and in-vehicle video with subtitles, as shown in Fig. 3.

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Fig. 1. Outline of the “Ippo-Campo” road pavement evaluation system

Fig. 2. Installed measurement systems

2.3 System Summary The Ippo-Campo system was designed for application to road surface pavement maintenance by providing in-vehicle video and three-axis motion sensor data with GPS position. The analyzed data are visualized for the road manager’s easy interpretation by graphical interface using a map-based system and a video of the road surface with subtitles of assessed road condition. The Ippo-Campo system has been used by some local governments. However, the video data in this system is not used for evaluating road pavement condition, but only for confirming the road condition from analytical due to motion sensor. Furthermore, the only road condition evaluated by this system is roughness due to x-axis acceleration. It is also important to evaluate the “cracking ratio” for road assessment. For this purpose, in-vehicle video data (road surface video) and object detection using AI are applied to evaluate these road conditions.

3 Ai-based Deformation Extract Function from Surface Video The purpose of deformation extraction from the surface video recorded by the IppoCampo system is to detect the condition of road pavement using object detection. This function is used by YOLO v3. In this study, object detections to evaluate roughness

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(a) Road assessment results visualized from the analysis data by GIS map

(b) Road assessment results from the analysis data visualized with subtitles on the invehicle video Fig. 3. Output of the pavement evaluation data on web map and in-vehicle video.

are “joint”, “man-hole”, “patching repair”, “sealant injection repair”, and “cracks”, as shown in Fig. 4. “Joint” and “man-hole” affect the z- axis acceleration standard deviation, which is used for evaluation in this system. This value affects the “good” or “bad” rating used to make a repair decision. The target routes in this study are national highways No6, No49, and No399; prefectural highway No26 passing through Iwaki City, Fukushiam Prefecture; and new national highway No.4 passing through Oyama City, Tochigi Prefecture. The system took in-vehicle video along 5 routes by a consumer 4k video camera. It then captured 57 still images from the movie. These still images were captured as adapted data augmentation, which were resized and rotated. After that, these augmented still images were annotated as learning data for YOLO v3 by “labelling”, which is one of the software annotation tools. The process of developing a function for

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extracting deformation data is shown in Fig. 5; namely, first building an environment, then making learning data for the AI learning process, learning with training data, and finally generating weights and accuracy of detection. In this study, the developer environment is as follow: Windows 10 OS, python 3.6.10 programming language, NVIDIA GeForce RTX 3070 GPU, and Keras 2.25 libraries. Before discussing annotation methods, we tried to apply deformation detection to simulated data. Cases 1 and 2 were simulated with hyperparameter and learning data as shown in Tables 1 and 2. Detection accuracy is shown in Table 3. The results found accuracy of the extracted detections to average 70% for all deformations, more than 90% for joints and repairs, more than 80% for manholes, and less than 40% for cracks. In the next chapter, we focus on improving the accuracy of extracting detections for “cracks”.

Fig. 4. Examples of object detection

4 Discussion About Annotation for Detecting Deformations 4.1 How to Annotate Annotation work means selecting a rectangular range in still images to illustrate a definition, such as crack, joint, etc., by “labeling”, which is an annotation software used for learning data. The engineer who annotates this work is called an annotator. To improve the accuracy of detection many learning data are needed. If many learning data are needed, many annotators are needed. To improve the quality of learning data, annotators must make a rectangle and must annotate under the same rules used in this study. Because of this, the decision about the rules for annotation are made by discussions with the road manager and professional engineers, as shown in Fig. 6. Optimum rectangle size (green rectangle in Fig. 7) is verified in a 3 step process, as shown in Fig. 7. The simulation parameters are as listed below: the number of datasets is 100; deformation

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Fig. 5. Development process for the deformation extraction function

Table 1. Hyperparameters for each case

Table 2. Number of learning data in detail Class name

Joint

Manhole

Crack

Repair

Total

Total number of data

3,668

720

6,471

7,050

17,909

Number of train data

3,301

648

5,824

6,345

16,118

367

72

647

705

1,791

Number of test data

is categorized as “alligator cracks”, “Cracks above the road line marking”, and “Line

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cracks”; and each rectangle size is determined in a 3 step pattern, as shown in Fig. 7. Results of this simulation found that the largest rectangle size has the highest accuracy as highlighted by the red rectangle in Table 4. The ratio in Table 4 signifies the number of learning data to the number of verification data. From this result, we determined that it is optimal to select deformations using a larger rectangle.

is not included in annotation because it is not clear.

The shoulder of a road and the opposite lane are also in the annotation area Shadows and dirt are not included.

Fig. 6. Annotation details

4.2 Annotation of Categorized Cracks, Such as Alligator Cracks and Line Cracks In general, cracks are divided into alligator cracks and line cracks, assuming that class categorization will improve accuracy due to easy recognition of deformation and pattern. In this research, we categorized six types (classes) of alligator cracks, cracks above the road line marking, line cracks, joints, manholes, and patching. 4.3 Annotation of Rich Data as Cracks in a Still Image Rich data means enlarging a part of a crack in a still image by trimming and resizing it in order to enforce learning data. This simulation categorizes five types (classes) of cracks, crack-lines, joint, manhole, and patching.

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Figure7. Validation of rectangle size in 3 steps

Table 4. Results of rectangle size verification

Alligator crack

Cracks above the road line marking

Line crack

Ratio

1

2

3

9：1

41.07%

39.90%

19.91%

8：2

65.09%

24.55%

23.53%

7：3

74.75%

20.81%

14.34%

9：1

78.89%

46.54%

10.22%

8：2

61.79%

40.07%

15.74%

7：3

62.78%

40.87%

17.49%

9：1

87.06%

22.26%

20.24%

8：2

73.85%

31.71%

16.24%

7：3

67.29%

25.12%

12.57%

4.4 Simulation Conditions This learning process used hyper parameters shown in Table 5. In Case 1, number of batches is 32 and number of subdivisions is 8; in Case 2, number of batches is 64 and number of subdivisions is 16; in Case 3 number of batches is 64 and number of subdivisions is 8; in Case 4, number of batches is 96 and number of subdivisions is 8. The ratio of leaning data and verification data is 9:1. 4.5 Results of Detecting Accuracy and Discussions Each categorized class and rich data were given for the four hyperparameters from Case 1 to Case 4 (simulation conditions). These results are shown in Tables 6 and 7. First, we will discuss categorized class. Accuracy of crack detection in previous research was

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H. Emoto et al. Table 5. List of hyperparameters

Number of data

Previous studies

Categorized class

Rish data class

Image size

17,909

Number of max_batch

416 × 416

Number od steps

18,000

Number of class

14,400, 16,200

Number of class

4

6

5

Number of filter

27

33

30

roughly 38%, as shown in Table 3. Accuracy of “alligator cracks”, “line cracks”, “cracks above the road line marking” from Table 6 was about 56–59%, 37–42%, and 24–34%, respectively. The categorized classes of “alligator crack” and “line crack” improved accuracy, especially with the hyperparameters from Case 3 and Case 4. Accuracy of “alligator crack” detection improved because the YOLO v3 system learned several crack types. But accuracy of detection does not improve to a great extent. The reasons for this are that the number of data is not enough for learning and that hyperparameters were not optimal. Secondly, for the rich data shown in Table 7, the accuracy of crack detection was about 62 to 64%. These results clearly improved compared to the previous study. In this case, “cracks above the road line marking” also improved. Finally, mAP (Mean Average Precision) improved about 78% in Case 3 and Case 4, as shown in Table 7. Here, mAP denotes the accuracy of the model. If mAP value is high, this model is a good model. Correspondingly, a low value of accuracy affects mAP. Table 6. Detection accuracy of each case by categorized class

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Table 7. Detection accuracy of each case by rich data class Class name Rich data class Case1 Rich data class Case2 Rich data class Case3 Rich data class Case4

Joint AP(％)

95.29

Manhole Repair 86.38

89.84

96.59

86.92

91.31

96.10

93.88

91.93

mAP(％) AP(％) mAP(％)

62.56

38.39

63.44

40.77

75.81

mAP(％) AP(％)

Cracks above the road line marking

74.49

mAP(％) AP(％)

Crack

64.15

44.71

78.17 97.65

95.18

91.95

63.65

43.23

78.33

5 Conclusions In this paper, we attempted to extract deformations, such as cracks, from a road surface video. In applying AI to the road surface assessment system, we proposed an annotation method. A common rule was determined for annotators because the leaning data set included a huge number of still images. We analyzed results to determine improvements in the detection of accuracy, especially in the class name “crack”. For other classes, “joint”, “manhole”, and “repair”, accuracy was more than 85%. Only the “crack” class was as low as 38%. So, we focused on categorizations, such as “alligator crack”, “line crack”, and “cracks above the road line marking”. This approach focused on rich data as cracks in a still image under 4 hyperparameters cases. The results determined that the accuracy of crack detection increased to 78% for the rich data class and increased in Cases 3 and 4 more than other cases. In this study, for Case 3 the number of batches was 64, and the number of subdivisions was 8; and in Case 4 the number of batches was 96, and the number of subdivisions was 8. This study also found that learning data from a rich data class was better. However, the accuracy of detection was not greater than the generally acceptable level of 80% to 90%. Further increases in accuracy detection likely require optimum hyperparameters and a greater number of learning data. Acknowledgements. We would like to thank the Tohoku Chiikizukuri Association for supporting our project. We also thank Takahashi industrial and economic research foundation. The authors are grateful to Mitsui Consultants co., LTD; CEO Mr. Motoyasu Kimachi of Higashinihon Construction Consultants Co., LTD.; and Intelligence, Informatics and Infrastructure Committee Chairman Prof. BANGJO Chun. We would finally like to thank MLI and local governments for providing road field and measuring opportunities.

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References MLT (Ministry of Land, Infrastructure, Transport and Tourism): Infrastructure Maintenance Information, Current status and future of aging of social infrastructure (2022a). https://www.mlit. go.jp/sogoseisaku/maintenance/02research/02_01.html MLT (Ministry of Land, Infrastructure, Transport and Tourism): Lessons learned and challenges faced from major disasters in recent years (2022b). https://www.mlit.go.jp/road/ir/ir-council/ sdt/pdf01/04.pdf MLT (Ministry of Land, Infrastructure, Transport and Tourism): Toward the establishment of a maintenance cycle for roads (2022c). https://www.mlit.go.jp/road/sisaku/yobohozen/yobo9_1. pdf Japan Road Association: Pavement Inspection Essentials, pp.16–23, pp.42–56 (2017) Yoshitake, T., Mizobe, K., Yasumura, N., Miyamoto, A.: Development of the road condition assessment system using digital movie, vehicle vibration and sound. J. Const. Manage. F4 69(1), 12–31 (2012) da Hugo, X. C., Emoto, H., Miyamoto, A.: Practical application of road condition assessment system to road networks in timor-leste. In: Asia-Pacific Computer Science and Application Conference (2014) Shiga, A., Emoto, H., Baba, Y., Yoshitake, T.: Application of Ai-based degradation extract function to a road pavement condition assessment system. Intell. Inf. Infrastruct. J1, 180–189 (2020) Civil Engineering Research Center: MCI (Maintenance Control Index) (2022). http://www.pwrc. or.jp/yougo_g/pdf_g/y1104-P053-054.pdf

Assessing the Sustainability Characteristics of Modified Asphalt Concrete G. Muna1(B) and M. Henry2 1 Division of Architecture and Civil Engineering, Graduate School of Engineering and Science,

Shibaura Institute of Technology, 3 Chome-7-5 Toyosu, Koto-Ku, Tokyo 135-8548, Japan [email protected] 2 Department of Civil Engineering, Shibaura Institute of Technology, 3 Chome-7-5 Toyosu, Koto-Ku, Tokyo 135-8548, Japan [email protected]

Abstract. The increasing concern on impacts of various sectors to sustainability has prompted the transportation sector to improve efforts on enhancing sustainability through various tools. Whilst extensive research has currently been done on various innovative pavement materials, their impact on sustainability is still yet to be properly understood and quantified, therefore a need to analyze the sustainability characteristics of various modified bituminous mixes on the sustainability of Asphalt Concrete. Asphalt Concrete consumes high volumes of natural resources and is energy intensive henceforth affecting sustainability. Warm Mix Asphalt (WMA), Crumb rubber modified Asphalt (CRMA), Reclaimed Asphalt Pavement (RAP) and Waste Plastic Asphalt (WPA) are all mixes that incorporate additives or recycled materials to negate the negative environmental impacts of conventional Asphalt Concrete and are therefore associated with improved sustainability. Sustainability indicators such as Energy Consumption, Green House Gas emissions, Human Toxicity and Cost Implications as evaluated in Life Cycle Analysis (LCA) from various literatures were used to compare the impacts of using the alternatives through relationship graphs. The results show that lowering the temperatures of production by about 19–63 °C in the case of WMA and replacing between 2 and 100% of either binder or whole mix with recycled material in the case of RAP, CRMA and WPA lowers most indicator values vis-à-vis baseline produced values, therefore achieving not only higher environmental benefits but in addition proving to be good alternatives that perform similar or better than virgin mixes. This notwithstanding, there are limits to the quantity of additives or recycled material that is used to modify the mixes due to their effect on overall mixture performance requirements. In conclusion a quantitatively based positive sustainability effect of the considered alternatives can be seen therefore proving that these alternatives when properly engineered can be used to improve sustainability goals in the road sector. Keywords: Sustainability · Indicators · Life cycle analysis · Asphalt concrete · Modified bituminous mixes

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1515–1527, 2023. https://doi.org/10.1007/978-981-19-7331-4_120

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1 Introduction 1.1 Sustainability in the Transportation Sector “Sustainability” is a concept that basically expresses the interest to preserve resources for the future as the practice of making the most of what is available is exercised. One of the most used definitions however is the one given by the World Commission on Environment and Development (WCED) in its 1987 report; Brundtland Commission Report that indicates that it is “the ability of humanity to ensure that it meets the needs of the present without compromising the ability of future generations to meet their own needs” (United Nations 1987). Transportation is considered to be a primary need of human beings, therefore, developing sustainable transportation facilities should be essential. Pavement construction in specific heavily consumes energy and causes Green House Gas (GHG) emissions (Pouranian and Shishehbor 2019) and therefore much emphasis has been made on the negative sustainability related impacts induced by the industry. Many efforts have been made to enhance sustainability in the pavement industry through varied methods among them is through the use of pavement material improvement. One of the world’s most widely used paving material is Asphalt Concrete (AC) which constitutes of about 95% aggregates and 5% asphalt binder (Pouranian and Shishehbor 2019) which are both natural resources that are non-renewable in nature. Due to the importance of roads in facilitating economic growth, the demand for AC is presumed to continue growing, therefore the need to enhance this materials sustainability impacts. Suggested general approaches for improving this materials’ sustainability include, among others, recycling of materials, use of industrial secondary products, use of innovative binders and the use of less energy consuming technologies (Florkova et al. 2021) therefore the creation of modified bituminous mixes. Researchers have suggested various mixes such as warm mix asphalt (WMA), crumb rubber modified asphalt (CRMA), waste plastic asphalt (WPA), reclaimed asphalt pavement (RAP), reclaimed asphalt shingles, vacuum tower bottoms, steel and copper blast furnace slag and glass (Bamigboye et al. 2021; Pouranian and Shishehbor 2019; Ozer et al. 2016) which mostly seem to have a positive influence of not only AC sustainability but also on its performance. This research will delve further into the concept of material improvement for enhanced sustainability with a focus on Asphalt Concrete (AC) as well as evaluate the performance and sustainability related impacts of using modified bituminous mixes. 1.2 Sustainability Through Modified Bituminous Mixes The scope of this study will focus on WMA, CRMA, RAP and WPA. The selection was based on acceptance levels in the pavement industry as well as the benefits to enhanced sustainability they exhibit. WMA is a type of AC that is manufactured at lower temperatures than typical Hot Mix Asphalt (HMA) (produced at about 170 °C (Giunta et al. 2019)) which reduces the viscosity of the asphalt and provides complete aggregate coating at lower temperatures (EAPA 2010). Technical advantages of using this material are better compaction of the road, increased haulage transportation, paving in colder seasons, higher durability of the pavement due to the lower aging of the binder during production, improved worker

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welfare due to reduced fumes etc. (Giunta et al. 2019; EAPA 2010) in retrospect, WMA technologies seem to be comparable or better in performance to HMA (Pouranian and Shishehbor 2019; EAPA 2010). Environmental benefits of WMA are related with the reduction of the energy consumption which in turn cause reduction of Green House Gas (GHG) emissions that emanate from AC production (Giunta et al. 2019; EAPA 2010; Pouranian and Shishehbor 2019). RAP is a modified bituminous mix in which a portion of recycled old pavement replaces a portion of virgin material in a new mix. This material is adopted in many countries with huge success in reduced resource consumption, cost reduction and reduced deconstruction waste (Jamshidi and White 2019). The reduction of virgin material leads to the reduction of both aggregate and binder content which causes improved sustainability parameters such as reduced global warming, energy consumption, water consumption, life cycle costs and hazardous waste generation (Jamshidi and White 2019; Pouranian and Shishehbor 2019) among others. In terms of performance, high RAP content mixes require rejuvenators otherwise they have increased cracking tendencies (Pouranian and Shishehbor 2019). Crumb rubber (CR) is mainly obtained from mainly recycled tires and is used in replacing either binder (18–25%) or aggregates (3–5%) in a new AC mix (Pouranian and Shishehbor 2019). These mixes usually exhibit enhanced mechanical properties that result in improved service life, noise reduction, reduced maintenance cost among others (Rodríguez-Alloza et al. 2015). As a result, positive sustainability related impacts such reduction of raw material, longer service life, reduced climate change and ozone depletion among others can be seen when the materials whole life cycle is assessed (Pouranian and Shishehbor 2019; Bartolozzi et al. 2013). WPA is a fairly new pavement innovation and so far about 12 countries have roads made from plastic waste (Good News Network 2021). Several studies have shown that these mixes generally replace between 5 and 10%, by weight of bitumen with plastic and this in turn helps improve AC performance indicators and therefore improved longevity and pavement performance (Pouranian and Shishehbor 2019). However, it is also worth noting that very few studies are available that mention the environmental aspect of using WPA due to the relatively new nature of these roads and hence forth difficulty in assessing comprehensive sustainability benefits. 1.3 Objective This study will focus on enhancing understanding on how WMA, RAP, CRMA and WPA affect pavement performance and various sustainability assessment parameters. To achieve this, pavement sustainability is assessed through the entire pavement life cycle (Ozer et al. 2016) as well as indicators to quantify the effects of sustainability. A typical road material life cycle constitutes various modules; material production, construction, service, maintenance and end of life (Pouranian and Shishehbor 2019) and it is critical to understand how sustainability can be affected by these phases as can be seen in Fig. 1. Thereafter comes the introduction of indicators which are quantitative or qualitative measures that allow sustainability to be quantified to assess and address certain issues (OECD 2008; Opon and Henry 2020). This indicator-based sustainability evaluation is commonly used to support various decision-making processes relating to

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material selection, methodology and progress assessment (Opon and Henry 2020). The approach coupled with secondary data collection as a source of data enabled the graphical representation of the effects of the four selected materials on various selected indicators.

Fig. 1. Asphalt concrete life cycle and various sustainability parameters

2 Methodology 2.1 Indicator Selection Indicator selection was the first most critical step. It was crucial that all three dimensions of sustainability (environmental, social and economic) be included in the assessment (S.R. CWA 17089:2016). Hence forth indicators were based on asphalt concrete and how it affects the three pillars of sustainability. In the assessment of various LCAs (Santero et al. 2011) found that for evaluated pavement materials, energy consumption was easily the most popular along with conventional air pollutants (e.g., Sulphur dioxide (SO2 ), Nitrogen Oxide (NOX ), Carbon Monoxide (CO), particulate matter (PM)) and other greenhouse gases. (S.R. CWA 17089:2016) suggested indicators such as energy demand, global warming potential, human toxicity, cost, traffic congestion due to maintenance among others which were also considered. The indicators were thereafter revised based on availability and subjectivity as seen in Table 1 according to further availability during the data collection process. 2.2 Data Collection Secondary data collection was the main source of data and over 150 research papers and 4 books were reviewed. The data collected was used to establish various scenarios which presented a comparison of various indicators for modified bituminous mixes vis-à-vis a conventional mix often HMA also known henceforth as the baseline. It is important to note that for every scenario the baseline HMA was varied based on the researchers’ mix design parameters, thus each scenario was assessed against its own specific baseline. Final data selection was based on analytical soundness, measurability, coverage, and relevance of the indicators to the pillars of sustainability and their relationship to asphalt concrete and the modified mixes (OECD 2008).

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Table 1. Indicators selected for analysis Abbr.

Indicator

Unit

Pillar

Phase

ER

Energy requirements

MJ

Environmental, economic

Production

CO2

Carbon dioxide

kgCO2

Environmental

Production

SO2

Sulphur dioxide

kgSO2

Environmental

Production

NOX

Nitrogen oxide

kgNOx

Environmental

Production

CO

Carbon monoxide

kgCO

Environmental

Production

VOC

Volatile organic compounds

kgVOC

Environmental, social

Production

C

Production cost

Cost/unit

Economic, social

Production

GER

General energy requirements

MJ

Environmental, economic

Life cycle

GWP

Global warming potential

kgCO2 eqv

Environmental

Life cycle

AP

Acidification potential

kgSO2 eqv

Environmental

Life cycle

HT

Human toxicity

1,4-DB

Social, environmental

Life cycle

FFD

Fossil fuel depletion

MJ/kg

Environmental, economic

Life cycle

WLC

Whole life cost

Cost/unit

Economic, social

Life cycle

MR

Maintenance requirements

No

Economic, environmental, social

Life cycle

ISL

Increased service life

%

Economic, environmental, social

Life cycle

Other factors of consideration were data validity and uniformity in the LCA. Due to the aspect that all LCA studies were location and project dependent, this paused a challenge for the analysis of the materials. However, to curb this careful consideration of the various researchers’ scopes and boundaries were considered. To enable some form of uniformity in final data, only system boundaries that covered the phases that have been highlighted in Fig. 1 were selected, studies that included extra phases such as the “use phase” which is another common phase in material oriented LCA’s were not included. Most phases were similar in setting to the baseline materials with an exception to the maintenance phases of the materials where WPA and CRMA showed reduced the maintenance cycles (represented in this research as the number of overlays done over a life cycle) and increase service life (represented in this research as a percentage increase or decrease). A major factor that also increased both data validity and uniformity is that all the Life Cycle Inventories (LCI) analysis were mostly based on international environmental databases in accordance with ISO (International Organization of Standardization) standards, mostly ISO 14040. In addition to this, LCI data was mostly sourced from various established databases e.g., Ecoinvent database (Bartolozzi et al. 2013), other literatures and interviews or source-based values (Giunta et al. 2019) which was the main source of data for the production phase data. Other factors that could contribute to uniformity are the tools and methods used to do the analysis. Methods such as the ReCipe method was quite commonly used by several researchers who contributed

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to the results highlighted in this paper. When it came to the actual data collection at the various phases, it is worth noting that depending on the method selected for analysis, not all indicators were catered for and only applicable indicator value data relevant to the study were selected. 2.3 Data Analysis Indicators should be normalized to render them comparable (OECD 2008) and therefore homogenized. Various forms of data normalization methods exist (OECD 2008), in this case, due to the presence of varying baseline materials which all the modified mixes were compared to, distance to a reference method was used and Eq. 1 was applicable. The data was then used to make graphical representations in which data was in the form of percentage increase or decrease of indicator values from values produced by the baseline, where a decrease shows an indicator contributes positively towards sustainability and vice versa for an incremental value. The only exception is the ISL indicator which shows a different directionality from the rest. Inorm =

Xm − Xb × 100 Xb

(1)

where: Inorm is the Normalized indicator value (%) Xb = Indicator value for baseline Xm = Indicator value for modified bituminous mix. The change in indicator values were plotted against the causative indicator (temperature reduction for WMA, reduced virgin material for RAP and reduced bitumen content in mix for WPA and CRMA) that is responsible for the change in the rest of the indicators. The results are as seen in the consequent chapter through Figs. 2, 3, 4, 5, 6, 7, 8 and 9.

3 Results and Discussion 3.1 The Effect of WMA on Selected Indicators The result of the analysis was therefore represented in Figs. 2 and 3 which show the plotted relationship graphs. The Figures represent the several studies that used various additives to achieve a temperature reduction range of between 19 and 63 °C resulting in indicator changes ranging between a 70% reduction of NOX produced at the production phase to a 3% increase in CO produced at the production stage. Most scenarios fall within the third quadrant implying improved sustainability due to a lowering of indicator values, this similar trend is also seen in Figs. 4, 5, 6, 7, 8 and 9 with an exception of the ISL indicator which has an opposite effect. There are however exceptions of the production cost and CO indicators which could possibly be attributed to the use of additives in the new mix. Improved sustainability for this material is due to reduced energy consumption and emissions hence lowered sustainability related impacts.

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3.2 The Effect of RAP on Selected Indicators The graphs shown in and Figs. 4 and 5 show the effects of a replacing between 10 and 100% of bitumen and aggregates with RAP which show varying impacts on indicators ranging between a 98% reduction of NOx produced during the production phase and a 4.8% increment in VOC production still at the production phase. By reducing virgin material use, large amounts of virgin materials can be spared, henceforth positively impacting the modified mixtures effect on the various indicators hence the observed elevated levels of sustainability. The positive results notwithstanding, there are still some scenarios that show that the indicators increased. Indicators such as CO2 , NOx , CO, VOC for RAP showed a negative effect by an increase due to the use of rejuvenators in mixes and extra burden of RAP processing. However, most results still show that even with these added processes and rejuvenators an enhanced sustainability is still seen, therefore emphasising the aspect of the variability of data from the different studies assessed. 3.3 The Effect of CRMA on Selected Indicators The effect of replacing between 5 and 25% of bitumen with crumb rubber on various indicators is shown in Figs. 6 and 7. The indicator change ranged from a 550% increase in service life to a 47% increase in CO2 at production regardless of the small replacement ratios in a new mix. This Indicator reduction (or improvement for ISL) is influenced by bitumen consumption reduction as well as the fact that polymers have a characteristic improving the performance of AC and therefore reducing maintenance cycles and increasing service lives hence improved durability. Regardless of most indicators showing improved sustainability, some of the scenarios in Fig. 6 i.e., CO2 , SO2 and cost indicators showed a negative effect by an increase of indicator values. The reason for this could be attributed to increased heating temperatures at production and processing of waste materials. 3.4 The Effect of WPA on Selected Indicators The contribution of improved sustainability due to waste plastic follows the same principles as those of CRMA and is shown in Figs. 8 and 9. This is due to the fact that they are both polymers. The results show the effect of 2–12% of bitumen with waste plastic to a new mix. These effects range from an increment of 281% of the service life and an 800% increase in cost of production albeit some lack of data for some indicators under consideration. Like all the other materials, some scenarios in the cost of production, energy consumption, CO2 and SO2 indicators showed a negative effect to sustainability mainly attributed to increased processing of waste materials. 3.5 Overall Effect of Modified Mixes on Selected Indicators There was a common observation that for all the scenarios and indicators, the whole life cycle assessment showed no negative effects on sustainability indicators, therefore furthering the aspect of the effectiveness of analysing the whole life cycle in order to realise the full benefits/detriments of a material. Another interesting trend that can be

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Fig. 2. Relationship graphs for various indicators versus reduced temperature in mix in production phase—WMA

Fig. 3. Relationship graphs for various indicators versus reduced temperature in mix in whole life cycle—WMA

seen is that as the causative indicators’ values rise, the more the reduction of indicator value, alluding to the fact the more the better. Mix performance is however crucial and the biggest limiting factor to this and therefore proper engineering and plant management should be highly adhered to.

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Fig. 4. Relationship graphs for various indicators versus reduced virgin material in mix in production phase—RAP

Fig. 5. Relationship graphs for various indicators versus reduced virgin material in mix in whole life cycle—RAP

Important to also note was the effect of the various modified materials to the actual improved performance and durability of the mix. A good example is how CRMA and WPA influenced the maintenance and service life of the asphalt material, hence forth in most cases they reported reduced maintenance cycles and increased service life as

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Fig. 6. Relationship graphs for various indicators versus reduced virgin material in mix in production phase—CRMA

seen in Figs. 7 and 8. This is contrary RAP and WMA mixtures seem to be engineered to perform the same as a normal mix therefore have the same maintenance and service life schedules as a normal HMA. This proves that these mixes do not only contribute to sustainability, but also improved durability and performance parameters of the material.

4 Conclusions The findings of this research show that these modified mixes do indeed improve sustainability and to what extent they affect some social, economic, and environmental parameters of sustainability as well as the importance of assessing these materials in a life cycle scenario. The use of modified bituminous mixes is beneficial in improving pavement sustainability, advocating for responsible consumption, and encouraging innovations in the industry and therefore more considerations should be given by policy and decision makers regarding their adoption. This research also shows that a good way to quantitatively assess sustainability is through indicators and not only their use but a comparison effect to baseline scenarios. This is an easy way to help the world better understand sustainability improvement or lack thereof.

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Fig. 7. Relationship graphs for various indicators versus reduced virgin material in mix in whole life cycle—CRMA

Fig. 8. Relationship graphs for various indicators versus reduced virgin material in mix in whole life cycle—WPA

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Fig. 9. Relationship graphs for various indicators versus reduced virgin material in mix in production phase—WPA

Acknowledgements. The authors would like to thank the Japan International Cooperation Agency (JICA) for their invaluable support through the opportunity availed and financial provision that enabled this research.

References Bamigboye, G.O., Bassey, D.E., Olukanni, D.O., Ngene, B.U., Adegoke, D., Odetoyan, A.O., Kareem, M.A., Enabulele, D.O., Nworgu, A.T.: Waste materials in highway applications: an overview on generation and utilization implications on sustainability. J. Cleaner Prod. 283, 124581 (2021). https://doi.org/10.1016/j.jclepro.2020.124581 Bartolozzi, I., Rizzi, F., Borghini, A., Frey, M.: Life cycle assessment of a rubberized asphalt road in Lamia, Greece. Fresenius Environ. Bull. 22, 2104–2110 (2013). Available at https://www.researchgate.net/publication/288117272_Life_cycle_assessment_of_a_rubberi zed_asphalt_road_in_lamia_Greece EAPA: The Use of Warm Mix Asphalt EAPA Position Paper. Belgium, Brussels (2010)

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Florkova, Z., Sedivy, S., Pastorkova, J.: The environmental impact of asphalt mixtures production for road infrastructure. IOP Conf. Ser. Mater. Sci. Eng. 1015(1), 012097 (2021). https://doi. org/10.1088/1757-899X/1015/1/012097 Giunta, M., Mistretta, M., Praticò, F.G., Gulotta, M.T.: Environmental Sustainability and Energy Assessment of Bituminous Pavements Made with Unconventional Materials. Lecture Notes in Civil Engineering, pp. 123–132. https://doi.org/10.1007/978-3-030-29779-4_12 Good News Network: 12 Countries Have Built Roads Out of Plastic—And they Can Perform as Well or Better than Asphalt (2021). Available at https://www.goodnewsnetwork.org/pavingwith-plastic-dent-global-waste-problem-yale/. Accessed 29 January 2022 Jamshidi, A., White, G.: Evaluation of performance and challenges of use of waste materials in pavement construction: a critical review. Appl. Sci. 10(1), 226 (2019). https://doi.org/10.3390/ app10010226 OECD: Handbook on constructing composite indicators—methodology and user guide. European Commission—Joint Research Centre (2008) Opon, J., Henry, M.: A multicriteria analytical framework for sustainability evaluation under methodological uncertainties. Environ. Impact Assess. Rev. 83, 106403 (2020). https://doi.org/ 10.1016/j.eiar.2020.106403 Ozer, H., Al-Qadi, I.L., Harvey, J.: Strategies for Improving the Sustainability of Asphalt Pavements, Report No. FHWA-HIF-16-012. Federal Highway Administration, U.S. Department of Transportation (2016). Retrieved from http://www.fhwa.dot.gov/pavement/sustainability/ hif16012.pdf Pouranian, M.R., Shishehbor, M.: Sustainability assessment of green asphalt mixtures: a review. Environments 6(6), 73 (2019). https://doi.org/10.3390/environments6060073 S.R. CWA 17089:2016: Indicators for the sustainability assessment of roads (2016). [online]. Available at https://infostore.saiglobal.com/preview/256758446659.pdf?sku=880160_SAIG _NSAI_NSAI_2091123. Accessed 28 January 2022 Santero, N.J., Masanet, E., Horvath, A.: Life-cycle assessment of pavements. Part I: critical review. Resour. Conserv. Recycl. 55(9–10), 801–809 (2011). https://doi.org/10.1016/j.resconrec.2011. 03.010 United Nations: Report of the World Commission of Environmental Development: Our Common Future (1987). Accessed 17th January 2022, https://sustainabledevelopment.un.org/content/ documents/5987our-common-future.pdf

Factors Affecting the Deterioration of Bituminous Pavements in Khyber Pakhtunkhwa Province, Pakistan Azam Amir1(B) and Michael Henry2 1 Department of Regional Environment Systems, Shibaura Institute of Technology,

Tokyo 135-8548, Japan [email protected] 2 Department of Civil Engineering, Shibaura Institute of Technology, Tokyo 135-8548, Japan [email protected]

Abstract. It is essential to study the factors that lead to the deterioration of bituminous pavement in order to prepare an effective maintenance plan. In developing countries, like Pakistan, a huge amount of budget is spent every year on the rehabilitation of road network due to the absence of an effective maintenance plan. The amount can be reduced by formulating the maintenance plan which will be based on the factors that cause deterioration of pavement surface. The objective of this study was to identify the factors which cause the deterioration of bituminous pavements in the Khyber Pakhtunkhwa province of Pakistan. The research was based on provincial highway network data, collected from the local highway department. The data consisted of 23 road characteristics, out of which 16 nos. Pavements’ condition-related data were selected. The pavement conditions of the provincial highways network of Khyber Pakhtunkhwa are divided into good, fair, and poor depending on the IRI index and vehicular speed. To scrutinize the factors that affect the pavement condition, cross-tabulation analysis was performed. It was concluded through analysis that among different factors, overloading, poor drainage, and pavement terrain had a major impact on the deterioration of bituminous pavements. Based on the results, recommendations were provided to highway engineers for prioritizing the pavement projects for a future pavement maintenance plan. Keywords: Road deterioration · Maintenance · Overloading · Pavement terrain · Poor drainage

1 Introduction The deterioration of road pavement greatly affects safety, serviceability, and riding quality of road. The bituminous pavement gradually deteriorates with the passage of time due to various factors and they need to be maintained. In developing countries like Pakistan, due to the absence of a maintenance plan, many roads are left unattended and the cost required to maintain the roads get doubled with time. For the development of © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1528–1538, 2023. https://doi.org/10.1007/978-981-19-7331-4_121

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a sustainable maintenance plan, it is very important to have knowledge of the factors which play a major role in the deterioration of the road network. The Khyber Pakhtunkhwa province of Pakistan having the 3rd largest provincial economy is more reliant on road transport due to the absence of other modes of transport. The provincial road network of Khyber Pakhtunkhwa consists of 3000-km of bituminous pavement. According to a report published by Asian Development Bank (ADB) in 2018, only 27.7% of provincial highways were in fair to good condition while the rest were in poor condition (ADB 2018). The main element which contributes toward the maintenance backlog is the absence of an effective maintenance plan to correlate the data for the development of the maintenance plan. Most commonly the maintenance activities are focused on three parameters i.e. unevenness index, pavement cracking, and rutting, whereas, other major factors which can be the main cause of pavement structure failure, are normally neglected (Kumar et al. 2010). Many researchers investigated a variety of factors that contributed to pavement deterioration in developing countries. Okigbo suggested that poor design and construction, heavy traffic, poor highway facilities, and poor maintenance culture are the main sources of highway failure in Nigeria (Okigbo 2012). Harischandra concluded that the type of construction, climate, and heavy loads are the main causes of pavement deterioration in Sri Lanka (Harischandra 2004). Wayessa et. al observed that the causes of deterioration of bituminous pavement are mainly due to the inadequacy of thickness of the base layer for the traffic loading, overloading, engineering properties of the pavement layers material, poor method of construction, poor design quality, and most importantly lack of side drainage (Wayessa et al. 2019). Saharuddin et al., identified 49 factors out of 111 factors, which were the most crucial factors causing road damages in developing countries (Saharuddin et al. 2019). In this research, the factors causing deterioration of bituminous pavement were found out by cross-tabulation analysis using the Chi-square test which was performed on the three (03) years of roads’ related data, obtained from the local highway department. The factors obtained from the analysis need to be considered during the formulation of a future maintenance plan. Based on the analysis, recommendations were made for the development of maintenance plan.

2 Methodology In order to find the factors causing road deterioration, first the data collection was done. The data of the pavement characteristics were taken from the Communication and Works (C&W) Department, Peshawar, Pakistan. The provincial road network of Khyber Pakhtunkhwa consists of 3000-km of provincial highways. About 99% of the provincial highways are bituminous pavement. The data comprised of 23 characteristics of bituminous pavements. Data cleaning was done to filter out the raw data and hence 16 pavement condition related roads’ characteristics were extracted from a large set of data for analysis. The data were analyzed by using the open-source statistical analysis software R (R Core Team 2022). Categorical data were used for analysis. Table 1 (page 4) shows the pavement condition-related data and their description. The pavement condition is divided into bad, fair and good, depending on the International Roughness Index (IRI) and vehicular speed. The definitions are given in Table 2. In the second step, analysis was done on the selected roads’ characteristics, for finding the relationship between

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road’s characteristics with pavement condition. This was done using statistical analysis. Categorical variables were used for analysis. The relationship between the dependent variable (pavement condition) and the independent variables (other road’s characteristics) was checked to find out the association of each road’s characteristic with three types of pavement conditions. This hypothesis was tested using cross-tabulation analysis with Chi-Square test for each individual variable with pavement condition. To find the dependency of pavement condition with other variables, the p-value was compared to the significance level. Usually, the significance level of 0.05 works well, whereas the p-value is the probability that measures the evidence against the null hypothesis. In the subject case, the null hypothesis means that there is no significant relationship between road characteristics and pavement condition. Normally, if the p-value is less than or equal to 0.05, it means that the null hypothesis can be rejected and it concludes that there is a statistically significant association between variables (Concato et al. 2016). Table 1. Road’s characteristics and description. S. No

Attributes

Types

Description

1–4

Division

1—Center

The road falls under the respective division depending on locality

2—North 3—South 4—East 5

Pavement terrain

Hilly/plain area

Shows the terrain on which roads is constructed

6

Blacktop width

–

Width of blacktop

7

Strategic importance

Less important

Road doesn’t lead to strategic sites, no movement of army convoy, road not leads to border area

High important

Road lead to strategic sites, movement of army convoy, road leads to border area

Less imp.

Ordinary Traffic with AADT up to 20,000

High important

Ordinary Traffic, Tourism or Industrial Traffic with AADT more than 20,000

Bad

Needs Rehabilitation

Average

Required maintenance

8

9

10

Importance

Condition of culverts

Condition of drain

Good

No maintenance required

Bad

Needs Rehabilitation

Average

Required maintenance

Good

No maintenance require (continued)

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Table 1. (continued) S. No

Attributes

Types

Description

11

Carriageway

Single/dual

Rep. single or double carriageway

12

Traffic load

Low

Ordinary Traffic with Farm to Market

Medium

Interprovincial traffic where interprovincial movement only depend upon provincial highway

High

Inter-Provincial traffic with industrial and tourism traffic

13

Tourism road

–

A road leads to or not lead to tourism

14

Industrial roads

–

A road leads to or not lead to industries

15

Mines or Mineral roads

–

A road leads to or not leads to mines or minerals

16

Section length

–

Length of the road

3 Results and Discussion The objective of this study was to find the factors which cause deterioration of the bituminous pavements by using the chi-square test which was performed on the data of provincial road network, obtained from the concerned department. The analysis of cross-tabulation showed the level of association between two variables. Table 2. Classification of pavement condition Pavement condition

IRI

Speed (kph)

Area damaged (%)

Bad

7–10

25–40

10–25

Fair

4–6

40–60

5–10

Good

0–4

Over 60

–

It was found that among 16 variables, 10 variables had a p-value less than 0.05, so its means that these 10 variables have an association with pavement condition as shown in Table 3. The result of the analysis of the variables which have a significant relationship with pavement condition are discussed below in detail. 3.1 Pavement Terrain Pavement terrain is defined as the type of terrain on which the road is constructed. Based on the terrain, the roads were classified as a plain or hilly area roads. Figure 1 shows the results of cross-tabulation analysis between the pavement terrain and pavement

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Table 3. p-values between pavement condition and road characteristics for the test for association (Chi-square test).

Pavement condition p-value Pavement condition p-value Pavement condition p-value Pavement condition p-value p-value

Pavement terrain 0.008 Mines and minerals roads 0.010 Drainage condition 6 × 10−16 South division 0.090 p > 0.05

Section length 0.2868 Tourism roads 0.047 Culvert condition 2.4 × 10-6 North division 0.145 Non-significant

Road importance 0.440 Industrial road 0.009

Traffic load 1.1 × 10-5 Centre division 0.002

Carriageway

East division

0.200 Strategic importance 0.130

0.060 Blacktop width 0.156

p ≤ 0.05

Significant

condition. It indicates that about 34% of the roads in hilly areas are in bad condition while the rest are in fair to good condition. On the other hand, only 13% of the roads in plain areas are in bad condition whereas more than 80% are in fair to good condition as shown in Fig. 1. In Khyber Pakhtunkhwa, the extreme climatic impact may be the cause of bad pavement conditions in hilly areas. In northern areas of Pakistan, there is a snowy season for 4 months. Poor drainage system and erosion may be the factors responsible for the poor condition of pavement in mountainous regions. In winter, when water fills small cracks in the pavement’s surface and it gets frozen, the expansion in volume can cause internal pressure and damage the pavement, and lead to erosion of roads. Salt used for deicing is another cause of road deterioration. When salt mixes with water, it increases freeze-thaw damage and road scaling problem (Althoey et al. 2021). The salt can compromise the structural integrity of concrete structures of roads. A road normally consists of many reinforced concrete structures i.e. longitudinal or cross drainage structures, bridges, and retaining walls. The deterioration of these structures also impacts the pavement condition. The salt soaks in concrete and causes corrosion of reinforcement which results in the deterioration of these structures. Due to the deterioration of these associated concrete structures, water starts seeping into the pavement structure and results in deterioration of the pavement. 3.2 Traffic Load Another important factor associated with pavement deterioration is traffic load. The traffic load was categorized as low, medium, and high, depending upon the type of traffic, as explained in Table 1. The analysis showed only 33% of roads with low traffic

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load are in bad condition while more than 60% of roads with low traffic load are in fair to good condition as shown in Fig. 2.

p-value < 0.05 Fig. 1. Relationship between pavement terrain and percentage of road in bad, fair and good pavement condition.

Fig. 2. Snow clearance on Nathiagali-Abbottabad road, east division.

The association of the pavement condition with traffic load can be best explained in the particular case as in Khyber Pakhtunkhwa with its quarrying, logging, and mining traffic, especially in the marble producing area, the overloading had been an issue for the provincial highway network since long. The pavements are designed on AASHTO specification with single axle load of 18,000 lb. According to a report published by Asian Development Bank (ADB), trucks in Khyber Pakhtunkhwa are overloaded up to 95% above the permissible load limits (ADB 2018). Due to overloading, the design life of pavement reduces and results in pavement deterioration. On the other hand, the results of the analysis for the high traffic load showed that more than 50% of roads with high traffic load are in good condition whereas 47% of roads with high traffic category are in fair to bad condition. The investigation of the data illustrated that during the prioritization of roads for maintenance budget, priority

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is given to the roads having high to the medium traffic load. It was observed that 54% of high traffic roads got budget for maintenance and rehabilitation in the year 2020–21 whereas only 9% of low traffic roads got budget in the respective year. 3.3 Drainage Condition For the purpose of analysis, the drainage condition was categorized as bad, average, and good as shown in Table 1. The results of the analysis showed that about 63% of roads in bad condition had bad drainage system while more than 70% of pavements were in good to fair condition with good drainage system as shown in Fig. 4. It was concluded that the drainage condition was another important factor associated with pavement condition. The drainage system is an important parameter that affects pavement performance. When the pavement fails, the bad drainage system is often the main factor. Many researchers verified that one of the main causes of road deterioration is poor drainage condition. Little and Jones examined the effect of moisture damage in pavements due to bad drainage system. They proved that loss of strength of pavements due to water is caused by loss of cohesion of asphalt layers, failure of the bond between aggregates and asphalt, and the degradation of aggregate particles subjected to freezing (Little et al. 2003). Similarly, N. P. Khosla et al. stated that moisture damage starts at the bottom of an asphalt layer or at the interface of two asphalt layers (Khosla et al. 1999) (Fig. 3).

p-value < 0.05 Fig. 3. Relationship between traffic load and percentage of road in bad, fair and good pavement condition.

The presence of water content in the base course, subbase, and subgrade cause early distress and lead to structural failure of pavements (Tiza et al. 2016). The maintenance activities requires to protect roads from deterioration not only include the provision of overlay but also include the maintenance of drainage infrastructure to enable the release of water that can weaken the pavement of the road within (Ismiyani et al. 2018). The drainage system is an important factor that plays an important role in the deterioration of the bituminous pavement.

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p-value < 0.05 Fig. 4. Relationship between drainage condition and percentage of road in bad, fair and good pavement condition.

3.4 Culvert Condition The culvert condition is one of the most important factors responsible for road deterioration. The analysis shown in Fig. 5 proved that about 80% of roads falling in the bad condition category are those having culverts in bad condition whereas just 20% of the roads having bad condition of culverts were in good condition. On the other hand, more than 80% of roads in fair to good categories were having good culvert condition.

p-value < 0.05 Fig. 5. Relationship between culvert condition and percentage of road in bad, fair and good pavement condition.

Culverts are defined as drainage structures or storm sewers crossing roads. In Pakistan, the majority of culverts are either concrete structures, pipe culverts, or random rubble masonry (RRM) structures with a concrete slabs. On some highways, multi-span box culverts are provided. It is usually observed that the condition of culverts deteriorates with the passage of time and they require to be maintained and check periodically. In case of damage in these culvert, the water starts seeping into the road structure causing deterioration to the road’s layer.

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p-value < 0.05 Fig. 6. Relationship between division wise roads and percentage of road in bad, fair and good pavement condition.

3.5 Topography of the Roads (Division Based) The analysis based on division showed that 50% of roads in the center division were in good condition whereas just 4% of the roads were in bad condition while the rest were in fair condition. Similarly, 36% of pavements in the east division were in good condition whereas 42% were in bad condition while the rest were in fair condition. In the south division, 62% were in good condition, while 24% were in bad condition and the rest of 14% were in fair condition as shown in Fig. 6. The center region consists of mainly plain areas and most of the important highways exist in this region. The climate of the area and the importance of the region may be one of the causes of relatively less percentage of roads in the bad category. The east division consists of mountainous regions and most of the pavements are in hilly areas. The snowfall, land sliding, and poor drainage conditions are the factors of a high percentage of pavements in the bad category. The south division consists of the region where flash floods are common. This division also includes many important industrial highways. Though 24% of the pavements are in bad condition but there is still a need of focus for maintenance activities in this region. 3.6 Mines and Minerals Roads, Industrial Roads Figures 7 and 8 show the result of cross-tabulation analysis between the variables, mines, and minerals road, and industrial roads and pavement condition which indicated that more percentage of roads which are not leading to mines and minerals areas and to industrial zones are in good condition. This factor is directly related to traffic loading. The Khyber Pakhtunkhwa province of Pakistan is very famous for its marble industry. In addition to the marble industry, there are also queries for water-bound macadam, crushed stone, and other minerals in the Khyber Pakhtunkhwa (KP) province. In KP province, the weighing machines are installed on very few important highways due to which overloading cannot be controlled. So, the overloading resulting from the transportation of minerals also contributes to the deterioration of the pavement.

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p-value < 0.05 Fig. 7. Relationship between the mine and mineral roads and percentage of road in bad, fair and good pavement condition

p-value < 0.05 Fig. 8. Relationship between the industrial roads and percentage of road in bad, fair and good pavement condition

4 Conclusions and Recommendations In this paper, factors affecting the bituminous pavement deteriorations were identified through cross-tabulation analysis using Chi-square test on the provincial roads’ data of Khyber Pakhtunkhwa province of Pakistan. Following conclusions were made through detailed study and analysis: 1. The roads having high traffic load should be given priority during the development of maintenance plan. 2. In the case of hilly terrain, the roads engineers should need to check the pavement before the snowy season. If any kinds of cracks are found, they must be rectified before the snowy season. In case of land sliding, protection works i.e. retaining walls, breast walls should be checked and maintained to minimize deterioration. 3. Longitudinal drainage and cross drainage works including culverts and bridges should be given the topmost priority in the case of maintenance plan. Without rectifying the drainage system which is the important source of structure failure, a good amount of overlay will be of no use. 4. For distribution of maintenance fund among different divisions, priority should be given to the east division due to extreme weather conditions.

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5. As the analysis showed that roads leading to mines and minerals and industrial areas are in bad condition, these roads must be prioritized for maintenance activities. Tough the development of maintenance plan depends upon the available budget but if the budget can be distributed based on the important factors of pavement deterioration i.e. pavement terrain, traffic load, climatic condition, and drainage condition, it can help in increasing the pavement life as well as it will be economical. Acknowledgement. The authors would like to express their gratitude to Japan International Cooperation Agency (JICA) for their support and to Pakhtunkhwa Highway Authority, Communication and Works Department, Peshawar for sharing the data and requisite information.

References ADB—Asian Development Bank. Board of Directors: Report and Recommendation of the President to the Board of Directors: Proposed Loans for the Additional Financing Islamic Republic of Pakistan: Khyber Pakhtunkhwa Provincial Roads Improvement Project. Asian Development Bank (2018) Harischandra, A.S.: Identification of road defects, causes of road deterioration and relationship among them for bitumen penetration macadam roads in Sri Lanka. Master thesis at the University of Moratuwa, Sri Lanka (2004) Ismiyani, E., Handayani, D., Rintis Hadiani, R.R.: The impact of drainage towards roads in maintenance cost. MATEC Web Conf. 195, 05012 (2018). ICRMCE Althoey, F., Stutzman, P., Steiger, M., Farnam, Y.: Thermo-chemo-mechanical understanding of damage development in porous cementitious materials exposed to sodium chloride under thermal cycling. Cem. Concr. Res. (2021) Saharuddin, I.N.A., Ingl, D.S.: Factors influencing road damage in developing countries. Int. J. Eng. Res. Manage. (IJERM) 06(02), 2349–2058 (2019) Concato, J., Hartigan, J.A.: P values: from suggestion to superstition. J. Investig. Med. 64(07), 1166–1171 (2016) Zumrawi, M.M.E.: Investigating causes of pavement deterioration in Khartoum State. Int. J. Civil Eng. Technol. (IJCIET) 7(2), 203–214 (2016) Little, N.D., Jones, R.D.: Chemical and mechanical processes of moisture damage in hot-mix asphalt pavements. In: Moisture Sensitivity of Asphalt Pavements—A National Seminar, San Diego, California. Transportation Research Board of the National Academics (2003) Okigbo, N.: Road maintenance in Nigeria, the way forward. Int. J. Res. Eng. Sci. (2012). Pan African Journal Series, ACCRA, Ghana Khosla, N.P., Birdsall, G.B., Kawaguchi, S.: An in-depth evaluation of moisture sensitivity of asphalt mixtures. NCDOT Research Project 1998-08 FHWA/NC/2002-102 (1999) Ogundipe, O.M.: Road pavement failure caused by poor soil properties along Aramoko-Ilesa highway, Nigeria. J. Eng. Appl. Sci. 3(3), 239–324 (2008) Kumar, P., Gupta, A.: Case studies on failure of bituminous pavements. In: Compendium of Papers from the First International Conference on Pavement Preservation, pp. 505–518 (2010) RStudio Team: RStudio: Integrated Development for R. RStudio, PBC, Boston, MA RStudio Team (2022). http://www.rstudio.com/ Wayessa, S.G., Abuye, D.G.: The major causes of flexible pavement deterioration and propose its remedial measures: a case study Bako to Gedo Road, Oromia Region, Ethiopia. Am. J. Eng. Technol. Manage. 4(1), 10–24 (2019) Tiza, M.T.: The effects of the poor drainage system on road pavement: a review. Int. J. Innov. Res. Multi. Field 2(8) (2016). ISSN 2455-0620

Investigation on Recycling Application of Waste Rubber Tyres in Concrete Shengtian Zhai1 , Yunsheng Zhang1,2(B) , and Laibao Liu3 1 School of Materials Science and Engineering, Southeast University, Nanjing 211189, China

[email protected] 2 School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China 3 School of Materials Science and Engineering, Southwest University of Science and

Technology, Mianyang 621010, China

Abstract. Rational and sustainable disposing and recycling of waste rubber tyres (WRT) has become a challenge with their numbers increasing and accumulating. According to statistics, the cumulative annual generation of WRT is about 1.5 billion; they cannot be degraded and are difficult to recycle. WRT was generally buried in the landfills, stacked in open storage, or used as fuel; which not only pollutes the environment but also wastes resources. The application of waste rubber powder in concrete not only improves the ductility of concrete but provides a new solution to the problem of waste rubber pollution. However, the workability and mechanical properties of concrete are greatly affected due to the poor compatibility between rubber particles and the cement matrix. To improve these weaknesses, a novel method to modify WRP by combining the organic and inorganic mixed slurry coating and filling effect was proposed in this study. The particle size distribution of rubber particles before and after modification, the effect of rubber particles on hydration heat and rheology of cement mortar, and interfacial bonding between rubber particles and cement matrix were explored. The compressive strength and splitting tensile strength of concrete with WRP and modified WRP (MRA) were determined. The results demonstrate this modification method was very effective, and the structure and properties of WRP were significantly improved. Under the same volume replacement percentage, the compressive strength and splitting tensile of concrete increased by 70.0% and 46.1%, respectively. The cavitation phenomenon between rubber particle and cement matrix disappeared, and the interface bonding was significantly improved. Keywords: Waste rubber tyres · Recycling · Sustainable · Modification · Concrete

1 Introduction As the most widely used and largest amount of building material worldwide today, the characteristics and properties of concrete have always been the focus of research and attracted much attention (Phiri et al. 2021). However, concrete is a brittle material, which has the disadvantages of insufficient toughness and poor durability under special service © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1539–1552, 2023. https://doi.org/10.1007/978-981-19-7331-4_122

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conditions (Liu et al. 2020a, b; Zhai et al. 2021). On the one hand, concrete materials and structures are prone to brittle failure under external extreme load, which will cause heavy casualties and huge economic losses. On the other hand, since the performance degradation of concrete materials and structure is accelerated and the damage degree is deep in extremely harsh environments (e.g. high altitude, large temperature difference, high salinity, high cold and drought, etc.), the service life is thus seriously shortened (Roy et al. 2020; Zyka and Mohajerani 2016). In addition, due to the strain-rate sensitivity, concrete is prone to chipping damage under the dynamic impact (Pereira and Lourenco 2017; Zhang et al. 2009; Zhou and Hao 2008). Therefore, for military structure and engineering, concrete not only needs to overcome the harsh service environment but also needs to improve the passive protection ability against modern high-tech weapons. Moreover, with the great development of the global economy, people’s demand for cars has been increased dramatically, which inevitably leads to an increase in waste rubber tires (WRT) (Sienkiewicz et al. 2017). As a harmful solid waste, WRT is mostly disposed of using stacking in the open, burying, burning and recycling. These disposals of means not only wasteland and resources, not only damage to the ecological environment and human health (Liu et al. 2020a, b; Rashad 2014). Therefore, facing the increasing requirements of global environmental protection, the reasonable disposal and recycling technology of WRT has become a worldwide problem (Mohajerani et al. 2020; Rana et al. 2016). Meanwhile, rubber as a viscoelastic polymer organic material has numerous characteristics, such as the low elastic modulus, good wear resistance and ageing resistance, sound insulation energy consumption and strong impact resistance etc. WRP crushed by WRT is usually incorporated into cement-based materials (Thomas and Gupta 2016; Eldin and Senouci 1993; Toutanji 1996), which can remit the brittle failure (Thomas and Gupta 2016), improve the durability (Roychand et al. 2020) and enhance high impact resistance and energy dissipation of cementitious materials (Siddika et al. 2019), as a result of the decreasing elastic modulus but increasing toughness (Siddika et al. 2019). However, the WRP is directly incorporated into the cement-based materials, which has a great impact on the workability of the concrete mixture (Malika et al. 2016), the mechanical properties (Amiri et al. 2021), the dynamic mechanical behaviour (Eltayeb et al. 2021), the law of damage and deterioration (Xiong et al. 2021), and the microscopic mechanism (Yu et al. 2019). Particularly, the compressive strength of concrete is greatly sacrificed and reaches up to 70%, thus the content of crumb rubber in the concrete is kept at a low level (Feng et al. 2012). Some researchers hope to improve the mechanical properties of rubberized concrete by selecting the appropriate rubber particle shape (Ferreira et al. 2012) and size (Pham et al. 2021; Richardson et al. 2016; Sukontasukkul and Tiamlom 2012). These results demonstrate that the mechanical properties have been enhanced to a certain extent, but the effect of improvement is not ideal. Meanwhile, the summary of many previous studies revealed that there are two main reasons for the reduction of mechanical properties of rubberized concrete. On the one hand, the crumb rubber can’t play the role of the skeleton in cementitious materials because its elastic modulus is extremely low. Rational and sustainable disposing and recycling of WRT has become a challenge with their numbers increasing and accumulating. WRT was generally buried in the landfills, stacked in open storage, or used as fuel; which not only pollutes the environment

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but also wastes resources. The application of WRT is crushed into WRP in concrete materials has been previously reported in some publications. The application of waste rubber powder in concrete not only improves the ductility of concrete but provides a new solution to the problem of waste rubber pollution. However, the workability and mechanical properties of concrete are greatly affected due to the poor compatibility between rubber particles and the cement matrix. To improve these weaknesses, a novel method to modify WRP by combining the organic and inorganic mixed slurry coating and filling effect was proposed in this study. The particle size distribution of rubber particles before and after modification, the effect of rubber particles on hydration heat and rheology of cement mortar, and interfacial bonding between rubber particles and cement matrix were explored. The compressive strength and splitting tensile strength of concrete with WRP and MRA were determined. The results demonstrate this modification method was very effective, and the structure and properties of WRP were significantly improved. Under the same volume replacement percentage, the compressive strength and splitting tensile of concrete increased by 70% and 46.1%, respectively. The cavitation phenomenon between rubber particle and cement matrix disappeared, and the interface transition zone was smooth. This finding not only can improve the mechanical properties of concrete but also can guide the application of WRT in concrete.

2 Materials and Test Methods 2.1 Materials Raw materials used in this investigation are listed as follows: P. II.42.5 Portland cement, rubber powder, river sand, water, water reducer, sodium silicate, sodium hydroxide, metakaolin, slag, the silane-coupling agent and polyvinyl alcohol. The chemical composition and physical properties of Portland cement, metakaolin, slag, sodium silicate and ordinary rubber powder are shown are in Tables 1, 2 and 3, respectively. The coarse aggregate is basalt with a particle size range of 5–15 and 15–25 mm. The density of river sand is 2580 kg/m3 , a fineness modulus of 2.8 was used as fine aggregate in the study. The waste rubber powder used in this research was obtained by shredding discarded tires at low temperatures. The apparent density of WRP is 1031kg/m3 . The size is about 80 Mesh. The water-reducing rate of polycarboxylic acid water reducer is 30%. Table 1. Chemical composition of the cement (wt%). Composition CaO Content

SiO2

Al2 O3

55.02 20.32 7.83

Fe2 O3

MgO SO3

2.79

0.09

R2 O P2 O5

4.74 1.71

5.23

MnO F-CaO 0.01

1.25

2.2 Determination of Rubber Particle Size Distribution WRA and MRA PSDs were measured using a laser particle size analyzer (S3500) manufactured by McGregor Company, which could analyze particles ranging from 0.01 μm to 28000 μm. Alcohol (AR) was used as a dispersion solution of rubber particles in this study, and the test was performed under ultrasound.

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Material Metakaolin Fly ash

CaO

SiO2

Al2 O3

Fe2 O3

MgO

SO3

Tio2

K2 O

0.15

52.37

45.03

0.47

/

0.03

1.34

0.19

42.22

31.56

12.51

2.14

0.18

2.16

7.08

0.74

Table 3. Composition of WRP Composition

Hydrocarbon

Carbon black

Alkene

Ash

Acetone extract

Metal

Other

Content

50.32

26.41

11.74

0.65

10.72

0.06

0.10

2.3 Heat of Hydration Measurements The heat of hydration of cement mortar was investigated using an isothermal calorimeter at an early age to study the effect of WRP and MRA on the heat of hydration rate and cumulative heat release. Initially, cement and different states of rubber powder were mixed in the dry state. Thereafter, dry mixtures were mixed with water using a portable hand-held mixer for 1 min (W/C = 0.5). Cement mortar of approximately 20 g was quickly transferred to a glass ampoule and put into a TAM Air eight-channel isothermal calorimeter. All mixtures were measured for the heat of hydration for 72 h at a controlled temperature of 25 °C. 2.4 Rheological Properties Measurements A rotational rheometer (Brookfield RST-SST) with parallel plates was used to measure the rheological properties of fresh mortar. After mixing, the fresh mortar was placed on the lower plate, and the upper plate was lowered until the gap between the upper plate and the lower plate became 2 mm. The upper plate was run by the test procedure in Fig. 1. The rheometer with a 4-bladed vane of a height of 40 mm and radius of 10 mm was utilized in the experiment. The outer cylinder, the radius of which is 30 mm, was stationary during the testing procedure. The total test time was 230 s where the rotation speed increased linearly within the initial 60 s, and then decreased step by step. The maximum rotation speed was 120 rpm. Each platform of the testing scheme maintained a stable rotation speed for 10 s to make the mortar reach a stable flow state. Reliable experimental results can only be obtained under the condition of steady flow. Finally, the shear stress-shear rate data can be acquired from the rheological test (Liu et al. 2021). 2.5 Environmental Scanning Electron Microscopy ESEM analyses were conducted FEI 3D (Thermo Fisher Scientific CO. Ltd, USA) Environmental Scanning Electronic Microscope to observe the microstructure changes of rubber particles and cement mortar samples with rubber. Before ESEM analyses,

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Fig. 1. The rheological scheme used to measure the rheological parameters of cement mortar

the mortar samples were completely dried and was cut in half to obtain a fresh crosssectional surface. Furthermore, the surface was polished using a polishing cloth coated with polishing paste. The surface was then coated with Au to prevent charging during observation in the ESEM instrument. 2.6 Waste Rubber Powder Modification and Concrete Specimens Preparation Process Rubber particles were modified before preparing concrete specimens. The organicinorganic coating slurry consisted of sodium silicate, metakaolin, fly ash, sodium hydroxide, polyvinyl alcohol and silane-coupling agent KH560, and the mass ratio is 200:215:65:15:4:1. Initially, the sodium hydroxide, polyvinyl alcohol and silanecoupling agent KH560 were poured into the sodium silicate solution and then stirred until completely dissolved. Subsequently, the metakaolin and fly ash were mixed and stirred well. Finally, the two mixtures are mixed in a blender for 30 min. Then, the slurry was immediately transported into the blender, and the WRP was added to the slurry. The mixture was put into the mixing device and stirred for 1 h until obtaining a uniform one. The mass ratio of WRP and slurry is 10:1. Finally, the treated WRP has stirred again and then added into the controllable ageing bunker. The temperature of the ageing bunker was set as 60 °C. After 24 h ageing, the rubber aggregate was taken out from the bunker and dispersed. The cement particles (CP), fine aggregate (FA), coarse aggregate (CA) and MRA were poured into the concrete mixer for dry mixing for 1 min. Then, the water and the polycarboxylate based plasticizer (PC) were mixed, and it was added to the dry mixture to continue stirring for 3 min. Thereafter, the fresh concrete was poured into a steel mould with 100 × 100 × 100 mm3 to prepare the concrete specimen. Finally, the specimens have removed from the mould and cured in the standard curing room for 7 and 28 d, respectively. Detailed mixture proportions are shown in Table 4. Three specimens were

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prepared for each mixture. The strength average value of three specimens as the final result was reported in this research (Fig. 2). Table 4. Mix proportions of concrete (kg). Groups

Cement

Fly ash

Water

Sand

WRP

MRA

Stone

PC

265.0

65

150.0

645.0

0.0

0.0

1220

CRC

265.0

65

150.0

512.0

90

0.0

1220

MCRC

265.0

65

150.0

512.0

0.0

100

1220

Fig. 2. Waste rubber powder modification and concrete specimens preparation process.

3 Results and Discussion 3.1 Apparent Morphology and Particle Size Distribution of WRP and MRA The surface character of WRP and MRA is shown in Fig. 3a and b. The surface of WRP has changed significantly after modification by comparing Fig. a and b. Firstly, the most obvious change is surface colour, WRP is dark brown, MRA is dark grey. This is mainly due to the coating effect of the modified slurry. In addition, there is significant agglomeration between rubber particles, which is mainly due to the interaction of charge, water and surface energy of van der Waals force carried by the particles. On the other hand, the surface of rubber particles is extremely rough due to mechanical shearing, and the mechanical meshing between the particles will also produce agglomeration. The larger its surface energy is, the more serious the agglomeration phenomenon is. This leads to the extremely uneven distribution of rubber powder in cement-based materials, and the floating phenomenon is more obvious. As shown in Fig. 5b, the agglomeration between rubber particles disappeared. This is mainly caused by the compatibilization

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Fig. 3. Apparent morphology and particle size distribution of WRP and MRA, (a) and (c) WRP, (b) and (d) MRA.

of fly ash and the coating effect of the modified slurry. Fly ash particles are filled in the cracks of rubber particles, which not only increases the bulk density of rubber powder but also reduces the specific surface area. Therefore, the surface energy of rubber powder is decreased, and the agglomeration is alleviated. Moreover, the modified slurry is coated on the surface of rubber particles, which not only increases the bulk density of rubber powder but also separates the contact between them. Therefore, the agglomeration caused by the charge of WRP is eliminated. The particle size distribution of WRP and MRA is shown in Fig. 3c and d. It can be seen that the particle size distribution of the rubber powder was changed by comparing the two photos. The particle size range changed from 20–420 μm microns before modification to 50–700 μm after modification, and the particle size with the largest proportion increased from 176 μm to 296 μm. This is mainly caused by two reasons one is that the surface area of rubber particles is enlarged due to increased surface cracks under the complex mechanochemical reaction. Meanwhile, fly ash is filled in these cracks to expand its volume. On the other hand, the surface of the rubber particle is covered by the modified slurry, so that the particle size is increased. Therefore, the particle size distribution of rubber powder changed obviously after modification, and the overall particle size of rubber powder has increased significantly.

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3.2 Hydration Heat Analysis of Cement Mortar

5

250

PC

MCRC

PC

b

CRC

4

MCRC

CRC

200

Hydration heat(J/g)

Hydration heat flow(mW/g)

a

3

2

1

150

100

50

0 0

12

24

36

Time/h

48

60

72

0

0

12

24

36

48

60

72

Time/h

Fig. 4. Hydration heat of PC, MCRC and CRC, (a) hydration heat flow, (b) hydration heat

The hydration reaction of Portland cement is the main reason for the setting, hardening and strength change of cement-based materials. The most convenient way to study the process of cement hydration reaction is to explore the change of heat during the hydration reaction, to analyze the cement hydration exothermic curve. Rubber powder is introduced into cement- based materials as fine aggregates. Although it does not participate in the hydration reaction of cement, it must have an impact on the reaction process. The hydration heat release curves of PC, MCRC and CRC are shown in Fig. 4a and b. The heat release rate curve and the cumulative heat release curve are shown in figures (a) and (b). Under the condition of 25 °C, the maximum heat release rate of the PC sample at the initial stage of hydration is 2.84 mW/g, and the cumulative heat release is 231.4 J/g at 3 d. The induction period of cement hydration is prolonged and the acceleration period is delayed with the incorporation of rubber particles. The hydration exothermic temperature peak of CRC is delayed by 9.5 h, and the maximum exothermic rate reaches 3.03 mW/g, which is 6.7% higher than that of the PC group. At the same age, the cumulative heat release increased by 4.5%, which was 341.8 J/g. This result indicates that the introduction of rubber particles significantly affects the hydration process of cement. The hydration heat release rate and cumulative heat release of cement increase significantly, but the maximum exothermic peak is significantly delayed. This is mainly because the surface of rubber particles is extremely rough, and a large number of cracks and voids are generated during the process of rubber crushing. At the initial stage of the reaction, some water is absorbed and retained in these cracks and voids, and thus the probability of full contact between water and cement particles is reduced. Thereafter, the water in the crack and void is continuously released along with the continuous hydration of the cement particles. The surrounding rubber particles become the attachment site of cement particle hydration, which promotes the progress of cement hydration. In addition, the exothermic peak point of MCRC is delayed compared with PC, and significantly earlier than that of CRC. The cumulative heat release of MCRC is 240.4 J/g at 3 d, which is almost the same as CRC. This is mainly because the cracks and

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voids on the surface of the rubber particles are filled and coated with inorganic powder and modified slurry. Part of the mixture participates in the hydration reaction, and thus the accumulated heat release is increased. Based on the above research results, it can be seen that rubber particles can promote the hydration of cement, but the heat release rate is delayed. It can be inferred that the early properties of rubber aggregate concrete are poor and the later performance is enhanced rapidly. The modification effect of rubber particles on cement hydration is more obvious than that of WRP. This will be beneficial to improving the early performance of rubber aggregate concrete. 3.3 Rheological Property Analysis of Cement Mortar

Fig. 5. Shear rate-shear stress curve of different mortars at 5 and 30 min, (a) (c) 5 min, (b) (d) 30 min

The time-dependent variation of the shear stress-shear rate relationship of cement mortar at 5 min and 30 min is determined according to the test scheme in Fig. 1. It can be seen in Fig. 5 that cement mortar with different rubber particles shows discrepant evolution of shear stress over time. The shear rate and shear stress of the deceleration section are used to draw the rheological curve. The straight line is obtained by linear fitting with the least square method are shown in Fig. 5c and d. The fitting variance R2 of all straight lines is greater than 0.97. The shear stress increases linearly with the shear

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Groups

τ/Pa 5 min

η/(Pa·s) 30 min

5 min

30 min

PC

44.78

56.84

1.12

1.42

MCRC

56.43

46.43

1.72

1.69

257.81

293.00

4.38

4.23

CRC

rate increases. The slope of the straight line represents the plastic viscosity of concrete, and the intercept represents the yield stress of concrete (Wallevik et al. 2015), which are shown in Table 5. Yield stress and plastic viscosity of PC are 44.78 Pa and 1.12 Pa s at 5 min. The yield stress and plastic viscosity of PC increased to 56.84 Pa and 1.42 Pa s, respectively with the increase of stirring time to 30 min. It is well known that the lower the yield stress and plastic viscosity of concrete, the better its flow properties (Liu et al. 2021). This result indicates that the fluidity of cement mortar decreases with the increase in mixing time. The yield stress and plastic viscosity of both CRC and MCRC are increased compared to the control group. This result shows that the incorporation of rubber particles reduces the fluidity of the cement mortar. This is mainly due to the irregular particle shape and larger surface roughness of rubber particles compared to river sand, and thus it needs more cement paste to wrap them. Comparing MCRC and CRC, it can be observed that the yield stress and plastic viscosity increase from 56.43 Pa, 46.43 Pa and 1.72 Pa s, 1.69 Pa s to 257.81 Pa, 293.00 Pa and 4.38 Pa s, 4.23 Pa s at 5 min and 30 min. This result indicates that the modification of rubber particles significantly increases the fluidity of the cement mortar. This mainly contributes to the reduction of the surface roughness of rubber particles because the cracks on their surface are filled and covered by modified slurry. Therefore, the modification of rubber particles is extremely beneficial to the improvement of the performance of cement mortar. This finding can guide the application of rubber aggregate concrete. 3.4 Interfacial Compatibility Between WRA/MRA and Cement Matrix The interfacial bonding state of the WRP-cement matrix and rubber MRA-cement matrix is shown in Fig. 6. As Fig. a, the interface transition zone between WRP and cement matrix is very obvious, and there is a large crack between them. In addition, the enlarged area is as shown in Fig. b, and a crack is shown more clearly. A small amount of cement paste is adsorbed on the edge of the rubber particle, and the cement paste on the transition zone is fluffy and irregular. This result shows that the adhesion between rubber powder and cement paste is very poor, and the rubber powder harms the formation of the structure of cement- based materials. This is mainly due to rubber being a kind of polymer organic material with lipophilic and hydrophobic performance, and its compatibility in cementbased materials is poor. When the WRP is directly incorporated into cement-based material, the defective interface between two kinds of materials is formed. Therefore, it

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Fig. 6. SEM images of interface between rubber particles and cement matrix, (a) (b) WRP, (c) (d) MRA

is speculated that the mechanical property of mortar is decreased with the increase of the WRP content. The interface transition zone between MRA and cement matrix is shown in Fig. 6c and d. The interface between rubber aggregate and cement paste is significantly improved, and the large crack at the interface disappeared. Meanwhile, a large amount of cement paste is accumulated around the rubber aggregate particle, and the interface is densely filled with slurry. The enlarged area is as shown in Fig. d, and the interface transition zone is only a boundary line of cement paste accumulation. This result shows that the adhesion between MRA and cement paste is very well, and the compatibility of the two materials is improved. This is mainly because the rubber particles are coated by the modified slurry in the modification process, and the surface performance is changed from lipophilic to hydrophilic. The adhesion between rubber particle and cement paste is improved, and an effective buffer zone will be formed in the interface area under the action of external load. Therefore, it is speculated that the mechanical property of MRA mortar is enhanced compared with the mortar with rubber powder. 3.5 Mechanical Properties of Concrete The compressive and splitting tensile strength of concrete with WRP and MRA are shown in Fig. 7a and b. The compressive strength of PC at 7 d and 28 d is 35.2 MPa and 47.8 MPa, respectively. The compressive strength of CRC decreases to 10.2 MPa and 20.3 MPa with the incorporation of rubber particles. This result indicates that rubber particles significantly reduce the compressive strength of concrete by 245.1% and 135.5%, respectively. However, under the same replacement percentage, the compressive strength of at 7 d and 28 d MCRC increases to 22.5 MPa and 34.5 MPa compared with that of CRC. This result indicates that the modification of rubber particles significantly improves the compressive strength of CRC, the strength is increased by 120.6% and 70.0%, respectively. These results show that the introduction of WRP or MRA will

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Fig. 7. Mechanical properties of concrete: (a) Compressive strength, (b) Splitting tensile strength

have adverse effects on the compressive strength of concrete, but the strength of MCRC is improved compared with CRC. This is mainly because on the one hand, the density of MRA is increased and the hydrophilicity becomes better after the filling and coating in the modification process. Therefore, the floating phenomenon of rubber particles no longer occurs in the mixing process of cement slurry, and they are evenly distributed in the cement matrix. On the other hand, the interface between rubber aggregate and cement paste is significantly improved due to the modification. As Fig. 7b, the early splitting tensile strength of PC, CRC and MCRC are 1.34 MPa, 0.71 MPa and 1.12 MPa. It can be observed that the strength of concrete is early reduced with the incorporation of rubber particles. The strength of CRC and MCRC is decreased by 88.7% and 19.6% compare with that of control concrete. The strength of concrete is enhanced as the curing age increase, which reflects a hydration process of cement concrete. The 7 d strength of PC reaches 74.9% of the 28 d strength, while CRC and MCRC are only 62.8% and 70.3%. This result indicates that the process of cement hydration is delayed by adding rubber particles to the concrete, and the effect of WRP is more obvious. This result is consistent with the hydration heat of cement mortar. Furthermore, before and after the modification of rubber particles, the strength of MCRC is increases by 63.4% and 46.1%, respectively. Two important factors affect the improvement, one is the improvement of interfacial bonding between rubber particles and cement matrix, another is the superelasticity and deformation property of rubber particles. When the concrete is damaged, the rubber particles play a bridging role to prevent the brittle failure of the concrete.

4 Conclusions The application of waste rubber powder in concrete not only improves the ductility of concrete but also provides a new solution to the problem of waste rubber pollution. However, the workability and mechanical properties of concrete are greatly affected due to the poor compatibility between rubber particles and the cement matrix. To improve these weaknesses, a novel method to modify WRP by combining the organic and inorganic mixed slurry coating and filling effect was proposed in this study. The following conclusions can be drawn from the results of the study:

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(a) The agglomeration of particles disappeared and the apparent morphology changed from black to grey after the modification of rubber powder. The particle size range changed from 20–420 μm microns before modification to 50–700 μm after modification, and the particle size with the largest proportion increased from 176 to 296 μm. (b) The induction period of cement hydration is prolonged and the acceleration period is delayed with the incorporation of rubber particles. The modification of rubber particles significantly promoted the hydration process of CRC, and the induction period of MCRC was advanced by 9 h compared with CRC. (c) The incorporation of rubber particles reduces the fluidity of the cement mortar. The yield stress and plastic viscosity increased from 44.78 Pa and 1.12 Pa s to 257.81 and 4.38 Pa s with the incorporation of WRP, respectively. The modification of rubber particles significantly increases the fluidity of the cement mortar, and the yield stress and plastic viscosity of MCRC degreased to 56.43 Pa and 1.72 Pa s. (d) The modification of rubber particles has a significant impact on the mechanical properties of rubber concrete. Under the same replacement percentage, the compressive strength and splitting tensile strength of MCRC were increased by 70% and 46.1% compared with that of CRC. This is mainly because the interfacial bonding between rubber particles and cement matrix was improved. The floating phenomenon of the rubber powder disappeared and particles were uniformly dispersed in the concrete.

Acknowledgements. The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (No. U21A20150 and No. 51978590).

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Author Index

A Aboutaha, R. S., 1387 Aboutaha, Riyad, 461 Adeagbo, Mujib Olamide, 758 Amir, Azam, 1528 Athisakul, Chainarong, 805 Aung, Zwe Yan, 860 B Bu, J. F., 1273 C Cai, Enjian, 739 Cai, Qi, 635 Cao, Jixing, 667 Cao, Thi Nguyen, 1403 Cao, Zhiwei, 533 Cao, Zihan, 677 Carneiro, Ludmila Soares, 1101 Chaisomphob, Taweep, 448 Chan, Weng Tat, 353 Chea, Bunya, 448 Chen, Cheng, 215 Chen, G. Y., 1481 Chen, Guan, 1241 Chen, L., 1135 Chen, Lin, 1193 Chen, Suwen, 1316 Chen, Xing, 1316 Chen, Xuejian, 1265 Chen, Yujie, 506 Chen, Yung-Tsang, 152 Chen, Zhifei, 1316 Chen, Zhihua, 140, 491

Chhetri, Dhan Raj, 403 Chornay, Morn, 905 Chu, Yung-Jeh, 771 Chucheepsakul, Somchai, 805 Cui, Zhendong, 416 D Dash, S. R., 116 Deng, Weixiong, 597 Diao, Mengzhu, 917 Do, Tin V., 1413 Dong, Heng, 533 Dong, Jingliang, 133 Dong, M. S., 264, 284 Du, Jing, 1070 Du, Yansheng, 140 Duan, W. H., 426 Duc, Do Minh, 1432 E Emoto, Hisao, 1503 F Fang, Lijing, 469, 929, 1015 Feng, Liuyang, 223 Fernando, Kenneth Edward Torrella, 326 Fitwi, Teklewoin Haile, 1050 Fongsamootr, Thongchai, 852 Fu, Qiang, 533 Fun, Wong Sook, 36 Futagami, Kei, 77 G Gan, Dan, 614, 1369

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 G. Geng et al. (Eds.): Proceedings of The 17th East Asian-Pacific Conference on Structural Engineering and Construction, 2022, LNCE 302, pp. 1553–1556, 2023. https://doi.org/10.1007/978-981-19-7331-4

1554 Gao, Fangyuan, 525 Gehl, Asher, 1413 George, Riya Catherine, 46, 68 Goh, Yang Miang, 388 Gourgiotis, P. A., 843 Gu, X. L., 187 Gu, Zhiwang, 730 Guan, Hong, 917 H Hamid, Roszilah, 581 Han, Y. L., 264 Han, Yilong, 284 Hanai, S., 101 He, Jiao, 730 He, Yuxuan, 721 Henry, M., 1515 Henry, Michael, 249, 326, 403, 1001, 1101, 1528 Hisazumi, Kazumasa, 1471 Ho, J. C. M., 1304, 1327, 1339 Hou, Yuzhou, 894 Hu, Chen-Xun, 691 Hu, Daohang, 1182 Hu, J., 783 Hu, Xinping, 388 Huang, Hongwei, 819 Huang, J., 1481 Huang, Jin, 140 Huang, Zhenyu, 236, 597 Hung, Tran Quang, 1432 Huu Duong, Nghi, 837 Hwang, J. H., 685 Hwang, Junha, 311 I Inoue, Y., 16 Inoue, Yusuke, 68 Ismasafie, Fadlin Sakina, 581 Iyoda, T., 3, 16, 1031, 1358 Iyoda, Takeshi, 24 J Jangid, R. S., 169 Jia, Hongtao, 1070 Jiang, S. S., 264 Jin, Y. Y., 1304 Jinping, Lu, 36 K Kaewunruen, S., 992 Kaewunruen, Sakdirat, 1455, 1464 Kanda, T., 1358 Kang, Ercong, 506, 515 Kang, Qing, 1265 Kang, Shao-Bo, 1040, 1291

Author Index Kato, Sou, 1471 Kawai, Kenji, 46, 68 Kawamura, K., 710, 943 Kawamura, Kei, 311, 437 Khan, Kashan, 491 Kim, T. K., 305 Kingkokgruad, K., 1382 Kiriyama, Kai, 437 Klaycham, Karun, 805 Kojima, M., 3 Kondo, Takuya, 77 Kong, K. H., 1087 Kong, Kian Hau, 545 Kuang, Kevin Sze Chiang, 353 L Lai, M. H., 1304, 1327, 1339 Lai, Zhichao, 199 Lam, Heung-Fai, 758, 771 Lars, Nyembo Ya Lumbu, 87 Le, Toan Minh, 860 Lertchanchaikun, Nutwadee, 805 Li, A., 1255 Li, Dan, 691, 1464 Li, Dong, 199, 819, 1159 LI, G., 1255 Li, Gang, 1211, 1225 Li, Guochang, 565 Li, K. F., 1273 Li, Pengfei, 959, 975 Li, Siyuan, 152 Li, Ting, 1455 Li, Yi, 917 Li, Zexiang, 1369 Li, Ziyang, 36 Liew, R. J. Y., 1087 Lim, Michelle, 360 Lim, Namyo Salim, 36 Lim, Taejeong, 702 Limkatanyu, Suchart, 873 Lin, Alexander, 388 Lin, Y. H., 1304 Lin, Yiteng, 819 Liu, B. D., 264, 284 Liu, Jiadi, 491 Liu, Kun, 1040 Liu, Laibao, 1539 Liu, Qizhang, 388 Liu, S. M., 1273 Liu, W.-L., 1255 Liu, Xingwang, 491 Liu, Y., 1481 Liu, Yao-Peng, 565 Liu, Yong, 1241, 1265 Liu, Z., 1135

Author Index Liu, Zhanhang, 1193 Lu, Xinzheng, 917 Luo, Hanbin, 1211, 1225 M Masunaga, Karen Midori, 24 Matsuda, K., 101 Matsuda, N., 3, 16 Matsumoto, Takashi, 448 Miang Goh, Yang, 360 Miyawaki, M., 1031 Mo, J. H., 1327 Mohammed, Amer, 140 Mona, Yuttana, 852 Mondal, G., 116 Muna, G., 1515 Muniandy, Shanmugam, 581 N Nagayama, Tomonori, 1471 Nagoya, Tomoki, 24 Nakada, Takuma, 46 Nakamura, H., 710 Nakamura, T., 943 Nanakorn, Pruettha, 829, 837, 884 Nguyen, C. K., 710 Nguyen, D. C., 305 Nguyen, Hai Yen Thi, 1403 Nguyen, Van-Loi, 873 Ni, H., 1387 Nie, Jia-Hao, 691 Nishimura, K., 1358 Nishioka, Y., 16 Numata, Miori, 1503 O Ogawa, Daichi, 1471 Ogawa, Yuko, 46, 68 Okamoto, Osamu, 437 Ou, X. L., 1339 P Pansuk, Withit, 1403 Panuwatwanich, Kriengsak, 249 Park, H. W., 685 Park, Hyun Woo, 702 Peng, Hua-Yi, 771 Prawatwong, U., 1382 Q Qian, Shunzhi, 36 Qian, Xudong, 55, 215, 223, 625 Qin, Haiyang, 730 Qu, Wenjun, 469, 929, 1015 Quek, Ser-Tong, 667

1555 R Radzi, Noor Azim Mohd., 581 Ren, Fengming, 525 Richard Liew, J. Y., 545 Rungamornrat, J., 843 Rungamornrat, Jaroon, 860, 873, 884 S Sae-ma, P., 1135 Safiena, Sufiana, 360 Sakamoto, R., 101 Sawamura, Shuji, 311 Sengsri, P., 992 Shen, Peng, 691 Shiga, Atsuki, 1503 Shim, C. S., 305 Shiozaki, M., 943 Song, Xiaobin, 133, 635 Sresakoolchai, Jessada, 1455 Sugiyama, A., 1031 Sun, F. F., 1481 Sun, L., 1135 Sun, Limin, 1193 Suttakul, Pana, 852, 884 T Tan, Kang Hai, 36 Tan, Xun-Tian, 1040 Tang, Jing, 515 Tang, Yongjing, 730 Tao, Pei, 959, 975 Tao, Ran, 625 Tay, Juliana, 360 Tay, Mavian Xin Yi, 343 Tay, Stephen En Rong, 343 Thawon, Itthidet, 852 Tiwari, Shubham, 116 Tominaga, Tomonori, 1471 Tong, Chenglong, 506 Tu, Tran Minh, 1432 U Ueda, Tamon, 651 Ul Islam, Naqeeb, 169 V Van Nguyen, Duc, 829 Vo, Duy, 829, 837, 860, 884 Vo, Khanh Minh, 1403 W Wang, C. M., 426 Wang, C., 1255 Wang, Dan-Dan, 1040 Wang, Fan, 959, 975 Wang, Gang, 1169

1556 Wang, Jiehui, 651 Wang, Junxuan, 545 Wang, Ruohan, 1241 Wang, Xiaoming, 959, 975 Wei, Z., 943 Wongviboonsin, W., 843 Wu, J. Y., 187 Wulandary, Kartika, 249 X Xiao, J. Z., 284 Xiao, Xuwen, 635 Xie, Jian, 482, 506, 515 Xie, Ping, 1225 Xing, Jiale, 565 Xiong, Hui, 1116 Xiong, Jun, 1291 Xiong, Mingxiang, 525 Xu, Chengguang, 625 Xu, J., 1273 Xu, Jia, 461 Xu, Jiajia, 625 Xu, Xubing, 416 Xue, Huizhong, 917 Y Yahiro, R., 1358 Yamano, Toru, 437 Yan, Biao, 614 Yan, Jia-Bao, 482, 491 Yan, Jiabao, 515 Yan, Jia-Bao, 691 Yan, Jie, 199 Yang, B., 264, 284 Yang, D. S., 426 Yang, S. J., 1327 Yang, Xiao, 1225 Yang, Yaohua, 1471

Author Index Yao, Jie, 1146, 1169 Yee, S. S., 1087 Yin, Tao, 677, 721 Yin, Ziwei, 1211 Yokoi, Katsunori, 77 You, Ruilin, 1464 You, Zhengjun, 1211 Yu, Q. Q., 187 Yu, Xiao-Fan, 1040 Yuya, R., 3 Z Zeng, M. R., 1327 Zhai, Shengtian, 1539 Zhang, J., 1273 Zhang, Jinhua, 87 Zhang, L. G., 1273 Zhang, Lina, 373 Zhang, Shengdong, 469, 929, 1015 Zhang, Wei, 223, 236 Zhang, Xiaogang, 133 Zhang, Xuhui, 1159 Zhang, Yao, 667 Zhang, Yi, 739 Zhang, Yunsheng, 1539 Zhang, Zheng Yu, 1159 Zhang, Zijuan, 565 Zhao, Jianling, 959, 975 Zhao, Xin, 894, 905, 1146, 1169, 1182 Zhen, Ni, 55 Zheng, Yonglai, 416 Zhou, Quanlin, 614 Zhou, Shu-Rong, 1291 Zhou, Xuhong, 1369 Zhu, Guifeng, 373 Zhu, Lei, 373, 1070, 1116 Zhuang, K. J., 783 Zou, L., 783