Advances in Civil Engineering: Select Proceedings of ARICE 2019 [1st ed.] 9789811556432, 9789811556449

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Lecture Notes in Civil Engineering

Rao Martand Singh K. P. Sudheer Babu Kurian   Editors

Advances in Civil Engineering Select Proceedings of ARICE 2019

Lecture Notes in Civil Engineering Volume 83

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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Rao Martand Singh K. P. Sudheer Babu Kurian •

•

Editors

Advances in Civil Engineering Select Proceedings of ARICE 2019

123

Editors Rao Martand Singh University of Surrey Guildford, Surrey, UK

K. P. Sudheer Indian Institute of Technology Madras Chennai, Tamil Nadu, India

Babu Kurian Muthoot Institute of Technology and Science Varikoli, Kerala, India

ISSN 2366-2557 ISSN 2366-2565 (electronic) Lecture Notes in Civil Engineering ISBN 978-981-15-5643-2 ISBN 978-981-15-5644-9 (eBook) https://doi.org/10.1007/978-981-15-5644-9 © Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are reserved 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

Contents

Unexpected Cracking in an RC Bridge Pier Cap—A Case Study . . . . . Indu Geevar, D. Adrija, Devdas Menon, and A. Meher Prasad

1

Flood Inundation Mapping of Cauvery River Using HEC-RAS and GIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abhijith Sathya and Santosh G. Thampi

15

The Potential Use of Biopolymers as a Sustainable Alternative for Liquefaction Mitigation—A Review . . . . . . . . . . . . . . . . . . . . . . . . . S. Smitha and K. Rangaswamy

25

Analysis and Mitigation of Delay in Construction of Multistoried Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. P. Muneera and K. J. Joe Maria

35

Behaviour of Concrete-Filled Fibre Tubes Under Axial Compression and Lateral Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Athira, Liji Anna Mathew, and U. K. Neeraj

51

Experimental Investigation of Coir Fibre on Its Potential for the Sorption of Hydrocarbons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. V. Praseeja and N. Sajikumar

75

Dynamic Phase Lag Studies of Damper Mounted Substation Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N. Srujana and T. Bhavani

91

Acoustic Emission Characteristics of Cementitious Materials During Early Age Hydration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Injila Hamid, Umair Ali Wani, Shafat Farooq, Aditya Sharma, and R. Vidya Sagar The Suitability of Marine Clay–Zeolite Mix as Landfill Liners . . . . . . . 129 Krishna Santhosh, G. Sanoop, Sobha Cyrus, and Benny Mathews Abraham

v

vi

Contents

Ductility Assessment of an RC Section . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Kshama Hemkar, Laxmi Kant Mishra, and Goutam Ghosh Finite Element Analysis of Shape Memory Alloy Ring Spring System for Steel Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Ashwin Jose and C Prabha The Development and Study of Fiber Reinforced Fly Ash Bricks . . . . . 177 P. Prathyusha and Kolli Ramujee Seepage Behavior of Fiber Reinforced Embankment Fill: A Review . . . 189 V. P. Devipriya, S. Chandrakaran, and K. Rangaswamy Ground Improvement with Stone Columns–A Review . . . . . . . . . . . . . . 197 Revathy Manohar and Satyajit Patel Effect of Fly Ash on Geotechnical Properties of Oil-Contaminated Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Veena Jayakrishnan, Aiswarya Gracious, and Anila C. Shaju Development of Pavement Performance Prediction Models for Low-Volume Roads Using Functional Characteristics . . . . . . . . . . . 233 Muhammed Shibil P, M. Sivakumar, and M. V. L. R. Anjeneyulu Design and Analysis of Diagrid Structural Systems for High-Rise Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Sneha Mole Jacob, N. Phani Charan, and Anju Raju Seismic Analysis of Composite Box Girders with Corrugated Steel Webs and Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 P. Aparna and Binol Varghese Experimental Study on the Effect of Natural Rubber Latex and Plastic Fiber in Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Elizabath M. John and Seethu Sunny Effects of Eggshell Powder and Granite Powder on the Strength Properties of Concrete by Partial Replacement of Cement and Fine Aggregate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Geethika G. Pillai and Manjusha Mathew Comparison of Seismic Response of a Multi-storied Building With and Without Liquid Damper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Arsha A. Deleep and Varsha Susan Thomas Enhancement in the Load-Carrying Capacity of RC Rectangular Columns Adopting CFRP and GFRP . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 Md Ibrahim and Y. K. Guruprasad

Contents

vii

Efficiency Assessment of RC Jacket Applied on a Distressed RC Column Using Different Codal Provisions . . . . . . . . . . . . . . . . . . . . . . . 321 Mazharuddin Mohammed and Y. K. Guruprasad A Feasibility Study of Colloidal Silica as Stabilizing Material for Passive Site Remediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 Prashansha Sharma, Jiji Krishnan, and Shruti Shukla A Critical Review on Mass Concrete Embedded Water Pipes as Permanent Roofing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 V. P. Jai Shankar and V. K. Jebasingh Rock Mass Rating and Geological Strength Index Relationship for Sandstone Along Rock Cut Slope at Markundi, Chopan, District Sonbhadra (U.P.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 Saurabh Kumar and H. K. Pandey Evolutionary Topology Optimization of Structural Concrete Under Various Load Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 V. R. Resmy and C. Rajasekaran Numerical Analyses of Geogrid Reinforced Embankment Over Soft Clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 C. Keerthana, M. P. Vibhoosha, and Anjana Bhasi Tensile Properties of FRP and Ferrocement—A Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 P. Bindurani, N. Ganesan, and P. V. Indira Analysis of PVD with Vacuum and Surcharge . . . . . . . . . . . . . . . . . . . . 407 R. Sujana and Anjana Bhasi Drivers Perspective on Wearing Seat Belt and Use of Mobile Phone While Driving in Metropolitan City . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 Ballem Praveen, Adepu Ramesh, and Molugaram Kumar Calibration of Fundamental Flow Model for Pedestrian Sidewalks in Urban Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 Nirnay Chintawar, Teja Tallam, and K. M. Lakshmana Rao Determination of Level-of-Service for Public Transport: A Case Study for Hyderabad Metro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 Teja Tallam, Harshini Yallabandi, and C. Naveen Kumar GFRP Reinforced RC Deep Beam with Multiple Web Openings . . . . . . 453 R. Murugan and G. Prasanna Influence of Superplasticizers on Blended Cement and Their Effect on Flow Characteristics by Incorporating PGBS as Partial Replacement for Fine Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 D. Arpitha, V. J. Sudarshan, Y. T. Thilak Kumar, and C. Rajasekaran

viii

Contents

Investigations on Flow Characteristics of Mortars Using Partial Replacement of Fine Aggregates with Processed Granulated Blast Furnace Slag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 V. J. Sudarshan, D. Arpitha, Y. T. Thilak Kumar, C. Rajasekaran, and Nagesh Puttaswamy Development of Satellite Data-Based Multiple Regression Equations for the Estimation of Total Coliform and Petroleum Hydrocarbons Along South West Coast of India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 Dinu Maria Jose, Venkata Ravibabu Mandla, Srinivasa Rao Neerukattu, and Sri Venkata Subbarao Saladi Analysis of Thin Plates Using Applied Element Method . . . . . . . . . . . . 507 D. Lincy Christy, T. M. Madhavan Pillai, and Praveen Nagarajan Study of Tilt on Adjacent Strip Footings . . . . . . . . . . . . . . . . . . . . . . . . 517 S. Anaswara and R. Shivashankar Structural Stability of Cold-Formed Steel Wall Studs Under Compression by DSM Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 Abhinav Dewangan, Govardhan Bhatt, and Chanchal Sonkar A Model for Estimation of Critical Gap and Its Distribution Behaviour at Un Signalised Intersections . . . . . . . . . . . . . . . . . . . . . . . . 537 M. Satya Deepthi and A. Ramesh Critical Review on Stress-Sensitivity and Other Behavioral Aspects of Arch Dams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 K. Jiji Panicker, Praveen Nagarajan, and Santosh G. Thampi Assessment of Safety of a Retrofitted Damaged Reinforced Concrete Column Based on the Bond Stress and the Stress Transfer at the Interface of the Reinforced Concrete Jacket and the Old Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567 Y. K. Guruprasad and K. S. Jayasimha Parametric Response Estimation Study on Cantilevered and Strutted Diaphragm Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 Anu James and Babu Kurian Numerical Studies on Impact Response of Reinforced Concrete Beams Using FE Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601 Anand Raj, B. Kiran Kumar Reddy, Praveen Nagarajan, and A. P. Shashikala Numerical Studies on Impact Response of Prestressed Beams Using FE Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 Anand Raj, Raunak Kumar, Praveen Nagarajan, and A. P. Shashikala

Contents

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Fracture Behaviour of Steel Fibre Reinforced Rubcrete . . . . . . . . . . . . 619 Anand Raj, P. J. Usman Arshad, Praveen Nagarajan, and A. P. Shashikala Performance of Diagrid Structures with the Addition of Shear Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629 Minu Ann Peter, A. S. Sajith, and Praveen Nagarajan Design of Box Girder Bridges Using Simplified Frame Analysis . . . . . . 639 J. Chithra, Praveen Nagarajan, and A. S. Sajith Use of FEM for Design of Reinforced Concrete Beams as Per IRC 112-2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 649 J. Chithra, Praveen Nagarajan, A. S. Sajith, and R. A. Roshan Estimation of Ultimate Strength of Concrete Box-Girder Bridges Using Space Truss Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659 Bajare Mayur Mangesh, J. Chithra, Nagarajan Praveen, and A. S. Sajith Performance Evaluation of Geopolymer Concrete Beam-Column Joints Using Finite Element Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 677 Aravinda Rajhgopal, Saranya P., Praveen Nagarajan, and A. P. Shashikala Numerical Studies on GGBS–Dolomite Geopolymer Concrete Short Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691 Akash Kumar Behera, P. Saranya, A. P. Shashikala, and Praveen Nagarajan Effect of Double Plastic Hinges on Seismic Performance of Strengthened Column . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 C. U. Aswin and Alice Mathai Plastic Hinge Relocation in RCC Double-Slotted Beam Connection . . . . 715 Anandhu P. Haridas and Alice Mathai Evaluation of Reliability Index for the Steel Beam Designed Using IS 800:2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725 Chinnu Sabu, Praveen Nagarajan, and P. Robin Davis Experimental Investigation on Bond Strength Properties of Geopolymer Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 P. Saranya, Praveen Nagarajan, and A. P. Shashikala Numerical Procedures for Simulation of Wave Propagation in Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741 Mohammed Aslam, Praveen Nagarajan, and Mini Remanan Study on Compatibility Issues and Flow Behavior of Copper Slag-Based Mortars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751 Y. T. Thilak Kumar, D. Arpitha, V. J. Sudarshan, C. Rajasekaran, and Nagesh Puttaswamy

x

Contents

Properties of Coconut Shell Aggregate Concrete: A Review . . . . . . . . . 759 A. Sujatha and S. Deepa Balakrishnan Effect of Rigidity on Seismic Analysis of Structures . . . . . . . . . . . . . . . . 771 M. Dhileep, P. D. Arumairaj, G. Hemalatha, and M. S. Sandeep Effect of pH on Compressibility Behaviour of Cement-Treated Soil . . . . 789 Suresh Kommu and SS Asadi Simplified Grid Strut and Tie Model Approach for Shear Walls . . . . . . 809 Kannan C Bhanu, N. Ganesan, and P. V. Indira Analysis of RC Buildings by Metamodel Approaches . . . . . . . . . . . . . . 817 Deepak Sahu, Pradip Sarkar, and Robin Davis Dynamic Analysis of Roll-Pitch Coupled Motion of Ship With or Without Gain and Delayed Feedback Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 Reena Devi Ningombam, Atul Krishna Banik, and Manoranjan Barik Correlation Establishment of Compressive Strength and Bond Strength of Fly Ash Brick Masonry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841 Santosini Sahu, Peri Raghava Ravi Teja, Pradip Sarkar, and Robin Davis Mechanical Strength, Voids, and Sorptivity Evaluation of Copper Slag Based Standard Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 851 Swetapadma Panda, Pradip Sarkar, and Robin Davis Application of Finite Element Modeling for Assessing the Fire Ratings of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865 Vivek Jain and Govardhan Bhatt Effect of Shear Span to Depth Ratio in Strut-And-Tie Model on Deep Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 879 Renu Sahu and U. K. Dewangan Optimal Design Techniques of Composite Payload Adapter for a Typical Launch Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895 V. Pavithra and Gangadhar Ramtekkar Nonlinear Static Analysis of a Rectangular Cable Supported Submerged Floating Tunnel (SFT) as an Alternate Crossing for Waterway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923 Md. Hafizur Rahman and Chhavi Gupta Nonlinear Finite Element Analysis of Plain Footing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 931 Rakhi Elizabeth Thankachan, Bennet Kuriakose, and Jitin Jacob

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Soil–Structure Interaction Analysis of Tall Steel Chimney Subjected to Wind Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945 Anjaly Mohan, Binny Lizia Jose, and Bennet Kuriakose Investigation of the Suitability of Water Demand Studies as an Indicator of Incompatibility Between Binders and Superplasticizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953 A. K. Swathy Krishna, T. K. Sreeranjini, and P. L. Vijayakumari

About the Editors

Dr. Rao Martand Singh is a Lecturer of Geotechnical Engineering in the Department of Civil and Environmental Engineering, University of Surrey, United Kingdom. Applying Geotechnical Engineering knowledge for solving problems relating to energy and environment is his passion. Previously he worked as a Research Fellow on geothermal energy pile foundation project at Monash University in Australia. He obtained his PhD from Geoenvironmental Research Centre, Cardiff University, MTech from IIT Delhi and BEng from MBM Jodhpur. His research interests include Geothermal energy pile foundation, soil-structure interaction, coal seam gas (CSG), wind farm collector system, gas/liquid permeability characteristic of cement bentonite used in cut-off walls and borehole walls, unsaturated geosynthetic clay liner (GCL), barrier design for nuclear waste, suction measurement techniques, thermo-hydro-mechanical (THM) behaviour of soils and geosynthetics and modification of bentonite to improve its retention capacity. He has several publications in peer-reviewed international and national journals. Prof. K. P. Sudheer is working as Professor in the Department of Civil Engineering, IIT Madras, India. He has been a faculty of this institute since 2003, first as Assistant Professor and then as Associate Professor and, now as Professor. He has also taken the role of visiting faculty for many international universities. K. P. Sudheer obtained his bachelor degree in Civil Engineering from Kerala Agricultural University, India. He obtained his master’s degree in Structural Engineering from IIT Kharagpur and PhD from IIT Delhi. His research interests include Hydrologic Modelling, Stochastic Hydrology and Hydrological forecasting. He has many papers published in Refereed International and National Journals. Prof. Babu Kurian is the Dean and Head of the Department of Civil Engineering at Muthoot Institute of Technology & Science, Kerala, India. He has a Master Degree from IIT Bombay in Structural Engineering and a PhD from Structural

xiii

xiv

About the Editors

Engineering Division of IIT Madras. He has more than 35 years of teaching and research experience. He is closely involved in the research and consultancy projects and is associating with various firms for finding practical solutions for problems related to Civil and Structural Engineering. He has published papers in reputed journals and conferences. He has served as a member of the Board of Studies (PG Engineering) of Mahatma Gandhi University and is an executive committee member of Institution of Engineers (India), Kerala Chapter.

Unexpected Cracking in an RC Bridge Pier Cap—A Case Study Indu Geevar, D. Adrija, Devdas Menon, and A. Meher Prasad

Abstract This paper presents an investigation on structural cracking observed in a reinforced concrete (RC) pier cap supporting a prestressed concrete box girder of 13 m span. Unexpected vertical cracks were observed at service loads on the sides directly under the bearings. A site visit revealed that the elastomeric bearings were compressed on one side with loss of contact on the other. The crack width measurements showed a crack width as high as 1 mm at some locations, where the cover provided was found to be 100 mm, more than the proposed cover of 50 mm. A detailed analysis using non-linear finite element analysis (NLFEA) established the reason for cracking as the reduced contact area at the bearings. The wide cracks were due to the unexpected high cover. The safety of the structure at ultimate loads was also checked using NLFEA and the strut and tie method, and is seen that the structure is safe at ultimate loads. Keywords Crack · Pier cap · Deep beam · Non-linear

1 Introduction Cracking was observed in some of the pier caps supporting a prestressed concrete box girder of 13 m span. The superstructure consists of longitudinally prestressed central spline and cantilever precast elements connected with the central spline with transverse prestressing. The total width of the deck is 20 m. The spine and cantilever system (superstructure) rest on elastomeric bearings on a pier cap projecting from the pier. The typical grid arrangement with bearing locations is shown in Fig. 1. This system is reproduced at many other locations as part of stations in an elevated rail I. Geevar (B) Rajagiri School of Engineering & Technology, Cochin, India e-mail: [email protected] D. Adrija Atkins, Bangalore, India D. Menon · A. Meher Prasad Indian Institute of Technology Madras, Chennai, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_1

1

2

I. Geevar et al. Grid where cracking was observed

A 1 2

B

C

D

E

F

G

H

I

J

K

B1 B2

3 Face having crack Fig.1 Grid Layout showing bearing locations

network in India. The pier cap at one end (Grid A) is more heavily loaded than other similar pier caps, which is where cracking was observed (near Bearing B2). The cracks were observed along the side faces directly beneath the bearings as shown in Fig. 2. Similar cracks were observed in a few pier caps at Grid A. This paper presents a detailed study of the causes of cracking using a non-linear finite element analysis (NLFEA). The ultimate load-carrying capacity of the pier cap was also checked to establish the safety of the structure, using both the strut-and-tie method and NLFEA.

2 Details of the Pier Cap 2.1 Geometry and Materials The geometry of the pier cap was chosen to suit the slender prestressed concrete spline and cantilever deck system and is given in Fig. 3. The pier cap consists of a primary corbel and a secondary corbel (Fig. 3). The pier cap under consideration is loaded primarily through two elastomeric bearings (B1 and B2) causing high moments on the pier, which is taken care of in the design of the pier. The depths of the corbels were decided based on the limiting shear stress consideration in IRS Concrete Bridge Code [1]. The pier cap under consideration is loaded primarily on one side causing high moments on the pier and is taken care of in the design of the pier. The characteristic cylinder strength of concrete, f c , used is 36 MPa. The yield stress of reinforcing steel, f y , is 500 MPa.

Unexpected Cracking in an RC Bridge Pier Cap—A Case Study

3

Crack location

a)

Crack location

b) Typical crack

c) Elastomeric bearing Fig. 2 Crack details

2.2 Loading With respect to Fig. 1, the heaviest loaded grid is A, which is where the cracks were observed. Table 1 shows the dead load (DL), superimposed dead load (SIDL), live load (LL), service load and the factored ultimate load on this grid. It may be noted that the gravity loads at Bearing B2 are larger than those at Bearing B1 and the cracks observed were near to the Bearing B2.

4

I. Geevar et al.

Fig. 3 Geometry of the pier cap

Bearing (B1)

B

Pier cap

C

350

1150 700

A

1700

Bearing (B2)

1150

A

600 (TYP

C

5700

Traffic direction

524.5 300

2500

78

4150

78 525

1550

B

1550

525 Bearing (B2)

Bearing (B1)

Secondary corbel

329 200 R100

450 345

R384 R384 Pier 150

2200

150

Section A-A

700

800 650 450 345 1600

Primary corbel 2500 Section B-B

All dimensions in mm

Unexpected Cracking in an RC Bridge Pier Cap—A Case Study

5

Table 1 Loads on the pier cap Bearing no DL (kN) SIDL (kN) LL (kN) Total load (service Ultimate load (1.25 load) (kN) DL + 1.25 SIDL + 1.75 LL) (kN) Grid A B1

1121

1049

437

2607

3477

B2

1121

1258

390

2769

3656

2.3 Structural design and detailing The depth of the pier cap was decided based on the limiting shear stress consideration in the IRS Concrete Bridge Code [1]. The force flow in the pier cap was assumed to be from the bearing region to the primary corbel, through the secondary corbel, and then to the pier. The pier cap (assumed to be consisting of two corbels) was then designed based on the corbel design given in IRS Concrete Bridge Code [1] derived from a simple strut-and-tie system also satisfying the corbel detailing requirements [2]. The main reinforcement was distributed uniformly throughout the width of the two corbels. The distributed reinforcement consisting of horizontal stirrups were provided as per corbel detailing requirements. The vertical stirrups were also provided in the corbels based on the provisions for flexural shear and torsion. The main reinforcement was distributed uniformly throughout the width of the corbels. The distribution reinforcement including vertical and horizontal stirrups was also provided. The vertical stirrups in the primary corbel were designed based on the provisions for torsion. The reinforcement details are shown in Fig. 4. The conventional methods used for the design of beams are strictly not applicable to the considered pier cap. It is observed that the shear provisions in codes based on a fixed angle or variable angle truss models are not suitable for span-to-depth ratios of less than one [3]. Also, the empirical corbel provisions in codes are developed based on limited tests on small-sized corbels [3] and are found to result in congested reinforcement in pier caps with high conservatism [4]. These methods also fail to consider the localised effect of the bearing pads on the strength of pier caps and do not give guidelines on the distribution of tie reinforcement. Strut-and-tie method is a rational method which can be used to design pier caps of any geometry, and is based on the actual flow of forces in the member at ultimate loads [5].

2.4 Crack Details The cracks were observed on the side face beneath the bearing (in the secondary corbel) and seem to have originated from point A (Fig. 2b). It has propagated further to the top (vertically) and bottom side of the secondary corbel. In one of the pier caps, the crack extended to the primary corbel and propagated diagonally to the pier, similar to a diagonal shear crack. The crack width measurements showed that the

6

I. Geevar et al. 1 1 3 3 3 3

1

S2 1 1

1 1

1 1

1 1

1 1

1 1 1 1 3 3 3 3

Bar S3 Mark 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 4 5 6 7 a) Primary corbel S1 S2 S5 S6 S3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 S4 7 7 S5 7 7 S6 7 7 S4 S4 S4 S4 S4 S4 S4

6 6

S1

6 6

S1

6 6

S1

6 6

S1

6 6

S1

S1

6 6 6 6

b) Secondary corbel

S1

6 6

Number & Diameter (mm) 24-Y32 (16+8) 16-Y12 2x4-Y16 Y12 24-Y32 (16+8) 16-Y12 2x3-Y16 14L-Y16 3x14L-Y16 2L-Y16 14L-Y16 3x14L-Y16 2L-Y16

Spacing (mm) 100 160 100 125 100 125

Clear cover = 50 mm fy = 500 MPa

Fig. 4 Reinforcement detailing of the pier cap

crack widths in some locations (near point A) were as high as 1 mm and depth of the cover was found to be around 10 mm. The clear cover measured using a cover metre showed cover as high as 100 mm in the region of crack origin. This was the case for almost all the cracked pier caps which was probably due to the architectural feature near point A, making it practically difficult to maintain the required cover of 50 mm. From the measurements, it can be inferred that the cracks are within the cover region. A site inspection showed that the elastomeric bearings resting on the pier cap were compressed on one side (near to the pier) and there was a loss of contact on the other side (farther from the pier) (Fig. 2c). This indicated that the heavy load was acting on a smaller area than expected, and the observed cracks were found to be closer to this region (towards the pier side). This is seen in Fig. 2b, where the cracks are on the left side (nearer to the pier) of the red line representing the centre line of the bearings.

3 Strength Check Using Strut-and-Tie Method Strut-and-Tie Method (STM) is a rational and efficient approach to designing ‘disturbed regions’ where the strain distribution is expected to be non-linear due to load/geometric discontinuities [5] as in pier caps. The method idealises the region

Unexpected Cracking in an RC Bridge Pier Cap—A Case Study

7

as a hypothetical truss consisting of concrete struts and steel ties, joined together at regions referred to as nodes capable of transmitting the load to the supporting structure. It is a lower bound method based on the theorem of plasticity where the predicted strength is always greater than the actual strength, provided sufficient distributed reinforcement is present to impart plasticity to concrete. Therefore, the configuration of the truss may be chosen optimally to minimise the amount of tie reinforcement at ultimate loads, also limiting the stresses in steel and concrete as per the permissible limits defined in codes [6]. The designer is also allowed to choose different truss models considering practicality and convenience in detailing of the reinforcement; this has been validated by Kuchma et al. [7] in deep beams. It is observed that after cracking, redistribution of stresses occur and the force flow becomes as per the assumed strut-and-tie model giving conservative estimates of strength. It is seen from experiments on pier caps that STM can be safely used for the design of pier caps [8, 9]. Serviceability is usually not checked while using STM. Codes generally specify a minimum distributed reinforcement across the struts prone to cracking, to control crack widths and also to ensure ductility [10]. The Strut-and-Tie Model shown in Fig. 5 is used to predict the strength of the considered pier cap using the provisions in Eurocode 2 [11] with the load path assumed to be from the secondary corbel to the primary corbel and then to the pier. In the model, it is assumed that the two loads on the Bearings B1 and B2 are equal (Fig. 1). Unequal loads will result in increased steel in the primary corbel; this is

ax B

ax B

P A

T1

A

α

T3

ay

C1 C B’ T

2

β

T3

zy C2 C

3

Fig. 5 Strut-and-tie model

B

C

ay

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I. Geevar et al.

Fig. 6 Localised strut-and-tie model to evaluate effective tie reinforcement

350 mm s

P/2

C4

T5

P/2 C5

ᵧ

T5

z1

T

not considered in the strength prediction as the failure of the primary corbel is not expected at failure as the difference between the two loads is small. The detailed calculations are presented in Appendix 1. According to STM, the entire main tie reinforcement of the secondary corbel is not fully effective, and this is accounted for in the calculations by evaluating the zone of effective tie reinforcement using a localised strut-and-tie model as shown in Fig. 6 which is used. Here, the load per bearing, P, is considered as two-point loads of magnitude P/2 each. The node positions are iteratively obtained to find a configuration which gives maximum strength [6]. The predicted ultimate strength is obtained as 4080 kN per bearing, more than the factored ultimate load of 3656 kN. Hence, the pier cap is considered safe at ultimate loads based on the strut-and-tie method. The expected failure is by crushing of diagonal strut C 1 after yielding of Tie T 1 in the secondary corbel.

4 Non-linear Finite Element Analysis 4.1 Modelling The non-linear finite element analysis is carried out using two models in TNO DIANA BV: (a) Model 1 assumes full contact area at bearings (bearing size of 600 mm × 700 mm as in Fig. 3) and (b) Model 2 assumes half contact area at bearings (shaded area in Fig. 3a) to simulate the loss of contact observed near the bearing region (modified bearing size of 600 mm × 350 mm). The constitutive behaviour of concrete in compression is represented by a smeared crack model with rotating cracks as the rotating crack model is found to be better at predicting crack patterns in reinforced concrete members [12]. The compressive stress-strain curve for the concrete is defined based on Hognestad [13] parabolic curve (Fig. 7a) and is represented by  f = f cd

ε 2 − εc



ε εc

2  (1)

Unexpected Cracking in an RC Bridge Pier Cap—A Case Study

f fc՛

9

σ ft

εc a)

wc

ε

Compression

b)

w

Tension

Fig. 7 Constitutive models for concrete

where εc is taken as 0.002, f cd is taken as 0.57 f c (= 20.25 MPa), where f c is the characteristic cylinder strength of concrete. The factors of safety as per Eurocode 2 are considered to check for the margin of safety in the design of the pier cap at ultimate loads. Constitutive tensile model for concrete is represented using an exponential softening path after tensile peak stress [14, 15]. This exponential relation has been proved sufficient to consider adequate tension stiffening and a gradual decrease in the ability of concrete to resist tensile stresses, and is perceived as a closer simulation of the actual behaviour of concrete in tension. The model is depicted in terms of stress versus crack opening (w) (Fig. 7b) and is represented by       w w 3 w σ − = 1 + c1 1 + c13 exp(−c2 ) exp −c2 ft wc wc wc

(2)

where w is the crack opening, f t is the tensile strength of concrete taken as 0.56 f c [3], where f c is the characteristic cylinder strength of concrete in MPa; wc is the crack opening at the complete release of stress given by 5.136 Gf /f t , where Gf (in N/m) is the Mode I fracture energy, taken as 10(dmax )1/3 ( f c )1/3 based on JSCE Guidelines for concrete [16], d max is the maximum aggregate size in mm (taken as 20 mm). Values of the constants, c1 and c2, are taken as 3 and 6.93, respectively. The reinforcement is modelled separately with a full bond between concrete and rebar. The detailing of reinforcement was provided as per the drawings. The constitutive model for steel is considered as elastic-perfect plastic with no hardening after yield point (with yield stress taken as 435 MPa considering a partial safety factor of 1.15). The mesh size is chosen as 100 mm and the meshed finite element model is shown in Fig. 8. It consists of 1,86,563 solid elements and 5232 reinforcement elements. A structural non-linear analysis is carried out with the Regular Newton Raphson solution method for the incremental iterative procedure. ‘Arclength’ technique is

10

I. Geevar et al.

Fig. 8 Finite element model

adopted for seeking convergence in the case of snap-through or snap-back behaviour. It modifies the load factor at each step so that the complete behaviour can be captured [15]. The convergence is assessed by the energy norm with a tolerance of 0.001.

4.2 Results The extent of cracking at different load steps is obtained from the model. The main steel (5) near to the bearing region and the bottom steel (S6) of the secondary corbel reach yield stress at failure similar to that obtained from strut-and-tie calculations. The cracking loads and the ultimate loads, obtained from the models, are given in Table 2 and Fig. 9. Horizontal cracks at top surface starting from the corners (Fig. 9a) were first observed at about 62% and 49% of service load for Model 1 and Model 2, respectively. With further increase in load (at about 86% and 61% of service load for Model 1 and Model 2, respectively), vertical side face cracks were observed (Fig. 9b). These Table 2 Results from finite element analysis at different stages of loading

Load on bearing B2 (kN) Model 1 Full contact

Model 2 50% contact

First top crack

1720

1366

First side crack

2375

1686

Ultimate

4160

3700

Unexpected Cracking in an RC Bridge Pier Cap—A Case Study

Load on bearing B2 Model 1: 2375 kN Model 2: 1686 kN

Load on bearing B2 Model 1: 1720 kN Model 2: 1366 kN a)

11

At first horizontal crack

b) At first side face crack

Load on bearing B2 Model 1: 4160 kN Model 2: 3700 kN c) At ultimate load Fig. 9 Propagation of cracks with increasing load

cracks were the ones observable at site. The ultimate strength (for design) considering material partial safety factors is higher than the factored load for Model 1 with about 14% safety margin. Hence, the structure may be considered safe at ultimate loads. Considering the 50% contact area in the bearing (Model 2), the pier cap is marginally safe. An 11% decrease in strength is observed for this case, when compared with Model 1. The ultimate strength predictions by the NLFEA and STM are close with only about 2% difference. Ameine et al. [17] have reported a more reliable strength prediction by STM than NLFEA from his study on deep beams due to divergence caused by high strain concentration near the loaded regions. To check the influence of cover in cracking, another model was analysed considering a higher side cover of 100 mm (near point A in Fig. 2) as measured at site instead of 50 mm. The cracking and collapse loads remained the same, however, the crack strain for side cracks was found to be higher. This may be the reason for the observed wide crack at site. However, flexural top cracks were not observed at site possibly due to lesser crack widths.

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I. Geevar et al.

5 Conclusions A non-linear finite element analysis was carried out to investigate the cracking in pier caps. The finite element results showed cracking at service loads similar to that observed at site. The primary reason for the observed cracking is the high side cover (as high as 100 mm). For such high covers, cracking is expected near to the surface. However, at the nominal cover level, cracks are likely to be of lesser crack widths. The crack depth measurements also show that the crack depth is within the excessive cover region. The loss of contact in bearing (leading to unequal load distribution) possibly have resulted in inducing the cracks at lower loads. Suitable measures were adopted to close the cracks to ensure durability. The pier caps are found to be safe at ultimate loads based on both non-linear finite element analysis and strut-and-tie method. The predicted failure is by yielding of steel and crushing of the diagonal strut of the secondary corbel of the pier cap.

Appendix 1: Calculation of Strength Based on Strut-and-Tie Method Ultimate Load, P = 4080 kN With respect to Fig. 6, stress checks in concrete and steel are given below. s (mm)

136.5

z1 (mm)

455.5

γ (°)

73.3

Zone of tie reinf. (mm)

1246

Strut, C 4 (kN) Strut area

(mm2 )

2129.6

Tie, T 4 (kN)

611.3 (mm2 )

218820

Reqd. Reinf.

Strut stress (MPa)

9.73

Provided Reinf.

Permissible stress (MPa)

12.33

Provided Reinf. (mm2 )

1407.4

Check

OK

Check

OK

611.3

Tie, T 5 5(kN)

Strut, C 5 (kN) Strut area

(mm2 )

1405.3 7-Y16 (S6)

2040 (mm2 )

35400

Reqd. Reinf.

Strut Stress (MPa)

17.27

Provided Reinf.

5-8L Y16 (S4)

4689.7

Permissible stress (MPa)

17.46

Provided Reinf. (mm2 )

8042.5

Check

OK

Check

OK

Zone of tie reinforcement is taken as two times the centre-to-centre distance between Ties T5 (Fig. 6).

Unexpected Cracking in an RC Bridge Pier Cap—A Case Study

13

Zone of tie reinforcement = 1246 mm Reinforcement effective in this region = 12-Y32 (5) With respect to Fig. 5 stress checks in concrete and steel are given below. ax (mm)

574

ay (mm)

575

zy (mm)

1169

α (°)

44.19

β (°)

63.81

Node A (top face) (kN) Area of node face

(mm2 )

4080

Tie, T 1 (kN)

4197 (mm2 )

420000

Reqd Reinf.

Stress (MPa)

9.71

Provided Reinf. No.

Permissible stress (MPa)

17.46

Provided Reinf. (mm2 )

9651.0

Check

OK

Check

OK

5855.8

Tie, T 2 (kN)

Strut, C 1 (kN) (mm2 )

Strut area (at the critical location)

475950

Reqd Reinf.

9648.3 12-Y32 (5)

2006.7 (mm2 )

4613.1

Strut Stress (MPa)

12.30

Provided Reinf. No.

Permissible stress (MPa)

12.32

Provided Reinf. (mm2 )

9651.0

Check

OK

Check

OK

Node C (bottom face) (kN)

4080

Tie, T 3 (kN)

4080

Area of node face (mm2 )

275000

Reqd Reinf. (mm2 )

9379.3

Stress (MPa)

14.84

Provided Reinf. No.

55-Y16 (S1)

Permissible stress (MPa)

17.46

Provided Reinf. (mm2 )

11058.4

Check

OK

Check

OK

4546.8

Strut, C 3 (kN)

Strut, C 2 (kN) Strut area

(mm2 )

(mm2 )

12-Y32 (1)

2006.7

373000

Strut area

Strut Stress (MPa)

12.19

Strut Stress (MPa)

7.02

286000

Permissible stress (MPa)

17.46

Permissible stress (MPa)

17.46

Check

OK

Check

OK

References 1. IRS, Concrete Bridge Code (1997) Code of Practice for Plain. Reinforced and Prestressed Concrete for General Bridge Construction, Research Designs and Standards Orgnanisation, Lucknow, India 2. Mattock AH, Chen KC and Soongswang K (1976) The behaviour of reinforced concrete corbels. PCI J 21(2)

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3. ACI 318-14 (2014) Building Code Requirements for Structural Concrete and Commentary. American concrete institute, Farmington Hills, Michigan 4. Armstrong SD, Salas RM, Wood BA, Breen JE and Kreger ME (1997) Behavior and design of large structural concrete bridge pier overhangs. Center for transportation research report CTR-1364–1, Austin, Texas 5. Schlaich J, Schäfer K, Jennewein M (1987) Toward a consistent design of structural concrete. PCI J 32(3):74–150 6. He ZQ, Liu Z and Ma ZJ (2012) Investigation of load-transfer mechanisms in deep beams and corbels. ACI Struct J 109(4) 7. Kuchma D, Yindeesuk S, Nagle T, Hart J, Lee HH (2008) Experimental validation of strutand-tie method for complex regions. ACI Struct J 105(5) 8. Sami A (1990) The response of reinforced concrete bridge pier caps. MS thesis, McGill University, Canada 9. Denio RJ, Yura JA, Kreger ME (1995) Behavior of reinforced concrete pier caps under concentrated bearing loads. Report No. FHWA/TX-97/1302–1, University of Texas, Austin, Texas 10. Birrcher DB, Tuchscherer RG, Huizinga M, Bayrak O (2013) Minimum web reinforcement in deep beams. ACI Struct J 110(2):297–306 11. EN 1992–1–1(1992) Eurocode 2: Design of concrete structures—part 1–1: general rules and rules for buildings. European committee for standardization, Brussels, Belgium 12. Claus T. (2009) Nonlinear finite element analysis of shear critical reinforced concrete beams. MSc thesis, Delft University of Technology, Netherlands 13. Hognestad E (1951) A study of combined bending and axial load in reinforced concrete members, 1951. University of Illinois Engineering Experiment Station, Bulletin Series No, p 399 14. Hordijk DA (1991) Local approach to fatigue of concrete. Ph.D. thesis, Delft University of Technology, Netherlands 15. TNO Diana (2007) Finite-element analysis user’s manual. Release 10.0. TNO Diana BV, Delft, The Netherlands 16. JSCE, Guidelines for concrete (2010) Standard specifications for concrete structures—2007. Japan Society of Civil Engineers, Tokyo, Japan 17. Amini Najafian H, Vollum RL, Fang L (2013) Comparative assessment of finite element and strut-and-tie-based design methods for deep beams. Magazine Concrete Res 65(16): 970–986

Flood Inundation Mapping of Cauvery River Using HEC-RAS and GIS Abhijith Sathya and Santosh G. Thampi

Abstract Flood is a natural disaster and causes loss of life and property destruction. The objective of the study is to prepare a flood inundation map for a stretch of the river Cauvery for different return periods. To perform hydraulic modelling, the software HEC-RAS was used. GIS was used for spatial data processing and HEC-GeoRAS for interfacing between HEC-RAS and GIS. The obtained inundation map shows total submergence of areas nearby along the chosen stretch, highlighting the need for an adequate flood warning system and proper flood protection works along the stretch. These in conjunction with proper land use management and afforestation can significantly reduce the adverse effects of flooding, particularly in the low-lying areas. Results of such studies will help the departments and agencies concerned to formulate appropriate strategies for mitigating the flood hazard in the river basin. Keywords Flood inundation mapping · HEC-RAS · GIS · HEC-GeoRAS · Hydraulic modelling

1 Introduction Flood is one of the major natural disasters that has been affecting many countries or regions in the world year after year. Floods can be defined as excess flows exceeding the transporting capacity of a river channel, lakes, ponds, reservoirs, drainage systems and any other water body, thereby inundating large areas of land in its vicinity. Flooding can be caused by heavy rain, dam failures, cyclones, ice and snow melts, etc. Floods lead to large-scale loss of life and property, and damage to buildings and other structures including bridges, sewerage systems, roadways and canals. It disrupts power transmission and also leads to quality degradation of drinking water. It also creates a larger risk of waterborne diseases like cholera. A. Sathya (B) · S. G. Thampi Department of Civil Engineering, National Institute of Technology, Kozhikode, Kerala, India e-mail: [email protected] S. G. Thampi e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_2

15

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A. Sathya and S. G. Thampi

An inundation map displays the spatial extent of probable flooding for different scenarios and can be presented either in a quantitative or qualitative manner. Inundation or hazard mapping is an essential component of emergency action plans; it supports policies and decision makers in deciding how to allocate resources, and can be useful in ecological studies and land use planning in flood-prone areas. Floodplain mapping determines the extent of land area submerged by flooding. Flood damages can be mitigated by two fundamental approaches: (i) by constructing flood protection walls or (ii) by giving warnings and evacuating people from the area at the time of flood. Flood inundation map can be used to determine the location of flood protection works, location of suitable flood shelters and the shortest route for evacuation [1–5]. Cauvery also called as Ponni is the third largest river in South India flowing through the states of Tamil Nadu and Karnataka. Cauvery basin has witnessed major floods in 1924, 1952, 1954, 1965, 1977, 1979, 1983, 1999, 2000 and 2005. Of these events the severe ones were those of 1997 and 2005. The 2005 flood was due to heavy rains in the Karnataka region during October–November and the subsequent release of floodwater from Mettur Dam. Cities affected include Tiruchirappalli, Madurai, Thanjavur, Pudukottai, Perambalur, Tiruvarur, Nagapattinam, Cuddalore, Puducottai, Ramanathapuram, Papanasam, Thiruvayur, Kumbakonam, Salem, Musiri, Lalgudi, low-lying suburban areas of Chennai city and Karaikal area of Pondicherry. Water reached up to about 7 feet in many places. The Cauvery breached its bank at Vengur near Tiruchi and overflowed at several other places. More than 2,00,000 people were affected, around 1000 acres of paddy crop was lost and 100 villages were badly affected (The Hindu, 2005) [6]. In this study, the 2005 flood event is simulated and the corresponding flood map is prepared.

2 Study Area and Data Used Cauvery originates in the foothills of the Western Ghats at Talakaveri, Kodagu, in Karnataka and flows towards southeast through Karnataka, Tamil Nadu, Kerala and the Union Territory of Pondicherry emptying into the Bay of Bengal in Poompuhar, Tamil Nadu. The total length of the river from its source to its outfall is about 800 km. It lies between 75° 27 E to 79° 54 E and 10° 9 N to 13° 30 N. Cauvery drains a total area of 81,155 sq.km (2.5% of the geographic area of the country) of which 34,273 sq.km lies in Karnataka, 43,856 sq.km lies in Tamil Nadu, 2,866 sq.km in Kerala and 160 sq.km in the Union Territory of Pondicherry. The major part of the basin is covered with agricultural land, accounting to 66.21% of the total area, 4.09% of the basin is covered by water bodies and 19.53% is under forest cover. The basin receives a normal annual rainfall of 945 mm, of which about 50% is received during the south–west monsoon, about 33 % in the northeast monsoon, roughly 10% in the pre-monsoon months and the rest in winter months. Maximum rainfall occurs in the month of August and also during October–November. The average flow in Cauvery is 677 cumecs. (Source: Cauvery Basin Report, CWC).

Flood Inundation Mapping of Cauvery River Using HEC-RAS and GIS

17

Fig. 1 Cauvery basin map. Source Cauvery Basin Report, CWC, 2014 [7]

Overall at the basin level, the climate is generally dry except during the monsoon months. There is a considerable variation in the mean daily maximum and minimum temperatures in the catchment. The mean daily maximum temperature ranges from 19.5 to 33.7° C, whereas the mean daily minimum varies from 9.1 to 25.2° C. The predominant soil types are red loamy soil, black soil, lateritic soil and alluvial soil. Alluvial soil is found in the delta region. More than 50% of the area of the basin is arable while 21.6% is non-arable. The major crops grown are paddy, ragi, sugarcane and jowar. The basin map of Cauvery is shown in Fig. 1. ASTER DEM of the river basin having 30 m resolution was downloaded from USGS Earth Explorer website (https://earthexplorer.usgs.gov/). The stretch of Cauvery extending from Gunaseelam to Koohur was selected for this study. The Kollidam river adjacent to this was also taken. From previous records, it is observed that major flooding has occurred in this stretch.

3 HEC-RAS Model Description Hydrologic Engineering Centre-River Analysis System (HEC-RAS) was developed by the Hydrologic Engineering Centre which is a division of the Institute for Water Resources (IWR), U.S. Army Corps of Engineers. It is used to perform

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A. Sathya and S. G. Thampi

one-dimensional steady flow, one- and two-dimensional unsteady flow calculations, sediment transport/mobile bed computations and water temperature/water quality modelling. The first version of HEC-RAS (version 1.0) was released in July of 1995 and the latest version 5.0 in 2015 [8]. HEC-GeoRAS is an ArcGIS extension specifically designed to process geospatial data for use in HEC-RAS. It permits the creation of geometry as an HEC-RAS input file with river centreline, banks, flow path, cross sections and other features like ineffective flow areas, storage areas, bridges, culverts, levees and blocked obstructions. The RAS mapping tool within HEC-GeoRAS helps in water surface generation and floodplain delineation. In the pre-processing stage, the geometry is developed and is exported to HEC-RAS. In the post-processing stage, the steady-state analysis results are used to develop the flood inundation map [9].

4 Methodology In this study, the HEC-RAS model was used to compute the water surface profiles for the selected stretch for floods of return periods 10, 50 and 100 years. The geometric data was developed from ASTER DEM in ArcGIS using the HEC-GeoRAS tool. The geometric data along with approximate discharge values and approximate Manning’s coefficient was input to HEC-RAS and steady-state analysis was carried out. The water surface profiles obtained from HEC-RAS were then exported to ArcGIS and using the same tool the flood inundation map was prepared. The flow chart of the methodology is presented (Fig. 2).

5 HEC-RAS Model Setup To start with the Digital Elevation Model (DEM) and the base map of the basin were input to ArcGIS. The DEM should be in projected raster (WGS 1984, 43 N). After that, the river cross-sections, stream centerline, stream bank lines, flow paths and other river geometry information were extracted from the DEM using the HECGeoRAS tool. The flow paths were assigned as left, channel and right along the flow direction. The guidelines followed in creating cross-section cutlines are as follows: (1) these are digitized perpendicular to the direction of flow; (2) they span over the entire flood extent to be modelled; and (3) are always digitized from left to right (looking downstream) [10]. After the RAS geometry data preparation, the HEC-GeoRAS model was used to generate the RAS GIS import file (final river geometry file) that can be used as the input to HEC-RAS. To the geometry, approximate Manning’s N values were assigned (0.02 for the left bank, 0.03 for channel and 0.025 for the right bank) [11]. The numbers of profiles corresponding to the floods of different return periods were given as three (10-year, 50-year and 100-year flood). Approximate peak discharge

Flood Inundation Mapping of Cauvery River Using HEC-RAS and GIS Fig. 2 Flow chart of the overall methodology

19

ASTER DEM

Creation of river geometry (centerline, banks and cross-sections) in GIS using HEC-GeoRAS

GIS to RAS Import

Steady flow analysis in HECRAS

RAS to GIS Export

Flood inundation map

values were also entered as 8,000 cumecs, 90,000 cumecs and 2,25,000 cumecs, respectively, for 10-year, 50-year and 100-year floods. The flow of 2,25,000 was observed during the 2005 flood and this value was taken as the 100-year flood (The Hindu Nov. 26, 2005) [12]. The initial boundary condition was assumed as the normal depth condition and the slope is entered as 0.0001. The steady-state analysis was carried out and the result was exported to GIS as an SDF file. In HEC-GeoRAS, the SDF file was changed to an XML file and the water surfaces were generated for different return periods. Water surface is created in a TIN format that defines a zone that will connect the outer points of the bounding polygon (includes area outside possible inundation). The floodplain delineation tool was used to convert the water surface TIN to a GRID, and then subtract the DEM from the water surface grid. All the cells in the water surface grid that result in positive values after subtraction are converted to a polygon, which is the final flood inundation polygon. By calculating the area of the polygon, the inundated area was determined and by noting the DN (Digital Number) value ranges in the water surface GRID the maximum, average and minimum flood depth was found out.

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A. Sathya and S. G. Thampi

Fig. 3 Water spread area for 10-year flood for the entire reach studied

Fig. 4 Water spread area for 50-year flood for the entire reach studied

6 Results and Discussions Flood inundation map for the entire river stretch for floods of different return periods is presented in Figs. 3, 4 and 5. The flood inundation map for different return periods is zoomed around Srirangam and presented in Figs. 6, 7 and 8. The area inundated, maximum, average and minimum flood depths are given in Table 1.

7 Conclusions The flood inundation map for the selected stretch was prepared here; also, the inundated area and the maximum, minimum and average flood depths were tabulated. From the flood inundation map it can be inferred that low-lying regions like Srirangam, Tiruchirappalli, Gunaseelam, Thennur, Pachur, Lalgudi and Koohur are

Flood Inundation Mapping of Cauvery River Using HEC-RAS and GIS

21

Fig. 5 Water spread area for 100-year flood for the entire reach studied

Fig. 6 Water spread area around Srirangam during the 10-year flood

greatly inundated even during a flood of relatively low return periods. The study points to the necessity for developing a robust flood warning system for the river, and implementation of appropriate flood protection measures in flood-prone areas.

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Fig. 7 Water spread area around Srirangam during the 50-year flood

Fig. 8 Water spread area around Srirangam during the 100-year flood

Flood Inundation Mapping of Cauvery River Using HEC-RAS and GIS

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Table 1 Inundated area and flood depths Return period (year)

Inundated area (hectares)

Depth of flooding (m) Min

Avg

Max

10

4101.93

1.49

2.78

50

24,466.03

3.02

5.92

4.07 9.63

100

32,833.03

8.32

11.21

14.02

References 1. Patel CG, Gundaliya PJ (2016) Floodplain delineation using HECRAS model-a case study of Surat City. Open J Modern Hydrol, 6 Issue, pp 34–42 2. Duvvuri S, Narasimhan B (2013) Flood inundation mapping of Thamiraparani River Basin using HEC-GeoRAS and SWAT. IJERT vol 2, Issue 7, July 2013 3. Icaga Y, Tas E, Kilit M (2016) Flood inundation mapping by GIS and a hydraulic Model (HECRAS): a case study of Akarcay Bolvadin Subbasin, in Turkey. Acta Geobalcanica, vol 2, Issue 2, pp 111–118 4. Sandhyarekha, Shivapur AV (2017) Floodplain mapping of River Krishnana using HEC- RAS model at two streaches namely Kudachi and Ugar villages of Belagavi district, Karnataka. IRJET, vol 04, Issue 08, Aug 2017 5. Nut N, Plermkamon V (2015) Floodplain mapping using HEC-RAS and GIS in Nam Phong River Basin, Thailand. IJERD, vol 6, Issue 1 6. As many as ten floods within a century and sleepless nights on the terrace; The Hindu Oct 2005 7. Cauvery Basin Report (2014) CWC (Central water Commission), Government of India, Ministry of Water Resources, Sewa Bhawan, R.K. Puram, New Delhi 8. United States Army Corps of Engineers (USACE-HEC) (2016) River analysis system HECRAS technical reference manual. Davis, California 9. United States Army Corps of Engineers (USACE-HEC) (2009) HEC-GeoRAS: GIS tools for support of HEC-RAS using ArcGIS, user manual. Davis, California 10. United States Army Corps of Engineers (USACE-HEC) (2016) River analysis system HECRAS user’s manual. Davis, California 11. Chow VT, Maidment DR, Mays LW (1998) Applied hydrology. McGraw-Hill, New York 12. Flood situation turns grim in Tiruchi, The Hindu Nov 26, 2005

The Potential Use of Biopolymers as a Sustainable Alternative for Liquefaction Mitigation—A Review S. Smitha

and K. Rangaswamy

Abstract Saturated cohesionless soils, when subjected to sudden loads like earthquake, will exhibit a phenomenon called liquefaction and start behaving like a liquid. This is due to the sudden build-up of excess pore water pressure that results in the complete loss of shear strength. Most of the traditional liquefaction mitigation approaches have several limitations like high cost and labour, disturbance to existing structures and other environmental issues. This paper reviews a series of researches that involve contemporary liquefaction mitigation practices and their mechanisms. It also presents a concise review of the application of bio-geotechnical methods for soil improvement, focusing on the use of biopolymers. Biopolymers are of biological origin and are environmentally friendly. They consist of repeating monomeric units bonded together to form a long polymeric chain and they are used commonly in the chemical as well as the food industry. In the past decade, numerous researches have been carried out to demonstrate their use in the field of geotechnical engineering to improve the various properties of soil. Biopolymers like xanthan, agar, guar, chitosan and starch were found to improve soil properties such as shear strength, permeability and compressibility significantly. Thus, biopolymers could be used to create engineered soil with modified properties in this epoch of depleting natural resources. Findings from the review of works of the literature indicate the prospective use of biopolymers as a sustainable substitute for preventing soil failure due to liquefaction in view of their pore filling and shear strength enhancement properties. Furthermore, the need for exhaustive research on the proposed concept is suggested. Keywords Microbial geotechnics · Liquefaction mitigation · Biopolymer

S. Smitha (B) · K. Rangaswamy Department of Civil Engineering, NIT Calicut, Kozhikode, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_3

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S. Smitha and K. Rangaswamy

1 Introduction An increase in the need for land due to rising population and urbanisation has led to the exploitation of even disaster-prone regions for construction purposes. Nowadays, the focus is being redirected to the development of marginal lands, which invariably would involve some risks due to the potential for liquefaction and other geotechnical concerns. Natural calamities like earthquakes, landslides, etc. cause a large loss to life and property. Nevertheless, the contribution of a geotechnical engineer in reducing the impact of such catastrophes is by relegating the ground failures caused by liquefaction or loss of shear strength of soil due to the disasters. Consequently, soil improvement has now evolved as a very relevant research in the present times. In this paper, a review of soil improvement methods against liquefaction has been focused upon, emphasising on the liquefaction mitigation potential of a class of materials called biopolymers. Some of the novel mitigation strategies to combat liquefaction which have evolved in the recent research epoch have also been reviewed. Study on the phenomenon of liquefaction, its mechanism and the causes from an engineering point of view had been widely started after the two major earthquakes of 1964—the Niigata (Japan) earthquake and the Alaska (USA) earthquake. Liquefaction is a phenomenon marked by a rapid and dramatic loss of soil strength, which can occur in loose, saturated soil deposits subjected to cyclic loading. Certain types of soil deposits, with significantly very less cohesive strength such as silty sand deposits, hydraulic fills and mine tailings of dams are particularly more susceptible to liquefaction. When such soils in their saturated condition are subjected to seismic or dynamic loading, the pore water pressure builds up suddenly, which causes a decrease in effective stress. And at a certain stage, the pore water pressure becomes equal to the total pressure, and the effective stress of soils becomes zero which, in turn, reduces its shear strength. This condition of the soil at which it has significantly very less shear strength and when it starts behaving like a liquid is termed as liquefaction. Liquefaction channelled slope failure and landslides are very common in high rainfall regions where pore water pressure build-up leads to strength loss and subsequent failure. A large number of past earthquakes have also witnessed huge losses to life and property due to the liquefaction phenomenon.

2 Liquefaction Mitigation As the liquefaction phenomenon is one of the major reasons for ground failure during an earthquake or during a heavy rainfall event, research on liquefaction mitigation and control should be particularly given more importance and focused on with more attention. In theory, liquefaction can be prevented by increasing the effective stress or/and by lowering the pore water pressure developed during loading. Liquefaction mitigation strategies have been widely discussed and reformed by various researchers and institutions over the past several years.

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PHRI summarised the ground improvement methods against liquefaction into two main categories: (i) Prevention of liquefaction and (ii) Reduction of structural damages due to liquefaction. Increasing the undrained shear strength, improving the resistance to deformation and dissipation of pore water pressure are methods for achieving the first category. Reducing structural damage could be accomplished by strengthening the foundation of the structures and the ground supporting the structures to prevent a reduction in bearing capacity or making the structures more flexible so that it can deform in accordance with the ground movement in case of buried structures [1]. Resistance to liquefaction can be improved by increasing the density, modifying the grain size distribution, stabilising the soil fabric, reducing the degree of saturation, dissipation of the excess pore pressures generated and intercepting the propagation of excess pore pressures. According to an alternate research inference, remedial measures against liquefaction can be carried out either by modifying the soil, pore water or structure [2]. Traditional liquefaction mitigation methods can be summed up into four kinds: densification, replacement, drainage and grouting techniques. These include vibro-compaction, dynamic compaction, blasting, cement grouting, lowering of groundwater table and so on. However, these traditional methods have various limitations, some of which are of major environmental concern. A succinct of the prevalent conventional and non-conventional methods, along with the basic principle of improvement is summarised in Table.1 A large proportion of sites that require remediation measures against liquefaction in sands are already fully or at least partially developed. But at built sites, it may be difficult in many cases to improve the soil using conventional methods [10]. Ground permeation with biopolymer solutions that can form a gel within the soil particles after sufficient time gap since permeation can offer a remediation solution that has almost no ground disturbance. Similarly, the liquefaction remediation strategies developed in recent years were advanced to eliminate the limitations of the traditional methods. The limitations were overcome to a certain extend by attaining non-disruptive liquefaction mitigation at developed sites particularly beneath susceptible structures, cost-effective mitigation strategy in large areas and by collaborating liquefaction remediation with environmental friendliness and low-carbon economy [11]. The research theme is unremittingly progressing, and the focus is to attain cost-effective and non-disruptive mitigation [12]. Many novel approaches for liquefaction mitigation are mainly focused on the modification of the pore water. The basic principles involved in pore water modification as a countermeasure for liquefaction are pore water pressure dissipation, lowering of groundwater level and replacement of pore water. It can be done either by traditional methods like prefabricated vertical drain, gravel drain, grouting, etc. or by the innovative methods like induced partial saturation, injection of air bubbles, etc. Most of the pioneering approaches have evolved in a similar line of traditional methods and have adopted the basic mitigation mechanisms of densification or drainage, etc. But still, they are different from traditional methods in many ways. Some of the prominent new methods are outlined in the following sections.

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Table 1 Remedial Measures against Liquefaction Types of methods

Principle involved

Remarks and conclusions

Prefabricated vertical drain [3]

Drainage

Sand compaction pile (SCP) [4]

Densification

Granular pile [5]

Densification

Best suitable for granular soils, but is costly if the improvement is to be carried out for a single deep layer existing in between non-liquefiable layers of soil since for these methods improvement occurs along the entire depth of insertion

Dynamic compaction [6]

Densification

Not suitable for soils under existing structures or for greater depth

Grouting:—Compaction grouting, Displacement grouting or jet grouting [7]

Grouting and densification

Suitable for even an isolated layer of soil as it can be injected to the required depth. But it might cause damage to underground utility lines. Furthermore, the chemical nature of the grout used may be harmful to the environment

Gravel drains Dewatering [8]

Drainage

Through the use of Earthquake Drains to provide drainage of excess pore water pressure and to reduce total settlements in liquefied soil layers. It can also be carried out by continuously pumping water from water-logged areas. May be difficult in areas where permanent recharge condition exists

Traditional additives (lime, cement, fly ash) [9]

Densification

Causes pollution to the soil as well as groundwater

2.1 Induced Partial Saturation Yoshimi et al. and Tsukamoto et al. [13, 14] found that cyclic strength doubled on reducing the degree of saturation to 90% from the fully saturated condition. Induced partial saturation technique was developed based on that finding. The method involves the introduction of a small amount of air or gas into fully saturated soil so that pore water pressure built-up due to loading reduces, which could prevent liquefaction significantly [15, 16]. Air could be introduced by a method such as by electrolysis or by drainage-recharge of the pore water [17]. Nagao et al. [18] adopted microbubble injection technology where microbubbles were introduced into the water that was circulated through soil mass and tested for liquefaction resistance. It was found that microbubbles spread into the pore spaces more homogeneously than air injection. Other researchers had desaturated soil mass by adopting the technology of biogas production from the wastewater treatment method [19]. Another method for soil desaturation is by using the aid of denitrifying bacteria that can release molecular

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29

nitrogen which occupies the pores of soil and thus reduces the degree of saturation. The changes to mechanical properties induced by the nitrogen were examined by Rebata-Landa and Santamarin [20]. He et al. [19] cultivated the denitrifying bacteria in the laboratory and performed shake table tests.

2.2 Calcite Precipitation DeJong et al. [21] proposed a bio-cementation method called microbial-induced carbonate precipitation (MICP) which is a bio-mineralisation technique where the characteristic of microbes containing urea helps in the precipitation of carbonates in the soil mass by hydrolysis. The carbonates gel the sand grains together, thus enhancing its shear strength. The initial bacterial concentration, the activity of the microbial enzymes in situ, pH, temperature, nutrient solution concentration and sand particle size distribution are the factors affecting the generation rate of carbonates in soil [22, 23]. But the calcium carbonate precipitated is just a biological binder; it is not stable and can be degraded by other micro-organisms [24]. Cheng et al. [25] performed dynamic triaxial tests and shaking table tests, and demonstrated that MICP technology could effectively increase liquefaction resistance. Similarly, Peng et al. [26] examined the effectiveness of MICP on the cyclic resistance as a function of cementation solution (CS) content, effective confining pressure and cyclic stress ratio (CSR) through a series of cyclic triaxial test programs and concluded that liquefaction resistance could be significantly improved. Other researches for mitigation of liquefaction using MICP were carried out by Burbank et al. [27] and Xiao et al. [28]. One of the drawbacks of MICP is that it requires the regular injection of microbial and nutrient supply, which may affect its economic feasibility.

2.3 Passive Site Stabilisation In order to eliminate the main disadvantage of most of the conventional methods being not suitable to be used in built areas, a new technology of non-disruptive liquefaction mitigation method was evolved [29]. The materials used for this purpose, colloidal silica grout and bentonite suspension, belong to the nanomaterial category. Colloidal silica grout is propagated along with artificial water or with groundwater so that it will travel to its targeted area. Due to its colloidal nature, it will cause cementation between the soil grains [30]. It was found from cyclic triaxial tests that both shear modulus and damping ratio increase with an increase in colloidal silica content [31]. Conlee et al. [32] performed centrifuge model testing to analyse the factors affecting the mitigation, further validating the effectiveness of this method. Bentonite suspension works in a similar manner to that of colloidal silica. Once injected into the soil, it forms bentonite gel binding soil particles together. It reduces the pore water pressure built-up during dynamic loads, thus imparting liquefaction resistance. El Mohtar

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S. Smitha and K. Rangaswamy

et al. [33] performed a series of cyclic triaxial tests whose results showed that the number of cycles to liquefaction increased in bentonite-treated sand when compared to untreated soil. Since bentonite is low in cost and is easily available, this method offers a promising solution to the problem of liquefaction.

2.4 Non-traditional Soil Additives Archaeologists have discovered evidence of using admixtures for soil improvement from different civilisations like Sumerian and Roman. From time immemorial, engineered soil has been used for construction purposes. Even though the term engineered soil has evolved recently, from 3500 BC natural materials like lime, straw, etc. have been used as a soil additive. After the industrial revolution, the use of cement gained popularity very quickly, not only for structural purposes but also as a soil stabiliser. But due to the numerous drawbacks of cement treatment, other sustainable additives which could be used for soil treatment against liquefaction have emerged. Nanoparticles like laponite [34, 35], poly-urethrene foam [36], and biopolymers like xanthan and gellan [37], beta-glucan [38] are some of the new additives that have been used as a replacement for cement for liquefaction remediation. Laponite is a synthetic, non-toxic nano-clay with a very high plasticity index. The cyclic behaviour and pore pressure response of sand laponite mixture were studied and it was found that with the increase in ageing time and percentage of laponite added, the cyclic strength was significantly improved [11, 35]. Alain El et al. [39] described the use of cryo-scanning electron microscopy to understand the micro-level interaction between sand and laponite. Laponite was mixed in dry form and as a suspension form in dry soil. Biopolymers have gained popularity in recent years for use as a soil improvement material due to its non-toxic nature and economic feasibility. A very small amount of biopolymer (0.5%) can impart significant strength and cohesion in cohesionless soil [40, 41]. Biopolymer enhanced the particle-to-particle contact by forming a coating around the soil grains and also by the creation of biopolymer bridges in between them. Dynamic behaviour of xanthan and gellan biopolymer-treated soil was evaluated by resonant column testing and an increase in shear modulus and damping was observed for the treated soil. The possible explanation for the increase in damping in spite of the enhanced connections is that there might be a phase change when the wave propagates along the sand grains and then the biopolymer gel [37]. Chang and Cho [38] evaluated the small strain geotechnical properties of β-1, 3/1,6-glucan-treated Korean residual soil by using a piezoelectric sensor entrenched oedometric cell and found that as the concentration of polymer increased in soil, the Poisson’s ratio decreased. Hence it was concluded that the rigidity of the soil increased with biopolymer content.

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31

3 Biological Approach: The Need of the Hour The manufacture of cement alone is responsible for the production of 5% of global carbon dioxide [42] which is one of the major greenhouse gases. Therefore, there is precarious pressure to replace cement in the construction industry since it will contribute to a significant reduction in carbon emission leading to a deceleration of global warming. In the soil improvement realm, biopolymer and other environmentfriendly materials are gaining popularity as a suitable replacement to conservative additives such as cement and likewise products. Biopolymers are a class of polymers which satisfy the criteria of sustainability in all aspects. They are of biological origin, i.e., they are derived or extracted from living species and hence are not synthetic products. If used for the treatment of soil, the biopolymers act in sync with the soil and they, in fact, support life in the soil to a certain extent in a sense that certain biopolymers like agar, gellan, etc. can support plant growth and micro-organism enrichment in the soil. They have been put to use to various applications in the field of geotechnical engineering. Unlike other soil improvement admixtures like cement, chemical grouts, etc. biopolymers are eco-friendly and do not harm the environment either in their production phase or their post-use period. To date, most of the studies conducted using biopolymers in the field of geotechnical engineering have focused on the improvement of the engineering properties of soil such as shear strength, permeability and compressibility. The application of biopolymers for seepage control and the hydrophilicity of certain biopolymers implicate that they can act as a novel and prospective candidate for reducing the pore pressure built-up in soils susceptible to liquefaction. Also, biopolymers have been proved to have a plugging effect which depends upon the structure of the biopolymer [43, 44]. The seepage control and reduction in hydraulic conductivity were due to the pore filling biopolymer gel formed in the pore spaces of soil particles. In saturated cohesionless soils prone to dynamic loading, if the pore spaces had deposits of biopolymer gel in them, then the pore pressure should positively reduce. Furthermore, a small-scale non-destructive test performed by Chang et al. [38] to understand the inter-particular behaviour of treated soil indicated that with the addition of biopolymer in the soil, the shear modulus of soil increased due to the enhanced fabric and contact behaviour between the particles. The augmented dynamic property of biopolymer-mixed soil obtained from a resonant column test also validates the possible application of biopolymers as an alternative for liquefaction remediation [37].

4 Conclusion Due to an expansion of habitat, the need for land is in high demand and it has become indispensable to find sustainable options for remediation of liquefaction susceptible soils. Most of the conventional methods practised have several drawbacks and many

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of them are not sustainable in terms of cost or environment affability. The class of materials called biopolymers have been recommended as an alternative option for liquefaction mitigation whose applicability needs to be further evaluated through extensive research.

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Analysis and Mitigation of Delay in Construction of Multistoried Building C. P. Muneera and K. J. Joe Maria

Abstract Any constructional project success can be realized by achieving its objectives within the planned time, budget and level of quality. One of the major problems that face the construction projects is being behind the schedule. Hence, there is a need to analyse the delays in the construction process followed by the mitigation process. This study focuses on the factor that causes a delay in the construction of multistoried residential buildings located in Kerala, India. The methodology adopted comprises data collection and analysis. Data collected include project type, duration of each activity, planned schedule and actual schedule. Time overrun of each activity was calculated, using this data. Duration Index and Delay Index was proposed and used to determine the critical activities. Delay prediction model was developed by considering its significant variables. The results from the prediction model revealed that the foundation, painting and masonry are the most influencing activities that contribute to the delay in the construction of a multistoried building. A questionnaire was developed in order to evaluate the cause of the delay in each activity. Data were gathered through the survey, ranked using Likert scale and relative importance index (RII) was found. Significant causes of delay and their severities on each activity were identified using RII. Response from the questionnaire survey concludes that the inadequacy of material and labour resources is the prominent cause of the delay in construction. This study paves a way in the construction engineering field to mitigate, analyse and overcome the overall delay in the construction of multistoried buildings. Keyword Construction delay · Delay index · Duration index · Relative importance index · Delay mitigation

1 Introduction Construction technology has a great potential to improve productivity and decrease project duration. Issue of delay in the construction sector is a worldwide problem. C. P. Muneera (B) · K. J. Joe Maria Department of Civil Engineering, MES College of Engineering Kuttippuram, Kuttippuram, Kerala 679582, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_4

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C. P. Muneera and K. J. Joe Maria

Delays occur in most construction projects, either simple or complex. In construction, delay can be defined as the extension of time in the completion of the project. Delay happens in many construction projects, although the priority of delay causes is different in various countries due to environmental effects [1]. Delays can lead to considerable negative effects such as lawsuits between owners and contractors, loss of productivity and revenue, and contract termination [2–4]. In some cases, to the contractor, delay causes higher overhead costs because of a longer construction period, as well as material costs may increase due to inflation. To the client, delay means losing profits that are planned to be earned after starting the investment at the scheduled time. Delays caused by the owner such as lateness in submitting drawings and specifications, frequent change orders and insufficient site information generate claims from both the main contractors and subcontractors which in many times entail lengthy court battles with huge financial repercussions. It is beneficial for the construction parties to recognize the project’s current situation and identify the delay causes at its early stages. This will help them a lot to take the necessary precautions in order to minimize the effect of those causes when they occur. Perusal of the literature reveals that a study has been conducted to estimate the delay causing parameters to the construction projects. The factor that contributes to delay can be the lack of resources, financial management policies, incapability of contractors’ site, proper schedule and its execution [5–7]. The effective way of delay mitigation is done by considering the most critical factor among the delay causing activities [8, 9]. This research work mainly concentrates to identify the activities that causing a delay in the construction of multistoried residential buildings by considering the categorical factors that effect delay for construction. Furthermore, this study seeks for predicting the delay of a multistoried residential building before its accomplishment, finding out the critical factors by ranking that can significantly influence delay and mitigation of delay from the combination of revealed and stated preference data. The primary objective of this study is to identify and analyse the factors causing a delay in the construction of multistoried residential buildings, to propose delay index and duration index to identify the maximum delayed activities, to develop the delay prediction model using the influencing activities in the residential multistoried buildings and to identify the delay mitigation activities based on the revealed preference data. Hence this study focuses on the development of a delay prediction model and the mitigation of delay. The developed model will help to predict the total delay that can occur in the construction of a multistoried residential building, also, the activities that have to be taken care of, so that the delay does not occur and can also be identified.

2 Literature Review Construction Delay is a major concern in the private projects’ construction industry. Construction delays can be defined as the late completion of works compared to the

Analysis and Mitigation of Delay in Construction …

37

planned schedule or contract schedule. Construction delays can be minimized only when their causes are identified. Based on the fact that construction delays are nothing but loss of time and money, a study was conducted to identify the factors that cause construction delays. The three main groups which consist of consultants, contractors and owners were questioned about Shortage of manpower, Delay in the approval of contractor submissions by the Engineer, Shortage of materials. The relationship between different subcontractors’ schedules was the most important factor that cause delays in private projects sector [10–13]. The construction delay and its impact factors are quantified around the globe and still, they have recurring nature [14–17]. Assbeihat et al. was conducted to identify the factor that causes the construction delays in Jordan. Questionnaire was prepared by three groups consisting of consultants, contractors and owners who were surveyed. The study reveals that the relationship between different subcontractors’ schedules was the most important factor that causes delays in private project sector in Jordan [18]. Aziz conducted a work attempting to identify, investigate and rank factors perceived to affect delays in the Egyptian construction projects with respect to their relative importance so as to proffer possible ways of coping with this phenomenon. This research has identified and, based on the quantified relative importance indices, determined the influence ranks of ninety-nine (99) factors causing a delay in construction projects in Egypt [19]. Rajgor et al. present the result of the questionnaires survey conducted to identify and evaluate the relative importance of the significant factors contributing to delay in construction projects. In this research, the project team members including the owner, contractor, consultant and Engineers are taken for a questionnaire survey to obtain the delay factors, and for research to identify the main causes and effects of delay in construction projects [20]. Research has been done for the problem understanding and the methodology to be followed for the estimation of construction delay. Senoucia et al. An extensive review of regional and international publications was conducted to get a better understanding of the problem and the various methodologies that were used to analyse it. They found that statistical tools are adequate for the cost overruns. [21] Braimah focused on developing knowledge and understanding of the most common delay analysis techniques (DAT) based on a case study, a review of the key relevant issues often not addressed by the techniques, and the necessary improvements needs. The evaluation confirmed that the various techniques yield different analysis results for the same delay claims scenario, mainly due to their unique application procedures [22]. Literature reviews reveal that the construction delay is recurring in nature since the construction of any building is associated with different activities complied by planning and scheduling. Based on the geographic locality and the resources of the building construction, the cause of delay may vary. Like every construction project around the globe, it is very essential to identify the cause of delay in the construction activities, then only the mitigation process to be incorporated for the smooth occurrence of construction project. Therefore, this study focuses on the delay in the construction of multistoried buildings located in Kerala, India. Additionally, after the identification of delay activities, the mitigation process has been recommended to reducing delay.

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3 Study Area and Data Collection Data were collected from three multistoried residential buildings in Calicut, Kerala, India. Multistoried buildings, with more than seven stories, were selected for this study. The secondary data such as the actual schedule and planned schedule of the above three projects were collected from the builders. Activities were categorized based on the actual duration and planned duration obtained from the data, and comparisons of both for each project were done. The planned schedule for a project is shown in Fig. 1.The sample of the actual schedule of a project is presented in Fig. 2.

Fig. 1 Bar chart of planned schedule for seven-storied building from the builders

Fig. 2 Sample of actual schedule data of seven-storied building

Analysis and Mitigation of Delay in Construction …

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Fig 3. Comparison of planned duration and actual duration of seven-storied building

4 Preliminary Analysis The data such as the actual schedule and planned schedule were obtained from the builders. From that data, actual duration and planned duration are calculated and categorizing of each activity was also calculated. After finding the planned duration and actual duration, comparisons of both for each project were done. The comparison of planned duration and actual duration is represented in Fig. 3. After finding the planned and actual duration, delay is calculated. Delay is the difference between the planned duration and the actual duration. Delay for each activity in the construction of the selected multistoried residential building was calculated and tabulated. The tabulated delay data of the seven-storied building is shown in Table 1.

5 Model Development The model development of construction delay is considered by taking the activities are independent variable. From the data set available from the two projects, after conducting the ANOVA test and tried to fit for the model. Of the different models tried with the linear regression model, and the best relation was selected as the final model. Along with the data collection of the completed projects, one ongoing project was also selected for validating the model. The model form found to be appropriate for predicting the construction delay is as follows.

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Table 1 Delay data Item

Delay

Total delay

1165

Earthwork and foundation

12

Civil-structural

50

Civil-masonry

89

Civil-plastering

96

Electrical work

221

Plumbing

15

Waterproofing

64

Tiling

20

Lift erection

0

False ceiling

68

Aluminium fabrication

72

Carpentry work

116

Industrial work

80

Painting

251

Table 2 Model for construction delay S. NO 1

Indices Construction delay

R2 0.944

Standard error Constant

Foundation

Painting

0.987

0.009

0.003

Total delay = 790.780 + 13.355 ∗ foundation + 0.852 ∗ painting

(1)

In this model, Statistical parameters for evaluating the models are given in Table 2. Statistical parameters for evaluating the construction delay parameters are given in Table 1. Considering R2 value from the table, the linear model provides a fairly good prediction. The estimated parameters are significant at 95 percentage confident intervals. The model proves that foundation and painting are the activities that cause delays for the construction project.

6 Delay Mitigation For the mitigation of construction delay, two indices were proposed namely duration index and delay index. Duration index is defined as the average duration of interruptions for a construction served during a specified time period. Duration index is mathematically expressed in Equation 2.

Analysis and Mitigation of Delay in Construction …

Duration Index = Average Time/Total Time

41

(2)

Delay index is the measure of the level of delays a specified construction project is currently experiencing. Delay index is mathematically expressed in Equation 3. Delay Index = Actual Duration/Planned Duration

(3)

A low Index indicates that construction is running relatively smoothly and higher Index indicates significant delays and work disruption. The activities with higher delay index are proposed as the most critical actives that caused delay in the construction project. The analysis revealed that waterproofing, aluminium fabrication, carpentry work, civil-plastering, tiling, earthwork and foundation, painting and civil-masonry are the activities with a higher delay index. Delay index of 12-storied buildings varies from 1 to 2.5 where 1 is obtained for external yard work and 2.5 for waterproofing which means that waterproofing is the most affecting activity of delay and external yard work is the least affecting activity of delay. Likewise delay index of seven-storied buildings varies from 1 (external yard work) to 2.9565 (waterproofing), and delay index of 14-storied buildings varies from 1 (external yard work) to 2.5 (aluminium fabrication). The activities with a higher delay index are selected, and questionnaires on the basis of that are made. Waterproofing, aluminium fabrication, carpentry work, civil-plastering, tiling, earthwork and foundation, painting and civil-masonry are the activities with a higher delay index.

6.1 Questionnaire Design Sets of 5 important factors of 8 construction activities were shortlisted on the basis of the delay index calculated. As a part of the preliminary study, advice was taken from experts for shortlisting important factors causing delay in the construction industry. There are a large number of factors that affect the delay in construction. Some of the major factors affecting the delay related to waterproofing, aluminium fabrication, carpentry work, civil-plastering, tiling, earthwork and foundation, painting and civilmasonry are listed in Table 4. And from the factors, a questionnaire was constructed. Questionnaire studies were conducted to find various factors affecting time delay in the Indian scenario. Then this could have helped some technocrats and bureaucrats to take corrective action for future project investment in India. These factors have to be mitigated for the on-time completion of multistoried residential buildings. The questionnaire was distributed to 40 construction personnel among professionals working in the construction industry, and subsequently followed up to obtain responses. To get the opinion of the factors affecting time overruns, five options (5— severe delay; 4—high delay; 3—moderate delay; 2—least delay; 1—no delay) were given where respondents were asked to mark their level of agreement to each question. The factors causing construction delay are presented in Table 4. In this research, a five-point Likert scale was adopted in view of its ease and fittingness for assessing

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Table 3 Likert scale Response 1: No delay

2: Least delay

3: Moderate delay

4: High delay

5: Severe delay

the outcome of each factor on the project time delay, derived from the respondent’s own decision based on working experience throughout their professional career in the construction industry. In order to examine the study of the responses, numerical values were allocated to the respondent’s opinion as follows: 5—Severe Delay; 4— High Delay; 3—Moderate Delay; 2—Least Delay; 1—No Delay. A Likert scale is used to scaling responses in the questionnaire survey and the labelling of Likert scale is shown in Table 3.

6.2 Analysis of Data from Questionnaire The data collected from the surveys was subjected to the descriptive Statistical analysis to rank the problems. The statistical analysis method adopted here is the RII method. All the questionnaire survey was conducted among Assistant Engineers, draftsman of different grade, Junior Engineers and others who have experience in this type of projects, and their educational levels ranged from Diploma of Engineering to Professional Qualification. Five problems affecting each selected activity duration of multistoried residential building construction were identified. All the factors are directly or indirectly related to the design, material and labour problems. For each category, critical factors are identified which results in problems of higher intensity for delay in a multistoried residential buildings construction. These factors were identified by the process of ranking using Relative Index Method. The relative importance index is mathematically expressed in Equation 4. 

RII =

W A×N

(4)

where W is the weighting given to each factor by the respondents (ranging from 1 to 5), A is the highest weight (i.e. 5 in this case) and N is the total number of respondents (here 40). Higher the value of RII, more important is the cause of delays. The ranking and relative importance index of activities based on the questionnaire survey are presented in Table 5. From the table, it is revealed that the main factors that affect construction delay are unexpected surface and subsurface conditions (soil, water table, etc.). Even though several activities cause construction delay in each activities such as time overrun is late delivery of materials in the case of waterproofing. Likewise, Unqualified/inadequate experienced labour, Design changes by owner or his agent during

Analysis and Mitigation of Delay in Construction …

43

Table 4 Factors causing construction delay Waterproofing

Inadequate contractor experience Rework due to errors Slow site clearance Late delivery of materials Poor quality of construction materials

Alluminium fabrication

Delay in providing services from utilities (electricity) Inadequate contractor experience Unqualified/inadequate experienced labour Changes in material types and specifications during construction Delay in manufacturing materials

Carpentry work

Delay in performing inspection and testing Delay in manufacturing materials Poor quality of construction material Design changes by owner or his agent during construction Low productivity of labour

Civil-plastering

Poor site management and supervision Rework due to errors Slow site clearance Shortage of labour Shortage of construction materials

Tiling

Rework due to errors Delay in performing inspection and testing Shortage of labour Slow site clearance Changes in material types and specifications during construction

Earthwork and foundation

Poor site management and supervision Ineffective project planning and scheduling Unclear and inadequate details in drawings Slow site clearance Unexpected surface and subsurface conditions (soil, water table, etc.)

Painting

Late in reviewing and approving design documents Unfavourable weather conditions Unqualified/inadequate experienced labour Inadequate site investigation (continued)

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C. P. Muneera and K. J. Joe Maria

Table 4 (continued) Late delivery of materials Civil-masonry

Delay in performing inspection and testing Design changes by owner or his agent during construction Shortage of labour Poor quality of construction material Shortage of construction materials

Table 5 Analysis of questionnaire data Group of activities

Identified factors that cause delay

Importance 1

2

3

4

5

I. Waterproofing 1

Inadequate contractor experience

3

7

18

8

4

0.615

2

Rework due to errors

2

9

18

7

4

0.61

3

Slow site clearance

2

13

14

7

4

0.59

4

Late delivery of materials

6

3

15

10

6

0.635

5

Poor quality of construction materials

3

10

11

13

3

0.615

1

Delay in providing services from utilities (electricity)

6

11

13

6

4

0.555

2

Inadequate contractor experience

3

13

11

12

1

0.575

3

Unqualified/inadequate experienced labour

2

8

13

10

7

0.66

4

Changes in material types and specifications during construction

2

9

17

9

3

0.61

5

Delay in manufacturing 4 materials

8

13

10

5

0.62

1

Delay in performing inspection and testing

5

15

14

3

3

0.52

2

Delay in manufacturing 1 materials

15

11

10

3

0.595

3

Poor quality of construction material

2

12

16

7

3

0.585

4

Design changes by owner or his agent during construction

0

8

12

16

4

0.68

5

Low productivity of labour

0

9

15

12

4

0.655

II.alluminium fabrication

III. Carpentry

S. No.

RII

(continued)

Analysis and Mitigation of Delay in Construction …

45

Table 5 (continued) IV. Civil-plastering

V. Tiling

VI. Earthwork and foundation

VII. Painting

VIII. Civil-masonry

1

Poor site management and supervision

4

10

13

11

2

0.585

2

Rework due to errors

1

10

11

11

7

0.665

3

Slow site clearance

3

10

14

9

4

0.605

4

Shortage of labour

1

7

16

12

4

0.655

5

Shortage of construction materials

5

6

14

9

6

0.625

1

Rework due to errors

2

7

16

14

1

0.625

2

Delay in performing inspection and testing

5

7

18

7

3

0.58

3

Shortage of labour

0

9

13

15

3

0.66

4

Slow site clearance

2

8

13

15

2

0.635

5

Changes in material types and specifications during construction

1

8

12

13

6

0.675

1

Poor site management and supervision

4

8

16

8

4

0.6

2

Ineffective project planning and scheduling

2

8

11

13

6

0.665

3

Unclear and inadequate 3 details in drawings

8

12

12

5

0.64

4

Slow site clearance

11

10

16

3

0.655

5

Unexpected surface and 1 subsurface conditions (soil, water table, etc.)

6

10

9

14

0.745

1

Late in reviewing and approving design documents

4

9

13

11

3

0.6

2

Unfavourable weather conditions

1

10

13

9

7

0.655

3

Unqualified/inadequate experienced labour

1

8

14

16

1

0.64

4

Inadequate site investigation

3

11

12

12

2

0.595

5

Late delivery of materials

1

7

10

10

12

0.725

1

Delay in performing inspection and testing

4

6

18

8

4

0.61

2

Design changes by owner or his agent during construction

1

14

7

13

5

0.635

3

Shortage of labour

1

7

8

20

4

0.695

0

(continued)

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C. P. Muneera and K. J. Joe Maria

Table 5 (continued) 4

Poor quality of construction material

3

8

11

13

5

0.645

5

Shortage of construction materials

2

3

14

12

9

0.715

construction, Rework due to errors, Delay in performing inspection and testing, Inadequate site investigation and Poor quality of construction material are the critical factors causing delay in aluminium fabrication, carpentry, plastering, tiling, earthwork and foundation, painting and masonry. The study reveals that the delay in the foundation of the project causes an excessive delay in the overall project. The study proposes that the critical factor, the foundation delay reduction, in multistoried buildings reduces the excessive delay in the construction projects in Kerala.

7 Conclusions The Present study is an attempt to identifying the activities that cause delay to the construction of multistoried residential buildings. The planned and scheduled data were collected from builders and each activity was categorized to identify the impacts of each activity to the delay in the construction. The following conclusions have been obtained. • Duration index and Delay index were proposed. A low delay Index indicates that construction is running relatively smooth and higher delay Index indicates significant delays and work disruption. From the study, it was found that waterproofing, aluminium fabrication, carpentry work, civil-plastering, tiling, earthwork and foundation, painting and civil-masonry are the maximum delayed activities in the construction of multistoried residential buildings. • From the prediction model, it was found that foundation and masonry are the most influencing activities that contribute to the delay in the construction of multistoried residential buildings. • For the delay mitigation purpose, a questionnaire survey was conducted, and impacts were quantified by relative importance index. It was found that late delivery of materials, inexperienced labour, design changes, delay in performing inspection and testing, inadequate site investigation and poor quality of construction material are the critical factors causing delay in the construction. This project work mainly concentrates to identify the activities that causing delay in the construction of multi-storied residential buildings. Furthermore, this study can be extended to identifying the cause and mitigation of delay in the other construction fields by considering each activity that causes construction delay.

Analysis and Mitigation of Delay in Construction …

47

Annexures Sample questionnaire form Name

Age

Designation Gender Department

Please indicate whether the factors of delay of each activity are severe delay, high delay, moderate delay, least delay or no delay with the statements that follow by ticking 5, 4, 3, 2, 1 as appropriate. 5—Severe Delay; 4—High Delay; 3—Moderate Delay; 2—Least Delay; 1—No Delay Questionnaire on delay in construction activities (Please mark one appropriate box unless otherwise stated) Respondent Name: Respondent Number: Activities

S.

Factors affecting delay

1 2 3 4 5

No Waterproofing

Alluminium fabrication

Carpentry work

1

Inadequate contractor experience

2

Rework due to errors

3

Slow site clearance

4

Late delivery of materials

5

Poor quality of construction materials

1

Delay in providing services from utilities(electricity)

2

Inadequate contractor experience

3

Unqualified/inadequate experienced labour

4

Changes in material types and specifications during construction

5

Delay in manufacturing materials

1

Delay in performing inspection and testing

2

Delay in manufacturing materials

3

Poor quality of construction material

4

Design changes by owner or his agent during construction (continued)

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C. P. Muneera and K. J. Joe Maria

(continued) Civil-plastering

Tiling

Earthwork and foundation

Painting

Civil-masonry

5

Low productivity of labour

1

Poor site management and supervision

2

Rework due to errors

3

Slow site clearance

4

Shortage of labour

5

Shortage of construction materials

1

Rework due to errors

2

Delay in performing inspection and testing

3

Shortage of labour

4

Slow site clearance

5

Changes in material types and specifications during construction

1

Poor site management and supervision

2

Ineffective project planning and scheduling

3

Unclear and inadequate details in drawings

4

Slow site clearance

5

Unexpected surface and subsurface conditions

1

Late in reviewing and approving design documents

2

Unfavourable weather conditions

3

Unqualified/inadequate experienced labour

4

Inadequate site investigation

5

Late delivery of materials

1

Delay in performing inspection and testing

2

Design changes by owner or his agent during construction

3

Shortage of labour

4

Poor quality of construction material

5

Shortage of construction materials

Analysis and Mitigation of Delay in Construction …

49

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Behaviour of Concrete-Filled Fibre Tubes Under Axial Compression and Lateral Loading N. Athira, Liji Anna Mathew, and U. K. Neeraj

Abstract The steel reinforcement in the infrastructures throughout the world undergoes corrosion and it leads to the need for a new product, to those involved with reinforced concrete structures. Concrete-filled fibre-reinforced tubes (CFFT) are formed by combining the concrete and the fibre-reinforced polymer (FRP) sheets with epoxy in which concrete is filled in the prebuilt FRP tube. CFFT columns can be effectively used for earthquake resistant designs, because the lateral confinement increases the ultimate axial strain and compressive strength of concrete (Ozbakkaloglu and Oehlers in Journal of Composites for Construction, 12:469–477, 2008). This work mainly deals with the performance of CFFT and conventional columns under combined axial compression and lateral loading using Ansys workbench. The objectives of this study were to compare the seismic action of conventional columns with CFFT columns using different FRPs such as carbon, glass and aramid, and CFFT columns using different FRP rods made of carbon, glass and aramid fibres. An experimental study was also conducted to validate the material properties of fibres which were used in the seismic study of columns. The compressive strength of ordinary concrete cylinders, concrete-filled glass fibre tube cylinders and concrete-filled carbon fibre tube cylinders were found out. The test results revealed that CFFT columns can produce huge inelastic deformation capacities under seismic loading. Keywords Concrete-filled FRP tube (CFFT) · Fibre-reinforced polymer (FRP) tube · Reinforced concrete

N. Athira (B) Department of Civil Engineering, AISAT, Ernakulam, Kerala, India e-mail: [email protected] L. A. Mathew · U. K. Neeraj AISAT, Ernakulam, Kerala, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_5

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1 Introduction The expeditive industrialization and increase in population results in the maximum use of land. Multistoried buildings have become inevitable. Nowadays, the number of tall buildings increases rapidly, both residential and commercial. The current tendency is towards taller and taller structures. It is possible to build high-rise structures in the areas susceptible to cyclones and earthquakes with the advancement in science and technology. Thus, the lateral loads like wind loads, earthquake forces, etc., are significantly considered in designs and it is difficult for almost every designer to provide sufficient strength and stability against lateral loads. This lateral load causes critical stresses, vibrations and, in addition, it causes lateral sway of the structure, which may result in failure of the structure. It has prompted the significance of a new product associated with reinforced concrete structures.

1.1 Concrete-Filled Fibre Tubes Concrete-filled fibre-reinforced tubes(CFFT) are formed by combining the concrete and the fibre-reinforced polymer(FRP) sheets with epoxy in which concrete is filled in the prebuilt FRP tube (Figs. 1 and 2). Depending on the requirement of the strength of the column, FRP tubes can be made with varying thickness. There are many methods for the fabrication of the FRP tube. The simplest way of the in-situ fabrication of FRP tube is hand layup process and filament winding process for the machine fabrication. FRP tube gives lateral confinement to the concrete under compression. FRP tubes are suitable for the structure exposed to harsh conditions such as freezing or thawing or the corrosive environment near a seashore because lateral confinement from the FRP tube can increase both the strength and the ductility of the concrete. FRP tubes are used for construction having advantages like sacrificial formwork. As per IS 456: 2000, It can reduce clear cover provisions for durability and reduce confinement reinforcement and longitudinal reinforcement. There are many methods available

Fig. 1 Concrete-filled fibre tubes

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Fig. 2 Detailed front elevation and cross-sectional view of CFFT with reinforcement

for analysis of FRP tubes filled with plain concrete or reinforced concrete for the application of CFFTs in construction.

1.2 Application of Concrete-Filled Fibre Tubes Figure 3 shows one of the potential applications of concrete-filled FRP tubes.

1.2.1

Piles

Concrete-filled FRP circular tubes (CFFT) is an innovative composite pile. The FRP tube has different layers of fibres along with the polymeric resin. In order to achieve strength and stiffness in both the axial and circumferential directions, the fibre layers are arranged in different directions with respect to the longitudinal axis of the tube.

1.2.2

Hybrid Bridge Structures

These are structures formed by combining elements made of conventional materials (usually girders) with elements made of FRP materials (usually decks or cables/tendons) [1]. The concrete core serves as the formwork for the FRP even

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Fig. 3 Application of CFFT

though it does not provide much of flexural stiffness and strength, other than compressive strength, to the cross section.

1.2.3

Columns and Piers

Concrete-filled fibre-reinforced polymer tube (CFFT) columns are durable than conventional reinforced concrete (RC) bridge piers. The FRP petrochemical pipe system with fibres wound at ±55° gives high capacity and ductility than conventional RC columns. For the flexural capacity and ductility of CFFT columns, ±55° fibre orientation is sufficient.

1.2.4

Tunnels

Steel grid and steel arch are mostly used structures for supporting the tunnel, but they cannot control the deformation of soft rock. Concrete-filled steel tubes (CFST) with high bearing capacity and plasticity have various applications. The local buckling resistance of the steel tube was increased by the filled concrete under compressive loading [2]. Simultaneously, the strength, toughness and plasticity of the concrete can also be enhanced. The deformation of surrounding rock could be reduced by CFST for roadway supporting.

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1.3 Materials Required for CFFT Construction The materials required for CFFT construction include. 1. FRP tubes, 2. Steel reinforcing bars and 3. Concrete. 1.3.1

FRP Tubes

Many fibre tubes such as carbon, glass, steel and aramid are used. The FRP tubes consist of fibres sheets made of resin. FRP tubes were designed to have an innermost layer of fibres oriented along the hoop direction followed by the skew layer of fibres [3]. This stacking sequence was repeated until the required thickness of FRP tubes was achieved.

Types of Fibres Used in CFFT Glass Fibres Glass fibres (GFs) are available in different forms such as longitudinal, woven mat, chopped fibre and chopped mats to increase the mechanical properties of the fibrereinforced polymers [4]. However, the behaviour of such composites was influenced by the nature and orientation of the fibres laid during preparation. Glass fibres are one of the commonly used polymer reinforcements [5]. Carbon Fibres Carbon fibres (CFs) are high-strength materials made of graphitic and non-crystalline regions. They have the highest specific modulus and strength among all reinforcing fibres. They can maintain their tensile strength at high temperatures and are independent of moisture. They do not easily break under stress. They also have high electrical and thermal conductivities with a low coefficient of thermal expansion. Steel Fibres The reduction in the strength after the local buckling of steel tube was decreased due to the restraining effect of the concrete when steel fibre sheet was used. Due to the confining effect provided by the steel tube, the strength of the concrete is increased and the strength reduction is not serious, because concrete spalling is prevented by the tube [6]. Drying shrinkage and creep of the concrete are less than in ordinary reinforced concrete [7].

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Aramid Fibres Aramid fibre is one among the high-performance fibres. It is made by extruding a solution of aromatic polyamide at a temperature between −50 and −80 °C into a hot cylinder at 200 °C. Fibres are then stretched and drawn to enhance their strength and stiffness. Aramid molecules become oriented in the longitudinal direction during this process. They have large static, dynamic impact and fatigue strengths.

2 Objectives 1. In order to validate the material properties of FRP materials used in the study, an experimental study was conducted. The objectives are a. To investigate the compressive strength of ordinary concrete cylinders, concrete-filled glass fibre tube cylinders and concrete-filled carbon fibre tube cylinders experimentally. b. To conduct a comparative study on the compressive strength of ordinary concrete cylinders, concrete-filled glass fibre tube cylinders and concretefilled carbon fibre tube cylinders using Ansys. 2. To compare the behaviour of conventional building columns and CFFT columns under the action of axial compression and lateral forces for the following conditions: a. CFFT columns using different FRP tubes made of carbon, glass and aramid fibres. b. CFFT columns using different FRP rods made of carbon, glass and aramid.

3 Materials and Proportions The compressive strength tests were done on plain concrete, concrete-filled glass fibre tube and concrete-filled carbon fibre tube. Table 1 shows the details of specimen casted. The nomenclatures adopted are as follows: R = Plain cement concrete. CFT = concrete-filled carbon fibr tube. GFT = concrete-filled glass fibre tube.

3.1 Experimental Investigation The thickness of a fibre tube is found out as follows.

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Table 1 Details of specimen cast S. No. Property studied

Cube

1

R

CFT

GFT

R

CFT

GFT

9

–

–

9

9

9

Compressive strength

Cylinder

Total specimens for 7, 14 and 28 days

The hoop stress for thin cylinder σ 1 = pd/2t

36

(1)

d Internal diameter of cylinder = 150 mm. p Compressive strength of concrete = 30 N/mm2 . ϭ1 Ultimate tensile stress of fibre. The ultimate tensile stress of carbon and glass fibre. were 3626 N/mm2 and 683 N/mm2 , respectively. The thickness of the fibre tube was found out using Eq. 1. The thickness of carbonand glass fibre tubes were obtained as 1 mm and 3 mm, respectively. The CFT and GFT having diameters of 149 mm and 147 mm, respectively, with a height of 300 mm were also modelled in ANSYS 16. A conventional cylinder of 150 mm diameter and 300 mm length was also modelled.

3.1.1

Preparation of Concrete-Filled Fibre Tubes

The wet layup process was used for making glass and carbon fibres tubes. These were made by hand using dry fibre sheets and a saturating resin. The detailed process is as follows: woven rovings (Fig. 4) (a type of glass fibre sheet) were cut into desired shapes and sizes as perimeter and height of the steel mould [1]. The cut sheets were then laid on a clean surface. The surface mat was used for the easy removal of the tube from mould. The resin to be applied on FRP sheets to make FRP tube was prepared in such a proportion that for 1 kg of isophthalic resin, hardeners such as 6 ml of cobalt naphthenate and 12 ml of ketone peroxide weres mixed. The surface mat was applied to the inner surface of the mould for the easy removal of the tube from mould using wax. Then the mix was applied with a brush to the FRP sheets in a direction perpendicular to the direction of the fibres. The FRP sheets were then pasted inside the moulds. Consecutive layers of resin and fibre sheets were placed before the complete cure of the previous layer of resin (Figs. 5, 6). Interlayer surface preparation like light sanding or solvent application was done after curing of previous layers. The fibre sheets had orientation along the hoop direction. After 24 h, the set FRP tube was removed from the steel mould (Fig. 7). A pan-type mixer machine was used for mixing the conventional OPC concrete in the proportions 1:1.73:3.16 (w/c ratio 0.39). Initially, dry constituents like coarse aggregate, fine aggregate and cement were added and mixed for 1 min. Mixing was

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Fig. 4 Woven rovings

Fig. 5 Placing of different layers of woven rovings

continued after adding water along with a chemical admixture to obtain a homogeneous mix. The mixes were then filled in the mould after compacting using a table vibrator. After remoulding, curing was done in water till the age of testing.

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Fig. 6 Mould after finishing

Fig. 8 shows R, CFT and GFT specimens after casting. Compressive strength of three specimens of each sample was tested at 7, 14 and 28 days, and the average was taken. The results of CFT and GFT cylinders were compared with R.

3.2 Numerical Investigation After generating the model, the meshing of the model was necessary for analysis. The compressive load was obtained from the STAAD analysis applied to the top of the cylinder along the axial direction. Axial load of 606 kN, 472 kN and 550 kN were applied for R, GFT and CFT specimens, respectively. The properties of the materials used are as follows (Table 2).

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Fig. 7 Glass FRP tube

Fig. 8 Specimens after casting

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Table 2 Properties of materials used Component

Material properties of concrete

Material properties of carbon fibre

Material properties of glass fibre

Density ( kN/m3 )

25

15.70

19.50

Coefficient of thermal expansion (/K)

1.4 × 10–5

2.10

2.10

Young’s modulus (MPa)

27,386

70,000

24,821

Bulk modulus (MPa)

1.3 × 104

2.916 × 104

Shear modulus (MPa)

1.19 ×

3.18 ×

Poisson’s ratio

0.15

104

0.10

104

2.916 × 104 5515.8 0.35

4 Analysis of a Residential Building A two-storied residential building to be constructed at Edappally, Kochi, (seismic zone3) was selected. Modelling and analysis were carried out with the help of the software STAAD.Pro (Fig. 10). Grade of concrete adopted was M30, and Fe 415 steel was used. During analysis, dead loads and live loads were found out from IS 875 (Part 1): 1987 and IS 875 (Part2): 1987, respectively, and their combinations were applied. Figure 9 represents the centre line diagram of the building and the location of different columns in the structure.

Fig. 9 Column positions

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Fig. 10 STAAD.Pro model

The column having maximum axial load and moment was selected for the seismic study. The design was carried as per IS 456: 2000 [8]. The load combinations were taken to obtain the maximum design loads, shear forces, moments, etc. The design was done as per IS 456: 2000 for the above combinations of load. Earthquake-resistant design of the structure was done as per IS 1893 (Part 1): 2002 and the detailing as per IS 13,920: 1983.

5 Load Calculation 5.1 General Data Utility of building: Residential building: No of stories: G + 1. Type of construction: R.C.C framed structure. Types of walls: Brick wall. Ground floor: 3 m. Floor-to-floor height: 3 m.

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5.2 Loads The significant loadings on a residential building include the self-weight of the building, the imposed loads, wind loads and earthquake loads. These loadings are explained in the following.

5.2.1

Dead Load

The dead load includes the weight of the concrete structure to be designed [9]. The density of concrete was considered as 25 kN/m3 . The values of the unit weight of the materials are as specified in IS 875 (Part 1): 1987. The dead load of the structural member was found out by the software STAAD.Pro.

5.2.2

Masonry Loads

The masonry load acts directly on the beam beneath the walls as uniformly distributed loads. Unit weight of masonry = 20 kN/m3 . Wall thickness = 0.2 m. Wall load for ground floor = 20 × 0.2 × 3 = 12 kN/m. Wall load for first floor = 20 × 0.2 × 3 = 12 kN/m. Parapet height = 1.2 m. Parapet load = 20 × 0.2 × 1.2 = 4.8 kN/m.

5.2.3

Live Loads

It consists of all loads other than dead loads of the structure. The value of the imposed load depends on the functional requirements of the structure. The standard values are stipulated in IS 875 Part 2: 1987 [9]. The imposed loads in the design of the buildings will be the highest loads that probably will be produced by the intended use, but will not be less than the equivalent minimum loads stipulated as per code is. All rooms and kitchens = 2 kN/m2 . Toilet and bath rooms = 2 kN/m2 . Corridors, passages, staircases including fire escapes. and store rooms = 3 kN/m2 . Balconies = 3 kN/m2 .

5.2.4

Earthquake (Seismic) Forces

Fig. 11 shows the sesmic data analysis in STAAD.

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Fig. 11 Seismic data used for analysis in STAAD

5.3 Load Combinations All the load cases were tested by taking load factors andthe building was analysed using different load combinations as per IS 1893( Part1): 2000. As per the IS code (part 1) clause 6.3.1.2, load combinations shown below were assigned. (DL—dead load, LL—live load, EQX—earthquake load in the X direction and EQZ—earthquake load in the Z direction). •1.5 (DL + LL) •1.2 (DL + LL ± EQX) •1.2 (DL + LL ± EQZ) •1.5 (DL ± EQX) •1.5 (DL ± EQZ) According to clause 7.3.1 of IS 1893: 2000, for various loading classes as specified in IS 875 (Part2), the earthquake force was calculated for the full dead load plus the percentage of imposed load [10].

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Fig. 12 Reaction summary

5.4 Analysis of the Structure From the various load cases assigned to the structure, the maximum load obtained was at node 17 for the combination 1.5 (DL + EQZ). The column having maximum axial load and the moment acting in that column were selected. The reaction summary as obtained in the analysis is shown in Fig. 12. As per clause 26.5.3.2 of IS 456: 2000, 6 mm diameter at 190 mm c/c was provided for the design column.

6 Results and Discussions 6.1 Results of Experimental Study on Compressive Strength of Ordinary Concrete and CFFT 6.1.1

Compressive Strength of Ordinary Concrete and CFFT Concrete

The rate of increase of compressive strength of GFT compared with R is 18.4%, whereas the rate of increase of compressive strength of CFT compared with R is 29.2% Fig. 14. Figure 13 shows the variation of compressive strength at 7, 14 and 28 days. The reason for this increase is the lateral confinement of the FRP tube to the concrete under compression. This lateral confinement can increase both the strength and the ductility of the concrete [11]. FRP tubes can be used in places where the structure is exposed to harsh environments such as freezing or thawing or the corrosive environment like

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Fig. 13 Compressive strength of specimens at 7,14 and 28 days

Fig. 14 Ordinary concrete after testing

near a seashore, because of these advantages [12]. The CFFT cylinder failed with the local rupture of the FRP tube at one end as shown in Fig. 15.

6.1.2

Finite Element Analysis on Compressive Strength of Ordinary Concrete and CFFT Concrete

The finite element analysis was performed on the ordinary concrete cylinder, CFT and GFT. The compressive strength results for the 3 models were obtained (Figs. 16, 17 and 18).

Behaviour of Concrete-Filled Fibre Tubes Under Axial …

Fig. 15 Local rupture of FRP tube

Fig. 16 Compressive strength of the conventional cylinder

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Fig. 17 Compressive strength of GFT

Fig. 18 Compressive strength of CFT

The following graph shows the variation of experimental and finite element analysis of ordinary concrete cylinders, CFT and GFT. The finite element results do not show much variation from experimental study results (Fig. 19).

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Fig. 19 Variation of experimental and finite element analysis results

6.2 Effect of Different Fibres and Rods in CFFT Column Subjected to Axial and Lateral Load. A total of 3 CFFT columns were modelled and subjected to constant axial compression and increasing lateral deformation cycles [13]. The moment along the direction, i.e., 103 kNm was applied as a seismic load. The models represent the lower portion of a single-storey building column with an inter-storey height of 3 m. It was designed to have a nominal cross-sectional dimension (D) of 300 mm. The moment and the axial compression loads were applied at the top of the column. A control column of height 3 m, i.e., height of one storey and diameter 3 m having 6 nos of 20 mm diameter bars with stirrups of 6 mm dia at 190 mmc/c were modelled based on the STAAD design. The thickness of CF and GF were 2 mm and 7 mm, respectively, with 3000 mm height were also modelled in ANSYS 16. After generating the model, meshing of the model was done necessarily for analysis. The result of the solution depends upon the quality of the grid. The ends of the column are assumed to be fixed. The compression load is applied to the top along the y-axis. Axial loads of 466 kN and moment of 103 kNm were applied for R, GFT and CFT specimens. Top and bottom nodes are used to impose all loads and boundary conditions to the model.

6.2.1

Results of Finite Element Study on CFFT Column Using Different Fibre Tubes

The finite element analysis was performed on the ordinary column, concrete-filled glass fibre tube column, concrete-filled carbon fibre tube column and concrete-filled

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Fig. 20 Deflection of conventional column

aramid fibre tube column. The deflection of 4 models was obtained as shown in Figs. 20, 21, 22 and 23.

Fig. 21 Deflection of concrete-filled glass fibre tube

Fig. 22 Deflection of concrete-filled aramid fibre tube

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Fig. 23 Deflection of concrete-filled carbon fibre tube

The deflections of conventional column, concrete-filled glass fibre tube, concretefilled aramid fibre tube and concrete-filled carbon fibre tube columns were obtained as 4.81, 4.06, 3.19 and 2.70 mm, respectively. In all results, the deflection is maximum at the top of the column and decreases towards the bottom. The deflection of concretefilled glass fibre tube, concrete-filled aramid fibre tube and concrete-filled carbon fibre tube decreases by 15.6%, 33.67% and 43.8%, respectively, than the conventional column.

6.2.2

Results of Numerical Study on CFFT Column Using Different Fibre Rods

Finite element analysis was performed on the concrete-filled carbon fibre tube columns, using steel, carbon, aramid and glass rods. The deflection of the 4 models was obtained as shown in Figs. 24, 25, 26 and 27.

Fig. 24 Deflection of concrete-filled carbon fibre tube using steel rod

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Fig. 25 Deflection of concrete-filled carbon fibre tube using carbon rod

Fig. 26 Deflection of concrete-filled carbon fibre tube using aramid rod

Fig. 27 Deflection of concrete-filled carbon fibre tube using glass rod

The deflection of concrete-filled carbon fibre tube columns using steel, carbon, aramid and glass rods were 2.58, 2.89, 2.70, 3.19 mm, respectively. Concretefilled carbon fibre tube columns using steel rods showed minimum deflection, the maximum value was at the top of the column and decreased towards the bottom.

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The deflection of concrete-filled carbon fibre tube using carbon, aramid and glass increased by 11.7%, 4.5%, and 23.8%, respectively, than steel rods. This may be because of the fact that steel has a higher modulus of elasticity than carbon, glass and aramid.

7 Conclusions The following conclusions are made from this study on the experimental and numerical analysis of concrete-filled fibre tubes: 1. The rate of increase of compressive strength of concrete-filled glass fibre tube compared with plain concrete (R) is 18.4%, whereas the rate of increase of compressive strength of concrete-filled carbon fibre tube compared with R is 29.2%. This variation is due to the lateral confinement provided by the FRP tube to the concrete under compression. This lateral confinement can increase the strength and the ductility of the concrete. 2. The deflection of the conventional column, concrete-filled glass fibre tube, concrete-filled aramid fibre tube and concrete-filled carbon fibre tube columns are 4.81, 4.06, 3.19, 2.70 mm, respectively. It is maximum at the top of the column and decreases towards the bottom. The deflection of concrete-filled glass fibre tube, concrete-filled aramid fibre tube and concrete-filled carbon fibre tube decreases by 15.6%, 33.67% and 43.8%, respectively, than the conventional column. Carbon fibre column showed the least deflection when compared to the others. 3. The deflection of concrete-filled carbon fibre tube columns using steel, carbon, aramid and glass rods are 2.58, 2.89, 2.70, 3.19 mm, respectively. Concrete-filled carbon fibre tube columns using steel rods give minimum deflection, because steel has a higher modulus of elasticity than carbon, glass and aramid [13]. 4. The results show that CFFT columns can develop high inelastic deformation capacities against lateral loading. The FRP tube material has significant influence on the lateral displacement capacity on columns, for both specimens confined by the FRP tubes and those manufactured using fibre rods [9].

References 1. Li B et al (2017) Cyclic behavior of FRP concrete bridge pier frames. J Am Soc Civ Eng (ASCE ) 04(05) 2. Mohamed HM et al (2014) Axial load capacity of concrete—Filled FRP tube columns: experimental versus theoretical predictions. J Am Soc Civ Eng (ASCE) 04(03) 3. Qi JJ et al (2015) Experimental study on seismic behaviors of steel concrete composite frames, vol. 3. Springer, Berlin, pp 919,131

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4. Moustafa A (2017) Strain rate effect on properties of rubberized concrete confined with glass fibre reinforced polymers. J Am Soc Civ Eng (ASCE) 09(03) 5. Mitchell J et al (2016) Tests and analysis of cantilevered GFRP tubular poles with partial concrete filling. J Am Soc Civ Eng (ASCE) 01(05) 6. Aval SBB et al (2016) Comprehensive composite inelastic fibre element for cyclic analysis of concrete-filled steel tube columns. J Am Soc Civ Eng (ASCE) 02(05) 7. Hou H, Ma S, Qu B, Liang Y, Jin Y, Zhu W, Chen L (2015) Structural behavior of thin-walled concrete-filled steel tube used in cable tunnel: an experimental and numerical investigation. Adv Mater Sci Eng 8. Lu YY et al (2015) Experimental investigation of axially loaded steel fibre reinforced high strength concrete-filled steel tube columns, vol. 3. Springer, Berlin, pp 119–1131 9. Zohrevand P (2015) Cyclic behavior of hybrid columns made of ultra high performance concrete and fibre reinforced polymers. J Am Soc Civ Eng (ASCE) 4:600–789 10. Ozbakkaloglu T (2015) Concrete-filled FRP tubes: manufacture and testing of new forms designed for improved performance. J Am Soc Civ Eng (ASCE) 7 11. Amir ZF et al (2013) Flexural behavior of concrete-filled fibre-reinforced polymer circular tubes. J Am Soc Civ Eng (ASCE) 01(06) 12. Ozbakkaloglu T, Oehlers DJ (2008) Concrete-filled square and rectangular FRP tubes under axial compression. J Compos Constr 12(4):469–477 13. Idris Y, Ozbakkaloglu T (2013) Seismic behavior of high-strength concrete-filled FRP tube columns. J Compos Constr

Experimental Investigation of Coir Fibre on Its Potential for the Sorption of Hydrocarbons A. V. Praseeja

and N. Sajikumar

Abstract Groundwater contamination due to petroleum hydrocarbons is a common problem worldwide. It occurs due to surface oil spills or leaking from underground storages. Nowadays, it becomes a threat to the quality of drinking water wells also. The field remediation methods usually practised involve treating the water by pumping out of the well and recharging it. In this study, an environmentally friendly sustainable solution using coir geotextile is proposed to suggest a remedial measure against hydrocarbon contamination. Hence, it should possess the capability to sorb the contaminants so that its migration towards the groundwater is controlled/arrested. This study aims to analyse the adsorption behaviour, degradation effect, surface morphology and the variation in the lignin-cellulose content of coir geotextile under the action of hydrocarbons. The experimental results exhibit better sorption capacity of oil by coir fibres. Moreover, it is observed that the degradation behaviour is not much influenced by the action of hydrocarbons. Keywords Coir geotextile · Degradation · Hydrocarbons · Natural fibre · Remedial measure · Sorption capacity

1 Introduction Though the problem due to petroleum hydrocarbons was primarily noticed only in oil spill areas, it also becomes a major cause of groundwater contamination also in recent times as indicated by newspaper reports regarding leaks from petroleum underground tanks. Hence, any remedial measure that is adopted in the subsurface should possess the capability to sorb the contaminants so that its migration towards the groundwater is controlled/arrested. In most of the practical applications of remediating oil-contaminated groundwater, synthetic oil-absorbing materials are used. The need for replacing synthetic sorbents with natural biodegradable sorbents is essential

A. V. Praseeja (B) · N. Sajikumar Government Engineering College, Trichur, Kerala, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_6

75

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[1–3]. Several studies highlighted the possibility of using natural biodegradable materials as oil sorbents [4–8]. Because of its availability and biodegradability, natural fibres are now in a position to replace synthetic polymers in various applications. The natural sorbents like cellulosic fibres, moss, straw, cotton, etc. are least expensive and effective which have already been utilized for removing the oil spill over water bodies [1–3]. But their application has not been explored in the region of the vadose zone in reducing the effect of contamination. In this proposed study, the potential of coir geotextile is to be investigated, as a measure for enhancing the natural retardation capacity of the vadose zone. To efficiently use coir geotextile as a remedial measure in the subsurface, it is necessary to investigate its morphology, sorption capacity and mechanical properties which are briefly investigated in this study. A suitable absorbent material shall have properties like hydrophobicity and oleophilicity, high uptake capacity, retention over time, biodegradability, etc. Moreover, the sorption capacity of sorbents can be enhanced using some pre-treatment methods, if it possesses at least some of these properties. Some of the researchers [1, 5, 7, 9, 10] practically demonstrated the use of cellulose-based materials as sorbents to mitigate the effects of oil spills over surface water bodies. Thus the addition of sorbents in the saturated zone has already been in practice, where the sorbents absorb the oil content and thus facilitate easy removal of the oil by removal of the absorbents. Among the fibrous materials, non-woven materials are widely used as liquid-absorbent materials [2, 11], which are characterized by their high rate of liquid absorption than woven materials. A sorption capacity model has been developed and validated by studying the recovery of the oil spill in land/water using natural fibres [8]. Both the intra-particle (S intra ) and inter-particle (S inter ) sorption capacity models were developed which is given in Table 1. Degradation behaviour of coir geotextile has been studied by many researchers [12–15] and its dependence observed on factors such as type of embedment soil, climatic conditions, organic content, moisture content and the type of coir used. It is also observed from the literature that major strength loss takes place in 4– 8 months [15], especially in the case of sandy soils. It is also reported by conducting experiments under similar environments that jute geotextile is degraded faster (within 1 year) than coir geotextile (8–10 years) [16].

2 Materials Coir is a hard and tough organic fibre extracted from the husk of coconut. Sri Lanka and India are considered to be the major coir fibre producers in the world, ff which, only 15% of the husks are used for extracting fibres, and the rest are abandoned in nature, hence becoming a cause of environmental pollution [17] Table 2 shows the physical and chemical composition of coir fibre. Due to its high lignin and cellulose content compared to other natural fibres, it is regarded as the strongest of all known natural fibres. The coir geotextile is made of these coir fibres, which have already

Experimental Investigation of Coir Fibre on Its Potential … Table 1 Sorption capacity models

Model

77 Equation

Penetration Absorbency (PA) Sintra = /Intra-particle sorption capacity   φ rc2

Wo W

=

φ Lρl dψρ f

=

 ρ gV θ ρl Pb + l 2 + 2γ rcos c rc   dL dt 8μdψρ f

Sorption Capacity (SC) Sinter = /Inter-particle sorption capacity

Wo W =  1−m 4γla cos θ 1+e f 1 1−ψ g kd f ρ f d ψ

Overall Sorption Capacity

S[g/ g] = Sinter[g/ g] + Sintra[g/ g]

Note r c is the radius of capillary [L]; F, the porosity of the entire capillary(dimensionless); Pb , the external pressure acting on the sorbent [ML−1 T2 ]; V, the volume of liquid drop [L3 ]; g, the gravitational acceleration [LT−2 ]; μ, the oil coefficient of viscosity [ML−1 S−1 ]; ρ f , the fibre density [ML−3 ]; ρ l , the liquid drop density [ML−3 ]; d, the sorbent thickness [L]; γ , the surface tension (wall tension) [N/m]; ψ, the sorbent packing density [ML−3 ]; L, the oil wetted length of the capillary [L]; γ la , the surface tension between liquid and air [N/m]; θ, the fibre contact angle; ef , sorbent shape factor and k, m represent two experimental constants that correlate sorbent/liquid proper

Table 2 Chemical composition and Physical properties of Coir fibre

Chemical composition

Unit

Value

Lignin

%

45.84

Cellulose

%

43.44

Hemicellulose

%

0.25

Ash

%

2.22

Pectin

%

3

Water soluble

%

5.25

Physical properties

Unit

Value

Length

cm

15–20

Porosity

%

40

Fibre density

g/cc

1.4

Sorbent thickness

mm

35

Fibre contact angle

0

39

proved their excellent qualities in various engineering applications [15–17]. The coir geotextiles used for the study are supplied from Coir Board, Thrissur, Kerala, India. The petroleum hydrocarbons are classified as Non-Aqueous Phase Liquids (NAPLs). The two common types of NAPLs (based on their liquid densities) are their lighter form (LNAPLs) and denser form (DNAPLs). Two types of LNAPL

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Table 3 Properties of Hydrocarbon Description

Petrol oil

Diesel oil

Density, kg/m3

746

835

Viscosity,

Ns/m2

Surface tension between liquid and air at 20 °C, N/m

0.6e−03

2.98e−03

0.029

0.031

(petrol oil and diesel oil) are employed in this study to investigate the oil sorption characteristics of coir fibre. The diesel oil and petrol oil were collected from petroleum storage pumps and were used without modification. Densities of the oils were measured using a gravimetric method. Table 3 shows the physical properties of these oils.

3 Experimental Studies 3.1 Sorption Capacity The experimental study is meant for testing the amount of oil absorbed by a sample, after immersing it in the LNAPL medium. The test is based on method EPA 9095B (2004). Both petrol and diesel oils are used in this study and their properties are given in Table 3. Each set of experiments was repeated thrice to minimize the percent of uncertainty and the average value is noted as the sorption capacity (qe ). (S1 − %AU) S2   AU × 100% %AU = S2 qe =

(1) (2)

where S 1 is the weight of fibre with absorbed oil and S 2 represents the remaining free oil collected in the beaker. The oil sorption capacity is then estimated using Eq. (1) by considering percent of uncertainty (%AU) which is given in Eq. (2).

3.1.1

Degradation Study and Change in Chemical Compositions

For conducting the experimental study, non-woven coir geotextiles of 600 and 900 GSM of size 20 × 20 cm are taken as the samples. The samples are embedded in wet lateritic soil (pH 6) mixed with petrol oil (hydrocarbon) for 12 months. The soil was collected from one metre below the ground level, sun-dried for 2 days, lumps and debris removed. For setting the samples in one tray, 10 kg of clean soil is taken, a small quantity of water is sprinkled over it, and uniformly mixed with petrol

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(0.5 L). The uniformly mixed soil is filled in two layers, such that coir samples were placed in between the first and second layers. The whole tray is then covered with a plastic sheet and holes are provided for aeration. The test on degradation behaviour, chemical composition and SEM analysis is conducted. The samples were tested in CCRI, Kalavoor, Alappuzha, Kerala.

4 Results and Discussion 4.1 Sorption Capacity As indicated in the previous section, the hydrocarbon (both petrol oil and diesel oil) sorption capacities of the coir fibre are determined. In the case of petrol oil, the sorption capacity is obtained as 4.84 g/g, whereas in the case of diesel oil it is about 5.45 g/g. For validating the results obtained from the experimental study, it is compared with the models given in Table 1 by substituting the values given in Tables 2 and 3. The total sorption capacity value of coir fibre is estimated from the sum of SC and PA models. The result shows 4.94 g/g and 5.27 g/g in the case of petrol oil and diesel oil, respectively, which agree well with the experimental results, with a percent of error that does not exceed 5%. The comparison of experimental results with the empirical model thus verifies the applicability of both SC and PA models for coir fibres in the case of oil sorption. Another study result shows the sorption capacity of coir fibre for crude oil ranges between 3.5 g/g and 6.0 g/g [18]. The obtained result in this study is within the range. The values are also compared with oil absorbency values of other natural fibres such as wheat (5.49 g/g) and oat straws (5.00 g/g), which is indicated as better absorbency values [8].

4.1.1

Effect of Sorption Time

Figure 1 shows the results for the effect of the sorption times on oil removal at different times of 1 h, 1 day, 2, 5, 10, 20 and 30 days. The same procedure for the test based on EPA method 9095B is repeated for 30 days. The zero-day in Fig. 1 corresponds to the sorption capacity for 1 h (0.042 days). The value of oil sorption gradually increased as sorption time increases from 1 h to 30 days. A time of 20 days– 30 days resulted in a maximum and constant oil sorption capacity of 5.65 g/g in the case of diesel oil and 5.14 g/g for the petrol oil. The initial fast adsorption may be due to the initial adsorption onto the surface of the material and subsequent penetration into the inner microscopic voids. The slow uptake in the later stages may be due to an attachment controlled process caused by less available voids for active sorption [9].

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Fig. 1 Effect of time on sorption of oil onto coir fibres

4.1.2

Adsorption Isotherms

Adsorption isotherms are essential to understand the adsorption capacity of a specific adsorbent. Several previous studies used Langmuir or Freundlich isotherm models to describe oil adsorption behaviour of the fibrous sorbent [9, 19, 20]. The Langmuir isotherm theory represents monolayer coverage of adsorbate over a homogenous adsorbent surface, where each molecule assumes to have equal sorption energy. This model is thermodynamically consistent and follows Henry’s law at low concentrations. Meanwhile, the Freundlich isotherm model is an exponential equation which assumes the multilayer adsorption on the heterogeneous surface of the sorbent. Theoretically, it means, an infinite amount of adsorption can occur. Unlike the Langmuir expression, it does not reduce to linear isotherm (Henry’s law) at low concentrations [20]. The data obtained in the present experiment were analysed using Langmuir and Freundlich isotherm models. The linear and non-linear forms of these models are given in Table 4. The symbols used in the models can be described as follows: qe is the amount of adsorbate per unit weight of adsorbent (mg/g); C e , the concentration of adsorbate in solution at equilibrium after the adsorption is complete (mg/L); K L , the Langmuir equilibrium constant, represents the amount of solute adsorbed/unit weight of an adsorbent informing a complete monolayer on the surface; K F , the Freundlich equilibrium constant which indicates the adsorptive capacity; b, the constant related Table 4 List of adsorption isotherms

Isotherm model

Non-linear form equation

Langmuir

qe =

Freundlich

qe = K FCe

K LCe 1+bCe

Linear form equation Ce qe

1/n

=

1 KL

+

b K L Ce

log qe = log K F + 1/n log Ce

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to the energy or net enthalpy of adsorption; and n is the Freundlich constant indicative of the affinity of the adsorbate for the surface of the adsorbent. The constants of these isotherms can be calculated from the linear form of each model. Hence the equilibrium experimental data for the coir-fibre adsorbents were analysed using Langmuir isotherm by plotting C e /qe against Ce (as shown in Fig. 2) and Freundlich isotherm by plotting log qe against log C e (as shown in Fig. 3). Figure 2 represents Langmuir adsorption isotherm which is a straight line of slope b/K L and intercepts 1/K L . The values of these constants are obtained and are given in Table 5. The essential characteristics of the Langmuir isotherm could be expressed in terms of a dimensionless constant, separation factor or equilibrium parameter r (Eq. 3) that is defined as follows.

Fig. 2 Langmuir adsorption isotherm of oil on coir fibre

Fig. 3 Freundlich adsorption isotherm of oil on coir fibre

5.69

6.73

Diesel

KL

Langmuir model

Petrol

Type of oil

0.06

0.04

b 0.25

0.33

r 0.91 0.94

Y = 0.0071x + 0.175

R2

Y = 0.0089x + 0.148

Y = mX + c

4.47

3.73

KF

Freundlich model

0.017

0.024

1/n Y = 0.0167x + 0.650

Y = 0.0237x + 0.571

Y = mX + C

Table 5 Parameters estimated and regression analysis for sorption of oil by coir fibre using Langmuir and Freundlich models

0.92

0.84

R2

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r=

1 1 + bC0

83

(3)

where C 0 is the initial adsorbate concentration (mg/L) and b is the Langmuir constant related to the energy of adsorption (L/mg). The value of r indicates the shape of the adsorption isotherm to know whether adsorption is unfavourable (r > 1), linear (r = 1), favourable (0 < r < 1), or irreversible (r = 0) [20]. The obtained values are given in Table 4. To examine the validity of these models, the values of R2 are used to compare the isotherm models. The R2 values of the Langmuir model tend to be much closer to 1 than those values obtained from the Freundlich model (Table 5). So Langmuir isotherm is best to describe the sorption of oils by the coir-fibre adsorbent. The results of the parameters estimated using Langmuir and Freundlich models are presented in Figs. 2 and 3, and adsorption of oil by coir fibre in Table 5. The isotherms yield constants whose values express the affinity of adsorbate for the surface of adsorbent [19]. Appling the Langmuir isotherm model, it was observed that KL varies from 5.69 to 6.73, b (L/mg) the Langmuir constant ranges from 0.04 to 0.06 and the values of r calculated by Eq. (3) are between 0 and 1, confirming that isotherm is favourable. Applying the Freundlich model, the values of K F vary from 3.73 to 4.47. The higher values of constants K L and K F indicate more sorption, so the results show that coir fibre offered a maximum sorption capacity in the case of diesel compared with petrol. 1/n values for petrol and diesel are 0.024 and 0.017, respectively. The smaller values of 1/n, the higher the affinity between adsorbate and adsorbent. Langmuir and Freundlich correlation coefficients (R2 ) are presented in Table 5. The Freundlich isotherms model gives lower correlation coefficients (R2 = 0.84– 0.92) compared with that of the Langmuir isotherms model (R2 = 0.91–0.94). Hence, Langmuir isotherm is best to describe the sorption of oils using coir-fibre adsorbent.

4.2 Degradation Behaviour 4.2.1

Durability Test

The tensile strength test is usually performed to determine the durability of coir geotextiles, following the procedure outlined in IS: 13,162 (Part 5) and ASTM D4595. The rate of degradation was studied by conducting tensile strength tests on coir geotextile samples after treating it for 1 month, 3 months, 6 months, 9 months and 12 months [21]. The overall strength reduction observed when embedded in a hydrocarbon environment for 1 year is about 61.54 and 73.10% in the case of 900 and 600 GSM, respectively, as shown in Fig. 4. The pH value of the soil considered in this study is 6, which can cause around 66% of degradation as per the results already presented [15]. Hence the degradation rate of geotextiles is not much influenced by the presence of hydrocarbons.

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Fig. 4 Percentage Strength reduction curve of treated coir fibre after 1 year [21]

4.2.2

Variation in Chemical Composition

The chemical compositions and mechanical properties of lingo-cellulose fibres can vary depending on their origin, maturity, species, extraction procedures and environmental conditions [22]. As the cellulose and lignin are the major constituents of the coir fibre, their percentage variation with the effect of hydrocarbons is required to be observed. Lignin content is much less hydrophilic than cellulose; it can prevent the absorption of water and also forms an effective barrier against attack by fungi [23]. The samples were taken from the same setup as for the degradation test. The lignin and cellulose content are checked after treating it for 6 months, 9 months and 12 months. The test was conducted in CCRI, Kalavoor, Alappuzha, Kerala. The cellulose content was determined using a standard procedure [24] and the determination of lignin content was carried out using a standard method [25]. Figure 5 shows the variation of lignin and cellulose content of treated coir fibre during 1 year period of testing. At the end of 6 months, the lignin content is reduced to 22.26% (about 50% reduction), and the percentage of cellulose content reduced to 29% (about 33% reduction). After treating the fibres for 1 year with hydrocarbons, a drastic reduction of both lignin (decreased to 6.5%, about 86% reduction) and cellulose content (decreased to 9%, about 79% reduction) was observed. The result is compared with another work [23] which shows the decreasing trend in lignin content is about 84%, by treating coir pith (initial lignin content was 30%) with urea for 30 days. In the present study, only a 50% reduction in lignin content of coir fibre is observed after 6 months, when treated with hydrocarbons. Therefore, this decreasing trend is comparable with other environmental conditions. Moreover, in order to identify the effect of this variation in the sorption capacity of fibres, it is necessary to check the sorption capacity of degraded fibres which is presented in the later session.

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Fig. 5 Variation in cellulose-lignin content of treated coir fibre after 1 year

4.2.3

Surface Morphology

For studying the morphology of coir fibre surface on degradation with the effect of hydrocarbons, a scanning electron microscope (SEM) model was used. The coir sample was taken from the same experimental setup used for degradation study. The samples of the sixth month and 1-year-treated samples were chosen for the analysis. The SEM images of coir fibres are shown in Figs. 6 and 7. The obtained images were compared with the SEM image of raw coir fibre [16]. It is observed that a significant number of pore spaces as well as fibre cracking have increased in the surface of fibres, in the case of treated samples than the untreated ones.

Fig. 6 SEM analysis of sixth month degraded coir sample treated with hydrocarbons

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Fig. 7 SEM analysis of 1-year degraded coir sample treated with hydrocarbons

4.2.4

Sorption Check of Degraded Sample

As a reduction in chemical compositions and more fibre crackings are observed in the case of treated samples at the end of 1 year, it is necessary to check how the degradation of fibre affects its sorption capacity. In order to observe the absorption behaviour of degraded fibre, the sorption capacity of treated samples (taken from degradation test setup) has been checked by the same procedure used for untreated ones. The 6th month, 9th month and 1-year-treated (degraded) samples were considered for this study. The sorption capacity is obtained by soaking the treated fibres in oil for 1 h and 24 h. The obtained value is compared with the sorption behaviour of untreated samples and the result is shown in Fig. 8. The zero treated time in Fig. 8 represents the sorption capacity value of untreated samples. From Fig. 8, it is clear that the degradation effect has not much influenced the sorption behaviour of coir fibres. In the case of sorption of oil (both petrol oil and diesel oil) by treated coir fibres for, it is observed that the sorption capacity (qe) value is slightly increased in the first 6 months and then decreased after 1 year, but the percentage reduction is less compared to untreated fibres. The same trend was observed by soaking the degraded fibres for 24 h also. The result is shown in Fig. 8. Fig. 8 Effect of degradation on sorption of oil onto coir fibres

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From the above result, it is clear that coir fibre can absorb oil as well, even though it gets degraded under natural conditions. Hence, the coir fibre can be recommended to be used as a better sorption media against hydrocarbon contamination.

5 Conclusions The results of studies carried out to identify the suitability of coir geotextile as a remediation measure in the unsaturated zone against hydrocarbon contamination lead to the following conclusions: • The coir fibre has an oil sorption capacity for petrol oil about 4.84 g/g and that for diesel oil as 5.45 g/g. The sorption experimental results were compared with the empirical model and the results match with a percent of error not exceeding 5%. The result shows that sorption capacity models can excellently predict the oil sorption of coir fibre. • The Freundlich and the Langmuir models have been used to explain the sorption behavior of oil on coir fibres. The result shows that the Langmuir model could well fit the adsorption isotherm and hence can be used for further modelling. • The adsorbed amount of oil increases with the increase of contact time and reaches equilibrium after 10 days. The separation factor, r-value in the present investigation, was less than one, indicating favourable adsorption of oil on coir fibres. • The degradation rate of coir geotextile treated with hydrocarbon-mixed soil is almost the same as the degradation rate under other environmental conditions (in untreated soils). Hence the degradation effect is not much influenced by the presence of hydrocarbons. • From the experimental result of the absorption behaviour of the degraded fibre, it is observed that the sorption capacity of coir fibres has not much been influenced by its degradation effect. Since coir is freely abundant, locally available, biodegradable and has a considerable high absorption capacity, the coir fibre may be treated as an economically viable solution for the absorption of oil from the subsurface system.

References 1. Abdelwahab O (2014) Assessment of raw luffa as a natural hollow oleophilic fibrous sorbent for oil spill cleanup. J Alexandria Eng 53(1):213–218. https://doi.org/10.1016/2013.11.001 2. Das D, Pradhan AK, Pourdeyhimi B (2012) Dependence of the liquid absorption behavior of nonwovens on their material and structural characteristics: Modeling and experiments. J App Poly Sci 126(3):1053–1060. https://doi.org/10.1002/36635 3. Karan CP, Rengasamy RS, Das D (2011) Oil spill cleanup by structured fibre assembly. Indian J Fibre Textile Res 36(2):190–200

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4. Al-Majed AA, Adebayo AR, Hossain ME (2012) A sustainable approach to controlling oil spills. J EnvManag 113:213–227. 10.1016/2012.07.034 5. Hubbe MA, Rojas OJ, Fingas M, Gupta BS (2013) Cellulosic substrates for removal of pollutants from aqueous systems: A review. 3. Spilled oil and emulsified organic liquids. J Bio Res 8(2):3038–3097 6. Paulauskien˙e T, Jucik˙e I, Jušˇcenko N, Baziuk˙e D (2014) The use of natural sorbents for spilled crude oil and diesel cleanup from the water surface. J Water Air Soil Pollut 225(6):1–12 7. Payne KC, Jackson CD, Aizpurua CE, Rojas OJ, Hubbe MA (2012) Oil spills abatement: factors affecting oil uptake by cellulosic fibers. J Env Sci Technol 46(14):7725–7730 8. Tijani MM, Aqsha A, Mahinpey N (2016) Development of oil-spill sorbent from straw biomass waste: Experiments and modeling studies. J Env Manag 17:166–176. 10.1016/ 2016.02.010 9. Nwadiogbu JO, Ajiwe VI, Okoye PA (2016) Removal of crude oil from aqueous medium by sorption on hydrophobic corncobs: Equilibrium and kinetic studies. J Taibah Univ for Sci 10(1):56–63. 10.1016/2015.03.014 10. Olga VR, Darina VI, Alexandr AI, Alexandra AO (2014) Cleanup of water surface from oil spills using natural sorbent materials. J Proc Chem 10:145–150. https://doi.org/10.1016/2014. 10.025 11. Radeti´c MM, Joci´c DM, Jovanci´c PM, Petrovic, Thomas HF (2003) Recycled wool-based nonwoven material as an oil sorbent. J Env Sci Technol 37(5):1008–1012. 12. Balan K, Rao GV (1996) Erosion control with natural geotextiles. In: Proceedings international seminar and technomeet on environmental geotechnology with geosynthetics. The Asian Society for Environmental Geotechnology, CBIP, New Delhi, pp 317–334 13. Lekha KR (2004) Field instrumentation and monitoring of soil erosion in coir geotextile stabilised slopes—A case study. J Geotexmem 22(5): 399–413. 10.1016/2003.12. 003 14. Marques AR, de Oliveira PPS, dos Santos FS, Monteiro ML, de Carvalho UD, de Souza RC (2014) Effects of the climatic conditions of the southeastern Brazil on degradation the fibers of coir-geotextile: Evaluation of mechanical and structural properties. J Geotexmem 42(1):76–82. https://doi.org/10.1016/2013.07.004 15. Rao GV, Balan K (eds) (2000) Coir geotextiles—Emerging trends. The Kerala state Coir Corporation Ltd (publishers), Alappuzha, Kerala 16. Mukkulath G, Thampi SG (2012) Performance of coir geotextiles as attached media in biofilters for nutrient removal. Int J Env Sci 3(2):784–794. https://doi.org/10.6088/ijes.2012030132005 17. Praveen A, Sreelakshmy PB, Gopan M (2008) Coir geotextile-packed conduits for the removal of biodegradable matter from wastewater. J Current Sci 95(5):655–658 18. Wahi R, Chuah LA, Choong TS, Ngaini Z, Nourouzi MM (2013) Oil removal from aqueous state by natural fibrous sorbent: an overview. J Sep Purif Technol 113:51–63. 10.1016/.2013.04.015 19. Alihosseini A, Taghikhani SA, Bastani D (2010) Equilibrium sorption of crude oil by expanded perlite using different adsorption isotherms. Int J Env Sci Technol 7(3):591–598. https://doi. org/10.1007/BF03326168 20. Okiel K, El-Sayed M, El-Kady MY (2011) Treatment of oil–water emulsions by adsorption onto activated carbon, bentonite and deposited carbon. Egyptian J Petrol 20(2):9–15. 21. Praseeja AV, Sajikumar N (2018) Degradation study on coir geotextiles treated with hydrocarbon mixed soil, proc. In: International conference on emerging trends in engineering science and technology (ICETEST 2018). CRC press Taylor and Francis, GEC Thrissur 22. Tomczak F, Sydenstricker, Satyanarayana KG (2007) Studies on lignocellulosicfibers of Brazil. Part II: Morphology and properties of Brazilian coconut fibers. Compos Part A: Appl Sci Manufac 38(7):1710–1721. 10.1016/2007.02.004 23. Radhakrishnan S, Reghuvaran A, Geena MG, Ravindranath AD (2016) Potential of biocomposting of coir pith using PITHPLUS substituting organic supplements alternate to Urea for Agri/Horti end uses. In: Proceedings of India International Coir Fair (IICF 2016) 24. Updegraff DM (1969) Semi micro determination of cellulose inbiological materials. J Anal biochem 32(3):420–424 25. Schoning AG (1965) Absorptiometric determination of acid-soluble lignin in semi chemical bisulfite pulp and in some wood and plants. Svensk Papperstidn 68:607–613

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26. ASTM D-4595 (2009) 11 standard test method for tensile properties of geotextiles by the wide-width strip method. ASTM International, West Conshohocken, USA 27. IS 13162: Part 5 (1992) Determination of tensile properties using a wide width strip. Bureau of Indian Standards, New Delhi, India. 28. Method EPA 9095B (2004) Paint filter liquids test. United States Environmental Protection Agency, Washington, DC.

Dynamic Phase Lag Studies of Damper Mounted Substation Structures N. Srujana

and T. Bhavani

Abstract Stability and safety of fragile equipment used in electric power applications are in demand against strong ground motions. Post-earthquake data necessitates the seismic studies on substation used porcelain components in evident to the poor serviceability of the equipment. The installed structures that failed at the field are experimentally tested and passed in laboratories under real-time earthquake motions. In addition to that, with the influence of the heavy movement of tectonic plates, the site-specific conditions are varying rapidly and consequently resulting in the progression of structural failure. Therefore, mitigating the vibration at the base level of the supporting structure is one possible solution to the undesirable ground accelerations. In this paper, two current transformers of different ratings supported on steel structure are considered and evaluated for response phase when subjected to site specified accelerations at critical frequencies with the help of experimental damping factor. Also, the structure is studied for viscoelastic damper attached at the base to recognize the phase shift with the specified ground accelerations. In both the cases of the structure with and without the damper, the system damping is extracted from shake table experiments of 0.3 g ground acceleration. Conclusions are derived for the model connected with damper during complete earthquake vibration using angles of phase versus frequency ratios. The results may be used in redesigning the structure prior to the standard recommended testing. Keywords Critical frequencies · Phase shift · Frequency ratio · Ground specified accelerations

N. Srujana (B) · T. Bhavani Deaprtment of Civil Engineering, Vardhaman College of Engineering, Hyderabad 501218, India e-mail: [email protected] T. Bhavani e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_7

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1 Introduction The power utility equipment has a significant role in retaining the accessibility of life-line systems after catastrophic events like earthquakes. The electric equipment which are generally material sensitive and rigid in nature certainly invite minimal earth vibrations into the structure that are sufficient enough to fail. Unfortunately, the failure of electric supply systems at 0.1 g ground acceleration is clearly visible from the past last forever seismic data. Hence, losses due to the failure in such systems are considered among aftermath studies. In disagreement with the standard recommended experimental test setups, the equipment drastically failed at the seismic site which was tested in the laboratory with promising conclusions. The possibility of the discrepancy is due to the auxiliary connections attached to the main equipment and varying movements of tectonic plates. Therefore, controlling the seismic resilient parameters of the structure and finding the solutions at these aspects are drawing the attention of researchers worldwide. It is identified from the past limited research, mitigating the ground acceleration before entering the structure, is one reasonable solution; dampers and isolation devices are proposed at the base of the equipment. Passive control systems have limitations in terms of cost, installation, maintenance and lack of awareness possessed by manufacturers. Usage of seismic protection techniques in substation equipment design are included in IEEE-693, 2005 [1]; as per the recommendation, the seismic qualification must be completed on base-isolated substation equipment with supports using shake table tests as installed configurations. There are difficulties involved in testing full-scale equipment due to huge weight and transporting to the testing laboratory. In special cases, qualification can be done using numerical analysis of finite element models with base isolation. To complete the qualification by analysis, isolation properties are estimated using experimental component testing and bounding analysis. This helps in identifying the response scenario (nonlinear force versus displacement) of the whole system and incorporating the results in the finite element model. Pavolacci 2008 [2] developed steel cable dampers (wire-rope) which were analyzed for displacement in vertical-tension, compression and horizontal shear directions. A 420 kV circuit breaker is studied with the effect of wire rope dampers for energy dissipation capacity. Saadeghvaziri 2010 [3] studied transformer-bushing system efficiency with the connection of the friction pendulum system. Observations are done during the uplift of the transformer; the base isolation accommodated the larger displacements of the equipment. The installation of the passive device in the structure gave the inference that uplift is not a hazard to the transformer geometry and peak ground acceleration. The current study takes advantage of the phase shift in estimating the response behavior of the system at the applied forcing frequencies. A couple of full-scale substation equipment mounted on the steel truss structure is analyzed with the damper provided at the base. Sine sweep resonance search tests of 0.3 g are carried out separately on the models to understand the preliminary dynamic parameters of the system in both the x and y directions. The equipment is analyzed for response shifts to the required ground accelerations by making use of the data obtained from resonance

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search tests. Although the methodology requires analytical studies along with the data extracted from partial experimental tests to retrieve the response in terms of phase angles.

2 Formulation of Acceleration Transmission of Isolated System The mathematical model is developed based on the idealization of a continuous system. The response displacement of the isolated system is expressed in terms of generalized coordinate and shape function of the system. Under the base excitation, the system responses to absolute motion rigidly with the ground (mass has no contribution), u¨ g (t) and relative steady-state motion, u¨ d (t) (with the influence of damper). The total response of the system is the combination of absolute and steady-state motions. The below analytical expressions are taken from Chopra 2010 [4]. u¨ td (t) = u¨ g (t) + u¨ d (t) Governing equation of motion for the system: m u¨ td + cu˙ td + ku td = cu˙ g (t) + ku g (t) where cu˙ g (t)+ku g (t) is the absolute motion of the system at ground motion u g (t) = sin(ω0 t). Equation of motion, m u¨ td + cu˙ td + ku td = F0 sin(ω0 t − α). Phase angle at absolute motion, α = tan−1 (2ζ r ). Consider, the response of the system, u td (t) = Udt (t)sin(ω0 t − α) Therefore, acceleration/force transmissibility ratio of the system Tr ,  U¨ dt (t) 1 + (2ζ r )2 Tr = =   U¨ g (t) 1 − r 2 + (2ζ r )2 frequency response ratio r = ωωn0 . The total response of the system u¨ td (t) = u¨ g (t)Tr sin(ω0 t − α − α1 ). r) where α1 = tan−1 (2ζ . (1−r 2 ) Finally, the phase difference between exposed ground acceleration to the response of the damper provided system is.

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(2ζ r )  α0 = α + α1 = tan−1 (2ζ r ) + tan−1  1 − r2

(1)

α and α1 are the phase shifts of absolute response of the system with the ground motion and relative response of the system with the ground.

3 Evaluation of Frequency Responses of Electric Equipment The electric equipment of 170 kV and 300 kV voltage ratings mounted on steel support structures are considered for the analysis. The study is divided into experimental investigation and result evaluation using analytical formulations.

3.1 Description of Electric Equipment Both types of equipment have a live tank at the top of the porcelain cylinder which consists of oil weighing 100 kg. Circuit current is controlled by mineral oil inside the porcelain insulator and the tank. The total mass of the 170 kV CT structure is 1700 kg and weight of the current transformer is 915 kg, and for 300 kV CT it is 1016 kg and 700 kg. The current transformer has an assembly of three parts such as a tank with bellow cover, porcelain cylinder and terminal box. The height of the porcelain insulator of 170 kV CT is 2.5 m, and 2.4 m for 300 kV CT. The inner diameter of insulators is 330 mm and 240 mm with wall thickness 30 mm. The insulator is connected to the tank at the top and to the terminal box at the bottom with aluminum bolt molds. The supporting structures of height 4.5 m and 5 m are fabricated with mild steel angles. The shake table-mounted 170 kV current transformer is shown in Fig. 1. Viscoelastic dampers are included in the two systems to study the dynamic displacement. These dampers are tuned to absorb energy in multiple modes of the system by isolating the structure from induced ground motions such that they move relative to the ground motion. Therefore, supplemental damping is provided to the system which reflects the reduction in displacement by influencing the fundamental frequencies of the system. The study is concerned to recognize the peak response acceleration at the top of the structure, therefore the dampers are added at the base of the support structure set up to lead the whole system (support structure and current transformer) as a single entity Fig. 2.

Dynamic Phase Lag Studies of Damper Mounted Substation Structures

Fig. 1. 170 kV Current transformer mounted on the shake table

Fig. 2. 170 kV Current transformer with damper mounted on the shake table

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3.2 Methodology Primary data of dynamic parameters—fundamental frequency and damping ratios of the system—is extracted using resonance search tests from the shake table experiments. In another way, the data of free vibration pull-out tests (response amplifications versus frequencies) may also be considered. The input shake table vibration of sine sweeps with 0.3 g acceleration is given to the full-scale experimental models of 170 kV CT and 300 kV CT as shown in Fig. 3. Amplified accelerations corresponding to fundamental frequencies of the system are obtained as test output, and data is derived from the user interface—DAP software tool. Fundamental frequencies of 170 kV CT and 300 kV CT are seen at 2.25 Hz and 1.75 Hz and shown in Figs. 4 and 5. Using half-power bandwidth method, the damping ratio of 25% for 170 kV CT and 15% for 300 kV CT is determined at system resonant frequencies. The data from the experiments is given in MATLAB code to find response dynamics at the site specified accelerations of zone V design spectra up to a 6 s time period. The code computes the damping ratio of the system at natural frequencies and continues to analyze the system at the required critical mode. System damping obtained from the analytical models is in line with the sine sweep tests. Response curves are plotted with respect to the phase angle and frequency response ratios of the equipment.

Fig. 3 Sine sweep acceleration of 0.3 g ground acceleration

Fig. 4 The fundamental frequency of 170 kV current transformer in the x-axis

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Fig. 5 The fundamental frequency of 300 kV current transformer in the x-axis

The phase results reveal the response behavior beyond the critical frequencies of the system during the earthquake event. The analysis is extended to the models of 170 kV CT and 300 kV CT along with dampers set at the ground level of the support structure. Resonant frequencies of the systems are extracted at 0.3 g sine sweeps, one octave per minute. Both systems attained 1 and 5 Hz with 31 and 17% system damping after providing dampers. The electric equipment along with dampers is analyzed for response accelerations at zone V seismic spectra to compare with the models of no dampers arranged. The design spectra of Zone V is obtained from IS 1893 (part I) 2016 [5] and is shown in Fig. 6. The responses with the forcing frequencies of ground accelerations are shown in Figs. 7, 8, 9 and 10. Phase shifts of the models 170 kV CT and 300 kV CT with and without dampers through excitation frequencies are plotted in Figs. 11 and 12.

Fig. 6 Design spectra of zone V acceleration

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Fig. 7 Response acceleration of the 170 kV current transformer

Fig. 8 Response acceleration of the 170 kV current transformer with damper

Dynamic Phase Lag Studies of Damper Mounted Substation Structures

Fig. 9 Response acceleration of the 300 kV current transformer

Fig. 10 Response acceleration of the 300 kV current transformer with damper

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Fig. 11 Phase curves of the 170 kV current transformer

Fig. 12 Phase curves of the 300 kV current transformer

4 Results and Discussions The study involves identifying resonant frequencies from experiments and analyzing the system to the zone V forcing frequencies using the data developed from experiments. 1. The natural frequencies 2.25 and 1.74 Hz for 170 and 300 kV current transformers are noticed. Using half-power bandwidth method, damping ratios of 25 and 15% are calculated for the respective models. According to the Indian standard IS 1893, zone V design spectra are applied to the analytical models of 170 kV CT and 300 kV CT. Response phase shifts with the ground are computed using MATLAB program to identify the nature of the system and to estimate the post-resonance behavior to the ground vibrations. From Fig. 11, at the values of frequency response ratio () below 1.0, i.e., applied frequency (ground forcing frequency), is less than the natural frequency of the system; the system steadily moves along

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with the ground and maintains in phase response with the ground. When = 1.0, forcing frequency is equal to the fundamental frequency of the system, the phase angle is 90° and the system generally attains higher acceleration. For 170 kV CT and 300 kV CT, resonance is noted at 55° and 65° and the response probability is less. At r = 1.414, the phase is shifted to more than 90° (crossed resonance), the structure stands with the opposing vibration giving the lesser response at frequencies after resonance frequency. It is observed in 110° and 130° for 170 kV CT and 300 kV CT. At r  1, the phase lag is reduced gradually as forcing frequencies are higher. Structure becomes stiff to the vibrations and will not take any response to the top. Peak ground accelerations at the first natural frequency of each system are determined as 8.53 m/sec2 and 14.48 m/sec2 . 2. The viscoelastic dampers are fixed at the base of the support structure and shake table experiments are performed. Fundamental frequencies of 1 and 5 Hz are observed at 31 and 17% damping ratio of systems 170 kV CT and 300 kV CT. With the site specified data, i.e., zone V ground accelerations, the systems 170 and 300 kV experienced 7.25 m/sec2 and 12.47 m/sec2 maximum accelerations at fundamental frequencies. Phase angles of the isolated system with varying ground forcing frequency are extracted and plotted. From Fig. 12, for r < 1.0, i.e., ω0 < ωn , system steadily moves along with the ground showing initial negligible responses with the ground motion, i.e., in phase to the ground. At = 1.0, ω0 = ωn , the phase angles are 55° 170 kV CT and 65° for 300 kV CT. Resonance is noticed at 55° and 65° and the response probability is less. At = 1.414, the phase is shifted to more than 90° (crossed resonance), the structure stands with the opposing vibration giving a lesser response at frequencies after resonance frequency. It is observed in 100° and 130° for 170 kV CT and 300 kV CT. At r  1, the phase lag is reduced gradually as forcing frequencies are higher. Structure becomes stiff to the vibrations and will not take any response to the top.

5 Conclusions Susceptibility of electric equipment in relation to the isolation device—viscoelastic damper—is intended to study through the interface of frequency response curves— phase angle and frequency response ratio. 1. The fundamental frequency of 170 kV CT is reduced with the addition of damper and there is an incremental fundamental frequency in 300 kV CT with the damper. However, systems with dampers exhibited less response compared with the systems without dampers. 2. From the phase studies, it is seen that both the equipment with and without dampers have no change in phase angle √ at resonance. Still, the equipment with dampers has reduced phase lag at = 2, displaying measurable response acceleration. For higher forcing frequencies, both √ the equipment with dampers have a relative reduction in phase shifts with = 2 approaching equilibrium. In detail,

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170 kV CT has a negligible response to r  1, but the bottom experiences continuous vibration of base excitation. Thus, the model is open for resolution. Nevertheless, the response acceleration of the structure at resonance is very less. In the case of 300 kV CT, the model stopped responding to the vibration after a r = 10. 3. The MATLAB program can be used to assess the behavior of the system prior to the code-specified experimental test setups. The proposed method allows the manufacturer to redesign and incorporate base isolations followed by shake table experiments.

References 1. IEEE Standard 693 (2005) IEEE recommended practice for seismic design of substations 2. Paolacci F, Giannini, R (2008) Study of the effectiveness of steel cable dampers for the seismic protection of electrical equipment. In: Proceedings of 14th world conference on earthquake engineering. Beijing, China 3. Saadeghvaziri Ala M, Feizi B, Kempner L Jr, Alston D (2010) On seismic response of substation equipment and application of base isolation to transformers. IEEE Trans Power Delivery 25(1):177–186. https://doi.org/10.1109/TPWRD.2009.2033971 4. Chopra AK (2010) Dynamics of Structures, theory and applications to earthquake engineering, 5th Edition, Pearson Education. 5. IS 1893 part-1 (2016) Criteria for earthquake resistant design of structures

Acoustic Emission Characteristics of Cementitious Materials During Early Age Hydration Injila Hamid, Umair Ali Wani, Shafat Farooq, Aditya Sharma, and R. Vidya Sagar

Abstract Acoustic Emission (AE) testing was used to study the hydration process in cementitious materials during the first 18 h of setting. AE activity was monitored in fresh cement paste, mortar and concrete specimens. The specimens had a different mixture of composition. It was observed that the AE activity depended on the size of the aggregate present in the cementitious mixture. More AE signals were recorded during the setting process in specimens with the lower w/c ratio than for the higher one. Specimen cast with cement paste showed more AE activity compared to the larger coarse aggregate size (20 mm). The AE activity in fresh concrete is accredited to cavitation in the pores of cement paste during the hydration process and shrinkage. The AE activity showed a notable trend during the time of setting, based on which it was divided into three stages namely, before hydration, partial hydration and complete hydration. The occurrence and duration of these stages varied for cement paste, mortar and concrete. In this study, it was observed that if more AE signals are recorded during the hydration process, higher will be the strength gained by the same concrete in-situ. Keywords Cementitious materials · Acoustic emission · Hydration · Cavitation · Setting time

1 Introduction Although there have been a number of important research articles published on Acoustic Emission (AE) monitoring of fracture process in cementitious materials, yet a significant improvement in our understanding of how AE relates to the physical processes that occur during the fracture is required. Also, knowledge about the I. Hamid · U. A. Wani · S. Farooq · A. Sharma Department of Civil Engineering, National Institute of Technology, Srinagar 190006, India e-mail: [email protected] R. V. Sagar (B) Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_8

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transition of concrete from a fluid state to a hardened state is important and needs further study. The study on early-age hydration process in cementitious materials is important because it can be used to predict the strength achieved by the cementitious materials in the later stages of hydration. Therefore, a further study on microstructural changes taking place during the hydration process will result in the prediction of mechanical properties of the hardened concrete. Acoustic Emission testing is one of the non-destructive testing (NDT) methods. It is useful for locating the fracture process in solids that are subjected to an external force in real time [1]. It is known that the internal structure of the material in a solid undergoes irreversible changes due to (i) fracture process (ii) plastic deformation (iii) temperature gradients. These changes cause the generation of elastic waves or stress waves [1]. Also, several studies confirmed that in the case of fresh cementitious materials, due to segregation and migration of aggregates during the hydration process, elastic waves are generated [2–4]. These elastic waves are known as acoustic emissions. The emitted AE propagate in spherical shapes from the source location to the whole volume of the solid resulting in small surface displacements, which can be recorded by mounting suitable piezoelectric transducers (PZT sensors) on the surface of the solid. A typical AE waveform and corresponding parameters are shown in Fig. 1. Recently, several researchers have applied AE testing to fresh cement paste, mortar and concrete specimens to study the process of setting and hardening [2–6]. It is known that acoustic emission can be generated by several sources during setting such as cavitation, hydration, shrinkage, water migration (capillary rise), displacement of grains/aggregates, microcracking. Various other sources for AE activity including initiation and coalescence of microcracks, propagation of cracks and fracture of

Fig. 1 A schematic representation of a AE waveform and related parameters [1]

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inclusions. Few important studies done in the past are summarized in Section-2 (literature review) for giving the importance and relevance of the present study.

2 Literature Review Several researchers used AE testing to study the setting and hardening in specimens cast with fresh cementitious materials. Thirumalaiselvi and Sasmal have observed the relationship between the AE signals and the hydration mechanisms. Clustering of AE signals was carried out based on hydration mechanisms [3]. Assi et al. used the AE testing to study the relationship between the recorded signals associated with stress waves and the mechanisms associated with the cement hydration [4]. Rafal et al. carried out unsupervised pattern recognition studies to classify the AE signals recorded during the hydration of cementitious composites [5]. Three stages of fracture process such as microcrack initiation; stable and unstable crack growth were observed. Nadeau and Mindess studied the hydration of cement paste by analysing the recorded AE [7]. It was observed that the AE activity due to drying increased rapidly with the time of hydration. The cause behind this increase in AE activity was found out to be the fractures that develop during the drying process. Chotard et al. studied the hydration process and mechanical properties of aluminous cement by using the AE parameters [8]. Also, the observations were compared with X-ray tomography and ultrasonic testing. Weiss et al. monitored the AE activity during the first 18 h of hydration process in cement paste [9]. Several hypotheses were considered to study the occurrence of AE hits due to cavitation, microcracking and formation of hydrates. Abeele et al. compared the AE events and temperature changes for different cement pastes during early hydration and hardening [10]. It was observed that the peak temperature for one mixture (w/c = 0.3) was more prominent than that cast with (w/c = 0.5). Aggelis et al. used RA (= rise time/peak amplitude) and AF (= counts/duration) with different w/c ratio of cementitious materials during early age hydration [11, 12]. It has been observed that the mechanical properties of the hardened concrete depend on the early age properties of fresh concrete [13]. Topolar et al. have examined AE parameters such as AE events, peak amplitude and energy during the early hydration and hardening of cement composites [14]. It was concluded that if more AE hits are observed during hydration, then more new formation of hydration products and microcracks will be developed. Also, more AE events were recorded during the fracture process in the same hardened concrete. Although several studies focused on AE released during the hydration process of cementitious materials, yet the studies relating to the influence of coarse aggregate size and w/c ratio, a/c ratio are minimal. However, a significant improvement in our understanding of how AE relates to the physical processes occurring during fracture is required. In other words, knowledge about how AE relates to the physical processes that occur during the fracture process is required. In fact, Aggelis et al. have suggested that further work is necessary for analysing trends and other correlations in cementitious composites like mortar and concrete [12]. In this study, authors used an

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aggregate of different sizes (10 mm, 20 mm) and monitored the early age hydration characteristics of concrete using AE testing in order to study the compressive strength developed after hardening. Moreover, results related to the different water to cement (w/c) ratio have also proved to be useful in predicting the same.

3 Aim of the Study The aim is to study the characteristics of AE during the hydration process of cementitious composites. And also, to study the variation in AE parameters which may provide information on compressive strength of the hardened concrete. The present study also aims to find the causes of AE generated during the early hydration process in fresh cementitious materials, and also during the fracture process in hardened cementitious materials. The further work considered to be done in this study is the effect of the size of aggregate on the generated AE during early age hydration. The outcome of the present study may lead to further understanding of the AE characteristics of cementitious materials and contribute to further application of AE testing to concrete structures.

4 Experimental Procedure 4.1 Materials and Test Specimens The cement used in this experimental study was 53 grade ordinary portland cement conforming to IS 4031 (Part 1): 1996, river sand and tap water [15]. The sand used was standard sand conforming to Zone- II as per IS: 383:1970 [16]. For concrete specimens, crushed coarse aggregate with maximum size of 10 mm and 20 mm was used. The test specimens were designed and cast using IS 10262 (2009) Concrete mix proportioning-Guidelines [17]. In this study, three cases such as the influence of (i) coarse aggregate size (ii) aggregate to cement ratio [a/c ratio] (iii) w/c ratio (by weight) in the cementitious mixture on AE generated during hydration process were considered, and the corresponding mixture details are given in Tables 1, 2 and 3, respectively. All the test samples were cast in steel cylindrical moulds of dimension 75 mm × 150 mm.

4.2 AE Monitoring Test Set-Up The AE monitoring system used in this experimental study consisted of piezoelectric sensors, pre-amplifiers and data acquisition system (PAC, NJ, USA). This system

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Table 1 Cementitious materials mixture details (for a single specimen) used to study the influence of aggregate size on AE released during hydration. Volume of each specimen = 0.662 m3 C-20a Cement (kg)

C-10A

Mortar

Paste-c

0.307

0.343

0.4

1.5

10 mm

0.612

0.612

–

–

20 mm

0.899

–

–

–

Sand (kg)

0.528

0.696

1.2

–

w/c

0.45

0.45

0.45

0.26

Aggregate (kg)

Table 2 Mixture proportions of Cementitious materials used (for a single specimen) to study the influence of a/c ratio on AE released during hydration. Volume of each specimen = 0.662 m3 Paste-C

C-10(A)

C-10(B)

Cement (kg)

1.5

0.8

0.6

Aggregate (10 mm) (kg)

–

0.35

0.55

Sand

–

0.45

0.65

w/c

0.26

0.3

0.3

a/c

0

1

3

Table 3 Mixture proportions of Cementitious materials used (for a single specimen) to study the influence of w/c ratio on AE released during hydration. Volume of each specimen = 0.662 m3 C-10(A)

C-10(B)

C-10(C)

Cement (kg)

0.378

0.343

0.929

Aggregate (10 mm) (kg)

0.573

0.612

2.19

Sand

0.676

0.696

2.80

w/c

0.40

0.45

0.6

allows the user to record AE waveforms and AE parameters such as count, hits, rise time, duration, counts, peak amplitude, energy, signal strength, absolute energy, average frequency, reverberatory frequency and RMS. A single differential resonant type AE sensor (R6D, with a frequency range of 35–100 kHz) was used to record the generated AE. The sensor was mounted on the side of the cylindrical mould at the middle from the bottom. The sensor features a dual BNC connector with integrated twin axial cable existing on the side. The signals were amplified (gain) using a preamplifier to 40 dB and fed directly to an eight channel AE acquisition system. The software package AEWIN SAMOS was used for the data analysis. AE hits with peak amplitude greater than 35 dB threshold were recorded. Silicon vacuum grease was used as a couplant between the sensor and the sample to ensure good contact and smooth transmission of AE signals from the sample to the sensor. The experimental set-up is shown in Fig. 2.

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Fig. 2 Experimental set-up in Structures Laboratory, Department of Civil Engineering, Indian Institute of Science, Bangalore, India to monitor the generated AE in concrete during the first 18 h of hydration

AE system

Pre-amplifier

Test specimen

4.3 Uniaxial Compression Testing of Hardened Concrete After monitoring the AE in test specimens during the first 18 h of setting and hardening, the specimens were demoulded and kept in a water curing tank. Before compression testing, the specimens were taken out and kept for drying. The specimens were tested under unconfined uniaxial compression using the MTS machine (1200 kN capacity) at a constant displacement method. The rate of loading was 0.0083 mm/s. Also, simultaneously the released AE was recorded. The AE sensor (R6D) was mounted on the side of the specimen and different AE parameters namely AE hits, energy, duration, average frequency (AF), absolute energy, signal strength were recorded. The experimental set-up is shown in Fig. 3.

5 Results and Discussion 5.1 Characterization of AE Signals Generated During Early Hydration in Cementitious Materials 5.1.1

AE Amplitude

Figure 4a shows a three-dimensional plot drawn using AE hits, hydration time and amplitude related to cement paste. During the first 2 h, the majority of AE

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MTS machine actuator

AE system

specimen

Fig. 3 Experimental set-up for testing of hardening concrete, Structures Laboratory, Department of Civil Engineering, Indian Institute of Science, Bangalore, India

hits possess amplitude of 35–45 dB in cement paste. Cement particles which are initially suspended in the fluid phase undergo chemical reaction resulting in clustering between particles.AE hits (with amplitude 35–55 dB largely) increased rapidly in cement paste which dictates the intense hydration reaction. But after 8 h, less AE hits were recorded. The reason behind this could be the high attenuation of AE in the fresh mixture which dampens the high frequency components. Very few AE hits, with amplitude 35–45 dB is recorded in cement mortar and concrete as shown in Fig. 4b, c. In cement mortar, AE hits with amplitude in the range of 35–55 dB start to increase after 2 h. Few hits registered between 6 and 18 h in concrete. scattering of AE waves is one of the reasons for the absence of hits. Generation of more AE hits keeps increasing in cement composites indicates the hydration process.

5.1.2

AE Energy

It is known that AE Energy is the area under the rectified signal envelope. In other words, AE energy is the time integral of absolute voltage [1]. S=

LTC 

|Vi |.t

(1)

FTC

where V i is successive readings of signal voltage. t is the time interval between successive readings. FTC is the first threshold crossing and LTC is the last threshold

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(a)

(b)

(c)

Fig. 4 AE hits versus hydration time and peak amplitude for a cement paste b mortar and c concrete cast with 10 mm aggregate

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Fig. 5 AE energy released during early age hydration for specimens indicated in Table 1

crossing. From Fig. 5, it is observed that the cement paste has generated more energy due to extensive hydration, shrinkage and bubble formation, then followed by mortar. In the case of mortar, energy release occurs due to hydration and micro-displacement of fine aggregate particles. However, in the case of cement paste bubble formation occurs more as compared to mortar which causes the release of energy larger than mortar, C-10 and C-20 concrete. Paste and mortar is followed by C-10 and C-20, out of which C-20 is at the bottom due to less intensive hydration than C-10.

5.1.3

Average Frequency of AE

Average Frequency (AF) for the recorded AE was obtained from all specimens made of different mixes of cement composites given in Table 1 was computed. The evolution of frequency domain spectra of the generated AE during hydration at different time periods for the same specimens is shown in Fig. 6. AF versus time plot provides an indication of the microstructural variations in the cementitious composite medium during hydration [3, 11]. AF is equal to the ratio between counts and duration. In cementitious composites, at different curing time both AF and amplitudes are changed with curing time.

Cement Paste It is observed that higher amplitude with low AF acoustic emission signals appeared during the first 3 h of hydration. As the hydration proceeds from the instance of mixing

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(a)

(b)

(c)

Fig. 6 Frequency domain spectra at various time duration of hydration time for a cement paste b mortar c C-20 concrete d C-10 concrete [3]. The specimen’s details are given in Table 1.

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(d)

Fig. 6 (continued)

water to cementitious material, AF shifts from (0–50 kHz) range to (0–20 kHz). The AE signals having high AF attenuate fast. This observation is as per the explanation that cement composite transforms from viscoelastic to a hardened state. Initially, during the hydration process/setting, AE propagates through transmission and reflection between water, air voids, inclusions, which highly attenuates the high frequency components. As the hydration proceeds further, cement particles coagulate, hydrates start forming which leads to the development of a solid phase. Thereby, enabling the high frequency components to propagate through the evolved solid pathway. AF component above 80 kHz is not found before 6 h. This depicts that the inter-connectivity of solid particles has not well developed yet [3]. It is also noticed that amplitude and AF grow in C-20 concrete. AE signal amplitude depends on the source of AE activity. High frequency AE propagates fast, initially in cement paste. And then in the cement mortar and concrete as shown in Fig. 6a–d. The reason could be the lower degree of heterogeneity which results in the lower amount of attenuation and high solid volume fraction [3].

5.2 Influence of Mixture Proportions on AE Generation During Early Age Hydration in Cementitious Materials The mixture proportions had an effect on the AE released during early age hydration time. Table 4 shows the various AE parameters such as hits, energy, absolute energy and signal strength recorded during early age hydration and also the uniaxial compressive strength (UCS). AE Hits are the AE signals that are detected by the PZT

Effect of w/c ratio

Effect of a/c ratio

Effect of coarse aggregate

Absolute energy (aJ)

162

85

84

36

162

182

96

69

84

221

Paste

Mortar

C-10

C-20

a/c = 0

a/c = 1

a/c = 3

w/c = 0.4

w/c = 0.45

w/c = 0.6

252

601

2100

606

1184

5302

424

601

998

5302

2.07e+06

3.9e+06

13,309,135

4.0e+06

7.9e+06

3.4e+07

2.7e+06

3.8e+06

6.4e+06

3.4e+07

3.08e+04

5.0e+04

7.0e+06

1.6e+05

3.9e+05

2.1e+07

1.7e+05

5.1e+04

1.3e+06

2.1e+07

–

83,919

106,631

306

56,602

30,879

104,719

106,631

1476

30,879

–

2,385,355

816,516

2490

1,588,762

1,464,021

1,148,170

816,516

10,555

1,464,021

Energy (Vs)

–

1.5136e+10

5.3826e+09

1.6425e+07

1.0081e+10

9.4147e+09

7.4605e+09

5.3826e+09

6.9757e+07

9.4147e+09

Signal strength (pVs)

–

1.9972e+09

9.9542e+08

7.6107e+05

5.2178e+09

2.1165e+10

2.1067e+09

9.9542e+08

4.7245e+06

2.1165e+10

Absolute energy (aJ)

Hits

Signal strength (pVs)

Hits

Energy (Vs)

During fracture process in hardened concrete

During hydration

Total AE parameters recorded

Table 4. AE parameters recorded during early age hydration and fracture process at hardened state (or curing period)

–

7.72

6.79

–

12.90

8.83

6.11

6.79

–

8.83

σ c (MPa)

–

10

10

16

16

7

10

10

–

7

Age (Days)

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sensors mounted on the specimen samples. Due to certain laboratory constraints, the Uniaxial compression tests were conducted at different curing times.

5.2.1

Effect of Size of Coarse Aggregate

Table 1 shows the cementitious mixture details related to the test samples used to study the influence of the size of aggregate on released AE during early age hydration. The size of aggregates influences the AE activity as shown in Fig. 7a. The reason behind this could be the relative movement of aggregates, phase transformation of cementitious materials. The other common causes may be shrinkage, water migration and cavitation. Figure 7a shows that with the decrease in aggregate size, the recorded AE hits increases. The reason behind this could be the decrease in aggregate size leading to the increased hydration reaction between cement and water. The reaction between cement and water increases as the specific surface area of the aggregate increases. With the decrease in aggregate size, the specific surface area (SSA) of the aggregate increases and results in more AE activity. In the case of cement paste, the increasing AE activity is because of air bubble formation and cavitation. But, in the case of concrete and mortar, AE generation in the initial phase of hydration is due to settlement and sliding of aggregates. The finer aggregates being smaller in size have relatively more freedom to be displaced (settle), and thus become the source for the generation of AE hits. The larger size aggregates show rather less and slower movement but release more energy with displacement.

5.2.2

Effect of a/c Ratio

Table 2 shows the samples’ mixture details to study the effect of a/c ratio on AE released. The influence of a/c ratio is shown in Fig. 7b. It is observed that with the increase in a/c ratio, the AE activity decreased. The reason for increasing AE activity with a decrease in a/c ratio can be accredited to the hydration reaction which increases as the cement proportion in the mixture. Another reason could be the decrease in acoustic impedance with a decrease in a/c ratio.

5.2.3

Effect of w/c Ratio

From Fig. 7c, it is observed that due to the decrease in the w/c ratio, the AE activity increased. The trend is shown in Fig. 7c. The reason for increased AE activity is the intensive hydration for the samples with a lower w/c ratio. Moreover, a rich cement paste (lower w/c ratio), tends to have more cavitation incidents as compared to a leaner paste cast with a higher w/c ratio. The reason could be due to the stiff bond between the aggregate and cement matrix that occurs during the final setting time. The displacement of the constituents of the concrete takes place under the influence of gravity starting from the time of casting. It takes place during the migration of

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Fig. 7 Influence of a coarse aggregate size on AE hits b a/c ratio recorded during the first 18 h of hydration. c variation of Ae energy with w/c ratio

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water and rearrangement of aggregates (grains) during the formation of pores and setting of concrete. The concrete with a lower w/c possesses thinner film of cement paste around aggregates as compared to that with a higher w/c ratio. Therefore, lower w/c cementitious mixture has less adhesion between aggregates and cement matrix. Thus, in concrete with a lower w/c ratio, the displacement of aggregates (or grains) during settlement and sliding tends to be relatively more abrupt or rapid and produces more AE activity [5, 9].

5.3 Sources Behind the Release of AE in the Fresh Cementitious Materials at Early Age 5.3.1

Hydration of Cementitious Materials

The feasibility of the occurrence of AE activity is attributed to (i) hydration, (ii) cavitation and (iii) shrinkage during the hydration process. Cement hydration involves a collection of coupled chemical processes, each occurs at a rate that is determined both by the nature of the process and by the state of the system at that instant. These processes have different chemical kinetic involvements and hence can have an influence on product formation and the overall process. The calculated C3 S composition using the Bogues equation in a typical Portland cement is 54.1%, which signifies that it actually had a major influence on hydration mechanism [18]. Early heat of hydration is mainly contributed from the hydration of C3 S. The hydration process of C3 S is described by the ‘Slow dissolution step hypothesis’, and is divided into different stages. According to Barret et al. in the initial stage of hydration, a superficially hydroxylated layer forms on C3 S surfaces in contact with water, and that the dissociation of ions from this layer occurs much more slowly than would be otherwise expected for a mineral in highly undersaturated solutions [19, 20]. Previous researchers had adopted this explanation for slow dissolution of C3 S, and subsequently developed an alternative mechanistic explanation for the initial reactions that are based on a steady state balance between the slow dissolution of C3 S and initially slow C3 S growth of C–S–H [21–24]. According to these previous studies, the apparent solubility of the hydroxylated C3 S is much lower than the one calculated for C3 S, and the dissolution rate decreases rapidly when the calcium hydroxide concentration increases due to dissolution.

Acceleration Period Rate-controlling step of hydration during this period is related to the heterogeneous nucleation and growth of C–S–H on C3 S, and perhaps on other mineral surfaces as well [25–27]. The evidence for this comes from a number of sources. C–S–H

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is observed to be formed primarily on surfaces of C3 S when observed by scanning, atomic force, or transmission electron microscopy [28–30]. Moreover, previous studies has reported using experimental measurements that the hydration rate of C3 S is proportional to the surface area of C–S–H as measured by nuclear magnetic resonance (NMR) spectroscopy. If the growth of C–S–H is rate-controlling, the hydration rate is expected to be proportional to the number of active growth sites for C–S–H (i.e., its surface area).

Deceleration Period The deceleration is caused due to consumption of smaller particles, leaving behind only larger particles to react, lack of space and of water [31]. If the specimen (or the reacting cementitious material) is large then more is the possibility of hydration reaction and chances of bubble formation which results in more AE activity.

Cavitation Cavitation is the phenomenon of formation of an empty space within a solid body. During setting, the cementitious materials like cement paste becomes stiff and starts resisting the volume change caused due to shrinkage, which, in turn, develops tensile stresses in pore fluid and compressive stresses in solid portion [32]. As the tensile stresses increase in pore fluid, cavities are formed along with the release of energy and subsequently are detected as AE activity [9]. During cavitation, the creation and collapse of bubbles takes place. When water is added to the cementitious materials, the exothermic reaction takes place. Due to the difference in the size of aggregates and the formation of cement paste, the gas is trapped between the voids of aggregate particles.

5.3.2

Shrinkage

The total volume of the cementitious material after hydration is slightly less than the combined volume of the reacting cement plus water (by about 5–10%). This decrease in total volume, known as shrinkage, leads to the formation of gas-filled porosity after setting and a decrease in internal relative humidity, which will decrease the hydration rate [18, 26, 27, 31].

5.3.3

Water Migration (Including Capillary Action)

In fresh concrete, during early age hydration, movement of water takes place throughout the concrete medium, this movement is known as water migration. The causes of water migration are capillary action and the movement of aggregates in a

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downward direction due to gravity. Subsequently, the gravitational force causes the air and water particles to move in an upward direction.

5.4 Microcracking in Cementitious Material During Early Hydration Another possible cause of the generation of AE events during the hydration process of cementitious materials is microcracking in the specimen samples [9]. During the early age hydration, concrete changes from the plastic state to the hardened phase, which results in the release of hydration heat, beginning of an increase in strength, changes in volume and so on. Volume reduction of the test specimen starts to take place right from the time cement reacts with water during the hydration to form new products. The test specimens experience internal restraint from aggregates that act to restrain the paste from shrinking, resulting in microcracking. This happens when the paste surrounding the aggregates shrinks, thereby compressing the aggregate. The aggregate pushes back the paste with an equal force, causing local tensile stresses to develop in the paste surrounding the aggregate. These localized tensile stresses can cause microcracking in the paste due to the low tensile strength of the matrix [33]. The AE recorded during the 18 h hydration of the cementitious materials can also be attributed to the cracks generated at the micro level which cannot be observed with the eye but recorded by the sensors in the form of hits.

5.4.1

Different Stages of Setting

Although the setting of cementitious materials has been discussed by several researchers in the past, a brief review of AE generated during the setting is discussed in this section [18]. The setting is known as the development of the stiffening of the fresh cement paste. Subsequently, hardening begins, which indicates that a useful and measurable strength is developing; although during setting the cement acquires some strength. Setting and hardening result from the continuing reaction between the cementitious material and water. The AE activity varies with time throughout the setting process in cementitious materials. It can be divided into three different stages, which correspond to different processes taking place in the material. These processes may be settlement, sliding of aggregates, water migration and formation of hydration products. The different physical and chemical phenomena taking place in the freshly casted specimen can be explained in terms of Cumulative AE Hits. The first stage, characterized by a high rate of AE activity, which corresponds to o-a portion on the graph shown in Fig. 8a, b, is the time of immediate and facile settlement and sliding of grains (aggregate) of concrete under the effect of gravity. Another reason for the higher AE activity in the o-a region is the extensive hydration which begins immediately with

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(a)

(b)

Fig. 8 Various stages of hydration process taking place in (a) fresh cement paste (b) c-10 concrete

the contact of water and cement. The second stage characterized by a very low rate of AE activity corresponds to a-b portion of the graph, which is a stage of predominant chemical activity (Hydration). Since the concrete has not gained sufficient strength by now to resist the shrinkage due to the formation of hydration products (which possess less volume than that of reactants), the concrete mass experiences reduction in volume. This stage can be called a silent period in terms of the occurrences of AE hits, because much of the displacement of aggregates/grains take place initially, leaving only the hydration process. The third stage, which is represented by the b-c portion of the graph, is the period when the concrete mass has gained sufficient strength to resist shrinkage due to hydration. With the gain in strength of concrete, there is the development of tension in the expanding and newly forming pores, which are filled with water and air, leading

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to the formation of bubbles. It leads to the phenomena of cavitation [8]. The concrete mass may also develop shrinkage cracks during this period. It leads to a surge in AE hits being recorded by the AE system. Thus, there is a sudden increase in the rate of AE hits recorded after a silent period. This time also corresponds to the final setting time of concrete [12]. AE absolute energy, duration and signal strength released during early age hydration is shown in Fig. 9. In the first 3 h, AE signals with high absolute energy, long duration and more signal strength are mostly observed in cement paste and mortar which indicates more hydration process has occurred. From 3–6 h peaks are predominantly observed in C-20 concrete, C-10 concrete and mortar due to displacement of aggregates. From 6 to 18 h peaks are observed in specimens which indicated that there is shrinkage in cement paste, cavitation and microcracking in concrete and mortar specimens.

5.5 Correlation of Early Age AE Parameter with Compressive Strength of Hardened Concrete The fresh cementitious material specimens monitored with AE testing facility for 18 h were also tested under unconfined uniaxial compression at the age of 7 days as indicated in Table 4 for the determination of their compressive strength. Comparison of early age AE parameters with the 28 days expected compressive strength is shown in Tables 5, 6 and 7. Figure 10 shows that compressive strength (curing period is different) variation for test samples made with the different cementitious mixture (Table 1 samples). When the coarse aggregate size changes the compressive strength also changes (but there is a slight variation in the curing period/age mentioned in Table 4. Tables 5, 6, and 7 shows the mean of RA and AF values at hydration time. A comparison of RA and AF recorded at the early stage of hydration and hardened concrete compressive strength values can be overserved. It is interesting to note that there may be a correlation that exists between the AE recorded during fresh state and compressive strength of hardened cementitious materials. Higher the RA value in the fresh state, the higher will be the compressive strength at the hardened state. Moreover, it is observed that lower AF value corresponds to the higher compressive strength of the specimens. The latter holds importance since it offers the possibility to evaluate the compressive strength of hardened cementitious material by non-invasive monitoring using the AE parameters during the early age and much earlier than mechanical tests such as rebound hammer test, also it is known that rebound hammer test requires a hard surface [11]. Although, this observation is already known the present study reconfirms it again. Table 7 shows the variation in RA and AF values when there is a change in the w/c ratio. RA and AF values were computed for each recorded AE hit for the first 30 min and the mean values of RA and AF are indicated in Tables 5, 6, and 7. Also, it is observed that when there is a change in the w/c ratio, compressive strength

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Fig. 9 Variation of AE parameters during early age hydration in test samples indicated in Table 1. a Duration b Signal strength c Absolute energy [3]

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Table 5 Twenty-eight day compressive strength and their correlation with early age hydration in test samples cast with coarse aggregate size 0–30 min RA AF 28-day Compressive strength (MPa)

C-20

C-10

0.6905 348.5 8.73

Mortar

0.3200 128.09 9.7

Paste

0.4248

0.2784

141.723

83.658

–

13.45

Table 6 Twenty-eight day compressive strength and their correlation with early age hydration in test samples cast with different a/c ratio 0–30 min RA

a/c = 0

a/c = 1

a/c = 3

0.2784

0.3254

0.3097

AF

83.658

68.2432

197.055

28-day Compressive strength (MPa)

13.45

13.88

–

Table 7 Twenty-eight day compressive strength and their correlation with early age hydration in test samples cast with different w/c ratio 0–30 min RA

w/c = 0.4 0.4060

w/c = 0.45 0.3200

w/c = 0.6 –

AF

24.774

128.09

–

28-day Compressive strength (MPa)

11.02

9.7

–

Fig. 10 AE hits recorded during the unconfined uniaxial compression of hardened concrete samples (Table 1)

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changes along with RA and AF. These changes exhibit characterization capacity and sensitivity to the w/c ratio. In the same framework, Table 6 contains the compressive strength values (in MPa) at the age of 28 days for the specimens with different a/c ratio. Also, Table 6 contains the total number of AE hits recorded during the 18 h of hydration for specimens with different a/c ratio. As it is obvious from Table 6, there may be a link between the early age AE parameter and the compressive strength of the hardened cementitious material. The lower the value of recorded AE hits, which correspond to higher aggregate content, the higher is the compressive strength. Figure 11 shows the Cumulative absolute AE energy and signal strength recorded during the first 20 h of hydration for specimens cast with different a/c ratio. Even though it is difficult to directly explain these correlations which most probably are attributed to wave propagation phenomena rather than differences in the actual sources, it is encouraging that there may a correlation that exists and allow projection to the compressive strength. Therefore, a relationship may be possible between early age AE activity and the compressive strength of concrete. As w/c ratio increases the compressive strength decreases which is shown in Tables 4 and 7. In the case of specimens with different a/c ratio, the strength increases with a decrease in a/c ratio. The trend is given in Tables 4 and 6. The trend for specimens with the different aggregate size is observed to be in opposite to the trend followed by samples with different a/c ratio and w/c ratio. The strength of concrete increases with an increase in the aggregate size, however, the activity shows a reverse trend as shown in Tables 4 and 5. Further experiments need to be conducted to check the same observation. From Tables 5, 6, and 7, it may be possible to predict the Compressive strength from the early age hydration process. With the decrease in w/c ratio the strength increases which is shown in Table 7. Same is explained in Fig. 7c, which shows an increase in activity with a decrease in w/c ratio. Compressive strength increases with a decrease in a/c ratio which is shown in Table 6. The AE activity also increases with a decrease in a/c ratio as shown in Table 4 and Fig. 11a, b. With the increase in aggregate size, compressive strength increases. However, the AE activity shows here the decreasing trend. with an increase in aggregate size which is reverse of the above discussed trends, and is shown in Table 4 and Fig. 7a. Although most of the observations made in this article are already known, the present study reconfirms the same [3, 11].

6 Conclusions In this study, it was observed that the AE parameters namely absolute energy and signal strength other than cumulative hits can be used to study the early age hydration of cementitious materials. Moreover, for a fixed w/c ratio the specimen with small aggregate size (10 mm) generated more number of AE hits than the specimen with a large aggregate size (20 mm). The study of early age hydration process in cementitious materials has importance because it can be used to predict the strength

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(a)

(b)

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Fig. 11 Cumulative a absolute AE energy and b signal strength recorded during the first 20 h of hydration for specimens cast with a different a/c ratio

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achieved by the cementitious materials in the later stages of hydration, as the authors observed that more the AE were generated more was the strength inherited by the hardened concrete. It holds importance for engineers/researchers as they can predict the mechanical properties of the cementitious materials. Early age hydration actually determines the final behaviour of cementitious materials. The early age hydration study can provide us information about mechanical behaviour (strength) of cementitious material. The advantage for the civil engineers is that they can predict the type of concrete mix batch that they should use. From a number of mixes, the engineer can use the early age hydration study to choose which concrete mix would be suitable for the engineering structure to be constructed.

References 1. Gross CU, Ohtsu M (2008) Acoustic emission testing. Springer, Heidelberg 2. Dzaye DE, Aggelis DG (2018) Study on mechanical acoustic emission sources in fresh concrete. Arch Civ Mech Eng 18:742–754 3. Thirumalaiselvi A, Sasmal S (2019) Acoustic emission monitoring and classification of signals in cement composites during early age hydration. Const Build Mat 196:411–427 4. Assi L, Matta F (2018) Unsupervised and supervised pattern recognition of acoustic emission signals during early age hydration of Portland cement paste. Cem Conc Res 103:216–225 5. Rafal A, Soltangharaei V, Assi L, DeVoi T, Zeihl P (2018) Identification of damage mechanism in cement paste based on AE. Cons Build Mat 164:286–296 6. Chotard TJ, Smith A, Rotureau D, Fargeot D, Gault C (2003) Acoustic emission characterization of calcium cement hydration at early stage. J Eur Cer Soc 23:387–398 7. Nadeau JS, Bennet R, Mindess S (1981) Acoustic emission in the drying of hardened cement paste and mortar. J Am Ceram Soc 64:410–415 8. Chotard T, Rotureau D, Smith A (2005) Analysis of acoustic emission signature during aluminous cement setting to characterize the mechanical behavior of the hard material. J Eur Ceram Soc 25:3523–3531 9. Lura P, Couch J, Jensen OM, Weiss J (2009) Early-age acoustic emission measurements in hydrating cement paste: evidence for cavitation during solidification due to self-desiccation. Cem Concr Res 39:861–867 10. van Den Abeele K, Desadeleer W, De Schutter G, Wevers M (2009) Active and passive monitoring of the early hydration process in concrete using linear and nonlinear acoustics. Cem Concr Res 39:426–432 11. Iliopoulos NS, El Khattabi Y, Aggelis DG (2016) Influence of the water and aggregate-tocement ratio on the AE activity of fresh concrete. In: Proceedings of 19th world conference on non-destructive testing (WCNDT 2016). Munic Germany, pp 1–8. 12. Iliopoulos NS, Khattabi EY, Aggelis DG (2016) Towards the establishment of a continuous non-destructive monitoring technique for fresh concrete. J Nondest Eval 35:37. https://doi.org/ 10.1007/s10921-016-0355-7 13. Qin L, Ren WH, Dong QB, Xing F (2014) Acoustic emission behaviour of early age concrete monitored by embedded sensors. Mater 7:6908–6918 14. Topolar L, Pazdera L, Kucharczykova B (2017) Jaroslav Smutny and Karel Mikulasek, Using acoustic emission methods to monitor cement composites during setting and hardening. App Sci 7:451 15. IS 4031 (1968) Methods of physical tests for hydraulic cement. Part I, Bureau of Indian Standards, New Delhi

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16. IS: 383 (1970) Specification for coarse and fine aggregates from natural sources for concrete, Bureau of Indian Standards, New Delhi 17. IS 10262 (2009) Concrete mix proportioning-Guidelines (First Revision), Bureau of Indian Standards, New Delhi. 18. Shetty MS (1987) Concrete technology -theory and practice. S. Chand publishers, New Delhi, India 19. Barret P, Ménétrier D (1980) Filter dissolution of C3 S as a function of the lime concentration in a limited amount of lime water. Cem Concr Res 10:521–534 20. Barret P, Ménétrier D, Bertrandie D (1983) Mechanism of C3 S dissolution and problem of the congruency in the very initial period and later on. Cem Concr Res 13:728–773 21. Garrault S, Nonat A (2001) Hydrated layer formation on tricalcium and dicalcium silicate surfaces: experimental study and numerical simulations. Langmuir 17:8131–8138 22. Damidot D, Bellmann F, Möser B, Sovoidnich T (2007) Calculation of the dissolution rate of tricalcium silicate in several electrolyte compositions. Cement Wapno Beton 12/74 (2): 57–67. 23. Garrault-Gauffinet S, Nonat A (1999) Experimental investigation of calcium silicate hydrate (C–S– H) nucleation. J Cryst Growth 200:565–574 24. Damidot D, Nonat A, Barret P (1990) Kinetics of tricalcium silicate hydration in diluted suspensions microcalorimetric measurements. J Am Ceram Soc 73:3319–3322 25. Thomas JJ (2007) A new approach to modeling the nucleation and growth kinetics of tricalcium silicate hydration. J Am Ceram Soc 90 (10):3282–3288 26. Bishnoi S, Scrivener KL (2009) μic: A new platform for modelling the hydration of cements. Cem Concr Res 39:266–274 27. Thomas JJ, Jennings MH, Chen JJ (2009) Influence of nucleation seeding on the hydration mechanisms of tricalcium silicate and cement. J Phys Chem C 113:4327–4334 28. Gartner ME, Young FJ, Damidot AD, Jawed I (2002) Hydration of Portland cement. In: Bensted J, Barnes P (eds) Structure and performance of cements (2nd Edn). Spon Press, New York, pp 57–113 29. Gauffinet S, Finot E, Lesniewska R, Nonat A (1998) Direct observation of the growth of calcium silicate hydrate on alite and silica surfaces by atomic force microscopy . Royal Acad Sci Paris Earth Planet Sci 327:231–236 30. Richardson GI (2004) To bermorite/jennite- and to bermorite/calcium hydroxide-based models for the structure of C-S–H: applicability to hardened pastes of tricalcium silicate, β-dicalcium silicate, Portland cement, and blends of portland cement with blast-furnace slag, metakaolin, or silica fume. Cem Concr Res 34:1733–1777 31. Priji EM, Perumal BS (2016) Hydration of Cement and its Mechanisms, IOSR J Mech Civil Eng (IOSR-JMCE) 13:17–31 32. Jensen MO, Hansen FP (2001) Autogenous deformation and RH-change in perspective. Cem Concr Res 31:1859–1865 33. Akhter BH, Pease B, Weiss J (2003) quantifying early-age stress development and cracking in low water-to-cement concrete restrained-ring test with acoustic emission. TRB 2003 Annual Meeting CD-ROM.

The Suitability of Marine Clay–Zeolite Mix as Landfill Liners Krishna Santhosh, G. Sanoop, Sobha Cyrus, and Benny Mathews Abraham

Abstract Feasibility of using marine clay modified with zeolite for the construction of landfill liner was studied. Compacted natural clays are commonly used as liner material due to their high containment, attenuation and cost-effectiveness. The material chosen for liner construction has to satisfy the standards set by Environmental Protection Agency (EPA), based on plasticity characteristics, hydraulic conductivity and shear strength. As per EPA standards, the hydraulic conductivity of the liner material should be less than 1 × 10–7 cm/sec. The feasibility of using marine clay–zeolite mixtures as landfill liner material is presented in this study, and the most acceptable zone was obtained for the same. The liner material was prepared by mixing marine clay with various percentages of zeolite (0–25%). Initially, the suitability of moist and sun-dried marine clay was assessed, because marine clay exhibits different index properties in the natural moist condition and dried condition. Experimental programme involved laboratory tests to determine the index properties, compaction characteristics, hydraulic conductivity and shear strength of marine clay and marine clay–zeolite mix. In order to study the strength development, samples were kept for curing for 7 days, 28 days and 3 months. From the results, 15–20% zeolite content in sun-dried marine clay was found to be optimum. Keywords Landfill liner · Marine clay · Zeolite · Acceptable zone

1 Introduction With the rapid increase in urbanization and industrialization, the amount of waste generation has increased tremendously throughout the world. Often the waste disposal sites have turned out to be sources of soil and groundwater contamination. Traditionally, the municipal solid wastes are disposed of in open dumps or landfills. When water percolates through the waste, leachate is generated and acts as a principal carrier of soluble, as well as suspended contaminants. As a result, K. Santhosh · G. Sanoop (B) · S. Cyrus · B. M. Abraham CUSAT, Kochi, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_9

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proper management of leachate is important. A geotechnical landfill liner is required to control the seepage of leachate present within the waste containment system. A hydraulic barrier used in the construction of waste disposal landfills is called the liner. They are constructed at the base and sides of the liner to prevent percolation of leachate from waste into the underlying soil and sub-surface water bodies. It is necessary to ensure that the liner does not deteriorates and performs this function during the construction phase, as well as the service life. In addition to the offer resistance to the flow of contaminants, liners should maintain the integrity of the structure, structural stability and should not exhibit any type of reaction with the contaminants. Compacted natural clays are widely used as liners because of their high containment attenuation capacity and cost-effectiveness compared to geosynthetic clay liners (GCLs). The Marine clay is effective for developing low permeability barriers because of its high heavy metal retention capacity, large surface area and low hydraulic conductivity [1]. If natural clays are not available, then kaolinite or bentonite mixed with local soils can be used as it is not advisable to use them alone due to its high cost and shrinkage cracks making it uneconomical and less durable. Traditionally, bentonite embedded sand (BES) mixtures have been effectively used in low permeability barriers. However, in some areas natural bentonite is not easily available, instead, an abundantly prevailing local expansive soil can be an alternative. Nowadays, sand is also becoming expensive and scarce. Thus, an effort has been done to replace sand by a material that is technically viable and economically feasible to improve the properties of the soil. Many investigators have used different materials for landfill liner such as fly ash, quick lime, silica fume, cement, quarry dust, etc. Cochin is the industrial capital of Kerala and has been a centre of manufacturing for a large number of chemicals and other raw materials. So, the need for landfill liners to store the effluent from these industries is of utmost interest. The subsoil of Cochin is dominated by marine clay in most of the areas near the seashore. Previous studies have found that these clay deposits have very low hydraulic conductivity and ability to attenuate leaching of inorganic contaminants. Mineralogical analyses of these soils indicate that they are made of illite, chlorite, kaolinite and montmorillonite minerals. They also have high water holding capacity and high plasticity; often very high compressibility in the natural state. Zeolites are crystalline solids, made of silicon, aluminium and oxygen at an elemental level, encountered in saline, alkaline lake deposits like soda lake, deep-sea deposits, volcanic or sedimentary rocks subjected to wall rock alterations. Cation Ion exchange capacity of zeolites is the reason for its value because this helps in retaining heavy metals from leachate when leachate permeates through zeolite. Zeolites are cheaper than sand and manufactured sand, making it highly economical. So the use of marine clay–zeolite mix as a liner mix is to be effectively studied. The local availability of marine clay, the severe scarcity of sand, the low cost and high cation exchange characteristics of natural zeolite are some of the added advantages of this particular liner mix.

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1.1 Zeolites Zeolites are commercial adsorbents with microporous structure and mineralogical structure indicate aluminosilicates. There are five types of naturally occurring zeolites: clinoptilolite, erionite, chabazite, mordenite and phillipsite. Zeolites are composed of tectosilicates with the open framework, consisting of cages and tunnels which adsorb smaller molecules, like a ‘molecular sieve’. Due to this, they filter leachate if they pass through the liner owing to its high adsorption property. Heavy metals are easily adsorbed on the surface of clinoptilolite zeolites. Industrial wastewater can be decontaminated for Co2+ , Cu2+ , Zn2+ and Mn2+ using the adsorption characteristics of clinoptilolite zeolites [2]. Also, it was concluded that adsorption ratios of clinoptilolite metal cations match to Langmuir, Freundlich and Dubinin–Kaganer– Radushkevich (DKR) adsorption isotherm data irrespective of the concentration of contaminants, the controlling parameters for the same being charge density and hydrated ion diameter [2]. If the cation to be adsorbed is Zn2+ , pH and concentration of Zn2+ controls the rate of adsorption by zeolites [3]. From time-dependent studies [4] on adsorption of Fe3+ , Zn2+ , Cu2+ and Mn2+ , it was observed that adsorption rate is maximum for the first 40 min and decreased further, and the selectivity sequence can be written as Fe3+ > Zn2+ > Cu2+ > Mn2+ . Zeolites are excellent pozzolanic materials compared to fly ash and their pozzolanic activity can be compared with silica fume [5, 6]. Presence of reactive SiO2 and high specific surface area are the reasons for this pozzolanic activity [5]. Geotechnical properties of zeolites are characterized by low swelling potential, moderate compressibility and low hydraulic conductivity which makes them suitable for landfill liner applications [7, 8]. They have low maximum dry density, high OMC and the hydraulic conductivity reduces with increasing moulding water content.

1.2 Zeolite–Bentonite Mixtures Bentonitic clays are preferred for landfill liners owing to its fine particle size and high surface charges. It also possesses low hydraulic conductivity and high adsorption capacity. From desiccation cracking of soil and hydraulic barriers [12], it was observed that compacted clay liners with an appreciable amount of bentonite can have problems with shrinkage and desiccation cracking. So as time progresses, the cracks can lead to low permeability of the mix. But the presence of coarser particles like sand can reduce this problem. They demonstrated that shrink–swell and/or freeze–thaw cycling cracks can be eliminated by using bentonite sand mixtures. But

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the sand does not have any adsorption properties. Zeolites possess high attenuation capacity and can trap heavy metals like Pb, Zn, Cd, Ni, Fe and Mn. From studies on removed heavy metals from effluent solution [13] it was found that this would reduce the thickness of clay liner by 25%, thus zeolites would also act as a chemical filter. Zeolite–bentonite mixtures (ZBM) are the ideal landfill liner materials and there performance was evaluated by Tuncan et al. [14]. These studies were extended [15– 17] and it was found that bentonite to zeolite ratio of 1:10 was found to be optimum. ZBM’s exhibited low hydraulic conductivity, high cation exchange capacity, low volumetric shrinkage and are as per specifications. Comparison of the properties of zeolite–bentonite mixtures (ZBMs), sand–bentonite mixtures (SBMs) and zeolite– sand–bentonite mixture (ZSBM) [17, 18] was done. At same bentonite contents, hydraulic conductivity was lower for SBMs compared to ZBMs. This was attributed to the porous structure of the zeolite, and the hydraulic conductivity of ZBM was found to be independent of zeolite particle size within the considered bentonite content range. The hydraulic conductivity of ZSBM was less than ZSM and more than SBM. From studies [19] of the effect of zeolite on consolidation behaviour and hydraulic conductivity of a soil–bentonite (SB) backfill for vertical cutoff walls, it was found that addition of zeolite had no significant amount on the consolidation behaviour or the hydraulic conductivity of the backfill, regardless of the amount and type of zeolite.

1.3 Cochin Marine Clays Marine clay deposits around Cochin are characterized by their dark greyish colour, high natural moisture content (>100%) and high Atterberg limits [1, 20]. They are moderately sensitive silty clays with up to 20% sand and nearly 40% clay and silt (each). They are highly compressible and have preconsolidation pressure in the range of 50 kPa. Owing to its high adsorption characteristics [21], heavy metals like zinc, lead, iron, cadmium and copper are retained from leaching through these clays. For bentonite, the retention increases with the concentration of the ions up to a particular limit and after that, it increases marginally or decreases. The maximum retention capacity of the marine clay varies with different cations. The maximum retention capacity is 112.4 mg/g for lead, 312.2 mg/g for zinc, 18.7 mg/g for cadmium and 65.4 mg/g for copper.

1.4 Selection of Liner Materials Classification of the individual geological deposits within Lincolnshire to unsuitable, marginal or suitable based primarily on plasticity criteria governs the selection of materials to form low permeability barriers in engineered waste disposal [22].

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The Moisture Condition Value Test was used as a means of acceptability testing, earthworks control and a guide to the degree of achievable compaction is discussed [23]. Attempted to modify the plasticity-based criterion proposed by Jones [22] for assessing the suitability of liner materials. A new plasticity-based criterion suitable for medium and high plastic soil has been proposed based on permeability, UCS and Cc. For this, bentonite fly ash mixes were made for representing a wide range of plasticity. Usually when plasticity is reduced, permeability increases. Here plasticity corresponding to 10−7 cm/s is taken. If we reduce plasticity further, permeability will increase beyond 10−7 cm/s. Whereas the upper limit was fixed considering the unconfined compressive strength and compression index, Cc, since the high value of plasticity leads to lower strength and high compressibility (UCS > 200 kPa and Cc < 0.3). Expansive clays are usually used for construction due to high swelling and shrinkage. But they have good self healing capacity if cracks are formed. Here adding zeolites control swelling and shrinkage of these clays so that we can use them for liner construction [24, 25]. The function of pollution control liners is to minimize pollutant migration by convection and/or diffusion. For soils to efficiently perform as a liner, it should possess high adsorption capacity. The main component of an engineered landfill is the liner system which prevents the percolation of leachate to the underlying layers. A liner system is usually a composite of compacted clayey soil and a synthetic membrane with various drainage and fluid collection layers. Natural and synthetic liners may be utilized as both collection device and to isolate leachate within the fill to protect the soil and groundwater below. The liner should maintain integrity and impermeability over the life of the landfill. The main objectives of this study were to determine the geotechnical properties, strength and hydraulic conductivity of marine clay–zeolite mixtures and to determine the most acceptable marine clay–zeolite mix as per EPA norms.

2 Materials As per the standards prescribed by the Environmental Protection Agency (EPA) the material for compacted clay liners should necessarily satisfy the norms for the coefficient of permeability/ hydraulic conductivity, plasticity index, minimum fines content and unconfined compressive strength. In this study, the suitability of marine clay–zeolite (M/Z) mix as liner soil, in accordance with EPA is studied. The marine clay used in the study was collected from Cheranellur, Kochi, Kerala. Boring was carried out using shell and auger method with the sides protected by casing pipes. Clay was obtained from a depth of 8–9 m. Care was taken not to include bentonite slurry during the boring operations as it might contaminate the soil samples. For uniformity, representative samples were collected from the same depth but different boreholes at various locations of the same site were pooled together and mixed thoroughly into a uniform mass and preserved in polythene bags. This is designated as the moist sample of Cochin marine clay. The properties of and the grain size

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distribution of moist marine clay used for the study are presented in Table 1 and Fig. 1, respectively. X-ray diffraction (XRD) is the technique most heavily relied on in soil mineralogical analysis. The engineering behaviour of the soil deposits depends on the mineralogical composition of the samples, and it is necessary to identify the minerals Table 1 Properties of clay and zeolite used in the study Property

Natural marine clay Sun-dried marine clay Zeolite

Natural moisture content (%)

90

8

1

Specific gravity

2.65

2.65

2.41

Liquid limit (%)

116

77

32

Plastic limit (%)

42

35

–

Plasticity index (%)

74

42

–

Shrinkage limit (%)

25

26

–

Particle size distribution Clay (0.075 mm)

52 26 22

40 28 32

4 62 34

Optimum moisture content (%)

–

27

18.7

Maximum dry density (g/cc)

–

1.44

1.60

Unconfined compressive strengtha – (kPa)

157

–

Coefficient of permeabilitya (cm/s) 3.80 × 10−8

3.31 × 10−8

3.42 × 10−8

a Performed

at 5% wet of OMC 90 Natural marine clay

Percentage finer N (%)

80 70

Sundried marine clay Zeolite

60 50 40 30 20 10 0 0.001

0.01

Particle size D (mm) Fig. 1 Grain size distribution of marine clay and zeolite used in the study

0.1

The Suitability of Marine Clay–Zeolite Mix as Landfill Liners

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present. It is a powerful tool in the identification of minerals in rocks and soils. The clay minerals are identified using the generated X-ray diffraction patterns (diffractogram) by the peak’s position, intensity, shape and breadth. The XRD patterns of the marine clay used in the study indicated the presence of Quartz, Gismondine, Montmorillonite, Illite and Kaolinite. The predominant mineral in this marine clay was found to be Quartz. The X-ray diffraction pattern of the marine clay was shown in Fig. 2. In order to understand the suitability of marine clay (in natural condition as well in dry condition), marine clay specimens were sun-dried by spreading the moist samples in large trays exposing it to sunlight and drying to constant weight. The lumps formed during drying were broken by a wooden mallet and the samples were sieved through 4.75 mm IS sieve. Table 1 and Fig. 1 show the properties and particle size distribution of sun-dried sample. Zeolites can be natural or synthetic. There are five types of naturally occurring zeolites. These are clinoptilolite, erionite, chabazite, mordenite and phillipsite. Among these, clinoptilolite has high cation exchange capacity and hence it is selected for the present study. The zeolite used was procured from Asstra Chemicals, Chennai, Tamil Nadu. It has a creamish colour and its photograph is shown in Fig. 3.4. The zeolite samples obtained were in powdered form. The chemical composition of zeolite was listed in Table 2, while the other properties are listed in Table 1. The grain size distribution of the zeolite used in the study is presented in Fig. 1.

10000 9000 8000

Lin (Counts)

7000 6000 5000 4000 3000 2000 1000 0 3

10

20

30

40

50

60

70

80

2-Theta - Scale File: SAIFXR180305D-02(E).raw - Step: 0.020° - Step time: 59.7 s - WL1: 1.5406 - kA2 Ratio: 0.5 - Generator kV: 40 kV - Generator mA: 35 mA - Type: 2Th/Th locked Operations: Background 0.000,1.000 | Import 01-083-2468 (A) - Quartz low, syn - SiO2 - Hexagonal - a 4.86780 - b 4.86780 - c 5.36580 - alpha 90.000 - beta 90.000 - gamma 120.000 - Primitive - P3121 (152) - 3 - 110.11 00-003-0014 (D) - Montmorillonite - MgO·Al2O3·5SiO2·xH2O 00-002-0050 (D) - Illite - 2K2O·3MgO·Al2O3·24SiO2·12H2O 01-072-2300 (C) - Kaolinite 1A - Al2Si2O5(OH)4 - Triclinic - a 5.14000 - b 8.91000 - c 7.26000 - alpha 91.670 - beta 104.670 - gamma 90.000 - Base-centered - C1 (0) - 2 - 32

Fig. 2 XRD pattern of the marine clay used for the study

136 Table 2 Chemical composition of natural zeolite (as provided by suppliers)

K. Santhosh et al. Constituent

Percentage

Silicon dioxide

63.87

Aluminium trioxide

11.47

Calcium oxide

2.37

Magnesium oxide

1.00

Sodium oxide

6.81

Potassium oxide

0.94

3 Experimental Programme The sun-dried marine clay was mixed with different percentages of zeolite by weight (0, 10, 15, 20 and 25%) in dry condition. All mixing was done manually and proper care was taken to prepare a homogeneous mixture. Clay mixed with zeolites were stored in air tight containers and cured for 7, 28 and 120 days before their properties were tested. Then, the samples were kept for a curing period of 7, 28 and 120 days. Geotechnical properties of each combination of mixes were determined as per relevant part of IS 2720. The liner mixes were compacted at water contents on wet side of optimum because they tend to have relatively low hydraulic conductivity. Compaction tests were carried out to assess the optimum moisture content and maximum dry density of all the mixes by standard proctor test as per IS 2720 Part 7. Unconfined Compressive Strength Test. Unconfined compression test was conducted as per IS 2720 (part 10-1991) for the varying percentages of zeolite. All the specimens were prepared at 76 mm height and 38 mm diameter. The soil samples were allowed to mature for 24 h in airtight containers after mixing it with the required water contents. The samples were prepared at 95% of MDD and at a water content on the wet side of optimum. The stress–strain curves were drawn for all the mixes and their unconfined compressive strength were found out. Also, a total number of 35 samples were prepared at varying percentages of zeolite in order to determine the strength characteristics of the liner mixes at a curing period of 7, 28 and 120 days. Figure 3.6 shows the curing of UCC samples. The permeability tests were carried out according to (IS: 2720 part 15-1986). Since fine-grained soils were involved, the falling head method was used to determine the coefficient of permeability. The head levels were noted for the time interval of 24 h. This was because of the very low permeability of clayey soils. For field application, the use of moist marine clay (natural condition) is easier. The change in plasticity characteristics of marine clay in the natural condition with the addition of zeolite is given in Table 3. The results show that the plasticity characteristics of the mixes decrease with the increase in zeolite content. This was because of the silty nature of zeolite. But, even with the addition of 40% zeolite, the moist marine clay does not satisfy the requirement with regard to plasticity index. When natural marine clay is sun-dried, its plasticity characteristics are further reduced. The change in plasticity characteristics of sun-dried marine clay with the

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Table 3 Variation in plasticity characteristics of natural marine clay with zeolite content Combinations

Liquid limit, LL (%)

Plastic limit, PL (%)

Plasticity index, PI (%)

100% MC

116

42

74

10% Z + 90% MC

104

41.7

62.3

20% Z + 80% MC

92

41.4

50.6

30% Z + 70% MC

82

40.3

41.7

40% Z + 60% MC

76

35

41

100% Z

32.4

Non plastic

Non plastic

addition of zeolite is given in Table 4. The results indicate that the plasticity characteristic of the mixes decreases due to the low plasticity nature of zeolite. As per EPA norms, the liner material should have a plasticity index > 10 and < 40. It was observed that even with the addition of 10% zeolite to sun-dried marine clay, the plasticity index was less than 40. The variation of plasticity index of moist and sundried marine clay with the addition of zeolite is shown in Fig. 3. As the liquid limit and plastic limit decreases with zeolite content, the plasticity index also decreases. Table 4 Variation in plasticity characteristics of sun-dried marine clay with zeolite content Combinations

Liquid limit, LL (%)

Plastic limit, PL (%)

Plasticity index, PI (%)

100% MC

77.2

35

42.2

10% Z + 90% MC

69.5

30.8

38.7

15% Z + 85% MC

66.2

30.4

35.8

20% Z + 80% MC

63.4

29.6

33.8

25% Z + 75% MC

59.3

28.8

30.5

100% Z

32.4

Non plastic

Non plastic

Plasticity Index , PI (%)

80

Moist Sample Sun Dried

70 60 50 40 30 20 10 0

0

20

40

60

80

100

120

Zeolite Content (%) Fig. 3 Variation of plasticity index of moist and sun-dried marine clay with zeolite content

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Table 5 Grain size distribution characteristics of marine clay–zeolite mixes Combinations

Fine sand (%) (0.425–0.075 mm)

100% MC

Silt (%) (0.075–0.002 mm)

Clay (%) (200 kPa. Figures 7, 8 and 9 shows the stress–strain curves for the mixes at 7, 28 and 120 days, respectively. In order to understand the strength development, the different MC–Z mixes were compared with that of sun-dried marine clay samples at 7, 28 and 120 days. The percentage increase in strength for the samples with time is shown in Fig. 10. Fig. 7 Stress–strain curves of MC–Z mixes at 7 days

18

Axial Stress (N/mm2)

16 14 12 10

0% Z 10%Z 15%Z 20%Z 25% Z

8 6 4 2 0 0.0

0.1

0.2

0.3

Axial Strain (%)

0.4

0.5

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Axial Stress (N/mm2)

25 0% Z 10% Z 15% Z 20% Z 25% Z

20 15 10 5 0

0

0.1

0.2

0.3

0.4

Axial Strain (%) Fig. 8 Stress–strain curves of MC–Z mixes at 28 days

Axial Stress ( N/mm2)

25 0% Z 10% Z 15% Z 20% Z 25% Z

20 15 10 5 0 0.0

0.1

0.2

0.3

0.4

0.5

Axial Strain (%) Fig. 9 Stress–strain curves of MC–Z mixes at 120 days

Percentage increase in Strength (%)

90 80 70

7th day 28 th day 120 th day

60 50 40 30 20 10 0 100% MC

10% Z+90% MC

15% Z+85% MC

Combinations Fig. 10 Percentage increase in strength with time

20% Z+80% MC

25% Z+75% MC

142 Table 8 Effect of zeolites on coefficient of permeability of marine clay

K. Santhosh et al. Combinations

Permeability (cm/sec)

100% MC

3.311 × 10−8

10% Z + 90% MC

3.912 × 10−8

15% Z + 85% MC

4.523 × 10−8

20% Z + 80% MC

5.124 × 10−8

25% Z + 75% MC

6.067 × 10−8

100% Z

3.419 × 10−8

The coefficient of permeability of different MC–Z mixes is presented in Table 4.6. The permeability of the mixes increased with the increase in zeolite content. The increase in zeolite content attributes to the increase in silt content which improves the pore space for fluid flow. It is observed that all the mixes have permeability 200 kPa criterion for compacted landfill liner materials, the range of liquid limit is 60 < LL < 75 and plasticity index is 30 < PI < 42. 230

LL PI

220 210 200 190 180 170 160 150 25

35

45

55

65

75

Water Content(%) Fig. 13 Variation in unconfined compressive strength with plasticity characteristics

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4.3 Proposed Acceptable Zone for Marine Clay–Zeolite Mixes The acceptable zone for MC–Z mixes by Jones plasticity criterion is between 10 and 25% zeolite content. According to Younus and Sreedeep [23], plasticity-based criterion 10–20% zeolite with marine clay can be accepted as a suitable mixture that can be used as the liner material. An acceptable zone was proposed for MC–Z mixes obtained by superimposing the acceptable zone proposed by Jones [22] and Younus and Sreedeep [23], as shown in Fig. 14. By combining both the acceptable zones, four zones are identified, namely ‘marginal’, ‘suitable’, ‘most suitable’ and ‘unsuitable’. It can be observed that all the moist marine clay samples lie below the A line, making it unsuitable. Zeolite content of 10–25% lies in a suitable zone, whereas the zeolite content between 15 and 20% is found to be most suitable. Thus, the final acceptable zone helps in identifying the most suitable material as landfill liners. Since marine clay and zeolite is naturally occurring materials and is found in large quantities, they are easily available. The traditionally used sand–bentonite mix as landfill liner has an acceptable combination of 80:20. Sand is becoming scarce and very costly nowadays. Hence utilization of marine clay–zeolite mix as liner material is economically viable and environmental friendly.

Fig. 14 Proposed acceptable zones for MC–Z mixes

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5 Conclusions The feasibility of utilizing marine clay mixed with zeolite as a low permeability liner material was studied. From laboratory investigation, evaluation of the acceptable zone of MC–Z mixes as liner material was also done. The following conclusions are made on the basis of the results obtained and discussions made in the study. • The Atterberg limits decrease with the addition of zeolite to marine clay. It is clearly due to the low plasticity of zeolite. • For moist samples, even with the addition of 40% Z, PI > 40, but for sun-dried samples with the addition of 10% Z, PI < 40. Thus, sun-dried samples were used for the study. • With the addition of zeolite to the mixes, the clay content decreases. But, all the MC–Z mixes have clay content >10%. • The maximum dry density and the optimum moisture content of the mixes were found to be between 25 and 27% and 1.4–1.6 g/cc, respectively. • Improvement in unconfined compressive strength was observed when zeolite was added to sun-dried marine clay. The maximum strength was attained for 20% zeolite samples, with 66% increase on curing for 120 days. • Coefficient of permeability of the mixes increase with the increase in zeolite content, this may be due to higher particle size. However, the permeability was within the specified limits for the liner soils. • The acceptable zone based on Jones plasticity criterion is 10 and 25% zeolite content in MC–Z mix, and that based on Younus and Sreedeep criterion is 12–23% zeolite content. • The ‘suitable’ mix of MC–Z by combining the criterion is between 10 and 25% of zeolite content and ‘most suitable mix’ is between 15 and 20% of zeolite content.

References 1. Rahman ZA, Yaacob WZW, Rahim SA, Lihan T, Idris WMR, Sani WNF (2013) Geotechnical characterisation of marine clay as potential liner material. Sains Malaysiana 42(8):1081–1089 2. Erdem E, Karapinar N, Donat R (2004) The removal of heavy metal cations by natural zeolites. J Colloid Interface Sci 280(2):309–314 3. Ören AH, Kaya A (2006) Factors affecting adsorption characteristics of Zn2+ on two natural zeolites. J Hazard Mater 131(1–3):59–65 4. Motsi T, Rowson NA, Simmons MJH (2009) Adsorption of heavy metals from acid mine drainage by natural zeolite. Int J Miner Process 92(1–2):42–48 5. Caputo D, Liguori B, Colella C (2008) Some advances in understanding the pozzolanic activity of zeolites: the effect of zeolite structure. Cement Concr Compos 30(5):455–462 6. Uzal B, Turanlı L, Yücel H, Göncüo˘glu MC, Çulfaz A (2010) Pozzolanic activity of clinoptilolite: a comparative study with silica fume, fly ash and a non-zeolitic natural pozzolan. Cem Concr Res 40(3):398–404 7. Ören AH, Özdamar T (2013) Hydraulic conductivity of compacted zeolites. Waste Manage Res 31(6):634–640

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8. Yukselen-Aksoy Y (2010) Characterization of two natural zeolites for geotechnical and geoenvironmental applications. Appl Clay Sci 50(1):130–136 9. IS 2720: Part VII: 1980 Methods of Test for soils—Part VII: Determination of Water content— Dry density Relation Using Compaction 10. IS 2720: Part 17: 1986 Methods of test for soils—Part 17: Laboratory Determination of permeability 11. IS 2720: Part 10:1991 Methods of test for soils: Part 10 Determination of unconfined compressive strength 12. Kleppe JH, Olson RE (1985) Desiccation cracking of soil barriers. In Hydraulic barriers in soil and rock, ASTM International 13. Kayabali K (1997) Engineering aspects of a novel landfill liner material: bentonite-amended natural zeolite. Eng Geol 46(2):105–114 14. Tuncan A, Tuncan M, Koyuncu H, Guney Y (2003) Use of natural zeolites as a landfill liner. Waste Manage Res 21(1):54–61 15. Kaya A, Durukan S (2004) Utilization of bentonite-embedded zeolite as clay liner. Appl Clay Sci 25(1–2):83–91 16. Kaya A, Durukan S, Ören AH, Yükselen Y (2006) Determining the engineering properties of bentonite-zeolite mixtures. Teknik Dergi 17(3):3879–3892 17. Ören AH, Kaya A, Kayalar AS¸ (2011) Hydraulic conductivity of zeolite–bentonite mixtures in comparison with sand–bentonite mixtures. Can Geotech J 48(9):1343–1353 18. Du YJ, Fan RD, Liu SY, Reddy KR, Jin F (2015) Workability, compressibility and hydraulic conductivity of zeolite-amended clayey soil/calcium-bentonite backfills for slurry-trench cutoff walls. Eng Geol 195:258–268 19. Hong CS, Shackelford CD, Malusis MA (2011) Consolidation and hydraulic conductivity of zeolite-amended soil-bentonite backfills. J Geotech Geoenviron Eng 138(1):15–25 20. Jose BT, Sridharan A, Abraham BM (1988) A study of geotechnical properties of Cochin marine clays. Mar Georesour Geotechnol 7(3):189–209 21. George S, Paul J, Jacob J (2014) Heavy metal retention of cochin marine clay. Int J Eng Res Dev 9(12):54–59 22. Jones RM, Murray EJ, Rix DW, Humphrey RD (1995) Selection of clays for use as landfill liners. Waste disposal by landfill-GREEN 93:433–438 23. Younus MM, Sreedeep S (2012) Evaluation of bentonite-fly ash mix for its application in landfill liners. J Test Eval 40(3):357–362 24. Öncü S, ¸ Bilsel H (2017) Effect of zeolite utilization on volume change and strength properties of expansive soil as landfill barrier. Can Geotech J 54(9):1320–1330 25. Tuncan A, Onur, MI, Akpinar K, uncan M (2016) Use of sepiolite and zeolite mixtures as a landfill liner. Int J Waste Resour 6(197):2

Ductility Assessment of an RC Section Kshama Hemkar, Laxmi Kant Mishra, and Goutam Ghosh

Abstract Ductility is considered to be an important ability of a material to undergo appreciable plastic deformations before the collapse, and therefore, it is a crucial factor for earthquake resistant design of reinforced concrete sections. Ductility depends upon reinforcement detailing describing the confining of an RC section and engineering properties of constituent materials apart from the structural configuration. The member ductility is generally defined in terms of strain ductility, curvature ductility, and rotational ductility, while safety is assessed through the overstrength factor. The grades of reinforcing steel specified in IS 1786–2008 also include an additional classification for improved material ductility. In the present study, the curvature ductility, plastic rotation capacity, and overstrength factor of an RC column section are evaluated to assess analytically the variation in ductility and safety with a varying spacing of confining steel using ductility-based grades of confining steel having characteristic yield strength as 500 N/mm2 . The confining steel used is Fe 500, Fe 500D, and Fe 500S. The effect of confinement has been considered applying Mander’s model. It has been observed that the curvature ductility, plastic rotation capacity, and overstrength factor decrease with an increase in spacing of confinement steel. However, the reverse trend has been observed with reference to the diameter of confinement bars. Keywords Mander’s model · Confined concrete · Curvature ductility · Overstrength factor · Plastic rotation capacity

K. Hemkar (B) · L. K. Mishra · G. Ghosh Department of Civil Engineering, Motilal Nehru National Institute of Technology, Allahabad, Uttar Pradesh, India e-mail: [email protected] L. K. Mishra e-mail: [email protected] G. Ghosh e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_10

149

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Notations M25 Fe500 Fly Flx f’l f’cc Ae Fy f’c εy ε fc εt εcu εcc Ec f ρs θu θy

Characteristic strength of concrete. Characteristic strength of Reinforcement. Effective lateral confining stress in y direction. Effective lateral confining stress in x direction. Effective lateral confining stress. Confined concrete strength. Area of effectively confined core concrete. Characteristic strength of steel. Confine stress. Design yield strain. Concrete strain. Concrete stress. Tension strain capacity. Ultimate strain capacity. Strain at peak stress. Modulus of Elasticity of Concrete. Characteristic Strength of Concrete. Ratio of volume to transverse confining steel to volume of confined concrete core. Ultimate rotation. Elastic Rotation Capacity.

1 Introduction For the structural point of view, the term “ductility” in the seismic design of structures is described as the ability of structure or member to undergo deformation after its first yield without significant loss in strength. Ductile member is generally able to dissipate considerable amount of energy during deformation and does not lose load carrying capacity. Ductility considerations in earthquake-resistant design of structure depend on material and sectional details of individual members of a structure, details of joint connection, and structural configuration. Many of the researchers have studied experimentally and analytically ductility behavior of RC sections considering various parameters such as tension reinforcement ratio, compression reinforcement ratio, grade of concrete, grade of steel reinforcement, yield and ultimate strain of reinforcement, geometry of cross section, and confinement ratio [1–4]. The most important engineering consideration which is applied to the ductility assessment of RC sections is stress–strain behavior of the materials [5]. The various analytical and experimental models [6, 7] are available for analyzing the stress–strain characteristics of confined concrete sections. The theoretical model for representation of stress–strain relationship of confined concrete proposed by Mander et al. [8], is

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151

commonly used in ductility analysis of RCC sections. In this study, the effect of variations in the spacing of confining steel on member ductility is expressed in terms of curvature ductility, plastic rotation capacity and over strength factor for an assumed column section with M25 grade of concrete and Fe 500, Fe 500D, and Fe 500S confining steel have been reported.

2 Member Ductility and Safety Assessment Generally, the member ductility and safety are expressed in terms of curvature ductility, plastic rotation capacity, and overstrength factor.

2.1 Curvature Ductility The behavior of structural member in flexure is understood by moment–curvature relationship. Structural members are subjected to axial and biaxial loading. Curvature ductility, rotational ductility, and stiffness of the reinforced concrete sections can be assessed by the moment–curvature relationship. The structural member ductility factor ranges from 3 to 6 [9]. Curvature ductility μ is defined as the ratio of ultimate curvature (φu ) to corresponding yield curvature (φ y ). μ=

φu φy

(1)

2.2 Plastic Rotation Capacity The rotational ductility factor R is defined as the ratio of rotations at the end of the post-elastic range (θu ) and at the first yield point (θ y ) of tension steel [10]. R=

θu θy

(2)

2.3 Plastic Hinge Length The deformations are assumed to be concentrated at the plastic hinge. Inelastic curvature in the plastic hinge is assumed to be constant over the plastic hinge length

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L p . The plastic hinge length is obtained by using the ACI-318 method for ductile beam-column connections. Lp =

H 2

(3)

L p = Plastic hinge length. H = Cross section dimension perpendicular to the axis of bending.

2.4 Overstrength Factor Overstrength in structural members is desirable from safety considerations while resisting the earthquake effects. Overstrength (So ) takes all possible factors that may cause a strength increase. These factors include a steel strength higher than the specified yield strength, additional steel strength due to strain hardening at large deformation, concrete grade higher than specified, section size larger than assumed, axial compression in the flexural member due to lateral restraint. The overstrength factor may be computed as follows [11]: ϕo =

So Si

(4)

ϕo = over strength factor. So = over strength. Si = ideal strength.

3 Engineering Properties of Constituent Materials Modulus of elasticity and compressive strength, are important engineering properties of concrete that influence member ductility. These properties of constituent materials are discussed below.

3.1 Modulus of Elasticity and Stress–Strain Relationship of Concrete The material behavior under the effects of direct and environmental loading is governed by its elastic behavior. The static modulus of elasticity for a material under tension or compression is given by the slope of the stress–strain curve of the material under uniaxial loading. The modulus of elasticity for concrete may be estimated as.

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153

Fig. 1 Stress–strain relation for concrete. Source 12: IS 456-2000

E c = 5000



f (N/mm2 )

(5)

where, f is characteristic compressive strength of concrete or maximum compressive strength of unconfined concrete [8, 12]. According to ACI 318 the modulus of elasticity for concrete E c is given by the following expression [13].  E c = 0.43w3/2 fc

(6)



where f c is cylinder strength and w is the density of concrete. The idealized stress– strain behavior of concrete as per IS 456-2000 is illustrated in Fig. 1. The experimentally investigated stress–strain behavior of different types of concrete reported by Wee and Chin [3], is given in Fig. 2.

3.2 Modulus of Elasticity and Stress–Strain Behavior of Confining Steel

Sample

Yield strength [N/mm2 ]

Ultimate % elongation

Sample 1

511

High

Sample 2

485

Low

Sample 3

380

Very low

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Fig. 2 Experimental stress–strain curve for different grade of concrete. Source 3: J. Mater. Civ. Eng. 1996, 70–76

The modulus of elasticity of confining steel for all grade is taken as 200 kN/mm2 [14]. The yield strain for High Yield Strength Deformed (HYSD) and Thermo Mechanically Treated (TMT) bars for design considerations is formulated as below [12]. εy =

0.87 f y + 0.002 Es

(7)

where, f y = Characteristic yield strength of steel and E s = modulus of elasticity of confining steel and design yield strain. The corresponding value of ε y = 4.175 × 10−3 . The experimentally obtained stress–strain curves of confined concrete containing Fe 415 grade TMT reinforcing steel with different yield strengths were reported by Prabir et. al. [10]. In their investigations, each sample was identified by its yield strength and ultimate elongation. The details of their three samples of TMT bars of grade Fe415 for which stress–strain curves are given in Fig. 3. The idealized stress–strain behavior of confining steel for HYSD bars as per IS 456-2000 is illustrated in Fig. 4.

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Fig. 3 Experimental stress–strain curve of steel. Source 10: The Indian Concrete J. p 19–30

Fig. 4 Stress–strain curve of HYSD. Source 12: IS 456-2000

4 Geometrical Properties of RC Column Section A 400 × 600 mm column section with a clear length of 4500 mm has been used for the analysis. The longitudinal reinforcement consists of 8 no’s of 20 mm diameter ribbed bars placed symmetrically with a clear cover of 40 mm. The transverse reinforcement

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Fig. 5 Cross section of RC section

600mm

8.no’s@20 mm 6 ø @288 mm c/c M25 Grade of Concrete & Fe 500 400mm

consists of rectangular stirrups of the diameter of 6, 8, 10, and 12 mm placed at 75, 150, 225, 288, and 300 mm spacing center to center. The details of the section are given in Fig. 5.

5 Evaluation of Various Parameters of Stress–Strain Curve of Confined Concrete Using Mander’s Model Reinforced concrete sections are confined with transverse reinforcement. Confinement improves material resistance against static and dynamic loading in terms of strength and ductility [1]. Mander et al. [8], proposed a method to analyze a confined concrete section using the stress–strain approach. The approach is simple and effective in considering the effect of confinement. This model is particularly used advantageously to evaluate the effective strength of columns confined by transverse reinforcement viz lateral ties or spiral stirrups, steel jackets, and even by FRP wrapping. Derived stress–strain behavior using Xtract software and the relationships included in the Manders model for monotonic loading of confined concrete are given in Fig 6. The defining values in stress–strain relationship of confined concrete are obtained by using expressions given in Mander’s model and Fig. 6 [8]. ε < 2 ∗ εt , f

(8)

ε < 0, f = ε ∗ E c

(9)

ε < εcu , f =

f cc ∗ x ∗ r r − 1 + xr

x = ε/εcc

(10) (11)

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Fig. 6 Mander’s stress–strain proposed model for confined and unconfined concrete. Source 8: J. Struct. Eng., 1988, 114

Table 1 Unconfined concrete properties used in analysis source 10: IS 456-2000 √ S. No Grade of concrete E c = 5000 f (N/mm2 ) Yield strain Crushing strain 1

M25

25,000

0.002





εcc = 0.002 1 + 5 ⎛

  f cc −1 f



f cc = f ⎝−1.254 + 2.254 1 + 

0.0035



(12) 

⎞

f 7.94 f l −2 l ⎠ f f

(13)

The confined strength of concrete as obtained from XTRACT Software is 25.40 N/mm2 . Core area of confined concrete is 47,056.43 mm2 and the volumetric confining steel ratio is 3.82 × 10−4 . The spalling strain of unconfined concrete is assumed as 0.0060 [4]. The unconfined properties of concrete are given below in Table. 1

5.1 Mechanical Properties of Rebar for Fe 500, Fe500D, Fe500S The high yield strength deformed Fe500, Fe 500D, and Fe 500S have characteristic yield strength as 500 N/mm2 , and D and S letters as suffix indicate the categories with the same specified minimum 0.2% proof stress or yield stress but with enhanced and additional requirement of ductility. Specifications of ductility-based grades of Fe500 reinforcing steel as per IS 1786-2008 [14] are given in Table 2.

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Table 2 Mechanical properties of rebar Fe 500, Fe500D, Fe500S S. No

Attributes

IS 1786-2008 Fe500

Fe500D

Fe500S

1

Tensile strength

8% more than the actual 0.2% proof yield stress should not be less than 545.0 N/mm2

10% more than the actual 0.2% proof yield stress should not be less than 565.0 N/mm2

14% more than the actual 0.2 % proof yield stress should not be less than 625.0 N/mm2

2

Minimum yield strength

500 N/mm2

500 N/mm2

500 N/mm2

3

Percentage elongation

12%

16%

18%

4

UTS/YS ratio

≥1.08, but UTS not less than 545.0 N/mm2

≥1.10, but UTS not less than 565.0 N/mm2

1.25

6 Analysis of Section Using XTRACT Software XTRACT is a Microsoft Windows-based software and it can run on any Windows OS and requires only a 32-bit operating system. It is used for the analysis of any cross section that can generate moment curvatures, axial force-moment interactions, and moment-moment interactions for concrete, steel, prestressed, and composite structural cross sections considering nonlinear behavior. Various parameters for determination of ductility of a section are readily obtainable from analysis of the section using XTRACT Software. The input data for determination of ductility of a section include (i) cross sectional details, (ii) specifications of cover concrete, (iii) area of core concrete and confinement reinforcement and ultimate loads and moments. The specifications of cover concrete consist of its 28– Days compressive concrete strength, tensile strength, yield strain (assumed), spalling strain, post crushing strain, failure strain and elastic modulus. Similarly, for confined concrete the specifications include transverse reinforcing bar yield stress, X and Y transverse reinforcing steel ratio, average distance between tied longitudinal bars, number of longitudinal bars around the core, confined core area, tie spacing along the member, modulus elasticity of steel, and crushing strain. Using these specifications, the compressive strength of confined concrete is directly obtained from the XTRACT software. The analysis results include curvature at first yield, ultimate curvature, moment at first yield, ultimate moment, energy per length, overstrength factor, plastic rotation capacity, and curvature ductility. The stress–strain representation of confined concrete using Mander’s model with varying size of the confining steel for normal Fe500 grade confining steel are shown in Fig. 7. The moment-curvature representation of confined concrete using Mander’s model with varying size of the confining steel for normal Fe500 confining steel are shown in Fig. 8.

Ductility Assessment of an RC Section

159

30

Stress (N/mm2)

25 20 15 6mm Confining Steel 8mm Confining Steel 10mm Confining Steel 12mm Confining Steel

10 5 0 0

0.001

0.002

0.003

0.004

0.005

0.006

Strain Fig. 7 Derived stress–strain behavior of confined concrete section using Mander’s model 7,00,000

Moment N-m

6,00,000 5,00,000 4,00,000 3,00,000

6mm 8mm 10mm 12mm

2,00,000 1,00,000 0 0.00

0.01

0.01

0.02

0.02

0.03

Curvature (1/m) Fig. 8 Derived moment curvature behavior of confined concrete section using Mander’s model

7 Results and Discussions The analysis results of the section for ductility assessment in terms of curvature ductility, plastic rotation capacity, and overstrength factor with confining steel having characteristic yield strength as 500 N/mm2 and ductility-based grades of Fe 500, Fe 500D and Fe 500S steel are presented in Table 3. The parametric evaluation of different sectional variations is illustrated through Fig. 8. The curvature ductility, plastic rotation capacity, and overstrength factor of analyzed sections are within the expected range. The sectional ultimate axial load carrying capacity of the column is 3542 kN, while its ultimate moment carrying capacity is 624.7 kN−m . The increase in spacing of confining steel leads to lowering

Fe500S

500 N/mm2

1.25

≥1.10

Fe500D 500 N/mm2

Fe500

≥1.08

2.292

2.160

2.059

2.042

225

288

300

2.037

300

150

2.061

288

2.433

2.158

225

75

2.288

2.041

300

150

2.061

288

2.435

2.158

225

75

2.434

2.293

75

150

0.009401 0.6439

0.009231 0.6467

0.001029 0.6848

0.001127 0.7324

0.001232 0.7812

0.009365 0.6424

0.009530 0.6480

0.001028 0.6832

0.001126 0.7303

0.001233 0.7792

0.009400 0.6428

0.009530 0.6480

0.001028 0.6827

0.001128 0.7302

0.001233 0.7784

2.045

2.063

2.234

2.360

2.513

2.071

2.087

2.236

2.361

2.519

2.071

2.086

2.232

2.359

2.520

10 mm

0.009419 0.6434

0.009536 0.6489

0.001085 0.7099

0.001177 0.7583

0.001295 0.8064

0.009601 0.6522

0.009731 0.6595

0.001084 0.7083

0.001177 0.7564

0.001297 0.8046

0.009604 0.6520

0.009725 0.6590

0.001083 0.7067

0.001177 0.7756

2.092

2.122

2.285

2.423

2.607

2.092

2.128

2.291

2.428

2.609

2.092

2.120

2.287

2.418

2.608

0.009785 0.6630

0.001001 0.6737

0.001123 0.7298

0.001225 0.7775

0.001371 0.8301

0.009679 0.6613

0.001006 0.6736

0.7286

0.001227 0.7759

0.001372 0.8270

0.009769 0.6609

0.009996 0.6720

0.001122 0.7264

0.001221 0.7729

0.00125

12 mm

2.122

2.171

2.333

2.466

2.680

1.992

2.248

2.331

2.474

2.687

2.120

2.172

2.331

2.379

2.682

Over strength factor 0.7621

0.001001 0.6737

0.001037 0.6882

0.001157 0.7470

0.001259 0.7930

0.001437 0.8497

0.001006 0.6736

0.001096 0.7154

0.001156 0.7449

0.001261 0.7917

0.001442 0.8466

0.009996 0.6720

0.001038 0.6864

0.001156 0.7442

0.00191

0.001438 0.8455

Over Curvature Plastic strength ductility rotation factor capacity

0.001372 0.8260

Over Curvature Plastic strength ductility rotation factor capacity

0.001298 0.8038

Characteristic UTS/YS Spacing Diameter of confining lateral steel strength of ratio of 6 mm 8 mm steel as per IS confining Curvature Plastic Over Curvature Plastic 1786-2008 steel ductility rotation strength ductility rotation capacity factor capacity

500 N/mm2

Grade of steel

Table 3 Curvature ductility, plastic rotation capacity, and overstrength factor of analyzed sections

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161

of confining stresses hence lowering of ductility. This effect is reduced when the size of the confining steel is increased. The results of the analysis also reveal that for the minimum spacing of confining steel viz. 75 mm the curvature ductility, plastic rotation capacity, and overstrength factor are maximum for the maximum size of the confining steel viz. 12 mm irrespective of grades of confining steel. In this analysis, the prescribed limits of the UTS/YS ratio for different ductility-based grades of confining steel are used. These ratios are not significantly different. Possibly due to this the effect of ductility-based grades of confining steel is not explicit. The effect of confinement for different ductility-based grade Fe500 rebar is shown from Fig. 9, 10, 11, 12, 13, 14, 15, 16, 17. Where Figs. 9, 10, and 11, represent the 3

Fig. 9 Variation of curvature ductility and confining steel at 6 mm

Fe500

Fe500D

Fe500S

Curvature Ductility

2.5 2 1.5 1 0.5 0 75

150

225

288

300

Spacing of Lateral Ties (mm) 3

Fig. 10 Variation of curvature ductility and confining steel at 8 mm

fe500

Fe500D

Fe500S

Curvature Ductility

2.5 2 1.5 1 0.5 0 75

150

225

288

300

Spacing of Lateral Ties (mm)

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K. Hemkar et al. 3

Fig. 11 Variation of curvature ductility and confining steel at 12 mm

Fe500

Fe500D

Fe500S

Curvature Ductility

2.5 2 1.5 1 0.5 0 75

150

225

288

300

Spacing of Lateral Ties (mm) 1.40E-03

Platic Rotation Capacity (rad)

Fig. 12 Variation of rotation capacity and confining steel at 6 mm diameter

Fe500

Fe500D

Fe500S

1.20E-03 1.00E-03 8.00E-04 6.00E-04 4.00E-04 2.00E-04 0.00E+00 75

150

225

288

300

Spacing of Lateral Ties (mm)

variation of curvature ductility, Figs. 12, 13 and 14, represent the variation of plastic rotation capacity, and Figs. 15, 16 and 17, represent the variation of overstrength factor with reference to the effect of confinement for varying ductility-based grades of Fe 500 reinforcing steel.

8 Conclusions From this study, it is concluded that Curvature Ductility, Plastic Rotation Capacity, and Overstrength Factor is found to be more sensitive with respect to the diameter

Ductility Assessment of an RC Section Fe500

1.40E-03

Platic Rotation Capacity (rad)

Fig. 13 Variation of rotation capacity and confining steel at 8 mm diameter

163 Fe500D

Fe500S

1.20E-03 1.00E-03 8.00E-04 6.00E-04 4.00E-04 2.00E-04 0.00E+00 75

150

225

288

300

Spacing of Lateral Ties (mm)

1.60E-03

Platic Rotation Capacity (rad)

Fig. 14 Variation of rotation capacity and confining steel at 12 mm diameter

Fe500

1.40E-03

Fe500D

Fe500S

1.20E-03 1.00E-03 8.00E-04 6.00E-04 4.00E-04 2.00E-04 0.00E+00 75

150

225

288

300

Spacing of Lateral Ties (mm)

and spacing of confining steel than the ductility-based grades of reinforcing steel as considered in the study. The Curvature Ductility, Plastic Rotation Capacity, and Overstrength Factor decrease with an increase in spacing of confining steel for given diameter and grade of confining steel. A maximum decrease of 20.95% in Curvature Ductility, 30.49% in Plastic Rotation Capacity, and 20.52% in Overstrength Factor have been observed with respect to increase of spacing of confining steel from 75 to 300 mm for Fe 500 grade steel with 12 mm diameter confinement bar. It has also been found that Curvature Ductility, Plastic Rotation Capacity, and Overstrength Factor increase with an increase in the diameter of confining steel. The maximum increase of 10.35% in Curvature Ductility and 16.95% in Plastic Rotation

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Fig. 15 Variation of overstrength factor and confining steel at 6 mm diameter

0.9 fe500

Over Strength Factor

0.8

Fe500D

Fe500S

225

288

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 75

150

300

Spacing of Lateral Ties (mm)

0.9

Fe500

0.8

Over Strength Factor

Fig. 16 Variation of overstrength factor and confining steel at 8 mm diameter

Fe500D

Fe500S

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 75

150

225

288

300

Spacing of Lateral Ties (mm)

Capacity have been observed with respect to increase of the diameter of confining steel from 6 to 12 mm for Fe500D steel with 75 mm spacing of confining steel. In the case of the Overstrength factor, the maximum increase of 9.08% has been observed with respect to increase of the diameter of confining steel from 6 to 12 mm for Fe500S steel with 225 mm spacing of confining steel. However, with respect to the grade of steel, the change of Curvature Ductility, Plastic Rotation Capacity, and Overstrength Factor have been found to be almost insensitive.

Ductility Assessment of an RC Section 0.9

Fe500

Fe500D

Fe500S

0.8

Over Strength Factor

Fig. 17 Variation of overstrength factor and confining steel at 12 mm diameter

165

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 75

150

225

288

300

Spacing of Lateral Ties (mm)

References 1. Saatcioglu M, Razvi S (1992) Strength and ductility of confined concrete. J Struct Eng 118(6):1590–1607 2. Sheikh SA, Yeh CC (1993) Analytical moment-curvature relations for tied concrete columns. J Struct Eng 119(3). (February, 1992, Vol. 118, No. 2) 3. Wee TH, Chin MS, Mansur MA (1996) Stress strain relationship of high strength concrete in compression. J Material Civ Eng, 70–76 4. Chan WWL (1995) The ultimate strength and deformation of plastic hinges in reinforced concrete frameworks. Mag Concrete Res 5. Hemkar K, Mishra LK, Ghosh G (2017) Ductility evaluation of an RC section with a variation in engineering properties of materials. In: Indian conference on applied mechanic, MNNIT Allahabad, ID-274 6. Chan W (1955) The ultimate strength and deformation of plastic hinges in reinforced concrete frameworks. Mag Concrete Res 7(21):121–132 7. Carreira DJ, Chu KH (1985) Stress-strain relationship for plain concrete in compression. ACI J Proc, 82(6) 8. Mander J, Priestley M, Park R (1988) Theoretical stress-strain model for confined concrete. J Struct Eng 114(8):1804–1826 9. Pam HJ, Ho JCM (2001) Flexural strength enhancement of confined reinforced concrete columns. ICE J, 363–370 10. Basu PC, Shylamoni P, Roshan AD (2004) Characterisation of steel reinforcement for RC structures an overview and related issues. Indian Concrete J, 19–30 11. Park R, Pauley T (1975) Reinforced concrete structures. John Wiley & Sons, New York, USA 12. IS: 456-2000. Plain and reinforced concrete. Bureau of Indian standards, New Delhi, 2000 13. Building Code Requirements for Reinforced Concrete (ACI 318–99), ACI Committee 318, American Concrete Institute 14. IS: 1786-2008. High strength deformed steel bars and wires for concrete reinforcement concrete reinforcement specification. Bureau of Indian Standards

Finite Element Analysis of Shape Memory Alloy Ring Spring System for Steel Frames Ashwin Jose and C Prabha

Abstract Shape Memory alloys (SMAs) are smart materials that are capable of recovering its shape under unloading. This phenomenon is mainly due to its two unique properties such as shape memory effect (SME) and superelasticity (SE). The post-earthquake damages suffered by traditional steel frames can be mitigated by the SMA ring spring system in beam-column junctions. An SMA ring spring system is a combination of an inner ring of high strength alloy enclosing an outer ring, made of shape memory alloy with tapered faces. The force generated due to the wedging action between the HSS inner ring and SMA outer ring is responsible for resisting the external loads. This paper deals with the potentiality of the SMA ring spring system in steel frames for seismic applications. A nonlinear finite element analysis using ABAQUS is carried out to study the response of the SMA ring spring system under cyclic loading. For the SMA outer ring, a user-defined material model based on Auricchio’s approach is used for expressing the superelastic behavior of SMA. A kinematic hardening model with von Mises yield criterion was used for evaluating steel material. A global analysis of a 3D multi-story frame is carried out to identify the most critical beam-column in the frame under seismic loading. Subsequently, the critical beam-column junction is modified with the SMA ring spring system. A dynamic implicit acceleration was given to the steel beam. The proposed connection shows a superior hysteresis loop and self-centering ability with a substantial increase in the load carrying capacity of the connection. Keywords Shape memory alloys · Ring spring system · Self-centering connection · Finite element analysis · Auricchio’s approach

A. Jose (B) · C. Prabha Mar Athanasius College of Engineering, Kothamangalam, India e-mail: [email protected] C. Prabha e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_11

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1 Introduction At the beginning of 1960, engineers believed that welded steel moment frames are the most suitable ductile system and invulnerable to earthquake damages. After the 1994 Northridge earthquake, FEMA has observed that a number of welded steel frames experienced a brittle fracture of the beam to column connections [1]. Through the FEMA research, partially restrained bolted connections were found to be a feasible alternative to a fully restrained welded connection. However, the performance of bolted connections can be improved by utilizing some smart metals such as Shape Memory Alloys (SMAs) at the elemental level. SMAs are a class of metals which can exhibit two important phenomena’s, Shape Memory Effect (SME) and Superelasticity (SE). When SMA is loaded in a low-temperature martensitic phase, it transforms from twinned martensitic to detwinned martensitic phase. Upon releasing a residual strain remains, but by heating, SMA can recover its deformed shape, called SME. When SMA loaded at a relatively high-temperature austenitic phase, strain recovery can be done without any additional heating. This phenomenon is called the SE effect. The superelastic behavior of SMA was identified as the feasible approach in the civil engineering industry [2]. Fang et al. [3], carried out a study on SMA Belleville washers. SMA washer in the steel beam-column junction shows good energy dissipation and self-centering capacity. But the load resistance of Belleville washers found to be inadequate for the civil engineering applications because the material within these elements is not fully mobilized when loaded. In 2014, Wang et al. [4], introduce SMA tendons in the critical beam-column junction which also shows good energy dissipation properties but grip failure was the main problem. Fang et al. [5], replaces conventional high strength bolts with SMA bolts. Here failure occurred at the threaded area of the bolt. This failure can be mitigated by increasing the net threadedto-shank area, but associated material wastage during the machining process makes it uneconomical. In order to achieve an efficient connection performance, a new system was developed, i.e. SMA ring spring system, which resolves problems such as low resisting load, grip failure, material wastage [6]. In this paper feasibility and seismic performance of the SMA ring spring system in steel, and the beam-column junction is discussed in detail. An SMA ring spring system is a combination of an inner ring of high strength alloy (HSA) enclosing an outer ring, made of shape memory alloy with mating tapered faces. The working principle of the SMA ring spring system is shown in Fig. 1. When the connection rotates, a compressive load is developed in the ring spring system to develop a wedging action which causes expansion of SMA outer ring and compression of HSA. The force generated due to the wedging action between the HSS inner ring and SMA outer ring is responsible for resisting the external loads. When the load is released the ring spring system comes back to its original position due to the superelastic characteristics of the SMA outer ring. HSA inner ring is designed in the elastic limit in order to reduce the residual deformation.

Finite Element Analysis of Shape Memory Alloy Ring Spring …

169

Fig. 1 Working principle and details of SMA ring springs

2 Comparison of Shape Memory Alloy Ring Spring System with Steel Ring Spring System 2.1 Numerical Modeling A nonlinear finite element analysis using ABAQUS 6.14 is carried out to study the response of the SMA ring spring system. SMA ring spring system consists of two SMA outer rings, one high strength steel inner rings, two half inner rings, and a rigid loading plate. Dimensions of the SMA ring spring system are shown in Fig. 2. A kinematic hardening model with von Mises yield criterion was used for evaluating steel material. The Young’s modulus, yield strength, and tensile strength at 10% strain are 205, 690, and 770 GPa. The superelastic behavior of SMA is modeled using a user-defined material model based on Auricchio’s approach [7]. The material properties of different phases of SMA are shown in Table 1. Hard contact with the friction of 0.15 is provided in the tapered faces. To act as a single unit, tie contact is provided between the loading plate and top inner ring. A displacement controlled cyclic load of 10 mm is applied to the top rigid plate and pinned boundary condition is provided to the other one. Eight-node linear brick element with reduced integration and hourglass control is provided for HSS inner rings to obtain accurate results. For SMA, hourglass effect is not developed so the C3D8 element with 1 mm size is adopted. Meshed assembly of the SMA ring spring system is shown in Fig. 3. When a compressive load was applied on the SMA ring spring system the inner HSS ring was squeezed, and the stress was transferred to SMA outer ring. From the

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Fig. 2 Details of SMA ring spring system

Table 1 Material properties of SMA

Material property

Values

Forward transformation stress σMs

400 MPa

Forward transformation stress σMf

500 MPa

Reverse transformation stress σAs

250 MPa

Reverse transformation stress σAf

150 MPa

Plastic stress σp

700 MPa

Young’s modulus (austenite) EA

70 GPa

Young’s modulus (martensite) EM

40 GPa

Modulus of plasticity Ep

3 GPa

Maximum transformation strain εL

5%

Poisson’s ratio (austenite)

0.33

Poisson’s ratio (martensite)

0.33

Fig. 4, it is clear that stress is transferred from inner to outer ring due to wedging action. Maximum von Mises stress developed in the SMA outer ring is 690 MPa so at the maximum compressive displacement SMA outer ring lies within the elastic limit. When the load is released SMA release it stresses due to its superelastic property and comes back to its original position as shown in Fig. 5. For the validation study, a ring spring system is made up of a steel outer ring and compared it with a ring spring system with SMA outer ring. From the stress–strain graph shown in Fig. 6, it is observed that on releasing the load, the steel ring spring system did not come back to its original position and there was a residual strain of 0.004 that has occurred. But in the case of the SMA ring spring system, after the load was released no residual strain was developed.

Finite Element Analysis of Shape Memory Alloy Ring Spring …

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Fig. 3 Meshed assembly

Fig. 4 SMA ring spring system under compression

3 Comparison of Control Ordinary Steel Beam-Column Junction and Beam-Column Junction with the SMA Ring Spring System A seven-story hospital building was analyzed using ETAB 2016, and the critical beam-column junction was identified. Based on the ETAB results, sectional properties for Beam: ISMB 600, Column: ISWB 600, Endplate: ISA 100 × 100 × 12.5 mm of length 300 mm and for connection 4 No, M22-10.9 Class bolts are provided.

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Fig. 5 SMA Ring spring system after load released

Fig. 6 Stress–strain graph of steel and SMA ring spring system

3.1 Numerical Modeling Modeling and analysis of steel beam-column junction (BCJ) was carried out in Abaqus 6.14. Material properties of parts of Beam-column joint are shown in Table 2 A surface to surface contact with relatively small sliding is provided in the sliding connection members. Frictional contact of 0.3 is made between endplate and beam, Table 2 Material properties of various elements in the beam-column junction

Specimen

f y (Mpa)

f u (Mpa)

E (Mpa)

Beam

340.14

448

210,000

Column

372

477

210,000

Endplate

369.44

503.45

210,000

Bolt

939.69

1018.67

210,000

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Fig. 7 Meshed assembly of steel beam-column junction

Fig. 8 Meshed assembly of steel beam-column junction with SMA ring spring system

endplate and column, and beam and column. Frictionless connection with hard contact is provided between bolt shank and bolt hole. A tie constraint is used to model the connection between the bolt head to the flanges of column and endplate. A dynamic implicit acceleration was given to the steel beam to simulate the Bhuj earthquake in 2001 at Gujarat [8]. Meshed assembly of conventional and connection with SMA ring spring system is shown in Figs. 7 and 8.

3.2 Results and discussions von Mises stress diagram for conventional steel beam-column junction and beamcolumn junction are shown in Figs. 9 and 10. It is observed that for the conventional steel beam-column junction, maximum stress occurred at the bolt and it gets yielded. The flange portion of the column and beam also yielded after acceleration. In the

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Fig. 9 von Mises stress diagram for conventional steel beam-column Junction

case of the beam-column junction with the SMA ring spring system, the maximum stress developed in the bolt is only 720 N/mm2 which is within the elastic limit. Stress occured in the flanges of column, beam, and endplate also lie in the elastic limit. This is due to the superelastic behavior and wedging action of SMA ring spring system. The stresses developed at the various elements of the beam-column junction are given in Table 3.

4 Conclusions SMA ring spring system is a novel alternative to the conventional bolt and washer system in the steel moment resisting frames. From the analytical study, the following conclusions were arrived.

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Fig. 10. von Mises stress diagram for steel beam-column junction with SMA Ring spring system

Table 3 Stress developed at various elements in the beam-column junction

Specimen

Conventional beam-column (N/mm2 )

Beam-column with SMA (N/mm2 )

Bolt

1018

720

Endplate

406

136.8

Column

392

98.2

Beam

347

82.9

• Under compressive loads, HSS inner ring get squeezed and SMA outer ring expand so the stress from inner ring was transferred to the outer ring due to wedging action. • Due to the superelastic behavior of the SMA outer ring, the stress gets released and the entire ring spring system comes back to its original position. • Comparing the stress–strain graph of steel ring spring system and SMA ring spring system, it was observed that the residual strain occurred in the steel ring spring

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system but the SMA ring spring system comes back to its original position without any residual strain. • The beam, column, endplate, and bolts of the conventional steel frame are yielded under dynamic acceleration with peak intensity of 0.35 g (Bhuj earthquake 2001). • But in the case of the beam-column junction with SMA ring spring system, under the same dynamic acceleration, beam, column, endplate, and bolts stresses lie within the elastic limit with no residual strain. It is due to the superelastic property of SMA and wedging force developed due to compression.

References 1. ATC (2000) FEMA 355E—State of the art report on past performance of steel moment-frame buildings in earthquakes. In: Fema-355 E, p 200 2. Song G, Ma N, Li HN (2006) Applications of shape memory alloys in civil structures. Eng Struct 28(9):1266–1274 3. Fang C, Zhou X, Osofero AI, Shu Z, Corradi M (2014) Superelastic SMA Belleville washers for seismic resisting applications: experimental study and modeling strategy. Smart Mater Struct 25(10):1–16 4. Wang W, Chan TM, Shao H (2015) Seismic performance of beam-column joints with SMA tendons strengthened by steel angles. J Constr Steel Res 109:61–71 5. Fang C, Wang W, Chen Y (2017) Self-centring behavior of steel and steel-concrete composite connections equipped with NiTi SMA bolts 150:390–408 6. Fang C, Wang W, Yang X, Chen Y, Eccles J, Sause R (2017) Innovative use of a shape memory alloy ring spring system for self-centering connections. Eng Struct 153(December):503–515 7. Auricchio F (2001) A robust integration-algorithm for a finite-strain shape-memory-alloy superelastic model. Int J Plast 17(7):971–990 8. Vemuri J, Kolluru S, Chopra S (2018) Surface level synthetic ground motions for M7. 6 2001 Gujarat erthquake. Geosciences 8:429. Doi: https://doi.org/10.3390/geosciences8120429

The Development and Study of Fiber Reinforced Fly Ash Bricks P. Prathyusha and Kolli Ramujee

Abstract Knowledge of the importance of environmental sustainability and overexploitation of nonrenewable resources in the field of civil engineering has brought tremendous growth in the research and development of various construction materials. One such alternate material is fly ash which is produced from the thermal industries as a waste material. Manufacturing of traditional clay bricks involves the extraction of high amounts of clay and also the removal of topsoil from the soil surface. Usage of such waste by-products extracted from various industries in the place of conventional construction materials is a forward step to reduce the substantial depletion of natural resources. The addition of fibers to concrete has proven to give higher results in terms of Mechanical Properties like compressive strength, flexural strength, etc. Similarly, one such development in bricks by adding fibers might bring higher performance and strength values. Since bricks are one of the basic components in the construction industry, they tend to bear bending loads in case of load-bearing walls and also are susceptible to Cracks. Hence parameters like compressive strength and durability of bricks alter the performance of walls. This paper shows the experimental program on properties like compressive strength, water absorption, and durability of fly ash bricks induced with different fibers like glass fibers and coconut coir in 1 and 2% (by weight of Fly ash). The composition of fiber reinforced fly ash bricks was 60% of fly ash, 10% of ordinary portland cement (OPC), and 30% of quarry dust. The Compressive strength of fiber reinforced fly ash bricks for 7 and 28 days, respectively, along with water absorption, impact resistance, and efflorescence are determined. Keywords Fiber reinforced fly ash bricks · Compressive strength · Nonrenewable resources · Glass fibers · Coconut coir fibers

P. Prathyusha (B) · K. Ramujee VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, India e-mail: [email protected] K. Ramujee e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_12

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1 Introduction In the building construction sector, materials like bricks, stones, clay, sand, cement, and gravel play a vital role in achieving strength parameters. These basic construction materials are extracted from natural resources directly or indirectly. Building bricks are the oldest and most extensively used building material. Manufacturing of bricks out of clay was proven to exist since the day of civilization. The depletion of natural resources for the production of construction has become an emerging issue globally. Especially the production of conventional bricks has lead to a worldwide shortage of natural resource materials. As a consequence, vast fertile land stretches are replaced by barren lands. The firing process indulged in the manufacturing of conventional clay bricks contributes to the atmospheric pollution making it a serious issue. The preference of bricks as a building material in the construction of structures has increased massively leading to substantial depletion of fertile landmasses and generation of air pollutants into the atmosphere. All such kind of arising environmental issues have urged to the advancement and search of innovative substitute building materials in the field of civil engineering. One such advancement in building materials is the Fly ash brick. Promoting the production of fly ash bricks reduces the emissions of carbon-di-oxide into the atmosphere. Balaraju Sivagnanaprakash et. al. [1] has also studied the hazards in clay brick and advantages in fly ash brick extending with a comparative study on material properties of clay brick and fly ash brick. Also, material processing of fly ash bricks requires less manpower and less area. Such kind of bricks can be used in road constructions, embankments, masonry walls, etc. These bricks reduce the usage of cement while plastering and during laying, which, in turn, reduces the cost of construction. Reinforcement of concrete using different kinds of fibers has proven to give higher strength values. Similarly, bricks reinforced with fibers dispersed throughout may give better strength values and helps to arrest initial crack formations. Cracks are always formed in the weak planes of masonry wall, since fibers are distributed throughout the brick iso-tropically, there will be no weak plane for a crack to develop and follow in walls as fibers obstruct the development of cracks in the brick. So, it is necessary to enhance the ductility of brick masonry in RC framed structures. The fibers which are used in the bricks are discontinuous, discrete acts as of reinforcing material and possess certain characteristics to arrest development of cracks. Generally, steel fibers, natural fibers, and synthetic fibers are used in the construction industry. Fibers help in increasing the tensile strength, durability, and toughness of the brick in brick masonry. Rajan Shikha et al. [2] used coconut fibers in enhancing the strength properties of concrete. Fiber reinforced fly ash bricks has weight approximately equal to conventional clay brick. It weighs around 2.6–3 kg per brick. Therefore, proper usage of fiber reinforced fly ash bricks promotes a sustainable environment.

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Fig. 1 Mixing of materials

1.1 Manufacturing of Fiber Reinforced Fly Ash Bricks Building bricks are the oldest and also the most extensively used building materials. Being a local material there exists considerable variations in the quality of raw material, their process of manufacture, and thereby in the quality of the finished product. The material composition used for fiber reinforced fly ash brick was 60% of Fly ash, 30% of quarry dust, 10% of ordinary Portland cement along with glass and coir fibers in 1 and 2%. All the batched materials were thoroughly mixed in a dry state. Water was added to the dry mixture to obtain the required consistency. The mixture or slurry was then fed into the brick molds of size 220 × 110 × 70 mm. The bricks were left for a day in the molds in a closed environment. After 24 h, bricks were de-molded and water cured (Fig. 1).

1.2 Methodology In order to bring uniformity in the quality and dimension of the bricks, Bureau of Indian Standards has laid down specifications for bricks. In this paper, a fiber reinforced fly ash brick of size 220 × 110 × 70 mm were taken for the study. The material property tests like water absorption, compressive strength, efflorescence, Impact resistance were conducted (Figs. 2–4).

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Fig. 2 Fiber reinforced fly ash bricks

Fig. 3 Interior of fly ash brick with coir fibers

Water absorption of bricks depends upon their porosity which is due to the presence of voids of various sizes. But a mere idea of water absorption or porosity is no indication as the brickwork will keep away the rainwater and protect the interiors from the deafness traveling from outside. When measured in accordance with the procedure laid down by IS3495-1992 (part 2), after immersion in cold water for

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Fig. 4 Interior of fly ash brick with glass fibers

24 h the bricks should have water absorption not greater than 20% by mass for class designation 12.5 and not greater than 15% by mass for higher classes. Compressive strength is an important parameter for the bricks, as they often had to withstand great compressive stresses. The durability of masonry structures largely depends on the strength parameters. The compressive strength of a standard brick should not be less than 3.5 Mpa. The water absorption and compressive strength of fiber reinforced fly ash brick were conducted as per IS 3495 (part 1 and 2); 1992 (Fig. 5). Soils used in the manufacturing of bricks should be free from harmful salts like Na and P. If such salts are present in the bricks then they will get dissolved when bricks come in contact with the moisture or water. When bricks containing such harmful salts are used as exposed surface then serious disfigurement shall occur. When such bricks are given a covering treatment, then the disruption of the surface takes place, this phenomenon is known as Efflorescence. Efflorescence is said to have occurred generally if certain white patches are found on the surface of the brick. The exact point where efflorescence will occur depends on the capillary properties of the material. Efflorescence test was conducted to determine the presence of salts confirming to IS 3495:1992.

1.3 Results and Discussions As per IS 3495:1992, the average compressive strength of a fly ash brick should not be less than 3.5 N/mm2 . The compressive strength of fiber reinforced Fly ash brick during the curing period of 7 and 28 days, respectively, is shown in Table 1 and Figs. 6–9.

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Fig. 5 Testing for compressive strength

Table 1 Compressive strength of fiber reinforced fly ash bricks with different fibers Compressive strength (N/mm2 )

Coir fibers

7 days of curing

1% 17.35

27.19

12.39

16.94

28 days of curing

31.05

33.47

20.24

24.79

Glass fibers 2%

1%

2%

The water absorption of fiber reinforced Fly ash brick with coir and glass fibers in 1 and 2% were determined confirming to IS 3495:1992. The value of water absorption reduced with the increase in the percentage of both the fibers. The values of water absorption are given in Table 2 and Figs. 10, 11. The depositions of white precipitates on the surface of the brick, when the salts present in the brick comes in contact with the water is known as efflorescence. Efflorescence test on FRF bricks was conducted confirming to IS 3495:1992.

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Fig. 6 Compressive strength of FRF bricks with 1% of coir fibers

Fig. 7 Compressive strength of FRF bricks 2% of coir fibers

Bricks with the addition of 1% of coir fibers showed moderate deposition of white precipitate on its surface. While the other bricks showed nil perceptible deposits of efflorescence. The deposition on the FRF brick with 1% of coir fibers is shown in Fig. 12. The Impact resistance test on FRF bricks with Coir and Glass fibers was conducted and the results are shown in Figs. 13 and 14.

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Fig. 8 Compressive strength of FRF bricks with 1% of glass fibers

Fig. 9 Compressive strength of FRF bricks 2% of glass fibers

1.4 Conclusions Depending upon the various tests performed to determine the material characteristics on fiber reinforced fly ash brick of size 220 × 110 × 70 mm, it concluded that FRF bricks gave better results in terms of Strength, environment, and economy to some extent. Since the base material used in making the FRF brick is fly ash, it helps in reducing the emission of greenhouse gasses into the atmosphere. The compressive strength of fiber reinforced brick with natural and artificial fibers was determined to be 33.4 N/mm2 for 2% of coir fibers and 24.79 N/mm2 for 2% of

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Fig. 10. Water absorption of FRF bricks with coir fibers

Fig. 11. Water absorption of FRF bricks with glass fibers

Glass fibers at 28 days of curing, which is 30% higher than the compressive strength of conventional fly ash bricks.

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Fig. 12 White precipitate on brick with 1% coir fibers

Fig. 13 Impact resistance of FRF brick with coir fibers

These reinforced bricks are durable and resulted in low water absorption values with the increase in the percentage of fibers, but the addition of more amount of fibers will make the brick more brittle. The addition of various fibers helps in increasing the resistance against initial crack strength. Fibers intercept the microcracks, thereby preventing the propagation cracks by controlling the tensile strength.

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Fig. 14 Impact resistance of FRF brick with glass fibers

Hence based on the strength and durability parameters of fiber reinforced fly ash brick, it is an environmentally sustainable alternative to conventional clay and fly ash bricks.

References 1. Sivagnanaprakash B, Murthi P, Sekaran A (2015) A study on structural applicability of fly ash brick with quarry dust-an ecofriendly alternative for clay bricks. Pol J Environ Stud 24(2):95– 699. Doi: https://doi.org/10.15244/pjoes/28357 2. Shikha R, Saxena AK, Jha AK (2015) Evaluation of compressive strength of concrete using coconut coir fiber. Int J Res Appl Sci Eng Technol (IJRASET) 3(IX). ISSN: 231-9653 3. IS 3495 (part 1 to part 4): 1992, Indian Standards Methods of tests of Burnt Clay Building Bricks 4. ASTM C67-13, Standard Test Methods for Sampling and Testing Brick and structural clay tile 5. IS 2212: 1991, Indian Standards Brick works-Code Of Practice (first Revision)

Seepage Behavior of Fiber Reinforced Embankment Fill: A Review V. P. Devipriya, S. Chandrakaran, and K. Rangaswamy

Abstract The earth structures like river embankments, levees, canal diversion structures, check dams, etc., have an important role in the irrigation and drainage projects. Construction of these earthen embankments with satisfying strength and stability requirements is a major challenge for the geotechnical engineers. One of the main reasons for the failure of the earthen structures is the piping erosion due to the seepage force from the water reservoir in the upstream side. Piping resistance of the embankment fill material is a major parameter that influences the stability of the structure, hence proper treatment is to be given to the fill material to enhance the seepage and piping resistance. The fiber reinforcement is one of the widely accepted methods of ground improvement. There are some studies that are focused on the seepage behavior of embankment made with fiber reinforced soil. The main aim of this paper is to review the possible applications of fiber reinforced soil as fill material for earth embankment which is more susceptible to seepage failures. With reference to the previous studies, a critical comparison is done in this paper to evaluate the relative importance of different parameters on the behavior of fiber reinforced embankment fill. Keywords Piping resistance · Seepage · Critical hydraulic gradient · Fiber reinforcement

1 Introduction Critical attention is to be given for ensuring the stability of water retaining earthen structures like earth dams, river levees, check dams, canal diversion structures, etc,. since the failure of these structures will result in a rapid flood and will be a threat to the life of people. From statistical analysis of previous case, it was observed that the seepage erosion in the form of piping is the primary reason for the failure of these hydraulic structures [1]. The seepage failure occurs due to the seepage force exerted V. P. Devipriya (B) · S. Chandrakaran · K. Rangaswamy Department of Civil Engineering, NIT Calicut, Calicut, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_13

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by the flow of water through the structure and will result in internal erosion and loss of fine particles from the soil sample. Continuous erosion of the soil particle will lead to the formation of the channel inside the soil formation and result in sudden failure of the structure. The studies conducted by researchers shown that the piping phenomena is most common in loose soil material due to its high permeability. The gradation, clay content, compaction density of the fill material has a significant influence in the piping behavior [1–3]. The selection of the fill material which is more resistant to seepage failures is an important step during the construction of earth embankment. The commonly used methods to improve the piping resistance of the earth fill include the construction of impervious blanket, soil improvement, filter layers inside the embankment fill, etc. In addition to these methods, the random distribution of fiber materials is also found to be an effective method for improving the piping resistance of the soil. Reinforcement of soil with the use of fiber material is an effective and reliable method of ground improvement which is commonly used during the construction of different structures like retaining wall, embankments, pavements, for stabilization of ground beneath the footing, etc. Both natural fibers like coir, jute, sisal, etc., and synthetic fibers like polypropylene, nylon, glass, etc., are the widely used fiber reinforcing element. Most of the previous studies were focused on the changes in the strength parameters of the fiber reinforced soil like friction angle, cohesion, compressive strength, stress–strain characteristics, penetration resistance, tensile strength, etc. Many researchers [4–9] observed that there is a significant increase in the strength and stiffness characteristics of the soil when fiber materials are randomly distributed into the soil. They have concluded that the interaction between the fiber and the soil particle is having a major role in enhancing the strength parameters of the sample. The relative importance of different parameters like fiber type, fiber aspect ratio, soil type, fiber content, etc., on the strength improvement was evaluated in these studies. The hydraulic response of the fiber reinforced soil formations are also studied by many researchers [10–12], and they have evaluated the possible application of fiber reinforced soil in barrier systems. In these studies, they have concluded that the fiber reinforcement is an effective method for improving the strength characteristics of the barrier systems without compromising the permeability of the same. In recent times many of the researchers are focused on the effectiveness of random fiber reinforcement of soil as piping erosion control measure, and to improve the stability of hydraulic structures. The random distribution of fibers into the soil will increase the strength characteristics of the soil, without forming weak zones inside the fill. This will contribute to improving the piping resistance of the reinforced fill material [13]. Both laboratory and large-scale model studies were conducted by many researchers to evaluate the seepage and piping behavior of soil-fiber composite, and they have shown that the addition of fiber into soil caused significant changes to the seepage behavior of soil and improved the resistance of soil material against internal erosion. The effectiveness of this method will depend upon the characteristics of both fiber and soil material. The primary objective of this paper is to review the effectiveness of the fiber reinforced soil sample as a piping resistant material and

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to use it as a material for the construction of hydraulic structures. By reviewing the previous literature available, an analysis of the influence of fiber and soil properties on the characteristics of fiber reinforced embankment fill material is also included in this paper.

2 Literature Review The application of the fiber reinforced soil as a seepage resisting material in the earthen dams was first introduced by Furumoto et al. [14]. Recently, many researchers have focused to study the influence of fiber reinforcement on the seepage behavior of the different types of soil formation. The influence of different parameters like fiber aspect ratio, fiber properties, Dosage of fiber, soil properties, etc., on the seepage characteristics of the fiber mixed soil were explained in the previous studies.

2.1 Influence of Fiber Content on the Piping Resistance Furumoto et al. [14], have evaluated the piping behavior of sandy soil mixed with synthetic polyethylene fibers with varying percentages (0–0.4%). They have observed that the critical hydraulic gradient value of the sample was improved 2.2 times with the addition of 0.4% fiber. Similar studies were conducted by Sivakumar Babu et al. [15], coir fiber reinforced cohesionless soil. The content of fiber was varied from 0 to 1.5%. They have concluded that with an increase in the fiber content, the piping resistance of the sand and red soil was improved by increasing the critical hydraulic gradient value. Yang et al. [16], also conducted a piping study on polypropylene fiber mixed sandy soil, and they have obtained 1% as optimum fiber content. Instead of cohesionless soil Das et al. [17], conducted similar studies on the fly ash, which is more susceptible to seepage erosion by conducting a series of piping tests. They have used synthetic polypropylene fibers as the reinforcing element. In this study, they have added fibers in a very small quantity varying from 0.05 to 0.1%. The maximum value of the critical hydraulic gradient was obtained at 0.05% addition of fiber. Further increase in the fiber content does not result in significant changes in the piping resistance of the soil. Das and Viswanadham [18] used polyethylene fibers for reinforcing the silty sand and evaluated the piping resistance of the mix. They have obtained a maximum improvement at 0.1%, and the further increase in the fiber content reduced the piping resistance value. Estabragh et al. [19], also evaluated the piping behavior of fiber reinforced silty sand by varying the fiber content between 0.5 and 1.25%. They have obtained a maximum value of critical hydraulic gradient at 1% of addition but the further increase does not make significant changes in the result. In general, for all types of soil, the increase in the fiber content resulted in significant improvement in the piping resistance of the soil. However, for a particular type of soil with the use of a similar type of fiber, the optimum fiber

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content has a wide variation that was resulted due to the changes in the fiber aspect ratio.

2.2 Influence of Fiber Aspect Ratio on the Piping Resistance One of the important parameters that influence the piping resistance of the fiber reinforced soil is the aspect ratio of the fiber. In the laboratory piping test conducted by Sivakumar Babu and Vasudevan [15], they have used naturally available coir fibers with the varying aspect ratio as an additive for soil. The diameter they have used was constant with a value of 0.25 mm and length was varying from 40–60 mm. They have concluded that the addition of fibers into the soil substantially reduced the seepage through the soil, and improved the piping resistance of the reinforced soil. The fiber length was a significant parameter that causes changes in the behavior of the reinforced soil. Maximum improvement in the piping resistance was observed for the sandy soil reinforced with coir fiber having a length of 50 mm. Further, an increase in the fiber length causes a decrease in the piping resistance value due to the nonuniform distribution of lengthy fibers. Similar results were observed for the red soil reinforced with coir fibers. The diameter of the synthetic polyester fiber used in the study conducted by Das et al. [17], for reinforcing fly ash material was very small in the order of micrometers (30–50 µm) and the length was varied from 10 to 75 mm. They have concluded that the critical hydraulic gradient at which piping initiates was increased with the increase in dosage and length of the fiber mixed with soil. The highest value of the critical hydraulic gradient was observed for a fiber length of 50 mm. In a similar study conducted by Das and Viswanadham [18], they have used polypropylene and polyester fibers with varying length (25 and 50 mm) and a constant diameter of (30 µm). For the silty sand also the optimum length of the fiber material was found to be 50 mm. A 40% increase in the critical hydraulic gradient value was observed with an increase in the fiber from 25 to 50 mm. Estabragh et al. [20], stated that the use of small diameter synthetic fibers will have difficulty in implementing in the field conditions, and hence they have used large diameter polyester and polyethylene fibers (0.2 mm) with three different lengths: 5, 25, and 35 mm for reinforcing the silty sand. They have observed that at lower fiber content the length of fiber has no significant effect on the piping behavior. However, as the length of fibers increased they observed an increase in the critical hydraulic gradient value of the sample. But in studies conducted by Yang et al. [16], they have used relatively shorter fibers (6, 9, and 19 mm) for improving the piping resistance of the sandy soil. They have concluded that the effect of fiber length on the improvement was less significant than other parameters like dosage and density of the fill. Seepage studies were conducted by Akay et al. [21], on the slope models constructed with polypropylene fiber reinforced sandy soil and they have evaluated the stability conditions of the reinforced slope. For this study, they have used short fibers of length 6 and 12 mm and a diameter of 32 µm. The maximum factor of safety was obtained for the slope reinforced with 12 mm fiber. In the majority of the previous

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studies, the optimum length of fiber for improving the hydraulic performance was selected within the range of 40–50 mm. Das et al. [17] stated that when very short fibers (about 10 mm) are used, the rate of improvement of the piping resistance will be less significant since there will not be adequate contact between the soil and fiber. The effect of the diameter of the fiber material in the seepage behavior is not clearly explained in the previous studies. The use of fibers having a small diameter as a reinforcing element is more effective to improve the piping resistance of soil since there will be a higher number of fibers per volume of soil fill [19]. The presence of more number of fibers in the soil will increase the contact area between the fibers and soil, which leads to improvement in the piping resistance. In the studies conducted by Sivakumar Babu and Vasudevan [15], in the sand reinforced using large diameter coir fiber (in the order of millimeters), the rate of improvement on piping resistance was comparatively less than the obtained for the sand reinforced with small diameter synthetic fibers [14]. But while considering the practical applications, the small diameter fiber reinforcement will be difficult to implement hence while selecting the fiber material we should consider field applicability also. However, the data obtained from the previous literature is not sufficient to make a conclusion about the optimum value of fiber diameter to get maximum improvement in the piping resistance. Another important conclusion made by Estabragh et al. [20], was that the significance of the fiber content on the piping behavior was more pronounced than the fiber aspect ratio in the case of smaller diameter fibers, but while using higher diameter fibers both fiber content and aspect ratio has a similar influence on the piping resistance of the soil-fiber mix.

2.3 Influence of Fiber Type on the Piping Resistance The physical properties of the reinforcing fiber is also a major parameter that affects the seepage resistance of the soil-fiber composite. Few researchers have conducted studies on the influence of the different types of fibers on the hydraulic performance of the soil. Das et al. [17], conducted studies on soil reinforced with polyester and polypropylene fibers and evaluated the piping behavior of soil in two cases. They have concluded that the fibers having low specific gravity value show a maximum improvement because at a particular dosage the fiber volume will be higher for the lightweight fibers. The preparation of a uniform mixture of soil and fiber was easier with the use of more flexible fibers hence higher improvement was observed in the piping resistance. Estabragh et al. [19], also studied the influence of fiber type on the piping resistance of the silty sand. They have also obtained a similar conclusion, that polyethylene fiber with low specific gravity show a maximum improvement than the polyester fiber of higher specific gravity. But in general, the influence of fiber type on the piping resistance is not significant when compared with that of the fiber aspect ratio. Raja et al. [22], studied the piping behavior of fly ash mixed with waste plastic fibers and geogrid waste. They have observed the maximum value of

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the critical hydraulic gradient for the soil reinforced with geogrid waste than that of waste plastic fibers. A 29% improvement in the critical hydraulic gradient value was obtained for soil reinforced with waste geogrid pieces. This was due to the higher shearing resistance between the geogrid and soil particles.

2.4 Influence of Properties of Reinforced Soil on the Piping Resistance The index and engineering properties of the soil will also affect the seepage characteristics of the fiber reinforced soil. Most of the previous studies were focused on the seepage behavior of the fiber reinforced silty sand and sandy type soil formations. The gap graded soil containing fine and coarse soil particles are more susceptible to internal erosion [1, 23]. Hence the presence of fine content in the soil has significant influence in the seepage behavior of soil formation. Das et al. and Estabragh et al. [18–20], have conducted a seepage test on the silty sand with fiber reinforcement. Among these studies with the use of polypropylene fiber reinforced silty sand, Das et al. [18], obtained more improvement in the critical hydraulic gradient value. The presence of clay content (10% clay) in the silty sand used in their study was found to be responsible for the higher improvement in critical hydraulic gradient. The presence of the clay particle has a significant influence on the hydraulic performance of the fiber reinforced soil [16, 18]. While comparing the rate of improvement in the silty sand and sandy soil mixed with a similar type of fibers, the silty sandy type soil obtained higher improvement than the sandy soil [12, 14]. Similarly, onedimensional piping test conducted by Sivakumar Babu et al. [15], have shown that the improvement in the piping resistance value was significantly higher for red soil mixed with coir fibers than the fiber mixed sandy soil. However, the study conducted by Das et al. and Raja et al. [17, 22] conclude that the rate of improvement in the piping resistance was higher for fiber reinforced soil samples than the fiber reinforced fly ash samples. This observation may be due to the presence of smooth and rounded nature of the fly ash particle.

3 Conclusion From the review of the literature on seepage behavior of fiber reinforced soil, the following conclusions are drawn: • The reinforcement of soil with the randomly distributed discrete fibers increased the piping resistance, and hence found to be an effective method for improving the stability of hydraulic structures.

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• The improvement in the piping resistance value was reported to be a function of both fiber characteristics (Fiber content, Fiber length, and diameter, other physical properties of fiber) and soil characteristics. • Depending upon the soil type and properties of the reinforcing fiber, the optimum percentage of fiber content and optimum length of the fiber was varied, however, it was observed that more lengthy fibers and higher dosage of fibers have a negative effect on the piping resistance of the soil. • Fibers having a length less than 50 mm and dosage within 1% is found to be effective for most of the soil, but while using fibers having a very small diameter (in the range of micrometers) the optimum fiber content was in the range of 0.1%. An increase in fiber content and length beyond these values resulted in the accumulation of fiber in different locations. • The fibers of low specific gravity and having more flexibility is found to be more effective for increasing the piping resistance. • The efficiency of the fiber reinforcement for increasing the critical hydraulic gradient value was more pronounced in the case of soil containing small percentages of silt and clay size particles. Most of the previous studies were only focused on the piping behavior a particular type of soil mixed with a fiber by varying the length parameters. A comparison of the effect of fibers on the different types of soils is not available in the previous studies.

References 1. Foster M, Fell R, Spannagle M (2000) The statistics of embankment dam failures and accidents. Can Geotech J 37(5):1000–1024. https://doi.org/10.1139/t00-030 2. Ojha CSP, Singh VP, Adrian DD (2003) Determination of critical head in soil piping. J Hydraul Eng 129(7):511–518. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:7(511) 3. Sherard JL, Dunnigan LP, Talbot JR (1984) Basic properties of sand and gravel filters. J Geotech Eng 110:684–700. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:6(684) 4. Al-Refeai TO (1991) Behavior of granular soils reinforced with discrete randomly oriented inclusions. Geotext Geomembr 10(4):319–333. Doi: https://doi.org/10.1016/02661144(91)90009-L 5. Gray DH, Ohashi H (1983) Mechanics of fiber reinforcement in sand. J Geotech Eng 109(3):335–353. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:3(335) 6. Maher MH, Gray DH (1990) Static response of sands reinforced with randomly distributed fibers. J Geotech Eng 116(11):1661–1677. https://doi.org/10.1061/(ASCE)0733-9410(199 0)116:11(1661) 7. Michalowski RL, Zhao A (1996) Failure of fiber-reinforced granular soils. J Geotech Eng 122(3):226–234. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:3(226) 8. Waldron LJ (1977) The shear resistance of root-permeated homogeneous and stratified soil 1. Soil Sci Soc Am J 41(5):843–849. https://doi.org/10.2136/sssaj1977.036159950041000 50005x 9. Zornberg JG (2002) Discrete framework for limit equilibrium analysis of fibre-reinforced soil. Géotechnique 52(8):593–604 10. Divya PV, Viswanadham BVS, Gourc JP (2018) Hydraulic conductivity behaviour of soil blended with geofiber inclusions. Geotext Geomembr 46(2):121–130. https://doi.org/10.1016/ j.geotexmem.2017.10.008

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11. Fowmes GJ, Dixon N, Jones DRV (2006) Use of randomly reinforced soils in barrier systems. In: Thomas HR (ed) Proceedings of 5th international congress on environmental geotechnics, vol. 2. Thomas Telford (Pubs), London, pp 709–716 12. Miller CJ, Rifai S (2004) Fiber reinforcement for waste containment soil liners. J Environ Eng 130(8):891–895. https://doi.org/10.1061/(ASCE)0733-9372(2004)130:8(891) 13. Sivakumar Babu GL, Vasudevan AK (2007) Evaluation of strength and stiffness response of coir fiber reinforced soil. J Ground Improv 113:101–110 14. Furumoto K, Miki H, Tsuneoka N, Obata T (2002) Model test on the piping resistance of short fiber reinforced soil and its application to river levee. In: Gourc, Girard (eds) Geosynthetics-7th ICG-Delmas, pp 1241–1244 15. Sivakumar Babu GL, Vasudevan AK (2008) Seepage velocity and piping resistance of coir fiber mixed soils. J Irrig Drainage Eng 134(4):485–492. Doi: https://doi.org/10.1061/(ASCE)07339437(2008)134:4(485) 16. Yang KH, Adilehou WM, Jian ST, Hsiung BC (2018) Experimental study of fiber-reinforced sand subject to seepage. In: Proceedings of the 2nd international symposium on Asia Urban geoengineering. Springer, Singapore. pp 49–62. Doi: https://doi.org/10.1680/jgein.17.00017 17. Das A, Jayashree C, Viswanadham BVS (2009) Effect of randomly distributed geofibers on the piping behaviour of embankments constructed with fly ash as a fill material. Geotext Geomembr 27(5):341–349. https://doi.org/10.1016/j.geotexmem.2009.02.004 18. Das A, Viswanadham BVS (2010) Experiments on the piping behavior of geofiber-reinforced soil. Geosyn Int 17(4):171–182. https://doi.org/10.1680/gein.2010.17.4.171 19. Estabragh AR, Soltannajad K, Javadi AA (2014) Improving piping resistance using randomly distributed fibers. Geotext Geomembr 42(1):15–24. https://doi.org/10.1016/j.geotexmem. 2013.12.005 20. Estabragh AR, Soltani A, Javadi AA (2016) Models for predicting the seepage velocity and seepage force in a fiber reinforced silty soil. Comput Geotech 75:174–181. https://doi.org/10. 1016/j.compgeo.2016.02.002 21. Akay O, Özer AT, Fox GA, Wilson GV (2018) Fiber reinforced sandy slopes under groundwater return flow. J Irrig Drainage Eng 144(5):04018004. https://doi.org/10.1061/(ASCE)IR.19434774.0001300 22. Raja J, Siva Kumar Babu GL (2011) Piping and seepage resistance of fly ash mixed with plastic waste. In: Proceedings of Indian geotechnical conference, vol. 15 23. Skempton AW, Brogan JM (1994) Experiments on piping in sandy gravels. Geotechnique 44(3):449–460. https://doi.org/10.1680/geot.1994.44.3.449

Ground Improvement with Stone Columns–A Review Revathy Manohar and Satyajit Patel

Abstract Soil improvement is rapidly gaining importance due to the paucity of good quality land for development, structures, and transportation infrastructures. A range of soil improvement methods is available amongst which stone column is one of the most efficient and effective techniques. It is generally used to improve soft and weak soil, having less bearing capacity, high compressibility, and high settlement. The improvement is due to its higher stiffness compared to the surrounding ground, and it is measured in terms of stiffness improvement factor. The stone column is designed as per IS 15284-2003 and is usually analyzed by using the unit cell concept. They are generally constructed using crushed stone aggregates and are ideally installed in an equilateral triangle pattern. The failure of the stone column is dependent on its critical length. This review paper is aimed to study some exemplary practices done while designing, constructing, or installing the columns. It also intends to analyze the effects of these practices, which include the pros and cons of each method. Some modifications include geotextile or geosynthetic-encased stone columns, rubber-drained columns, lime-fly ash columns, lime-mortar soil columns, and a column for liquefaction mitigation. Hence, it aims to access the suitability of these practices in the coming future to have increased effectiveness and overall efficiency. Further, some suggestions are made regarding the construction practices which may be pertinent in the near future. Keywords Stone column · Geosynthetic-encased columns · Lime columns · Dynamic response

R. Manohar (B) · S. Patel Sardar Vallabhhai National Institute of Technology, Surat, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_14

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1 Introduction Rapid urbanization has resulted in the scarcity of land having excellent geotechnical properties. As a result, engineers are forced to make constructions on weak soil. However to facilitate this, we have to either adopt deep foundations (like pile foundation) or make soil improvement, which can be mainly done by ground reinforcement, ground improvement, and ground treatment. Deep foundations are not feasible in all the cases chiefly due to economic considerations; therefore, soil improvement is the only solution in such cases. Soil improvement will help us to achieve improved bearing capacity, reduced settlements, and reduced liquefaction potential. If a structure has fewer stories and it can withstand a considerable amount of settlement (e.g., liquid storage tanks), then soil improvement is the most suitable option. Improvement of soil using a stone column is one of the most efficient and effective techniques. It is advantageously used in soft and compressible soil. It can improve the overall strength, stiffness, drainage, and consolidation rate. It can also reduce the pore water build up and can be used in liquefaction mitigation in earthquake-prone areas. A range of physical model studies, numerical analysis (using software like PLAXIS 3D and FLAC), and full-scale laboratory testing were conducted to predict the behavior of the improved strata.

1.1 Role of Stone Columns in Soil Improvement Stone column is mainly employed to improve soft soils, where it will act as reinforcement, thereby helping to improve the effective stiffness of the ground. Stone columns can be categorized into three, namely, flexible, semi-rigid, and rigid columns, where they are classified based on the material used for constructing the columns. If the material used for construction is stone, aggregates, etc., it is having a large number of voids in it, as a result of which it will deform and therefore falls into the flexible category. On the other hand, if it is made of concrete, voids are less, and it will not allow large deformation. Therefore, it is classified as rigid columns. And if the material used is neither too rigid nor too flexible, then it can be classified as semi-rigid columns (Fig. 1).

1.2 Design and Construction of Stone Columns Design and construction of stone columns are done as per the guidelines laid by IS 15284 [2]. It is usually constructed using vibroflotation techniques, with the help of vibrofloat. It can also be installed using the Franki method, wherein a steel casing is driven into the ground, and gravel is packed from the top which is compacted by means of a drop hammer (Fig. 2).

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Fig. 1 The effectiveness of stone column Source Som and Das [1]

Fig. 2 Vibro-replacement installation of the stone column using dry method. Source Bouassida et al. [3]

2 Basic Design Parameters (as Per IS 15284 [2]) Stone column diameter: In general, softer the soil larger the diameter so as to withstand the lateral displacement effected by the compaction during the installation process. It is also dependent on soil type, undrained shear strength, type of backfill material, and the method of construction. Installation Pattern: Usually, group columns are installed in a square or triangular pattern; equilateral triangle pattern is preferred as it gives a dense packing. Spacing: There are no specific guidelines regarding column spacing; it is site specific.

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Equivalent diameter: For each stone column, the neighboring soil forms a regular hexagon surrounding the column. It can be nearly approximated by an equivalent circular area with an equal total area. The diameter of this circle is given by Dc = 1.05 S for equilateral triangle pattern, = 1.13 S for square pattern. where S = spacing between the columns. Hence, formed equivalent cylinder in the composite ground will have a diameter of Dc, enclosing the neighboring soil as well as the stone column called unit cell (Fig. 3). Area Replacement Ratio (as): For the analysis of stability and settlement, the composite ground, which represents a widely loaded area, can be modeled with the aid of unit cell concept that comprises of the stone column and tributary soil which surrounds the column. To represent the amount of soil that has been replaced by the stone, as is used which is given by

Fig. 3 Unit cell concept. Source Barksdale and Bachus [4]

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as = As/A = As/(As + Ag)

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(1)

where As = area of the stone column, Ag = area of soil surrounding the stone column, A = total area enclosed by the unit cell. Stress Concentration Factor (n): As the stone column is stiffer compared to the neighboring soil, higher stress will be developed in the stone column. This stress concentration factor, n, developed due to external load applied to the soil σ, can be defined as the ratio of the average stress in the column (σ s) to stress developed in the ground that is contained within the unit cell (σ g) i.e., n = σ s/σ g

(2)

It usually ranges between 2.5 and 5. It is directly proportional to consolidation time and its value decreases along the stone column length. If the application of load to the composite ground is through a rigid footing, n value will be comparatively high. Failure Mechanisms: Failure of a single-loaded stone column is mainly dependent on the column length. For stone columns with the length more than its critical length (that is 4 times its diameter), the stone column will fail due to bulging, whereas the shorter column will fail due to general shear failure; if the column is end bearing type, a floating column will fail due to punching shear (Fig. 4).

Fig. 4 Stone column failure mechanisms. Source Barksdale and Bachus [4]

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3 Modifications in Stone Columns 3.1 Geosynthetic-Encased Stone Columns Nowadays, the stone column is increasingly being employed as an economical and environment-friendly alternative of soil improvement, mainly aimed at improving soft soils like silt, clay, and silty sands. However, for very weak soils (with Cu < 15 kPa) due to insufficient confinement, the generation of additional confinement requires the generation of radial deformations for the stone column, which can result in the failure of the same. Therefore, in order to prevent this, there is a need for enhancing lateral column confinement and enhancing the bearing capacity. This is accomplished by encasing the stone column with high stiffness and creep-resistant geosynthetic popularly known as geosynthetic-encased stone columns (GECs). Also, this encasement does not allow lateral squeezing of the aggregates out of the columns, thereby facilitating the minimal loss of aggregates as well as the faster installation of the stone column [5]. The encased stone columns concept was proposed by Van Impe in 1985. The advantages of encased stone columns in weak, collapsible soil were studied by Ayadat and Hanna [6]. Providing a geosynthetic encasement to the stone column helps them to have improved strength and stiffness. Various laboratory studies have been conducted to access their performance. The testing was done with the help of a model study in the laboratory. After installing the encased stone column in a tank, the experimental setup was placed in a loading frame and load was applied by means of a loading plate. The strain rate was 1.2 mm/min. The experiments were conducted by applying load over the stone column area in order to evaluate the advantages due to the encasement. A dial gauge was employed to measure the settlement of encased stone columns at suitable time intervals. The pressure acting on the stone column for various displacements has been measured by means of a proving ring. Quick and undrained loading simulated the actual field conditions. The diameter of the column was varied and three experiments were conducted. The first series of experiments were performed on clayey soil without stone columns; the second series of experiments were conducted on an ordinary stone column without any encasement. The third series of tests was on done on a geosynthetic-encased stone column. In both cases, column diameters have been varied and they were analyzed. And for the encased column, the type of geosynthetic encasement was also varied. The results were analyzed to obtain the relative performance as well as the improvement in load-carrying capacity of the stone columns [5] (Figs. 5 and 6). On comparing the obtained results, significant improvement was observed in terms of strength as well as stiffness of the stone column due to the encasement using geosynthetic. Based on the experimental observations, some design guidelines for geosynthetic-encased stone columns were suggested. The significant conclusions made are: (1) the geosynthetic encasement increased the load-carrying capacity of columns (by about three–five times) depending on the stiffness of geotextile used for

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Fig. 5 Variation of pressure with the diameter. Source Murugesan and Rajagopal [5]

Fig. 6 Load settlement curve for stone column (75 mm diameter) for different types of geosynthetic encasements. Source Murugesan and Rajagopal [5]

encasement. The pressure–settlement behavior of the geosynthetic-encased stone columns exhibited a linear behavior; implying that the failure is not catastrophic, unlike that of the conventional stone columns. (2) The diameter of the stone column controls the improvement in load-carrying capacity due to the encasement and it is inversely proportional. (3) The design guidelines for geosynthetic-encased stone columns are based on hoop tension theory [5] (Fig. 7). Some researchers have performed 3D analysis of encased stone columns. They had analyzed the effect of various parameters on the behavior of encased stone columns Fig. 7 Design charts for geosynthetic-encased stone columns. Source Murugesan and Rajagopal [5]

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by conducting 3D numerical analysis. Parametric studies were conducted for investigating the effects of various factors such as stiffness of geosynthetic encasement, modulus of elasticity, diameter of the stone column, and angle of friction of the material of the column on the behavior of encased column group. The numerical study was done with the aid of FEM modeling. After the detailed analysis, the authors made the following conclusions: • The settlement as well as lateral deformation of stone column can be controlled and adequate performance of the ground improvement system can be obtained by encasing a selected number of stone columns. The positioning of the selected set of stone columns depends on loading distribution and foundation stiffness. • There was an increase in the column stiffness with the increase in stiffness of the geosynthetic encasement. This, in turn, resulted in improved group performance of GECs. • From the numerical analysis, it was evident that with the increase in the angle of internal friction of the material, there was an increase in the column resistance against failure, and also the settlements and lateral deformations of the column decreased. Also, the performance of GECs was least affected by the internal friction angle of the material. • The sensitivity of the capacity of group encased columns to the variation of elasticity modulus of the material of the column was comparatively small. • With the increased diameter of the stone column, there was a decrease in the effect of the encasement possibly due to the increased lateral deformations. Also, the increased column diameter without altering the spacing was found to be equivalent to an increase in the effective Area Replacement Ratio of the group of stone columns. This had an increased effect on the group performance of GEC and resulted in an enhancement of the bearing capacity of the group [7]. The cyclic response of GECs was also studied. In a study done to analyze the settlement and bearing capacity behaviors of geosynthetic-encased stone column foundation, it was tested for both static and cyclic cases with area ratios of 4, 12, and 16% using small-scale models with scales of 1:6.5, 1:11.5, and 1:13 and fullscale models with the scale of 1:1. The cyclic loading was conducted in two stages as indicated below, the first sequence indicates low height embankment [i.e., low preloading pressure (25 kPa) and high cyclic stresses were expected on the soil (62.4 kPa)], in the second sequence of cyclic loading to simulate a high embankment done by applying low cyclic stress with an amplitude of 30.5 kPa and high preloading pressure 100 kPa). After the completion of the loading stages, the specimen has been subjected to an increase in static loads up to failure [8] (Fig. 8). The results showed that at the same stress levels, there was a higher settlement for dynamic or cyclic loading compared to static loading cases. It was also observed that during the first loading cycle, the settlement occurred very fast when compared to the second loading cycle. The authors confirmed that for a constant area ratio of 12%, loading stress 100 kPa, and model scale of 1:6.5 testing done on a geotextile coated stone column has reduced the settlement by more than 30% compared to that of the uncoated one [8].

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Fig. 8 The sequences of cyclic loading for railway embankment. Source Raithel et al. [8]

Various numerical and analytical studies were performed on geotextile-encased stone columns in the past to analyze its behavior, among which some were focused on the parametric study, which intended to analyze the effect of stiffness of geotextile encasement or the effect of geotextile encasement length. The numerical analysis done was mostly 2D simulations; a few were 3D as well [5, 7]. Several experimental investigations were carried out on the geotextile-encased stone columns to find the effect of geotextile encasement. It was done by performing small-scale laboratory experiments; by means of large diameter oedometric cells. It was aimed to analyze the variation of total stresses, pore water pressures, and settlements during consolidation. To achieve this, stress distribution in the soil column, pore pressure, and deformations in the soil were measured during the whole consolidation process. Various parameters were measured on a horizontal slice of a representative “unit cell” during the small-scale laboratory tests. The results indicated that the vertical stress carried by the encased column is approximately 1.7 times that carried by the non-encased one. It was also concluded that the stress concentration factor for encased columns lies between 11 and 25, which was a higher value compared to that of conventional stone columns (which is in the range of 3–6). Thus, it can be said that the stress concentration factor of encased columns, is almost double or four times that of conventional stone columns. In the case of samples with geosyntheticencased stone columns, the horizontal stress on the soil was found to be 30% less than that with conventional stone columns. Lastly, the improvement in terms of settlement was presented by means of settlement reduction factor (which is the ratio of deformation in the soils improved by means of stone columns to the deformation of untreated weak soil). The value was approximately 0.6 for the ground improved using the geosynthetic-encased stone column and was 0.8 for ground improved using the conventional stone column. The rate of consolidation also exhibited noticeable variations like the rate of dissipation of pore water pressure was 30% higher for samples having encased columns compared to those having conventional stone columns [9].

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The effect of geotextile encasement on the column performance has been assessed with the help of a drained triaxial compression test conducted on encased as well as non-encased gravel samples. The tests have been conducted on two sets of samples packed at different densities and two different types of geotextile. It was conducted at four different values of confining pressures–25, 50, 150, and 300 kPa. This study was mainly intended to find the strength gained by the encased samples compared to the conventional samples, additional confining pressure due to geotextile, and also to study the mobilized friction angle of gravel. Test results indicated an enhancement in the values for geosynthetic-encased gravel columns. The improvement was found to be more significant at lower values of confining pressure (in the range of 7.5–9.5 (based on density and the type of geosynthetic) for a confining pressure of 25 kPa and at an axial strain of 14%, 2.5 (approximately same for both the densities and geotextile) for a confining pressure of 300 kPa). The value of radial strain was also lower in the encased sample when compared to the non-encased samples. For 20% axial strain, the radial strain for geosynthetic-encased samples was around 6–7%; whereas in the case of non-encased samples, it ranged from 9 to 16.5%, according to the confining pressure [10]. The encased stone column group was also studied for analyzing the effect of the arrangement of the stone column in a group and the influence of column length. This was done by conducting 2D, 3D analysis using FEM in order to analyze the performance of the encased stone column groups beneath the rigid footing. As in the usual practice, the bonding between the columns, encasements and the soil was perfect at the interfaces in the FEM model, and this is due to their tight interlocking. Rigid footing assuming to be rough was modeled as a stiff plate having uniform settlement. For the footing, the finite elements used were 5-noded line elements (2D) and 6-noded triangular elements (3D). The elements had both rotational as well as translational degrees of freedom having their basic properties such as normal stiffness and flexural rigidity. Modeling was done using a staged construction process. The foundation settlement and stresses developed in the soil, column, and the encasement have been studied. Numerical analysis results showed that keeping the area replacement ratio and the ratio of encasement stiffness to the diameter of column constant, the arrangement of the stone column (number as well as the position of the columns) have a minor effect on the overall reduction in the settlement. For higher values of the stiffness of the encased material, it will be more beneficial to place the column near the edges of the footing on account of reduction in the settlement; but on the other hand, the maximum hoop force developed at the encasement will be considerably high. Some simple and modified approach to study the group of encased columns was also proposed accordingly. All columns in the group were converted into a single central column in this method. After analyzing this modified column model, it was concluded that there is a critical column length for fully encased stone columns in homogeneous soil, for controlling the deformations; and it was found to be about twice to thrice the footing width. Also, it was concluded that the critical encasement length for the partially encased stone column was lesser compared to that of fully encased stone columns. It was evident that column position had more influence compared to the number of columns which is due to the following reasons:

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(1) Edges of the rigid footing will have higher vertical stresses; due to which the stone columns at the edges will support more load. (2) Secondly, the columns at the center have more lateral confinement. These two effects will balance one another, and based on the case, one will be more beneficial compared to others. Also, for the floating columns, there is an additional effect–(3) Penetration or punching of the column into the soil underneath. These effects add to the increase in differences among various arrangements of the column and also it will disappear as soon as the column length is increased beyond the critical length [11] (Figs. 9 and 10). The performance of geotextile-encased granular columns under lateral loading was accessed by performing the shear test. The main aim of the experimentation was to study the effect of encasement on the lateral load-carrying capacity of the

Fig. 9. 2D and 3D FEM models (reference case). Source Castro [11]

Fig. 10 Critical partial encasement length for various encasements, area replacement ratios and soil properties (reference case). Source Castro [11]

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Fig. 11 Different types of shear failures for encased columns. Source Mohapatra et al. [12]

encased columns. Numerous box shear tests were conducted on the columns with encasement as well as without encasement. It was conducted in a shear box with a plan area of 305 × 305 mm. Testing was done at varying values of normal pressure (ranging between 15 and 75 kPa). Two different column diameters, three different plan configurations, and three types of encasements were studied for the analysis [12] (Fig. 11). The lateral load-carrying capacity of the encased granular columns was comparatively higher because of the mobilization of tensile forces in the encasement. The resistance offered by the encased columns increased with the shear displacements until the encasement material completely ruptured. While increasing the area replacement ratio, a considerable increase in strength was observed for the encased columns, whereas only marginal increase was there for ordinary granular columns. For encased columns, if the encasement ruptures, their strength reduces to the level of ordinary granular columns. In encased columns, the observed strength increased at smaller shear displacements mainly because of the increase in column stiffness, whereas, at larger displacements, the increase is because of the mobilization of tensile forces in the encasement. For ordinary granular columns, shear failure occurs along the shear plane; encased columns undergo bending deformations, without any rupture due to flexibility of the encasement. For the same area replacement ratio, group arrangement of stone columns mobilizes higher shear resistance than that of single columns [12]. The failure mechanism and strength of encased stone columns may be influenced by various factors such as strength, relative density, encasement length, as well as stiffness of the encasement material. A uniaxial compression test has been performed on encased stone columns to analyze the behavior. The columns had dimensions of 300 mm diameter and 600 mm height, and polypropylene woven geotextile tubes have been employed as encasement material. The testing was done for four different relative densities (0.42, 0.62, 0.70, and 0.78). Also, five types of geotextile were used having ultimate tensile strength as 33, 44, 52, 65, and 91 kN/m. The test was mainly intended to study the effect of encasing materials and the initial void ratio on the behavior of the columns under uniaxial compression. The test results indicated that

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the initial void ratio has no effect on the uniaxial compressive strength of the encased stone columns; it was mainly influenced by the tensile strength of the geotextile used for encasement. Loose samples will undergo initial compression; the stress–strain behavior was linear up to the peak strength, followed by plastic behavior. Whereas for dense samples, there was very less initial compression and compression modulus of the column was proportional to the tension modulus of geotextile. The stress–strain curve obtained for the geotextile-encased columns under uniaxial loading was nearly linear before failure, which means it exhibited elastic behavior at failure. The behavior at failure was similar to that of the behavior of geotextile under tension. Failure mode was rather sudden, or it exhibited semi-brittle type behavior under uniaxial loading conditions. It was also observed that at failure, the axial strain of samples had decreased with relative density. Contrary to the ordinary stone columns under triaxial loading, after reaching peak strength, geosynthetic-encased stone columns sustained larger plastic deformations, also stress reduced with strain, because of the extension of failure surface in the geosynthetic. It can be concluded that even after large deformation, as well as the failure of geotextile or geosynthetic, the encased stone column can carry a greater load. Failure strain in the geotextile affects the axial strain in the encased column. The tests concluded that the unconfined compressive strength of geosynthetic-encased stone columns could be described with the help of tensile strength of the geotextile encasement and internal friction angle of gravel. It was observed that under high confining pressures, even after maximum strength, the encased columns were able to withstand large deformations at relatively larger loads [13]. Further numerical and experimental model studies were conducted on stone columns having shear or lateral loading. This kind of study was aimed to find the lateral load-carrying capacity of encased columns, which may be prominent near the toe of retaining walls and embankments. The lateral load-carrying capacity is dependent on various parameters like overburden pressure acting on the soil, the stone column diameter, and the strength properties of encasing geosynthetic. An experimental study was done on encased columns by using large shear box apparatus, and the obtained results were numerically validated by using FLAC 3D software. In numerical analysis, the modeling of geosynthetic encasement was simulated as a geogrid-type shell element. This element behaved as a linearly elastic and isotropic material with no failure limit. The results clearly indicated that encasement using geosynthetic improved the load-carrying capacity of the stone column. Also, it has been observed that by installing the ordinary stone column, an improvement in shear strength was observed, which was dependent on area replacement ratio, but due to the installation, the increase in shear strength occurred, which was mainly due to the confinement effect from the encased material. Similar trends were obtained from numerical and experimental analyses. However, there were significant variations in the peak values of shear stress; still, at large horizontal displacements, the difference was reasonable. Here, the numerical analysis was mainly aimed to find the failure mechanisms of the columns (ordinary as well as encased columns). From the experimental results, it was concluded that the encased columns acted like a semi-rigid pile, and it provided passive resistance due to which there was higher shear stress

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Fig. 12 The horizontal stress development above the shear plane. Source Mohapatra and Rajagopal [14]

mobilization compared to that of the ordinary stone column. In addition to the passive resistance, the mobilization of hoop tension in the column encasement provided additional confinement to stone aggregates. This, in turn, increased the observed shear stress significantly [14] (Fig. 12). Shear resistance of both ordinary, as well as encased columns, increased with area replacement ratio. For encased columns, at large horizontal displacements, an increase in post-peak shear resistance has been observed, whereas, for ordinary stone columns, the post-peak shear resistance remained constant as a result of the column failure [14]. Comparative studies were conducted to evaluate the performance of conventional stone columns and encased stone columns. For the experimental investigation, a 30 mm diameter stone column with granite chips (size ranging between 2 and 6.35) was installed in soft clay. For encased stone column, geogrid or net was used as the encasing material. Tests have been performed on a single column of 30 mm diameter and at varying L/D ratios on a standard loading frame. The test was stress controlled. Settlements were recorded at 10 min interval in an hour. Load settlement curves were plotted for an ordinary stone column as well as encased columns (having different types of encasing material) at different L/D ratios. The plots had similar shapes. The encased columns showed increased resistance to load and reduced rate of settlement compared to the ordinary stone column. The reduction in settlement increased with the stiffness of encasement but was found to be insignificant beyond a stiffness of 2000 KN/m2 /m. If the vertical load is applied on the encased column, the column will dilate and induces a lateral pressure. The maximum bulging was 4 times the column diameter measured from the top. If the surrounding soft soil could not withstand the lateral pressure, the column will fail. The lateral strain in the column in turn induces hoop tension in the encasing material, which resulted in radial compression of the column. This hoop tension will give passive resistance to the stone column. The pressure developed also induces an upward thrust. It was observed that the stress concentration ratio increased for the encased stone column compared to the conventional stone column, and the magnitude of increase was dependent on the stiffness of the geosynthetic encasement used. Pore water pressure also reduced

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when encasement was given to the stone columns. This was because, in the case of unstabilized beds, the pore water distribution was concentrated below the foundation, whereas for ordinary and encased stone columns, pore pressure distribution was concentrated at deeper levels, with comparatively lesser magnitude [15]. Numerical analysis was performed using FEM software PLAXIS. Elasto-plastic behavior of the stone column was modeled with the help of Mohr–Coulomb yield criteria and the nonlinear nature of clay by using a soft clay model. The load– settlement curves obtained experimentally were similar to those obtained with FEM software. The failure mechanism of columns from the numerical analysis was in accordance with the classical theories. It was observed that load-carrying capacity has increased by 1.2, 1.5, and 2.2 times that of untreated clay bed for columns having L/D ratios 5, 7.5, and 10, respectively. L/D ratio was found to have a considerable effect on the stone column settlement. The settlement reduced with the increase in L/D ratio, up to L/D = 7.5. After L/D = 10, the settlement remained constant. As the length of the column increased, the load-carrying capacity also increased. L/D ratio was found to be ideal in the range 5–10 for both settlement and strength considerations. From the parametric study, it was concluded that the settlement reduction ratio for encased columns was 50% of ordinary stone columns (under identical conditions). The settlement reduction ratio was also found to be affected by the angle of shearing resistance of the column material. It the material was compacted at a higher angle of shearing resistance, the efficiency of the encased stone column was found to increase [15].

3.2 Composite Mixture Stone Columns Lime-mortar soil columns: Stone columns need not be made using a single material. It can be constructed using a composite mixture as well. For analyzing the performance of composite material, the column was constructed using lime and well-graded soil mixture (with varying proportions of lime and varying curing time) in the soft soil bed. Laboratory investigations have been carried out on ordinary (clayey) soil, lime, and composite material. The test was done using the CBR apparatus (as per ASTM standards). The soft computing technique was used for analyzing and comparing the observed results. An artificial neural network (ANN) was used efficiently to compare the results. By using the laboratory test results, it was possible for ANN to predict the CBR of each specimen under different conditions. MATLAB was the main computational software that facilitated this research. The specimens were categorized into three: dry, unsoaked, and soaked. The first two sets were trained using generalized regression neural network (GRNN) and radial basis function neural network (RBFNN), and the soaked specimens were trained by utilizing the feed-forward back propagation neural network (FFBPNN). Later the observations were compared. The results indicated that the composite mixture gave increased strength and reduced settlement of the column. The increase in lime content beyond 20% had no considerable effect on strength. As more clay content was present in the well-graded soil,

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more lime was required for stabilizing the mix. As clay content increased, the strength increased, which may be due to the chemical reaction between lime and silica with clay and clay filling the voids between coarser particles. It was concluded that an optimum mix of 20% lime and 22% clay improved the strength of soft clayey soils by 5–6 times. ANN helped to optimize the lime content in the composite mix. It indicated that specimens with 22% lime gave the strength of laboratory specimens with 25% lime [16]. Lime-fly ash columns: Experimental investigations were carried out on lime-fly ash columns for improving the weak fly ash ground. The ratio of dry weight of lime to fly ash was varied as 5, 10, 15, 20, and 25%. An unconfined compression strength test has been conducted on the samples having varying lime content and curing time. The test was done at a constant strain rate of 1.14 mm/min. The specimens were cured for 7, 14, 28, and 60 days. Some of the specimens were tested under soaked conditions. Full-scale physical model tests were conducted in the field and small-scale testing was conducted in the laboratory, on a foundation (rigid plate) improved with lime-fly ash columns in weak fly ash ground. The results indicated that the composite mixture improved the ground in terms of settlement and bearing capacity for lime content more than 10%. As lime content and curing time increased, the compressive strength also increased. 10–20% lime content was found to be ideal. But soaked specimens gave unsatisfactory results, as soaking reduced bearing capacity and increased settlements. Unsoaked specimens exhibited contraction at all confining pressures, whereas soaked specimens exhibited contraction at high confining pressures only and dilated at low confining pressures. The pozzolanic reaction between lime and fly ash produced a cementitious product which aided in internal confinement. For the same reason, lime can be advantageously utilized in the stabilization of weak fly ash ground. The field physical model studies indicated that the collapse settlement of the soaked specimen was around 19% more than that of unsoaked specimens for ground improved using fly ash-lime columns, and was 18.5% more than that of unsoaked for the ground improved with stone columns. (For the same vertical pressure 70 kPa). Thus, it was inferred that the bearing capacity of soaked fly ash ground was lower than the unsoaked ground. It was also indicated that the stress ratio (stone column to fly ash) for the soaked sample was 1.37 times that of the unsoaked sample. Due to the collapsible nature of fly ash, the soaked specimens showed large settlements and reduced bearing capacities. Therefore, it was concluded that fly ash ground without any improvements could not be utilized as a foundation bearing stratum [17].

3.3 Dynamic response of StoneColumns From the studies done in the past, monotonic, cyclic triaxial test results concluded that stone columns could be employed to improve the bearing capacity of soil by approximately 15–35% (by varying the column fill and the area replacement ratio). The increase in bearing capacity, in turn, resulted in an increased resilient modulus, threshold cyclic stress as well as the reduced settlements [18].

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These improvements need to be assessed properly to estimate the values by performing various cyclic tests. Hence, the obtained results can be used for constructing pavement layers, subgrade, railway tracks, machine foundations, and various other structures that may be subjected to cyclic loadings. Rubber-drained stone columns: A comparative study was conducted between rubber-drained columns and gravel columns concerning liquefaction mitigation. The study was conducted on saturated sandy soil using a shaking table. A physical model was made in the laboratory. A container was separated into two halves by means of a rigidly fixed plastic plate, and it had rubber and gravel drained columns on either side. The shaking table was designed for a resonating frequency of 2 Hz. The applied dynamic loading had not simulated the actual earthquake loading since it was 1D, having the same amplitude and frequency. It was just aimed to obtain comparative responses. The drainage materials used had high permeability in order to have liquefaction mitigation. Tire chips were used as rubber drains. The deformations experienced by both the samples were almost similar. It was inferred that increase in number and diameter of columns has improved the liquefaction resistance. For moderate accelerations, gravel drained columns are much better than rubber-drained columns. For higher accelerations, rubber-drained columns had comparatively lesser excess pore water pressure and settlement. It was also concluded that higher relative density soil improved using rubberdrained columns gave lesser excess pore water pressure as well as settlements. The drainage rate was higher for gravel drains. It was inferred that compaction is the most effective measure for liquefaction mitigation, rather than increasing the number of drains [19]. The behavior of silty soil improved using a stone column for liquefaction mitigation was also analyzed. The performance was analyzed using centrifuge model testing. Models were constructed under high-quality control. The improvement of stratum stiffness was the main focus of the study rather than densification and pore water pressure variations. The response of the soil under base dynamic excitation was studied for four separate model tests. It included soil without stone columns, with stone columns, free-field conditions, and with surcharge loading. The acceleration, settlement, and excess pore water pressures indicated that the stiffness had increased with the installation of stone columns. It had also reduced the build-up of excess pore water pressure, increased the overall stiffness, and reduced the settlement due to surcharge loading considerably. In the free-field condition, the improvement was effective only up to 5 m. Columns can reduce the settlements of up to 50%. Stone columns were found to have a marginal effect in reducing the pore water pressure, and in practical cases, confinement can be obtained with the weight of the structure [20]. A numeric study was conducted to evaluate the improvement of soil using a geotextile-encased stone column as a liquefaction countermeasure. 3D FEM analysis was done on sandy soil with a mild slope. The investigation was carried out for lateral ground deformations, thickness, permeability, and tensile stiffness of geosynthetic, diameter, and distributed load at the periphery of the encased stone column. It was inferred from the results that there was a reduction in the lateral deformation for

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encased columns. Also on the contrary to the expectations, as thickness and stiffness of the geosynthetic, column diameter were increased, the efficiency of the column decreased. The lateral ground displacements decreased when the permeability of the geotextile increased beyond 0.1 m/s. With larger surface loads, liquefaction was not prevented, but there were fewer displacements and very few permanent deformations. Both stone columns and encased columns were effective in reducing lateral displacements; encased columns were even better as it acted like stiffer ground reinforcements. With the increase in column diameter, lateral deformations reduced. There was virtually no lateral displacement for 1 m stone column diameter [21]. A model study has been conducted on an infinite beam with concentrated loading and motion at a constant speed, which rested on a geosynthetic-reinforced (granular) bed overlying weak soil stratum modified using a stone column. The granular bed was modeled as the Pasternak shear layer, and saturated, native soil was idealized by using the Kelvin–Voigt model; the stone columns were idealized as Winkler springs and the geosynthetic as an elastic, rough membrane. The performance of the soft soil, granular fill as well as the stone column was nonlinear and was represented with the help of constitutive relationships which were hyperbolic. The technique of iterations (finite difference method) was used to evaluate the performance of the system or Gauss–Seidel method has been adopted. The sensitivity of the system or its response was comparatively lower at lower speeds of the load. The response of the system at higher velocities has been influenced by damping. The ultimate shearing resistance of the granular fill had no effect on system response. When the column diameter to length ratio was increased from 0.0008 to 0.006, the beam deflection increased by around 65%; and when the ratio was increased from 0.006 to 0.008, the deflection had decreased by 28%. It has been indicated that the ultimate bearing capacity of the columns has a considerable influence on the soil foundation system response. Also, the relative stiffness between columns and soil had a considerable effect. The response of the system was independent of the ultimate shearing resistance of the granular fill [22]. Composite stone columns, along with dynamic compaction, were employed in controlling the liquefaction in silty soils. Numerical models were used to simulate and analyze the densification achieved during both the cases hence identified various parameters that controlled the soil density. An analytical method has been formulated and was employed to simulate the actual soil behavior during the installations. A semi-theoretical framework was formulated for the analysis of the densification process and for simulating the ground response. Silt content, hydraulic conductivity, and area replacement ratio were identified as factors affecting densification. The results indicated that silty soils with low hydraulic conductivity (10−8 m/s) can be effectively compacted by using stone columns (of 2 m diameter at a close spacing with area replacement ratio greater than or equal to 20% and supplemented with wick drains). Also, dynamic compaction along with wick drains in soils with low permeability, decreases consolidation time by improved drainage rate and thereby allowing greater improvement. Ground with higher hydraulic conductivity (exceeding 10−6 m/s) could be densified using either of the two technologies and without employing supplementary drains [23].

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Discrete columns are installed in liquefiable soil and are analyzed for shear stress variations. As the discrete columns are stiffer than soil, it will induce larger shear stress, hence lowering the shear stress in the nearby soil. Three-dimensional and linear FE analysis has been adopted. The test results indicated that discrete stone columns behaved in flexure and shear, in such a manner that compatibility assumption for the shear strain was not conservative. The evaluation also indicated that shear reinforcements in the stiff columns were less effective compared to the commonly used ones. A modified design equation was also formulated to find the shear stress reduction ratio in a conservative manner. This was found to have a more reasonable estimate of shear stress reduction for discrete circular columns [24].

4 Summary and Conclusions Geosynthetic-encased stone columns are popular due to improved confinement resulting in increased strength as well as stiffness of the stratum. Limited researches are available regarding the installation procedure of the encased columns. Also, the durability check of these columns needs to be assessed. From the literature review, it is evident that the group performance of the encased stone column is excellent. It can even be considered better than single columns. Therefore, a detailed study needs to be done in this area to have a detailed and reliable analysis as well as a design procedure. It is very much evident that numerous numerical analyses and physical model studies were performed on the geosynthetic-encased columns, but it is very much essential to have field testing as well. This needs to be done to ensure the reliability and also for comparing and validating the results with the numerical analysis and model study results. When lime columns were employed in the stabilization of weak fly ash grounds [17], the mode of failure as well as the load–settlement variations that took place need to be analyzed in detail, various mechanisms of fly ash (like soaking, contracting, and softening) have to be studied in detail for the same. Dynamic testing was done on stone columns mainly for evaluating the dynamic response of the improved strata and for liquefaction mitigation. Further, it can be done by varying certain parameters like area replacement ratio, column spacing, type of loading, L/D ratio, and the column diameter. Also, the response can be evaluated for various soils since most of the study was focused on silty soils. And the dynamic loading must simulate the actual field conditions as much as possible (e.g., the wave pattern should be similar to earthquake load, etc.), which is essential to have reliable results. This was not satisfied in most of the cases.

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References 1. Som MN, Das SC (2003) Theory and practice of foundation design. PHI Learning Pvt, Ltd 2. IS 15284 (2003) Design and construction for ground improvement: guidelines. Part 1: Stone Columns 3. Bouassida M, Ellouze S et al (2013) Numerical Study of the behavior of improved soft clay by stone column. In: Foundation and soft ground engineering conference, Thu Dau Mot UniversityICTDMU-1, Binh Duong 4. Barksdale RD, Bachus RC (1983) Design and construction of stone columns, vol. I (No. FHWA/RD-83/026; SCEGIT-83–104). Turner-Fairbank Highway Research Center 5. Murugesan S, Rajagopal K (2008) Performance of encased stone columns and design guidelines for construction on soft clay soils. Technology, 729–734. https://doi.org/10.1001/virtualmentor. 2013.15.2.ecas2-1302 6. Ayadat T, Hanna AM (2005) Encapsulated stone columns as a soil improvement technique for collapsible soil. Proc Inst Civ Eng Ground Improv 9(4):137–147 7. Keykhosropur L, Soroush A, Imam R (2012) 3D numerical analyses of geosynthetic encased stone columns. Geotext Geomembranes 35:61–68. https://doi.org/10.1016/j.geotexmem.2012. 07.005 8. Raithel M, Kirchner A, Kempfert HG (2009) German recommendations for reinforced embankments on pile-similar elements. In: Geosynthetics in civil and environmental engineering 9. Miranda M, Da A, Castro J (2017) Fluence of geotextile encasement on the behaviour of stone columns: laboratory study. Geotext Geomembr 45:14–22. https://doi.org/10.1016/j.geo texmem.2016.08.004 10. Miranda M, Da Costa A (2016) Laboratory analysis of encased stone columns. Geotext Geomembr 44:269–277. https://doi.org/10.1016/j.geotexmem.2015.12.001 11. Castro J (2017) Groups of encased stone columns: influence of column length and arrangement. Geotext Geomembr 45:68–80. https://doi.org/10.1016/j.geotexmem.2016.12.001 12. Mohapatra SR, Rajagopal K, Sharma J (2016) Direct shear tests on geosynthetic-encased granular columns. Geotext Geomembr 44:396–405. https://doi.org/10.1016/j.geotexmem.2016. 01.002 13. Chen JF, Wang XT, Xue JF et al (2018) Uniaxial compression behavior of geotextile encased stone columns. Geotext Geomembr 46:277–283. https://doi.org/10.1016/j.geotexmem.2018. 01.003 14. Mohapatra SR, Rajagopal K (2016) Experimental and numerical modelling of geosynthetic encased stone columns subjected to shear loading. Japanese Geotech Soc Spec Publ 2:2292– 2295. https://doi.org/10.3208/jgssp.igs-08 15. Malarvizhi SN, Ilamparuthi (2011) Comparative study on the behavior of encased stone column and conventional stone column. Soils Found 47:873–885. https://doi.org/10.3208/sandf.47.873 16. Malekpoor MR, Toufigh MM (2010) Laboratory study of soft soil improvement using lime mortar-(well graded) soil columns. Geotech Test J 33:225–235. https://doi.org/10.1520/GTJ 102291 17. Zhou C, Yin J-H, Ming J-P (2002) Bearing capacity and settlement of weak fly ash ground improved using lime—fly ash or stone columns. Can Geotech J 39:585–596. https://doi.org/ 10.1139/t02-011 18. Ashour S (2015) The response of stone columns under cyclic loading. Ph.D. thesis University of Birmingham 19. Bahadori H, Farzalizadeh R, Barghi A, Hasheminezhad A (2018) A comparative study between gravel and rubber drainage columns for mitigation of liquefaction hazards. J Rock Mech Geotech Eng 10:924–934. https://doi.org/10.1016/j.jrmge.2018.03.008 20. Adalier K, Elgamal A, Meneses J, Baez JI (2003) Stone columns as liquefaction countermeasure in non-plastic silty soils. Soil Dyn Earthq Eng 23:571–584. https://doi.org/10.1016/S0267-726 1(03)00070-8

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21. Tang L, Cong S, Ling X et al (2015) Numerical study on ground improvement for liquefaction mitigation using stone columns encased with geosynthetics. Geotext Geomembr 43:190–195. https://doi.org/10.1016/j.geotexmem.2014.11.011 22. Maheshwari P, Khatri S (2013) Response of infinite beams on Geosynthetic-reinforced granular bed over soft soil with stone columns under moving loads 13:713–728. https://doi.org/10.1061/ (ASCE)GM.1943-5622.0000269 23. It TS, Angeles L (2004) columns and dynamic compaction 3:39–50 24. Rayamajhi D, Nguyen TV et al (2012) Effect of discrete columns on shear stress distribution in liquefiable soil. In: GeoCongress 2012 © ASCE 2012 1908, pp 1908–1917

Effect of Fly Ash on Geotechnical Properties of Oil-Contaminated Soil Veena Jayakrishnan, Aiswarya Gracious, and Anila C. Shaju

Abstract Accidental oil spillage or leaking has caused severe damage to the environment. Oil contamination can adversely affect the soil microbes and plant as well as contaminate groundwater resources for drinking or agriculture. Hydrocarbon contamination will not just affect the quality of the soil but will also alter the physical properties of oil-contaminated soil, excessive settlement of tanks and breakage of pipeline. Contamination changes the behaviour of soil and also alters its engineering properties leading to several problems like loss in strength, differential settlement and cracks in existing foundation or structure. For any possible applications of contaminated soils, knowledge of the geotechnical behaviour of contaminated soil is required. The experimental programme was carried out in the present study to know the effect of diesel oil contamination (4, 8 and 12%, by dry weight) on geotechnical properties of locally available fine-grained soil and the efficacy of fly ash as a stabilizing agent at different percentages 20, 40 and 60% (w/w). The results show that the consistency limits and the strength parameters have been affected marginally due to contamination. The utilization of industrial by-products such as fly ash is of increasing importance as an option for stabilizing contaminated sites due to its pozzolanic nature and also in view of minimizing the environmental impact. The plasticity index of stabilized soil was observed to be not uniform with the increase in fly ash addition. The compaction characteristics, Unconfined Compressive Strength (UCS) and CBR value of soil decreased with the addition of contaminant and it regains marginally with the addition of fly ash. UCS and CBR values showed an increase of 29.5 and 73.5% with an addition of 60% fly ash. The results from the study may be beneficial for the engineers and researchers in reusing the contaminated soils for safe and economic construction of structures. V. Jayakrishnan (B) Cochin University of Science and Technology, Kochi, Kerala, India e-mail: [email protected] A. Gracious · A. C. Shaju Mar Baselios Institute of Technology and Science, Nellimattom, Ernakulam, Kerala, India e-mail: [email protected] A. C. Shaju e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_15

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Keywords Oil-contaminated soil · Stabilization · Fly ash · Pozzolanic nature · Unconfined compressive strength · CBR value

1 Introduction Unintentionally or intentionally humans contaminate soils from different sources. The contaminated soils are now a challenge for geotechnical engineers. The soil is subjected to a change in its engineering properties when contaminated by crude oil. Accidental oil spillage or leaking has caused severe damage to the environment. Oil contamination can adversely affect the soil microbes and plant as well as contaminate groundwater resources for drinking or agriculture. The hydrocarbon contamination will not just affect the quality of the soil but will also alter the physical properties of oil-contaminated soil [1]. Soil contamination is caused by manmade chemicals, which may alter the engineering properties of soil and may lead to several problems like strength loss, differential settlement, and cracks in existing foundation or structure. The high concentration of chemicals and toxic metals made the soil incapable for any intended engineering works. For any possible applications of contaminated soils, knowledge of the geotechnical properties and behaviour of contaminated soil is required. The oil contamination in soil causes a significant increase in the soil plasticity, loss in bearing capacity and increases its settlement. Construction in such contaminated sites is risky and increases the project cost [2]. A comprehensive laboratory-testing program was carried out by Habib-Ur-Rehman et al. [3] to compare the engineering properties of uncontaminated and contaminated clay with crude oil. The contaminated clay behaves more like a cohesionless material, owing to the formation of agglomerates. Soil stabilization is the process of improving the engineering properties of the soil and thus making it more stable. It is required when the soil available for construction is not suitable for the intended purpose. It is used to reduce the permeability and compressibility of the soil mass in earth structures and to increase its shear strength. Soil stabilization is required to increase the bearing capacity of foundation soil. In its broadest sense, stabilization includes compaction, pre-consolidation, drainage and many other such processes. However, the term stabilization is generally restricted to the processes that alter the soil materials itself, improve the natural soil for the construction of highways and airfields. To neutralize the effect of oil into the soil, several studies have been focused on the materials like lime, cement, fly ash, etc. Previous studies show that these materials play a significant role in stabilizing in contaminated soils [4]. The utilization of industrial by-products such as fly ash is of increasing importance as an option for stabilizing contaminated sites due to pozzolanic nature and also in view of minimizing the environmental impact. A lot of land and money are involved in the disposal of fly ash; thus, it is very useful to stabilize the contaminated soil using fly ash. Considering these issues related to soil contamination the present study focused on stabilization of diesel engine oilcontaminated soils with fly ash. The contaminated samples were prepared by mixing

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the soils with crude oil in the amount of 4, 8 and 12% by dry weight. The results indicated a decrease in strength, maximum dry density, optimum water content and Atterberg limits, similar to the previous studies [5, 6]. Oil contamination affected the Atterberg limits of soils. There is a lack of consensus on how oil contamination affects the Atterberg limits of the soil, however, it is seen in the literature that oil can either increase or decrease the Atterberg limits of the soil. There is a need to use different soils to investigate the effect of oil on the Atterberg limits of soils. This will contribute to existing knowledge. Studies show that the presence of crude oil has a remarkable effect on the geotechnical properties of soil [7, 8]. Variations in the behaviour of the contaminated soil when fly ash was added at 20, 40 and 60% were examined and showed good improvement in the geotechnical properties.

2 Materials and Methodology 2.1 Materials The soil sample was collected from the premises of Mar Baselios Institute of Technology and Science, Kerala. The sample collected was pooled together to ensure homogeneous mixing. Then, the sample was thoroughly oven dried and stored in polythene bags at room temperature. On the basis of Indian standard classification, the soil can be classified as fine-grained soil with silts and clay of medium compressibility (MI). The general properties of the soil were determined and shown in Table 1. For contaminating the soil artificially, diesel was brought from a nearby petrol station. The diesel engine oil is red in colour and has high density and viscosity. The physical property of diesel engine oil is shown in Table 2. Table 1 Physical properties of soil sample

Properties

Value

Uniformity coefficient (C u )

5.85

Coefficient of curvature (C c )

0.783

Effective size (mm)

0.14

Liquid limit (%)

40

Plastic limit (%)

25.1

Specific gravity

2.63

Max. Dry density (g/cc)

1.83

Optimum Moisture Content (%) Unconfined compressive strength CBR value (%)

18.6 (kN/m2 )

62.78 19.34

222 Table 2 Physical properties of diesel oil

Table 3 Properties of fly ash used

V. Jayakrishnan et al. Properties

Value

Kinematic viscosity, centistoke (at 40 °C)

130

Kinematic viscosity, centistoke (100 °C)

13.5–16

Viscosity index, Min

110

Flash point, (COC) C, Min

200

Pour point, C, Max

−21

Sulphated ash, %Wt, Max

0.68

TBN, mg KOH/g, Min

4.1

Colour

Red

A

Chemical properties

1

SiO2 + Al2 O3 + Fe2 O3

92.65%

2

SiO2

63.22%

3

MgO

0.58%

4

SO3

0.74%

5

Na2 O

0.68%

6

Total chlorides

0.007%

7

Loss on ignition

0.88%

B

Physical properties

1

Fineness––specific surface in (m2 /kg)

360

2

Particle retained on 45 microns

32.84%

For stabilizing the contaminated soil, the fly ash was collected from CVC ready mix plant situated in Kochi (Kerala). The fly ash used for the stabilization of the contaminated soil is classified as class F fly ash according to its chemical composition. Table 3 shows the properties of fly ash used [9].

2.2 Methodology The various operations involved in this study consist of evaluation of geotechnical properties of soil contaminated with diesel oil and its stabilization with fly ash. Experiments were carried out in two phases as shown in Fig. 1. Diesel-contaminated soil–oven-dried soil was contained with diesel engine oil at 4, 8 and 12 percentages. The volume of diesel was taken, corresponding to the percentage of dry weight of soil and contaminated soil sample was kept for a oneweek period of time to ensure thorough mixing of contaminant with soil. After one-week period, the tests were carried out on contaminated soil.

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Fig. 1 Sample preparation

Fly Ash Mixed with Contaminated Soil–Fly ash was added at 20, 40 and 60% to the 12% contaminated soil sample (as a percentage of the weight of contaminated soil) and kept for one-week period of time to ensure homogeneous mixing of fly ash with the contaminated soil. After one-week period, the tests were carried out on fly ash mixed contaminated soil.

3 Results and Discussion 3.1 Effect of Diesel Oil on Geotechnical Properties of Soil The soil sample was contaminated at 4, 8 and 12% diesel and these contaminated samples were kept for one-week period time maturation. After one-week period, various tests were conducted on these samples. The results obtained from the tests conducted on uncontaminated and contaminated soil samples are summarized in Table 4 and it is observed that as the oil content increases in the sample the strength characteristics showed a decreasing trend. Figure 2a shows a considerable increase in liquid limit and plastic limit with an increasing percentage of diesel oil. Oil caused a reduction in the amount of water that surrounded the clay and sand particles as reported in [10]. The presence of hydrocarbons in the engine oil which is a non-polarizing liquid has caused a reduction in the thickness of water film around the soil particles. The first contact of the oil was with the soil and not the water. Oil-contaminated soil deforms as liquid or plastic in

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Table 4 Results of various properties of uncontaminated and contaminated sample Properties

SAMPLE (% DIESEL) 0

4

8

12

Liquid limit (%)

40

36.4

34

30.4

Plastic limit (%)

25.1

23

21.5

20.6

Plasticity index (%)

14.9

13.4

12.5

9.8

Max. dry density (g/cc)

1.83

1.73

1.75

Optimum moisture content (%)

18.6

16.67

13.2

11.4

1.67

Unconfined compressive strength (kN/m2 )

62.78

53.95

47.08

38.25

CBR value (%)

19.34

16.94

13.7

10.6

the presence of water. This was less when oil content increased, hence, liquid limit and plastic limits generally reduced. Figure 2b shows a decreasing trend of OMC and max dry density at higher percentages of diesel content. Soils were sticky when wet. Diesel oil is hydrophobic and prevents the entry of water which interacts with soil and reduces the amount of water needed by the soil to reach its maximum dry density. Hence, optimum moisture content is reduced. Soil particles are less packed together which leads to a decrease in dry unit weight of contaminated soil. Figure 2c shows a decreasing trend of Unconfined Compressive Strength (UCS) with an increase in the percentage of diesel. Diesel oil decreases the soil density and loosens the soil particles and leads to the weakness of soil. Figure 2d shows a decrease in CBR value at higher percentages of diesel. This may be due to contaminants with polar organic liquids with lubricants effect, which may disperse the soil structure. It increases the chance of interparticle slippage thus reducing the strength of the diesel-contaminated soil and it indicates that the ground composed of contaminated soil is very weak for constructional purposes. The strength characteristics of the contaminated soil have been reduced. The contamination has affected the strength characteristics and from Fig. 2 it can be observed that the UCS and CBR values were decreased by 45.2% and 39%, respectively. Figure 3 shows a comparison plot for the compaction characteristics versus various percentages of diesel oil content for different types of soil along with corresponding data obtained from similar studies [2, 6, 10]. From this figure, the influence of oil content in maximum dry density and OMC are clearly shown and validates that as the oil content increases in soil, maximum dry density and OMC values showed a decreasing trend. Figure 4 shows a comparison plot for the strength characteristics versus various percentages of diesel oil content for different types of soil along with corresponding data obtained from similar studies [2, 10]. From this figure, the influence of oil content in Unconfined Compressive Strength (UCS) values are clearly shown and validates that as the oil content increases in soil, UCS values decrease. The diesel

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Fig. 2 Variation of geotechnical properties on the addition of various percentages of diesel oil

oil content leads to a decrease in the soil density and looses the soil particles, so it leads to the weakness of soil and decreases the strength as reported by [2]. This may have led to a drastic decrease in the Unconfined Compressive Strength (UCS) and increase in diesel oil contamination in the soil.

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Fig. 3 Comparison of results showing the influence of oil content in compaction characteristics of soils

Fig. 4 Comparison of results showing the influence of oil content in strength characteristics of soils

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3.2 Effect of Fly Ash on Properties of Contaminated Soil By examining the geotechnical properties of the contaminated soil, 12% contaminated soil showed the worst behaviour. Hence, stabilization was done to soil contaminated with 12% diesel oil content and the results obtained are summarized in Table 5. It can be observed from the table that as the percentage of fly ash content added to contaminated soil (with 12% diesel content) increases the geotechnical properties were improved. Variation of geotechnical properties on the addition of fly ash on contaminated soil is shown in Fig. 5. Figure 5a shows that liquid limit and plastic limit increases till 40% fly ash, further, addition causes a decrease in its value. The variation may be attributed to the inclusion of non-plastic fly ash and flocculation and agglomeration reaction. These

Fig. 5 Variation of geotechnical properties on the addition of fly ash on contaminated soil

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made the soil more granular and thereby reducing Atterberg limits. From Fig. 8, with an increasing percentage of fly ash, the plasticity index is found to be decreasing. This indicates that soil does not show plastic behaviour when mixed with fly ash. From Fig. 5b, it can be observed that maximum dry density and OMC increases with the addition of fly ash. Increase in maximum dry density is due to the infilling of voids. OMC increases with fly ash content as more water is required for lubricating the particles. Addition of fly ash resulted in an increase in unconfined compressive strength as shown in Fig. 5c. The increase in compressive strength may be due to the cementation reaction. Figure 5d shows that CBR value increases with increase in the percentage of fly ash. Increase in CBR value is due to the pozzolanic action of fly ash. This indicates that fly ash is an effective stabilizing agent and can be effectively used for economic construction of structures. The strength characteristics of the stabilized soil have been improved. The fly ash content has affected the strength characteristics and from Fig. 5 it can be observed that the UCS and CBR values were increased by 29.5% and 73.5%, respectively. Figure 6 shows a comparison plot for the Atterberg limits versus various percentages of fly ash content for different types of soil along with corresponding data obtained from similar studies [5, 9]. From this figure, the influence of fly ash on liquid limit and plastic limit values are clearly shown and validates that as the fly ash content increases in soil, Atterberg limits values showed an increasing trend. Figure 7 shows a comparison plot for the MDD versus various percentages of fly ash contents for different types of soil along with corresponding data obtained from

Fig. 6 Comparison of the influence of fly ash content on Atterberg limits of soil

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Fig. 7 Comparison of the influence of fly ash content on MDD of soil

similar studies [4, 9]. From this figure, the influence of fly ash on maximum dry density values are clearly shown and validates that as the fly ash content increases in soil, strength characteristics values showed an increasing trend. The addition of fly ash decreased the problematic nature of contaminated soil. Figure 8 shows a comparison plot for the UCS values versus various percentages of fly ash contents for different types of soil along with corresponding data obtained from similar studies [4, 9]. From this figure, the influence of fly ash on UCS values are clearly shown and validates that as the fly ash content increases in soil, strength characteristics values increase. Figure 9 shows a comparison plot for the CBR values versus various percentages of fly ash contents for different types of soil along with corresponding data obtained from the similar study [9]. From this figure, the influence of fly ash on CBR values is clearly shown and validates that as the fly ash content increases in soil, CBR values also increase.

4 Conclusion The contamination of local soil by diesel engine oil and its influence on geotechnical characteristics was presented. The stabilization of contaminated soil by fly ash improved the soil characteristics to some extent. The results showed that the addition

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Fig. 8 Comparison of the influence of fly ash content on Unconfined Compressive Strength (UCS) of soil

Fig. 9 Comparison of the influence of fly ash content on California Bearing Ratio (CBR) of soil

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of oil has adverse effects on the geotechnical properties of the studied soil. From the studies on diesel-contaminated soil, the following conclusions were drawn out: • The Atterberg limits of contaminated soil were lower than that of uncontaminated soil. • The maximum dry density and optimum moisture content dropped due to the increase in oil content. • Compressive strength and CBR value also decrease with increase in oil content. The changes in the properties of the contaminated soil by the addition of fly ash can be attributed as follows: • The consistency limits showed a non-uniform variation with the addition of fly ash. • All other properties like maximum dry density, optimum moisture content, CBR value and compressive strength increases with increase in fly ash. Contaminated soils might be used for geotechnical purposes and these results may benefit the engineers or decision-makers in recycling or re-using of contaminated soils. In this study, the effects of oil contamination on some geotechnical properties are clearly observed. The results clearly showed that the oil contamination on soil system has influenced the geotechnical properties of the soil. The stabilization of contaminated soil by fly ash improved the soil characteristics to some extent. Best results were observed when the soil was treated with a 60% fly ash. From the overall observations of the study, the stabilization of diesel engine oil-contaminated soil using fly ash has been observed to be effective. Hence, the study proves to be useful and beneficial for the engineers and researchers in reusing the contaminated soils for safe and economic construction of structures.

References 1. Hong JH, Kim J, Choi OK, Kyung-Suk C, Ryu HW (2005) Characterization of a diesel degrading bacterium, Pseudomonas aeruginosa IU5, isolated from oil-contaminated soil in Korea. World J Microbiol Biotechnol 21:381–384 2. Pradeepan VP, Reethi VS, Namitha N (2016) Effect of diesel contamination on geotechnical properties of clay.Int J Civil Eng Technol 7(2):152–158 3. Habib-ur-Rahman SN, Abduljauwad, Akram T (2007) Geotechnical behavior of oilcontaminated fine grained soils. Elect J Geol Eng 12 4. Phanikumar BR, Sharma RS (2007) Volume change behaviour of fly ash stabilized clays. J Mater Civil Engg 19(1):67–74 5. Srivastava LP, Bala Ramadu P, Prasad A (2009) Stabilization of engine oil contaminated soil using fly ash. IGC, Guntur, India 6. Rahman ZA, Hamazah U, Taha MR, Ithnain NS, Ahmad (2010) Influence of oil contamination on geotechnical properties of basaltic soil. Am J Appl Sci 7 7. Ukpong IC, Umoh EC (2015) Effect of crude oil spillage on geotechnical properties of lateritic soil in Okoroete. Int J Eng Appl Sci 7(01):12–24 8. Guptha M, Srivastava RK (2010) Evaluation of engineering properties of oil contaminated soils. J Inst Eng India. Civil Eng 90:37–42

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9. George S, Aswathy EA, Sabu B, Krishnaprabha NP, George M (2015) Stabilization of diesel oil contaminated soil using fly ash. Int J Civil Struct Eng Res 2(2):118–123 10. Khamehchiyan M, Charkhabi AH, Tajik M (2007) Effects of crude oil contamination on geotechnical properties of clayey and sandy soils. Engg Geol 89:220–229

Development of Pavement Performance Prediction Models for Low-Volume Roads Using Functional Characteristics Muhammed Shibil P, M. Sivakumar, and M. V. L. R. Anjeneyulu

Abstract Pavement evaluations are done to determine the functional and structural conditions of the pavement. The combined action of age, traffic, climate and environmental factors usually affects the surface course and causes functional deterioration of the pavement. This will adversely affect the riding quality as well as the vehicle operating cost. The present study aims in developing pavement performance prediction models for low-volume roads in Calicut district of Kerala state, India. The roads considered for the study have an age varying from 1 to 7 years. The data determining the present conditions of the pavement such as pavement distress data, roughness, skid resistance, texture depth, traffic data and geometric details were collected. Since the pavement condition also depends on the subgrade conditions, California Bearing Ratio (CBR) and maximum dry density of subgrade were also collected. The Pavement Condition Index (PCI) and International Roughness Index (IRI) were calculated from the distress data and roughness data, respectively. Three different models were developed to predict the PCI, IRI and Skid Number (SN) of the road sections. Multiple regression models developed correlates PCI, IRI and SN with different factors such as age, Average Daily Traffic (ADT), texture depth and CBR. The performance of each model developed was evaluated using selected performance criteria. The models so developed help the concerned authorities in making decisions on the maintenance strategies as well as the allocation of funds. Keywords Pavement performance prediction model · Pavement condition index · International roughness index · Skid number · Multiple regression analysis

1 Introduction Low-volume roads serve as one of the key infrastructure works for rural development. Deteriorating rural roads and reduced funding from the authorities are major problems faced by the local governments. The pavement deterioration rate is less M. Shibil P (B) · M. Sivakumar · M. V. L. R. Anjeneyulu Department of Civil Engineering, National Institute of Technology Calicut, Calicut, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_16

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in the earlier ages and as the age of pavement as well as traffic load increases, the pavement deteriorates at a faster rate. The pavement deterioration can be classified as structural deterioration and functional deterioration. Functional deterioration of pavement is due to the combined action of age, traffic, climate and environmental factors. In the case of bituminous pavements, the functional deterioration is marked by the development of undulations and other distress on the pavement surface. The performance of flexible pavements has been identified as an important factor in the design and maintenance. Pavement Condition Index (PCI), International Roughness Index (IRI) and Skid Number (SN) are the different numerical indicators that rate the surface condition of the pavement. If the concerned authorities are unable to conduct pavement condition surveys every year, reliable pavement performance prediction models can be used for predicting the expected condition of pavement sections. The main objective of the study is to develop pavement performance prediction models for an identified network of rural roads in Calicut district to assist the authorities executing the maintenance of roads as well as the agencies allocating funds. This requires a systematic set of data so that it would assist in the prediction of models developed over this robust database. The most economical maintenance strategy for a particular pavement section and prioritization of such maintenance activities in the event of a constrained budget should be planned and executed based on these models.

2 Review of pavement performance prediction models A review was conducted to understand what are the factors affecting pavement deterioration and the different models used for developing pavement performance prediction models. Kirbas and Karasahin [1] developed three different deterioration models that can predict the future performance of flexible pavements in urban areas. The pavement distresses were measured and the current condition of the pavements is represented as the pavement condition index (PCI). The models developed to predict the PCI were a function of pavement age. Deterministic regression analysis, Multivariate Adaptive Regression Splines (MARS), and Artificial Neural Networks (ANN) were used for the modeling. The detailed comparison of the performance of these three models infers that the ANN model is the most appropriate model for predicting the deterioration in urban HMA pavements. Chen et al. [2] proposed an asphalt pavement distress condition index based on various types of distress data through Structural Equation Modelling (SEM). The SEM method modeled the contributions of various distresses as well as the influence of other factors such as age, layer thickness, material type, weather, environment, and traffic on the overall pavement distress condition. A multiple regression model was developed to predict the pavement distress index using the measured distress data. The model developed shows that alligator cracking, longitudinal cracking in the wheel path, non-wheel path longitudinal cracking, transverse cracking, block cracking, edge

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cracking, patch, and bleeding were significant in predicting the pavement distress index. Harikeerthan and Jagadeesh [3] identified the factors influencing the rate of pavement deterioration and a Relative Deterioration Index (RDI) was developed. Using the RDI, pavement deterioration models, and progression models for each type of distress were developed. Multiple regression models were developed by collecting a large volume of distress data through automated as well as manual methods. A total of 100 km road stretch including arterial and sub-arterial roads of Bangalore city was considered for the study. The selected stretches were evaluated over 54 months for five cycles. The relative deterioration models indicate that the roughness had a dominant effect on the selected roads. Rejani et al. [4] evaluated the pavement condition with respect to distresses in the pavement. The condition of the pavement is presented in terms of the Pavement Condition Index. Pavement condition surveys are carried out periodically. The prediction of pavement deterioration in terms of PCI with pavement age was done using linear and quadratic regression models. Different maintenance treatments were identified for the roads depending upon the condition of the roads. An optimization model was developed using the different indices to optimize the maintenance activity with the pavement condition and the budget as the constraints. Meegoda and Gao [5] considered the roughness data of asphalt pavements for developing a reliable pavement performance prediction model. International Roughness Index (IRI) is considered as the basis for the development of the pavement performance prediction model, which is a measure of the ride quality. A quantitative relationship between roughness progression and accumulative traffic load, structural number, annual precipitation, and freezing index was developed and validated. The extent of pavement deterioration is expressed by developing five performance levels. This is coupled with a reliability analysis based on the Weibull model to estimate the remaining service life of asphalt pavements. Maintenance measures for each pavement condition level were also proposed, which can aid in prioritizing the maintenance activities and corresponding budget allocations.

3 Methodology The pavement condition is evaluated with respect to the distresses, friction and undulations in the pavement. The condition of the pavement is presented in terms of Pavement Condition Index (PCI), International roughness Index (IRI) and Skid Number (SN). The PCI is calculated using Deduct Curve method. Pavement performance prediction models are developed to predict the PCI, IRI and SN. Multiple regression analysis is used to develop models that correlate PCI, IRI, SN with age, traffic, texture depth and CBR. Also, the variations in PCI, IRI and SN with age, traffic, texture depth and CBR are studied. Different maintenance treatments are identified for the roads depending upon the condition of the roads.

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4 Study Stretches and Data Collection Twenty three rural roads of Calicut district in Kerala state, India, are selected for the study. The roads considered for the study have an age varying from 1 to 7 years. A 200 m section from each kilometre of the road is selected for the study. The road inventory, distress, roughness, skid resistance, traffic, texture depth, CBR and maximum dry density details on these sections are collected. Pavement distress survey includes identification of the distress type, quantification of each distress and identification of the severity levels of each distress. The various distresses considered for the study include different types of cracking, pothole, patching, ravelling, shoulder drop-off, bleeding, etc. Severity levels of distresses are noted as low (L), medium (M) and high (H). The measurement of distress is done in accordance with ASTM D 6433-07 standards. PCI of each section is calculated using the distress data collected. The roughness of the pavement sections is measured using MERLIN and the skid resistance using portable skid resistance tester. The texture depth is calculated using the sand patch method. The age and the subgrade details like CBR and maximum dry density are collected from the Calicut district Pradhan Mantri Gram Sadak Yojana (PMGSY) office.

5 Data Analysis 5.1 Calculation of Pavement Condition Index Using Deduct Curve Method Pavement Condition Index (PCI) is a numerical indicator (rating) of the present condition of the pavement. PCI is calculated based on the distress data collected from the pavement sections. It is also a measure of the structural integrity and surface operational condition of the pavement. It provides a basis for determining the maintenance strategies and priorities. The rate of pavement deterioration is determined by continuous monitoring of the PCI, which helps in identifying the major rehabilitation needs. PCI provides feedback for suggesting the improvements over current pavement design and maintenance procedures. According to ASTM D 6433-07, standard practice for roads and parking lots pavement condition index surveys. PCI is found out using deduct curve method. The total quantity of each distress type at each severity level is added up and they are recorded as the total severity. The total quantity of each distress type at each severity level is divided by the total area of the section and is multiplied by 100 to obtain the percent density of each distress type and severity. The deduct value (DV) for each distress type and severity-level combination from the distress deduct value curves are determined. The maximum Corrected Deduct Value (CDV) is determined from the total deduct value and number of deducts with a value greater than 2 (q) by looking up at the appropriate correction curve for the Asphalt Concrete (AC) pavements. The

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PCI of each section is calculated by using the equation PCI = 100 − max CDV

(1)

5.2 Calculation of International Roughness Index Roughness or unevenness is the total surface undulations present in unit length of the road, along the longitudinal profile of the pavement. The presence of roughness above a permissible limit will lead to an increase in vehicle operational cost, discomfort and reduction in safety. So the pavement surface should have minimum roughness. The maximum permissible value of roughness varies according to the class of road. International Roughness Index is a measure of the pavement unevenness, which is normally measured in mm/m or m/km. International Roughness Index is calculated from the MERLIN chart. The width of central 90% histogram (D) is measured from the MRLIN chart and the International Roughness Index is calculated using the formula IRI = 0.593 + 0.0471D

(2)

where IRI = International Roughness Index in m/km. D = Width of central 90% histogram from MERLIN chart in mm. The age, ADT, PCI, IRI and SN for all the road sections are shown in Table 1 and the rating scale of PCI is shown in Table 2.

6 Development of Pavement Performance Prediction Models 6.1 Pavement Condition Index Model An attempt is made to develop a Pavement Condition Index model, which correlates the PCI value with age, ADT, CBR, maximum dry density and Camber. Based on the data collected and the PCI calculated, the variations of PCI with other variables were observed. The correlations between the variables were checked and the correlation matrix is shown in Table 3. Since the correlation coefficients of age, ADT and CBR are more than 0.5 in the correlation matrix, the variables which are highly correlated to the PCI are age, ADT and CBR. The correlation coefficient for maximum dry density and Camber shows a very low value, which indicates the insignificance of maximum dry density and

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Table 1 Age, ADT, PCI, IRI and SN of sections Sl No.

Name of the road

Section

Age (in years)

1

Palangad Odupara

1

1

2

1

2

Iyyad Neroth

1

3

Engapuzha Theyyappara

4

Adukkath Maruthamkara

ADT (PCU/day)

PCI

IRI (mm/km)

SN

438

94

0.75

438

95

0.81

93

1

305

95

0.71

105

2

1

305

96

0.65

103

1

1

334

96

0.72

95

2

1

334

95

0.69

100

3

1

334

96

0.75

98

4

1

334

97

0.83

98

1

1

1256

91

0.97

84

2

1

1256

94

0.9

87

3

1

1256

95

0.87

85

728

91

1.05

85

91

5

Malapuram Vendakkemchal

1

2

2

2

728

90

1.14

82

6

Poonoor HS Mukku

1

2

2099

87

1.39

73

7

Koolimadu Adiparambu

1

3

336

93

1.03

92

2

3

336

95

1.11

93

Vazhikkadav Perumboola

1

3

687

88

1.58

82

2

3

687

91

1.36

78

3

3

687

88

1.62

80

Korothumukku Vannathipoyil

1

3

397

91

1.47

83

2

3

397

93

1.28

85

10

Kakkundu Chavalappara

1

3

427

89

1.53

81

2

3

427

91

1.55

82

11

Mavoor Ambilleri 1

5

2166

78

2.62

66

2

5

2166

83

2.28

63

8

9

12

Irude Puthupetta

3

5

2166

85

2.19

62

1

5

1371

84

2.14

68

2

5

1371

86

2.07

67

3

5

1371

79

2.36

70

Maikavu Chundakkunnu

1

5

1395

80

2.41

68

2

5

1395

85

2.08

67

Sl No.

Name of the road

Section

Age (in years)

ADT (PCU/day)

PCI

IRI (mm/km)

SN

14

Thevarmala Kanjillade

1

5

314

82

1.94

79

2

5

314

87

1.75

80

13

(continued)

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Table 1 (continued) Sl No.

Name of the road

Section

Age (in years)

15

Mannilkadavu Katharammal

1

5

2

5

3

PCI

IRI (mm/km)

SN

973

84

2.13

71

973

83

2.23

70

5

973

83

2.19

74

Pariyangad Ariyorammal

1

6

2752

60

3.78

38

2

6

2752

62

3.47

41

Kandiyil Chennoth Thazham

1

6

1813

67

3.16

51

2

6

1813

70

2.92

49

Santhinagar Thottathilkadavu

1

6

1566

59

3.51

53

2

6

1566

61

3.49

56

3

6

1566

68

3.25

55

4

6

1566

67

3.22

53

5

6

1566

68

3.31

53

Karoonji 1 Vettukallumpuram 2

6

1993

61

3.6

46

6

1993

64

3.49

47

20

Venappara Payyoli

1

7

2324

53

3.97

36

2

7

2324

51

4.06

34

21

Irode Kanjirattu

1

7

1187

63

3.57

48

2

7

1187

58

3.72

47

16 17

18

19

22 23

ADT (PCU/day)

3

7

1187

62

3.66

50

Chempukadav Jeerakappara

1

7

286

80

2.53

58

2

7

286

83

2.39

61

Vaidyarupadi Thottumuzhi

1

7

1030

65

3.48

52

2

7

1030

62

3.61

52

Table 2 Rating scale of PCI (ASTM D 6433-07)

PCI

Rating

86–100

Good

71–85

Satisfactory

56–70

Fair

41–55

Poor

26–40

Very poor

11–25

Serious

0–10

Failed

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Table 3 Correlation matrix for PCI model PCI

Age

ADT

1.000

−0.838

−0.641

0.523

Age

−0.838

1.000

0.472

−0.127

0.126

0.089

ADT

−0.641

0.472

1.000

−0.480

−0.271

−0.258

CBR

0.523

−0.127

−0.480

1.000

0.473

−0.003

PCI

MDD Camber

CBR

MDD 0.072

Camber −0.101

0.072

0.126

−0.271

0.473

1.000

0.283

−0.101

0.089

−0.258

−0.003

0.283

1.000

camber in the PCI model. So, these variables were excluded and a regression model for PCI is developed. The PCI model developed using regression analysis is given by PCI = 80.075 − 4.634 ∗ age − 0.002 ∗ ADT + 2.749 ∗ CBR

(3)

The model gives an adjusted R2 value of 0.87 and RMSE of 4.54. The variation of PCI with age, ADT and CBR is shown in Figs. 1, 2, and 3. From the scatter plot showing the variation of PCI with age, it is evident that PCI value reduces with an increase in age. That is, as age increases, the pavement deteriorates at a faster rate. Also, the variation of PCI with ADT shows that the pavement deteriorates with an increase in traffic loads. The variation of PCI with CBR shows that as CBR increases PCI also increases. That is the strength of subgrade at the construction phase is also influencing the PCI. Fig. 1 Variation of PCI with age

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Fig. 2 Variation of PCI with ADT

Fig. 3 Variation of PCI with CBR

6.1.1

Validation of PCI Model

Out of the 56 study sections, 37 sections are used for the development of the PCI model and the remaining 19 sections for the validation of the model. The observed versus predicted PCI of the 19 sections were plotted and checked the clustering of points near the 45° line. This is shown in Fig. 4. From the plot, it is clear that the points are clustered near the 45° line. Also, the observed and predicted PCI value shows an RMSE value of 6.59 for the validation set. So, these points lead to a conclusion that the regression model developed for the PCI is a good model in predicting the PCI of road sections.

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Fig. 4 Observed versus predicted PCI

6.2 International Roughness Index Model An attempt is made to develop an IRI model to correlate the IRI value with age, ADT and PCI. The correlation matrix showing the correlation between different variables are shown in Table 4. The correlation matrix shows that age and PCI are strongly influencing the IRI and the correlation coefficient of ADT is less compared to the age and PCI. So ADT is excluded in developing the IRI model. The regression model developed for correlating the PCI with age and PCI is given by IRI = 5.504 + 0.19 ∗ age − 0.052 ∗ PCI

(4)

The model gives an R2 value of 0.89 and RMSE of 0.11 and the variation of IRI with age and PCI is shown in Figs. 5 and 6. From the scatter plots, it is clear that the IRI value increases with age and decreases with increases in PCI value. Table 4 Correlation matrix for the IRI model IRI

Age

ADT

PCI −0.973

IRI

1.000

0.930

0.635

Age

0.930

1.000

0.472

−0.838

ADT

0.635

0.472

1.000

−0.641

−0.973

−0.838

−0.641

1.000

PCI

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Fig. 5 Variation of IRI with age

Fig. 6 Variation of IRI with PCI

6.2.1

Validation of IRI Model

The observed versus predicted IRI were plotted and checked the clustering of points near the 45° line. This is shown in Fig. 7. From the plot, it is clear that the points are clustered near the 45° line and the RMSE value for the validation set is 0.115. So, it can be concluded that the regression model developed is a good model in predicting IRI. Fig. 7 Observed versus predicted IRI

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Table 5 Correlation matrix for SN with model SN

Age

ADT

1.000

−0.910

−0.711

0.845

Age

−0.910

1.000

0.472

−0.672

ADT

−0.711

0.472

1.000

−0.765

0.845

−0.672

−0.765

1.000

SN

TD

TD

Fig. 8 Variation of SN with age

6.3 Skid Number Model An attempt is made to develop a Skid Number model which correlates the SN with age, ADT and texture depth. The correlation matrix showing the correlation between different variables are shown in Table 5. It shows that age, ADT and texture depth are highly correlated to SN. But, the regression model developed is giving negative values for SN for some sections. So the ADT is excluded and a regression model is developed. The regression model developed for SN is given by SN = 72.040 − 5.234 ∗ age + 23.391 ∗ texture depth

(5)

The model gives an R2 value of 0.92 and RMSE of 4.83 and the variation of SN with age and texture depth is shown in Figs. 8 and 9. From the scatter plots, it is clear that the value SN reduces with increase in age and increases with an increase in texture depth.

6.3.1

Validation of SN Model

The observed and predicted SN values of the 17 road sections used for the validation of the SN model the observed versus predicted SN were plotted and checked the clustering of points near the 45° line. This is shown in Fig. 10.

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Fig. 9 Variation of SN with texture depth

Fig. 10 Observed versus predicted SN

From the plot, it is clear that the points are clustered near the 45° line and the RMSE value for the validation set is 6.3. So, it can be concluded that the regression model developed is good enough for predicting SN.

7 Identification of Maintenance and Rehabilitation Treatments The maintenance activities are carried out to maximize the pavement performance by keeping the PCI values of the road sections high. Different maintenance activities are suggested for increasing the performance of the pavement. They are (1) Minor maintenance, (2) Major maintenance, (3) Minor rehabilitation, (4) Major rehabilitation. Minor maintenance results in improvement of PCI values by 0–5 units, which includes routine maintenance, crack sealing, etc. Major maintenance includes an overlay of 25 mm Semi-Dense Bituminous Concrete, which results in an increase of

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PCI by 10–15 units. Minor rehabilitation will increase the PCI values by 25–35 units and it includes surface treatment, crack sealing, crack filling and overlay of 40 mm Bituminous Macadam (BM) with a seal coat. For improving the PCI values by 45–50 units, major rehabilitation treatment such as strengthening of layers is suggested.

8 Conclusions • Age of the pavement, traffic, texture depth and subgrade conditions were identified as the major factors affecting the pavement performance. • Pavement Condition Index, International roughness Index and Skid Number were identified as the pavement performance indicators. • PCI decreases with an increase in age and ADT. Also, PCI increases with an increase in CBR. • IRI increases with an increase in age and reduces with an increase in PCI. • SN increases with an increase in texture depth and decreases with an increase in age. • Based on the pavement condition predicted from different models, various maintenance and rehabilitation strategies were suggested.

References 1. Kirba¸s U, Kara¸sahin M (2016) Performance models for hot mix asphalt pavements in urban roads. Constr Build Mater 116:281–288 2. Chen X, Dong Q, Zhu H, Huang B (2016) Development of distress condition index of asphalt pavements using LTPP data through structural equation modeling. Transp Res Part C: Emerg Technol 68:58–69 3. Harikeerthan MK, JaGadeesh HS (2016) Pavement deterioration modelling of urban roads in Bangalore city. In: Proceeding of the conference on transportation systems engineering and management. 4. Rejani VU, Sunitha V, Mathew S (2016) Urban pavement maintenance management system for Tiruchirappalli city. In: Proceeding of the conference on transportation systems engineering and management. 5. Meegoda JN, Gao S (2014) Roughness progression model for asphalt pavements using long-term pavement performance data. J Transp Eng 140(8):04014037

Design and Analysis of Diagrid Structural Systems for High-Rise Buildings Sneha Mole Jacob, N. Phani Charan, and Anju Raju

Abstract The diagrid is a framework of diagonally intersecting members that are used in the construction of buildings and roofs. It requires a lower percentage of steel than a standard design. The need for columns and can be obviated by the use of diagrids. Diagonal members in the system carry gravity loads as well as lateral forces. Due to the triangulated configuration of members, internal axial forces arise in the members, in turn minimizing shear racking effects. Diagrid structures are generally used in the construction of high-rise buildings as lateral forces get minimized. The primary goal of the research is the design and analysis of diagrid structural systems for the high-rise buildings. The modeling was done by using PATRAN software and was analyzed using NASTRAN software. The study includes analysis of the representative models of various geometric forms for optimal construction in terms of strength, stiffness, aesthetic appearance, material requirement, and low cost. The investigations also include the study of the optimal cross section of diagrid members. A quasi-static environment and geometric nonlinear analysis are considered in the analysis of diagrid structures. Keywords Diagrid · Optimal construction · Nonlinear analysis · PATRAN · NASTRAN

S. M. Jacob (B) · N. Phani Charan · A. Raju KTU, Muvattupuzha, India e-mail: [email protected] S. M. Jacob · A. Raju MGMCET, Navi Mumbai, India N. Phani Charan VSSC, Thiruvananthapuram, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_17

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1 Introduction The advancements in the construction of high-rise buildings have led to the implementation of diagrid structures. In the olden times, high-rise buildings were of typical portal frame systems with horizontal beams and vertical columns. Later on, additional bracings were introduced in order to take up the lateral loads more efficiently than that in the conventional building frame systems. The major difference of a diagrid building in comparison with a braced tube building is the absence of vertical columns in the system. With a lower requirement and maximum exploitation of materials, diagrid structures exhibit their effectiveness in contrast to conventional and braced frames. Diagonal members in diagrid structures act both as inclined columns and as bracing elements, thus carrying both gravity loads as well as lateral forces. With the axial action of diagonal members, it takes up the shear acting on it, thus reducing the shear racking effects. The unique geometric configuration of the system enhances structural stability along with the aesthetic appeal. It provides for a sustainable structure with greater stiffness and structural efficiency. Redundancy in the diagrid design helps in the transfer of load from a failed portion of the structure to another. A diagrid has better ability to redistribute load than a moment frame skyscraper, creating a deserved appeal for the system. The most commonly used material for the diagrid construction is steel and the system can be applied for various geometric forms. Geometric nonlinearities have led to the evolution of diagrid projects with hyperboloid, aerodynamic, cylindrical, irregular, twisted, tapered, tilted, and free forms, the most challenging among them being “twisted”. Examples for diagrid structures with the common geometric forms are the steel diagrids that can be created using modern 3D modeling software, as the mesh conforming to almost any shape is possible. With the redundancy factor, unusual structures and complex geometries have become possible for the system. The goal of this paper is to analyze and compare the geometric nonlinearity on diagrid structural systems. The different geometrical shapes considered are building plan sections of square, triangular, and circular. Each shape of the building is analyzed for lateral displacements by varying the cross sections of the members. The different cross-sectional geometries considered are rectangular, circular, hollow circular, and I-section. The study is carried out to obtain the optimal geometries for the building and cross section.

2 Objectives of the Study The objectives of the study include the following: • To analyze the representative models of various geometric forms for optimal construction in terms of strength, stiffness, aesthetic appearance, material requirement, and low cost

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• To study the optimal cross section of diagrid members.

3 Analysis of Diagrid Buildings Geometrical nonlinear analysis of G+26 story buildings with a plan area of 625 m2 is modeled using PATRAN software and analyzed using NASTRAN software considering the seismic behavior of the structure. Buildings of square, triangular, and circular plans are considered with varying member cross sections of rectangle, circle, hollow, and I-sections.

3.1 Structural Models Regular structures with the same cross-sectional areas are considered for the analysis. G+26 buildings of 75.75 m height, with a story height of 2.75 m and a footing height of 1.5 m is modeled in PATRAN software. Plan dimensions of buildings with different geometrical forms are as follows: • Square: 25 m × 25 m, shown in Fig. 1 • Triangle: Side, a = 38 m, shown in Fig. 2

Fig. 1 Plan, elevation, and 3D model of square building

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Fig. 2 Plan, elevation, and 3D model of triangular building

• Circle: Diameter,  = 28 m, shown in Fig. 3. Member cross sections are modeled for beam cross section to be 80,000 mm2 , diagrid cross section to be 90,000 mm2 , and footing cross section to be 36,0000 mm2 , and are as follows: • Rectangle: For beams—200 mm × 400 mm For diagrid—300 mm × 300 mm For footings—600 mm × 600 mm • Circle: For beams—319.154 mm  For diagrid—338.514 mm  For footings—677.028 mm  • Hollow circle: For beams—1 = 382 mm, 2 = 210 mm For diagrid—1 = 380 mm, 2 = 172 mm For footings—1 = 720 mm, 2 = 245 mm • I-section: For beams—Total height, H = 500 mm Flange width, W = 300 mm Web thickness, t w = 78 mm Flange thickness, t f = 92 mm For diagrid—Total height, H = 500 mm Flange width, W = 300 mm

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Fig. 3 Plan, elevation, and 3D model of circular building

Web thickness, t w = 78 mm Flange thickness, t f = 92 mm For footings—Total height, H = 500 mm Flange width, W = 300 mm Web thickness, t w = 78 mm Flange thickness, t f = 92 mm

3.2 Material Properties Material properties of steel are given as follows: • Density of steel = 7800 kg/m3 • Young’s modulus = 2.1 × 105 N/mm2 • Poisson’s ratio = 0.3

3.3 Loads and Boundary Conditions Boundary conditions are provided as fixed at the base.

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Fig. 4 Maximum lateral displacement obtained for square building with rectangular cross section

Dead load value for the roof is given as 1.5 kN/m2 and for all other floors as 4.5 kN/m2 . Live load values for all floors are given as 4 kN/m2 . Earthquake loads are calculated as per IS 1893(Part1):2002. 6 load cases and 13 basic load combinations were considered for the study.

3.4 Analysis Results Analysis results were taken based on lateral displacement as shown in Figs. 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15.

4 Conclusions The conclusions obtained are the following: • The minimum lateral displacement is obtained for square building and is maximum for triangular building. • The maximum displacements are obtained at load case 1.5 (DL+ELZ− ) for square and circular buildings and is 1.5 (DL+ELZ) for triangular building. • Buildings of members with circular cross section show the minimum displacement and with rectangular cross section shows the maximum displacement.

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Fig. 5 Maximum lateral displacement obtained for square building with circular cross section

Fig. 6 Maximum lateral displacement obtained for square building with hollow circular cross section

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Fig. 7 Maximum lateral displacement obtained for square building with I-section

Fig. 8 Maximum lateral displacement obtained for triangular building with rectangular cross section

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Fig. 9 Maximum lateral displacement obtained for triangular building with circular cross section

Fig. 10 Maximum lateral displacement obtained for triangular building with hollow circular cross section

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Fig. 11 Maximum lateral displacement obtained for triangular building with I-section

Fig. 12 Maximum lateral displacement obtained for cylindrical building with rectangular cross section

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Fig. 13 Maximum lateral displacement obtained for cylindrical building with circular cross section

Fig. 14 Maximum lateral displacement obtained for cylindrical building with hollow circular cross section

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Fig. 15 Maximum lateral displacement obtained for cylindrical building with I-section

References 1. Akshat GS (2018) Dynamic analysis of diagrid structural system in high rise steel buildings. Int J Civil Eng Technol 9(8):71–79 2. Pattar CS, Gokak SV (2018) Analysis of diagrid structures with plan irregularity. Int Res J Eng Technol 5(8):435–438 3. Panchal NB, Patel VR (2018) Diagrid structural system: strategies to reduce lateral forces on high-rise buildings. Int J Res Eng Technol 3(4):374–378 4. Yadav S, Garg DV (2018) Advantage of steel diagrid building over conventional building. Int J Manag Technol Eng 3(1):394–406 5. Rai AK, Sakalle R (2017) Comparative analysis of a high rise building frame with and without diagrid effects under seismic zones III & V. Int J Eng Sci Res Technol 6(9):95–101 6. Gopisiddappa D, Divyashree M, Sindhuja GJ (2017) Performance study of high rise building with diagrid system under dynamic loading. Int Res J Eng Technol 4(6):2690–2695 7. Szolomicki J, Golasz-szolomicka H (2017) Application of the diagrid system in modern highrise buildings. Int J Adv Sci Eng Technol 5(3):7–13 8. Pawar SV, Kakamare MS (2017) Earthquake and wind analysis of diagrid structure. Int J Res Appl Sci Eng Technol 5(7):1729–1739 9. Nawale UA, Kakade DN (2017) Analysis of diagrid structural system by E-Tab. Int Adv Res J Sci Eng Technol 4(6):193–196 10. Varkey D, George M (2016) Dynamic analysis of diagrid system with complex shape. Int J Innov Sci Eng Technol 3(8):484–488 11. Shah MI, Mevada SV, Patel VB (2016) Comparative study of diagrid structures with conventional frame structures. Int Res J Eng Technol 6(5):22–29

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12. Philip NG, Shashidharan D (2016) Analysis of circular steel diagrid buildings with non-uniform angle configurations. Int J Sci Eng Res 7(10):296–303 13. Bhale P, Salunke PJ (2016) Analytical study and design of diagrid building and comparison with conventional frame building. Int J Adv Technol Eng Sci 4(1):226–236 14. Kamath K, Ahamed N (2015) Effect of aspect ratio on performance of diagrid structure circular in plan. Int J Earth Sci Eng 8(2):411–416 15. Raghunath D, Deshpande SM, Patil SR (2015) Analysis and comparison of diagrid and conventional structural system. Int Res J Eng Technol 2(3):2295–2300 16. Khan R, Shinde SB (2015) Analysis of diagrid structure in comparison with exterior braced frame structure Int J Res Eng Technol 4(12):156–160 17. Revankar RK, Talasadar RG (2014) Pushover analysis of diagrid structure. Int J Eng Innov Technol 4(3):168–174 18. Singh RK, Garg V, Sharma A (2014) Analysis and design of concrete diagrid building and its comparison with conventional frame building. Int J Sci Eng Technol 2(6):1330–1337 19. Jani K, Patel PV (2013) Analysis and design of diagrid structural system for high rise steel buildings. Proc Eng 51(19):92–100 20. Mascarenhas DP, Aithal DS (2012) Study on diagrid structures with various aspect ratio under the action of wind. Int J Adv Res Ideas Innov Technol 3(4):521–526

Seismic Analysis of Composite Box Girders with Corrugated Steel Webs and Trusses P. Aparna and Binol Varghese

Abstract The concrete box girder is one of the most commonly used bridge structures due to its large flexural and torsional stiffness. For long spans, this will not be applicable since it increases the self-weight of the structure. To reduce the selfweight, steel–concrete composite bridges had been introduced. These steels have the potential to produce considerable weight savings, although a hindrance to their effective use in conventional stiffened flat web plate girders includes the potential for web instability, excessive deflections, and fatigue failure. To overcome the limitations, innovative designs have been proposed, including the use of corrugated webs to provide enhanced shear stability and eliminate the need for transverse stiffeners. This structure consists of a top concrete slab, corrugated steel webs, and two bottom concrete-filled steel tubes connected by trusses. The project work firstly studies the behavior of a pedestrian bridge and then continues with a road bridge and its seismic analysis using FEAST (Finite Element Analysis of Structures) software. The response spectrum method of analysis is used to evaluate the maximum deformation, and stress. Various parameters used for the study are thickness and diameter of concrete-filled steel tubes (CFST), corrugated web height, and corrugation length. A comparison between flat plate web and corrugated web is studied to confirm the efficiency of corrugated webs. Keywords Concrete-filled steel tubes (CFST) · Corrugated webs (CWs)

1 Introduction Composite box girders with corrugated steel webs and trusses are a new type of advanced bridge structure proposed recently. The structure consists of a top concrete slab, corrugated steel webs, and two bottom concrete-filled steel tubes connected P. Aparna (B) · B. Varghese Department of Civil Engineering, MGMCET, Navi Mumbai, India e-mail: [email protected] B. Varghese e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_18

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Fig. 1 Typical cross section of a composite bridges with top concrete slab, trusses, and bottom CFST; b composite bridges with CSWs and CFST

by trusses. The resistance to torsion and overturning of this kind of structure is larger than that of composite bridges with a single concrete-filled steel tube. This kind of structure is able to satisfy the requirement of rapid construction, environment protection, and cost-effectiveness. Two composite box girder bridges with corrugated steel webs and trusses have been constructed in China. The design of these two bridges will give the structural details of this new type of bridge, which will also provide valuable engineering experience for the further promotion of this kind of new bridge structure. Experimental research has been carried out to study the flexural behavior and the flexural capacity of the new bridge structure. The test results show that when the test beam is at the elastic stage, the cross section can be viewed as a plane section if only the strains of the concrete top slab and the bottom steel tubes are considered. A good ductile behavior is shown by the structure in the whole loading process. The first bridge of this kind constructed in France showed that such an improvement increases the ultimate flexural capacity of the bridge by nearly 80%. There are still some limitations. The first limitation is that the cross section is triangular, the torsional stiffness and the resistance to overturning are relatively small. Second, the space for some construction procedures such as the welding between the corrugated steel webs and the steel tubes is limited. To further improve this kind of structure, the composite box girder with CSWs and trusses is proposed. The most important feature is that the single concrete-filled steel tube in Fig. 1b is replaced by two bottom steel tubes filled with concrete and connected by trusses, Fig. 2, which enhanced the capability to resist torsion and overturning. The space for construction and maintenance within a bridge cross section is also enlarged.

2 Objective • • • •

To study the buckling strength of the structure; To study the seismic analysis of the structure; To conduct a comparative study with flat plate webs; To promote the new kind of structure.

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Fig. 2 Typical cross section of composite box girders with CSWs and trusses [1]

3 Methodology The methodology comprises of literature review on composite box girders with corrugated steel webs and studying the seismic behavior of the structure using Finite Element Analysis Of Structures software (FEAST) by response spectrum method of analysis. Finite element analysis consists of discretization of materials and making of finite elements for the application of loads on each of these elements for extracting the analytical performance of the model under seismic effects. Response spectrum analysis is a very useful tool for analyzing the performance of structures. If we can find out the natural frequency of the structures then the peak response of the structure can be estimated. A shock response spectrum of BUJJ earthquake data is generated for doing the response spectrum analysis. The major steps involved are described in detail as follows: • Literature review provides a major role in collecting the required data about the various effects, advantages, and possibilities of this kind of structure. • As per the reviews, material properties, and experimental results, validation of the results can be done and the numerical model is prepared by FEAST software. • Response spectrum analysis is done with the help of the shock response spectrum generated with the help of BUJJ earthquake data obtained from COSMOS. • Comparing corrugated webs with flat plate web. • Comparing the deck slab displacements and stresses with corrugated webs and flat plate webs.

4 Validation of the Approach Validation of the approach is done with a scaled model (1/5th) of Maluanshan Park Viaduct, China. The model consists of top concrete slab of 100 mm thickness and 2080 mm width and depth of structure as 560 mm. The bottom steel tubes are provided with 146 mm diameter and 6 mm thickness and these steel tubes are connected with

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channel sections of dimensions 2xL40x3, 2xL23x3, and 2x[5. The detailed figure is shown in Fig. 3. Figure 4 shows the validation model obtained from FEAST software. From the literature reviews, there was observed a flexural strength test of this new kind of bridge, and therefore linear analysis is done to validate the approach by comparing the results. For the linear analysis, live loads are simulated with concentrated loads on L/3 and 2L/3 locations of the bridge span. Dead load is simulated with 8 numbers

Fig. 3 a Scaled model. b Details of corrugation of web

Fig. 4 Validation model

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Fig. 5 Load–deflection curve for validation

of concrete blocks of 2.5 T each. And these are provided as pressure loads on the top of the slab. Live loads of 100, 140, and 200 KN are provided at L/3 and 2L/3 locations for doing the linear analysis, and the results are obtained from deflection for 100, 140 KN, and 200 KN as 17.75 mm, 21.19 mm, and 26.35 mm, respectively. The results are compared with the load–deflection curve obtained from the literature review and the validation of the approach is done successfully with results of the linear analysis as nearly as the load–deflection curve. The load–deflection curve is shown in Fig. 5.

5 Model for the Project Study For modeling the same approach as that for validation is adopted. Elements used for modeling involves brick element, shell element, and beam element. For top concrete slab and bottom tube, brick element is chosen. Although for corrugated steel web and outer side of concrete-filled tube, shell element is chosen. And, beam element is chosen for the trusses connecting the bottom steel tubes. Meshing is done with appropriate aspect ratios and then rigid links are used for connections of the top concrete slab and bottom steel tubes with corrugated webs. The material property of the structure is also the same as that of the validation approach. The modeling details of the structure include 3.3 m wide slab, 1.6 m deep with 51.2 m span. The top slab is having a depth of 300 mm at the center and 150 mm at the end of the cantilever part of the structure. In the corrugated web portion, the web is having a thickness of 12 mm and a height of 800 mm. The bottom concrete-filled steel structures are having diameters of 500 mm each with a thickness of 24 mm. Among the trusses connecting the bottom steel tubes, the horizontal trusses are of φ 168 × 6 mm and diagonal trusses are of φ 148 × 6 mm (Fig. 6).

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Fig. 6 Corrugated web corrugation [1]

Table 1 Material property of the structure Material Cement Steel

Location

Young’s modulus

Compressive strength

Poisson’s ratio

Top slab

3.96 ×

104

50.00

0.15

Inside CFST tube

3.68 × 104

50.00

0.15

Corrugated web

2.47 × 105

–

0.30

Bottom steel tube

2.03 ×

–

0.30

105

5.1 Material Property The materials used for the study are cement and steel. The material property of the structure is as mentioned in Table 1 with Young’s modulus, compressive strength, and Poison’s ratio at different locations. The composite action of steel and cement plays an important role in the structure. The top slab of the model is provided with a material property of M50 grade expansive concrete and the corrugated steel web provided in between the slab and bottom concrete-filled steel tubes are of Fe415 grade with corrugations as shown in Fig. 3 and a thickness of 12 mm. Also, the diameter of the CFST tube provided is about 500 mm each with a thickness of 24 mm. Again these bottom steel tubes are connected with trusses of diameter 146 × 6 mm and 168 × 6 mm. Firstly, the structure is modeled for a pedestrian bridge of 25.60 m, due to time constraints and by the positive results from analyses done on the pedestrian bridge, the structure is extended to a road bridge of 51.20 m.

5.2 Loads Applied Self-weight of the bridge structure is obtained from the software.

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Loading of the Pedestrian Bridge

Loading of the pedestrian bridge is done as per IRC SP:56 (2011). The live load is given as a pressure load of 500 kg/m2 .

5.2.2

Loading of Road Bridge

The road bridge model is loaded with the live load as per IRC 6 Class A loading for single-lane bridges, since the carriageway width of the model is less than 5.3 m. The other significant loadings provided are floor finish of 2 KN/m2 and footpath load of 2.5 KN/m2 .

5.3 Static Analysis of the Structure @25.6 m Span Static analysis of a structure is done for detecting the possible errors before doing a dynamic analysis of the structure.

5.3.1

Pedestrian Bridge

The displacement of the pedestrian bridge of 25.6 m after the static analysis is obtained as 8 mm and which is not exceeding 1/300 of the span [IRC SP:56(2011)], that is, 85 mm. Also, the bridge withstands the allowable stress within 16.67 MPa (M50 grade) as per IS 456 Table 9. Figure 7 shows Table 9 of IS 456 showing the permissible stress of concrete.

Fig. 7 Permissible stresses of concrete

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Fig. 8 Displacement of road bridge @25.6 m span

5.3.2

Road Bridge

According to the allowable stresses of concrete for M50 grade concrete, the allowable stresses of concrete of the road bridge after the static analysis is within the limits. And the displacement observed is 11.39 mm, which is not exceeding 1/300th of the span, and therefore the bridge is safe under static analysis (Fig. 8).

5.4 Static Analysis of the Structure @51.2 m Span 5.4.1

Road Bridge with and Without Concrete Inside CFST

Road bridge with concrete inside the CFST tubes is analyzed under static conditions and results were obtained as evidence of lesser displacements than a hollow section. The stresses are also obtained as greater for hollow sections than concrete-filled section. The composite action of CFST structures is again proving the efficiency of the structure. The confinement of CFST structures reduces the stresses of concrete inside the tube by an outside covering of steel. These also reduce the shuttering cost of concrete. Figure 9 shows the displacement of the hollow section and Fig. 10 shows the displacement of concrete-filled CFST bridge.

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Fig. 9 Displacement of bridge with hollow CFST at bottom

Fig. 10 Displacement of bridge with concrete-filled CFST at bottom

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6 Comparative Study with Flat Plate Web 6.1 Buckling Test Buckling test of the structure is done for calculating the critical load at which the structural fails. The load factor should be greater than 1 after the buckling test, otherwise, the structure should be redesigned. Here, the buckling test is done after calculating all the live loads and dead loads coming to the web. The calculated load is applied on all the nodes on the top portion of web as point loads. The bottom nodes of the web are provided with support conditions the same as given during static analysis. For the comparative study by buckling test of flat plate web and corrugated web, a new model of flat web should be obtained with the same web thickness, height, and same loading conditions (Fig. 11). The results obtained from buckling test of both kinds of bridges showed that the load factor of the corrugated webbed bridge is 10 times greater than the flat plate webbed bridge. This shows the structural efficiency of corrugated webbed bridges than plate webbed bridges and this confirms the buckling capacity of this new kind of structure. The corrugations make the bridge to carry the shear strength of the structure. The corrugated webs can provide the whole shear resistance to the structure. But these corrugated webs cannot take the bending moment of the structure, this result is obtained from literature reviews done on the flexural capacity of these kinds of structures. Also, the literature says the bending moment is resisted by the top concrete slab and bottom concrete-filled steel tubes (Fig. 12).

Fig. 11 Buckling analysis of flat plate web showing load factor of 2.73

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Fig. 12 Buckling analyis of bridge with corrugated web showing load factor of 27.40

6.2 Displacement Variations of the Whole Structure From Figs. 10 and 13, it is evident that the displacement of flat plate web is very much greater compared to the corrugated webbed bridge. Static analysis is done to obtain the displacement of the corrugated webbed bridge and flat plate webbed bridge. The reason for choosing corrugated web to the structure is strengthening by adding these results to the project work.

6.3 Displacement Variations of the Top Slab of Structure The comparative study involves creating the top slabs without all the bottom portions and providing support conditions of corrugated webs and flat plate webs to the top slabs. So that the displacement of corrugated webs can be easily obtained (Figs. 14, 15). The area of contact of support for top slabs of corrugated webs is greater than the flat plate web. This is the reason for greater displacements and stresses of top slabs of flat plate webs as compared with corrugated webs. The corrugations add much strength to the structure. Static analysis is done for obtaining the displacements of top slabs of corrugated webs and flat plate webs (Figs. 16, 17).

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Fig. 13 Displacement of flat plate webbed bridge

Fig. 14 Stress of top slab of corrugated webbed bridge

7 Dynamic Analysis Dynamic analysis is done to know the impact of earthquake loads on the structure. The vibration tests are very expensive, and therefore dynamic analysis during the design stages of a structure reduces the cost of testing. Here the dynamic analysis is done using the response spectrum method of analysis. For doing the same shock, the response spectrum should be obtained to get the frequency domain of BUJJ earthquake data, which is downloaded from the COSMOS virtual data center.

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Fig. 15 Displacement of top slab of corrugated webbed bridge

Fig. 16 Stress of top slab of flat plate webbed bridge

Fig. 17 Displacement of top slab of flat plate webbed bridge

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7.1 Shock Response Spectrum Shock response spectrum analysis is the plot that shows the responses of a number of single-degree-of-freedom systems to an excitation. The largest response is encountered for a particular SDOF system anywhere within the time. Damping ratio ranges from 0.01 to 0.05 and the final plot gives a frequency domain for the base excitation.

7.2 Response Spectrum Analysis Response spectrum is a function of frequency or time period showing the peak response of a single harmonic oscillator that is subjected to a transient event. The response spectrum is a function of natural frequency and damping. But, not a direct representation of frequency content of the excitation, and therefore shock response spectrum is required for the response spectrum analysis. The response spectrum analysis is done in two stages as mentioned above, firstly time versus acceleration data of BUJJ earthquake is obtained from the COSMOS Virtual Data Center and given as function in the form of a real table to do the shock response spectrum analysis and a shock response spectrum is obtained in the form of frequency versus acceleration data (Fig. 18). The SRS obtained from shock response analysis is given in the FEAST software for doing the response spectrum analysis along with damping is provided of 0.02 for the analysis (Fig. 19).

Fig. 18 SRS obtained from BUJJ earthquake data

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Fig. 19 Response spectrum analysis showing the maximum displacement

The response of maximum displacement and maximum stress is obtained and compared with the allowable stresses and displacements. Here the stresses are within the allowable stresses of concrete. And displacement is within 1/300th of the span. Hence it is safe (Fig. 20).

8 Conclusion The structure can be used for pedestrian bridges and road bridges of long spans. Static analysis showed satisfactory results of displacement and stresses. Comparative study between flat slab and corrugated webs are done with buckling test, displacement variations by static analysis and stresses and variation in stresses showed greater values for flat plate webbed bridge. Therefore, corrugated webs are preferred most effectively than flat plate webbed bridges. The bridges with and without concrete-filled inside concrete-filled steel tube are also analyzed. These also showed the efficiency of the bridge with concrete inside concrete-filled steel tubes. The response spectrum analysis is also done for analyzing the responses to base excitation. The maximum response of displacement and stresses are also obtained for the base excitation. The structure, therefore, gives satisfactory results and can be promoted not only for lower self-weight but also for faster construction with low cost and with effective environmental protection, since it reduces the emission of CO2 .

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Fig. 20 Response spectrum analysis showing the maximum stress of concrete

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11. Cho J, Moon J, Ko H-J, Lee H-E (2018) Flexural strength evaluation of concrete—filled steel tube composite girder. J Constr Steel Res 151:12–24 12. Hao CC, Han LH, Wang QL, Hou C (2016) Flexural behavior of circular concrete filled steel tubes under sustained load and chloride corrosion. Thin Walled Struct 107:182–196 13. Tao Z, Song T-Y, Uy B, Han L-H (2016) Bond behavior in concrete filled steel tubes. J Construct Steel Res 120:81–93 14. Wei X, Wen Z, Xiao L, Chentai Wu (2018) Review of fatigue assessment approaches for tubular joints in CFST trusses. Int J Fatigue 113:43–53 15. Jayakrishnan TJ, Lekshmi Priya R (2017) Analysis of seismic behavior of a composite bridge using ANSYS. Int J Eng Res Technol 6:473–475 16. IS: 1893 (Part 1): 2002 (2002) Indian standard criteria for earthquake resistant design of structures, Part 1: General provisions and buildings, Bureau of Indian Standards, New Delhi 17. IS 13920:1993 (1993) Indian standard code of practice for ductile detailing of reinforced structures subjected to seismic forces, Bureau of Indian Standards, New Delhi

Experimental Study on the Effect of Natural Rubber Latex and Plastic Fiber in Concrete Elizabath M. John and Seethu Sunny

Abstract In the modern construction industry, there are a lot of materials introduced for enhancing the properties of concrete. Natural Rubber Latex (NRL) is polymer latex obtained from renewable and locally available resources, which can be employed for the effective modification of cement composites thereby encouraging a sustainable construction practice. The Natural Rubber Latex modification significantly improves the plain concrete from porous to an impermeable and denser microstructure by forming a lining of latex film across voids, pores, and micro-cracks. Polyethylene Terephthalate (PET) is a polyester polymer obtained from recyclable bottles. This project work investigates the combined effect of rubber latex and PET fibers in M40 grade concrete. Various tests are conducted on the laboratory cast concrete specimens and their behaviors are observed and documented for 7 days and 28 days testing. The solution offered in the project by using waste plastic is one of the answers to the long-standing menace of waste disposal. Keywords Polyethylene terephthalate (PET) · Natural rubber latex (NRL) · Polyester polymer

1 Introduction The common practice in the modern construction industry is to make use of locally available and natural materials from renewable resources to produce highperformance cement composites thereby ensuring an energy-efficient and environmentally responsible construction system. Concrete is one of the most widely used construction materials in the world because of its high compressive strength, long E. M. John (B) · S. Sunny KTU, Muvattupuzha, India e-mail: [email protected] S. Sunny e-mail: [email protected] MGM College of Engineering and Technology, Pampakuda, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_19

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service life, and low cost [1]. But concrete has some inherent disadvantages such as low tensile strength, crack resistance, and limited ductility [2]. A discontinuous heterogeneous system exists in concrete even before the application of any external load. When a load is acting on concrete, micro-cracks are developed, and thereby tensile strength decreases. Application of external load leads to the formation of micro-cracks. It has been investigated that short plastic fibers are used to reinforce the concrete, which drastically improves the concrete performance and eliminates the disadvantages of normal concrete such as low tensile strength, low ductility, and low energy absorption capacity. One of the most important synthetic fibers, namely Polyethylene Terephthalate (PET) is used in industrial production. The present-day worldwide production of PET exceeds 6.7 million tons/year. In India, domestic waste plastics are increasing day by day and it causes reasonable damage to the environment. The main disadvantage of plastic waste is that it is nonbiodegradable and hence it is a big headache to the environment which needs effective disposal. Annually, about 40 million tons of solid waste is produced in India. Every year this is increasing at a rate of 1.5–2%. Plastics constitute 12.3% of the total waste and most of them are produced from discarded water bottles [3]. PET bottles cannot be disposed of by dumping or burning because they produce uncontrolled fire and contaminate the soil properties and vegetation. For overcoming these situations, one of the feasible solutions is using RPET as reinforcing short fibers in structural concrete.

2 Material Characteristics 2.1 Cement Cement is one of the ingredients of concrete that acts like a binder used for construction that sets, hardens, and adheres to other materials to bind them together. The cement used for the work is Ordinary Portland Cement with its grade as 53 [4]. The properties of cement are given in Table 1. Table 1 Properties of ordinary Portland cement

S. No.

Properties

Value

1

Specific gravity

3.15

2

Standard consistency (%)

33%

3

Initial setting time (in minutes)

89

4

Final setting time (in minutes)

283

5

Mortar cube compressive strength (MPa)

55

Experimental Study on the Effect of Natural Rubber Latex … Table 2 Properties of fine aggregate

Table 3 Properties of coarse aggregate

281

S. No.

Properties

Test results

1

Water absorption (%)

0.23

2

Specific gravity

2.6

3

Bulk density(kg/l)

1.51

S. No.

Properties

Test results

1

Water absorption (%)

0.36

2

Specific gravity

2.8

2.2 Fine Aggregate For the work, river sand is used as the fine aggregate. It should be passed through 4.75 mm [5]. The properties of fine aggregate are given in Table 2.

2.3 Coarse Aggregate Coarse aggregate is the crushed stone that is used for making concrete. 20 mm size of aggregate is used for the work [5]. The properties of fine aggregate are given in Table 3.

2.4 Natural Rubber Latex The Natural Rubber Latex is obtained from the tree, namely called Para rubber [6]. The term latex means a polymer with water-based liquid. Rubber trees are largely cultivated in South America in the initial stages and later it spread to Kew garden, UK, Sri Lanka, Indonesia, Singapore, and reached India. People of Kerala started growing Rubber trees first in India. Natural Rubber Latex is formed by a simple monomer combined through a reaction which is known as polymerization. Natural Rubber Latex is added as a polymer admixture to the concrete. Inclusion of Natural Rubber Latex improves the binding properties and adhesion with aggregates. This provides superior compressive strength to the concrete. In addition, they provide good adhesion to other materials as well as resistance to physical damages such as abrasion, erosion, impact, and chemical attack. The coagulation of Natural Rubber Latex can lead to compositional instability, which is here avoided by adding ammonia-tetramethylthiuram disulfide/zinc oxide.

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2.5 Polyethylene Terephthalate (PET) Fiber PET fiber of length 35 mm and breadth 1 mm is used for the work. PET fibers into the concrete gives high tensile strength but reduces the workability because PET fibers have a very weak bond with cement paste [7].

2.6 Admixture To enhance the workability, a superplasticizer Mapefluid R440 which conforms to IS: 9103:1999 is used in this work. As per Indian standards, the dosage of superplasticizer should not exceed 2% by weight of cement. After trials, the optimal dosage of superplasticizer was found to be 0.5 to produce a slump of 75 mm.

2.7 Water Potable water is used for mixing and curing of specimens.

3 Experimental Work 3.1 Specimen Preparation The concrete specimens are cast for M40 grade by adding Natural Rubber Latex of 0.5, 1, 1.5% of the weight of cement and PET fiber of 0.1, 0.2, 0.3% of the total weight of concrete. Concrete cubes specimens of size 150 mm × 150 mm × 150 mm are cast for finding compressive strength. Beams of size 100 mm × 100 mm × 500 mm are cast to determine the flexural strength. The cylindrical specimens having a diameter of 150 mm and a height of 300 mm are cast to determine the split tensile strength. Mixer machine is used for concrete mixing. Table vibrator and needle vibrator are used for compacting the concrete mixture. All the concrete specimens are cured for a period of 7 days and 28 days before the test. The results are compared with normal concrete for finding the best combination.

3.2 Mix Ratio for M40 Grade Concrete See Table 4.

Experimental Study on the Effect of Natural Rubber Latex … Table 4 Mix ratio for M40 grade concrete as per the mix design result obtained

283

Cement

Fine aggregate

Coarse aggregate

Water

1

2.07

3.9

0.4

4 Results and Discussions 4.1 Compressive Strength of Concrete Compressive strength of concrete is computed for varying the percentage of Natural Rubber Latex and PET fiber of 7 and 28 days. From the test results, it is observed that there is a variation in compressive strength when it is compared with normal concrete. Compressive strength of normal concrete and concrete with varying percentages of Natural Rubber Latex and PET fiber are shown in Tables 5, 6, 7, 8. Table 5 Compressive strength of normal concrete

Table 6 Compressive strength of concrete with 0.5% of Natural Rubber Latex and varying percentages of PET fiber

Table 7 Compressive strength of concrete with 1% of Natural Rubber Latex and varying percentages of PET fiber

Table 8 Compressive strength of concrete with 1.5% of Natural Rubber Latex and varying percentages of PET fiber

Days

7

28

Compressive strength(N/mm2 )

29.6

40

Combinations

Compressive strength (N/mm2 )

Rubber latex (%) PET fiber(%) 7 days

28 days

0.5

0.1

14.66

33.7

0.2

37.48

52.2

0.3

16.88

47.25

Combinations

Compressive strength (N/mm2 )

Rubber latex (%) PET fiber(%) 7 days

28 days

1

0.1

40.44

48.148

0.2

34.9

39.4

0.3

27.7

50.81

Combinations

Compressive strength (N/mm2 )

Rubber latex (%) PET fiber (%) 7 days

28 days

1.5

0.1

35.85

48

0.2

40

52.29

0.3

36

46.81

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From the above table, it is clear that the maximum compressive strength for 7 days curing period is obtained at 0.5% of Natural Rubber Latex and 0.2% of PET fiber. For 28 days curing period, the maximum compressive strength is obtained at the 0.5% of Natural Rubber Latex and 0.2% of PET fiber which is greater than the compressive strength of normal concrete. From the above table, it is clear that the maximum compressive strength for 7 days curing period is obtained at 1% of Natural Rubber Latex and 0.1% of PET fiber. However for 28 days curing period, the maximum compressive strength is obtained at 1% of Natural Rubber Latex and 0.3% of PET fiber which is greater than the compressive strength of normal concrete. Here it is found that the compressive strength is decreasing on further addition of PET fiber after 0.1% up to 0.2% and then the sudden increase at 0.3% is maybe due to the balling effect of fiber particles inside the concrete. From the above table, it is clear that the maximum compressive strength for 7 days curing period is obtained at 1.5% of Natural Rubber Latex and 0.2% of PET fiber. For 28 days curing period, the maximum compressive strength is obtained at the 1.5% of Natural Rubber Latex and 0.2% of PET fiber which is greater than the compressive strength of normal concrete.

4.2 Split Tensile Strength of Concrete Split tensile strength of concrete is computed for varying percentages of Natural Rubber Latex and PET fiber of 7 and 28 days. From the test results, it is observed that there is a variation in split tensile strength when it is compared with normal concrete. Split tensile strength of normal concrete and concrete with varying percentages of Natural Rubber Latex and PET fiber are shown in Tables 9, 10, 11, 12. From the above table, it is clear that the maximum split tensile strength for 7 days curing period is obtained at 0.5% of Natural Rubber Latex and 0.2% of PET fiber. However, for 28 days curing period, the maximum split tensile strength is obtained Table 9 Split tensile strength of normal concrete

Table 10 Split tensile strength of concrete with 0.5% of Natural Rubber Latex and varying percentages of PET fiber

Days

7

28

Split tensile strength (N/mm2 )

1.41

2.8

Combinations

Split tensile strength (N/mm2 )

Rubber latex (%) PET fiber (%) 7 day

28 day

0.5

0.1

2.12

3.53

0.2

2.758

3.11

0.3

1.83

2.26

Experimental Study on the Effect of Natural Rubber Latex … Table 11 Split tensile strength of concrete with 1% of Natural Rubber Latex and varying percentages of PET fiber

Table 12 Split tensile strength of concrete with 1.5% of Natural Rubber Latex and varying percentages of PET fiber

Combinations

285 Split tensile strength (N/mm2 )

Rubber latex (%) PET fiber (%) 7 day

28 day

1

0.1

2.12

2.68

0.2

2.33

2.68

0.3

2.2

2.546

Combinations

Split tensile strength (N/mm2 )

Rubber latex (%) PET fiber (%) 7 day

28 day

1.5

0.1

1.76

3.2538

0.2

1.69

2.82

0.3

1.8

2.122

at the 0.5% of Natural Rubber Latex and 0.1% of PET fiber which is greater than the split tensile strength of normal concrete. From the above table, it is clear that the maximum split tensile strength for 7 days curing period is obtained at 1% of Natural Rubber Latex and 0.2% of PET fiber. However, it is found that for 28 days curing period, 1% of Natural Rubber Latex and varying percentages of PET fiber did not achieve the target split tensile strength of normal concrete. From the above table, it is clear that the maximum split tensile strength for 7 days curing period is obtained at 1.5% of Natural Rubber Latex and 0.3% of PET fiber. But for 28 days curing period, the maximum split tensile strength is obtained at 1.5% of Natural Rubber Latex and 0.1% of PET fiber which is greater than the split tensile strength of normal concrete.

4.3 Flexural Strength of Concrete Flexural strength of concrete is computed for varying percentages of Natural Rubber Latex and PET fiber of 7 and 28 days. From the test results, it is observed that there is a variation in flexural strength when it is compared with normal concrete. Flexural strength of normal concrete and concrete with varying percentages of Natural Rubber Latex and PET fiber are shown in Table 13, 14, 15, 16. Table 13 Flexural strength of normal concrete

Days Flexural strength

(N/mm2 )

7

28

3.84

4.56

286 Table 14 Flexural strength of concrete with 0.5% of Natural Rubber Latex and varying percentages of PET fiber

Table 15 Flexural strength of concrete with 1% of Natural Rubber Latex and varying percentages of PET fiber

Table 16 Flexural strength of concrete with 1.5% of Natural Rubber Latex and varying percentages of PET fiber

E. M. John and S. Sunny Combinations

Flexural strength (N/mm2 )

Rubber latex (%)

PET Fiber (%)

7 day

28 day

0.5

0.1

3.4

5.2

0.2

2.8

5.6

0.3

3.2

4.88

Flexural strength (N/mm2 )

Combinations Rubber latex(%)

PET fiber (%)

7 day

28 day

1

0.1

2.88

5.36

0.2

3.6

5.92

0.3

4.4

5.92

Flexural strength (N/mm2 )

Combinations

Rubber latex (%) PET fiber (%) 7 days

28 days

1.5

0.1

4

5.28

0.2

3.76

6.32

0.3

3.44

5.2

From the above table, it is clear that no combinations were able to achieve the flexural strength of normal concrete in a 7-day curing period. However, it is found that the maximum flexural strength for a 28-day curing period obtained at the combination 0.5% of Natural Rubber Latex and 0.2% of PET fiber and it is a greater value when it is compared with the flexural strength of normal concrete. From the above table, it is clear that 1% of Natural Rubber Latex and 0.3% PET fiber composes the highest value for flexural strength in a 7-day curing period. It is found that the 1% of Natural Rubber Latex and 0.2% of PET fiber, 1% of Natural Rubber Latex and 0.3% of PET fiber have the highest flexural strength and it is a greater value when it is compared with the flexural strength of normal concrete. From the above table, it is clear that 1.5% of Natural Rubber Latex and 0.1% of PET fiber are having the maximum flexural strength in a 7-day curing period. However, it is found that the maximum flexural strength for a 28-day curing period is obtained at the combination as 1.5% of Natural Rubber Latex and 0.2% of PET fiber and it is a greater value when it is compared with the flexural strength of normal concrete.

Experimental Study on the Effect of Natural Rubber Latex …

287

5 Result Analysis After comparing the test results of varying percentages of Natural Rubber Latex and PET fiber, we can observe that the maximum compressive strength and flexural strength are obtained at the combination of 1.5% of Natural Rubber Latex and 0.2% of PET fiber for 28 days curing period. Maximum split tensile strength is obtained at 0.5% of Natural Rubber Latex and 0.1% of PET fiber for 28 days curing period.

6 Conclusions After analyzing the obtained results carefully, it is concluded that • Compressive strength is maximum at 1.5% of Natural Rubber Latex and 0.2% of PET fiber for 28 days curing period and it is obtained as 52.29 N/mm2 . • Compressive strength is maximum at 1.5% of Natural Rubber Latex and 0.2% of PET fiber for 7 days curing period and it is obtained as 40.44 N/mm2 . • Split tensile strength is maximum at 0.5% of Natural Rubber Latex and 0.1% of PET fiber for 28 days curing period and it is obtained as 3.53 N/mm2 . • Split tensile strength is maximum at 0.5% of Natural Rubber Latex and 0.2% of PET fiber for 7 days curing period and it is obtained as 2.758 N/mm2 . • Flexural strength is maximum at 1.5% of Natural Rubber Latex and 0.2% of PET fiber for 28 days curing period and it is obtained as 6.32 N/mm2 . • Flexural strength is maximum at 1% of Natural Rubber Latex and 0.3% of PET fiber for 7 days curing period and it is obtained as 4.4 N/mm2 . • It is proved that the combined effect of Natural Rubber Latex and PET fiber improves the mechanical properties of concrete. • The effective utilization of PET plastic fiber can create a solution for waste plastic disposal.

References 1. Nibudey RN, Nagarnaik PB, Parbat DK, Pande AM (2013) Strengths prediction of plastic fiber reinforced concrete (M30). Int J Eng Res Appl (IJERA) 3(1):1818–1825 2. Haridass M, Gunasekaran R, Vijayakumar V, Vijayaraghavan P (2017) Experimental study on concrete with plastic plate fibre reinforcement. Int J Chem Tech Res 10(14):74–81 3. Subramani T, Fizoor A (2017) An experimental study on the properties of pet fibre reinforced concrete. Int J Appl Innov Eng Manage (IJAIEM) 6(3):58–66 4. IS 12269:2013, Indian standard. Ordinary Portland cement, 53 grade—specification. Bureau of Indian standards, New Delhi, India 5. IS 2386:1963, Indian standard (1997) Methods of test for aggregates for concrete Particle size and shape. Bureau of Indian standard, New Delhi

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6. Shaji P, Aswathi KP, Hanna P, George JK, Shameer K (2017) Effect of Natural Rubber Latex as admixtures in concrete. Int Res J Eng Technol (IRJET) 4(4):2031–2034 7. Krishnamoorthy M, Tensing D, Sivaraja (2017) Flexural properties of polyethylene terephthalate fibre reinforced concrete. Int J Chem Tech Res 10(8):365–375

Effects of Eggshell Powder and Granite Powder on the Strength Properties of Concrete by Partial Replacement of Cement and Fine Aggregate Geethika G. Pillai and Manjusha Mathew

Abstract In construction industries, the usage of cement and fine aggregate gets increased rapidly. Due to the increasing demand and higher cost of cement and fine aggregate, cement is partially replaced by eggshell powder and fine aggregate by granite powder. Eggshell waste is evolved from poultry farms, restaurants and hotels and is made up of calcium which is very similar to cement. Calcium in concrete causes a substantial increase in strength and acts as an accelerator. Granite powder is obtained from granite industries while cutting huge rocks to the desired shape. The disposal of granite powder on land causes environmental hazards like air pollution. In this project, the effect of varying percentages of eggshell powder by the weight of cement and granite powder by the weight of fine aggregate is investigated without changing the mix M40. By utilizing the waste materials, specimens are cast and various tests are conducted such as compressive strength, split tensile strength, flexural strength. The behaviors of the concrete specimen are observed and compared with conventional concrete after 7 and 28 days testing. Keywords Eggshell powder · Granite powder · Fine aggregate

1 Introduction Concrete is known as the backbone of the infrastructure development of a nation and it is widely used for the construction of buildings, bridges, dams, etc. Cement and fine aggregates are the major components of concrete. Presently, huge demand is there for cement and fine aggregate and day by day the cost of cement and natural sand is also increasing. We need 1100 kg of earth resources like limestone during the manufacture of 1000 kg of cement. About 5% of carbon-di-oxide is emitted from G. G. Pillai · M. Mathew (B) KTU, Muvattupuzha, India e-mail: [email protected] G. G. Pillai e-mail: [email protected] MGMCET, Muvattupuzha, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_20

289

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different cement production plants all over the world, which acts as a silent killer in the environment in different forms [4]. Natural river sand is the most commonly used fine aggregate. Various developing countries have met some strain in the supply of natural sand in order to meet the increasing needs of infrastructural development in recent years. Hence construction industries are looking for a suitable and effective waste product that would greatly reduce the use of cement and fine aggregate. Therefore, in the present study cement is partially replaced by eggshell powder and fine aggregate by granite powder. India has the second position in the world with annual egg production. Eggshell waste is evolved from poultry farms, restaurants and hotels and is made up of calcium usually which are disposed of [9]. Disposal of these eggshells is a big problem because if they are sent to landfills it causes health and environmental problems. Eggshells are rich in calcium and have nearly the same composition that of cement [14]. Granite belongs to igneous rock family and is obtained from granite industries while cutting huge rocks to the desired shape. Granite industries in India produce more than 3500 metric tonnes of granite powder per day as a waste product. The disposal of granite powder on land causes environmental hazards like air pollution. The density of granite is between 2.65 and 2.75 g/cm3 , similar to sand and compressive strength will be greater than 200 MPa. Granite fines are used as a filler material in the concrete, replacing the fine aggregate which will help in filling up the pores in the concrete and increase the strength of the concrete.

2 Objectives of This Study The objective of project work is to study the mechanical properties of M40 grade concrete by a new combination between eggshell powder and granite powder. Utilization of granite powder and eggshell powder will reduce the cost of river sand and cement and also conserve natural resources.

3 Materials Used 3.1 Eggshell Powder Eggshells are agricultural throwaway products produced from farms, bakeries, restaurants which damages the environment and results in ecological issues. It is systematically accepted that the eggshell consists of 52.15% of calcium. The chemical composition of eggshell powder and cement are found to be similar [9]. The specific gravity of eggshell powder is 2.6. Eggshell powder is processing in four major steps. The first step is the collection of eggshells from various sources and then washed and dried. The second step is grinding and powdering of the collected eggshell. The

Effects of Eggshell Powder and Granite Powder on the Strength … Table 1 Physical properties of cement

291

S. No.

Properties

Values

1

Specific gravity

3.15

2

Standard consistency (%)

33

3

Initial setting time (in minutes)

89

4

Final setting time (in minutes)

283

5

Mortar cube compressive strength (MPa)

55

third step is sieving of ground eggshell powder in 75-µm sieve. And the last step cement is replaced by the sieved eggshell powder at various percentages.

3.2 Granite Powder Granite is the plutonic igneous rock because it is formed due to the solidification of magma at large depth. Density and specific gravity of granite are found similar to fine aggregate. Specific gravity and water absorption of granite powder are 2.63 and 0.44, respectively, and it comes under Zone II. Granite powder is processed in three major steps. The first step is the collection of granite powder from granite crushing and polishing sites. Then the collection of granite fines, which pass through 4.75 mm. The last step is fine aggregate that is replaced by the sieved granite powder at various percentages.

3.3 Cement The most commonly available ordinary Portland cement of 53-grade was used for the experiments [18]. Cement was bought from the source throughout the project work. During storing cement, all possible contact with moisture was avoided. Physical properties of cement are given in Table1.

3.4 Fine Aggregate In this study, the concrete mixes were prepared using river sand and which should be passing through 4.75 mm [19]. The sand was confining to Zone II. Specific gravity of the sand was found to be 2.6 and water absorption is 0.23. The bulk density of fine aggregate is 1.51 kg/l.

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3.5 Coarse Aggregate Crushed granite angular aggregate from a local source, having a maximum size of 20 mm, was used for the present study [19]. The specific gravity of the coarse aggregate was found to be 2.8 and water absorption is 0.36.

3.6 Water Water is a major element of concrete and it participates in the chemical reaction with cement. Generally, water used for drinking is suitable for concrete. Impurities in water affect strength and setting time or encourage corrosion of steel reinforcement. Locally available drinking water was used in this project work.

3.7 Admixture Superplasticizer was used during the investigation to improve the workability of concrete. As per Indian Standards, the dosage of superplasticizer should not exceed 2% by weight of the cement [20]. Higher dosage of superplasticizer may affect the hydration process. After trails, the optimal dosage of the superplasticizer was found to be 0.5% to produce a slump of 100 mm.

4 Methodology and Experimental Work In the present study, concrete cubes of size 150 mm × 150 mm × 150 mm for compression test, 150 mm diameter, 300 mm height cylinders for split tensile and 100 mm × 100 mm × 500 mm size beams for the flexural test. The specimens are cast for M40 grade concrete by replacement of cement by eggshell powder of 5%, 7.5%, 10% and fine aggregate by granite powder of 5%, 7.5%, 10%. Mixing machine is used for concrete mixing. After casting, required specimens are cured by normal water curing at temperature 27 ± 2 °C. After curing, cubes are subjected to compression tests, cylinders are subjected to split tensile test and beams are subjected to flexural strength test for 7 and 28 days. The results are compared with normal concrete for finding the best combination. Mix ratio for M40 grade concrete is given in Table 2. Table 2 Mix ratio for M40 grade concrete

Cement

Fine aggregate

Coarse aggregate

Water

1

2.07

3.9

0.4

Effects of Eggshell Powder and Granite Powder on the Strength …

293

5 Results and Discussions 5.1 Compressive Strength of Concrete From the test results, it is observed that the 7 and 28 days compressive strength of concrete with cement partially replaced by eggshell powder and fine aggregate partially replaced with granite powder is varied when compared to normal concrete. The values of the compressive strength are given in Tables 3 and 4. From the above table, it is clear that for 5% granite powder combinations the concrete with 5% granite powder and 7.5% eggshell powder gives higher strength for 7- and 28-days curing period. And for 7.5% granite powder combinations the concrete with 7.5% granite powder and 5% eggshell powder gives higher strength for 7 and 28 days curing period. From the last set of combinations, the concrete with 10% granite powder and 7.5% egg shell powder gives higher strength for 7 and 28 days curing period. After comparing the combinations, the higher strength was obtained at the combination of 10% granite powder and 7.5% eggshell powder for 28 days curing period. For 7 days curing period, higher strength is obtained at 7.5% granite power and 5% eggshell powder. Table 3 Test result of 7, 28 days compressive strength of normal concrete

Table 4 Test results of concrete with eggshell powder and granite powder

Days

7

28

Compressive strength (N/mm2 )

29.6

40

Combinations

Compressive strength (N/mm2 )

Granite powder (%)

Eggshell powder (%)

7 Days

5

5

12

50.74

7.5

39.96

54.8

10

23.11

46.51

5

41.62

46.37

7.5

32

42.07

10

26.6

41.62

5

35.5

50.8

7.5

40.14

57.03

10

20.8

40.2

7.5

10

28 Days

294 Table 5 Split tensile strength of normal concrete

G. G. Pillai and M. Mathew Days Split tensile strength (N/mm

Table 6 Split tensile strength of concrete with granite powder and eggshell powder

2)

Combinations

7

28

1.41

2.8

Split tensile strength (N/mm2 )

Granite powder (%)

Eggshell powder (%)

7 days

28 days

5

5

1.55

2.47

7.5

2.2

2.97

10

1.6

2.54

5

1.6

2.26

7.5

2.33

3.11

10

1.6

2.26

5

2.12

2.97

7.5

1.55

2.47

10

0.99

1.90

7.5

10

5.2 Split Tensile Strength From the test results, it is observed that there is a variation in tensile strength of the partially replaced concrete compared to the normal conventional concrete. The test result of normal concrete is given in Table 5. Tensile strength of concrete is usually found by testing plain concrete cylinders. The values of the split tensile strength are given in Table 6. From the above table, it is clear that for 5% granite powder combinations, the concrete with 5% granite powder and 7.5% egg shell powder gives higher strength for 7 and 28 days curing period. And for 7.5% granite powder combinations, the concrete with 7.5% granite powder and 7.5% eggshell powder gives higher strength for 7 and 28 days curing period. From the last set of combinations, the concrete with 10% granite powder and 5% eggshell powder gives higher strength for 7 and 28 days curing period. After comparing the combinations, the higher strength obtained at the combination of 7.5% granite powder and 7.5% eggshell powder for 28 and 7 days curing period.

5.3 Flexural Strength The determination of flexural strength is essential to estimate the load at which the concrete members may crack. The flexural strength at failure is the modulus of rupture. The results of normal concrete are given in Table 7.

Effects of Eggshell Powder and Granite Powder on the Strength … Table 7 Flexural strength of normal concrete

Days Split tensile strength (N/mm

Table 8 Flexural strength of concrete with granite powder and eggshell powder

2)

Combinations

295 7

28

3.84

4.56

Flexural strength (N/mm2 )

Granite powder (%)

Eggshell powder (%)

7 days

28 days

5

5

2.8

4

7.5

3.4

4.88

10

4

4.98

5

4.08

5.72

7.5

3.6

4.96

10

3.28

4.88

5

3.04

4.72

7.5

4

5.76

10

2.44

4.4

7.5

10

The results of flexural strength obtained with different percentages of partial substitutions of granite powder with fine aggregate and eggshell powder with cement are given in Table 8. From the above table, it is clear that for 5% granite powder combinations, the concrete with 5% granite powder and 10% egg shell powder gives higher strength for 7 and 28 days curing period. And for 7.5% granite powder combinations, the concrete with 7.5% granite powder and 5% eggshell powder gives higher strength for 7 and 28 days curing period. From the last set of combinations, the concrete with 10% granite powder and 7.5% eggshell powder gives higher strength for 7 and 28 days curing period. After comparing the combinations, higher strength was obtained at the combination of 10% granite powder and 7.5% eggshell powder for 28 days curing period. For 7 days curing period, higher strength obtained at 7.5% granite power and 5% eggshell powder.

6 Result Analysis Each set of combinations was compared with normal concrete and the combinations that give the highest values were determined. The compared results are given in Table 9.

296 Table 9 Comparison results

G. G. Pillai and M. Mathew Strength

Combinations 7 days

28 days

Compressive strength

7.5% GP + 5% ESP

10% GP + 7.5% ESP

Split tensile strength

7.5% GP + 7.5% ESP

7.5% GP + 7.5% ESP

Flexural strength 7.5% GP + 5% ESP

10% GP + 7.5% ESP

7 Conclusions When compared to normal concrete, • A new combination of granite powder and eggshell powder improves significantly the mechanical properties of concrete. • The specimen cast with the combination of 7.5% granite powder and 5% eggshell powder gives higher compressive strength and flexural strength for 7 days and 10% granite powder and 7.5% eggshell powder concrete combinations give higher strengths for 28 days. • Specimen cast with the combination 7.5% granite powder and 7.5% eggshell powder concrete gives higher split tensile strength for 7 and 28 days. • The new combination method mix gives good mechanical properties. Therefore, concrete with eggshell powder and granite powder can be considered as an economical alternative for normal concrete.

References 1. Kannam Ch, Vasudeva Rao Ch, Venkata Rao G, Akhilesh AYDT (2018) Experimental study on M30 grade concrete with partial replacement of cement with egg shell powder. Int J Civil Eng Technol (IJCIET) 9(5):575–583 2. Ramathilagam BH, Aravinth K, Ananth C, Arisivamani L (2018) An experimental investigation of eggshell powder as a partial replacement of cement in paver block. Int J Eng Sci Comput (IJESC) 8(6):17083–17085 3. Narmatha M, Vishali G, Noveena S, Uthra Megala R (2018) Partial replacement of sand by granite powder in concrete. Int J Precious Eng Res Appl (IJPERA) 3(1):16–20 4. Bandhavya GB, Sandeep K, Bindhushree GB (2017) An experimental study on partial replacement of cement with egg shell powder in concrete. Int Res J Eng Technol (IRJET) 4(6):2318–2323 5. Subbalakshmi U, Venkateswarlu D (2017) Experimental investigation of eggshell powder as partial replacement with cement in concrete. Int J Mech Eng Comput Appl (IJMCA) 5(5):172– 180 6. Nagaraju D, Sunil Pratap Reddy S (2017) An experimental study on partial replacement of granite powder in fine aggregate. Int J Res Adv Eng Technol (IJRAET) 6(1):310–319 7. Parkash A, Pardeep Kumar Yadav A (2017) A review study of egg shell powder as a cement replacing material in concrete. Int J Latest Res Eng Comput (IJLREC) 5(4):6–9

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8. Arulkesavan S, Jothi M, Satheeshkumar M, Tamilselvi V, Usha KB (2017) Experimental investigation on concrete with partial replacement of fine aggregate by granite powder. Int Res J Eng Technol (IRJET) 4(3):1623–1627 9. Mohamed Ansari M, Dinesh Kumar M, Milan Charles J, Vani G (2016) Replacement of cement using eggshell powder. SSRG Int J Civil Eng (SSRG—IJCE) 3(3):2348–8352 10. Chiranjeevi Reddy K, Yaswanth Kumar Y, Poornima P (2015) Experimental study on concrete with waste granite powder as an admixture. Int J Eng Res Appl (IJERA) 5(6):87–93 11. Praveen Kumar R, Vijaya Sarathy R, Jose Ravindraraj B (2015) Experimental study on partial replacement of cement with egg shell powder. Int J Innovations Eng Technol (IJIET) 5(2):334– 341 12. Arivumangai A, Felixkala T (2014) Strength and durability properties of granite powder concrete. J Civ Eng Res (JCER) 4(2):1–6 13. Gowsika D, Sarankokila S, Sargunan K (2014) Experimental investigation of egg shell powder as partial replacement with cement in concrete. Int J Eng Trends Technol (IJETT) 14(2):65–68 14. Yerramala A (2014) Properties of concrete with eggshell powder as cement replacement. Indian Concr J, 94–102 15. Prince G, Adin A, Suresh Kannan T (2013) Granite powder concrete. IRACST—Eng Sci Technol Int J (ESTIJ) 3(1):193–198 16. Felixkala T, Partheeban P (2010) Granite powder concrete. Indian J Sci Technol (IJST) 3(3):311–317 17. IS 456:2000 (1970) Indian Standard—plain and Reinforced concrete—code of practice, aggregates from natural source for concrete. Bureau of Indian Standards, New Delhi, India 18. IS 12269:2013, Indian Standard—ordinary Portland Cement, 53 Grade—specification. Bureau of Indian Standards, New Delhi, India 19. IS 2386:1963 (1997) Indian Standard—methods of test for aggregates for concrete particle size and shape. Bureau of Indian Standard, New Delhi 20. IS 9103:1999 (1999) Indian Standard—concrete admixtures-specification. Bureau of Indian Standard, New Delhi

Comparison of Seismic Response of a Multi-storied Building With and Without Liquid Damper Arsha A. Deleep and Varsha Susan Thomas

Abstract A tuned liquid damper is liquid confined in a container usually placed on top of a building that uses sloshing energy of water to reduce the dynamic response of the system when it is subjected to excitation. Usually, liquid dampers are strictly connected to the main structure. The seismic analysis, also known as pushover analysis, is a subset of structural analysis. It is the calculation of the response of a building structure to earthquakes. It helps in identifying critical members to reach limit states during the earthquake and hence proper attention can be given while designing and detailing. In this study, a comparison of the seismic response of a multi-storied building with and without liquid damper will be studied. Also, a comparison of various liquid dampers will be checked and various parameters like lateral displacement, storey drift, etc., will be studied for the building. Suitability of different liquids was also studied. The software selected for the analysis is SAP2000. Keywords Liquid · Damper · Earthquake · Analysis

1 Introduction Earthquake is the most dangerous and unpredictable among other natural calamities. Earthquake causes vibration on structures, which cause damage in them and can affect human life badly. The structures constructed on an earthquake-prone area should be designed properly by taking adequate precautions to reduce the effect of the earthquake (Source Ref. [1]). Many techniques are employed for such precautions. They are shear wall, dampers, etc. The most important among them is the use of dampers. A. A. Deleep (B) · V. S. Thomas MGMCET, KTU, Muvattupuzha, India e-mail: [email protected] V. S. Thomas e-mail: [email protected] MGMCET, Muvattupuzha, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_21

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Fig. 1 Sloshing damper. Source Ref. [4]

A damper is a device used to reduce the vibrations occurring on the building during the earthquake. The process of reducing vibration is known as damping. A liquid damper is a tank or a container filled with liquids. When it is tuned to a fundamental frequency, then it is called as a Tuned Liquid Damper. The liquids may be water, sugar solution, etc. It uses the sloshing energy of liquid to resist the earthquake vibrations. Different types of tuned liquid dampers are the following: 1. 2. 3. 4.

Tuned Sloshing Liquid Dampers, Tuned Liquid Column Dampers, Modified Tuned Liquid Column Dampers, Bidirectional Liquid Dampers.

1.1 Tuned Sloshing Liquid Dampers (TSD) A tuned sloshing liquid damper is a tank partially filled with liquids, generally water (Fig. 1). They are simple devices commonly known by their name due to the simplicity in construction. These dampers are commonly of rectangular and circular shape and they are generally provided on the top of the bulding. If water is used as the liquid, it can be used for firefighting purpose also. It resists the vibration by reducing the overall displacement of the building during an earthquake by the liquid motion inside the tank as shown in Fig. 2.

1.2 Tuned Liquid Column Dampers (TLCD) A tuned liquid column damper is an open or closed container with U shape containing liquids. This is also a common category. Also, it can be provided at the top of the building. During an earthquake, the liquid in the container moves from one vertical

Comparison of Seismic Response of a Multi-storied …

301

Fig. 2 Liquid motion during vibration. Source Ref. [4]

Fig. 3 Tuned liquid column dampers. Source Ref. [4]

column to another that produces horizontal damping force. The force is developed by collision on the vertical walls and liquid and tube in the horizontal part creating abrasion. A diagram of TLCD is shown in Fig. 3 (Source Ref. [4]).

1.3 Modified Tuned Liquid Column Dampers (MTLCD) Like the name, it is a modified form of TLCD shown in Fig. 4. It is prepared by placing two TLCD in orthogonal directions. In this type, they assume the effect of damping in both vibration directions the so-called Double Tuned Liquid Column Damper (DTLCD). Also, circular shape damper is available, that is the so-called circular or torsional Tuned Liquid Column Damper.

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Fig. 4 Modified tuned liquid column damper. Source Ref. [4]

1.4 Bidirectional Liquid Dampers (BLD) In this, sloshing effect occurs in the transverse direction and works in one direction as TLCD. This is also known as Combined Liquid Damper.

2 Objectives • To model a multi-storied building with and without liquid dampers. • To study the performance analysis of building in the presence and absence of liquid dampers. • To compare the seismic response of building with and without liquid dampers. • To compare the building with tuned sloshing damper and tuned liquid column damper. • To check the seismic response of the building with damper using different liquids such as sugar solution, oils, etc.

3 Scope • There are many types of liquid dampers, tuned sloshing liquid damper, and tuned liquid column damper were chosen for the study. • The suitability of different liquids such as sugar solution, oil, etc., in damper will be checked for the performance of dampers. • The software selected for the analysis is SAP2000 (Source Ref. [2]). • Comparison of tuned liquid column damper and tuned sloshing liquid damper is going to be done (Source Ref. [3]).

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303

Fig. 5 Methodology

4 Methodology See Fig. 5.

5 Modelling and Analysis of Building Using Sap2000 The model is a G + 20 storied reinforced concrete building with an area of about 4200 sq.

5.1 Material Properties and Section Properties • Beam dimensions: (i) 200 mm 600 mm, which consists of M30 concrete and Fe500 grade steel (Source Ref. [6]). (ii) 300 mm 1200 mm, which consists of M35 concrete and Fe500 grade steel

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• Column dimensions: (i) Slab as two-way slab of M30 grade concrete with thickness 100 mm (ii) Wall of thickness 21 and 10 mm.

5.2 Loads on the Building Dead Loads. These are the self-weights of the structure. The values of the unit weights of the materials (Source Ref. [7]). Live Loads. They are also known as imposed loads and consist of all loads other than the dead loads of the structure. The values of the imposed loads depend on the functional requirement of the structure. Commercial buildings will have comparatively higher values of the imposed loads than those of the residential buildings. Toilet: 2 KN/m2 Bed Room: 2.5 KN/m2 Corridors, Passages, Staircases: 4 KN/m2 . (Source Ref. [7])

5.3 Seismic Loads The impact of earthquake on structures depends on the stiffness of the structure, stiffness of the soil media, height and location of the structure, etc. The earthquake forces are prescribed in IS 1893:2002(Part-I). This building is located in Kerala (Zone III). Z (Seismic zone coefficient) RF (Response reduction factor) I (Importance factor depending upon the functional use of the structures) SS (Rock or soil sites factor)

0.16 (Source Ref. [8]) 3 (Source Ref. [8]) 1 (Source Ref.[8])

2 (medium soil)(Source Ref. [8]) (Figs. 6, 7, 8 and 9).

5.4 Seismic Analysis of the Structure Response Spectrum Analysis. Response spectrum analysis is a linear-dynamic statistical analysis method that measures the contribution from each natural mode of vibration to indicate the likely maximum seismic response of an essentially elastic structure. It is useful for design decision-making because it relates structural-type selection to dynamic performance.

Comparison of Seismic Response of a Multi-storied … Fig. 6 Plan of RC Building

Fig. 7 3D view of RC Building without damper

5.5 Modelling and Analysis of Liquid Column Damper Using Different Liquids Liquids. Different liquids used are Mobil oil and sugar solution.

305

306 Fig. 8 3D view of RC Building

Fig. 9 3D view of RC Building with sloshing liquid damper with liquid column damper

A. A. Deleep and V. S. Thomas

Comparison of Seismic Response of a Multi-storied …

307

Mobil Oil. Mobil oil is a synthetic engine oil recommended for all types of modern vehicles. This has outstanding thermal stability. Density of Mobil oil is about 8.55 kN/m3 . Viscosity is about 0.31 Pa s. Sugar Solution. Sugar solution is a mixture of glucose and water. Density of sugar solution is about 15.58 kN/m3 . Viscosity is about 1.51 Pa s.

6 Results 6.1 Comparison of Building with Liquid Dampers and Building Without Liquid Dampers Top Joint Displacement See Fig. 10. Base Shear See Fig. 11.

Fig. 10 Top joint displacement

Fig. 11 Base shear

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Fig. 12 Joint reaction

Joint Reaction See Fig. 12.

6.2 Comparison of Building with Liquid Damper Using Different Liquids Top Joint Displacement See Fig. 13. Base Shear See Fig. 14. Joint Reaction See Fig. 15.

Fig. 13 Top joint displacement

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Fig. 14 Base shear

Fig. 15 Joint reaction

7 Discussions • Top joint displacement in x-direction of the building when sloshing liquid damper was used, got reduced to 31.43% from building without damper. In y-direction, it was reduced to 46.25%. The reduction in joint displacement when liquid column damper is used, was 43.27% in x-direction and 43.15% in y-direction. • Base shear of building with sloshing damper was slightly increased and that with liquid column damper was slightly decreased when compared to building without damper. • The displacement of building under earthquake is reduced when damper is used. • Base shear is increased when damper is used and joint reaction also increased. • Joint reaction was almost the same in x-direction in all the three cases. But a slight increase was found when dampers used. • There was a decrease in displacement when sugar solution and Mobil oil were used when compared with water. • Base shear was almost the same when damper with water and sugar solution was used and it decreased when Mobil oil used.

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• When Mobil oil and sugar solution is used in damper instead of water, the displacement was reduced. Base shear and joint reaction were also reduced. • Joint reaction was almost the same in all three liquids used in x- and y-directions.

8 Conclusions In this study, a comparison of the seismic response of a multi-storied building with and without liquid damper was done. Also, the seismic response of that building when different liquids used in a liquid column damper provided was compared. From the seismic analysis conducted, liquid damper can perform great response under earthquake. Displacement of the building was reduced in the presence of sloshing liquid damper and liquid column damper when compared with building in the absence of damper. Also, base shear and joint reaction were increased in the presence of damper. When liquid column damper was used, the area for the damper can be reduced. The liquids other than water when used in liquid damper can provide a good response during an earthquake. There is a decrease in displacement when other liquids like Mobil oil and sugar solution were used when compared with water. The base shear and joint displacement were reduced when used liquids other than water.

9 Scope for Future Work • Analysis shall be carried out in irregular buildings with different soil conditions. • Analysis shall be carried out with different widths and depth dimensions of the water tank. • Comparison shall be done for different seismic zones. • Analysis shall be carried out for different positions of the liquid damper. • Comparison may be done for all types of dampers through analysis.

References 1. Akshatha NS, Vahini M (2017) Analysis of multi-storey buildings using water tank as a liquid damper using E-tabs. Int Res J Eng Technol 5(8):1036–1042 2. Rana AB et al (2018) Analysis of Tuned Liquid Damper (TLD) in controlling earthquake response of a building using SAP2000. Int Res J Eng Technol 5(10):79–96 3. Jacob VN et al (2018) Study of combined action of coupled tuned liquid and mass damper on earthquake response of buildings. Int Res J Eng Technol 5(10):755–762 4. Pandey R, Zafar S (2016) Reduced effect of vibration by using different liquids in tuned liquid column damper. Int J Sci Res Dev 4(2):2034–2036

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5. IS 456-2000, Plain and reinforced concrete-code of practice, Fourth Revision, Bureau of Indian Standards, 1–100 6. IS 875 PART 1-1987, Code Practice for Design Loads (Other Than Earthquake) for buildings and structures. Part 1—Dead Loads and Unit Weights of Building Materials and Stored Materials, Second Revision, Bureau of Indian Standards, 1–37 7. IS 875 PART 2-1987, Code practice for design loads (other than Earthquake) for buildings and structures. Part 2—Imposed Loads, Bureau of Indian Standards, 1–18 8. IS 1893 (Part 1): 2002, Criteria for earthquake resistant design of structures, general provisions and buildings, Bureau of Indian Standards, 1–39

Enhancement in the Load-Carrying Capacity of RC Rectangular Columns Adopting CFRP and GFRP Md Ibrahim and Y. K. Guruprasad

Abstract There exist various techniques for retrofitting of reinforced concrete structural elements that have undergone damage. The use of FRP wrapping is one of the retrofitting techniques to enhance the load-carrying capacity of reinforced concrete (RC) columns (up to 20% increase). In this work, enhancement of axial load-carrying capacity of distressed RC columns adopting CFRP and GFRP was carried out. An RC column having a cross-sectional dimension of 400 mm × 600 mm and a height of 4 m is considered for this study. The RC column considered for the study was initially designed using concrete having a compressive strength of 30 N/mm2 . Eventually, due to erroneous mixing and placing of concrete in the site, it resulted in the concrete in the column to have developed a lower compressive strength of 25 N/mm2 . This distressed RC column eventually tends to have a lower load-carrying capacity due to a reduction in the compressive strength of concrete. This RC column is retrofitted using fibre-reinforced polymer (FRP) composites by wrapping the column to restore its original load-carrying capacity through the confinement provided by the FRP wrapping. The FRP composites considered in this study are carbon fibre-reinforced polymer (CFRP) and glass fibre-reinforced polymer (GFRP) fabrics wrapped around the distressed RC column with the application of epoxy. The design and estimation of quantity of the retrofit using CFRP and GFRP are adopted based on ACI codal provisions (ACI 440.2R-08). It was learnt by carrying out the design of the retrofit for the distressed RC column, the number of CFRP and GFRP layers obtained for wrapping are five numbers and ten numbers, respectively. From this study, it is learnt that CFRP is better when compared to GFRP in terms of enhancement in strength and load-carrying capacity of the distressed RC column with a lesser number of layers of wrap. M. Ibrahim (B) Final Year M.Tech Student Structural Engineering, Ramaiah Institute of Technology, Bangalore 560054, India e-mail: [email protected] Y. K. Guruprasad Associate Professor, Department of Civil Engineering, Ramaiah Institute of Technology, Bangalore 560054, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_22

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Keywords Retrofitting · RC column · Increase in axial load-carrying capacity · CFRP · GFRP

1 Introduction Retrofitting/Strengthening is the modification of existing structures to make them more resistant to seismic activity, soil failure, or ground motion due to earthquakes. Most of the buildings failed or collapsed under seismic activity mainly due to column failure. Therefore, confinement of columns becomes an important parameter while increasing stiffness, ductility of structure. The idea of column confinement was originally developed back in the 1920s [1]. In India, most of existing structures are designed based on IS 456:2000 codal provisions. There exist various techniques for retrofitting of reinforced concrete structural elements that have undergone damage [2]. • Confinement with fibre-reinforced polymers (FRP) such as aramid fibres, carbon fibres and glass fiber-reinforced composite. • Confinement with external steel caging techniques. • Confinement with RC jacketing [7]. • Confinement with composite material. In the above, all techniques retrofitting with FRPs have less weight–strength ratio, no extra changes in cross section, easy to handle, and less labour cost. Yazdani et al. [2] carried out a computational analysis on various circular column specimens. They used the CFRP for strengthening and finite element analysis for the interpretation of results with given by ACI and NCHRP. The conclusion drawn is that CFRP wrapping increased peak load capacities and ductility of confined columns. Wang et al [3] performed experimental analysis on large-scale rectangular column retrofitted with CFRP under lateral loading in different directions and reported 60° is the weakest axis or critical axis other than 90° for both unretrofitted and CFRPretrofitted columns. Jaya and Mathei [4] has done an experimental and analytical study on beam–column wrapped with GFRP and CFRP. The column is wrapped with an increasing number of plies. The result has been recorded as an increase in axial load-carrying capacity and ductility. Parghi et al. [5] have carried out an experimental analysis on strengthening and repair of reinforced concrete structures using composite material. GFRP is used as a composite material for strengthening. It has found that a sufficient amount of increase in load-carrying capacity of column and beam compared to control specimen.

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1.1 Significance of Present Work By examining the research database, it is found that the comparative strength and cost estimation for distress RC columns repaired using CFRP and GFRP based on ultimate strain and confining pressure. That leads to the calculation of number of layers of FRP material that has been identified as an important, design-perspective point of view. In this work, reinforced concrete (RC) column having a cross-sectional dimension of 400 mm × 600 mm and a height of 4 m has been considered for the present study. The same column that is undergone distress due to the reduced compressive strength of concrete due to erroneous mixing and placing of concrete in the site is strengthened by externally wrapping it using CFRP and GFRP separately.

2 Methodology • The column considered for the study was initially designed using concrete having a compressive strength of 30 N/mm2 . • Eventually, due to erroneous mixing and placing of concrete in the site, it resulted in the concrete in the column to have developed a lower compressive strength of 25 N/mm2 . • The design and estimation of quantity of the retrofit using CFRP and GFRP is adopted based on ACI codal provisions (ACI 440.2R-08)

2.1 Design of retrofit using CFRP and GFRP (for Axial Load) Following cross-sectional details and properties of the materials used are as shown below.

2.1.1

Column Cross-Sectional Details and Properties

Required compressive strength of column, φPn req Width of column, b Depth of column, d Length of column, L Compressive stress in concrete, f c Specified yield strength of nonprestressed steel reinforcement, fy

3860 KN 400 mm 600 mm 4000 mm 30 N/mm2 415 N/mm2

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Total area of longitudinal rein- 3350 mm2 [6] forcement, Ast Specified compressive strength of 25 N/mm2 concrete, ƒ c Radius of edges of prismatic cross 25 mm section confined with FRPrc Gross area of concrete, Ag Strength reduction factor, φ FRP strength reduction factor, Ψ ρ g = Ast /bh

240,000 mm2 0.65 0.95 1.40%.

The column is located in an interior environment.

2.1.2

CFRP Properties

Thickness of ply t f Ultimate tensile strength ƒ * f u Rupture strain E * f u Modulus of elasticity E f 2.1.3

0.33 mm 3792 MPa 0.0167 mm/mm 227527 N/mm2

GFRP Properties

Thickness of ply t f Ultimate tensile strength ƒ * f u Rupture strain E * f u Modulus of elasticity E f

1.3 mm 552 MPa 0.020 mm/mm 27600 N/mm2 .

2.2 Strengthening of a Distress Rectangular RC Column for Confinement and Axial Load Increment 2.2.1

Design Steps as per ACI 440.2R-08 [8] for CFRP and GFRP Distress RC Column

Step-1: Design FRP material properties f fu = C E × f fu∗

(1)

∗ εfu = C E × εfu

(2)

Step-2: Required maximum compressive strength of confined concrete ƒ cc

Enhancement in the Load-Carrying Capacity of RC Rectangular …

f cc =

  Pn req 1   − f y Ast 0.85 A g − Ast 0.80ϕ

317

(3)

Step-3: Max confining pressure due to the FRP jacket f cc − f c 3.3κa

(4)

  Ae b 2 κa = Ac h

(5)

f1 = where

b (h−2rc )2 +( hb )(b−2rc )2 ] − ρg 1 − [( h ) Ae 3A g = Ac 1 − ρg

(6)

Step-4: Number of plies/layers √ f 1 b2 + h 2 n= ψ f 2E f t f ε f e

(7)

ε f e = κε ε f u

(8)

Step-5: Checking for the minimum coefficient ratio f1 ≥ 0.08 f c

(9)

Step-6: Verifying that the ultimate axial strain of the confined concrete Eccu ≤ 0.01  εccu = εc

  f 1 ε f c 0.45 1.5 + 12κb  f c εc

(10)

where   Ae h 0.5 κb = Ac b

(11)

318 Table 1 Design details of CFRP and GFRP as a retrofit

M. Ibrahim and Y. K. Guruprasad Parameter

For CFRP N/mm2

ƒ fu

3603

Efu

0.0159 mm/mm

ƒ

30

cc

N/mm2 N/mm2

For GFRP 552 N/mm2 0.015 mm/mm 30 N/mm2 7.456 N/mm2

ƒl

7.456

n

5 no’s

10 no’s

0.2982

0.2982

0.01

0.01

fl f c

≥ 0.080

Eccu ≤ 0.01

3 Results and Discussion The design is carried out for both the cases of wrapping with CFRP and GFRP. The numbers of plies/layers for CFRP and GFRP retrofit RC column thus obtained in the design are shown in Table 1. • The analysis was carried out for both cases; it is observed from the result that the layers with CFRP retrofit are five in numbers and GFRP retrofit are about ten in numbers for increasing the compressive strength of concrete in distress column through confinement pressure by 17.5% of column strength. • The reason for more number of layers for GFRP retrofit is due to its lower modulus of elasticity when compared to CFRP that has the larger modulus elasticity.

4 Conclusion • Retrofitting using FRP materials such as GFRP and CFRP is more convenient due to its ease of application and high strength-to-weight ratio. • Both CFRP and GFRP have improved load carrying capacity of distress RC column. • Due to higher modulus of elasticity, CFRP retrofit results in lesser number of layers to restore the distress RC column. • In the case of GFRP, more number of plies are required to restore the distress RC column due to the lower value of modulus of elasticity of GFRP. • Comparatively, when the economy is to be considered, GFRP is comparatively economical than CFRP to restore distress RC column. But when the numbers of layers are to be restricted to maintain aesthetic of the member, CFRP would better option for retrofit.

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References 1. Au C (2001) Behavior of FRP-confined concrete. Master of Science Thesis, Institute of Technology, Massachusetts 2. Yazdania N, Beneberub E, Mohiuddin AH (2018) CFRP retrofit of concrete circular columns: evaluation of design guidelines. Elsevier. https://doi.org/10.1016/j.compstruct.2018.02.066 3. Wang D, Wang Z, Yu T, Li H (2018) Seismic performance of CFRP-retrofitted large-scale rectangular RC columns under lateral loading in different directions. Composite Structures. https://doi.org/10.1016/j.compstruct.2018.03.029 4. Kaya KP, Mathei J (2012) Strengthening of RC column using GFRP and CFRP. 15WCEE Lisboa 5. Parghi A, Modhera CD (2012) Strengthening and repair of reinforced concrete structures using composite material. Research gate 10.1201/9780203864005.ch64 6. IS 456 (2000) Plain and reinforced concrete—code of practice [CED 2: Cement and Concrete] “Bureau of Indian Standards” 7. IS 15988 (2013): Seismic Evaluation and Strengthening of Existing Reinforced Concrete Buildings - Guidelines [CED39: Earthquake Engineering] “BUREAU OF INDIAN STANDARDS” 8. ACI 440.2R-08 guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. American Concrete Institute

Efficiency Assessment of RC Jacket Applied on a Distressed RC Column Using Different Codal Provisions Mazharuddin Mohammed and Y. K. Guruprasad

Abstract Reinforced structural elements undergo damage when they are subjected to external agencies such as earthquakes, exposure to fire and ageing due to environmental factors. When important reinforced concrete (RC) structures undergo damage that is within a repairable limit, repair or retrofit strategies are adopted to restore the strength, stiffness and stability of such damaged buildings. In this work, an RC column is considered having the dimensions 250 mm × 500 mm × 3200 mm. The RC column in this study is cast with concrete having a compressive strength of 18 N/mm2 . The distress in this case is in the form of low compressive strength of concrete leading to low load-carrying capacity. Due to this reason, a strength modification of the concrete compressive strength in the RC column is required to enhance the load-carrying capacity. In this case, the RC column is retrofitted with the external application of reinforced concrete (RC) jacket around it. The RC jacket retrofitting method is applied when the increase in the load-carrying capacity to be enhanced is more than 25%. The reinforced concrete jacketing which is to be provided around the distressed RC column is designed by Indian codal provisions (IS 15988: 2013) and ACI codal provisions (ACI 318: 2008) separately. The design parameters provided and obtained using these codes are compared. From this study, the optimum thickness of the RC jacket applied is also evaluated. The Indian codal provision takes into account an upper bound while considering the factor of safety for design and leading to the overestimation of design parameters and quantities. The effectiveness of design with respect to the strength can be achieved by considering the optimum requirement of the quantities as per ACI codal provisions such that the cost of the overall retrofit can be minimized.

M. Mohammed (B) Final Year M.Tech Structural Engineering Student, Department of Civil Engineering, Ramaiah Institute of Technology, Bangalore, India e-mail: [email protected] Y. K. Guruprasad Associate Professor, Department of Civil Engineering, Ramaiah Institute of Technology, Bangalore, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_23

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Keywords Retrofitting · Damage · RC jacketing · Distressed RC column · RC jacket thickness

1 Introduction There are various external agencies such as earthquakes, exposure to fire, creep, shrinkage and ageing due to environmental factors, which may cause damage to the structural members (beams, columns, slabs, masonry, shear wall) in the present structures. Earthquakes cause large-scale destruction to the existing structural buildings and people, especially the structures which are not designed for earthquake resistance. The Kachchh earthquake occurred in Gujarat, India, on 26 January 2001, is the typical example that effected over a wide range [1]. Most of the construction practices being carried out today comprise of reinforced concrete structures. These structures may undergo damage when subjected to earthquakes. The amount of damage that occurs to the structure depends on the magnitude of the earthquakes. The damaged structures are assessed for the residual strength and stability of the structure. Table 1 [2] shows when one should adopt the process of retrofitting. The mode of retrofit of the structure is adopted based on the strength requirements, economy and the availability of materials. The most popular mode of retrofitting that is being adopted to the structures is Jacketing [3]. It can be performed on almost all Table 1 Decision of retrofit S. No

Decision

Percentage of retrofit cost to the total reconstruction cost (as per current rates) Buildings part of critical and lifeline facilities

Residential and official facilities

1

Adopt retrofitting, if the cost of retrofit is

50%

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323

cases of existing structural members. It can be classified based on the materials used for jacketing, such as the reinforced concrete, steel and fibre-reinforced composite. Strengthening can also be done by the introduction of new structural elements such as steel bracings and shear walls to the existing structure enhancing its lateral strength and stiffness [4]. Reinforced concrete (RC) jacketing is the addition of new concrete around the existing member with reinforcements in both longitudinal and transverse directions. Comparatively, RC jacketing of slabs with beams are found to be more difficult than the columns for the good confinement. It is possibly due to the obstruction in RC jacketing caused by the slabs. In the case of structures which have waffle slab, structural efficiency can be improved by providing RC jacketing to some of the ribs and the columns. RC jacketing of columns helps to enhance the axial and shear capacity of the column retaining its flexural strength and also the strength of the beam–column joints. The flexural strength enhancement is achieved by providing longitudinal steel in continuous from slab system through RC jacket to the foundation with the anchorage. The ductility may not be improved successfully with RC jacketing. But the lateral load capacity of the column increases preventing the stiffness concentration. Hence, foundations may not require extensive strengthening. Since there is no considerable change in the original geometry, the functionality of the building can remain unchanged. Providing a jacket or any means of retrofit may not effectively enhance the behaviour if the other members are not ductile [3]. Vandoros and Dritsos [5] carried out an experimental investigation on RC jackets with different detailing of connectors under hydraulic jack loading. RC jackets with lateral ties welded at ends showed better confinement and restrained the buckling of bars. However, bent down bars connecting longitudinal reinforcements of the existing column and the RC jacket showed a higher rate of energy dissipation than the monolithic columns. Takeuti et al. [6] performed an experimental investigation on RC-jacketed columns with different cross sections under axial compressive load. It can be observed that transverse reinforcement provided in the columns provides confinement and also attributed to the ductility of the column. Kalogeropoulos and Tsonos [7] carried out experimental work on RC jackets on columns under cyclic loads with welding of short lap splices. The stiffness, flexural strength and also the energy dissipation is found to increase as compared to the columns without RC jackets. The welding of splices resulted in better load transfer in the reinforcements of the column. Chang et al. [8] performed the experimental analysis on RC-jacketed columns and columns retrofitted with wing walls under cyclic loads. It was found that RC jacketed columns fail under flexure, showing higher energy dissipation and ductility in comparison with the columns with wing walls which fail under shear.

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1.1 Significance of Present Work This work gives the comparative study of the RC jacketing for a distressed RC column using the ACI codes and the IS codes in terms of the strength and cost of the retrofit. To study the codal provision that provides the design details of the RC jacket is structurally safe and also economical.

2 Methodology • The column dimensions and reinforcement detailing considered for the purpose of this study is from [9] and is shown in Fig. 1. • In the present study, the concrete cylindrical strength adopted for the column is fc = 18MPa (fck = 22.5MPa—cube strength) for the same area of longitudinal reinforcement considered in [9] and having a lateral tie spacing of 8mm diameter rebar at 200mm centre-to-centre spacing, for a grade of steel adopted in this work as 415MPa, that would result in a load-carrying capacity of 1470.87kN, for the column that is axially loaded. Distress in the column in this study is introduced in the form of a larger value of spacing of lateral ties due to a construction/detailing error during the construction phase that resulted in the provision of lateral ties at a spacing of 8mm diameter at 450mm centre-to-centre spacing is provided. A larger lateral tie spacing value leads to lesser confinement of concrete, leading to a lower load-carrying capacity. Erroneous provision of lateral ties provided at a larger spacing (greater than the maximum spacing value of lateral ties to be provided-IS 456:2000) leads to a distressing condition of the column. Therefore, the load-carrying capacity of this distressed column due to the larger lateral tie spacing (8mm diameter at 450mm centre-to-centre spacing) is 955.531kN (Naxial load). This distressed column needs to be retrofitted to carry a residual load of 515.340kN (Pu-residual load-carrying capacity). The retrofitting of the RC column was considered based on the load ratio calculations [9]. Therefore, in the present study, the load ratio that is computed for the distressed column has a reduced load carrying capacity of 955.531kN. Fig. 1 Sectional and reinforcement details of the column

Efficiency Assessment of RC Jacket Applied on a Distressed …

325

• The details of the distressed column that is considered for the purpose of this study is shown in Table 2. where fc fy Asc v Ag Ac N

Cylindrical compressive strength of the distressed column. Characteristic yield strength of steel. Area of steel in compression. Load ratio = (N/Ac f c ). Gross area of the column section. Concrete area in the compression. Axial load carrying capacity of the column.

2.1 Design of RC Jacket as per IS Codal Provisions In this section, the design of RC jacket as per IS codal provisions [4, 10, 11] has been presented. • The design cube strength of the RC jacket to be provided is to be taken atleast 5 MPa greater than the characteristic cube strength of the concrete present in the existing column. • The concrete and steel requirement in the RC jacket section can be computed by using Eq. (1) Pu = 0.4 ∗ f ck ∗ Ac + 0.67 ∗ f y ∗ Asc

(1)

where Pu f ck fy A’c A’sc

Residual axial load to be carried by the column. Characteristic compressive strength of concrete. Characteristic yield strength of steel. Area of concrete in cross section of a column. Area of longitudinal steel at the cross section of the column.

• The column shall be provided with a minimum of 100mm RC jacket thickness. • To account for the losses, the area of concrete and steel in the cross section are increased using the respective formulae given in Eq. (2). Ac,r eq = (3/2)Ac and Asc,r eq = (4/3)Asc ,

(2)

where Asc,req and Ac,req areas of steel and concrete to be provided actually in the RC jacket.

Column dimensions

500

Length (mm)

250

Breadth (mm) 30

Cover (mm)

Table 2 Details of distressed RC column in the present study 18

f c (MPa) 415

f y (MPa) 18

Bar Dia (mm) 1017.876

Asc (mm2 )

0.42

v

125,000

Ag (mm2 )

123,982

Ac (mm2 )

955,531

N (N)

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Efficiency Assessment of RC Jacket Applied on a Distressed …

Asc  and Ac 

327

areas of steel and concrete to be provided which are determined from the formula given in Eq. (1).

• Provide the required amount of compression steel in the column specifying the diameter and number of bars. • The lateral ties are provided by taking the bar diameter to a minimum of 8 mm or one-third of the bigger diameter bar in longitudinal steel. • Centre-to-centre spacing of lateral ties vertically is calculated according to the formula given in Eq. (3). f y ∗ dh2 s= f ck ∗ t j

(3)

where d h diameter of the lateral ties. t j required RC jacket thickness. • Check for the minimum spacing of 200 mm at the centre of column and 100 mm near the joints within a length equal to one-fourth of the clear height of the column. • Lateral ties supporting the longitudinal steel should be provided having an included angle which should not be greater than 135°.

2.2 Design of RC Jacket as per ACI Codal Provisions In this section, the design of RC jacket as per ACI codal provision [12] has been presented. • The design cylindrical compressive strength of concrete is to be taken atleast about 5 MPa greater than the existing concrete cylindrical strength of the column. • The gross area of the RC jacket required at a cross section around the column can be calculated using the formula given in Eq. (4) A g jacket =

Pu    0.6375 (0.85 ∗ f c ) + ρ f y − 0.85 ∗ f c

where Pu f c fy Agjacket ρ

Axial load to be resisted by the RC jacket. Cylindrical compressive strength of concrete for RC jacket. Yield strength of steel reinforcement. Area of RC jacket required in the cross section. Percentage of longitudinal steel reinforcement in the section.

(4)

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• The RC jacket thickness required by the member can be calculated using the quadratic equation given in Eq. (5)   2 tjacket + (bi + ti )tjacket − Agjacket = 0

(5)

where bi Existing width of the column without RC jacket. Existing length of the column without RC jacket. ti t jacket Required thickness of RC jacket. • The longitudinal bars should not have a clear spacing lesser than 1.5 * d b (diameter of the bar) or 40 mm. • The longitudinal bars in the section should not have a lateral spacing of more than one and half times the diameter of a longitudinal bar multiplied by the RC jacket thickness, or 18 inches (450 mm), whichever is lesser. • The lateral ties in the cross section should not have a spacing more than 1.25 times RC jacket thickness or 12 inches (300 mm) or 48 * diameter of bar or least lateral dimension. • The lateral ties should have a standard 135-degree hook at one end and the other end a hook of 90°.

3 Results and Discussions • The distressed column member has an axial load carrying capacity of 955,531 N which needs to be strengthened [9]. • RC jacket provided is designed to carry the residual axial load of 515,340 N safely. Parameters adopted for the design of the RC jacket to strengthen the distressed RC column in the present study as per ACI and IS codes are shown in Table 3. • It can be observed from Table 3 that for the same residual axial load, the RC jacket thickness and the longitudinal reinforcement required are higher in the IS design method when compared to the ACI design method. • The lateral reinforcement is more in the ACI method than in the IS method which may tend to increase ductility in the column designed by the ACI method. • The sectional properties and the load capacities of the column with varying RC jacket thicknesses are compared with respect to American (ACI) and Indian(IS) codal provisions as shown in Table 4. • It is in Table 4, the IS method requires comparatively higher compression reinforcement for the same cross-sectional area of RC jacket increasing the cost of RC jacketing. • The variation of load-carrying capacity of the column with respect to the change in the RC jacket thickness is shown in Fig. 2.

Efficiency Assessment of RC Jacket Applied on a Distressed … Table 3 Parameters adopted for the design of the RC jacket as per ACI and IS codes

329

CODES

ACI 318 (2008)

IS 15988 (2013)

Units

Pu

515,340

515,340

N

f cj

24

24

MPa

f ck

30

30

MPa

tj

75

100

mm

Length

650

700

mm

Breadth

400

450

mm

Agj

135,000

190,000

mm2

Acj

134,325

188,480

mm2

Longitudinal reinforcement Diameter

18

mm

Number of bars 6

12

6

nos.

Ascj

679

1527

mm2

pc

0.50%

0.80%

Diameter

10

8

mm

Spacing

90

100

mm

Lateral ties

• From Fig. 2, it is observed that the load-carrying capacity of the retrofitted column designed by ACI provisions varies slightly higher from IS provisions for the same RC jacket thickness at each point. • Further, the steel required by the ACI provisions being lesser than the IS provision; it has higher load capacity for the same sectional area. • The increase in load-carrying capacity of the column with every 25 mm increase in RC jacket thickness is as shown in Fig. 3. • The increase in load capacity varies linearly with the increase in RC jacket thickness. • Comparatively, an increase in load capacity is seen higher in the ACI method than in the IS method. • All the above variations suggest that the IS methods underestimate the material strength such as steel when compared with ACI methods.

4 Conclusion • The sectional properties such as the area of concrete, area of longitudinal steel and spacing of lateral steel reinforcement are observed to be optimal based on American codal provisions in designing RC jackets. • The overall cost of RC jacketing reduces comparatively by adopting the design based on American codal provisions.

ACI

IS

ACI

IS

ACI

IS

ACI

IS

134,325

189,050

248,750

313,425

383,075

457,700

75

100

125

150

175

200

456,320

381,920

312,480

248,000

188,480

133,920

2300

1925

1575

1250

950

675

3680

3080

2520

2000

1520

1080

6889.88

5766.53

4718.07

3744.5

2845.82

2022.03

6499.064

5439.434

4450.446

3532.1

2684.396

1907.334

1123.35

1048.46

973.57

898.68

823.79

0

1059.63

988.988

918.346

847.704

777.062

0

t j (mm) Acj (mm2 ) Acj (mm2 ) Ascj (mm2 ) Ascj (mm2 ) Axial load capacity Axial load capacity (KN) Increase in load carrying Increase in load carrying (KN) capacity capacity (KN) (KN)

Codes

Table 4 Comparison of sectional properties and load carrying capacities due to varying RC jacket thickness

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Fig. 2 Load capacity versus RC jacket thickness

Fig. 3 Increase in load capacity versus increase in RC jacket thickness

• The Indian codal provisions underestimate the strengths of concrete and steel by considering higher factor of safety in comparison with the American code of design. • The degree of lateral confinement offered by the lateral ties in the RC jacket is observed to be comparatively higher based on American codal provisions due to lesser spacing of lateral ties in the RC jacket, thus making such a retrofit structurally stable. • It is learnt from this study that the design of the RC jacket as per ACI code is more preferable from a safety and economy point of view.

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References 1. Guidelines for repair, restoration and retrofitting of masonry buildings in Kachchh earthquake affected areas of Gujarat. GSDMA, Government of Gujarat, March 2002 2. National Disaster Management Guidelines (2014) Seismic retrofitting of deficient buildings and structures. ISBN No. 978-93-84792-00-8 3. Waghmare PB (2011) Materials and jacketing technique for retrofitting of structures. Int J Adv Eng Res Stud I(I) 15–19 October–December 2011. E-ISSN2249-8974 4. IS 15988 (2013) Seismic evaluation and strengthening of existing reinforced concrete buildingsguidelines 5. Vandoros KG, Dritsos SE (2008) Concrete jacket construction detail effectiveness when strengthening RC columns. Constr Build Mater 22:264–276. https://doi.org/10.1016/j.conbui ldmat.2006.08.019 6. Takeuti AR, de Hanai JB, Mirmiran A (2008) Preloaded RC columns strengthened with highstrength concrete jackets under uniaxial compression. Mater Struct 41(7):1251–1262 7. Kalogeropoulos GI, Tsonos AG (2014) Effectiveness of R/C jacketing of substandard R/C columns with short lap splices. Struct Monit Maintenance 1(3):273–292. http://dx.doi.org/10. 12989/smm.2014.1.3.273 8. Chang S-Y, Chen T-W, Tran N-C, Liao W-I (2014) Seismic retrofitting of RC columns with RC jackets and wing walls with different structural details. Earthq Eng Eng Vibr 13(2):279–292. https://doi.org/10.1007/s11803-014-0230-4 9. Bousias S, s-Loukas Spathis A, Fardis MN (2004) Seismic retrofitting of columns with lapsplices via RC jackets. In: 13th World conference on earthquake engineering, 1–6 August 2004. Paper No. 1937 10. IS 456 (2000) Plain and reinforced concrete—code of practice 11. Gupta N, Dhiman P, Dhiman A (2015) Design and detailing of RC jacketing for concrete columns. IOSR J Mech Civ Eng, 54–58. E-ISSN: 2278-1684, p-ISSN: 2320-334X 12. Al-Afandy T, Bakry M (2015) Required RC jacket thickness and reinforcement ratio for repairing RC tied rectangular and circular concrete columns, 9 March 2015

A Feasibility Study of Colloidal Silica as Stabilizing Material for Passive Site Remediation Prashansha Sharma , Jiji Krishnan, and Shruti Shukla

Abstract Passive site stabilization is a ground improvement method that causes minimal disruption to the site being treated. The concept is to allow a low-viscosity fluid to flow to the target area that solidifies there and create a bond between soil particles. Colloidal silica can be used as a stabilizing material in passive site remediation. This paper explores the chemical processes that are required to initiate the gelling process in colloidal silica. pH and ionic strength are the two parameters that most affect the gelation of colloidal silica. The paper aims to explore optimum pH and corresponding salt content which provide workable gel time in the field. Gel time has been observed for a maximum of 120 days at different pHs and, gel time curves are plotted for various combinations. It was found that increasing salt content leads to a decrease in the gel time. A pH range of 4.5–6.2 has been observed as the most optimum pH range. To find out the effects of gelation in the sand, unconfined compression tests were performed. Samples of 40% relative density grouted with four different colloidal silica percentages under a curing period of 3, 7 and 28 days were tested. A total of 36 samples was tested. It was found out that the strength of the treated sand increases with an increase in colloidal silica percentage and curing time. As a result of the findings of the present research, colloidal silica can be proposed as a suitable stabilizer for non-disruptive liquefaction mitigation. Keywords Colloidal silica · Liquefaction · Passive site remediation · Soil stabilization

1 Introduction Liquefaction occurs when saturated or partially saturated soil loses its shear strength under the application of an applied load. Commencement of liquefaction might occur due to monotonic or cyclic loading whereafter soil loses its stiffness and behaves like a liquid. Generally, liquefaction is observed in saturated loose sandy or non-plastic P. Sharma (B) · J. Krishnan · S. Shukla Sardar Vallabhbhai National Institute of Technology, Surat, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_24

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silty soils. When there is a sudden change in applied stress, loose sands compress, and excess pore water pressure is generated. All the stress is then born by pore water and sand loses its strength. With the increase in pore water pressure, effective stress reduces and ultimately becomes zero. Catastrophic losses occur when liquefaction occurs due to the earthquakes in built environments. Structures resting on the liquefiable soils immediately lose support leading to the damages caused by uneven settlements. Liquefaction mitigation methods that are conventionally used are soil replacement, lowering of the groundwater table, compaction of sand by various methods, grouting, deep mixing pile method and dissipation using screen piles. According to Huang and Wen [1] traditional methods of liquefaction mitigation suffers from three major problems: (1) ways to mitigate liquefaction at already developed sites which are susceptible to liquefaction; (2) finding cost-efficient methods in order to mitigate liquefaction in large areas; (3) exploring materials and methods for liquefaction mitigation which are environment-friendly. Conventional methods fall short under site constraints and are generally not applied to structures which are susceptible to vibrations or deformation at developed sites [2]. Passive site remediation is the process in which a low-viscosity grout is allowed to flow to the target location and solidify there. A suitable stabilizer must possess the ability to travel the required distance prior to gelation. In order to fulfil this requirement, the stabilizer must have low initial viscosity. The gel time must be controllable and stabilizer must be chemically and mechanically stable under typical site condition. Easy handling at the site and minimal environmental threat should be posed by the stabilizer. Colloidal silica possesses all the desired characteristics to be used as a stabilizer for passive site remediation [3]. Sand stabilized with colloidal silica also exhibits a consequential increase in liquefaction resistance as the silica gels fill the voids and create a bond between soil particles [4]. Colloidal silica is stabilized by the manufacturers using alkaline solutions, such as sodium hydroxide, to prevent the gelation process. Gelling occurs in colloidal silica when the pH of the solution ranges from 5 to 8. Using the combinations of salt and acid, pH can be altered, and gel times can be controlled. Rheological studies revealed that during gelling the viscosity of the colloidal silica solution increases [5]. This paper explores the feasibility of colloidal silica as a suitable stabilizer for passive site remediation. A number of laboratory experiments have been performed to evaluate the suitable pH range and corresponding ionic strength to arrive at a workable gel time, which would be required at the site. Gel time is defined as the time required for the colloidal silica solution to convert into a gel-like solid after mixing. Minimum gel times are observed in the pH range of 5–7. Outside this range, gel time can significantly increase [2]. Hydrochloric acid (HCl) and sodium chloride (NaCl) salt were used to maintain the pH in the desired range. Gel times corresponding to different pHs have been noted. Passive site remediation is based on the principle that the stabilizer has a low viscosity until it reaches the target location. In order to understand the rheological behaviour of colloidal silica solution in conjunction with the gels times, the viscosity of the solution was also observed.

A Feasibility Study of Colloidal Silica as Stabilizing …

335

In contemplation of understanding shear strength of sand grouted colloidal silica gel, unconfined compressive tests were run. These tests were performed on the samples that were grouted with four different CS weight percentages, 7.5, 10, 15 and 30%. Effects were studied for three different curing periods 3, 7 and 28 days.

2 Properties of Colloidal Silica Colloidal silica is an aqueous solution obtained after the dispersion of nanosilica particles which are obtained from saturated solutions of silicic acid [6]. CS is a chemically inert, environment-friendly material having eminent durability characteristics [7]. Using alkaline solutions such as NaOH colloidal silica is stabilized against gelation by the manufacturers. Alkaline compounds initiate ionization and cause silica particles to repel [6]. Gelation is the process in which the aqueous colloidal silica solution converts into gel formation. In order to commence the gelation, repulsive forces are to be reduced. Colloidal silica particles when interacting with each other siloxane bonds are formed [8]. A specific pH range is required by the colloidal silica particles to interact with each other and form a siloxane bond.

2.1 Effect of pH on Gelation of Colloidal Silica For the pH value greater than or equal to 8, O− particles on the surface cause repulsion between the particles, and for the pH less than 5, particles are either neutral or repel each other. It is only between the pH range 5 and 8 that the siloxane bond forms. The formation of a siloxane bond is illustrated in Fig. 1. The behaviour of the colloidal silica particles at different pH ranges has been illustrated in Fig. 2. Gel times depend upon the particle to particle interaction, and therefore, based on different levels of interaction, gel states have been categorized by Sydansk in 1990 [9]. 11 different gel states have been identified and are tabulated in Table 1.

2.2 Effect of Addition of NaCl Salt in the Colloidal Silica Solution Colloidal silica manufacturers stabilize the solution so that it doesn’t gel until being used. When salts are added to the colloidal silica solution double layer around the particles shrinks, this leads to higher interparticle collision and therefore results in lesser gel time. With an increase in the salt concentration in the solution, gel

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Fig. 1 Siloxane bond formation with gelling of colloidal silica particles (After Moridis et al. [8])

time decreases rapidly. It is observed that polyvalent cations have a greater effect on double-layer shrinking when compared to monovalent cations; hence polyvalent cations reduce gel time faster [10]. NaCl and NH4 Cl both can be used for reducing the gel time. In the present study, NaCl has been used.

3 Materials The sand used in the testing programme is the river sand passed by 2-mm sieve. The grain size distribution was done according to ASTM D422 [11]. The maximum density of the soil was obtained with the help of a vibrating table, as mentioned in ASTM D4253 [12]. For the minimum density and relative density calculations, ASTM D4254 [13] was referred. The properties of the soil tested in this study are tabulated in Table 2. Ludox® SM-30 was used to prepare the stabilizer in the present study. Properties are mentioned in Table 3. To alter the pH of the colloidal silica solution, 6 N hydrochloric acid (HCl) was used. Scientific analytical reagent sodium chloride (NaCl) was used to increase the ionic strength of the colloidal silica solution.

A Feasibility Study of Colloidal Silica as Stabilizing …

337

Fig. 2 Colloidal silica particle interactions at different pH magnitudes (a) pH ≥ 8: Repulsion between colloidal silica particles due to the presence of O− particles on the surface, (b) pH < 5: either particles repel each other or are neutral, (c) 5 < pH < 8: Formation of siloxane bonds (Si–O–Si) [2]

4 Test Procedures 4.1 Pilot Testing Pilot testing was done to identify the range of pH in which the gelation commences. Fifty-millilitre centrifuge tubes were used for preparing the samples. Thirty millilitres of Ludox® SM-30 were taken in 12 different centrifuge tubes (Fig. 3). Hydrochloric acid was added to the solution drop by drop with the help of a pipette, and pH was continuously observed using a pH meter. Following is the tabulation of pH

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Table 1 Gel states. Source Sydansk [9] Gel state

Description

1

No detectable gel formed. Gel appears to have the same viscosity (fluidity) as the original polymer solution, and no gel is visually detectable

2

Highly flowing gel. Gel appears only slightly more viscous than the original polymer solution

3

Flowing gel. Most of the obviously detectable gel flows to bottle cap upon inversion

4

Moderately flowing gel. A small portion (5–15%) of gel does not readily flow to bottle cap upon inversion

5

Barely flowing gel. Gel slowly flows to the bottle cap and/or a significant portion (>15%) of gel does not flow upon inversion

6

Highly deformable non-flowing gel. The gel does not flow to bottle cap upon inversion (gel flows to just short of reaching bottle cap

7

Moderately deformable non-flowing gel. Gel flows about halfway down bottle upon inversion

8

Slightly deformable non-flowing gel. Only gel surface deforms slightly during inversion

9

Rigid gel. There is no gel-surface deformation upon inversion

10

Rigid ringing gel. Tuning fork-like mechanical vibration can be felt or heard after the bottle is tapped

11

Rigid gel no longer ringing. No tone or vibration can be felt or heard, because the natural frequency of gel has increased

Table 2 Properties of sand

Parameters

Magnitude

Specific gravity

2.692

Maximum unit weight

1.856 g/cc

Minimum unit weight

1.574 g/cc

Effective grain size (D10 )

0.45

Coefficient of uniformity (Cu )

2.67

Coefficient of curvature

1.17

Indian standard soil classification

SP

emax

0.71

emin

0.45

maintained and the salt added to the centrifuge tube. The gel state identification process has been followed, as described by Gallagher [14]. The sample that was obtained in pilot testing after a curing period of 3 days has been shown in Fig. 4. Colloidal silica and sand bonded together, and a solid continuum was observed.

A Feasibility Study of Colloidal Silica as Stabilizing … Table 3 Properties of colloidal silica

339 Ludox® -SM

SiO2 /Na2 O (by weight)

45–56

Stabilizing counter ion

Sodium

Particle charge

Negative

Silica weight (%)

30

pH

9.7–10.3

Viscosity (cP)

4.8–6.8

Average particle size (nm)

7

Specific surface area (m2 /g)

320–400

Specific gravity

1.209–1.227

Fig. 3 Centrifuge tubes with different combinations of salt content and pH

4.2 Gel Time Observations For passive site remediation, gel time is one of the most significant criteria. This testing programme was conducted in order to find out the relation between pH, ionic strength and gel time. All the samples were made in 50-ml centrifuge tubes. Thirtymillilitre Ludox® SM-30 was diluted by mixing distilled water to make a 7.5 weight percentage. pH and ionic strength were altered to initiate gelation and gel times are monitored for different pH for three different ionic strengths, i.e. 0.01, 0.03 and 0.1 N. pH was constantly monitored with the help of a pH meter. The calculations for salt addition were done, as explained in Sect. 4.1. Gel times were observed until 120 days in the case of samples having pH < 5 and pH > 8. Gel times in all the samples have been observed until the attainment of gel state 9, according to Table 1.

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Fig. 4 The sample obtained from pilot testing after 3 days of curing period

4.3 Unconfined Compression Testing Colloidal silica grouted sand needs curing time, and no common consensus has been reached amongst various researchers working in this field. Some researchers have performed testing after 3 days of curing period others such as Moridis et al. [8] performed testing after 7 days of curing period. Modern researchers have conducted testing in accordance with the gel times. They chose the curing period to be four times as that of gel time. According to Gallagher and Mitchel [15], the most optimized curing period is 10 times as that of gel time. In this study, the curing period has been adopted as 3, 7 and 28 days. This was done in order to identify the optimized curing time for soil samples grouted with colloidal silica. Sand was weighed according to the calculations of mould volume and the corresponding relative density, which is 40% for this research. In order to get the desired weight percentage of colloidal silica, tap water was added to it. The volume of colloidal silica taken is the same as that of the void volume of the sample. After adjusting the pH and ionic strength, the colloidal silica solution was injected in the pre-measured sand. The samples were kept in the humidity chamber undisturbed for a curing period of 3, 7 and 28 days. A total of 36 samples were made and tested. ASTM D2166 [16] was followed while measuring the unconfined compressive strength of the sands grouted with colloidal silica. The strain rate that was used throughout the tests is 0.2% per minute. The sample was kept at the centre of the

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bottom plate. The loading device was so arranged that it was in contact with the sample. All the load-deformation readings were recorded in the data logger. Loading continued until the sample failed ultimately, i.e. it stopped resisting any load.

5 Results and Discussion 5.1 Pilot Testing Results While performing the pilot tests, food dye was mixed in the colloidal silica solution to observe the extent of seepage of colloidal silica in the voids of the loose sand. The main aim of pilot testing was to identify the suitable pH range in which gelation commences. From Table 4, different gel states were identified, and it was concluded that gelation commences at pH 4.2. Minimum gel time was observed to be in the pH range of 4.5–6.2. Figure 5 shows the SEM images of samples after 7 days of curing period. In order to study the molecular-level changes when colloidal silica is added to the sand particles, SEM analysis was performed. It can be seen that colloidal silica combines with sand, and a continuum is formed. Four different resolutions, ×100, ×500, ×5000 and ×10,000, have been shown below. The cracks observed in the image 4c are desiccation cracks. Colloidal silica covers the sand particles and makes a continuous material. From the SEM analysis, it was observed that the colloidal silica and sand continuum that gets formed is a brittle material. Table 4 Pilot testing data providing corresponding gel state for different pHs and ionic strength values

Test tube

pH

Salt content and ionic strength

1

1.1

2.922 g, 1 N

Gel state 1

2

3.4

2.922 g, 1 N

3

3

4.0

2.922 g, 1 N

7

4

4.2

2.922 g, 1 N

9

5

4.5

2.922 g, 1 N

11

6

4.8

2.922 g, 1 N

11

7

5

2.337 g, 0.8 N

11

8

5.5

1.753 g, 0.6 N

11

9

6

2.337 g, 0.8 N

11

10

6.2

1.753 g, 0.6 N

11

11

8

2.922 g, 1 N

8

12

10

2.922 g, 1 N

4

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Fig. 5 SEM images at different resolutions of colloidal silica grouted sand sample after 7 days curing period

A Feasibility Study of Colloidal Silica as Stabilizing … Fig. 6 Gel time curves for 7.5 wt% colloidal silica

343 no salt 0.1N NaCl

100

0.6N Nacl

Gel time (days)

10

1

0.1 4

5

6

7

8

pH

5.2 Gel Time Curves For two different ionic strengths, 0.1 and 0.6 N gel time curves have been plotted. The duration of gel time was observed without the addition of salt too. All the tests were done for 7.5 wt% colloidal silica. In Fig. 6, it can be seen that the minimum gel time is observed in the pH range of 4.5–6.2. This is the optimum pH range for gelation. The test programme in this research was done on a very small scale; therefore, the gel times are obtained in minutes and hours. These can be suitably altered while working in the field by choosing the correct combination of pH and ionic strength. Gel times were observed until a period of 120 days and therefore for pH < 4 and pH > 8. Gel times might be as long as a year [14].

5.3 Unconfined Compressive Strength Results Unconfined compressive strength tests were conducted on soil samples grouted with different colloidal silica weight percentages 7.5, 10, 15 and 30%. Results for the testing programme are plotted in Fig. 7. The UCS value is almost linearly increasing with the increase in the colloidal silica percentage. Higher unconfined strength values are obtained when the ionic strength is increased. It can be concluded that the higher ionic strength leads to the greater strength of particle to particle bond between colloidal silica particles due to which UCS value is found to increase linearly. The samples before and after testing are shown in Fig. 8. The shear plane was clearly observed in all the samples after failure.

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Unconfined compressive strength(kPa)

400

300

200

0.6N 0.8N 1N 100

Unconfined compressive strength (kPa)

(a)

20

30

Colloidal silica w% 0.6N 0.8N 1N

400

300

200

100

(b)

Unconfined compressive strength (kPa)

10

10

20

30

Colloidal silica w% 0.6N 0.8N 1N

400

300

200

100

(c)

10

20

30

Colloidal silica w%

Fig. 7 Unconfined compressive strength for different colloidal silica percentage (a) Curing period = 3 days (b) Curing period = 7 days (c) Curing period = 28 days

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Fig. 8 UCS samples before and after testing

6 Conclusion 1. The optimum range of pH at which gelation commences is 4.5–6.2. 2. As the ionic strength of the colloidal silica solution is increased, the gel time has been observed to decrease rapidly. It is advised to keep the ionic strength close to 0.6 N while working in the field. 3. Unconfined compressive strength of the samples is found to increase with the increase in the colloidal silica percentage. For liquefaction mitigation Gallagher [14] suggested 5 wt% colloidal silica will be adequate but according to our research, we suggest a 10 wt% colloidal silica in order to improve ground’s mechanical property along with liquefaction mitigation. 4. The shear parameters (c, ϕ) were significantly improved after the addition of colloidal silica. 5. Unconfined compressive strength was found to slightly improve with the curing period. It can be considered that while operating in the field, a minimum curing period of 3 days should be provided in order to achieve a considerable strength value.

7 Future Scope The current study dealt with the effects of salt and acid addition in the colloidal silica solutions. When passive site remediation will take place in the field and colloidal silica will be transported with the groundwater, cations such as calcium and magne-

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sium are ought to be present in the groundwater. The effect of such cations and heavy metals on the gelation process is yet to be studied. The current study was done at a very small scale; therefore, the readings of gel times obtained might change with the scale of application. A similar study should be done on a larger scale to determine more accurate gel times for the passive site remediation. Acknowledgements The authors would like to acknowledge the Ministry of Human Resource Development for providing financial assistance for this study. This research work was supported by Sardar Vallabhbhai National Institute of Technology.

References 1. Huang Y, Wen Z (2015) Recent developments of soil improvement methods for seismic liquefaction mitigation. Nat Hazards 76:1927–1938. https://doi.org/10.1007/s11069-014-1558-9 2. Gallagher PM, Pamuk A, Abdoun T (2006) Stabilization of liquefiable soils using colloidal silica grout. J Mater Civ Eng 19:33–40. https://doi.org/10.1061/(ASCE)0899-1561(2007)19: 1(33) 3. Gallagher PM, Mitchell JK (2000) Passive site remediation for mitigation of liquefaction risk. Proc MEDAT-2 Work MCEER, Univ Buffalo, SUNY, pp 149–155 4. Georgiannou VN (2017) Mechanical behaviour of sand stabilised with colloidal silica, 4 5. Wong C, Pedrotti M, El Mountassir G, Lunn RJ (2018) A study on the mechanical interaction between soil and colloidal silica gel for ground improvement. Eng Geol 243:84–100. https:// doi.org/10.1016/j.enggeo.2018.06.011 6. Gallagher PM, Lin Y (2009) Colloidal silica transport through liquefiable porous media. J Geotech Geoenviron Eng 135:1702–1712. https://doi.org/10.1061/(ASCE)GT.1943-5606.000 0123 7. Iler RK (1979) The chemistry of silica, solubility, polymerization, colloid and surface properties. SERBIULA (sistema Librum 2.0). Incluye bibliografía e índice 8. Moridis GJ, Pruess K, Persoff P, Apps JA (1995) Performance and properties of colloidal silica and polysiloxane grouts. Note presented at the international containment technology workshop. Baltimore, Maryland 9. Sydansk RD (1990) A newly developed chromium (III) technology. SPE Reservoir Engineering, August, pp 346–352 10. Noll MR, Epps DE, Bartlett CL, Chen PJ (1993) Pilot field application of a colloidal silica gel technology for in situ hot spot stabilization and horizontal grouting. In: Proceedings of the 7th national outdoor action conference. National Ground Water Association, Las Vegas, NV, pp 207–219 11. ASTM: D 422-06 (2006) Standard test method for particle-size analysis of soils 1. Annu B ASTM Stand 63:1–8. https://doi.org/10.1520/D0422-63R07E02.2 12. ASTM D4253 (2014) Standard test methods for maximum index density and unit weight of soils using a vibratory table. ASTM Int West Conshohocken, PA, 1–15. https://doi.org/10.1520/ D4253-14 13. ASTM D4254 (2006) ASTM D4254-00: Standard test methods for minimum index density and unit weight of soils and calculation of relative density. ASTM Stand I:9. https://doi.org/ 10.1520/D4254-00R06E01.1.3 14. Gallagher Patricia M (2000) Passive site remediation for mitigation of liquefaction risk dissertation submitted to the faculty of Virginia Polytechnic Institute and State University

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15. Gallagher PM, Mitchell JK (2002) Influence of colloidal silica grout on liquefaction potential and cyclic undrained behaviour of loose sand. Soil Dyn Earthq Eng 22:1017–1026. https://doi. org/10.1016/s0267-7261(02)00126-4 16. ASTM D2166-16 (2016) Standard test method for unconfined compressive strength of cohesive soil. ASTM Int 1–7. https://doi.org/10.1520/D2166

A Critical Review on Mass Concrete Embedded Water Pipes as Permanent Roofing V. P. Jai Shankar and V. K. Jebasingh

Abstract Tumbling the external energy demand of buildings has always been a challenge for researchers around the world. Supply–demand statistics has never dipped the cost of energy and has always compelled researchers to come with newer models and methods. These methods often lead to huge initial investment and tough maintenance schedules. Concrete, a roofing material in many countries has an excellent thermal mass and can be a source of energy. This when used in roofing structures with water pipes embedded running through it will decrease the external energy demand and maintain comfort conditions inside the building. Studies conducted in this area, even though smaller in number, have been thoroughly reviewed. Different studies conducted in this area, such as the use of PCM (Phase-Change Materials), roof integrated solar heaters, solar concrete collectors, and embedded pipes, removal of hydration heat of concrete, have been analyzed. It was evident that the work in the direction of the solar concrete collector which picked acceleration in the 1990s and early 2000s then gradually gave way for the use of PCM in roof’s concrete collector which was later found to be a failure by itself. Reviews conducted in this article point towards a very serious need for ongoing research in the area of mass concrete embedded water pipes as a permanent roof for achieving energy-efficient residential buildings. Heat extracted by water can then be used to meet different energy-consuming demands of the building itself like hot water for building’s hot water needs, coupling it with thermal power units, solar absorption refrigeration system or even a simple solar stills to produce potable water. Keywords MCEWP · Mass concrete embedded water pipes · Energy-efficient buildings · Solar energy

V. P. Jai Shankar (B) Department of Mechanical Engineering, NICHE, Kumarakovil, Tamil Nadu, India e-mail: [email protected] V. K. Jebasingh Department of Marine Engineering, NICHE, Kumarakovil, Tamil Nadu, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_25

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1 Introduction Solar energy has been known to mankind for centuries. Conversion of solar energy in economic and efficient ways is a challenging thing. Lesser exploded but a potential method of harnessing solar energy is by using MCEWP or the mass concrete embedded water pipes. Combined with the fact that concrete has an excellent thermal mass and is used as roofing material in many constructions, the MCEWP serves as a viable option that has not been completely tapped into. Stringent rules and star ratings for buildings are appealing researchers to explore more and more methods to harness energy and minimize the wastage. The ability to maintain the comfort condition inside the building, lesser investment, and reduced external energy demand are the advantages MCEWP compared to others. Previous studies were reviewed and found at the beginning of the MCEWP studies. It has also been seen that the research in this direction can be divided into two stages, a pre-2003 era. where a number of works in this direction have taken place and a post-2003 era, where the works have diminished considerably. The reason for the same is also analyzed in the paper.

2 Background of Solar Energy Harnessing Lesser evidences, but the use of solar energy can be dated to seventh century B.C, where magnifying glasses were used to concentrate solar radiations to make fire and burn ants. Burning mirrors were used to light torches in third century B.C. Reflectance of bronze shield was used by Greek scientist, Archimedes, to set fire to wooden enemy ships. Comfort conditions in the buildings maintained using the heat from the sun was done by construction of sunrooms at around sixth century A.D and south-facing cliff dwellings were used for living to harness maximum winter sun in North America at about 1200 A.D. Solar cooking boxes, an economizer using the sterling engine on solar energy, finding the increase in output of electrolytic cells when exposed to sunlight, solar cells, and many more were used between the mid-eighteenth century and later half of the nineteenth century dating it as the modern use of solar energy. William J. Bailey, in 1908, invented a solar collector with copper coils and an insulated box which was a follow-up work of the fining that combination of copper and cuprous oxide is a photosensitive and photovoltaic effect in cadmium sulfide. Sun has been the ultimate lesser understood source of energy for thousands of years. First known solar stills can be dated back to 1551when the same was first used by Arab alchemists Mehta et al. [1]. A number of articles notably by Rajaseenivasan et al. [2] and Kaushal and Varun [3] had reviewed the different aspects of harnessing solar energy in the form of solar stills and articles by Khanna et al. [4], Nijmeh et al. [5] has done experimental analysis to specify the geographical conditions for solar

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still, whereas articles by Sarada et al. [6] has reviewed thermal energy storage system design methodologies and the factors to be considered at different hierarchical levels for concentrated technologies.

3 Pre-2003 Stage of MCEWP A considerable number of researches were carried out before 2003 time forcing to classify it as a pre-2003 era. An appropriate article on active concrete solar collectors Olive [7] investigated the steady-state behavior and was the first one of its kind. In an earlier work, Gopffarth et al. [8] used statistical and experimental methods in determining the optical efficiency and the heat loss due to radiation and convection on a horizontal plastic solar water heater in 1968, while Spencer and Strud [9] used a metal plate as part of building elements for absorbing solar radiation. Some earlier works such as Sonwalkar [10], Peck and Proctor [11] attempted using such solar collectors in the buildings non-main structures in the years ranging from late ’70s and early ’80s. A simplified mathematical model for predicting the solar heat gain by water in tubes placed under a concrete surface was developed by Turner [12]. A highly noteworthy work came in 1989 by Nayak et al. [13] as it conducted a performance study on solar concrete collectors projected to produce hot water for domestic needs using thin concrete slabs with PVC (polyvinyl chloride) pipes embedded inside and evaluated the efficiency at 37%. This article sets the pitch of pipe at 6 cm which was later taken by some later works like Chaurasia [14, 15] and Bilgen and Richard [16]. Some more important articles in this regard came in the year 1992 by Bopshetty et al. [17] which present a transient analysis of solar concrete collectors for providing domestic hot water and presented a mathematical model to estimate the performance of such collectors by solving a two-dimensional time-dependent heat conduction equation with apposite initial and boundary conditions. In this article, an explicit finite difference analysis was conceded out to validate the model by comparing its predictions with several sets of investigational data. The consequence of various parameters on the collector performance was also analyzed. In 1992, an article by Sokolov and Reshef [18] came up which was a simulation study with solar collectors made out of a lattice of fluid conduits embedded within a concrete slab. Increasing the strength with glass fiber reinforcement and analyzing its feasibility was studied in this article, and its transient characteristics during a typical summer day with continuous or intermittent radiation were also presented. The work concludes with the need for some predictive control of the flow rate in achieving the stipulated efficiency and pointed the slow response of the system on demerit. An article on concrete flat plate collector, Jubran et al. [19] came in the year 1994 as a follow-up of another work [20] by the same authors. It was directed toward the response of a concrete solar collector over a conventional metallic setup, analyzing it computationally and established that an improvement of the annual solar fraction is about 19% using concrete collectors over the metallic collectors. This article validated

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Fig. 1 Close view of cement concrete slab for solar water heating (Chaurasia [14])

that concrete solar collector models gave a higher total life cycle savings than the conventional solar metallic collector. A paper by Avanti et al. [21] in 1996 gave significance to analysis of heat transfer processes in a transparent honeycomb-insulated solar collector which was made of such low-energy materials as sand, soil, concrete and established that the solar conversion efficiency is 30–60% on a collection temperature range 40–70 °C. In 1997, an established work is seen to appear in conference proceedings Chaurasia [14], which was on the construction of a solar concrete collector, checked its effectiveness as water heaters as shown in Fig. 1. The work was a success and suggests that the roof structure made of concrete with water jackets may be utilized to provide the hot water needs of the buildings. Since the author mentions his previous works in this paper, it is supposedly a follow-up of the works published by the same author in the year 1990 and 1995 but no valid reference available. Most appreciated work in this direction came in the year 2000 Chaurasia [15] when he came up with a standard work on water heating using the solar concrete collector. He used thin unglazed cement concrete slabs with a network of aluminum pipes embedded over its surface. The work was a huge success and concludes with an appeal on designers and architects on using the same for roof construction. Bilgen and Richard [16] in the year 2002 published an article regarding the use of horizontal slabs as passive solar collectors. Experimental studies were done on Natural convection, radiation, and conduction heat transfer of horizontal slabs. The article tried to develop correlations but was rendered less effective since the values varied hugely from the experimental ones.

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4 Post-2003 Stage of Solar Concrete Collector From the different publications reviewed, it can be seen that the number of works have considerably been reduced in the direction of concrete blocks embedded with water pipes intended to harvest solar energy in the post-2003 era. Massive solar–thermal collector (MSTC) design with a concrete solar collector (CSC) was analyzed in 2013 by D’Antoni and Saro [22] using exposed concrete structures as solar energy absorbers and embedding pipes into the structures for harnessing solar energy. A thesis work in 2004 by Abbott [23] constructed a precast concrete roof structure embedding water pipes. This work was a good and standard work in this direction. The work incorporated a glass cover. Thermal modeling of building-integrated thermal energy storage (BITES) systems was done by computational and experimental methods by Pomianowski et al. [24] in the year 2013. An article on the cooling effect of new hollow concrete brick revetment under gravel pavement in permafrost regions was done by Qian et al. [25]. This article was intended in increasing the cooling performance rather than offering a cooling effect to residential structures. Bellamy et al. [26] investigated the energy performance of novel concrete walls embedded with mini solar collectors and found that they offer considerable benefits. This journal publication was the latest from the same author with another three works in the same direction published in various conference proceedings by Bellamy et al. [26–28]. A work of importance by Sarachitti et al. [29] to the exact point of context of the study came in the year 2011 which investigated roof-integrated solar concrete collectors for reducing heat gain to a house and providing domestic hot water. The work used PVC pipes embedded in concrete slab used as a roof structure. This work was never given the required follow-up works. Integrated solar storage collector (ISSC) with embedded copper pipes was analyzed in the year 2010 by Hazami et al. [30]. Results show that the integrated solar storage collector, having energetic and exergetic efficiencies of 32% and 23.5%, respectively. Experiments were not performed on a roof-integrated model but a stand-alone unit. Xu et al. [31] have had a review article on the active pipe-embedded building structures and hence utilize low-grade energy. He elaborated various methods for achieving the energy needs of a building, which, at the same time, reduces the electrical energy consumption.

5 PCM Experimentations The work on the phase change material (PCM) got accelerated and even in direction of embedding PCM in concrete. This method is often complicated and requires much

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initial investment cost. Also, the maintenance cost associated with such a system is high. A study on the PCM for energy-storing wallboard was conducted by Chen et al. [32]. The result indicates that applying proper PCM to the inner surface of the wall in the ordinary room enhanced the indoor thermal comfort dramatically and utilization rate of the solar radiation. Another work by Martin et al. [33] examined a concept using PCM for storing cold, where the cold carrier (water) is in direct contact with the PCM. Even though with some practical applicability, the method was never even examined in detail. PCM-based cold storage technologies were reviewed by Osterman et al.[34] in many articles and identified that such materials would be suitable for use in buildings because they can store a large amount of cold water and phase change occurs at a constant temperature, thereby increasing thermal comfort. The drawbacks of the PCM technology, (a) limitation in thearea of contact between PCM and the air; (b) low convective heat transfer coefficients preventing the use of significant amounts of PCM; and (c) very low utilization factor of the cool stored due to the large phase shift between the time when cool is stored and time when it is required by the building, were pronounced in the paper by Álvarez et al. [35]. A review of thermal energy systems for cold storage applications using solid– liquid PCM has been carried out by Oró et al. [36]. The scope of the work was focused on different aspects: PCMs, encapsulation, heat transfer enhancement, and the effect of storage on food quality. A study by Evola et al. [37] was done to find a system for assisting the detection of the most appropriate PCM and its installation pattern as a function of the climatic operating conditions and the comfort requirements. Experimental setup to test PCM with two typical construction materials (conventional and alveolar bricks) for Mediterranean construction in real conditions was done by Castell et al. [38] and showed that PCM can reduce the peak temperatures up to 1 °C and smooth out the daily fluctuations. The electrical energy consumption was reduced in the PCM cubicles about 15% in summer. These energy savings resulted in a reduction of the CO2 emissions about 1–1.5 kg/year/m2 . Some works on the PCM integrated roofs were analyzed by Pasupathy et al. [39, 40]. They conducted some experiments and a series of numerical simulations with their test rig in India. In this work, water pipes were embedded inside the PCM panel to provide auxiliary cooling when PCM temperature was much higher than its phase change point.

6 Analysis and Outcomes of Earlier Works The tube spacing in solar concrete collectors has a predominant effect on its effectiveness. Bopshetty et al. [17] conducted a parametric study, wherein tube spacing from 0.06 to 0.15 m was accommodated. The article notes that there is a reciprocal relation between thermal storage ability and the response time of the collector. This

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was attributed to the fact that increasing the amount of concrete between the tubes causes an increase in the thermal storage and this, in turn, causes an increase in thermal resistance, thus creating a longer conduction path for the thermal energy has to conduct through to reach the fluid. Pitch used in this article was later adopted by a number of articles mainly by Chaurasia [14, 15], Bilgen and Richard [16] Black surfaces were given to the collectors to emulate a blackbody absorber Chaurasia [14] and Bopshetty et al. [17]. Chaurasia [14] found that temperatures increase an average of 3–5 °C when used blackboard paint as an exterior treatment for the top surface of the concrete. To reduce the losses during the night, some researchers used glass coverings. Bopshetty et al. [17] and Jubran et al. [19] used single panels of window quality glass giving an air gap between the collector top plate and the glass ranging from 0.004 to 0.04 m. Duffie et al. [42] illustrated that a large air gap could enhance the convective losses in the case of flat plate collectors. Aluminum tubes were used in the work by Chaurasia [14] on an experimental basis, while PVC piping cast was used by Bopshetty et al. [17] indented to reduce the cost. It was established that the usage of PVC increased the resistance to heat flow resulting from a less conductive material as well as a thicker tube wall. They accounted for the difference in outer and inner diameters by using a lumped heat transfer coefficient from the concrete to the water Abbott [23]. The work by Madsen and Goss [41] suggested that fatigue problems with non-metallic absorber may be related to the critical relations between good configuration design and the appropriate material specifications. Experiments on partially exposing the metal pipes were done by Chaurasia [14], with the remaining section within the concrete to allowing direct solar gain to the metal pipe. This method was thought to have a good response and also have availability even in the night. Pipes that are 30% exposed were used. He concluded exposed pipes will have high losses during evening hours. This problem was solved by Bopshetty et al. [17] using thin slabs of concrete with complete embedment which decreases the total thermal capacity of the concrete. In these types of experiments where life expectancy of the arrangement matters, it is remarkable that Chaurasia [14] did experiments in a concrete collector revealing it for over 5 years with no signs of degradation. A two-dimensional transient model to simulate the response of a solid concrete slab to a heat flux representing incident solar radiation was derived by Bilgen and Richard [16] taking all sides except the exposed surface to be insulated. Sokolov and Reshef [18] derived a transient model with glass-reinforced concrete but were confined for a one-dimensional circular cross section of the solar concrete collector. Two-dimensional (radial and axial) transient model of a concrete collector was presented by Bopshetty et al. [17]. The works in the direction of thermal analysis of the pipe cooling system used in hydration heat removal of concrete can be effectively used to MCEWP. Fowkes and Bassom [43] record that the first-ever pipe cooling system used in the removal of hydration heat was used while constructing the Hoover Dam, without which it would have taken 125 years for this amount of heat to get dissipated. Thermal analysis of

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the MCEWP can be done using the outcomes of some works by Yang et al. [44] and Kim et al. [45], wherein they have conducted the thermal analysis in hydration heat removal using embedded water pipes. Methodologies followed by Khedari et al. [46] which analyze the performance of roof solar collectors can be used in field measurements. The calculations for the comfort conditions inside the building can be done using the work of Liu et al. [47], where analysis of the in-slab heating floor was done.

7 Conclusion Articles available in MCEWP or its allied field have been reviewed. The shortage of articles in this field has limited the number of reviews. The direction of each paper has been thoroughly analyzed and in chronological order to form the conclusions. It is evident that the work on mass concrete embedded water pipes that picked momentum in the ’80s and the ’90s had ceased after 2003. Hence, pre-2003 era and post-2003 era can be used to identify the works. It was also seen that the works have continued even after 2003 to some extent in 2004 by Abbott [23] and 2011 by Sarachitti et al. [29]. No follow-ups works happened nor it got published in good journals. A lot of works were contributed by Bopshetty [13, 17], Turner [12], and Chaursasia [14, 15] in the early years. They have contributed much but there were no follow-up researchers to these works. It was understood that, for unforeseen reasons, P.B.L Chaurasia had discontinued the works in this field, even though he had published many articles in respectable arenas after Chaursasia [15]. It was seen that, in the absence of the earlier researchers, the newer ones chose to conduct researches in the field of a much new technology at that time, the PCM which later started to fade owing to the disadvantages in itself. It was found that there are only limited articles pertaining to the strength analysis of water pipes embedded concrete structures. Various articles on thermal analysis of the water pipes embedded into concrete for removal of hydration heat were reviewed and it was found that the same methodology can be adopted in thermal analysis of MCEWP in buildings.

References 1. Mehta A, Vyas A, Bodar N, Lathiya D (2011) Design of solar distillation system. Int J Adv Sci Technol 29 2. Rajaseenivasan T, Kalidasa Murugavel K, Elango T, Samuel Hansen R (2013) A review of different methods to enhance the productivity of the multi-effect solar still. Renew Sustain Energy Rev 17:248–259 3. Kaushal A, Varun (2010) Solar stills: a review. Renew Sustain Energy Rev 14:446–453

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4. Khanna RK, Rathore RS, Sharma C (2008) Solar still an appropriate technology for potable water need of remote villages of desert state of India—Rajasthan. Desalination 220(1–3):645– 653 5. Nijmeh S, Odeh S, Akash B (2005) Experimental and theoretical study of a single-basin solar sill in Jordan. Int Commun Heat Mass Transf 32(3–4):565–572 6. Kuravi S, Trahan J, Yogi Goswami D, Rahman MM, Stefanakos EK (2013) Thermal energy storage technologies and systems for concentrating solar power plants. Prog Energy Combust Sci 39:285–319 7. Olive G (1977) Un nouveau capteur solaire en beton. Etudes Thermiques et Aerauliques 8E(5):3–14 8. Gopffarth WH, Davison RR, Harris WB, Baird MJ (1968) Performance correlation of horizontal plastic solar water heaters. Sol Energy 12(2):183–196 9. Spencer DL, Strud RL (1979) Integration of solar collector in large prefabricated roof/wall sections. In: Proceedings of ISES Silver Jubilee congress. Atlanta, GA, pp 348–354 10. Sonwalkar N (1984) A study on the feasibility of utilizing building elements and materials for making solar collectors. M. Tech. Thesis, Indian Institute of Technology, Bombay 11. Peck MK, Proctor P (1983) Design and performance of roof integrated solar air heaters. Sol Energy 31(1):183–189 12. Turner RH (1986) Concrete slabs as summer solar collectors. In: Proceedings of international heat transfer conference. San Francisco, CA, pp 683–689 13. Nayak JK, Sukhatme SP, Limaye RG, Bopshetty SV (1989) Performance studies on solar concrete collectors. Sol Energy 42:45–56 14. Chaurasia PBL (1997) Solar water heating using concrete collectors in buildings. In: Proceedings of solar 97—Australian and New Zealand solar energy society, pp 93–96 15. Chaurasia PBL (2000) Solar water heaters based on concrete collectors. Energy 25:703–716 16. Bilgen E, Richard M-A (2002) Horizontal concrete slabs as passive solar collectors. Sol Energy 72(5):405–413 17. Bopshetty SV, Nayak JK, Sukhatme SP (1992) Performance analysis of a solar concrete collector. Energy Convers Manage 33(11):1007–1016 18. Sokolov M, Reshef M (1992) Performance simulation of solar collectors made of concrete with embedded conduit lattice. Sol Energy 48(6):403–411 19. Jubran BA, Al-Saad MA, Abu-Faris NA (1994) Computational evaluation of solar heating systems using concrete solar collectors. Energy Convers Manage 35(12):1143–1155 20. AL-Saad MA, Jubran BA, Abu-Faris NA (1994) Development and testing of concrete solar collectors. Int J Sol Energy 16, 27–30 21. Avanti P, Arulanantham M, Kaushika ND (1996) Solar thermal analysis of transparenthoneycomb-insulated ground collector-storage system. Appl Therm Eng 16(11):863–874 22. D’Antoni M, Saro O (2013) Energy potential of a massive solar-thermal collector design in European climates. Sol Energy 93:195–208 23. Abbott AB (2004) Analysis of thermal energy collection from precast concrete roof assemblies. Master’s Thesis, Virginia Polytechnic Institute and State University 24. Pomianowski M, Heiselberg P, Jensen RL (2013) Full-scale investigation of the dynamic heat storage of concrete decks with PCM and enhanced heat transfer surface area. Energy Build 59:287–300 25. Qian J, Qi-hao Yu, You Y-H, Jun Hu, Guo L (2013) Analysis on cooling effect of new hollow concrete brick revetment under gravel pavement in permafrost regions. Cold Reg Sci Technol 85:15–21 26. Bellamy LA, Mackechnie JR (2010) An experimental assessment of the energy performance of high thermal mass concrete walls in New Zealand. In: Proceedings of the New Zealand concrete industry conference, Wellington 27. Bellamy LA, Mackechnie JR, McSaveney LG (2009) Energy performance of exterior-insulated concrete walls embedded with mini solar collectors. In: Proceedings of CISBAT 2009, Lausanne 28. Bellamy LA (2012) Towards the development of new energy performance indicators for the external walls of residential buildings. In: Proceedings of the 2nd international conference on building energy and environment. Boulder

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Rock Mass Rating and Geological Strength Index Relationship for Sandstone Along Rock Cut Slope at Markundi, Chopan, District Sonbhadra (U.P.) Saurabh Kumar

and H. K. Pandey

Abstract The Rock Mass Rating (RMRb ) and Geological Strength Index (GSI) are widely employed in geotechnical engineering practice. An attempt has been made to analyze the RMRb and GSI using in situ data corresponding to sandstone rock collected from different outcrops in Markundi Hill along SH-5, Chopan, Sonbhadra. RMR and GSI have been analyzed in order to compare them with the results of the analysis conducted in this study. The Markundi Sandstone is categorized Poor rock mass and Fair rock mass at the locations from the data collected on the basis of RMRb . Finally, the best (most suitable) applied math relations between RMRb and GSI are shown and they are accustomed establish general correlations. Hoek (2013) generalized equation show the best regression relationship between RMRb and GSI for Markundi Sandstone rock. Keywords RMRb · GSI · Sandstone · Markundi

1 Introduction Road widening activities have exposed a continuous stretch of about 5–6 km of highly jointed rock mass along with the serpentine nature of road. In addition to this, the blocks of rock mass have become unstable along the joint planes due to blasting and mechanical excavation. This has resulted into a number of block failures. However, in similar cases as mentioned above, the occurrence of the large slope failure is uncommon and detachment of the rock mass blocks is commonly observed [1]. It is a difficult task to analyze the mechanical properties of rock mass in landslideprone area and requires regress analysis to address the behavior of deformed rocks. The RQD is one of the most important parameters to assess the RMRb as well as GSI [23]. Hoek and Brown [7] proposed a method for getting estimates of the strength for rock mass, primarily based on an assessment of the interlocking of rock blocks and

S. Kumar (B) · H. K. Pandey Civil Engineering Department, MNNIT Allahabad, Prayagraj 211004, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_26

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their surfaces. This methodology was modified over years to fulfill the requirements of users who applied it to issues. Among various available rock mass classification techniques, RMRb is undoubtedly a helpful tool for rock mass characterization, planning, and design in engineering applications. The applicability of RMRb has certain limitations to address the engineering geological problems. Therefore, the combination of GSI and RMRb is inevitable. GSI is an important input parameter of the Hoek–Brown failure envelope [7], which varies between 0 and 100 and also reflects the description of rock structure and block surface conditions [22]. GSI is quite applied nowadays as an engineering index for the categorization of rock mass quality. This acts as an input file into the continuum numerical analysis codes and closed-type solutions supported the Hoek– Brown failure criterion [15–17]. The precise determination of GSI value is extremely necessary for the precise calculation of the failure envelope or the deformation moduli of the rock mass. In the present study, the RMRb and GSI are estimated and compared to infer the nature of the rock mass, viz. fair and poor rock masses. The seven locations were selected and identified for the estimation and analysis of RMRb and GSI. The categorization of rock mass falling in the study area was also carried out. The GSI value gives a numerical representation of the overall geotechnical quality of the rock mass. The GSI is also estimated using field observation from the same location with the help of Hoek et al. [8, 10] and Barton [3] equations.

2 Study Area The study area, i.e., the Markundi Hill is located near Chopan along SH-5, Sonbhadra, (U.P.). The area is bounded between Latitude 24° 37 3 to 24° 37 25 N and Longitude 83° 3 3 to 83° 2 4 E which falls under the Survey of India Toposheet no. 63P/2. The SH-5 connects Uttar Pradesh to Madhya Pradesh, Chhattisgarh, and Bihar. It is the lifeline of Uttar Pradesh, Bihar, and Jharkhand. The rockfall generally occurs in and around the Markundi Hill which obstructs the transportation on SH-5. Due to this reason, passengers face heavy jam, and vehicles get damaged; it also hampers the daily need for goods availability (Fig. 1).

3 Methodology Data pertaining to the nature and volume of the joints were collected near the Markundi Hill from seven different locations along the SH-5. The RMRb and GSI were estimated on the basis of data collected from the study area. The joint wall condition and RQD are common factors between RMRb and GSI. Methods used to calculate the RMRb and GSI value are explained below:

Rock Mass Rating and Geological Strength Index Relationship …

Fig. 1 a–g Photographs showing the physical condition of rock mass and discontinuities

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Fig. 1 (continued)

3.1 Rock Mass Rating (RMR) Bieniawski [4] published the details of a rock mass classification known as the Geomechanics Classification or RMRb system. The modified RMRb [5] is used to classify the rock mass which involves only the first five parameters, viz. strength of intact rock, RQD, spacing of discontinuities, condition of discontinuities, and groundwater conditions [5, 19]. The equivalent IS code for obtaining the value of RMRb is IS:13365-Part 3 [13], while most of the parameters can be determined in the field itself. Experiments were conducted to determine the strength of the samples by uniaxial compression test as per IS: 9143-1979 in the laboratory [12]. RQD was estimated on the basis of volumetric joint count. The approximate relationship between RQD and Joint volume (J v ) [14] is given by the following equation; RQD = 115 − 3.3 Jv

(1)

where J v is defined as the number of joints intersecting a volume of 1 m3 . Jointing occurs mainly as joint sets. The volumetric joint (J v ) count was introduced by Palmstrom [18]. Jv = 1/S1 + 1/S2 + 1/S3 + · · · + 1/Sn where S1, S2, and S3 are the average spacings for the joint sets.

(1)

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363

3.2 Geological Strength Index GSI is the most commonly utilized and effective method as proposed by Hoek and Brown. Since the estimated values can be applied in practical engineering directly, especially for the closely jointed and heterogeneous rock mass. Therefore, it overcomes the drawback of RMRb method and becomes the widely used method in the world. The GSI values are estimated from the rock mass structure, the discontinuities surface condition, and the deformation modulus [9]. Meanwhile, it had been necessary to determine the affiliation between RMRb and GSI simultaneously. Hoek et al. [10] recommended the subsequent formula (Eq. 3) for GSI calculation: GSI = 1.5(Joint wall Condition) + 0.5 RQD

(3)

The widespread use of Barton’s Q system needs a particular specification for GSI determination. During this approach, J n (joint set number), J r (joint roughness number), and J a (joint alteration number) coefficients are used [2]:  GSI = 15 log

RQD Jr Jn Ja

 + 50

(4)

According to Hoek et al. [8], this equation was thought to be employed in the following form:  GSI = 9 ln

RQD Jr Jn Ja

 + 44

(5)

4 Results Rock mass characterization was carried out by applying RMRb as well as GSI methods. The rating value has been assigned to each parameter for the locations under study area as given in Table 1. Rating was given according to the average value of mean discontinuity spacing (mm), roughness, separation, continuity of joints and groundwater condition. RQD values were estimated on the basis of J v count. RQD enables the demonstration of the present condition of the rock mass. The variation in RQD as estimated in the study area is an indication of varying block sizes, responsible for irregular RMRb . The GSI was developed by Barton et al. [2] in which they considered the RMRb parameters, viz. joint set number, joint roughness number, joint alteration number, and RQD. These parameters were also used to develop an equation (Eq. 4). Later,

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Hoek developed a number of equations to estimate the GSI in different field conditions. The rating value of each parameter for locations under the study area (Table 2) shows a significant variation. The results obtained from the different locations in the study area are plotted on the standard graph of Barton’s [3] (Fig. 2). It shows that the results of all the samples except one are not following the linear relationship. The equation showing the relationship between RMRb and GSI is derived from the study area (Eq. 6) and is mentioned. RMRb = 1.1391GSI − 12.11; R 2 = 0.4426

(6)

Hoek’s et al. [8] and Barton’s [3] equations for GSI provide a similar linear regression relation for Vindhyan sandstone in the study area (Markundi) (Eqs. 6 and 7). The results obtained from the different locations in the study area are plotted on the standard graph by Hoek et al. [8] (Fig. 3). It shows that the results of all the samples except two are not following the linear relationship. The equation showing the relationship between RMRb and GSI is derived from the study area (Eq. 7) and is mention. Table 1 Rock mass classification based on RMRb in the study area Locations

RQD

SD

CD

UCS

GWC

RMRb

Rock mass class

S-1

17

10

15

4

12

58

Fair rock

S-2

13

8

15

2

10

48

Fair rock

S-3

13

5

12

2

10

42

Fair rock

S-4

8

5

10

2

10

35

Poor rock

S-5

13

8

11

4

10

46

Fair rock

S-6

13

8

12

4

12

49

Fair rock

S-7

8

5

15

2

13

43

Fair rock

Table 2 GSI values from the different authors of rock mass along the SH-5 Locations J r

Ja

RQD

Jn

J r /J a RQD/J n GSI Barton [3] Hoek et al. Hoek et al. [8] [10]

S-1

1.50 3.00 17.00

6.00 0.50

2.83

52.27

47.13

46

S-2

1.50 3.00 13.00

4.00 0.50

3.25

53.16

48.37

39.5

S-3

1.00 1.00 13.00

9.00 1.00

1.44

52.40

47.31

36.5

S-4

1.00 4.00

6.00 0.25

1.33

42.84

34.11

34

S-5

3.00 4.00 13.00 12.00 0.75

1.08

48.65

42.13

39.5

S-6

3.00 4.00 13.00

4.00 0.75

3.25

55.80

52.02

44

S-7

4.00 3.00

9.00 1.33

0.89

51.11

45.53

34

8.00

8.00

Rock Mass Rating and Geological Strength Index Relationship …

365

60 55

RMRb

50 45 40 35 30 30.00

35.00

40.00

45.00

50.00

55.00

60.00

GSI (Barton, 1995)

Fig. 2 Graphical relationship between RMRb and GSI [3] for the Vindhyan Sandstone at Markundi 60 55

RMRb

50 45 40 35 30 30.00

35.00

40.00

45.00

50.00

55.00

GSI (Hoek, 1995)

Fig. 3 Graphical relationship between RMRb and GSI [8] for the Vindhyan Sandstone at Markundi

RMRb = 0.8245GSI + 8.566; R 2 = 0.4426

(7)

Hoek et al. [10] equation, as developed for the GSI on the basis of several studies, is also used for the Vindhyan Sandstone in the study area (Markundi). The linear regression analysis was carried out which showed that most of the sampling points are either following or very close to the best-fit line (Fig. 4). The equation is derived (Eq. 8) from the study area taking the cognizance of Hoek’s et al. [10] equation. RMRb = 1.3776GSI − 7.9675; R 2 = 0.8191

(8)

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RMRb

50 45 40 35 30 30

32

34

36

38

40

42

44

46

48

GSI (Hoek, 2013) Fig. 4 Graphical relationship between RMRb and GSI [10] for the Vindhyan Sandstone at Markundi

5 Conclusion The study area is characterized by Vindhyan Sandstone (Markundi) which has undergone deformation and fracturing was necessitated to estimate the RMRb as well as GSI to classify the rock mass. The RMRb and GSI were estimated for Vindhyan Sandstone at different locations (Seven), and their results were also compared with standard equations/graphical methods. Analysis of the results concludes that the rock mass (Vindhyan sandstone) belongs to “fair rock” under rock mass classification at six locations (S-1, S-2, S-3, S-5, S-6, and S-7). However, the rock mass (Vindhyan sandstone) at location no. S-4 belongs to “poor rock” under rock mass classification. The relationship between RMRb and GSI has been analyzed for rock mass (Vindhyan sandstone) which concludes that Hoek’s et al. [10] equation is best suitable for classifying the Vindhyan sandstone in the study area.

References 1. Anbalagan R, Singh B, Chakraborthy D and Kohli A (2007) A field manual for landslide investigations. A Publication of Department of Science and Technology Government of India, pp 1–153 2. Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for the design of tunnel support. Springer, Oslo (Norway) 3. Barton N (1995) The influence of joint properties in modelling jointed rock masses. Keynote Lecture, 8. ISRM Congress, 3, pp 1023–1032 4. Bieniawski ZT (ed) (1976) Rock mass classification in rock engineering. In: Exploration for rock engineering, proceedings of the symposium, vol 1. Balkema, Cape Town, pp 97–106 5. Bieniawski ZT (1979) The geomechanics classification in rock engineering applications. In: Proceedings of the 4th congress of the international society of rock mechanics, vol 2. A.A. Balkema, Montreux, Switzerland. Rotterdam, pp 41–48 6. Ceballos F, Olalla C, Jiménez R (2014) Relationship between RMRb and GSI based on in situ data, Conference paper

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7. Hoek E, Brown ET (1980) Empirical strength criterion for rock masses. J Geotech Eng Div ASCE 106 (GT 9):1013–1035 8. Hoek E, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard rock. Balkema, Rotterdam 9. Hoek E, Brown ET (1997) Practical estimates or rock mass strength. Int J Rock Mech Min Sci Geomech Abst 34(8):1165–1186 10. Hoek E, Carter TG, Dietrichs MS (2013) Quantification of the geological strength index chart. In: Proceedings 47th US rock mechanics/geomechanics symposium. San Francisco, 2013 ARMA Ca, USA, pp 13–672 11. Hudson JA, Harrison JP (1997) Engineering rock mechanics—an introduction to the principles. Pergamon press 12. IS: 9143-1979. Method for determination of unconfined compressive strength of rock materials (BIS) 13. IS: 13365-1997. Quantitative classification system of rock mass-guidelines, Part-3, determination of slope mass rating. Bureau of India Standards, New Delhi 14. ISRM: 1978 Suggested methods for quantitative description of discontinuities of rock mass. Int J Rock Mech Min Sci 15:319–368 15. Marinos P, Hoek E (2001) Estimating the geotechnical properties of heterogeneous rock masses such as Flysch. Bull Eng Geol Environ 60:85–92 16. Marinos V, Marinos P, Hoek E (2005) The geological strength index: applications and limitations. Bull Eng Geol Environ 6:55–65 17. Marinos P, Hoek E, Marinos V (2006) Variability of the engineering properties of rock masses quantified by the geological strength index: the case of ophiolites with special emphasis on tunneling. Bull Eng Geol Env 65:129–142 18. Palmstrom A (1974) Characterization of jointing density and the quality of rock masses (in Norwegian). Berdal, Norway, Internal report, A.B, p 26 19. Roghanchi P, Kallu R, Thareja R (2013) A new expression of three adjustment factors of slope mass rating (SMR) classification. Int J Earth Sci Eng 1–9 20. Singh PK, Kainthola A, Singh TN (2015) Rock mass assessment along the right bank of river Sutlej, Luhri, Himachal Pradesh, India. Geom Nat Hazards Risk 6(3):212–223 21. Singh JL, Tamrakar NK (2013) Rock mass rating and geological strength index of rock masses of Thopal-Malekhu River areas, Central Nepal Lesser Himalaya, Bulletin of the Department of Geology, Tribhuvan University, Kathmandu, Nepal, vol 16, pp 29–42 22. Vasarhelyi B (2016) Determining the geological strength index (GSI) using different methods. In: Ulusay et al. (eds) Rock mechanics and rock engineering: from the past to the future 23. Zhang L (2015) Determination and applications of rock quality designation (RQD). J Rock Mech Geotech Eng 5

Evolutionary Topology Optimization of Structural Concrete Under Various Load Cases V. R. Resmy and C. Rajasekaran

Abstract Topology optimization has wide applications in the field of engineering as it derives the optimum material layout in a given design space with defined loads and boundary conditions. This article presents the topology optimization of structural concrete with different load cases using a bidirectional evolutionary structural optimization method (BESO). BESO method has several advantages over other optimization methods as it removes inefficient elements and adds efficient elements in each iteration. The methodology adopts the compliance minimization with volume constraint by utilizing the capabilities of ABAQUS finite element software. Strut and Tie model (STM) has been identified as an effective method in modeling discontinuity regions in reinforced concrete structures as it can find out the real load transfer mechanism in structures. With the aid of topology optimization, all the uncertainties related to STM can be avoided. Keywords Topology optimization · BESO · Strut and tie model · Compliance

1 Introduction Strut and Tie model (STM) conveys the stress patterns as triangular models. In 1987, Schlaich [1] utilizes the strut and tie model which is a generalization of the wellknown truss analogy method for modeling structural concrete in a reinforced and prestressed concrete structure. Truss analogy had been used by Ritter [2] for the design of reinforced concrete structure under shear. By using the concept of STM model, all uncertainties related to the design of D-regions in concrete structures can be eliminated. Conventional beam theory can only be used for the design of Bregions of concrete where linear strain distribution takes place. For disturbed regions or D-regions, where non-linear strain distribution arises as a result of geometrical V. R. Resmy (B) · C. Rajasekaran National Institute of Technology Karnataka, Surathkal, Mangaluru 575025, India e-mail: [email protected] C. Rajasekaran e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_27

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non-linearity or complex loading have to be designed with the help of strut and tie models. Conventional methods of STM modeling are elastic stress distribution and load path methods in which trial and error procedure has involved. The results from the conventional method are not as unique as it is based on the designer’s experience and perception. All the inaccuracies associated with strut and tie modeling can be avoided with the help of topology optimization as it is a scientific tool. Depending on the type of structure, two types of topology optimization exist such as discrete and continuous. Discrete structures normally indicate large bridges and steel truss structures, while concrete components refer to as a continuum. For the continuum structures, several methods have been developed for solving topology optimization. Solid isotropic microstructure with penalization is the widely used method for solving topology optimization. The design continuous variables in SIMP, x ∈ [0, 1], are one per element in the finite element discretization and are commonly interpreted as a density ratio [3]. Bruggi [4] generated truss-like patterns as initial STM by implementing minimum compliance optimization. Buhl et al. [5] used the SIMP approach along with the Method of Moving Asymptotes (MMA) to minimize various objective functions of geometrically non-linear structures subject to volume constraints. In 2001, Rietz [6] showed how the penalty function in the SIMP method was sufficient to give discrete solutions under some conditions. Evolutionary Structural Optimization (ESO) is a different approach for finding solutions to structural optimization problems. It was originally developed by Xie and Stephen [7]. The basic premise of ESO is to systematically remove material that appears to be the least important to the structure. Elements are removed based on their sensitivity number after each iteration. ESO can be categorized as a “hard-kill” method as it involves permanent action of removing elements, which cannot be added in the later stages [8]. BESO is an expansion of ESO in which efficient elements are added in addition to removing inefficient elements in subsequent iterations [9]. Sun et al. [10] performed topology optimization of a composite structure using BESO and extend its application to anisotropic materials. Shobeiri [11] applied the BESO method for compliance minimization in cracked structures. This study focuses on the topology optimization of 3D-Concrete dapped beams using BESO within the environment of ABAQUS finite element software.

2 Modeling of Dapped-End Beams Reinforced concrete dapped-end beams (RC-DEBs) are commonly used in concrete bridge girders and prepared concrete buildings. There are three types of dapped-end beams (DEBs) such as drop-in beam, beam to beam connection, and dapped beams in suspended span. By using DEBs, the erection of precast concrete members can be done. In many ways, the nib of a DEB is equivalent to an inverted corbel and they are supported by cantilevers, corbels, inverted T-beam, or columns. It permits the construction depth of a precast concrete floor or roof structure to be reduced by recessing the supporting corbels into the depth of the beams supported [12]. The

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371

main problem related to the design of RC-DEBs arise due to the recessing of the RC beam at end parts. High-stress concentration develops at reentrant corners due to geometrical discontinuity leads to diagonal cracks and failure in the absence of proper reinforcement [13]. Experimental and analytical studies have been conducted by several researchers to evaluate the performance of RC-DEBs. The present study aims to evolve a truss-like pattern of RC-DEBs with two daps using topology optimization. The model dimensions and boundary conditions are shown in Fig. 1. Four different load cases were selected for simulation. Load case-1: A Concentrated load at a distance of 430 mm from the left support (Fig. 2)

Fig. 1 Dimensions and boundary conditions of dapped beams

Fig. 2 Load case-1

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Fig. 3 Load case-2

Load case-2: Uniformly distributed load throughout the effective span (Fig. 3) Load case-3: Uniformly distributed load in the mid-third of the effective span (Fig. 4) Load case-4: Lateral load at both the ends of beam (Fig. 5).

Fig. 4 Load case-3

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Fig. 5 Load case-4

These load cases were selected for finding the optimized layout of DEBs after converging to an optimum layout based on optimality criteria. A concrete grade of 35 MPa with Poisson’s ratio of 0.15 has been selected for simulation.

3 Formulation of the Optimization Problem STM is a theoretical method based on the actual structural mechanics. Development of STM based on topology optimization removes the parts which are inefficient in carrying loads. This study adopts compliance minimization as the objective function with volume constraint. Compliance measures the external work done on the structure. It is the sum of all the displacements at the points where the load is applied weighted by the magnitude of loading. Thus, it is maximizing the stiffness of the structure by minimizing the deflection. The formulation of optimization is expressed as Eqs. (1) and (2). Minimize : C = F T U Subject to : V ∗ −



xe ve = 0

x

xe = 1 or xmin

(1) (2)

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xmin = 0.001 where C is the compliance, x e is the design variable indicates the presence or absence of the element, V * indicates the target volume, ve is the elemental volume, F and U are the global force vector and displacement vector, respectively, and x is the vector of the elemental relative densities. In the BESO method, design variable update is based on the element sensitivity α e [14], calculated as Eq. (3). ∝e = −

p p T Ee x u k0 u e = p xe e e xe

(3)

where p is the penalty exponent [3] with a value of 3 in this study, ue is the elemental p displacement vector, and k 0 is the element stiffness matrix. The term xe u eT k0 u e is exactly the element strain energy. To obtain a mesh-independent solution, a filtering scheme has been applied in this paper. The updating of current sensitivity is as follows (Eq. 4):   w rej ∝ j  j w(r ej )

 ∝en =

j

(4)

  where w(r ej ) = max 0, rmin − rej ; w(r ej ) is the weight factor of element e, r min is the filter radius, r ej is the distance between the centers of elements e and j, and α en is the modified sensitivity. To achieve a convergent solution, averaging of sensitivity (Eq. 5) with its historical information is recommended for discrete methods such as BESO [15]. ∝en =

∝ken + ∝k−1 en 2

(5)

where k is the current iteration number. BESO usually starts from full design and iteratively reduces the structural volume up to the target volume. In each iteration, the target volume of the next iteration derived based on the evolutionary ratio (ER) is expressed in Eq. 6. V k+1 = V k (1 ± ER)

(6)

where V k is the volume of the current iteration and V k+1 is the volume of the next iteration. Element status is updating based on the optimality criteria such that the elements with a sensitivity lower than the threshold are changed to solid, and the elements with a sensitivity higher than the threshold are changed to void.

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Fig. 6 Objective history of Load case-1

4 Numerical Examples 3D concrete DEBs have been modeled in the ABAQUS software environment along with loads, boundary conditions, and FE discretization. Sensitivity analysis, filtering, and updating of element status are according to the optimality criteria with the help of ABAQUS Scripting Interface. In all load cases, the mesh size of 40 mm has been adopted. This simulation adopts ER of 2% with a filter radius of 120 mm and a volume fraction of 30% in all the load cases.

4.1 Load Case-1 A load of 60 kN has applied 650 mm from the left end to get results for an unsymmetrical load. The iteration history of objective function and volume constraint are given in Figs. 6 and 7. A final topology in Fig. 8 has arrived based on our optimality criteria. Final topology has converged at iteration number 77.

4.2 Load Case-2 A load of 300 kN/mm was applied throughout the supported span. The von Mises stress at final iteration and final topology are given in Figs. 9 and 10. Final topology has converged at iteration number 53.

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Fig. 7 Volume history of Load case-1

Fig. 8 Final topology of Load case-1

4.3 Load Case-3 A load of 30 kN/mm has applied at mid-third of the effective span. The iteration history of the objective function and final topology are given in Figs. 11 and 12. Final topology has converged at iteration number 69.

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Fig. 9 von Mises stress at final iteration

Fig. 10 Final topology of Load case-2

4.4 Load Case-4 A lateral load of 25 kN was applied at both ends of beams to simulate the effects of lateral loads such as wind and earthquake. The iteration history of objective function and volume constraint are given in Figs. 13 and 14. A final topology in Fig. 15 has arrived based on our optimality criteria. Final topology has converged at iteration number 96.

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Fig. 11 Objective history of Load case-3

Fig. 12 Final topology of Load case-3

5 Conclusions The present study extends the usage of BESO method inside the ABAQUS software environment for topology optimization of three-dimensional concrete dapped beams as some parts of dapped beams belong to discontinuity regions. Four different load cases had applied for simulation to study the effects of real load cases including transverse as well as lateral loads. Minimum compliance optimization with volume

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Fig. 13 Objective history of Load case-4

Fig. 14 Volume history of Load case-4

constraint had adopted for all the load cases. From the results, it has been observed that objective history is different for all the load cases, while lateral load case took more iteration steps to converge. Final topology like truss pattern had arrived after a reasonable number of iteration which can be utilized for the appropriate generation of the strut and tie modeling.

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Fig. 15 Volume history of Load case-4

References 1. Schlaich J, Schäfer K, Jennewein M (1987) Toward a consistent design of structural concrete. PCI J 32(3):74–150 2. Ritter W (1899) The Hennebique design method (Die Bauweise Hennebique). Schweizerische Bauzeitung (Zurich) 33(7):59–61 3. Bendsøe M, Sigmund O (2003) Topology optimization-theory, methods and applications 4. Bruggi M (2009) Generating strut-and-tie patterns for reinforced concrete structures using topology optimization. Comput Struct 87(23–24):1483–1495 5. Buhl T, Pedersen CB, Sigmund O (2000) Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidis Optim 19(2):93–104 6. Rietz A (2001) Sufficiency of a finite exponent in SIMP (power law) methods. Struct Multidis Optim 21(2):159–163 7. Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896 8. Querin OM, Steven GP, Xie YM (1998) Evolutionary structural optimisation (ESO) using a bidirectional algorithm. Eng Comput 15(8):1031–1048 9. Huang X, Xie YM (2010) A further review of ESO type methods for topology optimization. Struct Multidis Optim 41(5):671–683 10. Sun XF, Yang J, Xie YM, Huang X, Zuo ZH (2011) Topology optimization of composite structure using bi-directional evolutionary structural optimization method. Procedia Eng 14:2980–2985 11. Shobeiri V (2015) The topology optimization design for cracked structures. Eng Anal Boundary Elem 58:26–38 12. Herzinger R (2008) Stud reinforcement in dapped ends of concrete beams 13. Huang PC, Nanni A (2006) Dapped-end strengthening of full-scale prestressed double tee beams with FRP composites. Adv Struct Eng 9(2):293–308 14. Huang X, Xie M (2010) Evolutionary topology optimization of continuum structures: methods and applications. Wiley 15. Huang X, Xie YM (2007) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elements Anal Des 43(14):1039–1049

Numerical Analyses of Geogrid Reinforced Embankment Over Soft Clay C. Keerthana, M. P. Vibhoosha, and Anjana Bhasi

Abstract Construction of embankments on weak foundation soils is a challenging task for civil engineers due to excessive settlement, bearing capacity failure and slope stability issues. To solve this problem, a variety of ground improvement techniques, including vertical drains, grouting, complete soil replacement, geosynthetic reinforcement and piling, are adopted. Geosynthetics provides an alternative and economical solution and has been increasingly applied as reinforcement in embankments on soft soil. In the present study, 3D numerical analyses using the finite element program ABAQUS was carried out to study the time-dependent behaviour of geogrid reinforced embankment. Parametric studies were carried out by varying the height of the embankment. Keywords Soft soil · Embankment · Numerical analyses · Geogrid · Settlement

1 Introduction Design and construction of the infrastructure is the most important need in the present time. Many times construction takes place on poor soil due to space constraints. Construction over poor quality soil with heavy loads is a challenging task for civil engineers. Shallow foundation construction on week soil leads to excessive settlement and low bearing capacity, which could ultimately lead to structural damage [4]. Replacement of weak soil by some strong soil or improvement of engineering properties of weak soil by different ground improvement techniques is used in such a situation. Geogrid reinforcement is an effective method to improve the stability and service life of different earth structures such as embankments, pavements, foundations and retaining walls. Reinforced embankments have been successfully used to reduce costs C. Keerthana (B) · A. Bhasi National Institute of Technology, Kozhikode, India e-mail: [email protected] M. P. Vibhoosha National Institute of Technology Karnataka, Surathkal, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_28

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and speed of construction compared to the conventional methods. The function of the geogrids is to improve the internal and external embankment stability, restraining the lateral deformation, reduce the settlement and pore pressure and significant improvement in the bearing capacity. It can increase the embankment stiffness and reduce the shear stress, strain magnitudes and plastic deformation in foundation soil [3]. In the case of geogrid reinforced embankment, reinforcement is placed at the base of an embankment and at a particular distance from the base. Hence, results of multiple layers of geogrid reinforced embankment were also studied. Mainly, reinforcement can increase the stiffness of embankment fill, but only some part of the mobilized tensile force helped to stiffen the fill and remaining went into the less stiff foundation soil.

2 Numerical Analyses of Model Embankment geometry and properties were adopted from the paper ‘Numerical modelling of geosynthetic-encased stone column-reinforced ground’ [1]. Figure 1 represents the right half of the embankment having 45 m wide and 6 m height with a side slope of 1V: 2H. The soft clay layer, which is 10 m deep, overlying a firm layer. A 1-m-thick sand mat was placed over the clay. Embankment construction was completed in three equal stages with 2 m fill placement. Each layer construction was done within 15 days followed by 10 days of waiting period for consolidation.

Fig. 1 Cross section of embankment

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383

Table 1 Summary of model parameters for clay, sand mat and fill material Property

Clay

Sand/fill

Model Modified cam clay Unit weight

(kN/m3 )

Mohr–Coulomb

18

19

Young’s modulus (kPa)

–

15,000

Poisson’s ratio

0.3

0.3

–

3

–

28



Cohesion, c (kPa) Friction angle, φ



Dilation angle, 



Critical state stress ratio, M

–

10

1

–

Logarithmic hardening constant for plasticity, 0.2 λ

–

Logarithmic bulk modulus for elastic material 0.02 behaviour, κ

–

Initial yield surface size, ao , (kPa)

50

–

Initial void ratio, eo

1

Permeability, k (m/s)

1.2 ×

– 10–6

1.2 × 10–2

2.1 Finite Element Modelling ABAQUS [2], a commercial finite element code was selected for the analysis, for considering soil non-linearity and stress–pore pressure-coupled problems. Modified cam clay material was used to model the soft clay. The sand mat and fill were modelled using the linear elastic, perfectly plastic model with the Mohr–Coulomb failure criterion. Linear elastic model was used for geosynthetics. Geogrids are modelled as membrane here. Parameters and properties of each component are given in Table 1. In this analysis, geogrid membrane thickness is taken as 15 mm and E is the Young’s modulus of elasticity (1.7 × 105 kPa). J is the secant stiffness of the geogrid, it can be defined as J = E t. Hence, J = 2500 kN/m.

2.2 Boundary Condition and Mesh Generation Vertical side boundaries of the model were horizontally fixed and full fixity at the clay bottom (Fig. 2a). The element type used to represent the clay layer was 20-node stress pore pressure elements with reduced integration (C3D20RP) and 20-node stress only element (C3D20R) were used to represent the sand mat and embankment fill. Eightnode membrane element (M3D8R) was used to model the geosynthetic reinforcement (Fig. 2b). The top boundary of the clay layer makes as drained, which means zero pore pressure boundary condition. The loading of embankment was simulated by adding individual layers of the embankment.

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Fig. 2 Three dimensional embankments: a model after boundary conditions; b structured mesh of the reinforced model

3 Results and Discussions The results obtained from the unreinforced and reinforced cases were compared in terms of settlement and pore pressure. A reinforced embankment was modelled using geogrid membrane elements. Two layers of geogrids were spaced 15 cm apart just above the sand mat.

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3.1 Settlement and Excess Pore Pressure Figures 3 and 4 represent the settlement of embankment at the top and excess pore pressure distribution at the mid-depth of the clay layer, respectively. Comparison of settlement and pore water pressure was done for both unreinforced and reinforced cases. Reinforced embankments over a weak soil can stiffen the base of the embankment and reduce the shear stress and plastic shear deformation. Reinforcement placed near or at the base of the embankment can increase the tensile stiffness of the embankment and this stiffness increases as the stiffness of geogrid increases up to an optimum value. A part of mobilized tensile force increases the embankment stiffness and the rest of the tensile force propagated from stiffer embankment fill to softer foundation soil. Time history of the settlements under the centre of the embankment was shown (top point of the third layer of embankment). Note that consolidation settlement started immediately when the first embankment layer was constructed. Here, the settlement starts only after 50 days. It can be seen that only a 4% reduction in settlement by comparing the plain case. Figure 4 represents the development of excess pore pressure for a 6 m embankment. Initially, water takes the external load and pore pressure increases. Then the soil skeleton absorbs the extra stress, the pore pressure decreases and the soil consolidates. It is essential to consider that both water flow (due to excess pore pressure dissipation) and deformation take place in the vertical direction only in many of the consolidation problems. Figure 4 shows how the excess pore pressure increases in steps as the embankment constructed and pore pressure dissipates gradually, after

Fig. 3 Development of settlement

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Fig. 4 Development of excess pore pressure

the end of construction. The maximum pore pressure is developed for unreinforced case compared to reinforced one; this difference is due to the less embankment load transfer to the clay layer when it is reinforced.

3.2 Embankment Height Versus Settlement and Pore Pressure Embankment height is a parameter considered for the parametric study. The settlement and pore pressure on changing the height of the embankment were evaluated. The embankments with height 2 and 4 m were Numerically simulated and the variation of settlement and pore pressure were studied according to the height change (Fig. 5). Settlement analyses of the embankment with different heights were carried out. These embankments were reinforced with two layers of geogrid placed 15 cm apart. It was found that the settlement reduced by 85.64, 25.58 and 4% for 2, 4 and 6 m, respectively. As the embankment height increases, the percentage reduction in the settlement was reduced. Figure 6 shows the deformation behaviour of both plain and reinforced embankment. Figure 7 illustrates the excess pore pressure variation with respect to time. The maximum pore pressure was developed in an unreinforced case,

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Fig. 5 Contour plots of vertical deformation of the unreinforced embankment with height 2 m

the difference in which was a direct consequence of the difference in load transfer to the clay layer. This trend was well supported in the development of settlement.

4 Conclusion For an embankment constructed over soft ground, settlement of the embankment and the pore pressure distribution on the soft ground were studied with time. The use of geogrid decreased the embankment load-induced excess pore water pressure on the foundation soil as well as the vertical settlement of embankment. The time-dependent settlement behaviour of geogrid reinforced embankment was compared with an unreinforced embankment. It was observed that the use of basal geogrid reduced the embankment settlement (end of consolidation) by 85.64, 25.58 and 4 for 2, 4, and 6 m height embankments, respectively. As the embankment height increased, the percentage reduction in settlement decreased significantly. From the study, it was observed that two layers of geogrid had a significant effect on the behaviour for embankments of small height (H emb ≤ 2 m). This can be compensated by incorporating multiple layers of geogrid.

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Fig. 6 Settlement behaviour for different embankment fill heights: a H emb = 2 m; b H emb = 4 m

Numerical Analyses of Geogrid Reinforced … Fig. 7 Excess pore pressure distribution for different embankment fill height a H emb = 2 m; b H emb = 4m

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References 1. Yoo C, Kim SB (2009) Numerical modeling of geosynthetic-encased stone column-reinforced ground. Geosyn Int 16:3 2. ABAQUS User’s Manual (2006) Hibbit, Karlson and Sorenson, Inc., Pawtucket, Rhode Island 3. Bonaparte R, Christopher BR (1987) Design and construction of reinforced embankments over weak foundations. Transp Res Rec 115 4. Rowe RK, Li AL (2005) Geosynthetic-reinforced embankments over soft foundations. Geosyn Int

Tensile Properties of FRP and Ferrocement—A Comparative Study P. Bindurani , N. Ganesan , and P. V. Indira

Abstract An experimental investigation was carried out to obtain the equivalent tensile properties of different composite laminates, namely glass fibre-reinforced polymer (GFRP), carbon fibre-reinforced polymer (CFRP) and ferrocement. This work is part of a study on the application of these composites for the purpose of rehabilitation/retrofitting of RCC structural elements under distress. Tension tests were conducted on flat coupons of FRPs based on ASTM D7565/D7565M-10 and ASTM D3039/D3039M-00. Similar tension tests were conducted for mesh reinforcement used in ferrocement. The CFRP consists of unidirectional carbon fibre-woven mats (230 g/m2 ) in an epoxy matrix (resin used was EPS), GFRP consists of bidirectionally woven glass fibre mat (225 g/m2 ) in the same epoxy matrix and mesh reinforcement for ferrocement consists of woven square GI wire mesh of gauge 12/29 (0.35 mm diameter wires at a spacing of 2.12 mm). Coupons of 25 mm width were made from the three different composites and tested until failure under tension in a digital universal testing machine. To find the equivalent number of layers of FRPs and mesh reinforcement in ferrocement, a total number of (i) 10 CFRP, (ii) 25 GFRP and (iii) 20 ferrocement tension specimens with a different number of layers were prepared. All coupons were tested to failure and the results are presented. It was found that GFRP with three layers and ferrocement with five layers of mesh reinforcement are equivalent to one layer of CFRP, based on the tensile strength. Similarly, CFRP with 2 layers is equivalent to GFRP with 7 layers and mesh reinforcement of 11 layers in ferrocement, for the materials considered in the study. Keywords Coupon testing · Carbon fibre-reinforced polymer · Glass fibre-reinforced polymer · Ferrocement · Rehabilitation

P. Bindurani (B) · N. Ganesan · P. V. Indira National Institute of Technology Calicut, Calicut, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_29

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1 Introduction Different rehabilitation methods for reinforced concrete structures are followed worldwide such as section enlargement, steel plate bonding, external prestressing, using fibre-reinforced polymer (FRP) or ferrocement. Finding an optimum solution for rehabilitation is challenging in the viewpoint of economy, execution time and other operational difficulties maintaining a highly efficient output. Within these different techniques, FRP is found to be a promising material. A lot of studies on rehabilitation using various FRPs like carbon fibre-reinforced polymer (CFRP), glass fibre-reinforced polymer (GFRP), aramid fibre-reinforced polymer (AFRP) are made by various researchers [1–5]. There are a lot of advantages in using FRP like high strength-to-weight ratio, corrosion resistance, minimal change in structural geometry, easy and rapid installation, etc. But, the certain disadvantages like the possible health hazards in handling FRP materials, its high cost and susceptibility to high temperature are some concerns. Ferrocement rehabilitation is proved to be an economic technique, which possesses many of the advantages of FRP and hardly any health problems are observed. There are a lot of studies in ferrocement rehabilitation [6, 7]. But, very few studies are carried out to compare these two techniques, say FRP and ferrocement in the strengthening of concrete elements. While comparing the efficacy of different materials on a purpose, like rehabilitation, the related properties of the materials in comparison should be equivalent. Hence, an experimental study was conducted to equalize the tensile property of FRP and ferrocement, which is the most important property that arises in a rehabilitation process. The FRP’s selected for this study are CFRP and GFRP since the availability of AFRP is less in India.

1.1 Tensile Properties of FRP and Ferrocement ASTM standards are available to study the tensile properties of FRP [8, 9]. According to these standards, the tensile properties can be experimentally determined by conducting tensile tests on FRP coupons. The dimensions of test specimens, its method of fabrication and experimental procedures are explained in these standards. The tensile strength can be expressed in either tensile force per unit area as per ASTM D3039/D3039M [8] or tensile force per unit width as per ASTM D7565/D7565M [9]. This study follows the expression in Eq. (1) from ASTM D7565 [9], since, while equating the properties, the number of required layers of CFRP and GFRP will be different, which means the thickness of the coupons will be different. Hence, expressing the tensile strength in force per unit width is the practically feasible solution. The width of the specimens will be the average of the width measurements at three different locations within the gauge length. The width tolerance should be ±1% of the width. F=

p max w

(1)

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where F maximum tensile force/unit width in N/mm. pmax maximum tensile force before failure in N. w width of the specimen in mm. Ferrocement consists of layers of wire meshes in cement mortar. Since cement mortar is weak in tension, the tensile strength of ferrocement is mainly contributed by the wire mesh within. Hence, conducting tension tests on the wire meshes alone will give the tensile strength of ferrocement. For equalising the properties, tension tests on coupons of wire meshes with a different number of layers, having the dimensions and preparation methods same as that of FRP is proposed in this study. The tensile strength can be determined using the same Eq. (1) and can be compared with that of FRP coupons.

2 Experimental Programme 2.1 Design of Experiments The experimental study includes (i) preparation of coupons of width 25 mm from three different materials—CFRP, GFRP and GI wire mesh of ferrocement as per ASTM standards and (ii) testing the coupons under tension. A total of 55 tension specimens were prepared from the three different materials, out of which 10 from CFRP, 25 from GFRP and 20 from wire mesh; with a different number of layers in each group. CFRP was tested in two groups with one and two layers, GFRP tested in five groups with the number of layers 2–6, and the wire mesh tested in four groups with 3–6 layers. In each group, five sample specimens were tested as per ASTM D3039/ D3039M [8] which recommends testing of at least five samples per test condition to get a reliable result.

2.2 Materials Used CFRP consists of unidirectional carbon fibre-woven mat (Fig. 1a) of weight 230 g/m2 impregnated in epoxy resin. Similarly, GFRP consists of bidirectionally woven glass fibre mat (Fig. 1b) of weight 225 g/m2 impregnated in the same resin material. The average thickness of dry mat was 0.26 and 0.18 mm for carbon and glass, respectively. The epoxy resin used for making both kinds of FRP was a two-part system (CERA EPS) supplied by Ceracom Pvt. Ltd., India. The base and hardener of the resin were

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(a) Woven carbon fibre mat

(b) Woven glass fibre mat

(c) Woven GI wire mesh Fig. 1 Materials used

combined in a mix ratio of 5:3 by weight. For preparing the FRP composite, the fibre and the resin were taken in a ratio 1:1 by weight. The wire mesh of ferrocement was a square, galvanized iron-woven mesh having a mesh size of 12/29 which means that 0.35 mm diameter wires are at a spacing of 2.12 mm (Fig. 1c).

2.3 Preparation of Specimens FRP Specimens. Specimens of both CFRP and GFRP were made by following the wet lay-up procedure given in ASTM D7565/D7565M [9]. A polymer release film of size 600 × 600 mm was placed on a 3-mm-thick glass plate which acts as a flat, smooth horizontal surface. OHP sheet applied with Vaseline on its surface was used as the polymer release film. This helps for the easy removal of cured FRP sheet since it will not adhere to the resin used for impregnating the fibre mats. A thin layer of resin, which was a thorough mixture of base and hardener in a ratio 5:3, was applied over the release film. A fibre mat of size 300 × 300 mm was cut from the mat roll and placed over the applied resin. Another layer of resin was applied over this mat and impregnated properly by using a roller. Subsequent layers of ply were stacked

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over this and each layer was impregnated with resin. The amount of resin per ply per unit area was taken as per the specifications provided by the manufacturer. A small flat-edged hand tool was used to remove the air bubbles between the plies, taking care that the fibres were not getting damaged. A second release film was placed over the final ply, and another glass plate was used to cover the entire system to protect it from any damage and also to provide a smooth horizontal top surface. The entire system was kept undisturbed for 4–5 days at ambient temperature for proper curing. After the resin was cured completely, the release films were removed from the laminate. Specimens of width 25 mm and length 280 mm were cut from this 300 × 300 mm laminate sheet, such that the edges were flat and parallel. Widths of specimens were fixed as per ASTM7565 [9] which recommends a minimum width of 25 mm for unidirectional wet lay-up specimens. Five specimens were fabricated in each layer groups as well as material groups, in a similar procedure as described above. The width and thickness of each specimen were measured at three locations and the average value was calculated, which is tabulated in Table 1. Wiremesh Specimens of Ferrocement. Specimens of wire meshes having layers of wire mesh strips with width 25 mm and length 280 mm were prepared by cutting the wire mesh sheet. The width and the length were selected to match with those of FRP specimens. The numbers of layers were taken as 3, 4, 5 and 6. The required number of layers of wire mesh strips were stacked and tied intermittently using the wire of the same diameter. Five specimens were prepared in each layer groups. Specimen Designations. The specimens were labelled with two digits and a letter in between. The first digit represents the number of layers and the second digit represents the specimen number in that group. The letter represents the material, such that C, G and F to represent carbon, glass and wire mesh of ferrocement, respectively. For example, 3G-4 represents the fourth specimen in the group of glass laminate with three layers. Test Coupons. ASTM D3039 [8] recommends the use of tabs at the gripping regions of the specimens to prevent gripping damage. It also helps to make sure that the failure occurs in the fibre direction while testing unidirectional materials. Following the recommendations given in the said standard, two flat rectangular Aluminium tabs of thickness 1.5 mm, width 30 mm and length 80 mm were glued on the opposite faces of the test specimens at each end. Araldite, which is a two-part epoxy adhesive, was used to make proper bonding between the tabs and the specimens. Tabs were cut from a single aluminium sheet so that the thickness variations were within ±1% of tab thickness as specified in ASTM D3039 [8]. The tab length was fixed as 80 cm after calculating the minimum required bonded tab length, as per the formula given in ASTM D3039 [8]. Similar tabs were glued at the gripping region of wire mesh coupons to avoid the failure within the grips. Figure 2 represents typical FRP coupons before adhering with the tabs and Fig. 3a–c represents the test coupons from three different materials with tabs.

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Table 1 Tensile properties of GFRP coupons No. of layers

Designation

Length (mm)

Width (mm)

Thickness (mm)

Tensile load (kN)

Load/width (N/mm)

Failure mode

2

2G-1

283

23.27

0.83

2.82

121.20

LGT

2

2G-2

281

22.73

0.77

2.65

116.57

LGB

2

2G-3

283

23.20

0.82

2.8

120.69

AGT

2

2G-4

282

22.90

0.83

2.7

117.90

LGM

2

2G-5

LGM

282

23.83

0.85

2.76

115.80

Average

282.20

23.19

0.82

2.75

118.43

SDa

0.84

0.42

0.03

0.07

2.42

CVb

0.30

1.82

3.81

2.57

2.04

3

(%) 3G-1

282

23.90

1.10

5.65

236.40

LAT

3

3G-2

282

24.20

1.07

5.8

239.67

LGT

3

3G-3

283

24.00

1.09

6.1

254.17

AGT

3

3G-4

282

25.27

1.13

6

237.47

AGB

3

3G-5

283

24.30

1.13

5.9

242.80

LGB

Average

282.40

24.33

1.10

5.89

242.10

SD

0.55

0.55

0.03

0.17

7.18

CV (%)

0.19

2.24

2.51

2.97

2.96

4

4G-1

284

26.90

1.43

8.5

315.99

LGM

4

4G-2

281

26.00

1.36

8.15

313.46

AGT

4

4G-3

281

27.37

1.34

8.53

311.69

AGT

4

4G-4

282

26.77

1.39

8.4

313.82

AGB

4

4G-5

283

27.33

1.45

8.4

307.32

LGM

282.20

26.87

1.39

8.40

312.46

Average SD

1.30

0.55

0.04

0.15

3.25

CV (%)

0.46

2.06

3.20

1.78

1.04

5

5G-1

281

26.60

1.79

10.2

383.46

LGM

5

5G-2

280

26.57

1.79

10.4

391.47

SGM

5

5G-3

280

26.40

1.82

10.7

405.30

LGM

5

5G-4

281

25.17

1.74

9.74

387.02

AGM

5

5G-5

AGM

281

25.57

1.75

9.78

382.53

Average

280.60

26.06

1.78

10.16

389.96

SD

0.55

0.65

0.03

0.41

CV (%)

9.27

0.20

2.51

1.85

4.03

2.38

6

6G-1

280

26.67

2.81

12.6

472.50

AGT

6

6G-2

280

26.23

2.77

12.5

476.49

LGM

6

6G-3

283

27.17

2.70

13.58

499.88

AGB (continued)

Tensile Properties of FRP and Ferrocement—A Comparative Study

397

Table 1 (continued) No. of layers

Designation

Length (mm)

Width (mm)

Thickness (mm)

Tensile load (kN)

Load/width (N/mm)

Failure mode

6

6G-4

281

26.23

2.59

13.06

497.84

LGT

6

6G-5

281

25.63

2.69

12.6

491.55

AGT

Average

281.00

26.39

2.71

12.87

487.65

SD

1.22

0.57

0.08

0.45

12.48

CV (%)

0.44

2.16

3.02

3.52

2.56

Notes a SD—The standard deviation; b CV—The coefficient of variation

Fig. 2 FRP coupons before bonded with tabs

2.4 Test Set-Up The experiment was conducted in a universal testing machine (model UTM-2011N), having a capacity of 200 kN, supplied by Krystal Industries, India. It has a hydraulic loading unit and the measurement unit consists of the ultra stable precision grade pressure transducer and encoder for displacement measurement. It displays the load and corresponding displacement digitally. The specimen was kept between the fixed and movable serrated jaws of the machine such that the longitudinal axis of the gripped specimen aligned with the test direction. Also, it was placed such that the grip jaws extended approximately 15 mm past the inner ends of tabs, to prevent failure at the tab ends due to excessive inter-laminar stresses (Fig. 4).

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P. Bindurani et al.

2C-1

3G-2

2C-2

3G-3

5F-1

4F-1

3F-1

6F-1

(b) GFRP

(a) CFRP

(c) Wire mesh of Ferrocement Fig. 3 Typical test coupons

Fig. 4 Test set-up: CFRP specimen placed in digital universal testing machine

Tensile Properties of FRP and Ferrocement—A Comparative Study

399

2.5 Test Results For FRP, the load was applied to the specimen at a constant rate such that the failure occurs within 1–10 min as specified in ASTM D3039 [8]. Loads and the corresponding elongations were noted from the machine at intervals of 0.2 kN. The load at failure of each specimen was recorded. The maximum tensile force per unit width was calculated following the recommendations in ASTM D7565 [9]. The average value, standard deviation and coefficient of variation (in %) were calculated for the measurements of specimen width, thickness and tensile load/width, in each group of specimens. For GFRP, a total of 25 specimens in five groups were tested and the measurements and calculations of the test coupons are tabulated in Table 1. Similarly, for CFRP, ten numbers of specimens in two groups were tested and the results are tabulated in Table 2. Similar test method was followed for 20 numbers of wire mesh coupons in four groups, and the results are tabulated in Table 3. Failure modes of the FRP specimens were noted and expressed in a standard description given in ASTM D3039 [8], using the three-part failure mode codes, in which the first character represents the failure type (A—angled, D—edge delamination, L—lateral, S—long splitting, X—explosive); the second character represents the failure area (G—gauge, A—at grip/tab, I—inside grip/tab); and the third character represents the failure location (B—bottom, T—top, M—middle). From the Table 2 Tensile properties of CFRP coupons No. of layers

Designation

Length (mm)

Width (mm)

Thickness (mm)

1

1C-1

282

24.83

0.79

1

1C-2

280

25.00

0.73

1

1C-3

283

26.33

1

1C-4

282

24.80

1

1C-5

283

Average

282.00

SD

1.22

CV (%)

Tensile load (kN)

Load/width (N/mm)

Failure mode

5.6

225.50

DGM

6.5

260.00

SGM

0.79

6.3

239.24

SGM

0.77

6.8

274.19

SGM

26.00

0.73

6.1

234.62

DGM

25.39

0.77

6.26

246.71

0.72

0.04

0.45

19.90

0.43

2.83

3.98

7.20

8.07

2

2C-1

282

24.03

1.19

12.1

503.47

DGM

2

2C-2

282

25.03

1.29

14.7

587.22

SGM

2

2C-3

282

23.53

1.29

12.2

518.41

DGM

2

2C-4

281

23.30

1.25

12.8

549.36

DGM

2

2C-5

281

23.73

1.23

13.0

547.75

SGM

281.60

23.93

1.24

12.96

541.24

Average SD

0.55

0.67

0.06

1.05

32.29

CV (%)

0.19

2.82

3.40

8.07

5.97

400

P. Bindurani et al.

Table 3 Tensile properties of wire mesh coupons No. of layers

Designation

Length (mm)

Width (mm)

Thickness (mm)

Tensile load (kN)

Load/width (N/mm)

3

3F-1

280

25.07

1.73

3.43

136.84

3

3F-2

280

25.20

1.80

3.50

138.89

3

3F-3

282

25.23

1.70

3.36

133.16

3

3F-4

280

25.17

1.67

3.54

140.66

3

3F-5

281

25.03

1.63

3.32

132.62

280.60

25.16

1.71

3.43

136.43

Average SD

0.89

0.09

0.06

0.09

3.51

CV (%)

0.32

0.35

3.76

2.69

2.57

4

4F-1

280

25.27

2.07

4.91

194.33

4

4F-2

283

25.40

2.23

4.86

191.34

4

4F-3

280

25.13

2.20

4.84

192.57

4

4F-4

281

25.27

2.27

4.96

196.31

4

4F-5

281

25.27

2.17

4.94

195.51

Average

281.00

25.27

2.21

4.90

194.01

SD

1.22

0.09

0.10

0.05

2.05

CV (%)

0.44

0.37

3.51

1.04

1.06

5

5F-1

282

25.03

2.63

6.08

242.88

5

5F-2

280

25.30

2.80

6.32

249.80

5

5F-3

281

25.17

2.70

6.24

247.95

5

5F-4

282

25.20

2.63

5.98

237.30

5

5F-5

280

25.33

2.73

6.12

241.58

Average

281.00

25.21

2.70

6.15

243.90

SD

1.00

0.12

0.07

0.13

5.03

CV (%)

0.36

0.47

2.62

2.18

2.06

6

6F-1

280

25.17

3.47

7.30

290.07

6

6F-2

282

25.30

3.43

7.46

294.86

6

6F-3

282

25.23

3.53

7.28

288.51

6

6F-4

280

25.10

3.53

7.32

291.63

6

6F-5

281

25.20

3.53

7.44

295.24

Average

281.00

25.20

3.50

7.36

292.06

SD

1.00

0.07

0.05

0.08

2.95

CV (%)

0.36

0.30

1.35

1.14

1.01

Tensile Properties of FRP and Ferrocement—A Comparative Study Fig. 5 Failure modes in FRP coupons

401

2C-1

2C-2 2C-1: Edge delamination (DGM) 2C-2: Long splitting (SGM) 3G-1 3G-2 3G-3 3G-1: Lateral failure at top grip/tab (LAT) 3G-2: Lateral failure at top of gauge region (LGT) 3G-3: Angled failure at top of gauge region (AGT)

5G-2 5G-1 5G-1: Lateral failure at middle of gauge region (LGM) 5G-2: Long splitting (SGM)

results in Tables 1 and 2, it is seen that almost all the failures happened in the gauge region, which is the recommended type. For CFRP specimens, long splitting and edge delamination in the middle gauge zone were the predominant modes of failure, while in GFRP, lateral or angled breaking failures were predominant. Figure 5 depicts the failure modes in a few typical specimens. For wire mesh specimens, the failure modes in all specimens were yielding and breaking of one or more layers within the gauge region.

2.6 Discussion Tensile force per unit width. Figure 6 shows the variation in tensile strength (in N/mm) with the number of plies in FRP as well as in the wire meshes of ferrocement. From the experimental results, the tensile force per unit width for one-layer CFRP,

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P. Bindurani et al.

Tensile load/width N/mm

600 500 400 300 CFRP

200

GFRP 100 0

FC 1

2

3

4

5

6

Number of layers Fig. 6 Variation of tensile load/unit width (N/mm) with a number of layers of FRP or wire mesh

three-layer GFRP and five-layer wire mesh were 246.71 N/mm, 242.1 N/mm and 243.9 N/mm, respectively, which were comparatively equal. A linear regression analysis was conducted on the test results and the numbers of layers of GFRP and wire mesh equivalent to two-layer CFRP were found out. The results, which are tabulated in Table 4, show that the tensile force per unit width for 2-layer CFRP (541.24 N/mm) is equivalent to 7 layers of GFRP (576.01 N/mm) and 11 layers of wire mesh (552.2 N/mm). The average tensile force per width and the corresponding elongation at every 0.2 kN interval during each coupon test were noted. These results for each layer group for GFRP and CFRP are depicted in graphical form in Fig. 7a, b, respectively. The results confirm the elastic nature of FRP material as the load-elongation graphs show Table 4 Tensile strength (in N/mm) of test coupons with various numbers of layers

Number of layers

GFRP

CFRP

FC

1

–

246.71

–

2

118.43

541.24

–

3

242.10

–

136.43

4

312.46

–

194.01

5

389.96

–

243.90

6

487.65

–

292.06

7

576.01a

–

345.79a

8

664.64a

–

397.47a

9

753.27a

–

449.15a

10

841.89a

–

500.82a

11

930.52a

–

552.50a

Note a represents the linear regression analysis values

Tensile force per unit width (N/mm)

Tensile Properties of FRP and Ferrocement—A Comparative Study

403

600 500 400

2G 3G 4G 5G 6G

300 200 100 0

0

2

4

6

8

Elongation (mm)

Tensile force per unit width (N/mm)

(a) GFRP 600 500 400 300

2C

200

1C

100 0

0

2

4

6

8

Elongation (mm)

(b) CFRP Fig. 7 Average tensile force per unit width versus elongation for FRP specimen groups with various numbers of layers

linear variation without yielding zones. The stiffness is found to be increasing with the increase in the number of layers in both types of FRP. In CFRP, the increase in stiffness from one layer to two layers was 233%, but the percentage elongation sustained by both layer group was nearly equal (5.7%). In GFRP, the increments in stiffness of 3–6 layer group from the two-layer group were 135, 181, 204 and 268%, respectively. The Width and Thickness of the Coupons. ASTM D7565 [9] recommends that the variation in specimen width should not be greater than ±1%. However, in a manual wet lay-up manufacturing procedure for FRP, it is difficult to achieve the variation of specimen width lower than this limit [10]. The experimental results are given in Tables 1 and 2 show the variation in specimen width. They are 2.83 and 2.82% for CFRP with one and two layers, respectively. For GFRP, the variations are 1.82, 2.24, 2.06, 2.51 and 2.16% for layers 2–6, respectively.

404

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Similarly, ASTM D7565 [9] recommends a maximum variation in specimen thickness of ±4% This limit was achieved in the experiment conducted and the variations are represented in Tables 1 and 2. For CFRP, the variations are 3.98 and 3.4% for oneand two-layer groups, respectively, and for GFRP with 2–6 layers, the variations are 3.81, 2.51, 3.2, 1.85 and 2.69%. Even though there are no standards for wire mesh test specimens, to match with FRP specimens, the variations in width and thickness of wire mesh coupons were also kept within ±1% and ±4%, respectively. The values are shown in Table 3.

2.7 Conclusions An experimental study has been conducted to equalize the tensile properties of CFRP, GFRP and ferrocement laminates in order to compare the rehabilitation potential of these composites on RC structural elements. The findings of the study are summarized as follows. For the selected FRP and ferrocement materials in this study, CFRP with one layer is found to be equivalent to (i) GFRP with three layers and (ii) ferrocement with five layers of wire meshes, in terms of tensile strength. Further, a linear regression analysis carried out indicates that CFRP laminate with 2 layers is equivalent to (i) GFRP with 7 layers and (ii) ferrocement with 11 layers of wire mesh, with reference to the tensile strength of the composites.

References 1. Aravind N, Samanta AK, Roy DKS, Thanikal JV (2013) Retrofitting of reinforced concrete beams using fibre reinforced polymer (FRP) composites—a review. J Urban Environ Eng 7(1):164–175 2. Baggio D, Soudki K, Noel M (2014) Strengthening of shear critical RC beams with various FRP systems. Constr Build Mater 66:634–644 3. Sarker P, Begum M, Nasrin S (2011) Fibre reinforced polymers for structural retrofitting: a review. J Civil Eng (IEB) 39(1):49–57 4. Sheikh SA, Derose D, Mardhuki J (2002) Retrofitting of concrete structures for shear and flexure with fibre-reinforced polymers. ACI Struct J 99(4):451–459 5. Spadea G, Bencardino F, Sorrenti F, Swamy RN (2015) Structural effectiveness of FRP materials in strengthening RC beams. Eng Struct 99:631–641 6. Al-Kubaisy MA, Jumaat Z (2000) Ferrocement laminate strengthens RC beams. Concr Int 22(10):37–43 7. Kaish ABMA, Jamil M, Raman SN, Zain MFM, Nahar L (2018) Ferrocement composites for strengthening of concrete columns: a review. Constr Build Mater 160:326–340 8. ASTM D3039/D3039M (2000) Standard test method for tensile properties of polymer matrix composite materials. ASTM International, West Conshohocken, PA

Tensile Properties of FRP and Ferrocement—A Comparative Study

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9. ASTM D7565/D7565M-10 (Reaffirmed 2017) Standard test method for determining tensile properties of fiber reinforced polymer matrix composites used for strengthening of civil structures. ASTM International, West Conshohocken, PA 10. Pham TM, Hadi MNS, Youssef J (2017) Effects of fabrication technique on tensile properties of fiber reinforced polymer. J Test Eval 45(5):1524–1534. https://doi.org/10.1520/JTE20150525. ISSN 0090-3973

Analysis of PVD with Vacuum and Surcharge R. Sujana and Anjana Bhasi

Abstract Improvement of soft clay for making the ground viable for construction has always been a dynamic area of research. One such ground improvement technique being widely used is the inclusion of Prefabricated Vertical Drains (PVD) in the soil to accelerate the consolidation. The effectiveness of using PVD can be further improved by combining surcharging with vacuum preloading. The paper deals with the 2D numerical modeling of soft soil stabilized with vertical drains subjected to combined vacuum-surcharge preloading using the finite element program ABAQUS. The predictions of settlement and pore-water pressure were compared with the experimental data reported in the literature. Keywords PVD · Vacuum consolidation · Two-dimensional analysis · Settlement · Pore pressure

1 Introduction Construction on soft soils is always a great concern for geotechnical engineers. Numerous studies are being conducted on the improvement of such soils, and various techniques have been successfully implemented throughout the world. Installation of Prefabricated Vertical Drains (PVDs) is such a technique being widely used presently for improving the problematic soils like soft clay and making them viable for construction. PVDs were developed from the idea of sand drains or wick drains. Due to the relative easiness of efficiency and economy, they overruled the latter. The concept of employing vacuum for ground improvement was initiated by Kjellman in 1952. But due to the limitation of materials then, it became popular after some period only. PVDs accelerate the consolidation process by reducing the drainage path and by establishing radial drainage. Vacuum-PVDs in addition to this, due to their suction effect will reduce the outward lateral movement. Another important characteristic of

R. Sujana (B) · A. Bhasi Department of Civil Engineering, National Institute of Technology Calicut, Calicut, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_30

407

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R. Sujana and A. Bhasi

the vacuum-PVD technique is the increase in effective stress without increasing the total stress. Presently, vacuum incorporated PVDs is a dynamic area of study for researchers and engineers. Analytical, numerical, and experimental studies are being conducted in the area on a large scale [7, 10]. Analytical solutions were proposed by Indraratna et al. [9] and Chai et al. [4] and later modified by various authors. Numerical modeling of the soil improved with vacuum-assisted PVD has proven to be a gateway for exploration in this area [2, 3, 6, 14]. Experimental studies have been conducted to understand the effects of various factors on the consolidation behavior of vacuumPVD improved soil. Numerical studies and field experience have proven the efficiency of vacuum-PVD technique over conventional preloading method [11, 13, 15]. Studies have shown that the results from 2D Plane Strain analyses of PVD improved soft ground are comparable with that from the time consuming and tedious full 3D analyses [10, 13], provided the analyses uses proper conversion techniques. The conversion from 3D to plane strain analysis can be done in different methods, viz., permeability conversion, geometry conversion, combined conversion [8].

2 Numerical Modeling The finite element method-based program ABAQUS is used for the numerical study of vacuum-assisted consolidation. The paper presents numerical analyses based on the laboratory study by Saowapakpiboon et al. [14]. Tests were conducted for both the cases, viz., with surcharge alone and combined vacuum-surcharge loading. Axisymmetric unit cell analyses were performed to study the settlement and pore pressure behavior of soil under the application of surcharge only and combined surcharge and vacuum. Due to the symmetry, only one half of the cell is modeled. Details of the laboratory test are given in Table 1. Cam-clay model based on the critical state soil mechanics is used for modeling the clayey soil. The equivalent diameter of the drain Table 1 Details of laboratory test

Parameter

Unit

PVD width (w)

0.0500

m

Thickness (t)

0.0035

m

Equivalent diameter (d w )

0.0268

m

Discharge capacity (qw )

100

m3 /year

Mandrel diameter (d m )

0.044

m

Smear zone diameter (d s )

0.0871

m

Thickness (l)

0.7

m

Surcharge (without vacuum)

100

kPa

Surcharge (with vacuum)

50

kPa

Vacuum applied

50

kPa

Analysis of PVD with Vacuum and Surcharge Table 2 Simulation parameters

409

Parameter

Unit

Unit cell diameter (d e )

0.45

Initial void ratio (e0 )

2.29

Vertical permeability (k)

6.3e−5

Logarithmic bulk modulus (κ)

0.055

Logarithmic plastic bulk modulus (λ)

0.569

Poisson’s ratio (ν)

0.3

Stress ratio (M)

0.8

Intercept (ecs )

4.51

m m/day

is calculated from the equation given by Rixner et al. [12]. Extend of smear zone is determined based on the correlation given in the literature [1, 5] as twice the mandrel diameter. The effect of the smear zone was taken into account by using a factored horizontal permeability for the zone. For the smear zone, permeability ratio (ratio of coefficient of horizontal permeability of undisturbed zone to that of smear zone, i.e., k h /k s ) is taken as 3. The ratio can vary from 1 to 10 [3]. Soil mass is considered to be orthotropic with the ratio of horizontal to vertical permeability as 2. Soil parameters used for the numerical simulation are given in Table 2. The unit cell used for the analyses is shown in Fig. 1.

3 Results and Discussion The analyses included the determination of settlement and excess pore pressure developed in the PVD-installed soil, loaded by a surcharge with and without vacuum using the finite element program ABAQUS. The results obtained from the simulations were compared with the laboratory results and were found to be in good agreement (Figs. 2 and 3). Also, the settlement and pore pressure behavior were compared for the cases of with and without vacuum (Fig. 4). It can be seen from the results that for both the specimens, viz., with and without vacuum, final settlement is the same. The rate of settlement is enhanced in the specimen with vacuum-PVD. Final settlement is achieved in the sample with PVD alone in around 50 days while it took only 42 days for the specimen with vacuum-PVD. The pore pressure in the vacuum applied specimen reaches a final value close to the applied vacuum pressure (Fig. 3b).

4 Conclusion Numerical analyses were done for studying the settlement and pore pressure behavior of soil specimens with PVD alone and vacuum-PVD. From the results, it can be seen

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Fig. 1 Axisymmetric model adopted for the analyses a surcharge loading; b combined vacuum and surcharge loading Time (days)

Time (days)

0 5 10 15 20 25 30 35 40 45 50 55

0.00

0.00

Settlement (m)

Settlement (m)

without vacuum (measured)

-0.10

5

10 15 20 25 30 35 40 45

With vacuum (FEM) With vacuum (measured)

without vacuum (FEM)

-0.05

0

-0.05

-0.10

-0.15 -0.15

(a)

(b)

Fig. 2 Settlement curve for the specimen with PVD and surcharge a with PVD b with vacuum-PVD

Analysis of PVD with Vacuum and Surcharge

411

90 with vacuum(FEM) With vacuum(measured)

60 without vacuum (FEM)

70

Without vacuum (Measured)

60 50 40 30 20 10

Pore pressure (kPa)

Pore pressure (kPa)

80

40 20 0 -20 -40

0 0

0

5 10 15 20 25 30 35 40 45 50 55

5

10 15 20 25 30 35 40 45

Time (Days)

Time (days)

(a)

(b)

Fig. 3 Pore pressure curve for the specimen a with PVD b with vacuum-PVD Time (days) 0.00 With vacuum (FEM) without vacuum (FEM)

Settlement (m)

80

5 10 15 20 25 30 35 40 45 50 55

-0.05

-0.10

Pore pressure (kPa)

0

with vacuum(FEM) without vacuum(FEM)

60 40 20 0 -20 -40 0

-0.15

5 10 15 20 25 30 35 40 45 50 55

Time (Days)

(a)

(b)

Fig. 4 Comparison for specimen with PVD alone and Vacuum-PVD a settlement, b pore pressure

that the final settlement is same for both the cases (around 125 mm), but the time taken for consolidation has been reduced to 42 days for vacuum PVD, whereas it takes 50 days for PVD alone. Thus the rate of consolidation is accelerated by the application of vacuum pressure. Regarding the pore pressure, it initially shoots up to approach the applied surcharge and gradually reduces. The final value of excess pore pressure in the vacuum-PVD case is approximately equal to the applied vacuum pressure.

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References 1. Bergado DT, Asakami H, Alfaro M, Balasubramaniam AS (1991) Smear effects of vertical drains on soft Bangkok clay. J Geotech Geoenviron Eng ASCE 117(10):1509–1529 2. Bergado DT, Anderson LR, Miura N, Balasubramaniam AS (1996) Soft ground improvement. In: Lowland and other environments. ASCE Press, pp 427 3. Chai J, Shen S, Miura N, Bergado DT (2001) Simple method of modeling PVD improved subsoil. J Geotech Geoenviron Eng 127(11):965–972 4. Chai J, Hong Z, Shen S (2010) Vacuum-drain consolidation induced pressure distribution and ground deformation. Geotext Geomembr 28:525–535 5. Hansbo S (1987) Design aspects of vertical drains and limit column installation. In: Proceedings 9th Southeast Asian geotechnical conference (Bangkok, Thailand) 6. Hird CC, Pyrah IC, Russell D (1992) Fin embankments on soft ground. Geotechnique 42 7. Indraratna B, Redana IW (1997) Plane strain drains. J Geotech Geoenviron Eng 123(5):474–478 8. Indraratna B, Bamunawita C, Redana I, McIntosh G (2003) Modeling of prefabricated vertical drains in soft clay and evaluation of their effectiveness in practice. J Ground Improve 7(3):127– 138 9. Indraratna B, Bamunawita C, Khabbaz H (2004) Numerical modeling of vacuum preloading and field applications. Can Geotech J 41:1098–1110 10. Indraratna B, Sathananthan I, Rujikiatkamjorn C, Balasubramaniam AS (2005) Analytical and numerical modeling of soft soil stabilized by prefabricated vertical drains incorporating vacuum preloading. Int J Geomech ASCE 5(2):114–124 11. Lam LG, Bergado DT, Hino T (2015) PVD Improvement of soft Bangkok clay with and without vacuum preloading using analytical and numerical analyses. Geotext Geomembr 43:547–557 12. Rixner JJ, Kraener SR, Smith AD (1986) Prefabricated vertical drains. Summary of research effort—Final Report. Federal Highway Administration, US Department of Commerce, Washington, D.C. Report FHWA-RD-86-169, vol 2 13. Rujikiatkamjorn C (2012) Physical modelling of soft clay consolidation using vacuumsurcharge method. Aust Geomech J 47(3):27–34 14. Saowapakpiboon J, Bergado DT, Voottipruex P, Lam LG, Nakakuma K (2010) PVD improvement combined with surcharge and vacuum preloading including Simulations. Geotext Geomembr 29:74–82 15. Sun L, Gao X, Zhuang D, GuoW HJ, Liu X (2017) Pilot tests on vacuum preloading method combined with short and long PVDs. Geotext Geomembr 46:243–250

Drivers Perspective on Wearing Seat Belt and Use of Mobile Phone While Driving in Metropolitan City Ballem Praveen, Adepu Ramesh, and Molugaram Kumar

Abstract Motorbikes and cars share a highest proportion (33.9 and 24.5%) of total crashes. Most of these crashes result in crash tragedy which increases the severity and is a result of not wearing seat belt or use of mobile. The study aims in analyzing the perspective of drivers toward wearing seat belt and use of mobile phone. Online and field survey was conducted along with observational survey. A logistic regression analysis is carried to find the risky factors influencing not to wear seat belt and use of mobile. It is observed that nearly 50% of drivers are not wearing seat belt, and 94.1% of passengers in rear end were also not wearing seat belts. Wearing seat belt by yellow plate drivers is 10% less that of white plate drivers. The use of mobile phone was noticed during morning hours of the day in the age group of 26–35 years. The highest risk of not wearing seat belt and use of mobile phone was observed on minor roads among the age group of 36–50 years and on weekends. The factors influencing are type of car, road type, time of day, and day of the week which are found to be significant for wearing seat belt and use of mobile phone. The results from this study will be useful for reducing the crash severity rates by implementing appropriate awareness and enforcement programs in and around the metropolitan cities. Keywords Driver’s characteristics · Perspective · Seat belt · Mobile phone · Risk factors

B. Praveen (B) · A. Ramesh Department of Civil Engineering, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, Telangana, India e-mail: [email protected] A. Ramesh e-mail: [email protected] M. Kumar Department of Civil Engineering, University College of Engineering, Osmania University, Hyderabad, Telangana, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_31

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1 Introductions India has 2nd highest crash rate among the 22 developed and developing countries [8]. Motorbikes and cars have the highest proportion in total road crashes in India, i.e., 33.9% and 24.5%, respectively. Mostly the increase in crash severity is due to the use of mobile phone and not wearing seat belts while driving [7]. The statistics as summarized by Ministry of Road Transport and Highway (MORTH [7]) show that 64% of drivers and 72% of passengers were met with fatality due to not wearing seat belt in the year 2017 and around 2.1% of total crashes are due to use of a mobile phone [8]. In this context, the crash rate and crash severity rate shall be addressed to reduce the crashes, while the attitude and knowledge of drivers vary based on sociodemographic variables of driver and topographic conditions of road network [11]. This can be achieved either by providing strict enforcement or awareness programs. Police enforcement toward not wearing seat belt and using mobile phone while driving was observed to be difficult in particular with metropolitan cities, awareness programs will be supplemented in reducing the crash severity. To meet the above requirements, the following objective was framed: (i) to observe the driver’s and passenger’s characteristics and analyze the driver’s attitude and knowledge toward wearing seat belt and using mobile phone while driving, and (ii) to identify the risk factors associated with the driver’s decisions for not wearing seat belt and use of mobile phone while driving.

1.1 Literature Review Many studies have explained the perspective of road users in their respective countries toward the road safety, very few studies were carried in India for explaining road user’s perspective toward wearing seat belt and using mobile phone. Drivers prefer to wear a seat belt while driving on highways than minor roads and for long distances than short distances [4]. The preference of wearing a seat belt and mobile use will also vary with the age of driver and passenger [4, 6]. Jermakian et al. [5] found that the fatality rate is higher among four-wheeler back seaters since most of the back seaters do not wear seat belt thinking that they were safer than front seaters. The effective use of seat belt can decrease the severity of the injury, prevents chest injury by restraining the driver/passenger chest hitting any object in front [1, 13]. Authors recommended a strategic awareness program and strict enforcement to increase the rate of seat belt wearing and to reduce the use of mobile phone while driving [6, 9, 11]. The drivers who wear seat belt sometimes were expecting a remainder system to buckle their seat belt [5], because most of the drivers forget to put on seat belt or habituated for not to wear seat belt seeks for someone to alert them to wear seat belt [2]. Most of the authors considered sociodemographic variables such as gender and age for analyzing the attitude and behavior of driver like reasons for not wearing seat belt, comfort, vehicle type, location, road type, time of day, etc. [3, 5, 11, 12] and used roadside

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interview [6], web-based and telephone survey [5, 10] and field observational survey for collecting drivers characteristics and perspective data [1, 4, 6].

2 Methodology The methodology adopted in this study includes a roadside observational survey, driver’s perspective survey, and statistical analysis which are detailed in this section and diagrammatically briefed in Fig. 1.

2.1 Roadside Observational Survey Roadside observation was performed at selected study locations (three arterial and three sub-arterial roads) of Hyderabad city. Each road section was observed for three times in a day, i.e., morning (8:00 am to 10:00 am), afternoon (12:00 pm to 2:00 pm), and evening (4:30 pm to 6:30 pm) on weekdays and also at the same time on weekends, i.e., on Saturday and Sunday. The four-wheelers and motorbikes are randomly observed which were passing through the selected point of the road. The variables recorded from each observed four-wheeler included seat belt use (by driver and passengers), gender, predicted age group (50 years), car type (white plate and yellow plate), road type, time of day and day of the week, and mobile phone use and from motorbikes, variables recorded include the use of mobile phone, gender, age group, road type, time of day, and day of the week. Data Collection Drivers Perspective Data Roadside Interview

Online Response Sheet

SPSS (Descriptive & Chi-Square test)

Drivers Attitude and Knowledge and their Relationship against gender and age

Drivers/Passengers Characteristics Data

1. Data Collection

Roadside Observational Survey SPSS (Descriptive & Logistic Regression)

Drivers/Passengers Rate of Use and Risky Factors

Fig. 1 Diagrammatic representation of methodology adopted for this study

2. Data Analysis

3. Output Results

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2.2 Attitude and Knowledge Survey A questionnaire was developed with the predominant questions adopted from literature [4, 5]. Two different questionnaire sheets were developed one for seat belt wearing and another for use of mobile phone while driving. Survey was carried through two approaches; one online response sheet and another roadside interview. Roadside interview was carried at locations, for the driver’s parked vehicle at supermarkets, service centers, asked opportunistically to answer the questionnaire. Another side an online response sheet link [(i) seat belt: https://goo.gl/forms/ xH6Ke7ImCOZ23y0R2, (ii) mobile phone: https://goo.gl/forms/COM1ZTgP0Pft MSd72] was circulated through social networks and requested to fill the response sheet. The questionnaire consists of attitude and knowledge related questions along with sociodemographic questions (gender and age group) as shown in Tables 4 and 7.

2.3 Data Analysis A descriptive analysis and chi-square test were performed using SPSS statistical module to identify the relationship between sociodemographic (gender and age) variables and attitude, knowledge of driver’s toward wearing seat belt, and using a mobile phone while driving. Logistic regression was also performed to identify the risk factors associated with the decisions not to wear a seat belt and to use a mobile phone while on driving.

3 Data Analysis Results This section gives the details of the results for seat belt and mobile phone. The results of seat belt analysis are discussed and later the use of mobile phone in subsequent sections.

3.1 Wearing Seat Belt Roadside observations. Tables 1 and 2 provide the results of roadside observations. Overall 2230 drivers and 1762 passengers were observed at all study locations. The wearing the seat belt was observed to be more in male drivers (49.6%) than female drivers (35.5%). Around 50% of drivers were not wearing a seat belt in all aspects. It was observed that white plate drivers (type of car) were nearly 10% more than yellow plate drivers for not wearing a seat belt. The rate of wearing a seat belt on

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Table 1 Characteristics of seat belt wearing among four-wheeler drivers in Hyderabad Seat belt wearing

Total

Not wearing (%)

Wearing (%)

48.3

51.7

2230

Male

49.6

50.4

2106 (94.4%)

Female

35.5

64.5

124 (5.6%)

50 years

50.9

49.1

432 (19.4%)

White plate

47.3

52.7

1690 (75.8%)

Yellow plate

58.1

41.9

540 (24.2%)

Major road

48.0

52.0

1538 (69%)

Minor road

60.7

39.3

692 (31%)

Driver characteristics Gender

Age group

Type of car

Road type

Time of day Morning

45.0

55.0

706 (31.7%)

Afternoon

52.8

47.2

906 (40.6%)

Evening

51.5

48.5

618 (27.7%)

Weekday

44.6

55.4

1507 (67.6%)

Weekend

50.3

49.7

723 (32.4%)

Day of week

minor roads (39.3%), at afternoons (47.2%), and weekends (49.7%) observed to be low. A few percentage (5.9%) of passengers were observed wearing a seat belt, most of them were front seaters. The rate of wearing seat belt among passengers was observed to be low in females (5.6%), on minor roads (5.4%), at evenings (4.2%), and on weekends (2.3%), and passengers on white plate cars were 3.5% more wearing a seat belt than on yellow plate cars. Logistic regression analysis (shown in Table 3) showed that the variables, type of car (white plate), road type, and time of day (morning) were significantly influencing the driver’s and passenger’s decisions toward wearing a seat belt. The highest risk of not wearing a seat belt was observed among male gender, age group 36–50 years, white plate passengers, on weekdays and in the afternoons for both drivers and passengers.

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Table 2 Characteristics of seat belt wearing among four-wheeler passengers in Hyderabad Seat belt wearing

Total

Not wearing (%)

Wearing (%)

94.1

5.9

1762

Male

93.8

6.2

1008 (57.2%)

Female

94.4

5.6

754 (42.8%)

50 years

93.7

6.3

666 (37.8%)

White plate

93.2

6.8

1314 (74.6%)

Yellow plate

96.9

3.1

448 (25.4%)

Major road

92.0

8.0

1436 (81.6%)

Minor road

94.6

5.4

324 (18.4%)

Morning

93.3

6.7

520 (29.5%)

Afternoon

93.5

6.5

642 (36.4%)

Evening

95.8

4.2

598 (33.9%)

Weekday

93.7

6.3

1588 (77.1%)

Weekend

97.7

2.3

405 (22.9%)

Passengers characteristics Gender

Age group

Type of car

Road type

Time of day

Day of week

Attitude and Knowledge Survey. Overall, 956 drivers were interviewed toward wearing a seat belt (shown in Table 4), and male (85.6%) respondents were more than females (14.4%). The female drivers (42%) were more uncomfortable for seat belt wearing than male drivers (37.7%). Around 50% of male and 40% of female drivers were reported that they do not prefer to wear a seat belt for shorter trips, and this factor is significantly affected by the age category. Almost 95% of the respondents agreed that wearing a seat belt is necessary at all times, and it is significantly affected by gender and age category also. Nearly 75% of drivers said that wearing a seat belt is necessary even for rear seaters and about 85% said that they will ask if someone in their car forgets to put a seat belt on. Almost 95% of respondents supported for seat belt mandatory systems in the car and this support is significantly affected by age category. When we asked to suggest some initiative to increase the rate of seat belt wearing, most of them suggested to increase awareness (36%) and to provide strict enforcement (25%).

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Table 3 Logistic regression examining parameters associated with not wearing seat belt Sig.

Odds ratio

95% confidence interval Lower bound

Upper bound

0.851

2.483

Drivers characteristics Gender Male

0.171

1.453

1350 kg/m3 as more compact structure can be developed in slag granules, and to achieve the best result, the jet water temperature must be less than 50° C and minimum water flow rate to be kept at 2500 m3 /hr [5]. The next stage of processing is to address the needle or flaky shape of the particles by subjecting it to customized shaping and screening process. The purpose is to increase the finer portion of material ( 1.5 2

 Py Pcr e

(4)

Local–global interaction, Pnl Pnl =

⎧ ⎨

 ⎩ 1 − 0.15 PPcrl ne

Pne

0.4 

Pcrl Pne

0.4

f or λl ≤ 0.766 Pne f or λl > 0.766

 and λl =

Pne Pcrl

(5)

Py Pcr d

(6)

Distortional Buckling, Pnd Pnd =

⎧ ⎨

 ⎩ 1 − 0.25 PPcryd

Py

0.4 

Pcr d Py

0.6

f or λd ≤ 0.561 Py f or λd > 0.561

 and λd =

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533

Nominal Strength, Pn Pn = min(Pne , Pnl , Pnd )

(7)

3 Results and Discussions The results obtained by semi-analytical DSM approach for different specimens based on the elastic buckling loads observed. The local–global interactive buckling is found to be dominant in the specimen with lower local slenderness ratio and long specimen. The stability of the specimens is tested here on the basis of varying slenderness ration, length of the section, and stiffeners in the cross-section of the specimen. The visualization of failure pattern is easy to observe in the decomposed mode of eigenvalue buckling as observed in Fig. 3. The effect on the resulting stability are discussed more deliberately below and depicted in the Table 2:

3.1 Effect of Length On Stability and Performance of the Cross-Section The major effect on the stability and performance of the CFS cross-section is the increase in the dominance of global instability over the primitive local instability. The genuine decrease in the nominal strength against the compressive loading has been observed. The most stable and highest performing configuration is E (specimen) configuration with medium height.

(a) Local Buckling

(b) Distortional Buckling

(c) Global buckling (Torsional)

Fig. 3 Modes of buckling considered in DSM approach in this study (B specimen)

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3.2 Effect of Stiffeners On Stability and Performance of the Cross-Section The main effect of stiffeners on the stability and the performance of the cross-section is the locally stable cross-section as observed from L1D TO L5E. The locally stable cross-sections are susceptible to bear more compressive load than any of the crosssections whether it is conventionally shaped or poorly optimized section.

3.3 Effect of Slenderness Ratio On Stability and Performance of the Cross-Section The slenderness ratio decreases with an increase in the local stability and the increase in the length of the cross-section. High performance of the cross-section under compression has been observed with decreasing local slenderness ration which results in dominant global instability over the local instability (Table 2).

4 Conclusions The structural performance and stability have been studied here on the basis of different parameters. The classical semi-analytical DSM approach has been utilized here to highlight the local–global interactive buckling with the dominance of global buckling. The concluding remarks observed in this study are as following: i.

When the local slenderness ratio goes lower than 0.766 in the analytical prediction then this is directly termed as global instability dominance problem. ii. The L5B is the only specimen where the Flexural–Torsional Buckling is dominant in all types of buckling and specimen classification. iii. It could be asserted from this study that if the length of the CFS wall studs increases the dominance of the buckling mode on the stability of section changes from local–global interactive to the global mode for standard sections. In the case of the optimized sections, the stability must be to assess the behavior and mode of buckling.

L1A L2A L3A L4A L5A L1B L2B L3B L4B L5B

L1C L2C L3C L4C

L5C L1D L2D L3D L4D L5D L1E L2E L3E L4E L5E

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

11. 12. 13. 14.

15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

3600 2400 2700 3000 3300 3600 2400 2700 3000 3300 3600

2400 2700 3000 3300

2400 2700 3000 3300 3600 2400 2700 3000 3300 3600

Length

No Distortional Buckling mode

Specimen configuration

s.no.

0.7900 0.5503 0.4833 0.422 0.367 0.318 0.4471 0.3856 0.3322 0.2861 0.246

1.2433 1.1339 1.0158 0.8976

1.4987 1.3572 1.233 1.1315 1.0479 1.2149 1.1022 0.9868 0.8651 0.7684

0.9715 0.9966 1.0011 1.0089 1.0118 1.0159 0.9321 0.9367 0.9505 0.9559 0.9608

0.9426 0.9500 0.9612 0.9632

1.0754 1.0855 1.0888 1.0942 1.0972

1.6573 1.0813 1.2103 1.3380 1.4638 1.5879 1.0335 1.1577 1.281 1.403 1.5237

1.1232 1.2586 1.3929 1.5258

1.3851 1.5452 1.7012 1.8539 2.002 1.1926 1.3351 1.4760 1.6149 1.7446

24.271 44.647 39.450 34.428 29.704 25.332 50.986 45.496 40.116 34.977 30.115

33.269 30.965 28.711 26.409

17.629 15.490 13.654 12.187 11.003 28.782 26.441 24.108 21.974 20.284

Pnl

58.985 54.774 54.576 54.235 54.113 53.935 63.148 62.918 62.221 61.950 61.705

60.375 60.015 59.476 59.380

49.437 49.049 48.923 48.714 48.603

Pnd

24.456 44.647 39.450 34.428 29.704 25.332 50.986 45.496 40.116 34.977 30.115

45.334 39.613 34.127 28.959

27.333 22.411 18.490 15.568 13.351 38.586 33.186 28.116 23.532 20.164

Pne

24.271 44.647 39.450 34.428 29.704 25.332 50.986 45.496 40.116 34.977 30.115

33.269 30.965 28.711 26.409

17.629 15.490 13.654 12.187 11.003 28.782 26.441 24.108 21.974 20.164

Pn

LGIB LGIB LGIB LGIB LGIB LGIB LGIB LGIB LGIB LGIB LGIB

LB LB LB LB

LB LB LB LB LB LB LB LB LB FTB

Mode of failure

Local-Global interactive mode of buckling with dominance of global mode

Slenderness ratio

Table 2 Nominal strength and failure mode of the specimen

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References 1. Schafer BW (2008) The direct strength method of cold-formed steel member design. J Constr Steel Res 64(7–8):766–778 2. Ye J, Mojtabaei SM, Hajirasouliha I (2018) Local-flexural interactive buckling of standard and optimised cold-formed steel columns. J Constr Steel Res 144:106–118 3. Ye J, Feng R, Chen W, Liu W (2016) Behavior of cold-formed steel wall stud with sheathing subjected to compression. J Constr Steel Res 116:79–91 4. Tian YS, Wang J, Lu TJ, Barlow CY (2004) An experimental study on the axial behaviour of cold-formed steel wall studs and panels. Thin-walled Struct 42(4):557–573 5. Sonkar C, Mittal AKr, Bhattacharya SKr, Kumar S, Dewangan A (2019) Experimental and analytical study of Cold-Formed Steel (CFS) single stud walls sheathed with FCB, CSB and MgO under compression. In: Stability and Ductility of Steel Structures 2019: Proceedings of the International Colloquia on Stability and Ductility of Steel Structures (SDSS 2019), September 11-13, 2019, Prague, Czech Republic, p 1042, CRC Press 6. Young B, Rasmussen KJ (1998) Design of lipped channel columns. J Struct Eng 124(2):140– 148 7. Dewangan A, Bhatt G, Sonkar C (2020) Axial strength estimation of cold formed steel wall panels through numerical modeling. In: Babu K, Rao H, Amarnath Y (eds) Emerging trends in Civil Engineering. Lecture Notes in Civil Engineering, vol 61. Springer, Singapore 8. Dewangan A, Bhatt G, Sonkar C (2019) Analytical assessment of CFS wall-panels sheathed with MgO board. In: Stability and Ductility of Steel Structures 2019: Proceedings of the International Colloquia on Stability and Ductility of Steel Structures (SDSS 2019), September 11-13, 2019, Prague, Czech Republic 2019 Aug 30, p 337, CRC Press 9. Li Z, Schafer BW (2013) Constrained finite strip method for thin-walled members with general end boundary conditions. J Eng Mech 139(11):1566–1576 10. AISI S100 (2016) North American specification for cold-formed steel structural members 11. Li Z, Schafer BW (2010) Buckling analysis of cold-formed steel members with general boundary conditions using CUFSM conventional and constrained finite strip methods 12. Schafer BW (2013) Sheathing braced design of wall studs 13. Vieira Jr LCM, Schafer BW (2013) Behavior and design of sheathed coldformed steel stud walls under compression. J Struct Eng 139(5):772–786 14. Schafer BW (2012) CUFSM 4.05–finite strip buckling analysis of thin-walled members. Baltimore, USA: Department of Civil Engineering, Johns Hopkins University 15. Zhang Y, Wang C, Zhang Z (2007) Tests and finite element analysis of pin-ended channel columns with inclined simple edge stiffeners. J Constr Steel Res 63(3):383–395

A Model for Estimation of Critical Gap and Its Distribution Behaviour at Un Signalised Intersections M. Satya Deepthi and A. Ramesh

Abstract Traffic congestion on the urban road network is a result of the increase in vehicular traffic as it is characterized by slow speed, longer trip lengths, and longer delays. Unsignalized intersections are provided for low volume traffic flow and its performance is also used to evaluate urban road networks. Delay is considered as the important parameter and evaluation of unsignalized intersections is achieved through gap acceptance behavior. Gap acceptance behavior is an important parameter for the determination of capacity and at unsignalized intersection. This article explicitly presents an overview of the estimation of critical gaps at unsignalized intersections by conventional methods like Raff’s method and maximum likelihood method. The parameters are compared with Indo-HCM for better identification of traffic characteristics. Data are collected through video graphic techniques at two locations in Hyderabad. Traffic parameters like speed, volume, approaching vehicle type, accepted and rejected gaps were extracted. The study has also examined the variables associated with occupancy factor, vehicle type, and socio-demographic features. It is observed that conventional Raff’s method gives accurate results compared with other methods for different types of vehicles. Indo-HCM is also one of the most simplified techniques and gives precise values, and the critical gap values vary at a difference of 0.15 s compared to Raff’s method. Keywords Critical gap · Stratified sampling technique · Conventional methods · And occupancy factor

M. S. Deepthi (B) Post graduate student, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, India e-mail: [email protected] A. Ramesh Department of Civil Engineering, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_41

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1 Introduction India is a developing country and cities have has rapid urbanization and modernization as a result there is an immense growth in road traffic following heterogeneous traffic causing delay and congestion to road users. This leads to longer trip lengths, slower speeds of vehicles, increased vehicle queuing, and vehicle operation cost [5]. Generally, in semi-urban and urban scenarios, unsignalized intersections are primary locations where a conflict occurs. Unsignalized intersection is implemented to regulate low-volume traffic flow. Based on the relative importance of two roads, they are generally designated as major and minor roads. Vehicular interactions are complex at unsignalized intersections, a driver must find a safe moment for moving into the intersection area. Drivers intending to enter an unsignalized intersections have a series of gaps between vehicles in a stream, where they cross or merge. Conflicts in traffic are created when two or more roads cross and they result in delay and congestion. The capacity at an unsignalized intersection is important for the evaluation of road network capacity [4]. Gap acceptance is an essential skill for safe driving and determines the delay and capacity at an unsignalized intersection. Gap acceptance behavior explains the road user behavior in traffic stream and develops training and technology to lower the risk of crashes. Guler [2] Critical gap as explained in Indo-HCM is the shortest time interval on the major approach that allows the minor stream vehicles to go into the intersection. Therefore, the driver’s critical gap is the lowest gap that would be acceptable [3]. A specific vehicle would reject any gaps smaller than the critical gap and would accept gaps larger than or equal to the critical gap. Critical gap is an important aspect of driver’s behavior which is considered in the design and analysis of intersections. Transportation Research Board (2000) suggested that the driver’s critical gap can be calculated based on the observations of the greatest rejected and lowest accepted gap for a given intersection [6]. Critical gap is an important parameter for calculation of capacity which cannot be measured directly on the field. Rejected and accepted gaps of a single vehicle in a minor stream can be analyzed and some statistical methods are used for estimation of critical gaps by conventional methods like Raff’s, maximum likelihood, probability of equilibrium, Ashworth, Greensheild, logit, Harder, Wu, acceptance curve Methods, etc. [9]. Estimation of delay, capacity, and gap acceptance behavior are extensively studied at unsignalized intersections. The effect of delay on the critical gap is calculated by considering the average delays of the vehicle to that of critical gaps in second [8]. The distribution of accepted and rejected gaps are divided into different ranges according to movements on major and minor roads [7].

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2 Objective The objective of the present study is to determine. i. To determine gap acceptance behavior, critical gap of priority junction using conventional methods. ii. To evaluate the impacts of factors affecting the gap acceptance criteria.

3 Methodology Literature Study

• Identification of locations and Methods for estimation of Critical Gap • Data collection and extraction Data analysis for finding gap acceptance behavior and critical gap by conventional methods

Estimation of Capacity, Delay and Level of service of unsignalised intersections.

Results and Discussions

4 Data Collection Traffic data are collected through video graphic techniques at the selected site. In the present study, traffic data is collected for 9 h for a week, i.e., from 19 to 25 November, 2018 from the traffic police department, and at each intersection, peak hour traffic is determined. At all locations, the peak hour was observed to be 18.00–19.00 pm on Friday. The objective of this study is to find the critical gap of unsignalized intersections using conventional methods like Raff’s method based on the gap acceptance procedure and they are compared to Indo-HCM 2017 method which is also based on the gap acceptance method.

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Fig. 1 Study locations

i. Vehicle Classification ii. Turning movements iii. Direction of travel.

4.1 Study Location Intersection was selected in such a way that they have fair geometry and least interference by pedestrians and parked vehicles. Major traffic problems occurring at unsignalized intersections in Hyderabad city were identified. 1. Pragathi Nagar—T intersection. 2. Bahadurapally Intersection.(four-legged Intersection) (Fig. 1).

4.2 Site Selection Criteria Intersections consisting of major and minor roads on an urban road in Hyderabad city were selected. At these intersections, the following major factors are considered. 1. 2. 3. 4.

There are few pedestrian and cyclists Roads are divided into two lanes There is no roadside parking adjacent to the lane Intersections are located in educational, recreational, and residential areas (Figs. 2 and 3).

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541

Fig. 2 Pragathi nagar

Fig. 3 Bahadurpally

4.3 Road Inventory Data Road geometric data like carriageway width, parking facilities, type of intersection, bus bay, median width, footpaths, and street lights are taken from selected junctions (Table 1).

4.4 Volume Count Study Traffic Volume Survey is an essential part of Town Planning in a road network. It includes counting the number of vehicles passing through the selected intersection.

542 Table 1 Road geometric data at study locations

M. S. Deepthi and A. Ramesh Road geometric data Facility

Location 1: Pragathi nagar

Location 2: Bahadurpally

Carriageway width

17

15.5

Type of intersection

T intersection

4-legged intersection

Bus bay

No

Yes

Median width

1m

0.5 m

Foot path

No

No

Street light

Yes

Yes

The study of Classified Traffic Volume Count is to understand the factors that form the basis of: Establishing the use of the road network by vehicles of different categories, traffic distribution, and PCU. Need for median shifting or road widening. The peak hour volume of locations 1 and 2, i.e., Pragathi Nagar and Bahadurpally are given in the above figures. It is noted that the peak hour volumes are 4106 PCU and 4243 PCU. respectively. Peak hour flow was calculated by video data collected from the Police Department, Hyderabad. The accepted and rejected gaps from the video are extracted by a stratified sampling technique for analysis and determination of critical gaps using Indo-HCM and Raff’s method (Figs. 4 and 5).

Fig. 4 Peak hour traffic at intersection 1 Pragathi nagar

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Fig. 5 Peak hour traffic at intersection 2 Bahadurpally

5 Determination of Critical Gap By Raff’s Method Raff’s method is a macroscopic traffic flow method and it is a popular technique for the estimation of critical gap under saturated flow conditions, known for its simplicity and efficiency. Raff’s method approximate critical lags based on accepted and rejected gaps, where large data are omitted statistically. Raff’s technique was extended by calculating critical gaps by taking into account only gaps [1]. The critical lag is the size of lag that has a number of accepted lags shorter than is the same as the number of rejected lags. Therefore, critical gap is the intersection point between accepted and rejected gaps. Raff’s method is expressed as (Figs. 6 and 7) 1 − Fr (t) = Fa (t) where t = headway of major stream. F a (t) = Probability of accepted gaps. F r (t) = Probability of rejected gaps.

(1)

544

M. S. Deepthi and A. Ramesh 100.0 Cum .R

Cu

Cummulative

80.0 60.0 40.0 20.0 0.0 0

1

-20.0

2

3

4

5

6

7

8

Gap (sec) Fig. 6 Raff’s method for determination of critical gap for intersection 1 (Right turning from minor lane to major lane)

90.0

Cummulative Probability

80.0 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 -10.0 0

1

2

3

4

Gap (sec)

5

6 Cum .R

7

8 Cum . A

Fig. 7 Raff’s method for determination of critical gap for intersection 2 (Right turning from minor lane to major lane)

5.1 Critical Gap Estimation by Indo-HCM Method Indo-HCM 2017 defines critical gap as “The minimum major stream headway during which minor street vehicle can make a maneuver,” that uses occupancy factor method for the calculation of critical gap and it considers drivers’ behavior. Data containing geometry of the road and classified volume count of peak hour traffic are taken. The following are the steps to calculate critical gap and capacity of an unsignalized intersection by the Indo-HCM method. • • • •

Input Data ( Geometry of road and traffic volume) Convert the volume of traffic into PCU Calculate conflict traffic flow Determine Critical Gap

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Table 2 Critical gap for location 1—Pragathi nagar Adjustment factor

Base critical gap

Leg

Critical gap formula

t c (sec)

0.46

2.7

Bachupally to Pragathi nagar (1)

t c = 2.7 + 0.46 × ln(0.17)

1.9

0.58

3.8

Pragathi nagar to Gandimaisamma (7)

t c = 6.8 + 0.58 × ;ln(9.46)

4.29

0.88

6.8

Gandimaisamma to Bachupally (5)

t c = 3.8 + 0.88 × ln(1.76)

8.1

• Capacity of Turning Moments The critical gap for any movement can be obtained by the equation Tc,x = tc,base + f LV × ln(PLV )

(2)

where, PLV = Proportion of Heavy Vehicles. F LV = Adjustment factor for a proportion of Large vehicles in conflicting Traffic Stream. T c, base = base critical gap for various movements. Capacity of each turning movement is given by the equation   a × Vc,x × e−Vc,x tc,x−b /3600 Cx = 1 − e−v tc,x f, x/3600

(3)

The base critical gap for four lanes divided and the adjustment factor for heavy vehicles are taken from Indo-HCM method (Tables 2, 3, 4 and 5). Table 3 Capacity and LOS of intersection 1 Movement T c,x Follow Conflicting a (Adjustment b (Adjustment Capacity v/c up flow factor) factor) cx time

LOS

Movement 1.9 1

D

1.14

514

0.8

1.3

769.68

0.66781

Movement 4.29 2.574 7

622

1

2.16

825

0.753939 D

Movement 8.1 5

986

0.9

1.971

1200

0.821667 E

4.86

546

M. S. Deepthi and A. Ramesh

Table 4 Critical gap estimation on study location 2 (4-legged) Movement

Base critical gap

Adjustment factor for light and heavy vehicle F LV

Proportion of heavy vehicle in conflicting stream

Critical gap

1

2.7

0.457

17.98

4.02

4

2.7

0.457

12.19

3.84

7

3.8

0.885

15.06

6.2

10

3.8

0.885

18.02

6.35

8

6.8

0.583

19.05

8.51

11

6.8

0.583

20.87

8.56

6 Results and Discussion The paper provides detailed notes on the determination of critical gap using IndoHCM method and Raff’s method. Stepwise analysis of the collection of data, extraction of traffic volume, accepted and rejected gaps calculation, plotting the critical graph, capacity estimation, and determination of LOS explain the procedure of IndoHCM method Both Indo-HCM and Raff’s methods were analyzed to investigate the potential factors of the methods and compared them. The following are some of the observations made during the investigation process. • The peak hour traffic of the three-legged Pragathi Nagar intersection is 4102 PCU and four-legged intersection is 4323 PCU under mixed traffic conditions. The capacity and LOS of intersection 1 calculated from Indo-HCM method is 845 veh/h with v/c ratio as 0.753 and LOS D. • The capacity and LOS of intersection 2 calculated from Indo-HCM method is 647veh/h and V/C ratio as 0.535 and LOS D. The critical gap of intersection 1 and intersection 2 were observed as 4.29 and 4.02 s, respectively, for vehicles traveling from minor road to major road right turns. • Raff’s method explains the critical gap of intersection 1 and intersection 2 as 4.35 and 3.90 s, respectively, for vehicles traveling from minor road to major road right turns. It is observed that both Indo-HCM 2017 and Raff’s methods provide similar results and Indo-HCM method is an accurate method compared to Raffs’s method under mixed traffic conditions (Tables 6 and 7).

Critical gap

4.02

3.84

6.2

6.35

8.51

8.56

Movement

1

4

7

10

8

11

5.136

5.106

3.81

3.72

2.304

2.412

Follow-up time

Table 5 Critical gap estimation

1873

1388

1139

1263

230

498

Conflicting flow

0.9

0.9

1

1

0.8

0.8

Adjustment factor ‘a’

5.04

5.04

2.16

2.16

1.3

1.3

Adjustment factor ‘b’

740.6

425.5

604.36

571

359.23

645.02

Capacity

599

217

128

173

298

345

Volume

0.809

0.510

0.212

0.303

0.830

0.535

v/c

E

C

B

B

E

D

LOS

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Table 6 Results of location 1 Pragathi nagar intersection Geometry

T intersection (Pragathi nagar)

Movement

Major left (1)

Major right (7)

Minor left (5)

Adjustment for base critical gap

2.7

3.8

6.8

Critical gap

1.9

4.29

8.1 s

Heavy vehicle adjustment factor

0.46

0.58

0.88

Adjustment factor ‘a’

0.8

1

0.9

Adjustment factor ‘b’

1.3

2.16

6.8

Capacity

770

825

1200

V/C

0.67

0.75

0.82

LOS

D

D

E

Table 7 Results of location 2 bahadurpally intersection Geometry

4-legged intersection (bahadurpally intersection)

Movement

Major right (1) Major right (4)

Minor right (7)

Minor right (10)

Major through (8)

Major through (11)

Adjustment for base critical gap

2.7

2.7

3.8

3.8

6.8

6.8

Critical gap

4.02

3.84

6.2

6.38

8.51

8.56

Heavy vehicle adjustment factor

0.457

0.457

0.885

0.885

0.583

0.583

Adjustment factor ‘a’

0.8

0.8

1

1

0.9

0.9

Adjustment factor ‘b’

1.3

1.3

2.16

2.16

5.04

5.04

Capacity

345

298

173

128

217

599

V/C

0.535

0.83

0.303

0.212

0.51

0.809

LOS

D

E

B

B

C

E

References 1. Brilon (1999) Useful estimation procedures for critical gaps. Transportaation Research Board (TRB). National Research council: Washington 2. Guler S (2017) Methodology for estimating capacity and vehicle delays at un signalised multimodal intersections 3. Harsh JA (2015) A review of critical gap estimation approaches at uncontrolled intersection in case of heterogeneous traffic conditions

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4. Mourya AK (2016) Estimation of critical gap for through movement at four legged uncontrolled intersection. Elsevier, pp 203–212 5. Pande PM (2012) Evaluation of delay and LOS for signalised intersection, pp 372–377 6. Ashalatha R (2011) Critical gap through clearing behaviour of drivers at unsignalised intersection. Springer, pp 1427–1434 7. Sahraei MA (2016) Determination of gap acceptance at priority junctions. Elsevier 8. Tian ZZ (2015) A further investigation on critical gap and follow up time. Interanational symposisum on highway capacity. Transportation reasearch circular, USA, pp 397–408 9. Wu N (2012) Estimating distribution functions of critical gaps at unsignalised intersections based on equilibrium of probabilities. pp 1–25

Critical Review on Stress-Sensitivity and Other Behavioral Aspects of Arch Dams K. Jiji Panicker , Praveen Nagarajan , and Santosh G. Thampi

Abstract Dams have an important role in the economic and social development of a nation. As per ICOLD statistics, there are not less than 59,071 registered large dams in the world of which 2332 are arch dams. Some of the existing dams have deficiencies w.r.t. design and some of them may not meet the present design standards. Further, apprehensions on the health of some of the dams have been raised on account of aging. Safety of dams is of paramount importance and warrants utmost priority as the water stored is a potential source of threat to the life and property of the stakeholders downstream of the structure. Safety inspections and safety evaluations of existing dams would cast light on whether the dam has any structural, hydrological, and operational deficiencies and if there is any deterioration. Periodical structural evaluation using advanced technological interventions are indeed essential. The behavior of arch dams differs unpredictably vis-à-vis that of other types of dams due to its shape, the mechanism of transfer of loads, and the response of the dam body against such loads. Identification of the nature and magnitude of loads acting on the arch and consideration of all possible combinations of loads is an important part of engineering analysis. Safety evaluation of an arch dam shall highlight the issues of strength, stability, and vibrations, as well as special problems of arches and arched structures when subjected to the anticipated loads. Modernday engineering has solutions for problems related to the strength and stability of arches, and vibrations encountered in its life period. Galleries and other openings are integral parts of arch dams too. Stress contours and intensities of stresses at various salient locations, cantilever motions/periodic movements of an arch dam vis-à-vis fluctuating impoundment levels, the effect of stress reversals due to temperature variations, dynamic behavior due to seismic loads, etc., are to be computed and K. J. Panicker (B) Kerala State Electricity Board Limited Kottayam, National Institute of Technology, Kozhikode, Kerala, India e-mail: [email protected] P. Nagarajan · S. G. Thampi Department of Civil Engineering, National Institute of Technology, Kozhikode, Kerala, India e-mail: [email protected] S. G. Thampi e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_42

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analyzed to understand the behavior of the dam. Computational models using the finite element method (FEM) are capable of modeling and simulating the dam structure as well as the dam–fluid–foundation interaction, In this paper, a brief review of literature pertaining to structural analyses of arch dams and case studies on its behavioral aspects under various loading scenarios is presented. Some of the issues that require further investigation will be highlighted. Keywords Safety evaluation · Arch dam · Gallery · Stress contour · Periodic movements · Impoundment · Stress concentration · Dynamic behavior · Alkali–aggregate reaction · Computational models · FEM · Loading scenarios

1 Introduction Arch dams transfer the loads acting on it to the abutments and a large part of the stability is through transmitting of the loads to the abutments or canyon walls. Here, the cantilever action as well as the individual arch action plays a decisive role in the load transfer and behavioral aspects. An integral monolithic structure with no structural discontinuities such as open joints or cracks is of utmost importance to ensure arch action in arch dams. Arch dams vary in their behavior responding to the loads acted upon and per the classification of these dams; the predicted response to loads varies vis-à-vis the classification such as, based on the theory used for computation of stresses; cylinder theory dams and elastic theory dams [1, 2] or as the case may be. The behavior of these types of dams is monitored by the movements at salient locations of the dams and analyzing for the stresses developed and the consequent development of any cracks or crack propagation, in response to the static, dynamic, and temperature loads. Materials and methods adopted for construction too affect the strength and behavior of the dams. Alkali–aggregate reaction and its’ effects as well as the presence of ettringite in concrete and fracture pattern, etc., are all factors deciding the strength and behavior of an arch dam [3]. Sensitivity analyses on stress pattern as well as the deformation are inevitable during the safety evaluation of existing dams.

2 Need for a Sensitivity Analysis for Arch Dam Analyses on arch dams are done primarily for two purposes; the design of new arch dams and the safety evaluation of existing dams. In both cases, various aspects such as design criteria, foundation rock considerations, abutment rock considerations, material properties, methods of analyses, predicted behavior, etc., are pertinent. The design criteria include various loading cases and combinations—as per the design standards—likely to be acted upon, whereas in the case of existing arch dams, the safety and structural integrity are evaluated by studying the performance of the dam

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Fig. 1 Out of the 59,071 registered large dams, 2465 are arch dams (4.173%) (Source ICOLD website [4])

under various scenarios and the variation w.r.t. predicted behavior are to be analyzed. The performance of an existing arch dam includes the stresses, stress contour in the dam body as well as dam–foundation/dam–rock interface and deformation at salient locations and influence of these values on safety w.r.t. various loading conditions. Depending on the functional use envisaged, the impoundment of water in the reservoir fluctuates between minimum water level and Full Reservoir Level (FRL). The loading scenarios may cause periodic movements and stress pattern (Fig. 1). Safety analyses for an arch dam start with simple analyses with conservative assumptions and if those analyses suggest any ambiguousness more rigorous analyses can be resorted to [5]. In order to assess whether the deformation/movement of the dam and the stress contour are in the expected lines of behavior, the guidelines, design criteria, different methods of design, and tools like mathematical modeling, computational methods using 3D FEM analyses are to be rightly utilized (Fig. 2). In the case of new dams, the analyses for structural safety and stresses are done as part of their design and construction whereas simple analyses and rigorous analyses form part of the safety evaluation of existing dams. In either case, the ultimate aim is to see that the governing criteria are met with for ensuring the safety of the dam structure and the stakeholders downstream. The Federal Energy Regulatory Commission (FERC) division of Dam Safety & Inspection Guidelines [5] in the U.S. gives light to various failure scenarios and safety evaluations in existing arch dams. The safety evaluation should identify all potential failure modes and the structural stability should be ensured accordingly. Overstressing of concrete arch dams may cause tensile stresses to develop and extensive joint opening and cracking which can result in sliding failure but this may be inhibited by the arch action that restrains movements. There can be potential sliding failures due to sliding of rock wedges within the foundation and in dam contact, and due to sliding along the contact between dam and foundation rock. Unstable wedges at abutments too can be a cause of failure as in the case of first arch dam failure

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Fig. 2 (Above) Plan of an arch dam; (Below) Central cantilever of the arch dam (Source CISM courses and lectures no. 367 [6])

at Malpasset dam in 1959. Alkali–aggregate reactions, foundation, and abutment erosion due to overtopping, etc., are also causes of instability and require analyses [5].

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2.1 Methods of Analyses of Arch Dams There are various methods of analyses of arch dams such as preliminary and approximate methods (thin and thick cylinder methods, elastic theory, Cain’s method, USBR criteria, R.S. Varshney’s equation, etc.), elaborate methods(inclined arch method, Tolke method, etc.), trial load analysis (USBR), more elaborate and computational methods (finite element method, shell analyses, 3D elastic solution, finite difference method, etc.), and experimental methods such as model studies [7]. The computational methods such as 3D FEM analyses with the use of computers with advanced processors have become handy for modeling various scenarios in loading more realistically and the subsequent interpretation of the stress-sensitivity analyses results. Generally stating, the trial load method may be used for static analyses where the geometry is simple and material properties of concrete and rock are uniform, whereas the 3D finite element analyses are preferred for static and dynamic analyses of stresses in arch dams [5]. Proprietary general–purpose software such as ANSYS, ABAQUS, ATENA ADINA, LS-DYNA, etc., are capable of facilitating the non-analyses of arch dams. The analyses using computers too have limitations of incorporating the behavior of materials and the construction methods. There are analyses by various researchers incorporating the linear behavior and non-linear behavior; static and dynamic loading scenarios; subjected to spatially uniform and non-uniform ground motions, as the case may be.

2.2 Need of More Elaborate Analyses of Arch Dams The analyses during the initial era of concrete dam construction did not closely monitor the peculiar behavior and movement of arch dams. With the passage of time and years of development in the downstream, the stakeholders and administration realized the need of ensuring the safety of dams. It necessitated monitoring of the performance/behavior of the dams. Most of the arch dams may not be adequately instrumented for studying the stresses and deformation. Even if they are equipped with instrumentation, they may not be adequate or may not be working for the comprehensive safety evaluation. The advent of digital computers and evolving of powerful processors and computer software made the analyses of even complex geometries of arch dam much easier. It helped analyze the structure by (i) 3D modeling, (ii) fluid–structure interaction, (iii) fluid–structure–foundation interaction, (iv) with galleries, (v) dynamic response—linear, (vi) dynamic response—nonlinear, etc.…, with more refined meshes. The movement of these cantilevers, crest, its’ upheaval, etc., could also be studied. Sophisticated FEM analyses can have reliable results. It is a numerical process based on piecewise polynomial interpolation that simulates the physical behavior of a subject analyzed through suitable modeling. As such, it is important to realize that

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FEM analyses are not merely the adeptness in meshing process and pre-processing but a problem analyses with a thorough idea of the problem area that visualizes the physical behavior and relates it to element behavior [8, 9]. This is strictly true in the analyses of the complex behavior of the arch dams having complex geometry and loading scenario.

2.3 Effect of Temperature Variation in the Arch Dam Temperature and its effects are a serious concern for arch dam, be it during construction or while in operation. Ill-effects of heat generated by concrete on arch dam were rightly understood by the scientific community. In the case of the Hoover Dam in Colorado, USA, it was estimated that it would take 125 years to cool down from the heat generated from the chemical reaction of the massively used cement concrete and in order to avoid cracking due to the slow cooling, an indigenous cooling method was devised. This consisted of a network of one-inch copper pipe in the formwork before placing the concrete and pumping icy water through the pipe till the concrete was expected to become cool. Over 528 miles of gout filled pipes are concealed in the Hoover Dam for this purpose [10]. The variation of stresses are affected by factors like concrete placement spacing, concrete strength, heat of hydration, change in temperature due to pipe water cooling, surface insulation, arch closure temperature, temperature of reservoir water, ambient air temperature, aggregates used for arch dam construction, etc. The difference in temperature and heat flow can be simulated and the stress contour, especially tensile stresses due to thermal loading can be computed. The sensitivity analyses conducted on the Idukki Arch Dam, Kerala, India, had identified differential shrinkage and temperature effects as important parameters to be included in the FEM analyses and stressed the need of having heat reflective white coating, especially at the intrados profile and the exposed parts of extrados to contain the impact of temperate [11].

2.4 Earthquake Analyses on Arch Dams Many studies were done on the dynamic analyses for the earthquake response of arch dams. Wang and Li (2006) researched on joint opening effects on its seismic response through shake table model studies on arch dams and observed that the response acceleration and tensile arch stresses reduce due to the opening of joints during strong seismic events but cantilever stresses on downstream face exceed the tensile strength and hence mass concrete cracking is expected in such areas [12, 13]. Wang and Anil [14] had studied the interaction effect on the earthquake response of dam–water–foundation rock w.r.t. the spatial variation of ground motions on the Mauvoisin Dam in Switzerland. The spatial variation of ground motion (i.e., nonuniform ground motion)considering water compressibility, foundation rock mass,

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or foundation rock damping (material and radiation) the semi-unbounded extent of the foundation rock and impounded water domains in this earthquake analyses where dam–reservoir–foundation rock is considered as a linear system [14, 15]. This research work used the following equations of motion for the three-dimensional finite element system for the dam substructure m cr¨ct + cc r˙ct + kcrct = Rbo (t) + Rho (t)

(1)

where, m c , cc , and kc are the mass, damping, and stiffness matrices, respectively, whereas rct is the vector of total displacements. The force vectors Rbo and Rho represents the forces at dam–foundation rock interface and hydrodynamic force at the upstream face of the dam, respectively. The foundation rock substructure, dam–foundation rock system, fluid domain substructure, and dam–water–foundation rock system were mathematically represented and the methodology for a response to the arbitrary ground motion at every node of the dam was arrived at. The excitation at each node of the foundation rock interface was arrived at by interpolating the values at the known points of ground motions. The accuracy of the analyses of the 250-m-high double-curvature arch dam was carried out using EACD-3D-2008 computer program in which 8-node-thick shell elements are used, whereas the boundary element mesh is used at the dam–rock interface.

2.4.1

Non-linear Analyses

Omidia and Lotfi [12] studied a symmetric implementation of pressure-based fluid– structure interaction for non-linear dynamic analyses of arch dams by an FEM code called SNACS. They used the HHT time integration scheme suggesting advantageous over sophisticated analyses as it can take care of sudden changes in the stiffness due to the opening/closing of pre-existing joints during an earthquake. First, a pseudo-symmetric technique is proposed to store the total matrices and symmetrically solve the coupled non-symmetric equations. Then the interface element formulation and stress update procedures of two discrete crack constitutive models suitable for contraction and peripheral joints of arch dams are detailed. Afterward, the results of the analysis on a typical arch dam are compared with the effects of water compressibility and reservoir bottom absorption. Though the proprietary general-purpose software available are capable of performing non-linear seismic analyses of arch dams, some researchers are of the opinion that there is a lack of information on the material properties to be used in the available nonlinear constitutive models for both joints and concrete blocks and they proposed simplified non-linear analysis may often be superior to a sophisticated analysis for which some basic information is not available.

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2.5 Factors Affecting the Performance of Arch Dam Compressive, tensile, and flexural strength of concrete, strength under dynamic and thermal loading, strength under triaxial loading, creep, shrinkage, elastic modulus, and thermal properties of concrete are factors to be considered of while designing a new concrete arch dam or for evaluating the stress-sensitivity analyses/deformation behavior of an existing arch dam. Another important aspect worth considering is the effect of Alkali–Aggregate Reaction (AAR) between the active silica constituents of the aggregates and alkali in cement. Alkali–Silica Reaction (ASR), Alkali–Silicate/Silica Reaction (ASSR), and Alkali–Carbonate Reaction (ACR) are three categories of reaction. The restraints and stresses on concrete influence the expansion and damage due to AAR. Aging, material properties of cement and aggregates, as well as external factors such as humidity, temperature, and compressive stresses, influence the extent of concrete deterioration due to AAR. This gelatinous silica hydrate when the internal humidity exceeds 80–90% tends to swell and induce internal stresses within the concrete and causes micro-cracking under favorable conditions which can sometimes extend. Though no dam failure was reported due to AAR effects, concrete deterioration and movements due to volume change may happen. Misalignment of joints, opening up of lift joints, u/s and d/s misalignments, etc., may also happen [16]. As per Tuthill (1982), ASR caused an increase in mid crest elevation by 8–12 cm and movement of crest centers by 10–15 cm. The movements of the dam cantilevers and arches can be monitored using instrumentation. Hence, suitable selections of construction materials are very important [16, 17]. The safety requirement of arch dams doesn’t mean the stability of the dam structure alone but the stability of the abutment to which loads are transmitted. Stability against sliding failure along weak planes by wedges at the abutment is a major point of concern and hence shall be analyzed appropriately. Stability of foundation too is a point of concern. The failure of the Malpasset Arch dam in 1959 throws light into the stability requirement of abutment and foundation and the necessity of monitoring stresses at abutment and foundation and at their concrete interfaces.

2.6 Stress Concentration at Openings Openings, in the form of inspection/drainage galleries, hydraulic openings, vertical shafts, isolated chambers with specific intentions, may become inevitable in dams. There can be galleries in longitudinal and transverse directions and often in multiple levels. Their shape would neither be circular, elliptical, or rectangular. The stress distribution around those openings is three-dimensional in nature and is usually much complicated [18]. In a situation where a circular hole is drilled in a homogeneous, isotropic plate when subjected to the biaxial stress field could cause a stress concentration of three times the applied pressure locally but diminishing rapidly at increasing distances from the holes.

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Most of the dams, especially masonry and concrete dams, contain a system of inspection/drainage galleries or openings on account of various installations such as elevators and for instrumentation and other purposes. In the case of doubly curved thin arch dams, due to the complex geometry and response behavior, sensitivity analyses, and the sophistic analyses for safety under various loading scenarios shall include these openings to study the stress concentration or possibility of micro-cracks around these openings.

3 Optimization in Arch Dam Design Before computerized design came into practice in the construction of arch dams, most of them were of a simple geometrical profile as it involved complex computations for complex geometry. Later, the design has become an iterative process commencing with an initial section later modifying by analyses of stresses and arch thrust direction w.r.t. dip and strike of the rock in foundation and abutments [16]. Presently, researchers and engineers are incorporating various optimization methods reducing the concrete volume which can complement the conventional and usual design practices. Seyedpoor et al. [19] simulated the linear dynamic behavior of dam–water–foundation rock system subjected to ground motion due to earthquake using FEM and then for optimization, a wavelet back propagation neural network (WBPNN) was designed to predict the response of the arch dam. In the process, a dam grading technique (DGT) was introduced. The optimization process carried out using Simultaneous perturbation Stochastic Approximation (SPSA) and was implemented in the Morrow Point Arch Dam, Colorado. The study conducted on the double-curvature arch dam had shown that computational efficiency can be achieved besides optimizing concrete volume for the dam–water–foundation rock system. The research suggested that DGT accurately predict the behavior of arch dam and emphasized that dam–water–foundation rock system have to be properly considered.

4 Need for Instrumentation in Analyzing the Behavioral Aspects of Arch Dams In the case of arch dams which are to behave monolithically, monitoring of displacement is vital. They should have provisions for measuring displacements in the horizontal plane, relative movements between points within the dam, and the movement of the dam relative to a remote fixed point, foundation movement, and relative movement of any major joint in the dam or in its foundation [20]. A group of instruments—electronic, mechanical, geodetic, and seismic—are to be installed in the dam to measure deformation, temperature, and seismic influence on the dam. They

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Fig. 3 Layout for collimation measurements used for an arch dam (Source Guidelines for instrumentation of large dams, central water commission, New Delhi)

consist of devices for monument triangulation, geodetic targets installed at predefined points for measuring the deflection of the dam, pendulums suspended from various points of salient blocks including crest, crest collimation for crest deflection, gallery leveling/crest leveling for finding the settlement/upheaval, and seismic instrumentation for recording the response to ground motion [21]. Monitoring of movements over cracks, for example, cracking of the upstream heel of the arch dam, can be made by sliding micrometers or similar instruments. Collimation, triangulation, and leveling are used to measure the movement of dam points in relation to reference points outside the dam. Collimation measurements are performed with a theodolite at the dam’s crest. Arch dam requires more targets or piers because of the curvature of the crest. The displacement of the point at the dam’s crest is the deviation of the movable target from the line of sight. Three to four measuring points are usually installed, and the results are combined with plumb line readings (Fig. 3). Monitoring devices are installed in zones with the largest expected values of stresses and deformations, and in places calculated stresses to compare and the number of devices will vary w.r.t. type, size, and complexity of the structure being monitored. Arch dams, which are more sensitive than gravity and buttress dams, require comprehensive monitoring. The instrumentation should ensure clear pictures of distributed stresses, deformations, and temperatures in the dam’s body as well as in its foundation and hence proper installation of the appropriate equipment at a critical location and the correct interpretation of the resulting data within a well-implemented surveillance program is an absolute requirement (Figs. 4 and 5). Carlson Stress Meter is usually employed for special purposes, such as measuring the vertical stresses at the base, i.e. foundation, and for comparison of results obtained with a strainmeter. In arch dams, these meters are used for the determination of the horizontal compressive stress in the thin elements near the crest. Opening of joints can be measured with Strain meters. Sliding micrometers or like instruments can monitor cracking of the upstream heel of the arch dam.

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Fig. 4 Layout for triangulation measurement 1 Measuring targets on dam surface; 2 Theodolite piers; 3 Measured baseline; 4 Computed baseline; 5 sightlines (Source Guidelines for ins trumentation of large dams, central water commission, New Delhi)

Fig. 5 Layout of the temperature monitoring for an arch dam a Cantilever section; b Arch section (Source Guidelines for instrumentation of Large dams, central water commission, New Delhi)

The technological intervention through digital computers and computer-based technologies facilitates for 3D Terrestrial LiDAR scanning, Global Navigation Satellite System, etc., for accurate, long-term and real time 3D surface monitoring intended toward the comprehensive real time structural health monitoring system capable of identifying the deformation and unusual behavior of the dam, if any, compared to that in its’ expected lines.

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5 Arch Dams Construction Development in China and Their Research Contribution China owns many ultra-high arch dams (Ht. > 200 m) in the world and with 305 m height, Jinping I arch dam in China tops the table of arch dams. Five out of the top ten ultra-high arch dams in the world, and the top three in the list are from China, and as such literature throws light on complex aspects of strength and stability as well as stress behavior in these Arch dams. Wang [22] describes the key technologies used in the design and construction of Jinping I ultra-high arch dam. Extremely high water pressure acting on the arch dam, high seismic design criteria and complex foundation, optimization required in the arch dam shape, temperature control in concrete, strength, and stability of rock foundation and the very complicated geological conditions, crack Prevention, etc., were challenges in design and construction. For increasing the bearing capacity and rigidity of abutment, foundation treatment by way of concrete cushion and thrust transfer tunnel were adopted. Shape optimization was done based on a flexibility coefficient, C, and stress-level coefficient, D, defined as follows [22]: C=

F2 ≤ 25 − 0.05H VH

D = C H < 3500

(2) (3)

where F, V, and H are the area of the dam mid-face along dam centerline (m2 ), V is the volume of dam concrete (m3 ), and H is the dam height (m).

5.1 Stress Sensitivity Behavior of Ultra-High Arch Dams Wang [22] highlighted the studies conducted on Jinping I arch dam finding out safety factors for dam concrete strength, sliding of each potential block of abutment (as large, smaller, ladder blocks), and the overall safety factor as well as overload safety factors. 3D nonlinear FEM and geo-mechanical model test can find out the above safety factors. Wang R. also emphasized that owing to the greater height of arch dams that produce a greater seismic response, seismic design for design earthquake motion with a 2% probability of exceedance 100 years and a checking earthquake with 1% probability of exceedance in 100 years. Seismic design of arch dams in China stipulates, analyses by trial load method, dynamic elastic FEM analyses, modal response spectrum analyses, etc., for the stress control indices besides dynamic stability analyses and for arch dam exceeding 300 m height, non-linear FEM and dynamic model studies are required [22]. The Institute of Water Resources and Hydropower Research (IWHR), China, had conducted shake table model tests of arch dams for simulating

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Fig. 6 The top 10 arch dam for their height shows that their thickness ratio (crest thickness/bottom thickness) of the crown cantilever does not have a similar trend. (All except Sayano Shushenskaya dam in China are doubly curved arch dams.). The tensile stress and compressive stresses developed in the dam as per the trial load analyses for basic combinations revealed no trend w.r.t. the increase in height. (Wang [22]).

the dynamic interaction between dam, transverse joints, dam foundation with major geological structures, and water in the reservoir and the dynamic responses, change in natural vibration behavior, opening and closing of contraction joints, and the potential of cracking, etc., were studied and the maximum combined stress due to static and dynamic loads was found to be occurring around the dam toe whereas some tensile stress was occurring in the upper area of the upstream face and in the bottom area of the downstream face (Fig. 6).

6 Case Study of the Stress Analyses of a New Doubly Curved Thin Arch Dam and the Sensitivity Study Through Sophisticated Analyses During Service The Industrial Research Institute, University of Waterloo, Ontario, in as early as 1971, had conducted an FEA of the doubly curved asymmetric thin arch dam at Idukki, Kerala, India, and the results of principal stresses and maximum displacements compared well with the trial load analyses and model studies [23]. In the static stress analyses using one element grid arrangement deployed curved boundary isoparametric 3D finite element with 20 nodes, for the doubly curved parabolic thin concrete arch dam and 26 elements were used to model the geometry of the

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complex dam. The analyses modeled the support conditions in two ways, viz. fixed supports at rock surfaces and left bank intersections with wing wall block, and flexible supports modeled by independent spring response. 3D boundary elements were used for modeling complex geometries of dam structures. Rock surfaces were dealt with separately. The dead loads incorporated from element to element as energy equivalent nodal forces and pressure loading due to water and silt were considered with the pressure distribution normal to the water face. The load cases were analyzed individually and the combined effect reported. The analyses on the doubly curved thin arch dam Idukki as early in 1971 using the trial load analyses and Finite Element Method revealed that stresses at the boundary and those within two times thickness from the boundary are affected and the lower portion is sensitive to boundary conditions. Besides, tensile principal stresses are found to exist along with the boundary elements. When there was no release from rock, increased tension was observed. Of various analyses, it was found that actual variation of stresses showed better conformity with model study results than trial load analyses. This was inferred as due to the non-existence of temperature loads in FEAs and as such a model study also conducted. The increase in the compressive stresses downstream and decrease in upstream are attributed to the temperature effect. The maximum compressive stress is observed at the toe of the dam (1000 psi, ~6.89 MPa) and maximum tensile stresses were found on the upstream face (150 psi, ~1.03 MPa) and the temperature effects are believed to be causing an increase in tensile stresses. The analyses done during the initial stages did not closely monitor and emphasize on the peculiar behavior and movement of arch dams. Program developed for effective and accurate analyses of 3D solid elastic continua analyses had calculated deflections and stresses and found matching with previous FEM analyses [7] (Fig. 7). However, a 3D FEM thermostatic analysis of the doubly curved thin arch dam with vertical block joint and the multilayered galleries were conducted using the ABAQUS software and the displacement vectors resulted confirmed observed deformation behavior through the instrumentation data of the dam; the dam–foundation compound 3D model was analyzed with the concrete assumed to behave as linearly elastic whereas the rock mass assumed to behave plastically as per the Mohr– Coulomb failure criterion [24]. The dam–foundation rock interaction was modeled with relative sliding restrained but allowing for opening. The model was analyzed after study on the physical, mechanical, and mineralogical properties of the concrete and testing for their values at its age of 40 years. The analyses were conducted for four different loading scenarios of operating water level and concrete temperature combination. The FEM analyses were in full agreement with the instrumentation data which validated the FEM modeling and analyses.

7 Conclusion Monitoring of high arch dams of complex geometry for the stresses and deformation at salient points is necessary to be done for safety evaluation of existing dams and study of these parameters using sophisticated analyses is very important in the

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Fig. 7 The 3D FEM model of the doubly curved thin arch dam and the rock mass (Source BRK Pillai et al. [24])

safe design Various important factors such as water compressibility, foundation rock mass and the damping effects, interaction effect of dam–water–foundation rock, spatial distribution of ground motion, non-linear response, etc., are to be considered in these analyses. Sensitivity analyses, Instrumentation using state of the art technologies, especially for monitoring the deformation, and comprehensive structural health monitoring bear an important role in the safety evaluation of arch dams.

References 1. Creager WP, Justin JD, Hinds J (1944) Engineering for dams 2. Bureau of Reclamation, United States Department of the Interior (1977) Design of arch dams, design manual for concrete arch dams. United States Government Printing Office, Denver, Colorado 3. Pillai BRK, Smiljkovic Z, Dhawan AK (2015) A brief study of arch dam behavior. First national dam safety conference-Chennai, India. Central water commission, pp 283–291 4. ICOLD (2019) General synthesis. Retrieved 23 March 2019, from International commission on large dams. https://www.icold-cigb.org/GB/world_register/general_synthesis.asp 5. Federal Energy Regulatory Commission, Division of Dam Safety and Inspections (1999) Engineering guidelines for the evaluation of hydro-power projects. In Arch dams (p. chapter 11). Washington DC: FERC 6. Pedro JE, Arch dams: designing and monitoring for safety, courses and lectures No. 367, International centre for mechanical sciences, Springer Wein GmbH, p 5

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7. Abraham S (2007) Ph.D. thesis on finite element method in the context of arch dams—a critical study. University of Calicut, India, Calicut 8. Cook RD (1995) Finite element modeling for stress analysis. Wiley, New York 9. Cook RD (n.d.). Finite element methods. Taylor and Francis 10. Mann E (2006) Hoover dam. Mikaya Press, New York 11. Dhawan AK, Arora VV, Paul A, Kumar M, Pillai BRK (2015) Assessment of current material properties of aged concrete arch dam-a case study, second national dam safety conferencebengaluru, India. Jan 2016. Central Water Commission, pp 185–190 12. Omidi O, Lotfi V (2016) A symmetric implementation of pressure-based fluid–structure interaction for nonlinear dynamic analysis of arch dams. J Fluids Struct 69(2017):34–35. Elsevier Inc. https://doi.org/10.1016/j.jfluidstructs.2016.12.003 13. Wang H, Li D (2006) Experimental study of seismic overloading of large arch dam. Earthq Eng Struct Dyn 35(2):199–216 14. Wang J-T, Chopra AK (2010) Linear analysis of concrete arch dams including dam–water–foundation rock interaction considering spatially varying ground motions. Earthquake engineering and structural dynamics; Published online 6 November 2009 in Wiley inter science (www.int erscience.wiley.com). 39:731–750. https://doi.org/10.1002/eqe.968 15. Chopra AK (2012) Earthquake analysis of arch dams: factors to be considered. J Struct Eng 138(2):205–214 16. Sharma HD, Concrete dams, publication no. 266, central board of irrigation and power, January 1998 17. Tuthill LR (1982) Alkali-silica reaction-40 years later. Concrete International, April 1982, pp 32–36 18. Varshney RS (2010) Hydro power structures(A compendium including canal and small hydro engineering). Nem Chand and Bros, Roorkee, India 19. Seyedpoor SM, Salajegheh J, Salajegheh E (2008) Shape optimal design of arch dams including dam-water-foundation-rock interaction using a grading strategy and approximation concepts. Appl Math Model 34(2010):1149–1163. Elsevier Inc. https://doi.org/10.1016/j.apm.2009.08. 005 20. Central Water Commission, Govt.of India (2018) Guidelines for instrumentation of large dams. CWC, New Delhi 21. Dhawan AK, Paul A, Vijay Y, Pillai BRK (2015) State-of-the art instrumentation for dam safety-case study of Idukki dam, second national dam safety conference-bengaluru, India. Jan 2016. Central water commission, pp 522–529 22. Wang R (2016) Key technologies in the design and construction of 300 m ultra-high arch dams, engineering 2(2016):350–359. https://doi.org/10.1016/J.ENG.2016.03.012 23. Industrial Research Institute, University of Waterloo (1971) Idukki arch dam, finite element analysis. University of Waterloo, Water loo, Ontario 24. Pillai BRK, Bikram P et al (2015) Understanding the unusual behaviour of an arch dam using FEM approach. Second National Dam Safety Conference, Bengaluru - January 2016 Central Water Commission, New Delhi, pp 266–271

Assessment of Safety of a Retrofitted Damaged Reinforced Concrete Column Based on the Bond Stress and the Stress Transfer at the Interface of the Reinforced Concrete Jacket and the Old Concrete Y. K. Guruprasad and K. S. Jayasimha Abstract Reinforced concrete columns in buildings undergo damage due to earthquakes, under-designed or erroneous designs, exposure to high temperatures, or due to overloading. Damaged reinforced concrete columns affect the safety and stability of the overall building. Hence, damaged reinforced columns are retrofitted to restore them, from strength and stability aspects, to improve their load-carrying capacity. In this study, retrofitting of an existing damaged reinforced concrete column of a commercial building has been carried out. The bond stress developed at the interface of the reinforced concrete jacket and the old concrete corresponding to the damaged reinforced concrete column is assessed by carrying out a three-dimensional finite element analysis. Based on the magnitude of the developed bond stress, the number of shear connectors to be provided to anchor the old and new concrete in the reinforced concrete jacket is decided. The shear and axial stresses developed in the shear connectors are also checked with the corresponding permissible material strength values. The safety of the retrofitted reinforced concrete column is assessed based on the bond stress values; the shear and axial stress developed in the shear connectors; and the number of shear connectors provided at the interface of the damaged reinforced concrete column and the reinforced concrete jacket. Keywords Damaged reinforced concrete column · Retrofitting using reinforced concrete jacket · Bond stress at interface · Shear connectors

Y. K. Guruprasad (B) Former Researcher and former PhD Research Scholar, Department of Civil Engineering, Indian Institute of Science, Bangalore, India e-mail: [email protected] K. S. Jayasimha STEDRANT Techno Clinic Private Ltd., Bangalore, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_43

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1 Introduction Reinforced concrete (RC) structures form a major stock of buildings in current cities. The structural members such as RC beams, columns, slabs, and shear walls in the building are damaged when they are subjected to an earthquake [1, 2], exposed to fire [3], due to aging [4], and due to erroneous structural designs. In most cases, multistory structures may not necessarily be demolished that have been damaged to some extent. Nondestructive testing methods [5–7] assist in assessing the degree and extent of damage that has taken place in the damaged structural elements. Repair and retrofit strategies are thereafter adopted to strengthen and restore the stability of such damaged structural elements and structures. Repair and retrofit are applied on structural members if the damage in the structural elements is within the repairable limits. In the event of damage, the structure’s stability totally relies upon the strength and stability of vertically oriented structural members such as RC columns and shear walls that transfer the vertical loads from RC slabs, masonry walls, and RC beams to the foundation. RC columns form the major portion of the structural members in a multistory building to transfer the vertical loads to the foundation. When RC columns undergo damages due to an earthquake, exposure to high temperature, or due to fire, there is a loss in strength and stiffness in RC columns which in turn causes the structure to develop a condition of low stability and reduced strength or lead to the collapse of the entire or a portion of the structure.. Therefore, retrofitting of such damaged RC columns to restore or increase its load-carrying capacity and to restore its stability help in increasing the overall strength, stiffness, and stability of the entire structure. There are various retrofitting methods adopted to strengthen damaged RC columns such as wrapping the columns with fiber reinforced polymers (FRP), carbon fiber reinforced polymers (CFRP) [8], glass fiber reinforced polymers (GFRP) [9], steel jacketing [10], and reinforced concrete (RC) jacketing [11] of structural members. Among the various retrofitting methods mentioned above, RC jacketing helps to strengthen damaged or distressed RC columns when between the load-carrying capacity of the damaged column differs by more than 20% when compared to its undamaged or original load-carrying capacity. RC jacketing method is relatively economical when compared to other retrofitting methods that may be applied to strengthen the damaged RC column. Hazem and Ahmed [11] carried out a study experimentally and theoretically to understand the effect of dowel action and RC jacket stirrups to generate shear friction, to increase the bond strength at the interface of RC columns and RC jackets. The authors experimented on seven RC cubes with RC jackets on two sides and four RC cubes with RC jackets on all four sides. The testing of the cubes was carried out through direct shear tests. It was inferred from their study that stirrups provided in the cubes with RC jacket on all four sides increased the bond strength and reduced the effect of dowel action. Monir [12] studied the slip taking place at the interface of the RC jacket and the structural RC member that could be an influence on the RC member’s load-carrying capacity, overall member stiffness, and the deformation capacity of the member.

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Based on this study the author developed an analytical model to investigate the RC members with RC jackets by carrying out an analysis, section wise by taking into account the inelastic behavior of the materials. Monir validated the analytical model by carrying out a parametric analysis of RC-jacketed sections to assess its efficacy and to further propose a modification to the model by considering the slip taking place at the interface. Monir also extended the analysis on RC-jacketed members by considering the effect of temperature. Campione et al. [13] investigated the axial and bending behavior of RC columns that were strengthened with the help of RC jacketing and a cross section-based analysis was developed by the authors for axial and bending behavioral conditions. The authors’ work led toward an understanding of the confinement developed at the core portion of the concrete in the RC column and the possible buckling behavior of the compression rebars. The analysis showed an improvement in the ductility and strength of jacketed RC columns. Eduardo and Fernando [14] performed experiments to study the effect of structural treatment provided at the interface of the RC column and the RC jacket to resist seismic forces in terms of maximum bending moment. The authors have also carried out a numerical analysis based on their experimental work. The authors concluded that, for columns that were undamaged and had a ratio of bending moment to shear more than one, there was no requirement to provide any structural treatment at the interface of the RC column and the jacket. From Eduardo and Fernando’s study, it was also concluded that the thickness of the RC jacket provided must be then 17.5% less than the width of the column to be able to develop a monolithic behavior of the retrofitted RC column.

1.1 Significance of the Present Work Based on the study of the literature/research database carried out, the present work has identified and looks at the variation of the interfacial bond stress or shear stress developed at the interface of the RC jacket and the damaged RC column. When the magnitude of the interfacial bond stress or shear stress developed becomes comparatively lower in value, the load transfer between the old concrete (RC column) and the new concrete present in the RC jacket is not effective, making the RC jacket retrofit inefficient in strengthening the damaged RC column to the required value of load-carrying capacity.

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2 Assessment of Retrofitted Damaged RC Column Using RC Jacket In the present work, an interior RC column in the basement floor of an existing commercial building that has undergone damage/distress due to erroneous structural design has been considered for the study. The building is constructed in Bangalore, however, the details of the commercial building such as the plan and structural layout have not been presented in this paper to maintain the confidentiality of the project. The column was cast with M25 grade concrete and Fe415 grade steel. The details of the RC column considered in this work has a cross-sectional dimension of 250 mm × 600 mm reinforced with six numbers of 32-mm-diameter rebars as longitudinal reinforcement and 12-mm-diameter lateral ties spaced at 250 mm center to center. The height of the RC column considered for the present study measures to 3.5 m (floor to floor height). The RC column was designed as per Indian codal provision (IS 456:2000). The damage in the RC column was accounted for an erroneous design, which led to about 23% reduction in the axial load-carrying capacity of the column. The error being provision of the less gross cross-sectional area of the column including with lateral ties provided at a larger spacing which is greater than the designed lateral tie spacing (~225 mm). The difference in the load-carrying capacity of the damaged/distressed RC column was determined by carrying out structural analysis on the structural model of the entire commercial building in ETABS. The RC jacket that was designed, for members with 23% reduction in the axial load-carrying capacity, was applied around the RC column with a thickness of 150 mm. A total number of ten rebars of a diameter of 20 mm was equally distributed on all the faces of the RC jacket. The clear cover provided to the longitudinal reinforcement in the RC jacket was 25 mm. Lateral ties with a diameter of 8 mm spaced at 150 mm center to center were provided. Rebars of 12 mm diameter were used as shear connectors. The shear connectors were bent into L-shape for a total length of 200 mm and were drilled into the old concrete to a depth of 100 mm spaced at 500 mm center to center in a staggered pattern. For about a length of 100 mm, a portion of the shear connector that had the L-shaped side projected out of the surface of the old concrete surface was hooked on to the lateral ties or the longitudinal reinforcement of the RC jacket reinforcement for anchorage. The shear connectors used have yield strength of 500 MPa. A bonding epoxy was applied on the surface of the RC column after the reinforcement mesh of the RC jacket was completed. The bonding epoxy was applied to create a good bond between the old concrete (RC column) surface with the new concrete surface (RC jacket). The concrete corresponding to the RC jacket was placed in the RC jacket formwork when the bonding epoxy is in a tacky state. While designing the RC jacket the interfacial bond stress or shear stress provided by the bonding epoxy is considered as 0.5–0.8 N/mm2 although the supplier specifies the bond stress or shear stress developed is about six times more than the value considered for design. This is mainly to take into account the variability and difficulty in the application of the bond epoxy using a brush on the old concrete surface after tying the RC jacket retrofitting reinforcement cage and fixing of the shear connectors.

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Table 1 Elements types adopted in the finite element model S. No.

Structural component

Element type

Mesh type

1

Concrete

3D stress elements (C3D8): 8-node linear brick elements

Hex(hexagonal)

2

Reinforcing steel rebars–longitudinal rebars, lateral ties in RC column and in RC Jacket retrofit

3-D linear 2-node truss element (T3D2)

Line mesh

3

Shear connectors

3D stress elements (C3D8): 8-node linear brick elements

Hex(hexagonal)

2.1 Finite Element Analysis of the Damaged RC Column Retrofitted Using RC Jacket A finite element (FE) analysis was carried out by modeling the damaged RC column along with the RC jacket applied around the column using Abaqus. The RC column and the RC jacket and the shear connectors were modeled as a solid, while the reinforcing rebars were modeled as a line element in a three-dimensional space. The details of the element types used in the finite element model (FEM) are shown in Table 1. A global mesh size of 0.015 was adopted for all elements. The displacement boundary condition at the support that was applied at the bottom end of the column was U1=U2=U3=R1=R2=R3=0 and at the top end of the column where the load was applied, as a pressure, was U1=U2=R1=R2=R3=0. The axial load is applied as a pressure on the loading face of the column. The pressure is computed by dividing the axial load by the gross cross section of the column. The axial load acting on the column that was obtained from the structural analysis is 1688 kN. It was learned from the structural analysis that this RC column was subjected to only uniaxial moment acting at the ends of the column that had a very low magnitude of 4 kN-m. The possible reason for the development of such a low value of uniaxial moment may be due to its central location with RC beams and other columns placed symmetrically around it and further, the floor load applied in the zone of the column is also symmetric. The material properties of concrete were entered using a concrete damage plasticity model that considers the nonlinear behavior of concrete in compression and tension. The material properties of reinforcing steel were entered considering the nonlinear portion of the stress–strain curve of the steel in tension. The parameters considered for concrete damage plasticity are shown in Table 2 corresponding to M25 concrete. Table 2 Element types adopted in the finite element model Dilation angle 

Eccentricity

Biaxial compression fb0/fc0

K C parameter

Viscosity parameter

36°

0.104

1.07

0.67

0.01

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The modulus of elasticity of concrete was adopted as per IS 456 (2000), that is, E = 5000sqrt (f ck ), where f ck = 25 MPa and the Poisson’s ratio considered was 0.27. The stress–strain data corresponding to Fe 415 steel was entered up to the fracture point and the modulus of elasticity and Poisson’s ratio for reinforcing steel that was considered were 200 GPa and 0.17, respectively. The reinforcement in the RC column and the RC jacket in the FE model is modeled as embedded. A cohesive interface property is assigned between the old concrete surface and the inner surface of the RC jacket. A static general type of analysis is adopted to apply the load and the analysis is carried out in Abaqus. A three-dimensional FEM showing the RC column modeled along with the RC jacket is shown in Fig. 1. Figure 2 shows only the reinforcement of the RC column and the RC jacket. The longitudinal reinforcement and lateral ties in the RC column and the RC jacket can be seen. The shear connectors are also seen embedded (100 mm) in the RC column in the FEM.

Fig. 1 Finite element model showing the RC column modeled along with the RC jacket

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Fig. 2 Reinforcement mesh of RC column (inner) and the RC jacket (outer)

3 Results and Discussions The results and discussion of the FE analysis of the retrofitted RC column that was carried out are presented in this section. The bond stress or shear stress developed on the surface of the RC column and on the inner surface of the RC jacket in the FEM has been shown in Figs. 3 and 4a, b, respectively. The maximum principal stress developed in the reinforcement present in the RC column, reinforcement present in the RC jacket and in the shear connectors are shown in Fig. 5. The axial stresses developed in the shear connectors are shown in Fig. 6. It can be observed from Fig. 3 that the maximum value of the bond stress or shear stress developed on the outer surface of the RC column in and around the loaded face of the RC column was about 0.8525 N/mm2 . A maximum value of bond stress or shear stress equal to 0.8525 N/mm2 is developed on the inner surface of the RC jacket near the loaded end of the RC jacket as can be seen in Fig. 4a, b, respectively.

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Fig. 3 Bond stress or shear stress developed on the surface of the RC column in the finite element model

It is also seen that along with the height of the RC column, the bond stress or shear stress developed in the FE model tends to have an average value of about 0.4 N/mm2 . It can be observed that the value of the bond stress or shear stress developed in the FE model (Average: 0.4 N/mm2 and maximum: 0.8525 N/mm2 ) and the value adopted for the design of the RC jacket (0.5 N/mm2 – 0.8 N/mm2 ), are in close correlation. It can be observed from Figs. 5 and 6 that the axial stresses that are developed in the shear connectors are much less than the yield strength of the shear connectors. It is inferred from this observation, that there is no yielding of the shear connectors which ensures there is an effective transfer of the load from the RC column to the RC jacket at the interface. However, if the shear connectors yield, dowel action would take place that may cause shearing off of the shear connectors or pullout of the shear connectors. From this study, it is learned that the results from the finite element model is comparable to the average value of the bond stress or shear stress developed at the interface of the RC column and the RC jacket which is actually adopted for the design purpose, by taking into consideration the actual design parameters of the retrofitted RC column such as the axial load, RC column dimensions, RC jacket dimensions, and reinforcement details into the analysis.

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Fig. 4 Bond stress or shear stress developed on the inner surface of the RC jacket in the finite element model

4 Conclusion • The efficacy of the RC jacket retrofit depends upon the magnitude of the interfacial bond stress or shear stress developed between the old concrete surface (damaged RC column) and the inner surface of the RC jacket. • For lower values of interfacial bond stress or shear stress developed between the old concrete surface and the RC jacket, the load transfer to the RC jacket from the damaged RC column becomes nominal causing distress and instability. • There is a higher possibility of the shear connectors yielding or getting sheared off or to get pulled out when the interfacial stresses developed between the old concrete surface and the inner surface of the RC jacket is low. • It is learned from the results of the finite element analysis that the magnitude of the axial stress developed in the shear connectors (seen in Fig. 6) is less than the yield stress value of the shear connectors. It is understood from this observation that the shear connectors remain intact and that there is an effective load transfer between the RC column and the RC jacket. • It is learned from the results of the finite element analysis that, the finite element model is able to closely predict the average value of the bond stress or shear

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Fig. 5 Maximum principal stress developed in the reinforcement present in the FE model of RC column, RC jacket and in the shear connectors

stress (0.5–0.8 N/mm2 ) developed at the interface of the RC column and the inner surface of the RC jacket which is adopted for the design purpose, by taking into consideration the actual design parameters of the retrofitted RC column such as the axial load, RC column dimensions, RC jacket dimensions, and reinforcement details into the FE analysis. • Therefore, before applying an RC jacket as a retrofit in site to any distressed RC member, one may perform a pre-analysis adopting finite element methods by considering the actual data as input in the FE model corresponding to the damaged RC column, to understand and know the magnitude and distribution of the bond stress is developed at the interface of the RC jacket and the old concrete for a particular design axial load acting on the RC column to assess the efficacy and safety of the retrofit.

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Fig. 6 Axial stress developed in all the reinforcement and shear connectors

References 1. Sołtysik B, Jankowski R (2015) Building damage due to structural pounding during earthquakes. J Phy Conf Ser 628(012040):1–11. https://doi.org/10.1088/1742-6596/628/1/012040 2. Karantoni FV, Bouckovalas G (1997) Description and analysis of building damage due to Pyrgos, greece earthquake. Soil Dyn Earthq Eng 16(2):141–150. https://doi.org/10.1016/ S0267-7261(96)00035-8 3. Schneider U (1988) Concrete at high temperatures—a general review. Fire Safety J 13(1):55– 68. https://doi.org/10.1016/0379-7112(88)90033-1 4. Cusatis G, Alnaggar M, Gardoni P, Ambrosia MD, Qu1 J (2015) Aging and deterioration of concrete structures. Learning from the past, assessing the present, and predicting the future: science or magic? CONCREEP-10 Conference, At Vienna, Austria. https://doi.org/10.1061/ 9780784479346.004 5. Wankhadea RL, Landage AB (2013) Non-destructive testing of concrete structures in Karad region. Procedia Eng 51:8–18. https://doi.org/10.1016/j.proeng.2013.01.005 6. IS13311 (1992) Non-destructive testing of concrete methods of test—Part1–Ultrasonic pulse velocity. Bureau of Indian standards 7. IS13311 (1992) Non-destructive testing of concrete methods of test—Part2–Rebound hammer. Bureau of Indian standards 8. Ghernouti Y, Li A, Rabehi B (2012) Effectiveness of repair on damaged concrete columns by using fiber-reinforced polymer composite and increasing concrete section. J Reinf Plastics Comp 31(23):1–12. https://doi.org/10.1177/0731684412458552

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9. Guoqiang L, Hedlund S, Pang S-S, Alaywan W, Eggers J, Abadie C (2003) Repair of damaged RC columns using fast curing FRP composites. Comp B Eng 34(3):261–271. https://doi.org/ 10.1016/S1359-8368(02)00101-4 10. Nameer A, Al-Zahid AA (2015) Behavior of reinforced concrete short rectangular columns strengthened by steel lattice framed jacket. In Oñate DRJ, Owen D, Peric, Chiumenti M (eds) XIII international conference on computational plasticity. Fundamentals and applications COMPLAS XIIIE 11. Elbakry H, Tarabia A (2016) Factors affecting bond strength of RC column jakets. Alexandria Eng J 55(1):57–67. https://doi.org/10.1016/j.aej.2016.01.014 12. Monir MMAA (2016) Behavior of fire-exposed RC frames before and after jacketing. PhD thesis. The university of Western Ontario. https://ir.lib.uwo.ca/etd 13. Campione G, Fossetti M, Giacchino C, Minafo G (2014) RC columns externally strengthened with RC jackets. Mat Struct Rilem 47:1715–1728. https://doi.org/10.1617/s11527-013-0146-x 14. Eduardo NBSJ, Fernando ABB (2008) Reinforced concrete jacketing—interface influence on cyclic loading response. ACI Struct J 105(4):1–7

Parametric Response Estimation Study on Cantilevered and Strutted Diaphragm Walls Anu James and Babu Kurian

Abstract Diaphragm walls are ideal solution for the productive utilisation of underground space to meet the modern-day demands of infrastructural development. The selection of appropriate wall and support configurations has a substantial impact on the economy, time and performance. Unsatisfactory implementation of such retaining systems during or after construction may cause heavy causalities. The practical significance of excavation induced deformations is large due to its potential damage to adjacent structures. Hence, reliable estimates of excavation related responses are vital for construction and implementation of diaphragm wall projects. Numerical studies performed to understand the effects of factors such as ground characteristics, excavation geometry and support criteria in the response of diaphragm walls are presented here. Detailed parametric analysis is conducted to comprehend the combined effects of these factors on both cantilevered and strutted diaphragm walls. Walls embedded in cohesive and non-cohesive backfills with varying groundwater locations are considered. Properties of struts and their influence on excavation geometries for various ground characteristics are assessed. Studies are performed to obtain the most effective combinations of excavation and embedded depths for cantilevered diaphragm walls. Numerical analysis was conducted using finite element software Plaxis 2D and values of lateral deflections, normal forces, bending moments, shear forces and axial strut forces are computed. Comparative charts are drawn to demonstrate the variations of wall responses with different combinations of influencing factors. Ideal wall and support configurations for any given ground conditions and excavation geometry can be perceived from the charts enabling fast and cost-effective implementation of projects.

A. James (B) Department of Civil Engineering (Research Scholar), Mar Athanasius College of Engineering, Kothamangalam, Kerala, India e-mail: [email protected] B. Kurian Department of Civil Engineering, Muthoot Institute of Technology and Science, Ernakulam, Kerala, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_44

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Keywords Deep excavation · Diaphragm wall · Parametric analysis · Embedded depth · Wall response

1 Introduction Infrastructural developments call for large-scale excavations within close proximity of high-rise buildings or in very confined spaces. Structures like underground transports, mass rapid transit systems, water pipelines, tunnels, etc., demand constructions deep below the ground level. One among the innovative solutions is the diaphragm wall support system which provides more rigidity and structural stability. The major concern regarding underground constructions involving deep excavation is its impact on ground stability and adjacent structures. Excavation systems should be designed to satisfy safety, economy and serviceability conditions. This necessitates reliable prediction of wall and ground responses to effectively formulate design procedures. The effects of the width of excavation on soil wall movements were studied by Bos and Som [2] along with the impact of prestressed braced supports for excavations. Finite element studies are widely employed for the analysis of deep excavations and diaphragm wall systems [1, 7, 8, 11]. Parametric studies performed on diaphragm walls provide better insights into the effects of influencing factors [4–6, 9, 12]. Lewandowska and Czajewska [10] analysed cantilevered, strutted and anchored diaphragm walls according to specifications in Eurocode and Polish codes. In order to effectively formulate the geometrical requirements of wall and support systems, it is necessary to have thorough knowledge regarding the effects of all possible combinations of field properties and support characteristics. This paper presents the results of numerical studies conducted to evaluate the combined effects of different parameters including ground characteristics, geometric properties and groundwater levels. Groundwater level (g.w.l) is a major factor contributing to lateral pressures and will significantly influence the design requirements of lateral supports. The groundwater level is considered as a varying parameter and all the analysis cases considered herein are performed for four assumed groundwater locations so that the response prediction studies are more practical. Results of deformations and forces developed on diaphragm walls and struts under different field conditions and support characteristics are illustrated in this study. The analysis results are presented in terms of design charts so that optimal combinations of influencing parameters can be perceived at a glance.

Parametric Response Estimation Study on Cantilevered …

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2 Methodology 2.1 Numerical Modelling Numerical response estimation studies were conducted to determine the degree of effects of different influencing parameters of a diaphragm wall system. The primary characteristics affecting the wall and ground responses are types of wall support and ground conditions. The analysis was carried using finite element simulations with Plaxis. Diaphragm walls are modelled as elastic plate element, defined by parameters such as normal and bending stiffness, Poisson’s ratio, etc. Soil masses were simulated as elastic–plastic material under Mohr–Coulomb failure criterion as it provides sufficient accuracy for geotechnical and foundation considerations such as deformation predictions [13–15]. For the finite element simulation, the field clusters are divided as 15 noded triangular elements for its ability to accurately calculate failure loads and stresses. Struts which are normally structural steel elements, were modelled using fixed end anchor element facility in Plaxis directory. The fixed end anchor element is a single-node elastic spring element with one end fixed and is defined by equivalent length and direction of installation. The symbols used in the analysis are denoted in Figs. 1 and 2. Material properties and ground conditions were varied in combination with four different groundwater locations for the parametric analysis. The g.w.l locations were assumed as one at every one-third of total excavation depth and dry ground state (WL1 , WL2 , WL3 and WLD ). The properties of soil profiles considered are summarised in Fig. 1 Symbols used

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Fig. 2 Cantilevered and strutted walls

Table 1. The soil profiles are so selected to consider effects for different ranges of cohesive and non-cohesive fields. Homogenous field conditions are chosen since the study aims to perceive a general outline regarding the wall behaviours for any field conditions. The actual field conditions may comprise of nonhomogeneous ground with multiple layers of varying soil properties. Response predictions performed on a particular field data cannot hold good for another location involving different soil layers at different depths and with varying soil characteristics. The current selection of field properties, hence, will assist in proper understandings of wall behaviours and variations considering the general nature of the ground. Diaphragm walls embedded in these ground conditions were in turn analysed for the effects on influencing parameters like ground conditions, excavation geometry, etc. The material properties of the wall were fixed as Modulus of elasticity, Ew = 30 kN/mm2 , Poisson’s Ratio = 0.19 and Thickness = 800 mm. A total number of 368 cases were analysed for cantilevered walls and 288 for strutted walls. Table 1 Soil properties considered for parametric analysis Support criteria

Soil profile

Cohesion, C (kN/m2 )

Angle of internal friction, φ (degrees)

Modulus of elasticity, E (kN/mm2 )

Cantilever wall

C1

10

27

30

C2

25

28

40

C3

0.3

35

70

Strutted wall

C4

0.3

40

80

S1

10

27

30

S2

25

28

40

S3

0.3

40

80

Parametric Response Estimation Study on Cantilevered …

583

Diaphragm walls may also be subjected to normal forces caused by self-weight, skin friction and possible heavy loads from the superstructures based on the purpose of the wall in consideration. Hence, combined effects of both bending and axial forces should be considered for the structural design of reinforced concrete diaphragm walls. Maximum values of lateral deflection, bending moments, normal forces, shear forces and strut forces are computed from analysis.

3 Results and Discussions Cantilevered and strutted diaphragm walls were analysed to identify the combined effects of different influencing factors. The results and their variations in lateral deflections, bending moments, normal forces, shear forces and strut forces are detailed here.

3.1 Cantilevered Diaphragm Walls Cantilevered diaphragm walls can be constructed only for comparatively shorter depths. These are preferred when structural embedded walls are to be built in densely populated areas. A reliable estimate regarding the effects influencing factors of cantilevered diaphragm walls will also assist in optimally adjusting the unsupported depths of braced or tie-back walls. This will ensure the minimum number of lateral support for stability, resulting in economic and safe construction. As diaphragm wall construction and excavations are expensive, these results will help in optimally adjusting the wall and support geometries in the most significant manner. For a laterally unsupported diaphragm wall, the load restraining capacity should be ensured by the depth of the wall below formation level. This requirement varies considerably with the ground characteristics. Variations in forces on the diaphragm wall system for different excavation depths (Dx ) and embedded depths (Dm ) are presented herein. The analysis was performed for four different ground conditions including two cohesive and two non-cohesive backfills and four groundwater locations.

3.1.1

Effects of Embedded Depth

Study of varying embedded depths corresponding to a specific excavation depth helps to estimate ideal values for different ground conditions. Diaphragm walls installed in cohesive and non-cohesive soils and different groundwater locations were analysed for Dx /Dm ratios of 1.5, 1.2, 1, 0.92 and 0.86. Lateral displacement pattern of a cantilevered wall is given in Fig. 3, Fig. 4 shows the variations in bending moment distribution for different soil conditions under two

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Fig. 3 Horizontal displacement of cantilevered wall for Dx /Dm ratio 0.92

extreme cases of groundwater levels and Fig. 5 shows the bending moment distributions with varying embedment depths. It can be observed that, for field conditions where groundwater level is below the depth of wall, the peak moment values does not vary significantly. Whereas, as the level is higher, variations are more prominent. The differences in variations underline the importance of accurate response estimations. Variations in axial force with different Dx /Dm ratios of the wall are shown in Fig. 6. The variations are not much pronounced for conditions of varying depths below formation levels. A comparative chart is given in Fig. 7 to estimate axial forces for different soil types. The soil profile C2 can retain the active loads effectively for all assumed ground conditions, while the retaining system fails for C1 and C4 when the groundwater level is at WL1 . For C3, the system is stable only for dry ground conditions at a Dx /Dm ratio of 1.5. For a ratio of 1.2, the system fails for WL2 and, for ratios of 1 and 0.92, failure occurs only at a g.w.l of WL1 . When Dx /Dm ratio varies from 1.5 to 0.86, the lateral wall deflections (for profile C1) got reduced to 39.39, 43.76 and 55.04%, respectively, for groundwater levels WL2 , WL3 and WLD . These values are 86.89, 85.69 and 88.23% for C2. Even though

Parametric Response Estimation Study on Cantilevered … Fig. 4 Bending moment distribution for different soil profiles

Fig. 5 Variation in bending moment distribution for varying depths

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160

Normal force, kN

158

1.2

156

1

154

0.92

152

0.86

150 148 146 144

C1

C3 Soil profile

Fig. 6 Normal forces developed for different Dx /Dm ratios

Normal force, kN

Fig. 7 Axial forces under different soil profiles 120

140

160

180

Soil profile

C4

C3 WLD C2

WL4

C1

there are no considerable variations with different values of Dm for profile C2, this soil profile shows a considerably lesser deflection relative to C1. The variations in lateral defections are presented in Fig. 8. The values of shear forces developed on the wall are given in Table 2.

C1

587

C2

C3

0.86

0.92

1

1.2

1.5

0.86

1

WLD

0.92

1.5

1.2

WL3

0.86

1

WL2

0.92

1.5

0.86

1

0.92

1.2

1.2

WL1

70 60 50 40 30 20 10 0 1.5

Deflection,mm

Parametric Response Estimation Study on Cantilevered …

C4

Dx/Dm

Fig. 8 Variations in lateral deflection

Table 2 Variations for shear force g.w.l

Dx /Dm 1.5

1.2

1

0.92

0.86

C1

1.5

1.2

1

0.92

0.86

C3

W L1

–

82.8

83.8

85.1

85.4

–

W L2

68.6

64.9

66.2

66.3

64.9

W L3

58.1

63.8

64.2

63.7

62.0

W LD

61.3

62.1

61.4

60.8

59.8

C2

–

–

–

178.2

–

–

130.9

117.2

108.9

–

106.7

85.4

85.8

85.7

132.1

98.7

85.2

85.5

84.7

C4

W L1

56.5

60.7

62.0

62.1

61.6

–

142.3

114.3

118.2

120.3

W L2

54.5

58.3

59.0

58.5

57.2

121.0

88.5

77.0

78.2

78.3

W L3

56.4

61.0

62.8

62.9

62.3

83.1

67.3

67.1

66.1

65.0

W LD

59.0

63.3

65.1

65.2

64.7

79.0

66.3

64.7

64.1

63.7

3.1.2

Effects of Varying Excavation Depth on Wall Behaviour

Six different retaining heights were analysed for three different embedded depths (4, 5 and 6 m). Each of the above combinations was analysed for four different soil profiles and groundwater levels. For some cases, the assumed embedded depth is found not sufficient for the particular excavation depth and results in failure of the entire system. In some conditions, failure occurs for a higher g.w.l with the same Dx /Dm ratio. All stable combinations of Dx and Dm for all soil profiles and groundwater locations are displayed in Fig. 9. This ensures an accurate estimation of initial dimensions that can be chosen for an unsupported wall under any ground conditions. Fig. 10 gives variations in bending moments for an embedded depth of 6m. The maximum values of shear forces computed from the analysis are listed in Table 3.

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Fig. 9 Stable combinations of excavation and embedded depths

6

WL2

6.5

WL3

WLD

7

7.5

C4

C3

C1

C2

C3 8

C4

C2

C1

C4

C2

C3

C1

C4

C3

C1

C2

C4

C2

C3

C1

C4

C3

C2

C1

Bending moment, kNm

WL1 800 700 600 500 400 300 200 100 0

8.5

Soil profile

Fig. 10 Variation of bending moments with Dm = 6 m

3.2 Strutted Diaphragm Wall A large number of literatures are available regarding factors influencing braced excavations. Nevertheless, studies describing the combined influence of these parameters are required for the accurate prediction of deformations and forces. Effects of varied excavation width, strut stiffness, horizontal strut spacing, soil properties and groundwater levels were compared to acquire optimum combinations. Characteristics of

8

7.5

7

6.5

6

Dx (m)

–

–

120.4

W L2

W L3

W LD

105.5

W LD

–

119.4

W L3

W L1

–

89.3

W LD

W L2

87.0

W L3

–

113.1

W L1

–

73.3

W LD

W L2

76.5

W L1

81.8

W L3

61.4

W LD

W L2

64.2

W L3

126.6

66.2

W L2

W L1

83.8

W L1

76.5

68.4

70.1

118.6

75.3

68.5

67.9

93.1

72.9

67.4

65.5

75.8

69.8

65.9

62.9

68.7

65.1

62.8

59.0

62.0

202.0

–

–

–

169.3

–

–

–

126.5

–

–

–

100.0

139.9

–

–

85.2

85.4

130.9

–

122.7

189.1

254.8

–

110.7

147.6

195.6

–

87.4

105.9

143.4

–

77.1

77.7

102.7

165.7

64.7

67.1

77.0

114.3

151.0

–

–

–

110.8

–

–

–

88.0

106.3

–

–

75.9

71.7

84.6

–

62.1

63.8

64.9

82.8

Dm = 5 m C4

C1

C3

C1

C2

Dm = 6 m

Table 3 Variation of shear force (kN)

76.2

69.5

70.3

104.4

74.0

68.0

67.7

82.3

71.2

66.3

65.1

71.8

67.8

64.3

62.3

66.2

63.3

61.0

58.3

60.7

C2

–

–

–

–

–

–

–

–

167.7

–

–

–

126.0

–

–

–

109.7

122.6

–

–

C3

171.4

–

–

–

125.2

176.8

–

–

100.1

135.9

178.6

–

81.1

104.3

127.2

–

66.3

67.3

88.5

142.3

C4

Dm = 4 m

–

–

–

–

149.4

–

–

–

99.2

–

–

–

72.0

88.4

–

–

61.3

58.1

68.6

–

C1

70.5

64.8

66.0

92.1

68.6

63.5

63.4

71.9

66.1

62.2

61.6

65.4

62.9

59.9

58.7

61.2

59.0

56.4

54.5

56.5

C2

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

–

131.3

–

–

–

104.2

137.3

–

–

79.0

83.1

121.0

–

C4

(continued)

132.1

–

–

–

C3

Parametric Response Estimation Study on Cantilevered … 589

8.5

Dx (m)

–

–

–

162.6

W L1

W L2

W L3

W LD

75.9

67.1

79.6

154.4

–

–

–

–

162.6

–

–

–

–

–

–

–

Dm = 5 m C4

C1

C3

C1

C2

Dm = 6 m

Table 3 (continued)

77.4

70.2

78.7

132.6

C2

–

–

–

–

C3

205.4

–

–

–

C4

Dm = 4 m

–

–

–

–

C1

71.7

68.2

79.0

133.8

C2

–

–

–

–

C3

–

–

–

–

C4

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excavation geometry and soil properties were analysed for four different groundwater locations. These combinations make response estimation more effective and significant.

3.2.1

Analysis with Constant Strut Spacing Along the Longitudinal Direction

Three backfill soil conditions are considered in combination with four groundwater level locations. The spacing of braced supports along the wall is fixed at 5 m. Excavations of width 15, 20 and 30 m are assumed to be supported by struts of stiffness 1 × 105 , 5 × 105 , 25 × 105 and 125 × 105 kN/m/m [4]. Effects of these parameters on deflection, bending moment, normal force and axial strut forces are studied. Variations in wall behaviours with varied strut stiffness for any particular excavation width were found to be marginal. Significant deviations were noticeable with varied excavation widths and groundwater levels. Figures 11, 12 and 13 show wall behaviours for different soil properties for a 20 m wide excavation with strut stiffness 5 × 105 kN/m. For soil profile S1 with g.w.l at WL1 , the lateral deflection of wall increased by 11.55% when excavation width is increased to 20 m from 15 m. The corresponding increase in axial strut force is 10.78%. When the width of excavation is further increased to 30 m, the system failed for the same g.w.l. For this maximum width considered, excavation is stable only for a higher support stiffness value of 125 × 105 kN/m. With g.w.l at WL2 , the percentage increase of deflection when excavation width is increased to 20 and 30 m are 19.31 and 71.18%, respectively. When g.w.l drops to WL2 , WL3 and WLD , axial strut force developed shows a reduction to 70.35, 62.19 and 51.19%, respectively. For bending moments, these variations were 68.69, 350

Deflection, mm

300 250 200 S1 150

S2 S3

100 50 0 WL1

WL2

WL3

Ground water level Fig. 11 Variations in lateral deflection

WLD

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A. James and B. Kurian 2500

Bending moment, kNm

2000

1500 S1 1000

S2 S3

500

0 WL1

WL2

WL3

WLD

Ground water level Fig. 12 Variations in bending moments

600

Strut force, kN

500 400 S1

300

S2 200

S3

100 0

WL1

WL2

WL3

WLD

Fig. 13 Variations in axial strut force

58.87 and 47.19%. The variations in these values are insignificant with variations in strut stiffness but prominent with varied widths of excavation. The variations are displayed in Figs. 14 and 15. For S2 with g.w.l at WL1 and support stiffness 1 x 105 kN/m/m, the variation in lateral deflection is 21.71 and 72.24% when the width is incremented to 20 and 30 m, respectively. The difference in lateral deflection for similar conditions for profile S3 is 29.94 and 42.61%. The maximum values of lateral deflections and strut forces are given in Tables 4 and 5. The distribution of axial force developed on wall sections are shown in Fig. 16.

Deflection, mm

Parametric Response Estimation Study on Cantilevered … WL1

300

593

WL2

WL3

WLD

250 200 150 100 50 0 15

20

30

15

20

S1

30

15

S2

20

30

S3

Excavation width (m)

Fig. 14 Variations in maximum lateral deflection for strut stiffness 1 × 105 kN/m WL1

Strut force, kN

500

WL2

WL3

WLD

400 300 200 100 0 15

20

30 S1

15

20

30

15

S2

20

30

S3

Excavation width (m)

Fig. 15 Variations in axial strut force developed with stiffness 125 × 105 kN/m

3.2.2

Analysis with Different Strut Spacing Along the Longitudinal Direction

Numerical studies were conducted to comprehend the effects of longitudinal spacing of struts. Three different spacings were assumed (L0, L1, L2) starting with 5 m (L0). The study was performed for two soil profiles (S1 and S2) and three excavation widths. Struts with stiffness values of 1 × 105 kN/m and 5 × 105 kN/m were assumed. All four groundwater-level conditions were assessed for all the combination of abovementioned parameters. The variations in wall responses are demonstrated in the Figs. 17 and 18. Maximum values of bending moments computed are listed in Table 6.

3.3 Stability Analysis for Excavations The c–phi reduction method in Plaxis is used to perform a stability analysis of excavations. The output of stability analysis is the safety factor for excavations. In the c–phi reduction method, input shear strength parameters are gradually reduced

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Table 4 Variations of maximum lateral deflection Strut stiffness (×10 5 kN/m)

Soil profile

S1

Excavation width (m)

15

S2

S3

20

30

15

20

30

15

20

30

u × 102 (mm) 1

5

25

125

W L1

2.48

2.76

–

0.74

0.90

1.28

1.06

1.33

1.86

W L2

1.63

1.95

2.79

0.48

0.58

0.80

0.81

0.92

1.36

W L3

1.45

1.75

2.52

0.46

0.54

0.74

0.69

0.86

–

W LD

1.27

1.53

2.13

0.46

0.52

0.70

–

0.82

–

W L1

2.47

2.92

–

0.74

0.90

1.27

1.05

1.32

1.86

W L2

1.63

1.95

2.80

0.47

0.58

0.80

0.74

0.91

1.36

W L3

1.44

1.74

2.51

0.46

0.54

0.74

0.68

0.85

1.22

W LD

1.27

1.53

2.12

0.46

0.52

0.70

0.66

0.82

1.13

W L1

2.36

2.77

–

0.74

0.89

1.26

1.04

1.32

–

W L2

1.63

1.93

2.79

0.47

0.57

0.79

0.74

0.90

–

W L3

1.44

1.74

2.51

0.46

0.53

0.73

0.63

0.78

1.14

W LD

1.27

1.52

2.12

0.45

0.51

0.69

0.66

0.81

1.12

W L1

2.41

3.70

–

0.73

0.89

1.25

0.73

0.89

1.25

W L2

1.63

1.93

2.78

0.47

0.57

0.79

0.47

0.57

0.79

W L3

1.44

1.73

2.51

0.46

0.46

0.72

0.46

0.46

0.72

W LD

1.27

1.52

2.12

0.45

0.51

0.69

0.45

0.51

0.69

just to maintain equilibrium. This reduction is regulated by total multiplier factor which is increased step-by-step until failure. A safety factor is given as the multiplier at failure. The safety coefficients computed for cantilevered walls are plotted in Figs. 19 and 20 and those for strutted walls are listed in Table 7. A comparison of the stability of every excavation system can be perceived from the charts.

4 Conclusions In the modern-day world, there is a greater demand for the development and expansion of existing infrastructures. These demands can be effectively met by diaphragm wall retaining systems if the construction domains are able for fast and cost-effective implementation of wall installations and excavations. A detailed response prediction analysis is carried out to study the combined effects of all influencing parameters of diaphragm walls. The designs will be satisfactory from all aspects if the structural elements are found safe and stable. Following are the conclusions drawn from the analysis.

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Table 5 Variations in strut force Strut stiffness (×10 5 kN/m)

Soil profile

S1

Excavation width (m)

15

20

30

S2 15

20

30

S3 15

20

30

5.05

4.56

–

1.56

1.51

1.43

2.43

2.29

2.12

F × 102 (kN) 1

W L1

5

25

Normal force on wall, kN

125

W L2

3.56

3.37

3.24

0.90

0.91

0.86

1.80

1.47

1.49

W L3

3.14

2.92

2.85

0.81

0.79

0.75

1.50

1.38

–

W LD

2.58

2.39

2.28

0.73

0.70

0.67

–

1.28

–

W L1

5.04

4.82

–

1.56

1.51

1.43

2.41

2.29

2.13

W L2

3.54

3.37

3.26

0.90

0.92

0.86

1.67

1.52

1.49

W L3

3.14

2.92

2.85

0.81

0.80

0.75

1.50

1.38

1.30 1.17

W LD

2.58

2.39

2.28

0.73

0.70

0.68

1.38

1.28

W L1

4.81

4.57

–

1.56

1.51

1.43

2.41

2.30

–

W L2

3.56

3.36

3.26

0.91

0.92

0.86

1.67

1.51

–

W L3

3.13

2.92

2.85

0.81

0.80

0.76

1.38

1.28

1.22

W LD

2.58

2.39

2.29

0.73

0.70

0.68

1.38

1.28

1.17

W L1

4.90

–

4.24

1.55

1.50

1.43

2.40

2.29

–

W L2

3.56

3.36

3.25

0.91

0.92

0.86

1.68

1.51

1.49

W L3

3.13

2.91

2.86

0.81

0.80

0.76

1.39

1.28

1.22

W LD

2.59

2.39

2.29

0.74

0.70

0.69

1.37

1.28

1.17

400 350 300 250 200

S1

150

S2

100

S3

50 0 20

15

Strut sttifness 25kN/m

20

Strut sttifness 5kN/m

Excavation width, m Fig. 16 Variation in normal forces

5

596

A. James and B. Kurian WL1

WL2

WL3

WLD

Deflection, mm

250 200 150 100 50 0 15

20

30

15

20

30

L0

15

20

L1

30

L2

Excavation width, m

Fig. 17 Variation of lateral deflection for profile S2 200

Strut force, kN

Fig. 18 Variation of axial strut force for profile S2

150

WL1 WL2 WL3

100

WLD 50

15

20

30

Excavation width, m Table 6 Variation in bending moments (M × 103 kNm) for soil profile S1 Strut spacing (m)

L0

Excavation width (m)

15

L1 20

30

15

L2 20

30

15

20

30

Strut stiffness 1 × 105 kN/m W L1

2.14

2.24

–

–

–

–

–

–

–

W L2

1.47

1.54

1.66

1.58

1.66

1.66

1.66

1.68

1.64

W L3

1.26

1.29

1.34

1.31

1.34

1.36

1.34

1.36

1.3

W LD

1.01

1.0

0.961

1.0

0.961

0.953

0.961

0.965

0.923

Strut stiffness 5 × 105 kN/m W L1

2.15

2.29

–

–

2.25

2.4

–

2.24

–

W L2

1.46

1.54

1.67

1.46

1.53

1.66

1.46

1.54

1.65

W L3

1.26

1.29

1.34

1.26

1.29

1.33

1.26

1.29

1.33

W LD

1.01

1.01

0.959

1.01

0.958

0.960

1.01

0.959

0.963

597

2.4 2.2 2 1.8 1.6 1.4 1.2 1

WL1 WL2

C1

C2

C3

WLD

0.92

1.2

0.86

1

1.5

0.92

1.2

0.86

1

WL3 1.5

Safety factor

Parametric Response Estimation Study on Cantilevered …

C4

Dx/Dm

Fig. 20 Safety factor for cantilevered wall with constant embedded depth (Profile C2)

Safety factor

Fig. 19 Safety factor for cantilevered wall with constant excavation depth

2.2 2 1.8 1.6 1.4 1.2 1

WL1 WL2 WL3 WLD 6

7 4

8

6

7

8

5

6

7

8

6

Dx, m Dm, m

1. Wall behaviours studied under different field conditions and support characteristics emphasise the necessities of accurate response prediction models. It is found ideal to include the location of groundwater level in estimation charts, as it comprises a major parameter contributing to lateral pressures and excavation procedures. 2. Studies on cantilevered diaphragm walls with two pairs of cohesive and noncohesive soil properties will give a better idea about the geometric requirements of the wall system and stable unsupported heights. This will assist in deriving cost-effective layouts for supported excavations such as tieback walls and braced walls. 3. Variations are less pronounced for soil profile representing stiff clays for all groundwater locations. Medium sands with higher groundwater levels and lower embedded depths resulted in excavation failures demanding requirements of extra lateral support. 4. For strutted walls, the variations in design values are not much pronounced with variations in support stiffness, whereas it is more significant with variations in

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groundwater levels. Bending moments and strut forces should be checked for the stability of wall and struts respectively. 5. Lateral deflection gets reduced to around 60% when excavation width is halved and the variation for axial strut force is about 90%. When the longitudinal spacing of braced support is doubled, lateral deflection varies to around 55% for S1 profile and about 60% for S2. 6. From the stability analysis, initial dimensions and properties can be easily chosen so that the deflections and forces are within permissible limits and will not cause excessive deformations, failure of the wall and adjacent structures. Table 7 Safety coefficients calculated for braced walls Excavation depth

W L1

W L2

W L3

W LD

S1 15

1.103

1.227

1.324

1.635

20

1.107

1.223

1.322

1.633

30

–

1.229

1.322

1.629

15

1.103

1.229

1.323

1.635

20

1.103

1.224

1.321

1.630

30

–

1.229

1.321

1.632

15

1.109

1.227

1.321

1.634

20

1.106

1.226

1.321

1.634

30

–

1.229

1.321

1.633

15

1.106

1.228

1.325

1.636

20

–

1.223

1.321

1.629

30

1.109

1.229

1.321

1.632

15

1.436

1.565

1.661

1.956

20

1.436

1.568

1.663

1.956

30

1.438

1.570

1.666

1.971

15

1.435

1.566

1.661

1.956

20

1.436

1.567

1.663

1.950

30

1.437

1.569

1.664

1.966

15

1.435

1.564

1.662

1.952

20

1.436

1.568

1.663

1.964

30

1.437

1.569

1.666

1.968

15

1.434

1.565

1.661

1.955

20

1.436

1.567

1.663

1.954

30

1.437

1.567

1.666

1.969

S2

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7. The results presented in terms of comparison charts and safety factors can assist a designer to choose optimum design parameters for any proposed diaphragm wall project.

References 1. Abdallah M (2017) Numerical modelling of various support systems to stabilize deep excavations. Int J Geol Environ Eng 11(7):609–614 2. Bose SK, Som NN (1998) Parametric study of a braced cut by finite element method. Comput Geotechics 22(2):91–107. https://doi.org/10.1016/S0266-352X(97)00033-5 3. Chowdhury SS, Deb K, Sengupta A (2013) Estimation of design parameters for braced excavation: numerical study. Int J Geomech 13(3):234–247. https://doi.org/10.1061/(ASCE)GM. 1943-5622.0000207 4. Chowdhury SS, Deb K, Sengupta A (2017) Estimation of design parameters for braced excavation in clays. Geotech Geol Eng 35(2):857–870 5. Conti R, Viggiani GMB (2013) A new limit equilibrium method for the pseudostatic design of embedded cantilevered retaining walls. Soil Dyn Earthq Eng 50:143–150. https://doi.org/10. 1016/j.soildyn.2013.03.008 6. Goh ATC, Zhang F, Zhang W, Chew OYS (2017) Assessment of strut forces for braced excavation in clays from numerical analysis and field measurements. Comput Geotechics 86:141–149. https://doi.org/10.1016/j.compgeo.2017.01.012 7. Hashash YMA, Whittle AJ (1996) Ground movement prediction for deep excavations in soft clay. J Geotech Eng 122(6):474–486. https://doi.org/10.1061/(ASCE)0733-9410(1996)122: 6(474) 8. Hsiung BCB, Yang KH, Aila W, Hung C (2016) Three-dimensional effects of a deep excavation on wall deflections in loose to medium dense sands. Comput Geotechics 80:138–151. https:// doi.org/10.1016/j.compgeo.2016.07.001 9. Lewandowska AS, Czajewska MM (2007) Design of diaphragm walls according to EN 1997– 1:2004 eurocode 7. In: Proceedings of the 14th European conference on soil mechanics and geotechnical engineering, Madrid, pp 291–296 10. Lim A, Ou CY, Hsieh PG (2010) Evaluation of clay constitutive models for analysis of deep excavation under undrained conditions. J GeoEng 5(1):9–20 11. Phienwej N (2008) Ground movement in station excavations of bangkok first MRT. In Proceedings of the 6th international symposium on tunnelling for urban development (IS-Shanghai 2008), Shanghai, China, pp 181–186 12. Yajnheswaran B, Akshay PR, Rajasekaran C, Rao S (2015) Effect of stiffness on performance of diaphragm wall. Procedia Eng 116:343–349. https://doi.org/10.1016/j.proeng.2015.08.305 13. Yong CC (2016) Deformation analysis of deep excavation in clay, Ph.D Thesis, Griffith University 14. Zhang W, Goh ATC, Xuan F (2015) A simple prediction model for wall deflection caused by braced excavation in clays. Comput Geotechics 63:67–72. https://doi.org/10.1016/j.compgeo. 2014.09.001

Numerical Studies on Impact Response of Reinforced Concrete Beams Using FE Software Anand Raj, B. Kiran Kumar Reddy, Praveen Nagarajan, and A. P. Shashikala

Abstract Recently, the demand for structural safety subjected to blast and impact loading has been increased. For this reason, various studies for predicting the behaviour of structures under blast and impact loading have been actively performed. Finite Element Analysis (FEA) represents a numerical method, which provides a solution to problems that would otherwise be difficult to obtain without incurring significant expenses. In the present study, the impact energy absorbed by the reinforced concrete beam under point impact load up to the formation of initial cracks and their crack pattern, under falling-weight impact was studied numerically using FE software ANSYS. Simply supported rectangular reinforced concrete beams of 100 × 100 mm in cross-section and 1200 mm overall length was used to compare the impact response of RCC beams of different reinforcement percentages (0, 0.56, 1, 1.57 and 2.26%) using FE software to assess the effect of reinforcement on the impact behaviour of reinforced concrete beams. The impact energy absorbed by the beams were increased with an increase in the percentage of reinforcement up to a certain extent. Afterwards, it decreased due to an increase in the brittleness of the beam after crossing the over reinforced limits. Keywords RCC beams · Impact load · Initial crack · Crack pattern · Impact energy · Finite element method

A. Raj (B) · B. K. K. Reddy · P. Nagarajan · A. P. Shashikala National Institute of Technology Calicut, Kozhikode, Kerala, India e-mail: [email protected] B. K. K. Reddy e-mail: [email protected] P. Nagarajan e-mail: [email protected] A. P. Shashikala e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_45

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1 Introduction The blast or impact response is the most critical to evaluate when a reinforced concrete beam is subjected to a blast or impact load. Large forces are generated within a short period of time, which leads to the splitting of the concrete in the blast area or crushing of concrete in the impact region [1]. Thus, ductile materials are required for the design of structural elements subjected to blast or impact loads. The present study aims to evaluate the behaviour of a reinforced concrete beam subjected to impact loading using finite element methods. The beams were modelled in ANSYS, and explicit dynamics analysis was carried out to find out impact energy. The impact energy and the crack pattern were find out by trial and error method till the first crack appears [2].

2 Finite Element Analysis Finite element analysis provides a tool to simulate the structural components with real-life boundary conditions and loading patterns and to obtain approximate solutions to a variety of structural problems because of its diversity and flexibility [3, 4]. ANSYS is an advanced finite element analysis and design software that can be used for structural engineering problems. In the present analysis, the explicit dynamic analysis had been adopted. The loads and constraints for which the specimen needs to be solved were defined. The impact load had been assigned by assigning some velocity to the impactor. The trial and error method was done to evaluate the velocity at which the first crack was formed and then the impact energy and the crack pattern was found out.

3 Specimen Details The beams were designed according to Indian standard codes and the impact energy absorbed by the beams was determined. The design and detailing of the reinforcement of all beams were done according to IS 456:2000 and SP-34. The cross-sectional dimensions of the beams were 100 mm × 100 mm. The span of the beams was 1200 mm. HYSD (FE 500) bars of diameter 6, 8, 10 and 12 mm were provided as the longitudinal reinforcement at beam top and bottom. HYSD bars of 6 mm diameter were provided as stirrups in beams. The spacing of stirrups was provided based on calculations to satisfy minimum spacing criteria. The reinforcement detailing of various beams are shown in Table 1 and Fig. 1.

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Table 1 Details of the beams considered Beam

Top reinforcement

Bottom reinforcement

Stirrups

% of tension reinforcement

Beam 1

–

–

–

0

Beam 2

2 no’s 6 mm

2 no’s 6 mm

6 mm @75 mmc/c

0.56 (under reinforced)

Beam 3

2 no’s 6 mm

2 no’s 8 mm

6 mm @75 mmc/c

1.00 (under reinforced)

Beam 3

2 no’s 6 mm

2 no’s 10 mm

6 mm @75 mmc/c

1.57 (over reinforced)

Beam 4

2 no’s 6 mm

2 no’s 12 mm

6 mm @75 mmc/c

2.26 (over reinforced)

Fig. 1 Auto CAD model of beam

4 Finite Element Modelling 4.1 Element Types Concrete: Concrete of grade M35 was assigned to the beam. Reinforcement: In beams, main reinforcement bars of 6, 8, 10 or 12 mm diameter and 2-legged stirrups of 6 mm diameter were adopted. Supports: Supports were made of structural steel and were of 100 × 100 × 50 mm. These supports were fixed at the bottom and kept at a distance of 50 mm from the ends. Impactor: Impactor was made up of structural steel with 100 mm diameter and 100 mm height. The weight of the hitter was 6.16 kg.

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Fig. 2 ANSYS model of beam

4.2 Beam Modelling and Meshing The designing and modelling of the beams were carried out in the geometry design modeller. The material properties were defined in the engineering data. Then the analysis was carried out in the model interface. Assignment of material properties and analysis setting parameters were provided in the model interface. Mesh size of 20 mm was provided after carrying out convergence studies. After meshing, initial velocity was assigned to the impactor along with the boundary conditions. Model and meshing of the beam are shown in Figs. 2 and 3.

4.3 Boundary Conditions and Load Application Displacement boundary conditions have to be provided in order to simulate the reallife support conditions. The bottom of the supports was restrained. The load applied was at the top of the beam in the centre. The velocity of the impactor was assigned in the downward direction, as shown in Fig. 4.

4.4 Analysis Type Explicit dynamic analysis of the beam model was carried out. The ANSYS program carries out the analysis and checks for the convergence of the solution. In solution controls, the analysis options were given as total deflection, internal energy, kinematic energy and the total energy. After running the analysis for a particular velocity, it was

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Fig. 3 Model after meshing

Fig. 4 Velocity of impactor

verified whether a crack was formed at the bottom of the beam. Similarly, velocity was incremented to find out velocity at which the first cracks appear. This velocity was used to find out the impact of energy.

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5 Results 5.1 Impact Energy The impact energy absorbed by the different specimens were found out. These results are shown in Table 2. It was observed that the impact energy increased with an increase in the percentage of reinforcement up to some extent, but decreases after that. The over-reinforced Beam 4 performed better than other beams in the study. The impact energy for Beam 2 was 70% more than that of Beam 1. The impact energy of Beam 4 was 1056% more than Beam 1 (Fig. 5). Table 2 Ultimate load of specimens Beam

% reinforcement

Velocity at which the first crack appeared

Impact energy(in joules)

Beam 1

0%

888 mm/s

2.42

Beam 2

0.56% (under reinforced)

1159 mm/s

4.13

Beam 3

1.00% (under reinforced)

1615 mm/s

8.03

Beam 4

1.57% (over reinforced)

3015 mm/s

27.99

Beam 4

2.26% (over reinforced)

2788 mm/s

23.94

Impact energy absorbed by beam

Pt v/s Impact energy 27.99

30

23.94

25 20 15 8.03

10 5 2.42 0

0

4.13

0.5

1

1.5

Pt

Fig. 5. Plot of Pt verses impact energy

2

2.5

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Fig. 6 Crack pattern for Beam 1

5.2 Crack Pattern In the present analysis, the crack patterns obtained for the different specimens were studied. The first crack was observed to be very close to the mid-span in all the beams. The crack pattern for different beams are shown in Figs. 6, 7, 8, 9 and 10.

6 Conclusions The impact behaviour of beams with various reinforcement percentages was studied analytically using ANSYS software. The following conclusions can be drawn from the results. 1. The impact energy absorbed by the beams for the first crack was increased by the addition the reinforcement. 2. The impact of energy was increased up to Beam 4 (1.57% reinforcement) but decreased afterwards. 3. A procedure for the analysis of the beams, where there is a need to find out impact energy absorbed by the beams had been developed.

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Fig. 7 Crack pattern for Beam 2

Fig. 8 Crack pattern for Beam 3

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Fig. 9 Crack pattern for Beam 4

Fig. 10 Crack pattern for Beam 5

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References 1. John BR, Shah SP (1990) Mixed-mode fracture of concrete subjected to impact loading. J Struct Eng 116:585–602 2. Ožbolt J, Sharma A (2011) Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads. Int J Impact Eng 38:940–950. https://doi.org/ 10.1016/j.ijimpeng.2011.08.003 3. Kaewunruen S, Remennikov AM (2007) Experimental and numerical studies of railway prestressed concrete sleepers under static and impact loads. Civ Comput 25–28 4. Vaziri R, Quan X, Olson MD (1996) Impact analysis of laminated composite plates and shells by super finite elements. Int J Impact Eng 18:765–782. https://doi.org/10.1016/s0734-743x(96)000 30-9 5. IS 456:2000 (2000) Indian standard plain and reinforced concrete—code of practice. Bureau of Indian Standard, New Delhi, India 6. SP34 (1987) Handbook on reinforcement. Bureau of Indian Standard, New Delhi, India, pp 155

Numerical Studies on Impact Response of Prestressed Beams Using FE Software Anand Raj, Raunak Kumar, Praveen Nagarajan, and A. P. Shashikala

Abstract Impact is a high-intensity shock load applied for a short interval of time. Such a force is more damaging than a lower magnitude force applied over a proportionally longer period of time. Prestressed concrete (PSC) beams encounter these loads from a variety of sources during their service life as structural members. Here, an endeavour to carry out numerical studies to study the effect of prestressing force on the impact resistance of a PSC beam is undertaken using finite element software ANSYS. In this paper, a simple supported rectangular prestressed concrete beam of 100 mm × 100 mm in cross-section and 1200 mm length is used to compare the impact strength of prestressed beams due to prestressing forces of 4, 6, 8, 10 and 12 kN. The results of the study indicate that the capacity of the beam to absorb energy increases with an increase in prestressing force. Keywords Prestressed beam · Impact load · Initial crack · Crack pattern · Impact energy · Finite element method

1 Introduction When an impact load is applied to a prestressed concrete beam, the stress generated is much higher when compared to that of a static load [1]. Generally, the structures are not designed to withstand impact loads. Most of the design methodologies remain silent about the features that need to be added for withstanding impact loads. This paper aims to evaluate the behaviour of a prestressed concrete beam subjected to impact loading under various prestressing forces using finite element methods. Finite element software ANSYS is used for the modelling of the beams. The impact energy and the crack pattern were found out by trial and error method at the time of appearance of the first crack [2].

A. Raj (B) · R. Kumar · P. Nagarajan · A. P. Shashikala National Institute of Technology Calicut, Kozhikode, Kerala, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_46

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612 Table 1 Details of the beams considered

A. Raj et al. Beam ID

Reinforcement

Prestressing force (kN)

Beam 1

2 nos. 4 mm

12

Beam 2

2 nos. 4 mm

10

Beam 3

2 nos. 4 mm

8

Beam 3

2 nos. 4 mm

6

Beam 4

2 nos. 4 mm

4

2 Finite Element Analysis The finite element analysis is gaining importance in engineering research and development processes. ANSYS (Analysis System) is a finite element analysis and design software that can be used for various structural engineering problems [3, 4]. Various mesh sizes have been tested to remove convergence error, and a suitable mesh size has been arrived upon. The different steps involved in a finite element analysis are as follows [5, 6]: • Modelling the beam including meshing • Assigning the required boundary conditions • Solution (Analysis types, loading and solving). The trial and error method was done to evaluate the velocity at which the first crack was formed, and then the impact energy and the crack pattern was found out.

3 Specimen Details The beam was designed and had cross-sectional dimensions of 100 mm × 100 mm. The clear span of the beam was 1200 mm. High tensile bars of diameter 4 mm were provided as the longitudinal prestressing tendons with prestressing of values (12 kN, 10 kN, 8 kN, 6 kN, 4 kN) one at a time. Table 1 presents the details of beams considered in the study.

4 Finite Element Modellings 4.1 Element Types Concrete: Concrete of grade M40 (in explicit materials) was assigned to beam. Reinforcement: In this beams, main reinforcement bars of 4 mm diameter were used.

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Fig. 1 ANSYS model of beam

Prestressing: A prestressing force of 12–4 kN was given to each bar with values stepping down by 2 kN. Supports: These were made of structural steel and are of 100 × 100 × 50 mm in size. These supports were fixed at the bottom and kept at a distance of 50 mm from the ends. Impactor: This is made up of structural steel and 100 mm diameter and 100 mm in height. The weight of the hitter is 6.21 Kg. Figure 1 shows the ANSYS model of the beam.

4.2 Beam Modelling and Meshing After selecting the materials in the engineering data from explicit materials, the beam was designed in the geometry command, and properties of various elements were assigned in modal command. All the volumes were meshed using mesh command. A mesh size of 20 mm was considered. After meshing, the velocity of the hitter and fixed support conditions were assigned. The model for meshing is shown in Fig. 2.

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Fig. 2 Model after meshing

4.3 Boundary Conditions and Load Application Displacement boundary conditions to simulate simple support conditions have been provided. Prestress was applied as surface load by selecting the cross-sectional area of each tendon at the face of the beam. The bottom of the supports was restrained. The impact load was applied at the top of the beam in the centre. The velocity of the hitter was assigned in the downward direction, as shown in Fig. 3.

Fig. 3 Impact load application

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Table 2 Ultimate load of specimens Beam

Prestressing force (kN)

Velocity at which the first crack appeared (mm/s)

Impact energy (J)

Beam 1

12

7700

184.1

Beam 2

10

4860

73.33

Beam 3

8

3615

40.58

Beam 4

6

3280

33.40

Beam 5

4

1480

6.8

4.4 Analysis Type The beam was subjected to explicit dynamic analysis. The convergence of the solution was arrived at before finalising the mesh size. A trial and error process was carried out to ascertain the velocity at the time the cracks appeared.

5 Results 5.1 Impact Energy The impact energy absorbed by the different specimens was found out. These results are shown in Table 2. It was observed that the impact energy increased with an increase in prestressing force. The impact energy for Beam 2 and Beam 3 was 60.16 and 78%, respectively, less than that of Beam 1. Subsequently, the reduction in impact energy for Beam 4 and Beam 5 was 82 and 96%, respectively, in comparison to that of Beam 1. The trend shows that there is an increase in the impact energy required for crack initiation with an increase in prestressing force.

5.2 Crack Pattern In the present analysis, the crack patterns obtained for the different specimens were studied. The first crack was observed to be very close to the mid-span in all the beams as expected. The crack pattern for different beams is shown in Figs. 4, 5, 6, 7 and 8.

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Fig. 4 Crack pattern for beam 1

Fig. 5 Crack pattern for beam 2

Fig. 6 Crack pattern for beam 3

6 Conclusions The impact behaviour of beams with various prestressing force was studied analytically using finite element software ANSYS. The following conclusions can be drawn from the results

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Fig. 7 Crack pattern for beam 4

Fig. 8 Crack pattern for beam 5

1. The impact energy absorbed by the beam for the first crack was increased by increasing the prestressing force. 2. The percentage decrease in impact energy was maximum for that beam in which prestressing force was most at higher prestressing range (12 to 10 kN). For a reduction of 16.6% in prestressing force, the corresponding decrease in impact energy was 60.16%. 3. Beams with more prestressed tend to absorb more impact energy. 4. At lower prestress force (6 to 4 kN), 33% of the decrease in prestressing sees a relatively higher decrease in impact energy absorption is 79%. 5. At moderate prestress, the decrease in prestressing force (8 to 6 kN) of 25% sees a corresponding decrease of 17.5%; hence, the effect of reduction in prestress on impact is minimum here.

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References 1. Kaewunruen S, Remennikov AM (2009) Impact capacity of railway prestressed concrete sleepers. Eng Fail Anal 16:1520–1532. https://doi.org/10.1016/j.engfailanal.2008.09.026 2. Ožbolt J, Sharma A (2011) Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads. Int J Impact Eng 38:940–950. https://doi.org/ 10.1016/j.ijimpeng.2011.08.003 3. Rust W, Schweizerhof K (2003) Finite element limit load analysis of thin-walled structures by ANSYS (implicit), LS-DYNA (explicit) and in combination. Thin-Walled Struct 41:227–244. https://doi.org/10.1016/S0263-8231(02)00089-7 4. Kaewunruen S, Remennikov AM (2007) Experimental and numerical studies of railway prestressed concrete sleepers under static and impact loads. Civ Comput 25–28 5. Armstrong CG (1994) Modelling requirements for finite-element analysis. Comput Des 26:573– 578. https://doi.org/10.1016/0010-4485(94)90088-4 6. Bhavikatti S (2005) Finite element analysis

Fracture Behaviour of Steel Fibre Reinforced Rubcrete Anand Raj , P. J. Usman Arshad, Praveen Nagarajan, and A. P. Shashikala

Abstract Discussions on the failures in quasi-brittle materials like concrete provide a better understanding of its response to loadings when it is presented with the backdrop of fracture mechanics. Rubcrete is a term used to denote a concrete in which mineral aggregates are replaced by crumb rubber. An idea about the energy utilised to open the unit area of a crack surface can be obtained by using Fracture Energy (Gf ). Results of experimental investigations on M40 grade concrete with steel fibres and crumb rubber to determine the Gf as per RILEM TC50 FMC is presented in this paper. The rubcrete variants considered in this paper include M40 grade concrete in which fine aggregates are replaced by 5, 10, 15 and 20% with crumb rubber. The steel fibre reinforced concrete variants have steel fibre proportions of 0.25, 0.5, 0.75 and 1% of the total volume of the mix. Steel fibre reinforced rubcrete mixes have a rubber content of 15%. It can be concluded that, with the addition of steel fibres of about 1% by the total volume of the mix, the Gf increases by 51% and 84% for the ordinary concrete and the rubcrete specimen, respectively. Keywords Fracture energy · Rubcrete · Steel fibre reinforced concrete · Steel fibre reinforced rubcrete

1 Introduction The push for one of the basic needs of human beings, shelter, and that too luxurious ones have led the exploitation of concrete to limits beyond imagination. The turnover of the cement manufacturing companies has been on the rise, ever since the advent of this century. Concrete is often referred to as flowing stone owing to the ability to take up the shape of the mould that it fills. Addition of steel reinforcement imparts some amount of ductility to otherwise brittle concrete. Researchers from various part of the globe have been trying to develop a type of concrete that is more ductile than ordinary concrete for being used in earthquake-resistant structures. The demand for A. Raj (B) · P. J. Usman Arshad · P. Nagarajan · A. P. Shashikala Department of Civil Engineering, National Institute of Technology Calicut, Kozhikode, Kerala, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_47

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increased impact resistance of concrete has also been on the rise. As part of the process to develop a type of concrete with the above-mentioned qualities, the constituents making up concrete have partially or wholly been replaced by alternate materials. The possibility of the addition of rubber in concrete has been explored in researches spanning over four decades. These studies have found that the addition of rubber in place of aggregates can enhance the ductility and impact resistance. Addition of rubber to concrete usually results in a decrease in workability of concrete. Unit weight of concrete also reduces owing to the lighter weight of crumb rubber [1, 2]. Studies on rubber concrete have identified a reduction in strength characteristics with the addition of rubber content. However, pre-treatment of rubber particles has resulted in enhancement of strength characteristics. When steel fibres are added to concrete, a slight improvement in the strength properties can be noticed [3]. Crimped steel fibres can hold the materials together after the initiation of cracks. Thus, steel fibres help in prolonging further development of initiated cracks thereby resulting in increased strains.

2 Fracture Energy Fracture mechanics is that branch of mechanics in which the development and propagation of cracks in structures with different materials can be studied. Techniques of fracture mechanics of concrete provide us with an idea of how the intrinsic defects in a heterogeneous material like concrete develop and result in failure. Fracture energy (Gf ) is the energy that has to be expended for the generation of the unit area of a crack surface. A combination of steel fibres and rubber in concrete has the potential to be utilised in many structures that require higher ductility and impact resistance. However, any material that has to be used in structures should undergo thorough and rigorous scrutiny before that can be put into mass production. A proper understanding of the behaviour of M40 grade steel fibre reinforced concrete and rubcrete which have inherent defects owing to the heterogeneous nature of the concrete is essential. Gf provides us with an idea of the amount of energy required to generate and propagate the inherent defects that are present in the concrete.

3 Experimental Studies on Beams The fracture energy of notched concrete beams is found out using RILEM TC-50 FMC (1985) by conducting a three-point bend beam (3PBB) test. The 60 mm × 100 mm × 500 mm beams with a central notch of 30 mm were used for the study. Initial notch depth to overall depth ratio of 0.3 has been used to avoid vast areas with high stresses on the exterior of the fracture zone.

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3.1 Material Properties and Mix Proportions The mix proportions of M40 grade concrete used for the study was finalised after conducting numerous trials. Crushed stones of size less than 12.5 mm and locally available M sand conforming to Zone 2 as per IS: 383-1970 were used as coarse aggregates and fine aggregates, respectively. The specific gravity of coarse aggregates used in the study is 2.79. Fine aggregates and crumb rubber used in work have a specific gravity of 2.61 and 0.6, respectively. Portland Pozzolana cement was used as the binder. 5, 10, 15 and 20% by volume of fine aggregates have been replaced with crumb rubber in such a manner that the combination of the fine aggregates and crumb rubber also conforms to Zone 2 of IS: 383-1970. Details of the 13 mixes used in the study are provided in Table 1. In Table 1, M40R0, M40R5, M40R10, M40R15 and M40R20 indicate the mixes with 0, 5, 10, 15 and 20% rubber content, respectively, in M40 grade concrete. Analysis of the strength test results indicated a considerable decrease in compressive strength of 30% for the rubcrete mix with 20% rubber content. So, the rubcrete mix with 20% crumb rubber content replacing fine aggregates was discarded. M40R0SF‘X’, where ‘X’ takes values 0.25, 0.5, 0.75, 1, stand for the percentage of steel fibres added to the concrete represent the designations of steel fibre reinforced concrete. Last four mixes where the designations are of M40R15‘X’, where ‘X’ takes the same values as in steel fibre reinforced mixes represent the concrete with steel fibres and 15% rubber. Table 1 Details of specimen used in the study Specimen ID M40R0

Rubber content (%) 0

Steel fibre content (%)

Number of specimens

0

3

M40R5

5

0

3

M40R10

10

0

3

M40R15

15

0

3

M40R20

20

0

3

M40R0SF0.25

0

0.25

3

M40R0SF0.5

0

0.5

3

M40R0SF0.75

0

0.75

3

M40R0SF1

0

0.1

3

15

0.25

3

M40R15SF0.25 M40R15SF0.5

15

0.5

3

M40R15SF0.75

15

0.75

3

M40R15SF1

15

1

3

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Fig. 1 Schematic diagram of the testing arrangement for three-point bend beam test

3.2 Testing of Beams Schematic diagram of the test arrangement used for the test is presented in Fig. 1. Span of the beam between supports is 400 mm. Loading was applied by means of a UTM with the rate of loading at 0.2 mm/min. Figure 2 depicts the testing of beams in a displacement-controlled Universal Testing Machine of capacity 10kN. Sample load–deflection curve for the test is presented in Fig. 3. The fracture energy (Gf ) per unit projected area is calculated by the Eq. (1) [4] and: Gf =

W0 + 2Pw δ0 (d − a0 )t

(1)

Stress that the notch can withstand f is calculated using the Eq. (2) [5]: f =

3 Fmax L 2 b(d − a0 )2

Fig. 2 Testing of beams in Universal Testing Machine of capacity 10kN

(2)

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Fig. 3 Sample load–deflection curve for the 3PBB test

where W 0 represents the area under the load–deflection curve and F max is the maximum load. The effective length of the specimen is represented by L. b and d are used to represent the width and overall depth of the beam, respectively, δ 0 is the deflection of the beam due to self-weight of the beam Pw , t indicates the thickness and a0 is the initial notch depth [6–8].

4 Results and Discussions The load–deflection curves of M40 grade rubcrete variants with 0, 5, 10 and 15% by the volume of fine aggregates replaced by crumb rubber is shown in Fig. 4. It can be observed that the load–deflection curve of rubcrete specimen exhibited lower peaks when compared to the beam without rubber. After the peak load has been reached, a reduction in the softening is noticed with an increase in rubber content. From a visual inspection of the failure surface of the beams, it has been brought to the notice that the ordinary concrete beam has a relatively smooth failure surface, whereas there is slight roughening in the failure pattern of the rubcrete beams. Figure 5 graphically depicts the variation in fracture energy of rubcrete specimen. When the rubber content was increased to 15%, the fracture energy was enhanced by 9%. This means that 9% more energy needs to be expended for the generation of unit area of a crack in rubcrete specimens. Figure 6 represents the p–δ behaviour of steel fibre reinforced concrete beams with 0.25, 0.5, 0.75 and 1% by the total volume of concrete as the steel fibre content. The peak load is enhanced with the addition of steel fibre content. It can be noticed that as

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Fig. 4 Load–deflection curve for rubcrete specimens

Fig. 5 Variation in Gf for rubcrete specimens

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Fig. 6 Load–deflection curve for steel fibre reinforced concrete specimens

the steel fibre content increases, there is a reduction in the softening behaviour of the load–deflection curve after the peak load is reached. This behaviour can be attributed to the ability of the steel fibres to bridge the gap between the cracks and resist their propagation. The irregularities in steel fibres, help to hold the materials in position till significant loads act to break the bonding. Thus, when compared to ordinary concrete, concrete with steel fibres have the ability to undergo more deformation without substantial reduction in load-carrying capacity. It can be noticed that there is an enhancement in deflection value at peak load as the fibre content increases. Figure 7 represents the variation in fracture energy of steel fibre reinforced concrete specimen. When compared to the ordinary concrete specimen 50 and 76% more energy is required to generate a crack of unit area. Figure 8 represents the p–δ curve for the steel fibre reinforced rubcrete beams. A predominant shift in the value of deflection corresponding to ultimate load can be noticed with the addition of steel fibres as a portion of the total volume of concrete with 0.25, 0.5, 0.75 and 1%. Addition of steel fibres can result in mitigating the softening trend when compared to ordinary concrete. An observation of the failure pattern has revealed a rougher surface than steel fibre reinforced concrete. From Fig. 9, it can be seen that for generating unit area of a crack in steel fibre reinforced rubcrete specimen with 15% rubber content and 1% steel fibre content, 83% more energy has to be expended when compared to that of the conventional concrete specimen. Table 2 presents the fracture energy and ultimate stress at notch obtained from Eqs. 1 and 2. It can be noticed from Table 2 that, when crumb rubber replaces fine

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Fig. 7 Variation in Gf for steel fibre reinforced concrete specimens

Fig. 8 Load–Deflection curve for steel fibre reinforced rubcrete specimens

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Fig. 9 Variation in Gf for steel fibre reinforced rubcrete specimens

Table 2 Results of fracture studies Specimen ID

Fracture energy [Nm/m2 ]

Percentage increase in Gf Maximum stress at the notch [N/mm2 ] [%]

M40R0

131.400

0.00

M40R5

133.200

1.37

4.69

M40R10

137.060

4.31

4.49

M40R15

143.200

8.98

4.29

M40R0SF0.25

142.493

8.44

4.80

M40R0SF0.5

152.439

16.01

4.94

M40R0SF0.75

198.156

50.80

5.12

M40R0SF1

231.375

76.08

5.35

M40R15SF0.25

148.090

12.70

3.50

M40R15SF0.5

180.557

37.41

4.29

M40R15SF0.75

221.600

68.65

4.49

M40R15SF1

241.618

83.88

4.79

4.69

aggregates by 15%, the ability to withstand the stress at the notch reduced by 8.6%. When steel fibres are added to concrete by 0.25, 0.5, 0.75 and 1% the maximum stress that can be withstood by the notch increased by 2%, 5%, 9% and 14%, respectively.

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5 Conclusions Three-point bend beam tests were conducted on M40 grade rubcrete specimens by replacing fine aggregates with crumb rubber by 5, 10 and 15%. Energy absorption increased with an increase in rubber content. When steel fibres of 0.25, 0.5, 0.75 and 1% by the total volume of concrete were added noticeable improvement in the behaviour of conventional concrete and rubcrete specimens were observed. The conclusions of the study conducted are listed below. • Fracture energy of rubcrete specimen was enhanced by about 9% for a crumb rubber content of 15%. • Improvement in fracture energy was in the range of 8.5–51% when steel fibres were added to conventional concrete. • A 12–84% improvement was noted for rubcrete specimens with 15% crumb rubber when steel fibres were added. • The maximum stress that the notch can withstand reduced by 8.5% for a crumb rubber content of 15% for conventional concrete. • Steel fibres of 1% by the total volume of concrete has enhanced the maximum stress that could be withstood by the notch by 14%.

References 1. Raghavan D, Huynh H, Ferraris CF (1998) Workability, mechanical properties, and chemical stability of a recycled tyre rubber-filled cementitious composite. J Mater Sci 33:1745–1752 2. Khatib ZK, Bayomy FM (1999) Rubberized Portland cement concrete. J Mater Civ Eng 11:206– 213 3. Rossi P, Acker P, Malier Y (1987) Effect of steel fibres at two different stages: the material and the structure. Mater Struct 20:436–439 4. Hillerborg A (1985a) The theoretical basis of a method to determine the fracture energy G F of concrete. Mater Struct 18:291–296 5. Barros AO, Sena Cruz J (2001) Fracture energy of steelfibre-reinforced concrete. Mech Compos Mater Struct 8(1):29–45 6. Peterson PE (1980) Fracture energy of concrete: method of determination. Cem Concr Res 10:79–89 7. Šimonová H, Zahálková J, Rovnaníková P, Bayer P, Keršner Z, Schmid P (2017) mechanical fracture parameters of cement-based mortars with waste glass powder. Proc Eng 190:86–91 8. Karihaloo BL (1995) Fracture mechanics and structural concrete. Longman Sci Tech

Performance of Diagrid Structures with the Addition of Shear Links Minu Ann Peter, A. S. Sajith, and Praveen Nagarajan

Abstract Diagrid structures are an innovation in high-rise buildings for the efficient resistance of lateral loads. They can be considered as an extension of the truss system, as they consist of triangulated modules in the exterior in place of vertical columns in conventional framed tubular structures. The triangulated system contributes to the structural efficiency, i.e. the lateral and gravity loads are transferred through the axial action of the members. The disadvantages of diagrid structures are their limited energy dissipation capacity and ductility. In order to overcome this difficulty, the incorporation of shear links to the diagrid system is suggested. This paper aims in assessing the performance of shear links in diagrid buildings. In this paper, shear links of different lengths are introduced in diagrid frames and comparison of the performance is evaluated. Keywords Diagrid · Shear link · Energy dissipation capacity · Ductility

1 Introduction Diagrid structures are one of the recent developments in the case of tall buildings. Diagrid structures make use of inclined columns when compared to vertical columns in conventional framed tubular structures. The inclined columns are also termed as diagrids, which span over multiple floors. The gravity and lateral load on the structure are transferred by the compression and tension in the diagrid [1, 2]. The triangulated configuration makes the structure efficient and pleasing to the eye. The interior core in the structure needs to be designed to take the gravity load alone, helping in improving the flexibility of the plan of the structure. The triangulated M. A. Peter (B) · A. S. Sajith · P. Nagarajan Department of Civil Engineering, National Institute of Technology Calicut, Kozhikode, India e-mail: [email protected] A. S. Sajith e-mail: [email protected] P. Nagarajan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_48

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configuration makes the structure stiffer and in turn this affects the ductility of the structures [3]. The addition of shear link will help in order to overcome this difficulty. A link is a member connecting two braces or a brace and a beam or a beam and column. The main advantage of a link is that it helps the other structural members to remain in elastic state and acts as sacrificial fuse by having sufficient plastic deformation capacity. Links can be classified as shear, intermediate and flexural links based on the length of the links. Study shows that shear links are more effective in energy dissipation. These can be easily replaced without affecting the function of other members, whereas replacing the diagrids or the inclined columns is not easy. This paper aims in assessing the performance of diagrid structures with the addition of shear links.

2 Problem Considered This work is done to evaluate the advantage of shear link in the performance of diagrid buildings. For this, diagrid building of 24 storey is modelled. The plan and elevation of the 24 storey diagrid buildings without and with shear links are shown in Fig. 1. The storey height of the frame is 3.6 m and plan dimension is 32 m × 32 m. In this case, the diagrid spans over three storeys. The analysis is carried out in diagrid buildings for different link lengths. The lengths used for the analysis are 400, 500, 600, 700, 800, 900 and 1000 mm. The sections used for the various members are shown in Table 1. The interior column section is shown in Fig. 2. The yield strength of the members is 250 MPa. The floor slab is RCC of thickness 150 mm. A design dead load and live load of 3.75 kN/m2 and 2.5kN/m2 , respectively, is applied on the floor slab. ETABS is the software used for modelling and analysis of the buildings. The connections of beam, columns and diagrids are hinged. At the base, fixed support condition is provided. The design of shear links is done as per the provisions given in AISC 341-16 [4]. The shear link length, e, as per the provision is given in Eq. 1. e≤

1.6Mp Vp

(1)

where M p is the moment capacity and V p is the plastic shear of a link. These are determined by Eqs. 2 and 3. Vp = 0.6 Aweb σ y

(2)

Mp = Z σ y

(3)

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Fig. 1 a Elevation of diagrid buildings without shear links, b elevation of diagrid buildings with shear links and c plan of the diagrid buildings

Table 1 Section details of 24 storey building Beams

Diagrids

Interior columns

Shear link

B1: ISMB500 400 mm pipe sections of 20 mm thickness 1400 mm × 1400 mm ISMB500 B2: ISWB550

Fig. 2 Interior column section

where σ y, Aweb and Z are the yield strength, cross-sectional area of the web and plastic modulus of the link cross section, respectively.

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3 Linear Static Analysis The building models are subjected to modal analysis and the time period of the buildings are obtained. The building is subjected to earthquake and wind loads. For computing design earthquake load, IS: 1893-2016 [5] codal provisions are used, considering medium soil condition, zone factor pertaining to zone IV. The response reduction factor is five and importance factor is one in this study. IS 875 Part 3 2015 [6] provisions are used to apply the wind load. The basic wind speed is taken as 50 m/s, and terrain category III is selected. The risk coefficient, importance factor and topography factor are all taken as one. Since the building is symmetric, earthquake and wind loads are applied only in one direction in the study.

3.1 Time Period The improvement of the performance of buildings is noted with the parameters time period and storey displacement. The time period of the first three modes of the diagrid buildings without and with shear link are shown in Table 2. The above table shows that with the addition of shear link, the time period of the building increases. It can also be noted that as the length of shear link increases, the time period is found to increase indicating a reduction in stiffness. Table 2 First three-mode time periods of 24 storey building

Building

Mode 1 (s) Mode 2 (s) Mode 3 (s)

Diagrid

2.129

2.122

1.011

Diagrid with 400 mm link

3.369

3.362

1.773

Diagrid with 500 mm link

3.802

3.793

2.032

Diagrid with 600 mm link

4.25

4.24

2.296

Diagrid with 700 mm link

4.712

4.699

2.564

Diagrid with 800 mm link

5.183

5.168

2.835

Diagrid with 900 mm link

5.654

5.645

3.105

Diagrid with 1000 mm 6.152 link

6.134

3.385

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3.2 Storey Displacement The plot of storey displacement due to the given lateral load is shown in Figs. 3 and 4.

Fig.3 Storey displacement for earthquake load

Fig.4 Storey displacement for wind load

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It can be noted that the displacement increases as the length of the link increases. But the maximum permissible deflection taking into consideration the serviceability condition is height/500. The results show that for a link length of 700 mm onwards this limit is exceeded for the wind load.

4 Non-linear Static Analysis For predicting the actual behaviour of the buildings, non-linear static analysis is carried out. A target displacement of 1000 mm was applied on the building models. The non-linear behaviour of the members is modelled using plastic hinges as per the guidelines in FEMA 356 [7].

4.1 Pushover Curve Based on the results obtained, the pushover was plotted for the diagrid building models. Figure 5 shows the pushover curve of the diagrid building without shear link and diagrid building with shear link length varying from 400 to 1000 mm.

Fig. 5 Pushover curve

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4.2 Energy Dissipation Capacity The energy dissipation values of the 24 storey buildings without and with shear links are compared. From the curve obtained in Fig. 4, the energy dissipation capacity is found by calculating the area under the curve. The energy dissipation value of diagrid without shear link is obtained as 2720.19 kNm. Table 3 shows the energy dissipation obtained after performing the pushover analysis. The variation is also plotted in Fig. 6. The energy dissipation values for diagrids with the addition of links is more than 1.5 times than that for diagrid buildings without links. Table 3 Energy dissipation for various link lengths

Link length (mm)

Energy dissipation capacity (kNm)

400

4113.04

500

4242.64

600

4171.21

700

4641.28

800

4841.34

900

4203.24

1000

4420.15

Fig. 6 Variation of energy dissipation with varying link lengths

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Fig. 7 Hinge formation steps in diagrid building without shear link

4.3 Hinge Formation The location of hinge formation in the various models are noted. In the case of diagrid buildings without shear links, the hinges are formed in the diagrids. The diagrids being the primary load-carrying members, hinge formation affects the stability of the building. Some of the steps in the hinge formation are shown in Fig. 7. The hinge formation steps in diagrid buildings with shear link of length 400 mm are shown in Fig. 8. From the figure, it can be observed that the hinge formation is in the shear link. The shear links can be easily replaced when compared to diagonal columns and the stability is not affected.

5 Conclusions From the above observations, the following conclusions are made. • The time period and storey displacement of diagrid buildings with shear link increase as the length of the shear link increases. • The top storey displacement for the buildings with shear link length greater than 600 mm was found to exceed the permissible limit. Hence, the length of the link needs to restricted to 600 mm. • The addition of shear links helps in making the diagrid buildings less stiff.

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Fig. 8 Hinge formation steps in diagrid building with shear link of length 400 mm

• The energy dissipation capacity is increased almost 1.5 times due to the addition of shear links, i.e. the ductility of diagrid buildings can be enhanced by the incorporation of shear links. • In case of diagrid buildings with shear links, the hinge formation occurs in the link. The link is easily replaceable when compared to diagonal columns.

References 1. Moon KS (2012) Structural design and construction of diagrids for complex-shaped tall buildings. Int J Struct Eng World Congr 2(1):12–16 2. Korsavi S, Maqhareh MR (2014) The evolutionary process of diagrid structure towards architectural, structural and sustainability concepts: reviewing case studies. Architectural Eng Technol 3(2):1–11 3. Moghaddasi BNS, Zhang Y (2013) Seismic analysis of diagrid structural frames with shear link fuse device. Earthq Eng Eng Vibr 12:463–472 4. ANSI/AISC 341–16, An american national standard, seismic provisions for structural steel buildings, American institute of steel construction, Chicago, July 12, 2016 5. IS 1893 (Part 1)-2016: Indian Standard Criteria for Earthquake Resistant Design of Structures, Part 1, General Provision and Buildings (Sixth Revision), Bureau of Indian Standards, New Delhi, December 2016 6. IS 875 (Part 3)-2015: Design Loads (Other than Earthquake) for Buildings and Structures— Code of Practice, Part 3, Wind Loads (Third Revision), Bureau of Indian Standards, New Delhi, April 2015 7. FEMA 356–2000, Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Federal Emergency Management Agency, ASCE, November 2000

Design of Box Girder Bridges Using Simplified Frame Analysis J. Chithra, Praveen Nagarajan, and A. S. Sajith

Abstract As box girder bridges are inevitable kind in the field of bridge engineering, studies on them is always a fascinating job for researchers. The inherent nature of its cross-section can resist many structural actions. Even though, the geometry of these kinds of bridges is simple their design procedures are not. Mostly Three-Dimensional Finite Element Analysis (3D-FEA) is done to design these structures. As 3D-FEA is time consuming, various simplified methods are used by design engineers for the preliminary study and analysis. Simplified Frame Analysis (SFA) is one among such simple methods used by bridge engineers to conduct trial design on box girder bridges. SFA is an easy method to find the transverse bending moments in box girder bridges. This paper focuses on how to use the results of Simplified Frame Analysis (SFA) for the transverse design of box girder bridges. Keywords Box girder bridges · Transverse analysis · Simplified method

1 Introduction Box girder bridges are large span bridges with girders in the shape of a hollow box with either rectangular or trapezoidal cross-section. They can be of reinforced concrete, prestressed, structural steel or even composite sections. These kinds of bridges do excellent services in regions of elevated transport as it provides better vertical clearance underneath the deck when compared with T-beam or I-girder bridges. Yet another advantage which makes the bridge designers to choose box cross-section is the load-carrying capacity and its inherent nature to resist bending and torsional moments. Due to many of its intrinsic worth, it is the most preferred kind for long-span bridges. As the popularity increases the design of such bridges

J. Chithra (B) Research Scholar, National Institute of Technology Calicut, Kozhikode, Kerala, India e-mail: [email protected] P. Nagarajan · A. S. Sajith National Institute of Technology Calicut, Kozhikode, Kerala, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_49

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requires special attention. Before moving to the design part it is necessary to discuss the various structural actions acting in a box cross-section. Flexure, shear, torsion, distortion, warping and shear lag are the major structural actions found in box girder bridges. For readers, the cause of these actions can be briefly discussed here as follows: (1) Any load placed on the deck is transferred to the web by the flexural actions of the deck. (2) The beam action in the longitudinal direction results in longitudinal flexural as well as shear stresses in box sections. (3) The presence of an eccentric loading results to torsion in the cross-section as well as shear and warping stresses in the longitudinal direction. (4) Eccentric loading also leads to distortion which results in stresses in both transverse and longitudinal directions. (5) Unevenly distributed longitudinal stresses lead to shear lag along the width of the top flange. For the analysis and design of box girders, there are different methods like simple beam theory, simplified frame analysis, beam on elastic foundation, Knittel’s method, equivalent beam method, Kupfer’s method, grillage theory, folded plate and three dimensional finite element analysis. Among all the above methods only folded plate and three-dimensional finite element analysis consider all the structural actions in a box girder bridge for analysis. For example, using simple beam theory only the longitudinal analysis can be done, whereas methods like beam on elastic foundation and simplified frame analysis can be performed for the transverse analysis. Usually for design of box girder bridges only two analyses are done; one in longitudinal direction and the other in transverse direction and to account for all other effects like that of distortion, shear lag and warping the results are increased by 10–20%. Research work has been conducted to understand the exact variations due to the effects of distortion and warping in transverse analysis [1]. This paper aims to analyse and design the deck of a box girder bridge using Simplified Frame Analysis (SFA). SFA is a simplified method used in design offices to find the transverse moments in a box girder bridge. This helps to conduct an initial study to arrive at required cross-sectional details.

1.1 Simplified Frame Analysis While designing a box girder, the longitudinal and transverse analysis are conducted separately. For longitudinal analysis, the entire box girder is considered as a beam and analysed to obtain the critical moments. Whereas for transverse analysis, a box frame of unit width (simplified frame) is assumed and loads are kept at the critical positions to evaluate the moment arising in flange, web and web flange junctions. SFA is a method approved by the highways and railway authorities for transverse analysis of box girder bridges. As the calculations involved in this method are simple,

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it is widely accepted all over the world. As the paper focuses on the transverse design of a box girder bridge, an overview on this method is provided below. Maisel and Roll [2] were the prime researchers who proposed SFA. In 1974, they proposed this method for the transverse analysis of box girder bridges. A box frame of unit width is considered for the analysis. The frame is supported on fictitious hinge supports at the bottom web flange junctions. Figure 1 will help the reader understand how to take a frame of unit width for SFA from the deck of a box girder bridge. The frame so obtained is loaded with a concentrated load calculated using the effective width method. Figure 2 depicts the frame which is to be analysed in STAAD Pro. Now, the modelling of vehicular load has to be understood in detail. This is because, only unit width of the entire deck is considered for transverse analysis. In SFA, the vehicle load act as a concentrated load which is calculated using the effective width method. For a vehicular load W, the concentrated load can be calculated as W /be , where be is the effective width. A detailed explanation of the effective width method is provided in IRC 112-2011. Effective width can be obtained as be = αx(1 − x/l) + bw

Fig. 1 Deck of single-cell box girder bridge

Fig. 2 Frame modelled for simplified frame analysis

x

P

l

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where (particularly for box girder bridges). α = a coefficient whose value depends on span to width ratio (b/l). l = effective span (distance between the web). x = distance of load from the nearest support (web). bw = breadth of concentration area of load.

2 Design of Box Girder Bridges Deck A simply supported single-cell box girder bridge with no overhangs is considered for the design. Cross-section of the bridge deck used for design is shown in Fig. 3. The loading considered is single lane 70R tracked vehicle placed at the mid-span. Details of the box girder Span = 30 m Depth = 2.75 m Thickness of web = 0.25 m Thickness of flange = 0.25 m Width of flange = 5.25 m. The top view of the deck with 70R track loading is shown in Fig. 4 (not to scale). 0.25m 0.25m 2.5m

5m Fig. 3 Cross-section of bridge deck

30m x

4.57 0.84

Load 1 Load 2

1.22

Fig. 4 Top view of box girder bridge deck with 70R tracked vehicle loaded at mid-span

5m

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Before any design, it is necessary to find the critical load positions. It is the same in case of transverse design of bridges too. Hence to find the critical load position the loads are moved in the transverse direction. Hogging and sagging moments are found for various load positions, and the positions of maximum moments are noted. This is performed using STAAD Pro. Here two sets of load positions are identified; one for maximum hogging moment and the other for sagging moment. For maximum hogging moment the distance of load from the nearest web has to be 1.4 m, and for maximum sagging moment it has to be 2.2 m. Now, after finding the critical load positions, the tracked load has to be converted to concentrated load using effective width method. Load positions for maximum hogging and sagging moments and their respective STAAD results providing the maximum values of moments are shown in Figs. 5a, b and 6a, b. Once the moments are estimated the required reinforcement can be found out. The reinforcement detailing for transverse direction is shown in Fig. 7.

Fig. 5 a Frame modelled with critical load positions for hogging moment. b STAAD results for maximum hogging moment

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Fig. 6 a Frame modelled with critical load positions for sagging moment. b STAAD results for maximum sagging moment

A sample calculation for the design of top flange considering the maximum hogging moment is provided below. For load 1 (see Fig. 4) b/l = 30/5 = 6 α = 2.6 (IRC 112-2011) x = 1.4 m (Distance of the load from nearest web) be1 = 2.6 × 1.4 (1−(1.4/5)) + 4.57 = 7.19 m W / be1 = 350/7.19 = 48.67 kN/m. Similarly, for load 2

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Fig. 7 Transverse reinforcement details for the box girder bridge

x = 1.54 m (Distance of the load from nearest web) be2 = 2.6 × 1.54 (1 - (1.54/5)) + 4.57 = 7.34 m W / be2 = 47.68 kN/m. So obtained loads are applied on the frame modelled for SFA and moments are obtained. The maximum hogging moment obtained is 49.601 kNm (see Fig. 5b). For which the reinforcement required is 20 mm diameter bars at 250 mm c/c. Similarly, reinforcement required in the webs are also found out and is shown in Fig. 7.

3 Comparison of Results of SFA with Three-Dimensional Finite Element Analysis For the confirmation in accuracy of the values of transverse analysis done by SFA. The results are verified using an accurate three-dimensional finite element analysis (3D-FEA). Here CSI bridge software is used for 3D analysis of the bridge. Here four-noded shell elements are used to model the bridge deck. It is meshed at 250 mm × 250 mm with an aspect ratio 1 throughout the deck. Vehicle loads were applied as pressure loads. Figure 8 shows the bridge modelled with vehicle loading in CSI bridge software. Here the bridge deck is loaded with one lane 70R loading. It is noted that the results from SFA and 3D-FEA are almost the same, and hence the results from SFA can be directly used for design purpose. In Table 1, the results obtained from both SFA and 3D-FEA are provided when loaded for maximum hogging moment. Figure helps to identify the points taken for comparison (Fig. 9). From Table 1, it is clear that the results from SFA match with that of 3D-FEA. Hence the results from SFA are reliable for design purposes.

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Fig. 8 Box girder bridge with vehicle loading modelled with CSI bridge software

Table 1 Results of transverse analysis from SFA and 3D-FEA (modelled for maximum hogging)

SFA (kNm/m)

3D-FEA (kNm/m)

Hogging moment in top flange (A)

48.6

48.86

Sagging moment in top flange (B)

47.16

54.54

Hogging moment in top flange (C)

48.2

47.38

Hogging moment in bottom flange (D)

15.31

16.13

Sagging moment in bottom flange (E)

3.34

4.7

Hogging moment in bottom flange (F)

14.89

15.3

4 Conclusions From this study, it is concluded that the results from SFA and 3DFEA are closer, and hence SFA can be used for estimating the transverse reinforcement required in a box girder bridge. It can also be concluded that as SFA is less time consuming it can be used for the initial design of box girder bridges.

Design of Box Girder Bridges Using Simplified Frame Analysis Fig. 9 Cross-section with points where the moments of SFA and 3D-FEA are compared

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F

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B

C

E

D

References 1. Kurian B, Menon D (2005) Correction of errors in simplified transverse bending analysis of concrete box girder bridges. J Bridge Eng 10:650–657 2. Maisel BI, Roll F (1974) Methods of analysis and design of concrete box beams with side cantilevers, C and CA publications

Use of FEM for Design of Reinforced Concrete Beams as Per IRC 112-2011 J. Chithra, Praveen Nagarajan, A. S. Sajith, and R. A. Roshan

Abstract To design reinforced concrete beams, engineers all over India refer to IS 456-2000. Nowadays finite element software is used for any design rather than hand calculations. In the appendix of the latest revised code for bridges IRC 112-2011, design procedures using three-layer sandwich model based on finite element analysis has been included for the design of reinforced concrete structures. In the sandwich model, a shell element is divided into three layers. The top and bottom layer are supposed to take out of plane moments and the core carries out of plane shear. In this paper, sandwich model has been used for the design of reinforced concrete beams. Here solid and hollow rectangular beams are considered for the design. The results are then compared with IS 456-2000. Keywords Beams · Design · Three-layer sandwich model

1 Introduction Concrete beams are those elements in a structure which are supposed to carry transverse loads. They act as supports by carrying loads from slabs, walls, other beams and sometimes column. These loads are then transferred to columns. Loads acting on the beam result in bending moment and shear force across the length of the beam. In some cases, torsion and distortion also develop when the load is eccentric. Beams can be differentiated based on many criteria like the shape of cross-section, support conditions, materials used, etc. In this paper, the design of rectangular beams using three-layer sandwich model provided in IRC 112-2011 is compared with the most common method of design as outlined in IS 456-2000. Generally, the design procedures used in Indian codes such as IRC 21 and IRC 18 are based on working stress method (WSM). A new revision of code combining IRC 21 and 18 based on ultimate limit state (ULS) have been recently released as J. Chithra (B) · P. Nagarajan · A. S. Sajith · R. A. Roshan National Institute of Technology Calicut, Kozhikode, Kerala, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_50

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IRC 112-2011. No design aids have been developed for this new version of code, and hence a design aid would make the design work more simple. This new version of code introduces a design method based on linear elastic finite element analysis for concrete structures known as the three-layer sandwich model. The clauses of the existing code based on ULS (IS 456-2000) differ significantly from the newly revised code IRC 112-2011. Reinforced concrete beams are generally designed using IS 456-2000 based on rectangular parabolic stress distribution. IRC 112-2011 suggests rectangular as well as rectangular parabolic stress distributions. To understand the design method in detail, solid and hollow beams with and without torsion are designed using three-layer sandwich model according to IRC 112-2011 and compared with IS 456-2000. The basics of concrete shell element method are briefly explained below.

1.1 Concrete Shell Element Method In a shell element as shown in Fig. 1, there are three plate components which are the axial and shear components (ηEdx , ηEdy , ηEdxy = ηEdyx ), three slab components namely the moment and torsion components (M Edx , M Edy , M Edxy = M Edyx ) and two transverse shear components (V Edx , V Edy ). Initially, Ottossen failure criteria are used to find the locations of crack and reinforcement is provided to control the crack propagation. If the section is not cracked, then check whether minimum principle stress is less than design compressive stress. If the section is cracked the shell element is considered as a three-layer sandwich model in which the outer layers take membrane forces (three plate component and three slab components) and the middle layer takes transverse shear. Equations to find the membrane forces and stress are provided in the code IRC 112-2011. A brief literature survey on the development of this method is provided below.

Fig. 1 Concrete shell element

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Morley [1] worked on the optimization of reinforcement for the required strength in a shell element. He considered the rate of energy dissipation in yield lines, the development of yield criteria in terms of stress resultants [1]. Prodromos [2] proved that after cracking the force and moment tensors appear with axial and shear forces of steel bar. This is to obtain the angle of crack [2]. Perry and Weishi [3] presented a procedure to design transverse reinforcement in concrete slab and walls subjected to combined effect of transverse shear, membrane forces and bending moment. The method includes a rational distribution of concrete making it suitable for members with little or no transverse reinforcement [3]. A technical note on “Concrete shell reinforcement design” in 2017 deals with the design of reinforcement of concrete shells in accordance with a predetermined field on moments based on the Euro code-2 [4].

2 Comparative Study on Design of Beams Using IRC 112-2011 and IS 456-2000 Here solid and hollow beams are designed using shell element method and the conventional IS 456-2000 and are then later compared to understand the variation in the amount of steel required using various design methods. Both solid and hollow beams are then subjected to forces which are symmetric as well as eccentric in nature. The purpose of providing eccentric loading is to understand the effect of torsion in design of beams. Beams are modelled and analysed using CSI bridge.

2.1 Solid Beam With Symmetric Load A simply supported beam with a span of 6 m having breadth and depth 250 mm and 450 mm, respectively, is subjected to a uniformly distributed load of 20 kN/m. M25 and Fe415 are the grade of concrete and steel. Main bar with 25 mm diameter and 8 mm stirrups with a clear cover of 20 mm is provided. The beam is modelled in CSI bridge software using shell elements as shown in Fig. 2, and the corresponding moment and axial force distribution are provided in Figs. 3 and 4, respectively. In Table 1, the area of reinforcement required for the given loading when designed using the two different design methods is provided. For solid beams without torsion, the area of steel using IS 456 in flexure is 16% more than that of shell element method. In shear reinforcement, IS 456 gives lesser value when compared with the three-layer sandwich model.

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Fig. 2 Loading on beam in CSI bridge with symmetric loading

Fig. 3 Moment distribution over the beam

Fig. 4 Axial force distribution over the beam

Table 1 Area of steel required for solid beam with symmetric loading IS 456-2000 IRC 112 shell element IS 456/IRC 112 Flexural reinforcement (mm2 ) Shear reinforcement

(mm2 /unit

1062 length) 265

913

1.16

370

0.72

2.2 Solid Beam with Asymmetric Loading A fixed-fixed beam with a span of 5 m having breadth and depth 300 mm and 500 mm, respectively, was subjected to a uniformly distributed load of 5 kN/m with an eccentricity of 0.25 m from the centre as shown in Fig. 5. M25 and Fe415 were used. 16 mm main bar and 8 mm stirrups with a clear cover of 20 mm are provided. Moment distribution of the beam is shown in Fig. 6. Table 2 provides the amount of reinforcement required.

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Fig. 5 Solid beam with asymmetric loading in CSI bridge

Fig. 6 Moment distribution over the beam

Table 2 Area of steel required for solid beam with asymmetric loading IS 456-2000 IRC 112 shell element IS 456/IRC 112 Flexural reinforcement

(mm2 )

311

288

1.07

Shear reinforcement (mm2 /unit length) 500

494

1.01

When the beam is subjected to torsion the flexural reinforcement increased by 7% when designed using IS 456-2000 and shear reinforcement by 1% when compared with shell element method.

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Fig. 7 Hollow beam with UDL along the span

Fig. 8 Axial force distribution over the hollow beam

2.3 Hollow Beam with Symmetric Loading A hollow beam having 200 mm thickness, overall depth of 1 m, overall width of 2 m and having a span of 10 m is subjected to a uniformly distributed load of 20 kN/m along the span. Materials M25 and Fe415 are used. Figure 7 shows the beam modelled. Figures 8 and 9 give the axial force distribution and moment distribution along the beam. Table 3 to get the area of reinforcement For hollow beams without torsion, flexure reinforcement designed using IS 4562000 is 6% less, and shear reinforcement is 17% more when compared with IRC 112-2011.

2.4 Hollow Beam with Asymmetric Loading A hollow beam having 200 mm thickness, overall depth of 1 m and width 2 m and with a span of 10 m was subjected to a uniformly distributed load of 20 kN/m at an eccentricity of 500 mm from the centre as shown in Fig. 10, with materials M25 and Fe500 was designed using IS 456 and IRC 112 shell element and area of steel was

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Fig. 9 Moment distribution over the hollow beam

Table 3 Area of steel required for hollow beam with symmetric loading IS 456-2000 IRC 112 shell element IS 456/IRC 112 Flexural reinforcement

(mm2 )

2452

Shear reinforcement (mm2 /unit length) 495

2616

0.94

420

1.18

Fig. 10 Loading on hollow beam in CSI bridge with torsion

compared. Figures 11 and 12 show the axial force and moment distribution along the length of the beam. In Table 4 the area of steel required is provided. For hollow beams with torsion, the IS 456 values for flange and web reinforcement are 3% and 57% less, respectively, when compared with IRC 112-2011.

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Fig. 11 Axial force distribution over the hollow beam

Fig. 12 Moment distribution over the hollow beam

Table 4 Area of steel required for hollow beam with asymmetric loading IS 456-2000 Flexural reinforcement

(mm2 )

Shear reinforcement (mm2 /spacing)

IRC 112 shell element

IS 456/IRC 112

2676

2772

0.97

385

670

0.57

For the design of hollow beam, axial force is the governing stress resultant while for solid beams it is longitudinal bending when designed using the three-layer sandwich model.

3 Conclusion It is found that the area of reinforcement required by the beams when designed using two different approaches match very closely. It is seen that in the case of shear reinforcement in hollow beams subjected to torsion, there is a notable difference in the amount of reinforcement when designed using two different methods. The reason behind this variation is that linear elastic finite element analysis is done for three-layer sandwich method (IRC 112-2011) hence the required area of reinforcement will be much higher when compared with IS 456-2000 in which ultimate limit state is used.

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But this difference is not seen for flexural reinforcement as the lever arm distance in elastic as well as in ultimate stage do not show much difference in variation. Usually, using IS 456-2000 only typical beams can be designed but three-layer sandwich model which uses finite element analysis can provide design reinforcement for any practical case. Hence the concrete shell element method which is newly added to the code can very well be used in place of the conventional method in design of beams as per IS 456-2000.

References 1. Morely CT (1979) Yield criteria for elements of reinforced concrete slabs. Article-IABSE reports 1979 of the working commissions, pp 34–47 2. Prodromos DZ (1986) State of stress in rc plates under service conditions. J Struct Eng 112(8):1908–1927 3. Perry A, Weishi H (1994) Infiuence of membrane forces on transverse shear reinforcement design. J Struct Eng 120:1347–1366 4. Technical paper concrete shell reinforcement design. Computer and structure. inc, 2017, pp 1–10

Estimation of Ultimate Strength of Concrete Box-Girder Bridges Using Space Truss Analogy Bajare Mayur Mangesh, J. Chithra, Nagarajan Praveen, and A. S. Sajith

Abstract The box section has high torsional stiffness and bending stiffness which makes it a very efficient structural system to resist different forces acting on it. Owing to its complex geometry, the analysis and behavior at the ultimate stage of a boxgirder bridge are not yet completely understood. Among the existing theories, Space truss analogy is the basic theory to understand the behavior of box sections at its ultimate stage. For reinforced concrete box-girder bridges subjected to a combined action of bending and torsion, space truss analogy visualizes the structure as a space truss formed by inclined diagonal concrete elements as struts and reinforcing cage as ties. In the present study, box-girder bridges are modeled and their ultimate strength is predicted using the theoretical formulations of space truss analogy and strut and tie model. In analysis, the various load patterns are considered to incorporate the actual bending and twisting effects which are generated due to eccentric load. The numerical computations for the space truss are performed using STAAD, and the results are compared with those available from literature. Keywords Box-girder bridge · Space truss analogy · Strut and tie model

1 Introduction Bridge is a structure which carries a road or railway across a natural or artificial obstacle such as, a river, canal or other road. Bridge is a structure having the heaviest responsibility in carrying a free flow of traffic. It is the most significant component of a transportation system in case of communication over gaps for whatever reason such as aquatic obstacles, valleys, gorges, etc. Development and planning of efficient transportation system, with rapid increase in traffic and population is becoming a challenging task, leading to various new types of structural systems for bridges. One of them is box-girder bridge. The box section has high torsional stiffness and bending stiffness which makes it very efficient structural system for the design of bridges. B. Mayur Mangesh (B) · J. Chithra · N. Praveen · A. S. Sajith National Institute of Technology, Kozhikode, Kerala, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_51

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Analysis of box-girder bridges is difficult due to its 3D behavior consisting of bending in longitudinal and transverse direction, torsion, and distortion. A lot of theoretical and experimental research is done on the behavior and collapse load prediction of simply supported, single cell, box-girder bridges. There are two different theories to understand the strength of reinforced concrete structures, skew bending theory and space truss theory. Out of these two, the space truss theory is very basic and compatible method to analyze the reinforced concrete structures subjected to torsion. This theory was derived from the truss analogy for the design of reinforced concrete beams subjected to shear. The space truss theory of torsion considers a reinforced concrete member as a space truss formed by inclined concrete element as strut and reinforcing cage as tie, which is a mechanism-based model. This model not only helps in visualizing the behavior of member, but it also makes the numerical computations easy. From literature review it is observed that, once torsional cracks have occurred, the contribution of core concrete in resisting torsion is very less. Hence, both solid and hollow reinforced concrete members are considered as tube elements. Thus the diagonal concrete elements along with reinforcement form a plane frame on each side of the member. The plane frames, on all sides, once combined forms a space frame.

2 Literature Review The box-girder bridges subjected to eccentric loading experience significant torsional moments along with bending moments in both directions. Generally in structural analysis, effects of bending, shear, and axial forces are considered and that of torsion are neglected. That is because, the stresses generated due to torsion, in normal structures are not that critical. But in case of certain types of structures, even small torsional moments can cause critical stresses. Box-girder bridges are one of them. Rausch (1929) first used the concept of space truss analogy, to study the torsional behavior of reinforced concrete structures. He derived the equations, based on space truss analogy, to calculate torsional strength of reinforced concrete elements. Lampert and Thurliman (1972) used the concepts proposed by Rausch and derived equations to predict ultimate strength of beams subjected to bending and torsion. The analysis was based on the upper bound and lower bound theories of plasticity. The formulations developed were compared with the experiments performed on box sections. Hsu and Mo considered the effect of diagonal cracking on the compressive strength of concrete struts, and softening effect. Hsu used the space truss model presented by Rausch with angle of struts as 45o and came up with the equations for shear modulus and torsional stiffness of a cracking beam. Vecchio and Collins derived a three-dimensional behavioral truss model to analyze rectangular reinforced concrete beams subjected to combined action of shear and torsion. The model was based on the Modified Compression Field Theory (MCFT). The developed analytical model considers the effects of biaxial bending, biaxial shear, torsion, and axial force. The

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comparisons of results, obtained from analytical model, with experimental investigations show that the model is a compatible tool to calculate the response of sections subjected to combined loading [1]. Csikos and Hegedus [2] have presented various methods to analyze reinforced concrete members. The theoretical formulations followed by various codes are compared with each other. The theoretical computations were compared with numerical computations, and they showed good agreement [2]. The experimental studies on box-girder section subjected to eccentric load showed that corner plastic hinges are developed at mid-span section and did not extend up to diaphragms. Kurian and Menon [3] proposed modifications to the theoretical formulations and compared with the experimental results. It is understood that magnitude of error is related to the nature of asymmetrical loading and the ratio of longitudinal to transverse reinforcement. Experiments were carried out on single-cell box-girders models, and it is found that the collapse load predicted using proposed modified theory matches closely with the experiments conducted [3]. In common design practice, box-girder bridge is modeled as a rigid jointed frame. However, there is a significant error in transverse bending moments calculated using Simplified Frame Analysis (SFA). The transverse bending moments calculated using SFA are compared with those calculated using 3D-FEA. Kurian and Menon (2005) presented correction factors depending on the load location, contact dimension, spacing of the webs and ratio of web thickness to flange thickness [4]. Bernardo and Lopes [5] have developed simple computation technique to predict the behavior of reinforced concrete beams under pure torsion. Both plain and hollow normal strength beams were considered for analysis. The comparison is made among various theoretical methods. From this study, it is seen that concrete core does not affect the ultimate strength of concrete member. The procedure developed gives very good compatible results [5]. Nie and Zhu [6] have introduced beam-truss model for the design and analysis of composite box-girder bridges. The beam-truss models for composite box-girder bridges were prepared, and then the model strategies were formulated using grillage analysis. The beam-truss model predicts the correct behavior of composite box-girder bridges [6]. Rahal [7] has presented a simplified method for the design and analysis of non-prestressed and prestressed concrete beams subjected to pure torsion. The results of the method were compared with experiments performed on reinforced and prestressed concrete beams, and results are quite compatible [7].

3 Space Truss Theory When a moment acts about the longitudinal axis of a member it is called as torsional moment. In case of box-girder bridges, torsion results from eccentric loading. A torsion moment on a structure causes shearing stresses on cross-sectional planes. It is assumed that torsion is resisted by shear flow across the perimeter of the member.

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As in case of tubular sections, the shearing stresses are distributed very efficiently across the cross-section; they are often used in bridges. The space truss analogy, to calculate torsional strength of beams, is a combination of the thin-walled tube analogy with plastic-truss analogy, and it gives a model based on mechanics that is very easy to visualize. The mechanics-based model consists of diagonal concrete shell elements as struts and reinforcing steel at corner as ties. From literature review, it has come to attention that once torsion cracks have occurred, the contribution of concrete in the center of the member in resisting stresses due to torsion is very less. Hence, both solid and hollow members are considered as tubes. So, once the cracks are propagated, beam is considered as a hollow truss with stirrups, longitudinal bars at the corners and diagonal compression struts. The assumptions made while deriving space truss analogy are given by Pandit and Gupta [1]: 1. The twisting moment is assumed to be constant over the entire length of the member. The cross-section of the member is assumed to be free to warp so that the warping torsion is absent. Only St. Venant’s torsion is taken into account. 2. The magnitude of the applied torque is assumed to be greater than the cracking torque but smaller than the torque causing yielding of the reinforcement. In the postcracking range the tensile strength of concrete is ignored. 3. The concrete diagonals are assumed to be adequately supported on the longitudinal bars at the corners of the cross-section. The problem of corner spalling is ignored. 4. The members are assumed to be under-reinforced so that both categories of reinforcement reach yield stresses at failure. 5. The shear resisted by concrete in the compression zone and that by the dowel action of the reinforcement are ignored. 6. The steel and the concrete are assumed to obey Hooke’s law.

3.1 Effective Wall Thickness (td ) In the present study of behavior of hollow beams under combined action of bending and torsion, reinforced concrete box-girder bridges are considered. So, the space truss analogy of only tubular sections is studied. In case of box sections with relatively thick walls, the full thickness is not assumed to contribute in resisting torsional stresses. For such box-girders the effective wall thickness, i.e., thickness of diagonal struts t d is less than original wall thickness t. The effective wall thickness is calculated. according to CEB-FIP Model code [1] as,  td =

Do 6

 (1)

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where Do is the diameter of the largest circle inscribed in the rectangle, and according to Collins [1], td =

3 × Ao 4 × uo

(2)

where Ao is the area of rectangle formed by connecting centers of the corner reinforcement bars and uo is the perimeter of rectangle. Since, the effective wall thickness t cannot be larger than original thickness t, t d should be taken as smaller of Eq. (1), Eq. (2) and the original wall thickness t.

3.2 Inclination of Cracks (α) The inclination of diagonal crack (α) depends upon various parameters, such as spacing of longitudinal and transverse reinforcement, allowable stresses in longitudinal and transverse reinforcement and the amount of longitudinal and transverse reinforcement. α also depends upon whether the reinforcement is uniformly distributed or not. Crack pattern for beams subjected to pure torsion is spiral, and the angle of crack is assumed to be inclined at 45°. Many researchers have given simplified equations to calculate crack inclination for the cases of pure torsion and torsion interacting with bending moment. Consider a case with longitudinal and transverse bars having same cross-section and spacing in all walls of the box-girder. The inclination of diagonal crack for box-girder subjected to pure torsion is given by [1], cot 2 (α) =

Al × fly × s as × f sy × u o

(3)

where l s Al as f ly f sy

Spacing of longitudinal bars. Spacing of stirrups. Total area of longitudinal steel. Area of one leg of stirrup. Yield stress of longitudinal steel. Yield stress of stirrup steel.

Practically, the case of pure torsion is not observed. Most of the times torsion is associated with flexure. The relation between torsion and flexure is derived by unified theory of reinforced concrete by Hsu and Thomas [1]. The crack inclination (α) for the case of combined action of flexure and torsion is given by [1],

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  2 × Alb − Al f × flby × s cot (α) = as × f sy × u o   Mu Al f = Alb × Muo 2

(4) (5)

where Alb Alf f lby Mu M uo

Area of longitudinal steel at bottom. Fictitious area. Yield stress of bottom longitudinal steel. Bending moment at a section. Ultimate bending moment in pure flexure

Alb × fly × jd

(6)

where jd is the lever arm of a box section having effective depth d. From Eq. (4), it can be seen that the inclination of concrete diagonals depends upon the amount of bending moment at a section. The inclination of crack along the span increases with increase in bending moment. In case of simply supported beam with point load at mid-span, crack inclination is maximum at center and it decreases towards the support. The crack inclinations along the span for one wall are calculated and it is assumed that the remaining faces also have same crack inclination. The space truss model formed by inclined diagonal struts and steel ties should be such that, its behavior matches closely with the one considered for study. Lampert and Thurlimann combined the two theories, space truss analogy and plastic theory, to study the behavior of beams and slabs subjected to combined action of bending, shear, and torsion. According to their study, if stresses in the two types of reinforcements are lower than the actual respective yield stresses and stress in concrete diagonals is less than the compressive strength of concrete, the strength based on the space truss model must be lower than the actual ultimate strength in accordance with the lower bound theorem.

4 Modeling of Space Truss Kurian and Menon [3] have done a study on behavior and collapse load of single-cell reinforced concrete box-girder bridges. They have proposed theoretical formulations to predict collapse load of single-cell reinforced concrete box-girder bridges using the concepts of plasticity of structures. For experimental studies, single-cell boxgirder with flanges overhanging on both sides in the cross-section as shown in Fig. 1

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Fig. 1 Reinforcement details of box section used for experimental investigations by Kurian and Menon (2007)

is selected. The results of experiment on the model are presented in the literature. For the present study, the same single-cell box-girder bridge is selected and its behavior is observed.

4.1 Model Details and Experimental Investigations The cross-section and reinforcement details of box-girder are as shown in Fig. 1. The span of the model is 5 m with thickness of both webs and flanges as 60 mm. Ordinary portland cement with characteristic compressive strength approximately 40 MPa was used for concreting. For reinforcement, mild steel rods of 6 mm diameter with yield stress of 636 MPa were selected [3]. The spacing of reinforcement, which was provided in two layers, along both longitudinal and transverse direction was 100 mm center to center. In order to create simply supported conditions at two ends, elastomeric bearing pads were used. In present study, behavior of box-girder under the

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Fig. 2 Single-cell box-girder subjected to eccentric load (P) on top of web

combined action of bending and torsion is observed using space truss analogy. Hence, the experimental results of box-girder subjected to eccentric loading are incorporated in the study. Load was applied gradually on steel plate of size 500 mm × 300 mm at mid-span location of box-girder on top of one web as shown in Fig. 2. The failure of the model was reported to be by the distortion bending collapse mechanism due to yielding of the bottom flange longitudinal reinforcement at a load of 169 kN [3].

4.2 Positioning of Struts and Ties The longitudinal reinforcement is uniform throughout the cross-section as shown in Fig. 3. In order to model space truss of box-girder, longitudinal reinforcement is divided symmetrically and is provided with equivalent diameter steel bar at each corner as shown in Fig. 3. Subsequently, the diameter of the top and bottom longitudinal tie is calculated as shown below. π 

× 36 = 565.2 mm2 4 Diameter of equivalent top corner reinforcement bar = 26.83 mm π  Total area of bottom corner reinforcement = (4 + 7 + 3) × × 36 = 395.64 mm2 4 Diameter of equivalent bottom corner reinforcement bar = 22.45 mm Total area of top corner reinforcement = (4 + 7 + 6 + 3) ×

As mentioned above, crack inclination depends upon ultimate bending moment of box-girder and bending moment at a point. The box-girder is subjected to dead load, i.e., self-weight and eccentric point load as shown in Fig. 2. The point load is applied on one of the web which results   in bending moment along the longitudinal direction and twisting moment, P × b2 in transverse direction as shown in Fig. 4. The space truss shape formed by inclined diagonal struts and corner ties changes with change in applied point load. So, in order to come up with trial space truss shape one requires a trail point load. Hsu and Mo have given an equation [8], based on Thin Tube Theory, to compute cracking torque, T cr , of reinforced concrete rectangle hollow box-girders.

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Fig. 3 a Longitudinal reinforcement division across cross-section.b Equivalent corner longitudinal ties

Fig. 4 Equivalent structural actions on a box-girder subjected to eccentric load

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   Tcr = 2 × Ac × t × 0.2076 × f c

(7)

where Ac Area limited by the outer perimeter of the section. f c Characteristic compressive strength of concrete in MPa. Therefore, Cracking torque, T cr = 58.23 kNm. As beam is not cracked at cracking torque, the ultimate cracking torsion moment, T ult , is more than T cr . So assuming ultimate torque, T ult , as 60 kNm the point load, P, corresponding to this ultimate torque is calculatedas below.   , and assumed Torsion due to point load on the box girder = P × b2 = P × 0.84 2 T ult = 60 kNm. Equating both equations gives value of point load, P = 142.83 kN ≈ 145 kN. For computation of bending moment and crack inclination along the span, MSexcel has been used. Table 1 shows crack inclination along the half span of box-girder. In Table 1 jd × cot(α) is the horizontal projection of inclined diagonal crack. Figure 5 shows the crack pattern along the half span of the box-girder. In Fig. 5, it can be seen that there are three regions, P, Q, and R. In region P most of the cracks have horizontal projection approximately 100 mm. Similarly regions Q and R are corresponding to horizontal projections approximately 200 mm and 300 mm, respectively. In case of region P, horizontal projection is approximately 100 mm and stirrup spacing is 100 mm, which is constant throughout. So, in region P it is assumed to have inclined diagonal struts between two stirrups as shown in Fig. 5. The same assumptions are made for regions Q and R. Now the inclination of struts is obtained, next step is to find the position of ties corresponding to these struts. In Table 1 Crack inclination along half span for box-girder subjected to eccentric load of 145 kN Span (x) (m)

M ux (kNm)

Alf (mm2 )

cot (α)

2.5

193

767

0.185

2.45

190

753

2.35

182

724

2.25

175

2.15 2.05

jd cot (α) (mm)

Tie diasiance (m)

73

50

0.233

92

100

0.307

121

100

695

0.366

145

100

168

666

0.418

166

100

160

636

0.464

184

200

1.85

145

577

0.545

216

200

1.65

130

517

0.616

244

200

1.45

115

457

0.681

270

200

1.25

100

396

0.740

293

300

0.95

76

303

0.822

326

300

0.65

53

209

0.898

356

300

0.35

28

113

0.969

384

250

0.1

8

33

1.025

406

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Fig. 5 Crack pattern and assumed shape of struts for half span of box-girder

region P the struts are assumed to be inclined between two adjacent stirrups, so the ties are provided at 100 mm interval with diameter equivalent to two 6 mm diameter reinforcement bars, as the stirrups are provided in two layers. Similarly for regions P and Q, the ties are provided at 200 mm and 300 mm distance, respectively, with diameter of bar calculated in similar manner to that calculated for region P.

 

2 × π × 36 4  π  The diameter of tie in region P = = 8.48 mm 4



 

2 × 2 × π × 36 4  π  = 12 mm The diameter of tie in region Q = 4



 

3 × 2 × π × 36 4  π  = 14.7 mm The diameter of tie in region R = 4

As load is symmetrical to span, the plane truss, Fig. 6, is assumed to have similar pattern for other half span. Once the plane truss for whole span is obtained, it is provided similarly on all other three sides and thus the space truss is obtained. The

Fig. 6 Final plane truss for half span of box-girder

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Fig. 7 Space truss model for box-girder

above-obtained space truss is modeled using STAAD software and corresponding cross-section properties are assigned to the struts and the ties. The concepts of plastic-truss model are applicable to space truss if the truss is determinate. So it is made sure that space truss model shown in Fig. 7 is determinate. In this case for 1st trail model, number of members (m) = 308, number of joints (j) = 104, and number of support reactions (r) = 4. Therefore Ds = (m + r ) − 3 × j = (308 + 4)—104 × 3 = 0. Thus the space truss model is determinate. Figure 7 shows the isometric, side, and top views of space truss model in STAAD. Once the cross-sections of all the struts and ties are assigned the final 3D view of model looks like as depicted in Fig. 8.

4.3 Load Prescription The load is considered to be applied on one of the webs, so that the box-girder is subjected to bending along longitudinal and transverse direction and twisting moment

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Fig. 8. 3-D view of space truss model

in transverse direction. The eccentric load results into bending moment and twisting moment, the effect of which can be imposed in many ways. The dead load of the box-girder is calculated and provided in the form of point load above each web as shown in Fig. 9. The point load which is applied on one of the webs as shown in Fig. 4 is converted into symmetrical equal point loads on each web to incorporate bending effect, and the twisting moment so generated is converted into moment about longitudinal direction at the center of top flange as shown in Fig. 4. Most of the time, in practical situations, box-girder bridges are subjected to a distributed patch load instead of a point load. In case of the box-girder selected for the present study, in experimental investigations,

Fig. 9 Dead load applied as equivalent point load

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Fig. 10 Load pattern 1

load is applied in the form of distributed load on the patch of size 230 mm × 500 mm. So, there are many possible ways to assign these loads, which will result in equivalent bending and twisting moments, on the box-girder for analysis.

4.3.1

Load Pattern 1

The load is applied in the form of point loads which are symmetrical to mid-span and equal on both the webs. These unidirectional loads results in bending along the longitudinal direction. Similarly, in order to incorporate twisting moment, a pair loads which are acting in opposite direction but equal in magnitude are applied on top of each web as shown in Fig. 10.

4.3.2

Load Pattern 2

In order to simulate bending effect, point loads are applied at mid-span on top of each web. The twisting moment so generated due to eccentricity of loading is divided in the form of two sets of equal and opposite point loads on each web as shown in Fig. 11.

Estimation of Ultimate Strength of Concrete Box-Girder Bridges …

Fig. 11 a Load pattern 2 and b Load pattern 3

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Fig. 12 Load pattern 4

4.3.3

Load Pattern 3

This load pattern is similar to load pattern 1. Only change is, in order to incorporate bending effect, six equal point loads are applied on each web and two symmetrical point loads but opposite in direction are applied to simulate twisting moment as shown in Fig. 11.

4.3.4

Load Pattern 4

This load pattern is similar to load pattern 1. But the load values and their locations are different as shown in Fig. 12.

5 Results and Discussion The box-girder model is analyzed using STAAD for all the above load patterns. The load in each case is increased to the point till the force in the tie reaches to yield value of steel, 636 N/mm2 [3]. As said earlier, if stress in the reinforcement is lower than

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the actual yield stress and stress in concrete diagonal is less than the compressive strength of concrete, the strength based on the space truss model must be lower than the actual ultimate strength in accordance with the lower bound theorem. As the approximate load range is known, for which stirrups are about to reach yield stress, the stresses in inclined diagonal struts should be checked. The concepts of strut and tie are used to check the stresses in struts. The calculation for width of strut is done as shown below. Maximum force in Strut = 42.05 kN Maximum allowable stress in nodal zone, f ce [8] = 0.85 × 0.75 × f c = 0.85 × 0.75 × 40 × 145.03 = 4000 Psi. Maximum allowable stress in strut [8] = 0.85 × 0.75 × f ce = 0.85 × 0.75 × 4000 = 2550 Psi = 17.6 MPa. Effective thickness of box − girder, td = 60 mm Width of strut, ws = (42.05 × 1000)/(60 × 17.6) = 39.81 ∼ = 40 mm. Thus 60 mm × 40 mm cross-section is provided for the strut. This way the crosssections of the struts are assigned in the particular regions, so that all the struts have approximately same value of axial stress. For all the four load patterns dimensions of struts are calculated by above procedure and its pattern is as shown in Fig. 13. The various dimensions of struts throughout the space truss are 35 mm × 60 mm, 50 mm × 60 mm, 75 mm × 60 mm, and 90 mm × 60 mm. Table 2 shows the details of stresses in struts and ties for various load cases. It can be seen that the value of the ultimate load for all the four load patterns is approximately same. From analysis results it can be seen the members for which the axial stresses are about to reach yield value. Table 2 shows the steel ties that reach yield stress value for each load pattern considered. The experimental failure load of the model is 169 kN. Therefore from above analysis results, we can say that ultimate load by space truss analogy is in the range of 140–142 kN.

Fig. 13 a Plane truss for loaded web b Plane truss for web opposite to loaded web

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Table 2 Ultimate load and maximum stresses in struts and ties for each load cases Sr. No

Load pattern

Load (P) kN

Twisting moment (T ult ) kNm

Tie No

Max. compressive stress (MPa)

Strut No

Max. tensile stress (MPa)

1

1

142

59.64

174

638.56

330

17.6

2

2

142

59.64

162

638.5

268

17.38

3

3

141

59.22

174

636

394

17.7

4

4

140

58.8

59

637

331

17.6

6 Conclusions From the detailed study of using space truss analogy for the estimation of collapse load of box-girder bridges the following conclusions are made. The method provides more conservative results for collapse load when compared to those of experimental studies. The choice of using space truss analogy for the estimation of collapse load is found to be better in two aspects. Firstly, cost involved in experimental investigations can be saved. Secondly, this is found to be computationally effective when one compare it with a more sophisticated 3D finite element analysis. It is felt that the method has sufficient potential to be extended for even complex loading cases and further to multi-cellular box-girder bridges.

References 1. Pandit GS, Gupta SP (1991) Torsion in concrete structures 2. Csikos A, Hegedus I (1998) Torsion of reinforced concrete beams, 2nd Int. Ph.D. Symposium in Civil Enginering Budapest. 3. Kurian B, Menon D (2007) Estimation of collapse load of single cell concrete box girder bridge. J Bridge Eng 12:518–526 4. Kurian B, Menon D (2005) Correction of errors in simplified transverse bending analysis of concrete box-girder bridges. J Bridge Eng 10(650):657 5. Bernardo LFA, Andrade JMA, Lopes SMR (2007) Behaviour of concrete beams under torsion: NSC plain and hollow beams. Mater Struct 41:1143–1167 6. Nie JG, Zhu L (2014) Beam-truss model of steel-concrete composite box-girder bridges. J Bridge Eng 19(7):04014023 7. Rahal KN (2001) Analysis and design for torsion in reinforced and prestressed concrete beams. Struct Eng Mech 11(6):575–590 8. Bernardo LFA, Andrade JMA, Lopes SMR (2012) Modified variable angle truss-model for torsion in reinforced concrete beams. Mater Struct 45:1877–1902

Performance Evaluation of Geopolymer Concrete Beam-Column Joints Using Finite Element Methods Aravinda Rajhgopal, Saranya P., Praveen Nagarajan, and A. P. Shashikala

Abstract The beam-column joints are the most critical zones in a reinforced concrete building. They are subjected to forces in all directions during earthquakes, and their behaviour has a significant influence on the structure. Thus, highly ductile materials are required for the design of beam-column joints. Geopolymer concrete is environmentally friendly and contributes to sustainable development. As it attains higher compressive and tensile strengths and increases the durability of structures, it can be an effective substitute to OPC. The use of Finite Element Analysis (FEA) to analyse various structural components is gaining widespread importance nowadays. The aim of this paper is to predict the behaviour of GGBS-dolomite geopolymer concrete exterior beam-column joints using ANSYS. Limited experimental studies have been done and further behaviour is studied using Numerical Methods. For this purpose, constitutive relationships are developed from experimental investigations. The displacements, stresses, strains and forces at any point can be determined under different loading conditions. The deflection characteristics, first crack load and ultimate load of beam-column joints are determined. Non-linear finite element analysis is carried out in several load steps taking care of the force and displacement convergence criteria to study the specimen’s behaviour from first crack load to ultimate load. Keywords GGBS · Dolomite · First crack · Ultimate load · Finite element method

A. Rajhgopal (B) · P. Saranya · P. Nagarajan · A. P. Shashikala National Institute of Technology Calicut, Kozhikode, Kerala, India e-mail: [email protected] P. Saranya e-mail: [email protected] P. Nagarajan e-mail: [email protected] A. P. Shashikala e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_52

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1 Introduction The beam-column joints are the crucial zones when a reinforced concrete building experiences an earthquake. The large forces and moments produced during severe ground shaking leads to diagonal cracking and crushing of concrete in the joint region. Thus, highly ductile materials are required for the design of beam-column joints. Beam-column joints can be classified into interior, exterior and corner joints. The longitudinal bars of a beam need to be anchored into the column to ensure a proper grip, especially in the case of exterior beam-column joints. The capacity of the beam in an exterior joint is governed by the moment created by shear capacity of beam rather than its flexural capacity. Geopolymer concrete is earning attention nowadays for its low CO2 emissions and as a sustainable alternative to ordinary portland cement [1]. The term “geopolymers” was first coined by Joseph Davidovits in 1978 to classify a Three-Dimensional (3D) polymeric network of alumino-silicate binders. An alkaline activator solution is used in the geopolymerisation reaction which acts as a catalytic liquid system. GPC can be cured under ambient conditions thus reducing the usage of water compared to conventional curing methods. Heat cured specimens gained strength immediately but more compressive strength was obtained for specimens which were cured in ambient conditions [2]. A combination of Sodium Silicate (Na2 SiO3 ) and Sodium Hydroxide (NaOH) solutions are commonly used in the production of Geopolymer Concrete (GPC). The compressive strength of GPC specimens increased with the increase in concentration of NaOH solution [3], ratio of Na2 SiO3 to NaOH solutions, mixing time, curing time and curing temperature [4, 5]. GGBS and fly-ash are the most commonly used source materials in the production of GPC. The usage of GGBS and dolomite together as binders is a comparatively new method in the production of GPC. Ground Granulated Blast Furnace Slag (GGBS) is a by-product released from the blast furnaces of the iron industry. It is evident from the experimental studies that inclusion of GGBS enhances concrete workability, durability, density, compressive strength and reduces the setting time [6]. Dolomite is a by-product from rock crushing industry and contains higher CaO content which can significantly improve the strength of concrete [7]. However, it has never been used in the production of GPC. Hence, it is expected that inclusion of dolomite for preparing geopolymer concrete can yield some better results and reduce its disposal problem as well. The present study aims to evaluate the behaviour and performance of steel fibre reinforced dolomite-GGBS geopolymer concrete beam-column joints under monotonic loading using finite element methods. Beam-column joints are modelled by using the Finite Element Method [FEM]-ANSYS to evaluate the response of joints under monotonic loading.[8, 9] Non-linear analysis has been carried out to study the behaviour of the beam-column joint models under gradually increasing monotonic load applied at the bottom of the free end of the beam. The crack/crush patterns, deflections and stresses at various points were evaluated for steel fibre reinforced GPC.

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2 Experimental Details 2.1 Specimen Size A typical 5-storey building was selected and the structural elements were designed. The beam-column joints were designed according to ACI code and the shear strength of the joint was determined. The design and detailing of the reinforcement of all members were done according to IS 456:2000 [10] and SP-16. The code for ductile detailing IS 13,920 was also followed while designing the specimen. The crosssectional dimensions of beam and column were 150 mm × 200 mm. The clear span of the beam was 800 mm and the column height was 1000 mm. The beam-column joint specimens were designed using IS 456:2000 and SP 16 and were scaled down using a scale factor 2. Four 10 mm diameter High Yield Strength Deformed (HYSD) bars were provided as the main reinforcement for column, and two 10 mm diameter HYSD bars were provided as the longitudinal reinforcement at beam top and bottom. 6 mm diameter HYSD bars were provided as transverse ties in columns and stirrups in beams. Spacing of stirrups is also based on calculations to satisfy minimum spacing criteria. The dimensioning and reinforcement detailing of the beam-column joint specimen is shown in Fig. 1.

Fig. 1 Reinforcement details of specimen

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2.2 Test Variables All the material properties that need to be given as input in ANSYS analysis have been found out experimentally. The ratio between GGBS and dolomite is kept as 70:30. Steel fibres were added in proportions of 0.25%, 0.50%, 0.75% and 1% by volume. Modulus of Elasticity, Poisson’s ratio and stress–strain relations were found experimentally as per ASTM procedure. Mix proportioning of GPC and OPC are shown in Tables 1 and 2 respectively [11]. The compressive strength and split tensile strength test of steel fibre reinforced GPC are shown in Table 3. These tests are conducted according to the code IS 516.

3 Finite Element Analysis The finite element analysis is gaining importance in engineering research and development processes. This technique has been used to obtain approximate solutions to a variety of structural problems because of its diversity and flexibility. Finite element analysis provides a tool to simulate the structural components with real-life boundary conditions and loading pattern. In FEM, a complex region can be sub-divided into a number of simple shapes called elements. These elements have a finite number of degrees of freedom. Analysis System (ANSYS) is an advanced finite element analysis and design software that can be used for structural engineering problems. All types of analysis (dynamic, static, linear and non-linear) is supported by ANSYS. The different steps involved in a finite element analysis are as follows: • • • • •

Pre-processing or modelling the structure including meshing Assigning different material properties Assigning the required boundary conditions Solution (Analysis types, loading and solving) Post-processing.

The crack/crush pattern, stresses and deflections at various points can be obtained, and its accuracy can be checked accordingly.

4 Finite Element Modelling 4.1 Element Types The ANSYS elements for different materials are shown in Table 4. Concrete elements. The material model number 1, SOLID65 elements represent concrete material. The multilinear isotropic material uses Von-Mises model to define

% Steel fibres

0

0.25

0.5

0.75

MIX

GPC

SFGPC 0.25

SFGPC 0.5

SFGPC 0.75

277.9

278.6

279.3

280

GGBS (kg/m3 )

Table 1 Mix proportioning of GPC

119.1

119.4

119.7

120

Dolomite (kg/m3 )

238.2

238.8

239.4

240

Solution (kg/m3 )

1013.84

1016.40

1018.95

1021.5

Coarse aggregate (kg/m3 )

641.35

642.97

644.58

646.2

Fine aggregate (kg/m3 )

6.95

6.965

6.98

7

Superplasticizer (kg/m3 )

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Table 2 Mix proportioning of OPC specimen (in kg/m3 ) MIX

Cement

Water

Coarse aggregate

Fine aggregate

Superplasticizer

OPC

555.56

158

1066.18

698

10.25

Table 3 Variation of compressive strength and tensile strength with change in % of steel fibres % Steel fibres

Compressive strength (MPa)

Splitting tensile strength (MPa)

0

72.5

5.35

0.25

73

6.12

0.5

73.4

6.45

0.75

74.7

6.89

1

72

5.1

Table 4 ANSYS element material properties Material model

Real constants

Material

Purpose

1

1

Plain concrete

Concrete

2

2

Reinforcement

Longitudinal Steel (10 mm dia)

2

3

Reinforcement

Stirrups (6 mm dia)

concrete failure. Ec is the Elasticity Modulus of concrete (EX) and ν is the Poisson’s ratio (PRXY). The stress–strain values for the concrete element were developed by using cylinders of height 300 mm and diameter 150 mm cast with the required mix. The stresses and strains obtained from the curve and elastic modulus and Poisson’s ratio calculated according to the code ASTM C469-M14 [12] are given as material properties for the model as shown in Tables 5 and 6 respectively. The specimens with 0.25%, 0.5% and 0.75% steel fibres are designated as SFGPC 0.25, SFGPC 0.5 and SFGPC 0.75 respectively. The value of open and closed shear transfer coefficients usually range from 0 to 1. The value 0 represents a smooth crack or a complete loss of shear transfer while the Table 5 Stress–strain values for multilinear isotropic behaviour of concrete (SFGPC 0.25)

Strain (mm)

Stress (N/mm2 )

0

0

0.000151

6.171

0.000305

11.323

0.00055

18.647

0.0022

56.352

0.0028

58.513

0.0043

58.513

Performance Evaluation of Geopolymer Concrete Beam-Column … Table 6 Elastic modulus and Poisson’s ratio of different specimens

Designation

Modulus of elasticity (N/mm2 ) Poisson’s ratio

GPC

3.86 × 104

0.184

SFGPC 0.25

4.09 × 104

0.198

SFGPC 0. 50 4.24 ×

Table 7 Material properties of concrete (for GPC specimen)

683

104

0.205

SFGPC 0.75

4.39 × 104

0.213

OPC

3.91 × 104

0.185

Density of concrete

2.5 × 10–6 kg/mm3

Modulus of easticity

40,852 N/mm2

Uniaxial cracking stress

5.1 N/mm2

Poisson’s ratio (PRXY)

0.184

Open shear transfer coefficient

0.3

Closed shear transfer coefficient

1

Uniaxial crushing stress

60

Biaxial crushing stress

0

Hydrostatic pressure

0

Hydrostatic biaxial crushing stress

0

Hydrostatic uniaxial crushing stress

0

Tensile crack factor

0.6

value 1 represents a rough crack or no loss of shear transfer. The Poisson’s ratio and modulus of elasticity vary for different specimens and these values are mentioned in Table 6. The uniaxial crushing stress represents the compressive strength of concrete which is 60 MPa. The uniaxial cracking stress represents the modulus of rupture, and the values obtained from experiments are given as input data. The hydrostatic pressure is always 0 as the specimen is not subjected to any kind of hydraulic force. The material properties given for concrete are shown in Table 7. Reinforcement elements. In this beam-column junction, main reinforcement bars of 10 mm diameter and 2-legged stirrups of 6 mm diameter are included. For representing these reinforcements 3-D bar element LINK180 is used. The area of crosssection for main reinforcement and stirrups are 78.5 mm2 and 28.27 mm2 respectively. The yield stress and tangent modulus as shown in Table 8 are the bilinear isotropic hardening properties of the HYSD steel used.

4.2 Beam-Column Joint Modelling and Meshing Using the pre-processor modelling commands, nodes are first generated in the outer dimension of the column specimens. Nodes are also created at the required location

684 Table 8 ANSYS reinforcement material bar properties for LINK180 elements

A. Rajhgopal et al. Linear isotropic Elastic Modulus (Es)

2.1 × 105 MPa

Poisson’s Ratio (PRXY)

0.3

Density (DENS)

7850 kg/mm3

Bilinear isotropic Yield stress

500 N/mm2

Tangent Modulus

0.8

of the main reinforcement bars, and they are joined together so as to form an area at the base of the column. This area is extruded up in the Y-direction so as to form a volume and this volume is offset up to each shear link level. Similarly, the beam portion is extruded in the X-direction as a volume and the model obtained is shown in Fig. 2. All the volumes are meshed using mesh mapped command. After meshing, all the elements have been assigned as Solid65 for concrete, and each node is connected with LINK180 elements for reinforcement bar as shown in Fig. 3.

Fig. 2 ANSYS model of Beam-Column Joint

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Fig. 3 Reinforcement details of the Beam-Column joint model

4.3 Finite Element Discretisation The complex model is sub-divided into a number of small elements and this process is known as meshing. Selection of a suitable mesh density is very important in finite element modelling as this can alter the accuracy of the results obtained. The stresses and strains can be calculated at each node/keypoint after the load is applied. An adequate number of elements should be used in a particular model to obtain more accurate results. This is achieved only when a further change in the mesh density has a negligible effect on the results obtained. A uniform mesh was created using square elements, and the mesh attributes are assigned to the concerned elements. Figure 4 shows the three-dimensional view of the model after meshing.

4.4 Boundary Conditions and Load Application Displacement boundary conditions have to be provided in order to simulate the reallife loading conditions. The column top and bottom nodes have been restrained along the UX, UY and UZ direction in their respective planes to simulate the experimental support conditions. The load applied was at the bottom of the free end of the beam

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Fig. 4. 3-D view of model after meshing

and it was equally distributed as nodal forces to replicate the model similar to the experimental loading conditions. The models have been analysed till it reached its maximum failure capacity where the program cannot be converged.

4.5 Analysis Type Non-linear finite element analysis of the beam-column joint model is carried out. The total load is applied in a series of increments known as load steps. The ANSYS program carries out the analysis and checks for the convergence of the solution. For analysis of the model, static analysis was used. In solution controls, the analysis options were given as small displacement static. Automatic time stepping was selected and the number of sub-steps was given as 100. The maximum number of iterations was given as 20. The convergence criteria for this load step were determined by force and displacement with tolerance values of 0.5 and minimum reference disabled as −1.

Performance Evaluation of Geopolymer Concrete Beam-Column … Table 9 Ultimate load of specimens

Specimen

687

Ultimate load (in kN)

GPC

12.7

SFGPC 0.25

13.5

SFGPC 0.5

14.6

SFGPC 0.75

14.8

OPC

10.1

5 Results and Discussions 5.1 Ultimate Load The ultimate load taken by the different specimens are found from the results. These are shown in Table 9. It was observed that the ultimate failure load was highest for the SFGPC 0.75 specimen and least for OPC specimen. The ultimate load increased considerably with the addition of steel fibres. The ultimate load for SFGPC 0.75 was 46.5% more than the ultimate load of OPC model and 16.53% more than the ultimate load of GPC model without any fibres. The addition of steel fibres increased the ultimate failure load which is indicative of the increased ductility of the joint and arrests the propagation of cracks to a great extent.

5.2 Load–Deflection Characteristics The load–deflection curves obtained from ANSYS post-processing stage for each specimen is evaluated and they are shown in Fig. 5 in comparison to the other specimens. The load in kN is plotted on the Y-axis while deflection in mm is plotted on the X-axis.

5.3 Crack Propagation The non-linear analysis results are available in the general post-processor stage. In the present analysis, the ultimate load at joint failure, the load–deflection characteristics and the crack patterns obtained for the different specimens are studied. The first crack was observed to be very close to the joint in the shear span. During further stages of loading, it was observed that the initial cracks propagated further and new cracks developed at loads closer to the ultimate load. The behaviour of the concrete elements was such that after crushing to a maximum extent, the material showed a softening behaviour in all directions leading to the distortion of the linked

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Load in kN

12 10

OPC 100

8

GPC

6

SFGPC 0.25 4

SFGPC0.5 SFGPC 0.75

2 0

0

5

10

15

20

25

Deflection in mm Fig. 5 Load–Deflection characteristics of different beam-column joint specimens

elements. The propagation of the crack from the initial stages of loading to the ultimate load is clearly shown in Figs. 6(a)–(e). The ultimate load was found to change with change in the material properties, stress–strain behaviour of the material and the type of finite meshing adopted in

(a)

(b)

(d)

(c)

(e)

Fig. 6 Propagation of crack from initial loading stage to ultimate failure load

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689

the model. The crack/crush pattern obtained from the ANSYS model for different specimens are as shown in Fig. 7(a)–(e). From the above crack patterns, it can be observed that there are more number of microcracks formed in SFGPC specimens but the crack width was smaller compared to OPC and GPC beam-column joints. Wider cracks were formed in OPC beamcolumn joints and the propagation of cracks could not be arrested due to the absence

Fig. 7 Crack Pattern for different beam-column joint models. (a) OPC model. (b) GPC model. (c ) SFGPC 0.25 model. (d)) SFGPC 0.50 model. (e) SFGPC 0.75 model

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of steel fibres. This is indicative of the fact that the ductility of the beam-column joints increases with the addition of steel fibres, and this is responsible for the higher ultimate failure of load of the SFGPC specimens.

6 Conclusions • The ultimate load at which the specimens failed was highest for SFGPC 0.75 beam-column joint model. This ultimate load was 46.5% more than the ultimate load of OPC model and 16.53% more than the ultimate load of GPC model without any fibres. • The addition of steel fibres increased the ultimate failure load which is indicative of the increased ductility of the joint and arrested the propagation of cracks to a great extent. • The area under the load–deflection curve was also high for SFGPC beam-column joints which increased its ductility compared to OPC and GPC models. • From the different crack patterns observed, it can be concluded that there are more minor cracks produced in SFGPC joints but the presence of steel fibres restricted the crack propagation. On the other hand, fewer and wider cracks formed in the OPC joints.

References 1. Meyer C (2009) The greening of the concrete industry. Cement Concr Compos 31(8):601–605 2. Sarker PK, Haque R, Ramgolam KV (2013) Fracture behaviour of heat cured fly ash based geopolymer concrete. Mater Des 44:580–586 3. Rattanasak U, Chindaprasirt P (2009) Influence of NaOH solution on the synthesis of fly ash geopolymer. Miner Eng 22(12):1073–1078 4. Hardjito D (2005) Studies on fly ash-based geopolymer concrete. Ph.D. thesis. Curtin University of technology 5. Hardjito D, Vijaya Rangan B (2005) Development and properties of low-calcium fly ash-based geopolymer concrete. 6. Nath P, Sarker PK (2014) Effect of GGBS on setting, workability and early strength properties of fly ash geopolymer concrete cured in ambient condition. Constr Build Mater 66 163–171 7. Szybilski M, Nocu´n-Wczelik W (2015) The effect of dolomite additive on cement hydration. Procedia Eng 108:193–198 8. Ganesan N, Indira PV, Sabeena MV (2014) Behaviour of hybrid fibre reinforced concrete beam–column joints under reverse cyclic loads. Mater Des 1980–2015(54):686–693 9. Lowes LN, Altoontash A (2003) Modeling reinforced-concrete beam-column joints subjected to cyclic loading. J Struct Eng 129(12):1686–1697 10. IS 456-2000 Indian Standard plain and reinforced concrete-code of practice 11. Ng TS, Stephen JF (2013) Development of a mix design methodology for high-performance geopolymer mortars. Struct Concr 14(2):148–156 12. ASTM C469-M14-standard test method for static modulus of elasticity and poisson’s ratio of concrete in compression

Numerical Studies on GGBS–Dolomite Geopolymer Concrete Short Columns Akash Kumar Behera, P. Saranya, A. P. Shashikala, and Praveen Nagarajan

Abstract In recent years, Geopolymer Concrete (GPC) is gaining popularity as a greener construction material compared to conventional concrete which is made up of Ordinary Portland Cement (OPC). Many studies have been conducted on fly ash and GGBS-based geopolymer concrete. The use of GGBS and dolomite to form GPC will increase the workability of concrete. In addition to this, the overall cost is also expected to come down as dolomite is a cheaper industrial waste. Since the strength development mechanism of GPC is different from that of OPC binder, it is necessary to obtain a suitable constitutive model to predict the load–deflection behaviour and strength of GPC structural members. The aim of this paper is to predict the behaviour of short columns subjected to axial load using ANSYS, a commercially available finite element software. The analysis determines the displacement, stresses, strains and forces at any point under different boundary conditions. The deflection, ultimate load and crack pattern have been determined from the model. Keywords Dolomite · GGBS · Geopolymer Concrete (GPC) · Finite Element Method · Short Columns

1 Introduction Concrete is a significant contributor to greenhouse gases and the resulting emission from cement production is expected to increase more rapidly in the coming future, which indicates its impact on global warming indices. Hence to overcome the A. K. Behera (B) · P. Saranya · A. P. Shashikala · P. Nagarajan Department of Civil Engineering, National Institute of Technology Calicut, Kozhikode, India e-mail: [email protected] P. Saranya e-mail: [email protected] A. P. Shashikala e-mail: [email protected] P. Nagarajan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_53

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problem, many solutions have come out to replace cement partially or completely for the production of concrete, which is greener as compared to conventional methods. Geopolymer is a new binder. It is generally produced from industrial by-products such as fly ash, GGBS and capable of replacing cement by 100% in the production of concrete which makes it an efficient and economical option. GPC is recognized well for its low CO2 emission. Materials containing silicon and aluminium in their chemical composition when get synthesized with alkaline solution produce a cementitious paste. A three-dimensional polymeric chain results from the chemical reaction of aluminosilicate material under alkaline condition. Concrete can be prepared by adding coarse aggregate and fine aggregate to this cementitious paste and is termed as GPC. The chemical composition of the alkaline activators and source materials normally affects the final product of geopolymerization. In the past, many investigators have added GGBS with fly ash to produce geopolymer concrete and have got excellent results [1]. Dolomite is a by-product from the rock crushing industry and contains higher CaO content which can significantly improve the strength of concrete. Moreover being an industrial by-product, the overall cost of concrete production can also be expected to come down with its addition [2]. A design mix for GPC can be found out by trial and error method [3]. GPC concrete shows higher strength compared to OPC concrete of the same grade [4]. Addition of steel fibres decreases workability and water absorption but improves mechanical strength [5, 6]. With proper inputs, finite element analysis of reinforced concrete structure obtains credible results. For the application of GPC in the practical field, it is essential to study its performances as different structural members. Column is a very primary member in any structural model which predominantly transmits the weight of the structure through compression. In places of structures being subjected to lateral loads, columns need to be designed considering the ductility provisions in a precise manner. In this report, a detailed numerical study on the GGBS–Dolomite geopolymer concrete columns using commercially available software, ANSYS is carried out to investigate its behaviour along with experimental studies.

2 Experimental Investigation The material properties which are required for the analysis in ANSYS have been found out experimentally. By trial and error, a mix proportion has been reached. To understand the behaviour of concrete with varying fibre content, a number of cubes and cylinders have been tested. All the GPC specimens have been tested on the twenty-eighth day of ambient curing. 28 days of curing with water have been done for OPC specimens. Table 1 shows the mix proportion considered for the present study. OPC concrete mix in Table 1 has been designed as M60 grade concrete. GPC

280

279.3

278.6

277.9

–

GPC

SFGPC 0.25

SFGPC 0.50

SFGPC 0.75

OPC

GGBS (kg/m3 )

Mix

–

119.1

119.4

119.7

120

Dolomite (kg/m3 )

Table 1 Mix proportioning of GPC and OPC

555.56

–

–

–

–

Cement (kg/m3 )

–

238.2

238.8

239.4

240

Solution (kg/m3 )

158

–

–

–

–

Water (l/m3 )

1066.2

1013.8

1016.4

1018.9

1021.5

Coarse aggregate (kg/m3 )

698

641.35

642.97

644.58

646.2

Fine aggregate (kg/m3 )

10.25

6.9475

6.965

6.9825

7

Superplasticizer (kg/m3 )

0

58.875

39.25

19.625

0

Steel fibres (kg/m3 )

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Stress (MPa)

50 40 30

GPC SFGPC 0.25

20

SFGPC 0.5 10

SFGPC 0.75 OPC

0 0

0.001

0.002

0.003

0.004

0.005

0.006

Strain Fig. 1 Stress–strain curve

concrete proportion has also been selected to show similar kind of strength as that of M60 grade OPC concrete. Mixes designated as SFGPC 0.25, SFGPC 0.5 and SFGPC 0.75 represent GPC mixes with 0.25%, 0.5% and 0.75% steel fibres, respectively. With further increase in fibre content, workability decreased significantly and has not been considered in the study. Three cylinders of each proportion have been cast to find out the stress–strain curve and are demonstrated in Fig. 1. From the stress– strain diagram, Young’s Modulus and Poisson’s ratio have been calculated as per the guidelines given in ASTM C469M-14.3 and are listed in Table 2. As per the Indian standard, all the hardened properties (compressive strength, flexural strength and split tensile strength) have been calculated and are listed in Table 3. A fivestoried building is designed using STAAD-PRO. The column size and reinforcement requirements from the design are scaled down with a scale factor of 3 to obtain the final model which has been considered in the present study and is demonstrated in Fig. 2. Table 2 Modulus of elasticity and Poisson’s ratio

Designation

Modulus of elasticity (N/mm2 ) Poisson’s ratio

GPC

3.86 × 104

0.184

SFGPC 0.25

4.09 × 104

0.198

SFGPC 0. 50 4.24 × 104

0.205

SFGPC 0.75

4.39 ×

104

0.213

OPC

3.91 × 104

0.185

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Fig. 2 Dimension of column

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Designation

Workability (mm)

Compressive strength (MPa)

Split tensile strength (MPa)

GPC

155

72.5

5.35

SFGPC 0.25

143

73

6.12

SFGPC 0.50

130

73.4

6.45

SFGPC 0.75

112

74.7

6.89

OPC

90

71.5

5.1

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3 Numerical Investigation A numerical investigation is carried out on columns prepared from GGBS–dolomite GPC using ANSYS to study their behaviour under compressive load. The analysis of structure in ANSYS is performed in three different phases, namely, preprocessing phase, solving phase and post-processing phase. In pre-processing, the material is modelled by defining the material using the properties such as element types (SOLID65, SOLID45, LINK8, etc.), real constants (cross-sectional area, initial strain, etc.) and material models (density, modulus of elasticity and Poisson ratio). The non-linearity parameters are defined under the material model section. Using all these properties, physical modelling is done to replicate the original specimen. Analysis solver is normally used for solving the model. The loads and constraints for which the specimen needs to be solved are defined here. The type of analysis (static, fatigue, harmonic, etc.) and solution control values (number of iterations, non-linearity, etc.) are also defined in this stage. In the post-processing stage, analysis results such as deformations, stresses, crack patterns, etc. are obtained either in contour plots or in list form. In this study, the model given in Fig. 2 is analysed with different proportioned concrete as explained in Table 1. To find out the results, different ANSYS models have been developed for different concrete material. The material properties found experimentally as explained in Sect. 1 has been entered as input for different models to represent different concrete materials.

3.1 Concrete––SOLID65 For representing column, solid brick elements were used. Depending upon the characteristics of the structure, the solid features such as the geometry, node locations and element coordinate system are changed. In this study, SOLID65 is used for representing concrete which has eight nodes with three degrees of freedom at each end––translations in X, Y and Z directions. It is assumed that the concrete is homogeneous throughout and hence real constant 1 has been defined and assigned to represent concrete. Further, ‘material model 1’ has been defined, and under this material model, all the structural properties of concrete have been assigned. All the data that has been entered in this current model to define the materials has been tabulated in Table 4. The solid models of the column are demonstrated in Fig. 3a. The material properties entered for representing the properties of SOLID65 element have been found out experimentally as explained in Table 4. The solid model as demonstrated in Fig. 3a is the same for all ANSYS model; the properties provided to represent the SOLID65 element in each ANSYS model is different.

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Table 4 Properties for SOLID65 element Description

GPC

SFGPC 0.25

SFGPC 0.5

SFGPC 0.75

OPC

Density of concrete

2.5 × 10−6 kg/mm3

2.5 × 10−6 kg/mm3

2.5 × 10−6 kg/mm3

2.5 × 10−6 kg/mm3

2.5 × 10−6 kg/mm3

Modulus of elasticity (EX )

3.86 × 104

4.09 × 104

4.24 × 104

4.39 × 104

3.91 × 104

Uniaxial cracking stress

5.35

6.12

6.45

6.89

5.1

Poisson’s ratio (PRXY)

0.184

0.198

0.205

0.213

0.185

Open shear transfer coefficient

0.3

0.3

0.3

0.3

0.3

Closed shear transfer coefficient

1

1

1

1

1

Uniaxial crushing stress

72.5

73

73.4

74.7

71.5

Biaxial crushing stress

0

0

0

0

0

Hydrostatic pressure

0

0

0

0

0

Hydrostatic biaxial crushing stress

0

0

0

0

0

3.2 Reinforcements––LINK8 In the column modelling, longitudinal reinforcement and lateral ties for columns are included. For representing these reinforcements, 3-D spar element LINK8 is used. For main steel 12 mm diameter bar and for stirrups 8 mm diameter bars have been used. Real constant 2 and 3 have been defined to represent main steel and lateral ties, respectively, and the respective cross-sectional area has been provided. ‘Material model 2’ has been defined to enter the structural properties of steel. Arrangement of LINK8 material is demonstrated in Fig. 3b. Under the ‘material model 2’ density, linear elastic properties and bilinear stress–strain properties of steel have been defined. For each ANSYS model, same grade steel (Fe 500) and the same arrangement has been considered.

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(a)

(b)

(c)

Fig. 3 a Concrete model. b Reinforcement model. c Meshed column model

3.3 Meshing and Loadings The elements created in the desired location by connecting through the nodes of the concrete element such that concrete and steel mesh share the same nodes, and concrete occupies the same regions which were occupied by reinforcements. The minimum size of elements created is 25 mm, and the total number of elements created is 2656. The extreme bottom nodes were constrained translation in X, Y and Z directions. The extreme top nodes were constrained in the X and Z directions. Vertically downward loads have been applied at the top as nodal loads. For the analysis, 500 ton is applied to the columns. The number of nodes present at the top surface where the load was supposed to be applied was 81; hence, the nodal load applied on these nodes was 6.25 tons downward. Figure 3c shows the meshed column.

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3.4 Analysis After the creation of the model in ANSYS, the solution controls are set before running the analysis. For the analysis of the model, static analysis was used. Then, the solution control analysis option has been set as small displacement static. Time at the end of the load step is set as 1. Time step size and the minimum time step is provided as 0.01. Max time step is set as 0.1.

4 Results and discussions From the analysis, ultimate loads, load–deflection behaviour and crack pattern have been found out. The ultimate load found for each ANSYS model is listed in Table 5. Load–deflection behaviour is demonstrated in Fig. 4. From these results, following observation is made. Table 5 Ultimate load

Description

Ultimate Load (kN)

GPC

2374

% deviation from OPC 2.55

SFGPC 0.25

2546

9.98

SFGPC 0.50

2630

13.61

SFGPC 0.75

2762

19.31

OPC

2315

0.00

350 300

Load (×10 kN)

250 200 GPC

150

SFGPC 0.25 SFGPC 0.5

100

SFGPC 0.75 50 0

OPC 0

0.05

Fig. 4 Load–deflection curve

0.1 0.15 0.2 Deflection (×10 mm)

0.25

0.3

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GPC concrete column proved to have higher ultimate strength than that of OPC column. In general, the strength of the column increased with increase in steel fibre content. It may also be noted that the maximum increase in ultimate load due to the addition of steel fibre is around 20% which is obtained at a volume fraction of 0.75%. From the curve, it is observed that the effect of fibres is negligible until the first crack load. After the first crack, the steel fibres arrested the crack propagation and offered confining reaction which contributed to the increase in ultimate load. Moreover, the area under the load–deflection curve increased with increasing fibre content. This indicates that concrete is becoming tougher with the addition of fibres. The crack pattern developed in the column during failure as predicted by ANSYS is demonstrated in Fig. 5a–e. It can be seen that the number of microcracks developed in GPC columns are less when compared to OPC columns at the time of failure. Further with the increase in fibre content, the microcracks are found to increase in SFRGPC models. This indicates that with an increase in fibre content the strength of concrete is more efficiently used to resist the load.

(a)

(b)

(c)

(d)

(e)

Fig. 5 a Crack pattern for GPC. b Crack pattern for SFGPC 0.25. c Crack pattern for SFGPC 0.5. d Crack pattern for SFGPC 0.75. e Crack pattern for OPC

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5 Conclusion Following conclusions are made from the study. • The Ultimate load of GPC concrete column is found to be higher than OPC concrete columns. With the addition of steel fibre up to 0.75% by volume of concrete, the ultimate load further increased. Further increment of fibre content is not recommended because the workability of concrete becomes significantly low. • With the addition of steel fibre, the area under the load–deflection curve is increased significantly. This indicates that the concrete becomes tougher with steel fibre addition. • The number of microcracks is observed to increase with the increase in fibre content. This indicates that the addition of steel fibre helps in utilizing the strength of concrete more efficiently.

References 1. Nath P, Sarker PK (2014) Effect of GGBFS on setting, workability and early strength properties of fly ash geopolymer concrete cured in ambient condition. Constr Build Mater 66:163–171 2. Azimi EA, Abdullah MMAB, Ming LY, Yong HC, Hussin K, Aziz IH (2016) Review of dolomite as a precursor of geopolymer materials. In: MATEC web of conferences, vol. 78. EDP Sciences, p 01090 3. Anuradha R, Sreevidya V, Venkatasubramani R, Rangan BV (2012) Modified guidelines for GPC mix design using Indian standard 4. Rajamane NP, Nataraja MC, Lakshmanan N (2011) An introduction to GPC. BIOGRAPHIES Prof. Vishwajeet A. Kadlag, ME Structure Co-ordinator, Civil Engineering Dept., Dr D. Y Patil School of Engineering and Technology, Pune, India. Mr Mahesh Shewale, BE student, Civil Engineering, Dr D. Y Patil School of Engineering and Technology, Pune, India 5. Ganesan N, Indra PV, Santhakumar A (2013) Engineering properties of steel fibre reinforce GPC. Adv Concrete Construct 1(4):305–318 6. Abdullah MMAB, Faris MA, Tahir MFM, Kadir AA, Sandu AV, Isa NM, Corbu O (2017) Performance and characterization of GPC reinforced with short steel fibre. In: IOP conference series: materials science and engineering, vol. 209, No. 1. IOP Publishing, p. 012038

Effect of Double Plastic Hinges on Seismic Performance of Strengthened Column C. U. Aswin and Alice Mathai

Abstract The RCC bridge columns are generally severely damaged during disastrous earthquakes. Traditionally, strengthening methods by bonding with steel plate, FRP or other strengthening materials are employed in RCC columns. The deformation capacity is improved for strengthened column, and they can withstand large earthquake due to the energy dissipation effect of the non-elastic phase. The plastic hinge formation is a major factor in the deformation of the column and plays an important role in the seismic performance of the column. Strengthening partial height of column with steel plate and by optimizing the plate thickness, two plastic hinges could be formed simultaneously at two positions, one at the column bottom and other at the upper edge of the strengthening steel plate. A cantilever bridge column of rectangular hollow section is modelled in ABAQUS, and a comparative study on the seismic performance of the unstrengthened and strengthened columns with single and double plastic hinge is done. In the column, the double plastic hinge formation improved the ultimate deformation, stiffness and its strength capacity. Keywords Seismic performance · Strengthened column · Double plastic hinges

1 Introduction Bridges tend to give the impression that they are of rather simple structural systems. They have a simple structural form compared to buildings, which can satisfy their functional requirement as well. Functionally efficient bridge structures can hence be developed without compromising with its aesthetics. Even though this structural simplicity makes their design easier, bridges, especially those constructed in prestressed or reinforced concrete, under seismic attack have not performed very well historically. C. U. Aswin (B) · A. Mathai Mar Athanasius College of Engineering, Kothamangalam, India e-mail: [email protected] A. Mathai e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_54

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Generally, the RC bridge columns are heavily damaged during severe earthquakes. After severe earthquakes, the investigation of seismic damage on major highway bridges shows that the main type of damage in the bridges is the column damage. Bridges usually have no or low redundancy, as a result of which failure of one element of the structure or a connection would likely result in the collapse of the entire structure. The lower redundancy makes the seismic response prediction simpler while it also tends to make the results more sensitive to design errors. The common strengthening methods for RC column include bonding with FRP [1–3] or steel plates [4, 5]. The seismic performance of reinforced concrete columns is studied. A great emphasis is made on the improvement of the seismic performance in terms of deformation capacity, which is found to be better for strengthened columns [6, 7]. The non-elastic phase in the structure allows for greater energy dissipation and enables the structure to withstand large earthquakes without failure [8]. Plastic hinge formation mainly contributes to this deformation of the column and plays an important role in its seismic performance. In his study on post-tensioned precast. concrete segmental bridge columns, Chung-Che Chou approved the possibility of formation of two plastic hinges in cantilever structures [9]. Seismic design of structures makes use of a combination of ductility and strength. Such design involves formation of plastic hinges in specified areas in the structure and is designed to withstand inelastic deformation, while the rest of the structure undergoes elastic deformation. Yielding in these zones predominantly determines the dynamic performance of the structure. The approach where the plastic hinge regions are selected and accordingly detailed while the undesirable plastic hinge locations, or undesirable inelastic deformation mechanism, such as shear, are avoided is known as capacity design. In this paper, columns were modelled in ABAQUS, and analysis was carried out for the columns under cyclic loading to study the effect of double plastic hinges on seismic performance of the strengthened column.

2 Finite Element Modelling and Analysis The strengthened and unstrengthened columns are modelled in ABAQUS and are analysed under cyclic loading. The strengthening is done using steel plates, and the double plastic hinges are obtained by optimizing the strengthening steel plate thickness.

3 Section Details A scaled model of a highway bridge in Fujian, China is used for modelling. The bridge column is of 45 m height and has a box section, 4.5 m × 6.25 m. A scaling factor of 1:14 is adopted. The scaled model is as shown in Fig. 1, with longitu-

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Fig. 1 Section details

dinal reinforcement of 288 and having stirrups of 6 mm diameter at a spacing of 100 mm. M50 grade of concrete is used having elastic modulus of 35.4 GPa. The elastic modulus of the reinforcement and steel plate used is 210 GPa and 207 GPa, respectively.

3.1 Modelling Modelling of strengthened and unstrengthened columns was done using ABAQUS 6.14–2. Concrete was defined as 3D deformable solid extrusion type element (Homogenous). Reinforcement was defined as beam element. Bond between concrete and reinforcement was included by defining embedded region. Interaction between the column face and strengthening steel plate was defined as a tie constraint. Encastre boundary condition was defined at the fixed end. Figure 2a shows the model of the reinforcement cage provided in both the strengthened and unstrengthened columns. Figure 2b, c show the model of unstrengthened column and a column strengthened with steel plate at the fixed end, respectively. The strengthening steel plate is given to a height of L/4 from the base of the column. Hex meshing was adopted, having meshing element for the column as C3D8R, which is an eight-node linear brick element with reduced integration and hour glass control. Element B31 is used in reinforcement for meshing. It is a two-node linear beam element in space. Fixed boundary condition was provided at one end of the

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(a)

(b)

(c)

Fig. 2 a Reinforcement model, b Column model, c Strengthened column model

column. Displacement controlled cyclic loading consisting of a single cycle of 10 mm deflection was applied at the free end of the column. The loading cycle is as shown in Fig. 3. An area load of 2.234 N/mm2 was provided axially at the free-end surface. Three columns were considered: unstrengthened column, without any strengthening steel plate, strengthened column, with a strengthening steel plate of 4 mm thickness and optimized column, with a steel plate thickness of 0.44 mm. Each of the columns considered is subjected to the loads as given above, and the corresponding stress and strain patterns are obtained. The regions of strain concentration were observed for each of the considered columns, and the variation of location of maximum strain concentration with the addition of strengthening plate for various thicknesses was observed.

Effect of Double Plastic Hinges on Seismic Performance of Strengthened Column

707

Fig. 3 Loading cycle

4 Results and Discussions Figure 4a, b show the stress and strain patterns in concrete and Fig. 5a, b show the stress and strain patterns in the reinforcement cage for the unstrengthened column.

Fig. 4 a von-Mises’ stress in concrete and b Maximum principal strain in concrete for the unstrengthened column

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Fig. 5 a von-Mises’ stress in rebar and b Maximum principal strain in rebar for the Unstrengthened column

The region of strain concentration was near the fixed end of the column for both concrete and the reinforcement suggesting the formation of plastic hinge at the base. Figure 6a, b show the stress and strain patterns in the column strengthened with steel plate of 4 mm thickness. Figure 7a, b show the stress patterns in concrete and Fig. 8a, b show the strain patterns in the reinforcement cage for the strengthened column. The strain concentration shifted from the fixed end in the unstrengthened column to the region at the top of the strengthening steel plate in the strengthened column. For the same displacement, the stress in concrete is found to be greater in the strengthened column compared to the unstrengthened column due to stiffening action of the strengthening steel plate. The strain in the fixed end for the reinforcement is lower in the case of the strengthened column. The strengthening plate is having greater stress and strain concentration at the fixed end. Figure 9a, b show the stress and strain patterns in concrete for the optimized column, strengthened with a steel plate of 0.44 mm thickness. Figure 10a, b show the stress and strain patterns in the reinforcement cage for the optimized column.

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Fig. 6 a von-Mises’ stress and b Maximum principal strain for the strengthened column

For the optimized column with an optimum steel plate thickness of 0.44 mm, the region of strain concentration is obtained both near the fixed end of the column and near the edge of the strengthening steel plate as observed in Figs. 9b and 10b suggesting the formation of double plastic hinges. The location of the region where the maximum strain concentration occurs in the columns and the corresponding strain in the reinforcement bars at these locations are shown in Table 1.

5 Conclusions The possibility of formation of double plastic hinges in an RC column is studied in this paper. Satisfactory stress patterns are obtained for the strengthened and unstrengthened models, and the following conclusions can be drawn from the analysis results.

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Fig. 7 a von-Mises’ stress in concrete and b Maximum principal strain in concrete for the Strengthened column

1. Region of strain concentration shifted from the fixed end in the unstrengthened column to the end of the strengthening plate in the strengthened column. 2. The strengthening of column with steel plate improved the shear capacity of the column when compared with the unstrengthened column. For the same displacement, the column stiffness is increased. 3. Strain concentrations are obtained simultaneously at the fixed end and at the end of the strengthening plate in the optimized column. Hence, double plastic hinges can be formed in optimized column.

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Fig. 8 a von-Mises’ stress in rebar and b Maximum principal strain in rebar for the strengthened column

Fig. 9 a von-Mises’ Stress in concrete and b Maximum principal Strain in concrete for the Optimized column

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Fig. 10 a von-Mises’ Stress in rebar. b Maximum principal strain in rebar for the optimized column

Table 1 Location of region of maximum strain concentration for the columns Column

Location of max. Strain concentration region from base (in m)

Max strain in rebar

Unstrengthened

0

5.5 × 10−4

Strengthened

0.8

5.39 × 10−4

Optimized

0 0.8

5.1 × 10−4 5.1 × 10−4

References 1. Wu ZS, Zhang DC, Karbhari VM (2010) Numerical simulation on seismic retrofitting performance of reinforced concrete columns strengthened with fibre reinforced polymer sheets. Struct Infrastruct Eng 2. Tastani SP, Pantazopouloua SJ (2007) Detailing procedures for seismic rehabilitation of reinforced concrete members with fiber reinforced polymers. Eng Struct 30(2):450–461 3. Pantelides CP, Gergely J (2002) Carbon-fiber-reinforced polymer seismic retrofit of RC bridge bent: design and in situ validation. J Compos Construct 6(1):52–60 4. Sezen H, Miller E (2007) Retrofit of circular reinforced concrete columns using FRP, steel and concrete jackets. New Horizons and Better Practices, Structures Congress

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5. Rodrigues H, António A, André F, Patrício R (2015) Seismic behavior of strengthened RC columns under biaxial loading: an experimental characterization. Construct Build Mater 6. Alaedini S, Kabir MZ, Hejabi H (2016) Seismic ductility evaluation of shear- deficient RC Frames strengthened by externally bonded CFRP sheets. KSCE J Civ Eng 7. Ozcan O, Binici B, Ozcebe G (2010) Seismic strengthening of rectangular reinforced concrete columns using fiber reinforced polymers. Eng Struct 8. Ouyang LJ, Gao WY, Zhen B, Lu ZD (2007) Seismic retrofit of square reinforced concrete columns using basalt and carbon fiber-reinforced polymer sheets: a comparative study. Compos Struct 162:294–307 9. Chou C-C, Chang H-J, Hewes JT (2012) Two-plastic-hinge and two dimensional finite element models for post-tensioned precast concrete segmental bridge columns. Eng Struct 46:205–217

Plastic Hinge Relocation in RCC Double-Slotted Beam Connection Anandhu P. Haridas and Alice Mathai

Abstract Plastic hinge relocation is the technique to relocate the plastic hinge away from the beam-column junction, i.e. to the beam. Over last few years, several plastic hinge relocation techniques were introduced to avoid penetration of strain into beamcolumn junction and to ensure strong column–weakbeam behaviour. The main drawback of these techniques is difficulty in prediction of centre of rotation of beam element. In this paper, an innovative type of beam-column connection known as Double-Slotted Beam (DSB) is developed, as a plastic hinge relocation technique with high level of accuracy in prediction of centre of rotation. Here, the beam consists of two vertical slots at top and bottom fibres of beam member. The slots are introduced to control the location of centre of rotation. The location of vertical slots is shifted from face of column towards the beam in each specimen, in order to relocate plastic hinge away from beam-column junction. Finite element analysis of beam-column connection with and without vertical joints was done using ABAQUS, in order to study the behaviour of structure under seismic loading. Displacement-controlled cyclic analysis of DSB connection was conducted. The double-slotted beam connection achieved plastic hinge relocation, minimum damage in concrete and reduction in deterioration of bond in joint. Keywords Double-slotted beam system · Plastic hinge relocation · Strong column–weak beam system

1 Introduction Earthquakes can cause great damage in terms of life, money and failures of structures. The principal objective in seismic design of reinforced concrete structures is to provide a system that allows significant amounts of energy to be dissipated in a controlled ductile mechanism. Ye and Qu [1] studied the local and global failure mechanisms of building structures under earthquake. For a framed structure, the A. P. Haridas (B) · A. Mathai Department of Civil Engineering, Mar Athanasius College of Engineering, Kothamangalam, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_55

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most desirable mechanism is a ‘strong column–weak beam’ system with ductile flexural yielding occurring in the beams. According to Paulay and Priestley [2], a capacity design procedure can ensure that this mechanism is maintained throughout a major earthquake with reasonable protection against column yielding mechanisms or brittle failures. In a conventionally reinforced frame structure under seismic loading, plastic hinges generally occur at the ends of the beams where moments are highest. Ductility requirements result in wide cracking, large steel strains and penetration of yield into the beam-column joints particularly after a number of load reversals. Possible undesirable consequences of this behaviour are sliding shear failure in the beam, loss of bond of flexural steel in the joint and a shear failure in the joint itself. Sliding shear failures can be controlled by diagonal reinforcing in the plastic hinge zone. Joint behaviour can be improved by diagonal reinforcing in the joint itself, or by relocating the beam hinge away from the joint so that it remains elastic. Yan and Au [3] conducted nonlinear dynamic analysis of frames with plastic hinges at arbitrary locations. In the case of ductile frames, it is undesirable to have plastic hinges in the columns because of the following reasons. Plastic hinges in the beams have larger rotation capacities than in columns. Mechanisms involving beam hinges have larger energy absorptive capacity. Eventual collapse of a beam generally results in a localized failure, whereas collapse of a column may lead to a global failure. Columns are more difficult to straighten and repair than beams in the event of residual deformation and damage. The structural system should be so designed such that the plastic hinges should be formed at suitable locations that result in the failure of the individual elements, but will not lead to progressive collapse. According to Ahmadi and Kodag [4], the engineering concept requires a ductile material, and the facility for the structure to deform plastically at least at key locations. One suitable method is to improve the failure strain of concrete by confining reinforcement. According to Ye and Qu [1], the designability of structural systems means that the failure mechanism of the structure system under unexpected disasters can be designed. The control of the failure mechanism is to make the structure system fail under earthquake following a desirable failure mechanism. An effective method to increase seismic resistivity in structures is by plastic hinge relocation.

1.1 Double-Slotted Beam System Oudah and El-Hacha [5] introduced an innovative plastic hinge relocation technique with high level of accuracy in determining the centre of rotation. It is called the Double-Slotted Beam (DSB). The system consists of two vertical slots each at bottom and the top sides of the beam member. The DSB system with vertical slots at face of column is illustrated in Fig. 1. Oudah and El-Hacha [6] conducted experimental study of single-slotted beam system also. Large amount of diagonal reinforcement is provided in the slot region,

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Fig. 1 Schematic drawing of the DSB system in RC frame [5]

in order to enhance the shear resistance and avoid sliding shear failure. The diagonal reinforcement is designed such that it will remain elastic during the plastic rotation of the beam. The top and the bottom reinforcements act as energy dissipation devices since they both yield in tension and compression. Byrne and Bull [7] presented several issues with current design provisions for slotted beams. Amount of top and bottom reinforcement provided was less than diagonal reinforcements. As a result, the system fails by the yielding of top and bottom reinforcement rather than the diagonal reinforcement. The top and bottom reinforcement was debonded from the concrete for a distance of half the depth of the beam from the slot. Since concrete is present only at the vicinity of diagonal reinforcement and steel was debonded from concrete at the yielding region, concrete damage anticipated will be less. Styrofoam can be used at the locations of the vertical slots during construction to maintain the depth and the width of the vertical slots. In this paper, the effectiveness of double-slotted beam system as a plastic hinge relocation technique was evaluated.

2 Modelling and Analysis A beam-column junction is modelled in ABAQUS with a beam size of 450 × 600 mm and column size of 450 × 660 mm. Both concrete and reinforcements were modelled with adequate material properties and constraints.

2.1 Material Properties and Detailing Figure 2 shows the detailing of the frame used in the study. 15 mm bars were used as longitudinal reinforcement and 20 mm bars were used as diagonal reinforcement. Stirrups were made with 10 mm diameter bars. The modulus of elasticity was 187.1, 180.5 and 194.8 GPa, the yield stress was 484.8, 484.0 and 435.6 MPa, the yield strain was 0.0026, 0.0027 and 0.0022 and the ultimate stress was 730.4, 729.5 and 588.2 MPa for the 10, 15 and 20 M bars, respectively. Concrete modulus of elasticity was defined as 33.4 MPa.

718 Fig. 2 Reinforcement detailing [5]

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2.2 Constraints and Boundary Conditions Interaction between concrete and reinforcement was defined as embedded region. In the constraint definition, concrete was defined as host region and reinforcement was defined as embedded region. Interaction between beam and column surface was defined as tie connection. In the constraint definition, beam surface was defined as host surface and column surface was defined as slave surface. At both ends of the column, special boundary condition was defined. In the boundary condition definition, displacement in vertical direction was restrained and all other deformations were allowed.

2.3 Meshing Hex meshing was adopted for the models of OMRF and DSB. Element C3D8R is used in beam for meshing. It is an eight-noded linear brick element with reduced integration and hour glass control. Element B31 is used in reinforcement for meshing. It is a two-noded linear beam element in space. For OMRF, a mesh size of 67 mm was provided for both beam and column and mesh size of 65 mm was provided for reinforcements. For DSB, due to complexity in shape, more than one mesh size was adopted, i.e. 67 and 5 mm for concrete elements and 65 mm for reinforcement.

3 Results and Discussions A cyclic loading consisting of a single cycle of 5 mm deflection was applied at the beam end for a period of 1 s. At the ends of column, deflection vertical direction was restrained. Figure 3 shows the von-Mises’ stress pattern of concrete in ordinary momentresisting frame. From figure, it is clear that region of stress concentration extends to beam-column junction. Figure 4 shows the von-Mises’ stress pattern of concrete in double-slotted beam system. From the figure, it is clear that area of stress concentration shifted from beam-column junction to the position of vertical slot. This marks the achievement of strong column–weak beam condition. Figure 5 shows the von-Mises’ stress pattern of reinforcement in ordinary moment-resisting frame. From the figure, it is evident that region of stress concentration extends to reinforcements in beam-column junction region. Figure 6 shows the von-Mises’ stress pattern of reinforcement in double-slotted beam system. From the figure, it is clear that region of stress concentration changed from beam-column junction to the portion of reinforcement in the slotted region. So, stress penetration into the reinforcement in the beam-column junction region reduced significantly.

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Fig. 3 von-Mises’ stress in concrete––OMRF

Fig. 4 von-Mises’ stress in concrete––DSB

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Fig. 5 von-Mises’ stress in reinforcement––OMRF

Fig. 6 von-Mises’ stress in reinforcement––DSB

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Fig. 7 Deflection in OMRF

Figure 7 shows the deformed shape of ordinary moment-resisting frame during cyclic loading, and Fig. 8 shows the deformed shape of double-slotted beam system. From figure, it is clear that in the case of double-slotted beam system, the centre of rotation is formed at the position of vertical slot, whereas in the case of ordinary moment-resisting frame, centre of rotation formed at beam-column junction. So, in the case of double-slotted beam system, prediction of centre of rotation is possible. In OMRF, the stress concentration was observed at the beam-column junction. But in the case of DSB, stress concentration was observed at the vicinity of vertical slot. So from the analysis, it is understood that the location of maximum stress concentration is shifted from beam-column junction to the position of vertical slot by providing vertical slot with appropriate reinforcements in the beam. Since stress concentration was observed mainly at vertical slot, anticipated concrete damage will be less. Also in DSB, the centre of rotation was formed at slot region. So, centre of rotation can be predicted easily.

4 Conclusions Numerical analysis of ordinary moment-resisting beam and double-slotted beam was done and results were compared. The key conclusions obtained from the study were.

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Fig. 8 Deflection in DSB

In the case of ordinary moment-resisting frame, stress concentration was obtained at beam-column junction. This will result in the early failure of column, which is not desirable. In the case of double-slotted beam system, stress concentration was obtained at the region of vertical slot. So, the strong column–weak beam condition achieved and concrete damage anticipated will be less. Centre of rotation formed at the position of vertical slot in double-slotted beam system. So, centre of rotation can be predicted accurately. Hence, the double-slotted beam system is an effective plastic hinge relocation technique. As compared to the other plastic hinge relocation techniques, this particular method has the advantage that prediction of centre of rotation is possible with high level of accuracy.

References 1. Ye L, Qu Z (2009) Failure mechanism and its control of building structures under earthquakes based on structural system concept. J Earthq Tsunami 3(4):249–259 2. Paulay T, Priestley MNJ (1992) Seismic design of reinforced concrete and masonry buildings. Wiley, New York 3. Yan ZH, Au FTK (2009) Nonlinear dynamic analysis of frames with plastic hinges at arbitrary locations. Struct Des Tall Spec Build 801:n/a-n/a

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4. Ahmadi N, Kodag PB (2017) Plastic hinge replacement and enhancing the load carrying capacity of the RC joints using CFRP. Int J Eng Sci Res Technol 2277–9655 5. Oudah F, El-Hacha R (2017) Plastic hinge relocation in concrete structures using the doubleslotted-beam system. Bull Earthq Eng 15(5):2173–2199 6. Oudah F, El-Hacha R (2017) Seismic performance of modified single-slotted-beam concrete connection. J Earthq Eng 21(5):726–751 7. Byrne JDR, Bull DK (2012) Design and testing of reinforced concrete frames incorporating the slotted beam detail. Paper Number 65. NZSEE Conference 2012

Evaluation of Reliability Index for the Steel Beam Designed Using IS 800:2007 Chinnu Sabu, Praveen Nagarajan, and P. Robin Davis

Abstract This study presents an evaluation of the reliability index of the steel beams designed according to limit state of collapse in flexure as per IS 800:2007. The safety evaluation is based on structural reliability analysis of beams using Hasofer and Lind’s method, which are laterally supported. The parameters, yield stress, dead and live loads are considered as random in the reliability evaluation. It is assumed that failure function is a linear combination of basic variables. The effects of geometrical imperfections and stresses in beam are taken into account. Keywords Reliability index · Probability of failure · Hasofer and lind’s method · Random variables · Steel beam

1 Introduction The performance of a structure is assessed by its safety, serviceability and economy. In the presence of uncertainties, the absolute safety of a structure is impossible due to the unpredictability of loads on a structure during its life, in-place material strengths and human errors. With respect to risk of life, the structural safety is important. Although it is clear that the purpose of building codes is to provide adequate safety in the design and construction of structures, Beck et al. [1] suggest that the level of safety cannot be measured quantitatively based on the codes alone, since they hide a myriad of safety margins and conservative approximations. Reliability functions return the probability of a performing system or component failing during a specific period of time. Papadrakakis et al. [2] proposed that the reliability analysis of structures enables the determination of the probability of deterioration or collapse associated with a limit state, as well as providing data for a more coherent design with such perspectives. The reliability function represents a downward curve, showing regular wear as well as structural fatigue. Bhatnagar et al.

C. Sabu (B) · P. Nagarajan · P. R. Davis National Institute of Technology, Calicut, Kozhiode, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_56

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[3] studied, AFOSM method which was used for calculating safety index and Limit State Design (LSD) for factor of safety for particular random variables. The evaluation of safety of a beam is much important task. The safety of a beam depends on the resistance ‘R’ of the beam and action ‘S’ (load or load effects) on the beam. The action is a function of loads (live load, dead load and super dead) which are random variables. Steel beam is a structural element that primarily resists loads applied laterally to the beam axis. Its mode of deflection is primarily by bending. Similarly, the resistance or response of the steel beam depends on the physical properties of the materials, and geometrical dimensions of the beam which are also subjected to statistical variations, and are probabilistic. Hence to be rational in the estimation of the structural safety, the random variations of the basic parameters are to be taken into account. Afshan et al. [4] employed a First Order Reliability Method similar to that used for concrete filled steel columns, hot rolled sections and stainless steel sections. Since load and strength are random variables, the safety of the beam is also a statistical variable. In the present work, an attempt is made to assess the safety of a beam by establishing reliability index using Hasofer and Lind’s method. Reliability analysis is defined as the consistent evaluation of design risk using probability theory. The reliability is the probability of an item performing its intended function over a given period of time under the operating conditions encountered.

2 Computation of Structural Reliability In real situations, both R and S are random variables. The plots of the density functions of R and S are shown in Fig. 1. The shaded portion is an indicative measure of the probability of failure. According to Ranganathan [5], reliability is defined as the probability that a structure will not attain each specified limit (flexure or shear or torsion or deflection criteria) during a specified reference period (life of the structure). The reliability R0 is defined in terms of the probability of failure, pf , which is taken as R0 = 1 − p f Fig. 1 Probability of failure for random variations of S and R

(1)

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The structure is said to fail when the resistance of the structure is less than the action. That is, p f = P(R < S) = P(R−S < 0)

(2)

2.1 Hasofer and Lind’s Method The failure function is considered as the function of independent basic variables X 1 , X 2 , …, X n , i.e. g(X 1 , X 2 , …, X n ). The basic variables are then normalized using the relationship: Zi =

xi + μi σi

i = 1, 2, . . . , n

(3)

In the z coordinate system, the failure surface is a function of Z i . In the z coordinate system, the failure surface equation is written in the normalized coordinate system. This failure surface also divides the design sample space into two regions, safe and failure. This system has a rotational symmetry with respect to the standard deviation, and the origin O will usually lie in the safe region. As the failure surface moves away from origin, reliability increases, and as it moves closer to the origin, reliability decreases. Hence, the position of the failure surface with respect to the origin in the normalized coordinate system determines the measure of reliability. Reliability index, β is related to the failure surface when it is a linear function of basic variables.   β = −φ −1 p f

(4)

Non-normal Distribution In practical situations, many of the basic variables are non-normal like live loads, strength of material, etc. In such cases, the value of β can be obtained using equivalent normal distributions at the design point. For this purpose, the cumulative probability of the original non-normal variable X i is made equal to the cumulative probability of the equivalent normal variable X i  . If μ xi and σ  xi are the unknown mean and standard deviation of X i  , then Zi =

X i − μxi σxi

where Z i is the reduced or normalized variate.

(5)

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The reliability index is invariant since it is related to the failure surface and not to the failure function, and equivalent failure functions result in the same failure surfaces. For linear functions, the indices defined by Cornell and Hasofer and Lind coincide. The problem of finding the shortest distance β in the normalized space is strictly a minimization problem.

3 Design of Steel Beams using IS 800:2007 Beams are the members in the structure, which resist loads primarily through flexure. A beam may be exposed to simple bending, biaxial bending or unsymmetrical bending depending on the plane of loading, geometrical properties of the section and slenderness ratio of the compression flange. Strength, stiffness and stability are the three criteria which govern the design of a beam. For beams which are laterally supported and whose buckling stress is greater than the allowable bending stress, strength and stiffness govern the design rather than stability.

3.1 Design Criterion: Bending Moment For laterally supported beams, the factored design moment, M, at any section in a beam, due to external action satisfies the relationship M < M d , where M d is the design bending strength of the section. The design bending strength of a laterally supported beam is governed by the yield stress. Shear force does not have any influence on the bending moment for values of shear up to 0.6 V d , where V d is the design shear strength. When the design shear force V d is less than 0.6 V d , the design bending strength, M d will be Md =

β0 Z p f y 1.2 Z e f y ≤ γm0 γm0

(6)

where β 0 = 1.0 for plastic sections, Z p and Z e are the plastic and elastic section modulus of the cross section, respectively, f y is the yield stress of the material and γ m0 = 1.10 is the material partial safety factor as per IS 800:2007. Four sets of laterally supported I beam sections were considered for the study under various live load to dead load ratio (L n /Dn ) with a span of 5 m and yield strength f y of 250 N/mm2 . The beams were designed using IS 800:2007, and nearest available sections were chosen. The sectional properties are listed in Table 1. Having arrived at the section, the reliability analysis of each section is carried out. The limit state equation considered was

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Table 1 Sectional properties of various I section Designation

Depth of section (mm)

Width of flange (mm)

Thickness of flange (mm)

ISMB 450

450

150

17.4

ISHB 450

450

250

13.7

ISWB 500

500

250

ISWB 550

550

250

Section modulus (cm3 )

Plastic modulus (cm3 )

9.4

1350.7

1533.36

9.8

1742.7

1955.03

14.7

9.9

2091.6

2351.35

17.6

10.5

2723.9

3066.29

R = Z p fy −

Thickness of web (mm)

WD L WL L − 4 4

(7)

where Z p depends on the sectional properties of the I beam considered. The statistical distribution of the relevant random variables is given in Table 2. The reliability analysis is done using Hasofer and Lind’s method. The results are tabulated in Table 3. It may be noted that the limit state equations with respect to shear and other local failures are not critical compared to that due to bending moment. The variations in actually provided section modulus and the structurally needed section modulus are from 14.01 to 18.48%. But from Fig. 2, it is observed that the β value varies from 2.47 to 2.98. The corresponding value of probability of failure varies from 0.00144 to 0.00248. Generally, the reliability-based design is conducted for the sections with a target reliability index of 2.75. In this study, most of the reliability indices are lying above 2.75 under the specified design situations. Table 2 Statistical distribution of the relevant random variables Variable

L n /Dn

Yield strength of steel (f y )

Flange width (bf )

Flange thickness (t f )

Depth of section (D)

Web thickness (t w )

Statistical distribution

Lognormal

Normal

Normal

Normal

Normal

Normal

Table 3 Reliability Index of fully restrained beams L n /Dn

Section as per IS 800:2007

Variations between Reliability Index actually provided and using Hasofer and structurally needed Lind’s method section modulus (%)

Probability of failure

0.5

ISMB 450

15.82

2.47

0.00676

1.0

ISHB 450

18.48

2.95

0.00159

1.5

ISWB 500

14.01

2.98

0.00144

2.0

ISWB 550

15.96

2.81

0.00248

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Reliability Index

3 2.5

2.98 2.75

2.95 2.75

2.75 2.47

2.81 2.75

2.75 Target Reliability Index

2 1.5

Reliability Index using Hasofer and Lind's Method

1 0.5 0 0.5

1

1.5

2

Ln/Dn Fig. 2 Reliability index variation of laterally supported beams with reference to target reliability index

4 Conclusion The typical flexural members are considered for the design and reliability analysis. Only dead load and live load combination is considered. The reliability index values are determined for different L/D ratios, i.e. from 0.5 to 2.0 in increments of 0.5. A target reliability index of 2.75 is chosen on a semi-intuitive basis. When partial safety factors are applied as per IS 800:2007, the reliability index is improved and is higher than 2.75 for almost all design situations. The probability of failure varies from 0.00676 to 0.00144 for the variation of actually provided and structurally needed section modulus from 14.01 to 18.48%. It is observed that a reasonably uniform reliability index is achieved for different design situations.

References 1. Beck AT, Doria AS (2008) Reliability analysis of I-section steel columns designed according to new Brazilian building codes. J Braz Soc Mech Sci Eng 300:152–159 2. Papadrakakis M, Papadopoulos V, Lagaros ND (1996) Comput Methods Appl Mech Eng 136:145–163 3. Bhatnagar SD, Sehgal VK, Gopal K (2010) Computational technique for reliability analysis and design of steel beam. J Inf Technol Knowl Manag 2:511–513 4. Afshan S, Francis P, Baddoo NR, Gardner L (2015) Reliability analysis of structural stainless steel design provisions. J Constr Steel Res 114:293–304 5. Ranganathan R (1990) Reliability analysis and design of structures, Tata McGraw-Hill

Experimental Investigation on Bond Strength Properties of Geopolymer Concrete P. Saranya, Praveen Nagarajan, and A. P. Shashikala

Abstract Geopolymers are new alternative binders for the development of concrete. Geopolymer concrete can overcome the environmental impact of cement concrete. Highlight of the work is development of geopolymer concrete from industrial byproducts such as Ground Granulated Blast Furnace Slag (GGBS) and dolomite. Performance of structural elements mostly depends on the bond between concrete and reinforcement. Enhanced bond stress was observed in geopolymer concrete than that of cement concrete. Different equations were evaluated for the prediction of bond stress. Effects of addition of different percentage of dolomite on bond strength are also investigated. Addition of GGBS and dolomite can reduce the production cost of concrete and can also reduce its disposal problem. Keywords Bond strength · Dolomite · Geopolymer concrete · GGBS

1 Introduction Geopolymer concrete is a recent form of concrete in which cement is fully replaced with industrial by-products which reduces the environmental impacts of cement [1, 2]. Fly ash, GGBS, metakaolin, etc. are used as source materials for geopolymer concrete. Aluminium silica-based materials along with the alkali solution lead to polymerization process which gives strength for geopolymer concrete. The advantages of geopolymer concrete include high strength, high durability properties, high early age strength and higher resistance to heat [3, 4]. Highlight of the work is the development of geopolymer concrete from two industrial by-products such as

P. Saranya (B) · P. Nagarajan · A. P. Shashikala National Institute of Technology Calicut, Kozhikode, Kerala, India e-mail: [email protected] P. Nagarajan e-mail: [email protected] A. P. Shashikala e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_57

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GGBS and dolomite. GGBS and dolomite are two industrial by-products from steel industries and rock crushing plant, respectively [5–7]. Bond strength is one of the important parameters which influences the ultimate load-carrying capacity of concrete. Bonding between concrete and reinforcement mainly depends on the material and geometry of the reinforcement [8, 9]. When the reinforcement bar embedded in concrete is pulled, bar will show tendency for slipping. After the initial slip, force is transferred to the concrete by friction and bearing. Therefore, the concrete may fail either by slipping or sliding during pull out test [10–12]. Present study highlights the bond behaviour of geopolymer concrete by pull out test. Bond strength of GGBS–dolomite geopolymer concrete was compared with cement concrete. Different prediction equations were evaluated and compared with experimental results.

2 Experimental Programme 2.1 Materials Used Ground Granulated Blast Furnace Slag (GGBS). GGBS and dolomite are the byproducts from steel industries and rock crushing plants, respectively. Physical and chemical properties of GGBS and dolomite are shown in Table 1. Aggregate. The property of aggregates used in the study, satisfying IS 2386–3 [13], is shown in Table 2. Alkaline Solution. Combination of sodium hydroxide and sodium silicate was used as an alkaline medium for the test. Sodium hydroxide pellets having purity 97% were dissolved in water one day before casting, since it is an exothermic reaction. Sodium silicate in solution form is composed of SiO2 (27.2%), Na2 O (8.9%) and H2 O Table 1 Physical and chemical properties of GGBS, dolomite and OPC

Cement

GGBS

Dolomite

Colour

Grey

Off white

Pure white

Specific gravity

3.14

2.9

2.85

Blaine’s fineness (cm2 /gm)

2435

4032

3500

CaO

61.53

38.9

35.58

SiO2

20.36

33.5

20.78

Al2 O3

4.31

10.68

8.54

Fe2 O3

5.98

2.35

2.45

MgO

1.36

9.45

20.58

LOI

6.46

5.12

12.07

Experimental Investigation on Bond Strength Properties … Table 2 Properties of aggregates

Table 3 Mix proportioning of GPC

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Property

Fine aggregate

Coarse aggregate

Size

Passing through 1.18 mm sieve

Maximum size 12 mm

Water absorption

1.4%

0.93%

Fineness modulus

2.75

6.8

Quantity (kg/m3 )

Sl. No.

Material

1

Binder content

400

2

Alkaline solution

175

3

Fine aggregate

4

Coarse aggregate

5

Superplasticizer

618 1196 6

(63.9%). Solutions of sodium silicate and sodium hydroxide were mixed together at least one hour before casting [3]. Sulphonated naphthalene-based superplasticizer is also added to improve the workability.

2.2 Mix Proportioning Of Geopolymer Concrete There are no proper mix design guidelines available for GGBS geopolymer concrete under ambient curing condition. Mix proportion for M60 concrete was carried out based on trial and error basis for GPC and is shown in Table 3. GPC was filled in each mould in three layers and compacted on a vibrating table. All the specimens were demoulded within 24 h and cured under ambient condition (25–28 °C).

2.3 Preparation of Specimens Specimens were prepared as per the mix proportions given in Table 3. GGBS was replaced with dolomite in different proportions (Table 4).

2.4 Specimen Details Specimens for pull out test were prepared as per the dimensions recommended by IS 2770 (Part 1)-1967 [14]. Cube specimens having size 100 × 100 × 100 mm were used for the study. Reinforcement bar having diameter 12 mm is embedded in vertical

734 Table 4 Proportions of GGBS (G), Dolomite (D) and OPC

P. Saranya et al. MIX

GGBS

Dolomite

Cement

G100:D0

100

0

0

G90:D10

90

10

0

G80:D20

80

20

0

G70:D30

70

30

0

G60:D40

60

40

0

G50:D50

50

50

0

OPC100

0

0

100

Fig. 1 Test specimens for pull out test

direction through the central axis of concrete. Specimens were prepared in different proportions of GGBS and dolomite and shown in Fig. 1.

2.5 Test Setup Compressive strength test was performed on 150 × 150 × 150 mm concrete cube specimens as per the procedure specified in IS 516:1959 [17]. Three specimens for each mix were cast with various proportions of GGBS and dolomite. Bonding strength of geopolymer concrete and cement concrete was evaluated as per the procedure given in IS 2770 (Part 1)-1967. Direct pull out test was conducted as shown in Fig. 2. Cube with vertical reinforcement is inserted through the space

Experimental Investigation on Bond Strength Properties …

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Fig. 2 Pull out test setup

between the bottom and adjustable platen. Adjustable platen was moved up and down to keep the specimen exactly in position. Reinforcement is tightened at the top grip and the specimen is placed vertically.

3 Results and Discussion 3.1 Bond Strength Maximum compressive strength and modulus of rupture was obtained for GGBS– dolomite ratio of 70:30.

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Table 5 Pull out strength test results Mix

Compressive strength MPa

Modulus of rupture MPa

Pull out load kN

Bond strength MPa

G100:D0

64.5

6.42

37

9.80

9.84

G90:D10

68.4

6.59

38

10.00

10.16

G80:D20

70

6.76

38.5

10.21

10.23

G70:D30

72.5

7.15

39.5

10.46

10.5

G60:D40

65.7

6.83

39

10.30

10.40

G50:D50

60.4

6.22

38

10.08

10.08

OPC100

71.5

6.17

32.5

8.61

8.65

Specimen 1

Specimen 2

Cube specimens with rebar were tested at the age of 28 days in a Universal Testing Machine. Rate of loading was kept as 72 N/s as per RILEM TC, 1994. Load was gradually increased until the complete failure of the specimen occurred. Pull out load for different specimens was noted and given in Table 5. Bond strength can be calculated from the following equation: fb =

P π ×d ×l

(1)

where P is the pullout load, d and l are nominal diameter and bonded length of the rebar, respectively. Pull out load was found to increase along with the addition of dolomite to GGBS geopolymer concrete up to 30%, thereafter the load was reduced. GGBS geopolymer concrete (G100:D0) has 14% more bond strength than that of cement concrete (OPC100). Maximum pull out load was observed for G70:D30 mix which is 22% more than cement concrete. In the case of geopolymer concrete, strength gaining process will take less time as compared to cement concrete. This is giving more strength to geopolymer concrete as compared to cement concrete.

3.2 Failure Modes and Crack Patterns Specimens failed either by sliding or splitting during pull out test. Splitting failure was commonly observed in the present study. As per the ACI committee report 408(2003), sliding failure will occur when large cover to reinforcement is maximum. Since specimens have only 44 mm cover, splitting failure was observed in the specimens. Failure pattern for different specimens are shown in Fig. 3. Failure pattern for both geopolymer concrete and cement concrete was found to be similar. When the load reaches its peak value, specimens were split into three pieces. Split surface of the concrete along with rebar is shown in Fig. 4, and split surface of both geopolymer concrete and cement concrete is shown in Fig. 5.

Experimental Investigation on Bond Strength Properties …

Fig. 3 Crack pattern of specimens

Fig. 4 Split surface of concrete along with rebar

Fig. 5 Split surface of geopolymer and cement concrete

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From Fig. 5, it is observed that geopolymer concrete specimens were failed by splitting aggregate into pieces. While for concrete specimen, failure occurred through cement matrix. This indicates that geopolymer matrix is stronger than cement matrix.

3.3 Comparison of Bond Strength with Existing Prediction Equations Characteristic compressive strength of concrete, diameter of the rebar and bonded length of the bar are the factors which affect the bond strength of concrete. Different equations are observed in literatures for the prediction of bond strength of concrete and are shown below [15–18]. Orangun et al. [15] d c fb √ = 0.1 + 0.25 + 4.15 d l fc

(2)

Darwin et al. [19] T 1

f c4

  Cmax = (1.5 × l(Cmin + 0.5d) + 51A) 0.1 + 0.9 Cmin

(3)

Esfahani and Rangan [17]      1 + 0.5d) 1 + (C min M T Cm   cmin 0.12 + 0.88 1 = Cmin + 3.6 (1.85 + 0.24M) d f c4

(4)

Harajli et al. [20] f b = 0.75 ×

  2/ fc c d 3

(5)

ACI committee 408 [18] T 1

f c4

  Cmax = (1.43l(Cmin + 0.5d) + 57.4 A) 0.1 + 0.9 Cmin

(6)

From Table 6, ACI committee 408(2003) expression gives the closest value of bond strength to the experimental results.

Experimental Investigation on Bond Strength Properties …

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Table 6 Experimental and predicted bond strength (MPa) MIX

Bond strength MPa Experimental (present)

Harajli et al. [20]

Orangun et al. [15]

Darwin et al. [19]

Esfahani et al. [17]

ACI committee (2003)

G100:D0

9.82

12.77

10.88

9.44

5.99

9.70

G90:D10

10.08

13.15

11.20

9.57

6.08

9.84

G80:D20

10.22

13.30

11.33

9.63

6.11

9.90

G70:D30

10.48

13.54

11.54

9.72

6.17

9.99

G60:D40

10.35

12.89

10.98

9.48

6.02

9.75

G50:D50

10.08

12.36

10.53

9.28

5.89

9.54

OPC100

8.63

13.44

11.46

9.68

6.15

9.95

4 Conclusion The following conclusions were made from the experimental studies: • Enhanced bond strength was observed in geopolymer concrete compared to cement concrete. GGBS geopolymer concrete (G100:D0) has 14% more bond strength than that of cement concrete (OPC100). • Maximum bond strength was observed for G70:D30 mix which is 22% more than cement concrete. • Bond strength obtained from experimental investigation is found to be comparable with the value obtained from ACI Committee 408, 2003. Acknowledgements The authors thankfully acknowledge the financial support provided by Kerala State Council for Science, Technology and Environment [TDAP/01/2017/KSCSTE], Kerala, India.

Appendix T = Concrete contribution to total bond force A = Area of bar Cmax = maximum (cb , cs ) Cmin = minimum (cb , cs ) Cb = bottom cover Cs = minimum (cso , csi + 6.4 mm) Cso = side cover Csi = half of the bar clear spacing

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References 1. Li C, Gong XZ, Cui SP, Wang ZH, Zheng Y, Chi BC (2011) CO2 emissions due to cement manufacture. In: Materials science forum, vol 685. Trans Tech Publications, pp 181–187 2. Malhotra VM (2002) Introduction: sustainable development and concrete technology. Concr Int 24(7) 3. Davidovits J (1991) Geopolymers: inorganic polymeric new materials. J Therm Anal Calorim 37(8):1633–1656 4. Juenger MCG, Winnefeld F, Provis JL, Ideker JH (2011) Advances in alternative cementitious binders. Cem Concr Res 41(12):1232–1243 5. Nath P, Sarker PK (2014) Effect of GGBFS on setting, workability and early strength properties of fly ash geopolymer concrete cured in ambient condition. Constr Build Mater 66:163–171 6. Deb PS, Nath P, Sarker PK (2014) The effects of ground granulated blast-furnace slag blending with fly ash and activator content on the workability and strength properties of geopolymer concrete cured at ambient temperature. Mater Des 1980–2015(62):32–39 7. Nath P, Sarker PK (2012) Geopolymer concrete for ambient curing condition. In: Australasian structural engineering conference 2012: the past, present and future of Structural Engineering. Engineers Australia, p 225 8. Sarker PK (2011) Bond strength of reinforcing steel embedded in fly ash-based geopolymer concrete. Mater Struct 44(5):1021–1030 9. Castel A, Foster SJ (2015) Bond strength between blended slag and class F fly ash geopolymer concrete with steel reinforcement. Cem Concr Res 72:48–53 10. Kusbiantoro A, Nuruddin MF, Shafiq N, Qazi SA (2012) The effect of microwave incinerated rice husk ash on the compressive and bond strength of fly ash based geopolymer concrete. Constr Build Mater 36:695–703 11. Topark-Ngarm P, Chindaprasirt P, Sata V (2014) Setting time, strength, and bond of highcalcium fly ash geopolymer concrete. J Mater Civ Eng 27(7):04014198 12. Albitar M, Visintin P, Ali MM, Lavigne O, Gamboa E (2016) Bond slip models for uncorroded and corroded steel reinforcement in class-F fly ash geopolymer concrete. J Mater Civ Eng 29(1):04016186 13. IS 2386 (Part III)-1963: methods of test for aggregate for concrete, Part 3-specific gravity, density, voids, absorption and bulking, bureau of Indian standards, New Delhi 14. IS 2770 (Part 1)-1967: Methods of testing bond. In: Reinforced concrete, bureau of Indian standards, New Delhi 15. Orangun CO, Jirsa JO, Breen JE (1975) The strength of anchored bars: a reevaluation of test data on development length and splices. Research report no. 154–3F, center for highway research, The university of texas at austin, texas, January, p 78 16. Darwin D, Tholen ML, Idun EK, Zuo J (1996) Splice strength of high relative rib area reinforcing bars. ACI Struct J 93(1):95–107. https://doi.org/10.14359/968 17. Esfahani MR, Vijaya BV (1998) Local bond strength of reinforcing bars in normal strength and high-strength concrete (HSC). ACI Struct J 95(2):96–106. https://doi.org/10.14359/530 18. ACI committee 408 (2003) Bond and development of straight reinforcing bars in tension (ACI 408R-03). American concrete institute, farmington hills, MI 48331 USA 19. Darwin D, Tholen ML, Idun EK, Zuo J (1996) Splice strength of high relative rib area reinforcing bars. University of Kansas Center for Research, Inc 20. Harajli M, Hamad B, Karam K (2002) Bond-slip response of reinforcing bars embedded in plain and fiber concrete. J Mat Civil Eng 14(6): 503–511

Numerical Procedures for Simulation of Wave Propagation in Plates Mohammed Aslam, Praveen Nagarajan, and Mini Remanan

Abstract Structural health monitoring (SHM) using wave propagation technique is an emerging method that can be used to detect, locate, and quantify the structural damages before catastrophic failures. Advancement of several finite-element simulation programs has helped scientists and engineers in validating the numerical solutions with the experimental results. Most of the researchers use explicit procedures for wave propagation problems. However, for electromechanical problems where piezoelectric materials are used for exciting waves, the explicit procedure is not available in most cases. Hence, implicit procedures are used to account for the piezoelectric effect. It becomes necessary to choose which procedure is apt for obtaining sufficient accuracy and to run the problem within reasonable computational time. This paper presents a comparative study of different finite-element procedures for modeling wave propagation in plates. Three different analysis procedures are studied, namely implicit analysis, explicit analysis, and implicit–explicit co-simulation analysis. The results show that the co-simulation model is more reliable and efficient compared to other models. Keywords Lamb waves · Finite-element method · Implicit · Explicit · Co-simulation

1 Introduction Wave propagation technique is well known for its ability in structural health monitoring and damage detection. The elastic waves can be generated and captured using piezoelectric transducers (PZT) adhesively bonded to the structures [1]. Plate structures are used in various fields of engineering. They find applications in aircraft, bridges, industrial buildings, storage vessels, ships, warehouses, and oil rigs. Specific types of elastic waves, namely “Lamb waves,” propagate in plate structures. These waves are called as guided waves and can travel a large distance from a single source M. Aslam (B) · P. Nagarajan · M. Remanan National Institute of Technology Kozhikode, Calicut, Kerala, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_58

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[2]. One of the major challenges facing with Lamb waves is that they are multimodal and dispersive [3]. In SHM, the presence of a defect is identified by quantitative wave parameters, like frequency, wavelength, amplitude, wave velocity, and phase. The progress of many finite-element analysis programs has led to growing interest in whether data obtained from the simulation can be verified by experiments. A brief review of different methods for simulating wave propagation can be found in Willberg et al. [4]. In transient wave propagation problems, direct time integration is used for obtaining finite-element solutions. In general, there are two types of time integration schemes: implicit scheme and an explicit scheme. If the solution procedure requires factorization of an effective stiffness matrix, it is called implicit; else it is explicit [5]. Both schemes can be used for transient analysis. However, for wave propagation problems explicit method is widely used [6]. When piezoelectric materials are used to generate and receive wave signals, the only option is to use an implicit integration method because coupled piezoelectric finite elements are not available for the explicit procedure. Therefore, a suitable analysis procedure is essential to obtain enough accuracy and to solve the problem with minimum cost. This paper presents a comparative study of different finite-element procedures for modeling wave propagation in plates. Three different solution procedures are studied, namely implicit method, explicit method, and combined implicit–explicit method. The modeling aspects in each case are explained in subsequent sections. The simulation is carried out using commercially available software package Abaqus CAE 2016. The wave parameters, like group velocity, wave amplitude, and mode shapes, obtained from different simulation methods are compared. The group velocities calculated using numerical data are also compared with the theoretical dispersion curve.

2 Numerical Model For the present study, a steel plate having a uniform thickness of 1.6 mm is used. The geometry of the plate and the location of the PZT actuator is shown in Fig. 1. A distance of 500 mm is provided between the actuator and sensor for capturing both fundamental wave modes S0 and A0. The plate and PZT are assumed to be of infinite extent in the z-direction (plane strain condition). A four-node bilinear plane strain

Fig. 1 The geometry of the plate and location of PZT actuator

Numerical Procedures for Simulation of Wave Propagation …

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Fig. 2 Time history and power spectrum of a five-count tone burst voltage signal with a central frequency of 100 kHz

quadrilateral element (CPE4) is used to mesh steel plate and a four-node bilinear plane strain piezoelectric quadrilateral element is used to mesh PZT layer. The PZT is excited with a five-count tone burst voltage signal with an amplitude of 10 V. The central frequency is swept from 25 to 500 kHz. A limit of 500 kHz is chosen to avoid higher wave modes. Figure 2 shows the excitation waveform centered at 100 kHz and its corresponding power spectrum. The material properties of PZT-5H used for the study can be found in Aslam et al. [7].

2.1 Implicit Model Coupled piezoelectric finite elements are available in Abaqus implicit. In implicit method, Newton’s method is used to solve the equilibrium equation. An implicit operator, Hilbert-Hughes-Taylor is used. The integration for displacement and velocity is based on Newmark’s formulae [8]. In the implicit method, there is no limit on time step size as they are unconditionally stable. However, a maximum increment of T /10 (where T is the period) is chosen for obtaining reasonable results [8]. The implicit model is shown in Fig. 3. Here PZT is bonded to steel plate assuming that there is no slip between the layers.

Fig. 3 Implicit finite-element model

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Fig. 4 Explicit finite-element model

2.2 Explicit Model In the explicit method coupled piezoelectric finite elements are not available. Here displacement boundary conditions are specified on related nodes in contact with the piezoelectric actuator. In most cases, it is assumed that the PZT plate exerts a force in the x-direction as shown in Fig. 4 [9]. This force is a line load per unit length. Explicit solution imposes an upper limit on time step size. Explicit method is conditionally stable. Hence, choosing a suitable time step is vital for obtaining accurate solutions. The time step (t) is chosen such that t < L min /C, where L min is the smallest element size and C is the wave speed. The mesh size for all the models is taken such that the spatial resolution of propagating waves is achieved. It is suggested that at least 10 elements are required per wavelength [10].

2.3 Implicit–Explicit Co-simulation Model In implicit–explicit method Abaqus allows the user to make use of both implicit and explicit procedures. Here piezoelectric analysis is performed using the implicit method and the output is used as the input for explicit analysis. The whole finiteelement model is subdivided into the implicit and explicit model. Then by using an interactive interface, the data are exchanged in a synchronized manner. The cosimulation model is illustrated in Fig. 5.

3 Results and Discussion The sensor response obtained from the three numerical models were compared and studied. The comparison of the magnitude of displacement response at the sensor when PZT is actuated at 125 kHz central frequency is shown in Fig. 6. It is observed that all the three models captured both S0 and A0 wave modes. However, the implicit model showed a slight time delay. The magnitude of implicit and co-simulation models is comparable, whereas the magnitudes of the explicit model were found to

Numerical Procedures for Simulation of Wave Propagation …

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Fig. 5 Co-simulation model

x 10

4

x 10-9

-9

Magnitude (m)

3

8

A0 mode

S0 mode

6

2

4

1

2

0

0

-1

-2

-3 -4

-4

Implicit Co-simulation Explicit

-2

0

50

-6 -8 100

150

200

250

300

Time ( s) Fig. 6 Sensor response at 125 kHz

be higher. This might be due to the reason that the prescribed effective displacement may be higher than the actual displacement. By knowing the time of flight of S0 and A0 wave modes, the group velocities were calculated and compared with that of the theoretical dispersion curve of steel plate. Figure 7 illustrates the comparison of group velocities obtained from the numerical study with the theoretical group velocity [11]. It is noted that at lower frequencies, the group velocity predicted is well matching with the theoretical curve. For higher frequencies, the implicit models show lower velocities which are due to slight delay in phase. This delay can be adjusted by reducing the time increment and the element size, but the computational cost would become excessive. A typical plot showing the contour of resultant displacement of A0 and S0 modes is illustrated in Fig. 8. The plot corresponds to co-simulation model. Similar contour is obtained for the other two models. The first mode arriving the sensor is the S0 mode followed by A0 mode. As expected, it can be observed that the particle displacement

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Group Velocity (m/s)

6000 5000

S0 S0 (Implicit) S0 (Explicit) S0 (Cosimulation)

4000 3000

A0 A0 (Implicit) A0 (Explicit) A0 (Cosimulation)

2000 1000 0

100

200

300

400

500

Frequency (kHz) Fig. 7 Comparison of group velocity dispersion curve for 1.6 mm steel plate

Fig. 8 Typical finite-element record showing displacement amplitude of A0 and S0 mode at time step 8.1e-5 s

in the x-direction (U1) is more compared to the particle displacement in the y-direction (U2) for S0 mode and vice versa in case of A0 mode. For the present study, a desktop computer with an Intel R Core™ i5-5200U processor is used. Table 1 presents the computation time taken for each analysis models. The time is normalized with respect to minimum time. It is noted that as frequency increases the run time increases for both implicit and co-simulation models. However, the time required for co-simulation is less compared to implicit. The average run time for implicit, explicit, and co-simulation analysis is 3463, 22.7, and 1040 s, respectively. This indicates that explicit analysis is computationally effective compared to the other two models. The variation in amplitude with respect to excitation frequency is plotted in Fig. 9. It is observed that both implicit and co-simulation models show a similar trend for both the wave modes. In an explicit model, an extra peak is observed in S0 mode near to 250 kHz. In A0 mode, the amplitude of the second peak is close to the first peak for the explicit model. This might be due to the assumption of line loading in the explicit model. Figure 10 presents the displacement components along x and y directions (U1 and U2) through the thickness profile. All the displacement components are normalized with respect to their maximum values. The graph reveals that the mode shape predicted by all the models are similar. For S0 mode, the displacement along xdirection is symmetric with respect to the midplane, while the displacement along

Numerical Procedures for Simulation of Wave Propagation …

Normalized Amplitude

0.4

Frequency (kHz)

Normalized run time Implicit

Explicit

Co-simulation

25

110.84

1.68

54.74

50

122.84

1.32

44.37

75

132.21

1.26

42.26

100

128.89

1.16

37.68

125

141.63

1.16

43.16

150

154.58

1.16

40.58

175

154.58

1.16

33.79

200

117.79

1.11

49

225

130.42

1.16

32.42

250

131

1.42

25.95

275

184.32

1.11

49.74

300

200.53

1.21

35.84

325

248.47

1.16

45

350

212.63

1.11

67.89

375

307.79

1.16

85

400

225.95

1.32

54.63

425

266.16

1

49.47

450

231.05

1.05

99.53

475

226.84

1.11

95.47

500

221.74

1.11

104.11

Implicit 1.0 Co-simulation

0.3

Explicit

0.8

0.2 0.6 0.1 0.4 0.0

0

100

200

300

400

500

0.5

Normalized Amplitude

Table 1 Comparison of CPU time

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Implicit Co-simulation

0.4

1.2

0.8

0.3 0.2

0.4

0.1 0.0

Explicit 0

100

200

300

400

Frequency (kHz)

Frequency (kHz)

(a)

(b)

500

Fig. 9 Predicted variation of amplitude with excitation frequency a S0 mode, b A0 mode

0.0

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1.2

Thickness (mm)

Thickness (mm)

1.6

0.8 0.4

Implicit Explicit Co-simulation

1.2 0.8 0.4

0.0

0.0 -1.0

0.9968 0.9976 0.9984 0.9992 1.0000 Normalized Amplitude (U1)

-0.5 0.0 0.5 1.0 Normalized Amplitude (U2)

(a)

1.2

1.6 Implicit Explicit Co-simulation

Thickness (mm)

Thickness (mm)

1.6

0.8 0.4 0.0 -1.0

-0.5

0.0

0.5

Normalized Amplitude (U1)

1.0

1.2 Implicit Explicit Co-simulation

0.8 0.4 0.0

(b)

0.960

0.970

0.980

0.990

1.000

Normalized Amplitude (U2)

Fig. 10 Mode shapes of wave modes at 125 kHz a S0 mode, b A0 mode

y-direction is antisymmetric. For A0 mode, the displacement along x-direction is antisymmetric with respect to the midplane, while the displacement along y-direction is symmetric.

4 Conclusions The study presents a comparison of three different analysis procedures models, namely implicit, explicit, and co-simulation method for wave propagation in plates. All the three models are implemented in software package Abaqus. The elastic waves were excited using piezoelectric transducers. In the co-simulation model, it combines an implicit model, which includes piezoelectric finite elements and explicit model for wave propagation. The results show that the co-simulation model is more reliable and efficient compared to other models. The implicit model is found to be unsuitable for modeling wave propagation as it shows considerable time delay. The computational time required for the analysis is also higher for implicit models. The explicit model

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is found to be cost-effective compared to the other two models. However, the magnitude of displacement is found to be higher in this case. The maximum percentage difference obtained is 80%. This can be modified by an improved actuator loading condition.

References 1. Nienwenhui JH, Neumann JJ, Greve DW, Oppenheim IJ (2005) Generation and detection of guided waves using PZT wafer transducers. IEEE Trans Ultrason Ferroelectr Freq Control 52:2103–2111 2. Giurgiutiu V (2014) Structural health monitoring with piezoelectric wafer active sensors, Elsevier Academic 3. Raghavan A, Cesnik CES (2007) Review of guided wave structural health monitoring. Shock Vib Dig 39:91–114 4. Willberg C, Duczek S, Vivar-Perez JM, Ahmad ZAB (2015) Simulation methods for guided wave-based structural health monitoring: a review. Appl Mech Rev 67:010803 5. Noh G, Bathe KJ (2013) An explicit time integration scheme for the analysis of wave propagations. Comput Struct 129:178–193 6. Chang SY, Liao WI (2005) An unconditionally stable explicit method for structural dynamics. J Earthq Eng 9:349–370 7. Aslam M, Nagarajan P, Remanan M (2018) J Inst Eng India Ser A https://doi.org/10.1007/s40 030-018-0340-5 8. Abaqus A (2016) Theory and user–s manuals. Dassault systems, USA 9. Giurgiutiu V (2003) Lamb wave generation with piezoelectric wafer active sensors for structural health monitoring. In: Smart structures and materials 2003: smart structures and integrated systems, vol 5056. pp 111–123 10. Yang C, Ye L, Su Z, Bannister M (2006) Some aspects of numerical simulation for Lamb wave propagation in composite laminates. Compos Struct 75:267–275 11. Atashipour SA, Mirdamadi HR, Hemasian-Etefagh MH, Amirfattahi R, Ziaei-Rad S (2013) An effective damage identification approach in thick steel beams based on guided ultrasonic waves for structural health monitoring applications. J Intell Mater Syst Struct 24:584–597

Study on Compatibility Issues and Flow Behavior of Copper Slag-Based Mortars Y. T. Thilak Kumar, D. Arpitha, V. J. Sudarshan, C. Rajasekaran, and Nagesh Puttaswamy

Abstract With the growing constructions industries, sand availability has become a headache for the builders and engineers. In this paper an attempt has been made to understand the flow characteristics of partially replaced copper slag (10, 20, 30, and 40%) in mortars with varied water binder ratio (0.35, 0.4, and 0.45) for different percentages of superplasticizers dosage (0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, and 2.0). Thus, the test results drawn help to identify the optimum dosage of superplasticizer required for different percentage replacement of fine aggregates and water binder ratio and understand the flow behavior characteristics of mortars. Keywords Copper slag · Mortars · Flow behavior · Water binder ratio · Superplasticizer

1 Introduction Today, the problem of sand deficiency gives an advance task for researchers and engineers to explore the suitable alternatives for fine aggregates. Apart from water and air, humble sand is the natural resource most consumed by human beings. People use more than 40 billion tons of sand and gravel every year as mentioned in past studies. There is so much demand that riverbeds and beaches around the world are Y. T. Thilak Kumar · D. Arpitha (B) · V. J. Sudarshan · C. Rajasekaran Department of Civil Engineering, National Institute of Technology Karnataka, Mangalore, India e-mail: [email protected] Y. T. Thilak Kumar e-mail: [email protected] V. J. Sudarshan e-mail: [email protected] C. Rajasekaran e-mail: [email protected] N. Puttaswamy UltraTech Cement Ltd., Bengaluru, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_59

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being stripped bare. Desert sand generally doesn’t work for construction; shaped by wind rather than water, desert grains are too round to bind together well. Hence the amount of sand being mined is increasing exponentially. Copper slag is a waste glassy granular product with high specific gravity of around 3.65 generated in the matte smelting process during the extraction of copper, and has shown a better performance when replaced partially as fine aggregates in concrete in previous research works. Approximately 3 tons of copper slag are generated for every ton of copper production [2]. Annually around 24.5 million tons of copper slag bi-product are generated worldwide among which 6–6.5 million tons are generated in India [6]. In the last few years experiments on CS are being done because of the usage of same water binder ratio. For all different partial replacements, the strength of CS-replaced concrete decreases. This paper tries to convey the detailed behavior of CS-replaced mortar which works with different types of water binder ratio and different dosages of superplasticizers which effectively contributed in enhancement of workability in fresh state for blended cement, which is a fly-ash-based cement.

2 Materials and Properties Cement: Portland pozzolona cement of 53 grade has been used in the study. Specific gravity is 2.85, fineness is 1.9%, and it is fly-ash-based cement, which includes 30% fly ash. Sand: Locally available river sand is used for replacement whose specific gravity is 2.6 and it falls under zone II. Copper slag: For this study copper slag is bought from Sterlite Industries India Limited (SIIL), Tuticorin, Tamil Nadu Fig. 1 and Table 1. Superplasticizer: Poly carboxylate ether (PCE) based Glenium sky 8233 was used, which is supplied by BASF.

3 Experimental Procedures Flow table test. To check out the flow behavior of the mortar, the normally adopted method is mini slump cone method, which can be called as flow table test. When truncated mini slump cone is lifted vertically mortar flows with gravity and the measurements (edge to edge of flow) are taken. Here inertial force and viscous force play a substantial role in aggregation with gravitational force [7].

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Sieve Analysis of Copper Slag Zone-2 UL Zone-2 LL River sand CS

Cumulative % of passing

100

80

60

40

20

0 0.15

0.3

0.6

1.18

2.36

4.75

Sieve size Fig. 1 Sieve analysis of copper slag and river sand which are used in the study

Table 1 Physical properties of copper slag and river sand which are used in the study

Properties

River sand

Copper slag

Specific gravity

2.6

3.65

Zone

II

II

Water absorption

1.5%

0.15%

Fineness modulus

4.59

3.54

Particle shape

Irregular

Irregular

In the present study mortar of 1:3 ratio is being used (cement to sand ratio, respectively). Horbart mixer is used to mix mortar. Mortar is filled in the truncated cone in three layers; each layer is tamped with 25 number with a tamping rod and then truncated cone is lifted vertically upward allowing mortar to flow. Sand is partially replaced with 10, 20, 30, and 40% copper slag.

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Flow for 0.35 WC Ratio 0.5

% flow

0.4

0.3

0.2

0.1

10% 20% 30% 40%

0.0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

% SP Dosage Fig. 2 Flow behavior of mortar for 0.35 W/B ratio

4 Results and Discussions 4.1 Behavior of Mortar Flow for Different W/B Ratio 4.1.1

Flow Behavior of CS-Based Mortar with Different Percentage of CS Replacement for 0.35 Water Binder Ratio

From Fig. 2, it is concluded that for 10% of CS replacement and for 0.35 water binder ratio, the ideal superplasticizer dosage is 1.2%, for 20% replacement it is 1.1; for 30% replacement, 1.05%; and for 40% replacement, 1% dosage of superplasticizer can be used. With the 0.2% of dosage the mortar was full harsh for every individual different replacement mix, and after 0.6% of dosage the mortar started to work with good flow in all different replacements.

4.1.2

Flow Behavior of CS-Based Mortar with Different Percentage of CS Replacement for 0.4 Water Binder Ratio

From Fig. 3, it is conferred that for 0.4 W/B ratio different percentages of CS-replaced mortar behave differently and they are observed as follows: for 10% CS-replaced mortar 1.0% dosage of superplasticizer is required, likewise for 20% replacement 0.8%, for 30% replacement 0.8% and for 40% replacement 0.7% of superplasticizer dosage is required. At initial stage for 0.2% superplasticizer dosage for 10 and 20%

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Flow for 0.40 WC ratio 0.5

% flow

0.4

0.3

0.2

0.1

10% 20% 30% 40%

0.0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

% SP Dosage

Fig. 3 Flow behavior of mortar for 0.4 W/B ratio

replacement, the flow came out to be harsh. For more than 1.4% dosage, the mortar started to bleed for all the different replacements.

4.1.3

Flow Behavior of CS-Based Mortar with Different Percentage of CS Replacement for 0.45 Water Binder Ratio

From Fig. 4, we can see a huge difference in flow when compared to 0.35 and 0.4 W/B ratio. This is due to the less porosity of CS which allow CS to absorb less water content when compared to lesser percent of CS replacement. In this W/B ratio the flow of mortar was very high in the initial dose of superplasticizer. For 10% of CS replacement 0.65%, for 20% CS replacement 0.6%, for 30% CS replacement 0.6%, and for 40% replacement 0.4% dosage of superplasticizer is required for better flow. From the 0.2% dosage itself the mortar flow was good and with the increase in dosage of superplasticizer its cohesiveness increased and after 1% of dosage it started to bleed for 40% replaced aggregate, whereas for 10, 20, and 30% the flow even increased up to 1.4% dosage and later it started to bleed. As it was added 0.5 water binder ratio, the mortar started to bleed and hence the flow test was stopped for 0.45 water binder ratio.

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Flow for 0.45 WC Ratio 0.7 0.6

% flow

0.5 0.4 0.3 0.2

10% 20% 30% 40%

0.1 0.0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

% SP Dosage

Fig. 4 Flow behavior of mortar for 0.45 W/B ratio

4.2 Optimum Flow Behavior of CS-Based Mortar for Different Percentage of CS Replacement Figure 5 gives a graph plotted after finding out optimum dosage of superplasticizer for different replacement of mortar and different water binder ratio. From Fig. 5, the final water binder ratio and the dosage of superplasticizer are fixed. For 10% of CS-replaced mortar, the optimum dosage of water binder ratio is 0.4 and the dosage of superplasticizer is 1%; for 20% copper slag-replaced mortar water binder ratio is 0.38 and superplasticizer dosage is 0.8; 0.37 W/B ratio and 0.85 superplasticizer dosage can be used for 30% CS-replaced mortar, whereas for 40% CS-replaced mortar 0.35 water binder ratio and 1% of superplasticizer can be used for better workability and flow.

5 Results and Discussions • With the increase in copper slag content in the mortar water binder content can be reduced up to maximum extent compared to conventional mortar because of less porosity content in copper slag. • With the less absorption of water by copper slag it requires less water for good flow and hence it results in good performance with both fresh and hardened states.

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0.5

% of Flow

0.4

0.3

0.2

10% 20% 30% 40%

0.1

0.0 0.25

0.30

0.35

0.40

0.45

% of W/B ratio Fig. 5 Flow behavior of mortar for optimum dosage and W/B ratio

• As copper slag works better when compared to sand, the problem of dumping of copper slag can be reduced with the usage of copper slag in mortars. • Use of copper slag increases the self-weight of concrete.

References 1. Arpitha D, Rajasekaran C, Puttaswamy N (October 2018) Investigations on compatibility of cement-superplasticizer interaction and its influence on mortar workability incorporating copper slag as fine aggregate. In: IOP conference series: materials science and engineering, vol 431(8). IOP Publishing, p 082009 2. Mithun B, Palankar N (2016) Strength performance of alkali activated slag concrete with copper slag as fine aggregate exposed to elevated temperatures 3. Al- KS, Saidy AH, Taha R (2011) Effect of copper slag as a fine aggregate on the properties of cement mortars and concrete. Constr Build Mater 25(2):933–938 4. Brindha D, Nagan S (2011) Durability studies on copper slag admixed concrete 5. Ambily PS, Umarani C, Ravisankar K, Prem PR, Bharatkumar BH, Iyer NR (2015) Studies on ultra high performance concrete incorporating copper slag as fine aggregate. Constr Build Mater 77:233–240 6. Geetha S, Madhavan S (2017) High performance concrete with copper slag for marine environment. Mater Today Proc 4(2):3525–3533 7. Saak AW, Jennings HM, Shah SP (2004) Cement Concr Res 34(3): 363–371

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8. Krishnan D, Ravichandran PT, Gandhimathi VK Experimental study on properties of concrete using ground granulated blast furnace slag and copper slag as a partial replacement for cement and fine aggregate 9. Dos Anjos MAG, Sales ATC, Andrade N (2017) Blasted copper slag as fine aggregate in portland cement concrete. J Environ Manage 196:607–613

Properties of Coconut Shell Aggregate Concrete: A Review A. Sujatha and S. Deepa Balakrishnan

Abstract The demand for concrete has increased since it became an unavoidable construction material worldwide. Coarse aggregate is one of the main ingredients of concrete. Depletion of aggregate deposits occurs due to continuous extraction of aggregates, which leads to environmental degradation and thus ecological imbalance. Therefore, trends in concrete technology are currently directed toward searching for alternative sustainable materials for aggregate in order to minimize over reliance on natural resources. Many substitute materials such as aggregates from industrial wastes and byproducts are used for production of concrete. Coconut shell is a waste material from agricultural industries and available in plenty throughout the tropical regions worldwide. Coconut shells are used for many useful purposes, but most of the coconut shell wastes are yet to be utilized commercially. A promising solution to the challenges in coconut waste management involves coconut shell as aggregate in concrete. Many researches were conducted on coconut shell aggregate concrete in the last decade. This paper presents an overview of physical, mechanical and chemical properties of coconut shells, followed by a discussion on the physical, mechanical, bond and durability properties of coconut shell aggregate concrete. Structural behaviors such as shear, flexure and torsion of coconut shell aggregate concrete are also discussed. Some applications of the coconut shell aggregate concrete are also highlighted. The current understanding of coconut shell aggregate concrete provides basis for further research in this field. Keywords Aggregate · Concrete · Durability · Mechanical properties · Physical properties · Coconut shell

A. Sujatha (B) · S. D. Balakrishnan School of Engineering, Cochin University of Science and Technology, Kochi, Kerala, India e-mail: [email protected] S. D. Balakrishnan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_60

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1 Introduction Concrete is the most consumed manmade material in the world. The global production of concrete has remarkably increased in the last century, and it is expected that the demand for concrete continues to rise in future also. Major volume of concrete (about 70–80%) is occupied by aggregates [25]. Owing to increased rate of production of concrete, the demand for ingredients of concrete, especially aggregate, increases. Natural aggregates such as sand and gravel or crushed stones are used for production of concrete. The continuous extraction of these natural aggregates not only depletes their resources but also leads to serious environmental impacts such as threat to river ecosystem, non-reversible land erosion and so on, as listed in Table 1 [2]. As a result of environmental concerns, restrictions on mining of aggregates as well as banning of mining are implemented in some parts of the world [1, 18]. Current trends are directed toward finding alternate sustainable materials for production of concrete for maintaining the sustainable development. Coconut is grown in more than 94 countries, and India is the third largest coconut producer in the world. Countries with the highest coconut production are shown in Fig. 1 [26]. Coconut shells (CS) are the non-biodegradable byproducts of coconut industry and used for many beneficial purposes, such as for the production of charcoal-activated carbon and so on. But most of the CS waste is yet to be utilized commercially. Coconut shell waste from coconut industry is as shown in Fig. 2. A promising solution to the challenges in CS management is to use CS as aggregate in concrete since CS exhibits acceptable properties comparable with that of conventional coarse aggregates. Scientific research on the use of CS as aggregate replacement materials in concrete has been in progress since last decade, with the aim of establishing its feasibility for practical applications. This paper presents a literature review of the developments in lightweight coconut shell aggregate concrete (CSAC). Table 1 Summary of the major consequences of extraction of aggregate sources [27] Impact on

Description

Biodiversity

Impacts on related ecosystems (e.g. fisheries)

Land losses

Both inland and coastal through erosion

Hydrological function

Change in water flows, flood regulation and marine currents

Water supply

Through lowering of the water table and pollution

Infrastructures

Damage to bridges, river embankments and coastal infrastructures

Climate

Directly through transport emissions, indirectly through cement production

Landscape

Coastal erosion, changes in deltaic structures, quarries and pollution of rivers

Extreme events

Decline of protection against extreme events (flood, drought, storm surge)

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Fig. 1 Countries with the highest coconut production in 2016 [26]

Fig. 2 Coconut shell waste

2 Properties of Coconut Shells 2.1 Physical and Mechanical Properties The specific gravity and bulk density of CS were found to be 1.15 and 650 kg/m3 , respectively [23]. These values are far less than the conventional aggregates, and hence, they can be used for the production of lightweight aggregate concrete. It was found that the average moisture content and water absorption of the CS are 4.20 and 24.0%, respectively [7]. Aggregate crushing value and the impact value of CS are 1.6 and 3.94%, respectively [7]. Hence, CS exhibits better resistance against crushing and impact. Its surface texture is fairly smooth on concave and rough on convex face, which makes the concrete workable. An experimental study found that there

762 Table 2 Physical and mechanical properties of coconut shell aggregates [7]

A. Sujatha and S. D. Balakrishnan S. no

Physical and mechanical properties

Coconut shells

1

Maximum size (mm)

12.5

2

Moisture content (%)

4.20

3

Water absorption (24 h) (%)

24.00

4

Specific gravity

1.05–1.20

SSD apparent

1.40–1.50

5

Impact value (%)

8.15

6

Crushing value (%)

2.58

7

Abrasion value (%)

1.63

8

Bulk density

(kg/m3 )

650

Compacted loose

550

9

Fineness modulus

6.26

10

Shell thickness (mm)

2–8

is no need to treat the CS before use as an aggregate except for water absorption [21]. Physical and mechanical properties of coconut shells used for the production of CSAC are shown in Table 2 by Gunasekaran et al. [7].

2.2 Chemical Properties CS has high lignin content that makes the composites more weather resistant and low cellulose content which makes it to absorb less moisture as compared to other agricultural waste [6]. Concrete is an alkaline material that will be readily attacked by acids. Sugar has a strong retarding effect on the setting and hardening of concrete. Unlike wood, the presence of sugar in the coconut shell, as long as it is not in a free sugar form, is not going to affect the setting and strength of concrete [8].

2.3 Microstructural Properties Investigation on the microstructure of CS through SEM analysis revealed that CS specimens comprise very closely spaced discrete cells of sizes between 16.36 and 29.33 µm, and that micropores with sizes varying from 760.6 nm to 1.64 µm are present within the cells. Similarly, CS specimens also have some long continuous chain-linked cells with different widths in the range of 7.35–8.88 µm. These discrete and continuous chain-linked cells of CS specimens could be the reason for imparting more impact, crushing and abrasion resistance to CS specimens [8]. The SEM images of CS are shown in Fig. 3.

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Fig. 3 SEM images on CS specimens: a discrete cells of CS and, b continuous cells of CS [8]

3 Coconut Shell Aggregate Concrete 3.1 Mix Proportioning Conventional mix design procedures such as ACI and Indian standard methods cannot be applied to the mix design of concrete with agro-waste materials [22], since the water content of the cement paste in the fresh concrete mix is reduced progressively through absorption by the CS. Further, the compressive strength of CSAC is not only influenced by the strength of the mortar but also by the aggregate used. Hence, it is recommended to go for trial mixes for designing lightweight CSAC. Lower wood–cement ratio will result in weak bonds. CS is a wood-like material, so it is necessary to consider wood–cement ratio also during mix design. It is recommended that cement content of 480–510 kg/m3 and optimum wood–cement ratio of 0.65 may be taken to satisfy the criteria of structural LWC strength [7].

3.2 Workability and Density CSAC attains better workability because of the smooth surface on one side of the shells and the small size of CS. The 28-day air-dry densities of CSAC of the typical mixes were found to be less than 2000 kg/m3 , and hence CSAC falls under lightweight concrete [7].

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3.3 Curing Experimental studies were conducted to investigate the effect of curing conditions on compressive strength and bond strength [8]. The curing conditions considered were full water curing, intermittent water curing and no curing (full air-drying of specimens). Intermittent curing condition produced the highest CSAC strength followed by full water curing and then by air-dry curing. In another study conducted, three curing types like water curing, stream curing and conceal curing were adopted for their study. It was found that conceal-cured CSAC attained greater compressive strength than that of water cured and stream cured concrete [18].

4 Properties of CSAC 4.1 Mechanical Properties The 28-day compressive strength of CSAC was found as 19.1 N/mm2 under full water curing and it satisfied the requirement of structural lightweight concrete [4]. An experimental investigation was carried out by Gunasekaran et al. [7] to determine the mechanical and bond properties of CSAC. The mix was designed to get more compressive strength (27.1 N/mm2 ) than previous studies, and it was found that the flexural strength, split tensile strength and bond strength of CSAC were comparable to that of other lightweight aggregate concretes. CSAC with 25% cement replacement with GGBFS attained compressive strength of 27.4 N/mm3 for conceal curing. CSAC exhibits good flexural strength and highest modulus of rupture. The water-cured CSAC specimens behaved well in flexural test and conceal-cured CSAC behaved well in compression test [18].

4.2 Bond Properties A study was conducted to determine the bond between CSAC and steel reinforcement by Pullout test. It was found that the bond strength decreased with increase in coconut shell aggregate replacement but more than that of normal and lightweight concretes [24].

4.3 Durability Properties From studies conducted to determine the durability properties of CSAC, it was understood that the durability properties such as absorption, volume of permeable voids,

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765

sorptivity, rapid chloride penetrability, chloride concentration profile, resistance at elevated temperature, color changes and residual strength are comparable with other lightweight concretes [13]. It was found that the water absorption, effective porosity, sorptivity and abrasion resistance were higher for CS mixes than that of control mix and addition of mineral admixtures improved the durability properties [23].

5 Structural Behavior of Coconut Shell Aggregate Concrete 5.1 CSAC Beam Behavior Under Flexure Gunasekaran et al. [9] conducted a study on CSAC beam to study its flexural behavior. It was found that the flexural behavior of coconut shell aggregate concrete is comparable to other lightweight concretes. CSAC is able to achieve its full stain capacity under flexural loading. Deflection and cracking characteristics of CSAC were comparable with that of normal concrete [9]. The end rotations of CSAC just prior to failure values were comparable to other lightweight concretes. Horizontal cracks were not observed, which indicates the absence of bond failure. CSAC beams exhibit good ductility behavior. In another study conducted by Prithika and Jain, it has been observed that the deflection and crack width of CSAC is comparable with permissible values as given in IS 456 [19].

5.2 CSAC Beam Behavior Under Shear Flexural mode of failure was observed in beams with shear reinforcement, and diagonal shear mode failure was observed in beams without shear reinforcement. CSAC beams with and without shear reinforcements exhibited higher ductility ratios than conventional concrete. The predicted shear strength calculated using IS 456 was comparable with experimental value. The short narrow cracks with roughness in CSAC without shear reinforcement indicate good aggregate interlocking property [10].

5.3 CSAC Beam Behavior Under Torsion The behavior of CSAC beam under torsion is comparable to that of conventional concrete. The ultimate torque resistance of CSAC beams was found to be more than that of conventional concrete beams. Compared to conventional concrete CSAC specimens showed more ductility. This may be due to the natural fiber content present in coconut shell aggregate [12].

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5.4 Plastic Shrinkage and Deflection Characteristics of CSAC Slab Gunasekaran et al. [11] conducted a study to investigate the deflection and plastic shrinkage characteristics of CSAC slab. It was found that when percentage of coconut shell aggregate in concrete increases plastic shrinkage crack area decreases and the deflection increases. This implies that CSAC led to reduced plastic shrinkage cracking and more deflection compared to conventional concrete. CSAC gives warning before its failure compared to conventional concrete [11].

6 Studies on Applications of Coconut Shell Aggregate Concrete 6.1 Hollow Blocks Hollow blocks produced from coconut shell aggregate concrete were studied for the basic properties, viz., shrinkage characteristics, durability properties and bond strength. It was found that CS played a significant role in reducing the shrinkage cracks in CSAC compared to the conventional concrete. Water absorption of CSAC was found well within the allowable limits. The experimental bond stress was more than the theoretical values. Since CSAC hollow blocks are lightweight in nature, their material transport and handling cost is less. The study gives encouraged results to use CS for the production of hollow blocks [16]. In an earlier study, hollow blocks and precast slabs were produced with CSAC and constructed for practical use as shown in Fig. 4 [9]. CSAC precast slab was supported on CSC hollow blocks. Since 2007, these elements are being subjected to some practical loading (sand bags and wood

Fig. 4 CSAC used in practice a during construction and, b under service [11]

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Fig. 5 Coconut shell flooring tiles [15]

wastes). These elements are functioning without any problems and no deflection, bending, crack or damage for the past 11 years [9].

6.2 Flooring Tiles Coconut shell flooring tiles were produced and tested as suggested in IS 1237:1980. Parameters tested were flatness, perpendicularity, straightness, water absorption and wet transverse strength. The flatness, perpendicularity, water absorption and transverse strength results of conventional and coconut shell flooring tiles have given satisfactory results as per IS 1237:1980, and it was also understood that coconut shell flooring tiles are light in weight as compared to conventional tiles. Test results and performance of coconut shell tiles encourage the use of coconut shells for flooring tiles. Figure 5 illustrates the coconut shell tiles [14].

6.3 Non-pressure Pipes Non-pressure pipes normally used for drainage, irrigation and for crossdrains/culverts carrying medium traffic of reinforced CSAC pipes were selected for the study. The comparison was done for CSAC and conventional pipes. The general behavior of coconut shell aggregate concrete pipe is comparable to that of conventional concrete pipe. Three-edge bearing test results show that both coconut shell aggregate concrete and conventional concrete pipes abide more load than load specified as per IS 458:2003. The application of hydrostatic pressure did not result in the formation of beads of water on the pipe surface during the application of the test pressure of 0.07 N/mm2 as per IS 458:2003. Absorption properties of both coconut shell aggregate concrete and conventional concrete pipes are well within the allowable limits as per IS 458:1988 on the conditions specified. Test results and performance of coconut shell aggregate concrete pipes encourage the use of coconut shell as an aggregate for the replacement of conventional coarse aggregate in reinforced concrete pipes production. [15].

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7 Conclusions The journals referred provide significant information regarding the mechanical, durability, bond properties and structural element behavior of CSAC and also provide some of the possible applications of coconut shell aggregate concrete. This paper is useful for further investigation on CSAC and its applications. The following conclusions can be drawn from this study: • CS is lightweight in nature and its properties are comparable with that of other conventional aggregates, and hence CS can be used to produce LWC. • Behavior of CSAC under flexural, tensile and bond strength tests is comparable with that of conventional concrete. • Durability tests on CSAC specimen have given promising results to use CS as an alternate aggregate in the concrete production. • Structural behaviors of CSAC beams under flexure, shear and torsion were comparable with other LWCs. • CSAC slabs when tested gave more warning time before it failed, compared to conventional concrete. • Flooring tiles, hollow concrete blocks, precast slabs and non-pressure pipes are some of the practical applications of CSAC. • Further studies have to be conducted on practical applications of CSAC.

References 1. Anya CU (2015) Models for predicting the structural characteristics of sand-quarry dust blocks PhD thesis, University of Nigeria, Nsukka, Nigeria 2. Eziefula GU, Ezeh JC, Eziefula IB (2018) Properties of seashell aggregate concrete: a review. Constr Build Mater 192:287–300. https://doi.org/10.1016/j.conbuildmat.2018.10.096 3. Gagg CR (2014) Cement and concrete as an engineering material: an historic appraisal and case study analysis. Eng Fail Anal 40:114–140 4. Gunasekaran K, Kumar PS (2008) Lightweight concrete using coconut shells as aggregate. International conference on advances in concrete and construction, ICACC, Hyderabad, India, pp 450–459 5. Gunasekaran K, Kumar PS (2010) Compatibility studies on the coconut shell cement composites. Indian Concr Inst J 11(1):27–31 6. Gunasekaran K, Kumar PS, Lakshmipathy M (2011a) Study on properties of coconut shell as an aggregate for concrete. Indian Concr Inst J 12(2):27–33 7. Gunasekaran K, Kumar PS, Lakshmipathy M (2011b) Mechanical and bond properties of coconut shell concrete. Constr Build Mater 25:92–97 8. Gunasekaran K, Annadurai R, Kumar PS (2012) Long term study on compressive and bond strength of coconut shell aggregate concrete. Constr Build Mater 50:208–215 9. Gunasekaran K, Annadurai R, Kumar PS (2013a) Study on reinforced lightweight coconut shell concrete beam behaviour under flexure. Mater Des 46:157–167 10. Gunasekaran K, Annadurai R, Kumar PS (2013b) Study on reinforced lightweight coconut shell concrete beam behaviour under shear. Mater Des 50:293–301 11. Gunasekaran K, Annadurai R, Kumar PS (2013c) Plastic shrinkage and deflection characteristics of coconut shell concrete slab. Constr Build Mater 43:203–207

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12. Gunasekaran K, Ramasubramani R, Annadurai R, Prakash Chandar S (2014) Study on reinforced lightweight coconut shell concrete beam behaviour under torsion. Mater Des 57:374–382 13. Gunasekaran K, Annadurai R, Kumar PS (2015) A study on some durability properties of coconut shell aggregate concrete. Mater Struct 48:1253–1264 14. Gunasekaran K, Pennarasi G, Soumya S, Richards JN (2017) Study for the relevance of coconut shell aggregate concrete flooring tiles. Int J Civil Eng Technol 8(6):370–379 15. Gunasekaran K, Annadurai R, Chandar PS, Anandh S (2017) Study for the relevance of coconut shell aggregate concrete non-pressure pipe. Ain Shams Eng J 8(4):523–530. https://doi.org/10. 1016/j.asej.2016.02.011 16. Gunasekaran K, Pennarasi G, Thattai TD, Brinda TN (2018) Study on coconut shell concrete hollow blocks and the shrinkage, durability and bond properties of mixes used. Europeon journal of environmental and civil engineering. Published online: 24 Oct 2018. https://doi.org/ 10.1080/19648189.2018.1516165 17. Imbabi MS, Carrigan C, McKenna S (2012) Trends and developments in green cement and concrete technology. Int J Sustain Built Environ 1:194–216 18. Jaya Prithika A, Sekar SK (2016a) Mechanical and fracture characteristics of Eco-friendly concrete produced using coconut shell, ground granulated blast furnace slag and manufactured sand. Constr Build Mater 103:1–7 19. Jaya Prithika A, Sekar SK (2016b) Stress-strain characteristics and flexural behaviour of reinforced Eco-friendly coconut shell concrete. Constr Build Mater 117:244–250 20. Kanojia A, Jain SK (2017) Performance of coconut shell as coarse aggregate in concrete. Constr Build Mater 140:150–156 21. Kulkarni SVP, Kumar GB (2013) Comparative study on coconut shell aggregate with conventional concrete. J Eng Innov Technol 2(12):67–70 22. Mannan MA, Ganapathy C (2004) Mix design for oil palm shell concrete. Int J Cem Concr Res 31:l323-1325 23. Nadir Y, Sujatha A (2018a) Durability properties of coconut shell aggregate concrete. KSCE J Civil Eng 22(5):1920–1926 24. Nadir Y, Sujatha A (2018b) Bond strength determination between coconut shell aggregate concrete and steel reinforcement by pull-out test. Asian J Civil Eng 19(6):713–723 25. Shetty MS (2006) Concrete technology, theory and practice. Chand and Company Ltd, NewDelhi 26. The world leaders in coconut production. https://www.worldatlas.com/articles/the-world-lea ders-in-coconut-production.html 27. UNEP Global Environmental Alert Service, Sand, Rarer than One Thinks, 2014. See https://europa.eu/capacity4dev/unep/document/unep-globalenvironmental-alert-servicegeas-sand-rarer-one-thinks Accessed 3 July 2017

Effect of Rigidity on Seismic Analysis of Structures M. Dhileep , P. D. Arumairaj, G. Hemalatha, and M. S. Sandeep

Abstract In response spectrum method, the modal seismic response is a combination of the damped periodic part and a rigid part. In high-frequency modes, the damped periodic part of the response is negligible and the response becomes rigid. The proposed methods and the current practices that have been used to account the effect of rigid part of the response into the seismic analysis of structures and their modal response combination methods are reviewed. Case studies on (i) a squat shear wall with an aspect ratio less than unity to show the behavior of a structure in highfrequency region of a spectrum and (ii) a building with a stiff base supporting a tower to show the effect of “missing mass” on the seismic analysis of structures with rigid modes are presented. The paper concludes with a set of methods for considering the effect of rigidity in earthquake analysis of irregular structures based on the latest developments in the field. Keywords Rigid response · Damped periodic · Modal response combination · Squat shear wall · Response spectrum

1 Introduction During an earthquake, a large amount of energy is released which is transferred through the earth in the form of seismic waves. This energy is transmitted to the structure through their foundations and causes the structure to sway back and forth. The mass of the structure resists the motion and sets up inertia forces throughout the building. The effect of the earthquake on a structure depends on earthquake ground acceleration, size, and shape of the building, the arrangement of structural elements, and the distribution of mass and stiffness irregularities [1]. A short period (high M. Dhileep (B) · M. S. Sandeep Department of Civil Engineering, Muthoot Institute of Technology and Science, Ernakulam, India e-mail: [email protected] P. D. Arumairaj · G. Hemalatha Department of Civil Engineering, Karunya Institute of Technology and Sciences, Coimbatore, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_62

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frequency) structure is very stiff and it moves together with the ground. The peak acceleration in such a system is almost the same as that of peak ground acceleration which is called zero period acceleration (ZPA) [2, 3]. Deformation for such system will be comparatively lesser as its mass will move along with the ground [4]. For structures with a very long period (low frequency), the structure is extremely flexible. The mass of such structures will remain stationary while the ground below it is in motion [3, 4]. However, in actual, the building structures are neither fully flexible nor completely rigid. In earthquake-resistant design and analysis of structures, the most popular and widely used method is the response spectrum method. The structural response of the structure in high-frequency modes is static or rigid, while at low frequencies modal responses are damped periodic. In intermediate frequencies, the structural response has a combination of changing proportion of damped periodic and rigid parts. The minimum frequency in the high-frequency region beyond which the spectral acceleration becomes equal to ZPA is conventionally defined as the rigid frequency [3]. Due to the computational difficulties in the analysis of large structural models, only a few lower modes are used in the analysis and high-frequency modes are truncated [5]. The modal truncation of high-frequency vibration modes plays an important role in the response calculation of irregular, stiff, and complex structures. Sometimes, the lower vibrational mode shapes in an irregular flexible system may be a localized mode that may not have any effect on certain parts of the structure [1]. The modal responses of high-frequency modes may introduce additional error if their modal responses are not combined properly [3]. The truncation of high-frequency rigid modes results in the missing of some mass which participates in the structural response. Significant stresses are produced due to this “missing mass” [1, 5] in irregular and stiff structural systems. The maximum error due to “missing mass” for a particular piping system [3, 6, 7] was as high as 98.6%, which shows that the calculated value was only about 1.4% of the response. In buildings with stiff base and flexible towers, the error due to the “missing mass” is greater than 50% of the total building mass [8]. Attempts to correct the missing terms from the modal expansion of the high-frequency modal response were originally proposed in a different approach by Lord Raleigh in his famous work on the theory of sound in 1877 [9]. “Missing mass” correction methods have been developed to incorporate the rigid response in the truncated high-frequency modal response into account [1, 3–5, 9, 12–22]. Since the behavior of high-frequency modal response is stiff and static, its behavior generally lies in the elastic range. The behavior of high-frequency vibration modes is due to the effect of varying proportions of the damped periodic and rigid parts. The “missing mass” correction methods developed to take the effect of rigid response part and their modal combination are reviewed in this paper.

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2 Behavior of Rigid Structures For a structural system subjected to ground motion, the equation of motion is given by ¨ + CU ˙ + KU = −MUb u¨ g MU

(1)

where M, C, and K are the mass, damping, and stiffness matrices, respectively; U is the displacement vector; Ub is the static displacement vector when the base of the structure undergoes a unit deflection in the direction of the earthquake; and u¨ g is the ground acceleration. The structural response U is expressed as the superposition of modal contributions Ui as U=

N 

Ui =

i=1

N 

φi X i =

i=1

N 

i φi S Di

(2)

i=1

where φi are determined from the general eigenvalue problem Kφi = ωi2 Mφi . By using Eq. (2), Eq. (1) can be transformed into a system of uncoupled equations in modal coordinates: X¨ i + 2ξi ωi X˙ i + ωi2 X i = i u¨ g , i = 1, 2 . . . N

(3)

where i = φiT MUb is called the modal participation factor and ξi is the damping ratio for the ith mode. In the response spectrum method, the contribution of ith mode to nodal displacements U is given by Ui = φi X i = i φi S Di

(4)

where φ i can be determined from the general eigenvalue problem, Xi is the modal coordinate, S Di is the maximum spectral relative displacement for the ith and damping ξi . In high-frequency vibrational modes, the response of the structure becomes rigid and static and the periodic part of the response becomes negligible [3, 25]. Let U be the response in first “n” damped periodic modes and Uo be the stiff static response in the remaining modes having frequencies higher than the rigid frequency. Then we have, U =

n  i=1

Ui =

n  i=1

φi X i ; Uo =

n  i=n+1

Ui =

n 

φi X i

(5)

i=n+1

U = U + Uo For high-frequency vibration modes, Eqs. 1, 5, and 6 give

(6)

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¨ o + CU ˙ o + KUo = −MUbo u¨ g MU

(7)

where Ubo = Ub −

n 

φi i

(8)

i=1

Inertia and damping have no effect on the rigid response of high-frequency vibration modes. Therefore, Eq. 5 becomes, KUo = MUbo u¨ g

(9)

The ground motion in Eq. (7) is ZPA in the rigid zone and the response can be determined by static analysis. The rigid modal responses can be combined algebraically since they are in phase with each other.

3 Rigid and Damped Periodic Regions in a Response Spectrum The spectral regions, in an earthquake response spectrum, are divided into three categories: low-frequency region, where responses are damped periodic; a mid-frequency region, where responses are combinations of changing proportions of both damped periodic and rigid part; and a high-frequency region, where responses are rigid [3, 23, 25, 26]. In high-frequency region of the spectrum, the rigid modal responses are in phase with each other. However, the damped periodic responses in low-frequency modes are not in phase with each other. This region is also called an accelerationsensitive region because the structural response is related to ZPA. The frequencies lower than rigid frequency also have a rigid content [3, 25]. The rigid content decreases at lower frequencies and becomes zero at some key frequency f 1 [2, 3, 25]. This region where there is a transition of rigid content from zero to one is known as the mid-frequency region. The response in this region contains a rigid as well as a damped periodic part. This region is velocity-sensitive since the structural response is related to ground velocity. The low-frequency region is displacement-sensitive because the structural response is related to ground displacement. As the frequency increases, the contribution of the damped periodic portion of response decreases and the contribution of rigid content toward modal response increases [3, 23, 25, 27]. The rigid part of the modal responses combines algebraically, while the damped periodic part of the response combines according to the modal response combination rules. While the modal responses are being combined using modal combination rules, the changing proportions of rigid content and their behavior have to be taken into account. The three spectral regions in a response spectrum for 5% damping for El Centro (1940) earthquake ground motion are shown in Fig. 1.

Effect of Rigidity on Seismic Analysis of Structures

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Fig. 1 Spectral regions for El Centro (1940) earthquake

3.1 Rigid Frequency The minimum frequency at which the response becomes rigid and spectral acceleration becomes approximately equal to ZPA was conventionally defined as the rigid frequency [3]. This conventional definition was not so accurate and hence the results in various rigid frequencies are based on individual judgments. An alternate definition is proposed based on the visual determination from the spectral curves as the frequency at which spectral curves with different damping ratios converge with each other [2]. Beyond rigid frequency, spectral curves for different damping ratios have the same spectral acceleration. The studies conducted on 40 earthquake ground motions [25] show that curves with different damping ratios converge at different frequencies. The curves with lower damping ratios become rigid at a higher frequency than a curve with a higher damping ratio. Therefore, the rigid frequency is redefined as a damped rigid frequency. Damped rigid frequency is the frequency at which a spectral curve with a particular damping ratio converges with all other spectral curves with higher damping ratios. The modal responses become rigid above damped rigid frequency defined for a particular damping ratio, instead of the conventional rigid frequency [25].

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3.2 Key Frequencies The region between key frequency f 1 and rigid frequency f r in a response spectrum is conventionally defined as the mid-frequency region. Gupta [3] gives expressions for evaluating key frequencies. The studies conducted on 12 earthquakes [2] give an alternative expression for key frequency f 2 as 0.84 times of rigid frequency. The average value may vary depending upon the ground motions considered. These expressions involve rigid frequency, maximum spectral acceleration, S Amax, and spectral velocity SV max . Further, USNRC 2006 [23] gives an alternate procedure to identify key frequency f 2 during the generation of a spectrum. Studies [25] show that the value f 2 varies for different damping ratios. The numerical studies conducted on earthquake ground motions show that [2, 25] the values of key frequencies f 1 does not exhibit any trend. The value of maximum spectral acceleration S Amax and maximum spectral velocity SV max varies according to the damping ratio [25]. Further, the numerical studies show that the variation in correlation coefficient curves with different damping ratios with respect to frequency tends to become rigid at different frequencies, rather than at a constant rigid frequency. Therefore, instead of key frequency f 2 and a single rigid frequency for structures with different damping ratios, the damped rigid frequency f ζr can be used for a spectral curve with damping ratio ς [25]. The key frequency f 1 and damped rigid frequency f ζr for a spectral curve with 10% damping ratio of El Centro (1940) earthquake ground motion are shown in Fig. 4. The values of damped rigid frequency, f ζr and key frequency, f 1 for 20 earthquakes are shown in Table 1.

4 Case Study 1: Behavior of a Rigid Structure To study the behavior of a rigid structure, a squat shear wall with an aspect ratio less than unity is considered. The behavior of a squat shear wall during an earthquake is relatively complex. The deflection and strength of a squat shear wall are controlled by shear. The failure behavior of the squat shear wall is studied experimentally by applying monotonic and cyclic load. The energy dissipation in squat shear walls by flexural yielding was examined by Paulay et al. [28]. The stiffness of these structures is studied experimentally by conducting static, shake table, and hybrid testing [29– 34]. The details of the squat shear wall taken from a specimen used for full-scale testing [30, 31] are used. For a single degree of freedom system, Eq. (9) reduces to KU = Mu¨ g

(10)

S. California 1952

Superstition hills 1987

Nahanni Canada 1985

Irpinia, Italy 01-1980

N. Palm Springs 1986

Taiwan SMART1 1986

Friuli, Italy 09-1976

Northridge 1994

Loma Prieta 1989

12

13

14

15

16

17

18

19

20

Trinidad 1980

6

Chi-Chi, Taiwan 1999

Friuli, Italy, 05-1976

5

11

Borrego Mount. 1968

4

Brama, Greece 1985

N. California 1954

3

Kocaeli, Turkey 1999

Kern County 1952

2

10

El Centro 1940

1

9

Earthquake

S. No.

13.00

24.00

12.00

14.00

32.00

23.00

74.00

27.00

17.00

16.00

5.00

35.58

20.00

40.00

27.00

15.00

18.00

11.00

23.00

11.00

9.00

25.00

21.00

71.00

25.00

15.00

14.00

5.00

35.12

19.00

32.00

23.00

13.00

16.00

31.00

9.00

21.00

10.00

8.00

21.00

18.00

68.00

23.00

14.00

12.00

4.00

35.00

18.00

30.00

20.00

11.00

14.00

25.00

8.00

20.00

9.00

7.00

19.00

15.00

67.00

22.00

13.00

10.00

4.00

35.32

17.00

30.00

19.00

10.00

12.00

21.00

0.97

3.33

0.83

0.80

1.67

5.28

14.56

0.98

1.38

0.32

0.69

3.01

1.56

0.42

1.10

0.68

1.44

1.50

0.02

38.00

Damping ratio, ζ 0.20

0.02

0.10

Damping ratio, ζ 0.05

Key frequency f 1 , Hz

Damped rigid frequency, f ζr , Hz

Table 1 Damped rigid frequency, f ζr , Hz and key frequency, f 1 , Hz

0.91

3.85

0.82

0.78

1.77

1.58

14.20

1.10

1.39

0.87

0.76

3.18

1.53

0.41

1.22

0.69

1.16

1.47

0.05

0.84

4.02

0.81

0.80

1.88

1.27

13.59

1.36

1.39

0.91

0.82

3.24

1.53

0.40

1.25

0.70

0.32

1.43

0.10

0.73

3.98

0.80

0.82

2.08

1.08

11.58

1.40

1.42

0.86

0.89

3.22

1.51

0.40

1.24

0.70

0.70

1.39

0.20

Effect of Rigidity on Seismic Analysis of Structures 777

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Fig. 2 Geometrical details of the reinforced concrete specimen

4.1 Structural Description and Modeling To study the behavior of squat shear wall, the test specimen used for full-scale experimental testing [30, 31] is selected. The details of the reinforced concrete specimen are given in Fig. 2. The specimen consists of a wall with an overhanging beam, both on top and at the bottom. The wall is 0.4 m thick, 1.2 m in height, and 3 m long. The beams are 1.25 m thick, 0.8 m in height, and 4 m long. The overhanging portion at each end from the wall is 0.5 m. The aspect ratio of the wall is 0.4. The strength of concrete is 54 MPa, and the yield strength of the steel is 500 MPa. An additional mass of 60 tons is acting on the structure. The structure is modeled as a single degree of freedom system with the whole mass lumped at its center of gravity. The structure is analyzed using linear time history analysis and the response spectrum method. The yield strength and stiffness is taken from the load–displacement curves of the fullscale test. From the full-scale test, a modified Takeda hysteresis model with pinching is developed.

4.2 Seismic Analysis The structure is analyzed linearly using direct integration of the equation of motion. The Newmark average acceleration method is used for numerical integration. El Centro (1940) ground motion is used for structural excitation. In addition, a numerical integration is conducted, ignoring the effects of inertia and damping forces. The results of excitation force, dynamic time history analysis, and static time history are shown in Fig. 3. The results are compared with the response spectrum method of analysis and a static analysis using Eq. (10) and zero period acceleration. The results are shown in Table 2. It is observed that the structure is so stiff that it remains in the linear range for El Centro (1940) ground motion. The analysis is repeated with an additional mass of 60 tons. The corresponding results are shown in Table 3. The results show that the behavior of the structure is static and lies within the high-frequency range of the spectrum. Therefore, the response can be

Effect of Rigidity on Seismic Analysis of Structures

779

Fig. 3 a Excitation force due to El Centro (1940) ground motion. b Displacement history, direct integration method. c Displacement history from static time history analysis

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Table 2 Response corresponding to various analysis methods Analysis

Time history dynamic

Time history static

Response spectrum

Static analysis

Shear Force kN Error w.r.t direct integration %

79.14 (0.00)

80.64 (1.89)

80.65 (1.91)

80.47 (1.68)

Table 3 Response corresponding to various analysis methods with additional 60-ton mass Analysis

Time history dynamic

Time history static

Response spectrum

Static analysis

Shear Force kN Error w.r.t direct integration %

293.20 (0.00)

285.65 (2.58)

292.05 (0.39)

285.92 (2.48)

evaluated using Eq. (10), using zero period acceleration of the spectrum instead of dynamic analysis. In the present case, the yield strength of the structure is so high compared to the shear force demand of the ground motion.

5 Modal Response Combination The modal response and combined response attain their peak values at different time instants. Earlier an absolute sum (ABSSUM) of the modal responses is taken, ignoring their algebraic sign and assuming that all modal peaks occur at the same time. However, the upper bound is too conservative and therefore in 1951, E. Rosenblueth in his Ph.D. thesis developed the square root sum of squares (SRSS) rule for modal response combination [4]. Although SRSS modal combination gives excellent results for well-separated modes, it is replaced with a complete quadratic combination rule (CQC), which is applicable to structures with a wide range of frequencies [35]. In CQC, a correlation coefficient [36] is introduced and it varies between 0 and 1. The CQC reduces to SRSS if the modes are well separated and to ABSSUM if the modes are closely spaced [25]. For combining modal responses in pushover analysis, SRSS is recommended for modal responses whose frequencies are well-separated modes and CQC for others. In high-frequency region the modal responses are rigid and are in phase with each other. The modal responses are static in nature and they combine algebraically irrespective of whether the modes are well separated or closely spaced. The combination of rigid response from high frequencies is attended by Gupta [3]. The correlation factor used in CQC is further modified to take the effect of rigid content of highfrequency modal response into account (also known as modified double sum method). The correlation coefficients are further modified to include the effect of non-classical damping in modal response combination [2]. Gupta method and Lindley and Yow

Effect of Rigidity on Seismic Analysis of Structures

781

method are recommended for the modal response combination by the United States Nuclear Regulatory Commission [23]. The Gupta method has no limitation for the combination of the modal responses in the low-frequency region [26, 27]. Rigid frequency is redefined based on damping ratios as damped rigid frequency and a modal response combination rule is modified accordingly [25]. The peak value of the total structural response R is expressed as the combination of peak modal response of individual modes as, R2 =

N 

Ri2 +

N  

ε i j Ri R j

(11)

i=1 j=i

i=1

where Ri is the maximum value of modal response in the ith mode and εi j is the modified correlation factor given by     1 − αi2 1 − α 2j εi j εi j = αi α j +

(12)

where αi is the rigid response coefficient in the ith mode and εi j is the correlation coefficient of the damped periodic part of modal responses, given by the complete quadratic combination (CQC) rule. For damped periodic modes, α = 0; therefore, the modified double-sum equation reduces to CQC and for εi j = 0, the modified doublesum method further get reduced to the square root of the sum of squares (SRSS). Equations (11) and (12) include the effect of the rigid response of high-frequency modes in the modified correlation coefficient εi j . The rigid response coefficient α i is defined as [2, 3],

td αi = −

x¨i (t)u¨ g (t)dt

0

td σix¨ σ u¨ g

(13)

where x¨i (t) is the acceleration response, σix¨ and σ u¨ g are the standard deviations of x¨i (t) and u¨ g (t), respectively, and td is the duration of responses. The value of α gradually reduces from one to zero, from the rigid frequency for a particular damping ratio to a key frequency f 1 [6, 10, 12]. The key frequency f 1 is the frequency at which the rigid response coefficient becomes zero. An approximate equation for α i can be represented by a straight line between the key frequency f 1 and rigid frequency for a particular damping ratio on a semi-logarithmic graph, and is given by Dhileep and Nair [25], αi =

ln f i / f 1 , 0 ≤ αi ≤ 1 ln f ςr / f 1

(14)

where f i is the modal frequency in hertz and the key frequency f 1 can be expressed as,

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f1 =

S Amax , Hz. 2π SV max

(15)

where S Amax = maximum spectral acceleration, SV max = maximum spectral velocity. International building codes of practice recommend CQC and SRSS for wellseparated modes [37–47]. However, Indian code IS 1893:2016 recommends CQC for modal response combination, SRSS for well-separated modes, and summation of the absolute value of response for closely spaced modes. The IS code recommends modal response combination for modes up to 33 Hz and “missing mass” correction using well-established principles of structural dynamics. New Zealand code NZS 1170-5 recommends CQC and refers [3] for other methods. In addition to CQC and SRSS, ASCE/SEI 7-10 (2010) recommends the CQC-4 (ASCE 4-16) method used for each of the modal values where closely spaced modes have a significant cross-correlation of translational and torsional responses. According to ASCE4-16, the acceptable procedure for combining modal response includes CQC. For general cases which include the rigid and periodic modes, Gupta or Lindley-Yow method is recommended. When high-frequency modes are combined into a single residual response mode, the residual rigid response shall be combined algebraically with additional rigid modes considered. The resulting total rigid response shall be combined with the periodic response by the SRSS method.

6 “Missing Mass” Correction Methods Methods for correcting “missing mass” have been developed to take the effect of the rigid part of the response in the truncated high-frequency modes into account. The most widely used methods are the mode acceleration method [4, 9, 13, 19], and residual mode method [5–8, 12–18, 22]. Comparative studies are conducted to address the advantages and disadvantages of these methods [10, 11, 20, 21]. The studies show that “missing mass” correction method using residual mode is more advantageous than other methods to take into account the effect of uncalculated modal responses of the high-frequency modes. The residual mode method approximates the damped periodic part of the response as well in addition to the rigid static part. This helps in reducing the effect of subjective rigid frequencies by engineers based on their judgments. The rigid residual mode can be included as an additional mode like other modes in the response spectrum method of seismic analysis. The residual mode method is comparatively easier and the corresponding residual response can be combined with other modal responses using the modal response combination rules [21].

Effect of Rigidity on Seismic Analysis of Structures

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7 Case Study 2: “Missing Mass” Effect The effect of “missing mass” is studied with the help of a building structure with a stiff base supporting a flexible tower [8], as shown in Fig. 4. The modal properties of the structure are given in Table 4. The fifth mode is a rigid mode and lies in the rigid zone of the response spectrum and its modal mass participation is 57.48%. El Centro (1940) ground motion is used for seismic excitation. The structure is analyzed using all the modes. The fifth mode with a frequency higher than 33 Hz is truncated and the structure is analyzed using the first four modes. The modal mass contribution of the first four modes at mass points (nodes) is given in Table 5. Further, a missing mass correction using residual mode is applied for the truncated rigid mode. The response corresponding to the residual mode is combined with the responses of the Fig. 4 Five storied building with a stiff base supporting a flexible tower, case study 2

Table 4 Modal properties of five-storied building shown in Fig. 4

Modal properties Mode number

Frequency (Hz)

Damping ratio (%)

Mass participation (%)

1

4.25

5

38.06

2

12.12

5

3.54

3

18.18

5

0.78

4

21.61

5

0.12

5

78.85

5

57.48

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Table 5 Modal mass contribution at each node Modal properties Node number

Modal mass contribution at each node from the first 4 modes

1

0.004

2

1.021

3

0.999

4

1.000

5

1.000

Table 6 Error in spring force (N) of 6 DOF system shown in Fig. 3 Seismic analysis

Element 1

All modes

5.87 × 105 4.21 × 105 3.5 × 105

Element 2

Element 3

Element 4

2.38 × 105 9.71 × 105

Element 5

Modes till 33 Hz Error w.r.t. all modes

4.23 × 105 4.22 × 105 3.5 × 105 (−27.9) (0.23) (0.00)

2.38 × 105 0.97 × 105 (0.00) (−90.01)

Modes till 33 Hz + Residual 5.87 × 105 4.21 × 105 3.50 × 105 2.38 × 105 9.71 × 105 mode (0.00) (0.00) (0.00) (0.00) (0.00) Error w.r.t. all modes w.r.t. = with respect to

other modes using the Gupta method. The results are shown in Table 6. The error is calculated by comparing the analysis results with the combined response of all modes. The results show that truncation of the fifth mode results in the underestimation of storey shear in the first storey and top storey. The error in the estimation of top storey shear is as high as 90%. The mass participating in the first four modes is only 42.53%. The spatial distribution of modal mass contribution shows that the modal mass participating at node 1 is only 0.004, whereas at node 2 it is 1.21. The frequency of the residual mode is 78.85 Hz. The results show that the error in using residual mode is 0% in this case.

8 Number of Modes Required for Dynamic Analysis Considerable research is done regarding the importance of higher modes and modal analysis, but only a few researchers have addressed the issue of the required number of modes [1, 49] for earthquake analysis of structures. The total mass of the structure is equal to the sum of the effective modal masses in all the modes. The truncation of higher modes results in the missing of some mass participating in the truncated modes of the structural system. This “missing mass” is generally distributed throughout the building depending on their spatial distribution. Most of the seismic design codes

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around the world specify that at least 90% of the total structural mass should participate in the number of modes considered in either direction [37–48]. Additionally, Euro Code recommends all modes with effective modal masses greater than 5% of the total mass to be taken into account. The studies on irregular buildings [1] and by Mehrraoufi [50, 51] on multiframe bridges show that the criteria of 90% structural mass participation for the number of modes to be considered for dynamic analysis of structures given by the seismic building codes of practice may not result in correct responses in all the structural elements of an irregular buildings. Therefore, for irregular structures, all the modes up to damped rigid frequency have to be considered and “missing mass” correction beyond damped rigid frequency.

9 Conclusions As seen from the review, considerable progress has been made toward the understanding of the seismic behavior of high-frequency vibration modes. The behavior of high-frequency modes and the effect of rigidity in different spectral zones in an earthquake response spectrum are reviewed. The rigid frequency and the associated frequencies are discussed and suitable recommendations are given. A case study of seismic analysis of squat shear wall is presented to show that the behavior of a structure in the high-frequency region is essentially static. The frequency of the squat shear wall lies in the high-frequency region of the spectrum. It is observed that the response of stiff structures can be evaluated using a static analysis subject to a force equal to the product of the mass of the structure and zero period acceleration. Further, it is observed that the provisions given in codes are not adequate to take the effect of rigid content into account. Various modal response combination rules and “missing mass” correction methods are reviewed in detail and the superior method which takes the effect of rigid content is suggested. Based on the review, for earthquake analysis of stiff and irregular structures, all the modes up to damped rigid frequency have to be considered. The effect of truncated rigid response corresponding to high-frequency modal responses beyond damped rigid frequency has to be considered using a residual mode method. The modal responses and residual mode response have to be combined using CQC with modified correlation coefficient and rigid coefficient evaluated using damped rigid frequency. The effect of truncated rigid response and the “missing mass” effect are illustrated using a case study of a stiff structure with a flexible tower. The recommended methods may be incorporated in building codes of practice and commercial software used for earthquake resistant design and analysis of structures.

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References 1. Dhileep M, Bose PR (2009) Seismic analysis of irregular buildings: “missing mass” effect. J Struct Eng SERC 35:359–365 2. Gupta AK, Hassan T, Gupta A (1996) Correlation coefficients for modal response combination of non-classically damped systems. Nuclear Eng Des 165:67–80 3. Gupta AK (1992) Response spectrum method: in seismic analysis and design of structures. Blackwell Scientific Publications, Boston, Mass 4. Chopra AK (2008) Dynamics of structures: theory and applications to earthquake engineering. Prentice-Hall of India, New Delhi 5. Powel GH (1979) Missing mass correction in modal analysis of piping systems. In: Transaction of the 5th interntional conference on structural mechanics in Reactor Tech, vol k(b) 6. Gupta AK, Jaw JW (1984) Modal combination in response spectrum analysis of piping systems. In: Seismic effects in PVP components. PVP. ASME, p 88 7. Gupta A, Gupta AK (1998a) Missing mass effect in coupled analysis I: complex modal properties. J Struct Eng ASCE 124:490–495 8. Salmonte AJ (1982) Considerations on the residual contribution in modal analysis. Earthq Eng Struct Dyn 10:295–304 9. Geradin M, Rixen D (1997) Mechanical vibrations: theory and applications to structural dynamics. Wiley, Chichester, England 10. Hure D, Morysse M (1976) Comparative methods for analysis of piping systems subjected to seismic motion. Nuclear Eng Des 38:511–525 11. Krause G (1979) Residual load method for modal analysis of piping systems subjected to seismic excitation. Nuclear Eng Des 55:315–322 12. Vashi KM (1981) Computation of seismic response from higher frequency modes. In: Transaction of ASME, Pressure Vessels and Piping, 03 13. Cornwell RE, Craig RR, Johnson CP (1983) On the application of the mode acceleration method to structural dynamics problems. Earthq Eng Struct Dyn 11:679–688 14. Hadjian AH, Lin ST (1986) Higher modes contribution to total seismic response. In: Proceeding of U.S. National Conference on Earthquake Engineering, vol ll, Charleston S.C. 15. Maldonado GO, Singh MP (1991a) An improved response spectrum method for calculating seismic design response: part 1 classically damped structures. Earthq Eng Struct Dyn 20:621– 635 16. Maldonado GO, Singh MP (1991b) An improved response spectrum method for calculating seismic design response: part 2 non-classically damped structures. Earthq Eng Struct Dyn 20:637–649 17. Mitchell LD (1994) Modal test methods: quality, quantity and unobtainable. J Sound Vibr 28:10–17 18. Gupta A, Gupta AK (1998b) Missing mass effect in coupled analysis II: residual response. J Struct Eng ASCE 124:496–500 19. Clough RW, Penzien J (1993) Dynamics of structures. McGraw-Hill Book Co., New York 20. Dickens JM, Nakagawa JM, Wittbrodt MJ (1997) A critique of mode acceleration and modal truncation augmentation methods for modal response analysis. Comput Struct 62:985–998 21. Dhileep M, Bose PR (2008) A comparative study of “missing mass” correction methods for response spectrum method of seismic analysis. Comput Struct 86:2087–2094 22. Zhao J, Gupta A (2002) Redundancy in residual vectors for missing mass effect in coupled modal synthesis. J Struct Eng ASCE 128:1231–1235 23. USNRC (2006) Combining modal responses and spatial components in seismic response analysis. Regulatory guide 1.92, Office of nuclear regulatory research, US Nuclear Regulatory Commission R2. 24. Chopra AK (1996) Modal analysis of linear dynamic systems: physical interpretation. J Struct Eng ASCE 122:517–527 25. Dhileep M, Nair SS (2012) Effect of rigid content on modal response combination. In: Proceedings of the ICE—Structures and Buildings, vol 165, pp 287–297

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26. Morante R, Wang Y, Chokshi N, Kenneally R, Norris W (1999) Evaluation of modal combination methods for seismic response spectrum analysis. In: 15th international conference on structural mechanics in reactor technology, Seoul 27. Saigal RK, Gupta A (2007) Combination of modal responses: a closed-form formulation for rigid response coefficient. Nuclear Eng Des 237:2075–2082 28. Paulay T, Priestley MJN, Singe AJ (1982) Ductility in earthquake resisting squat shear walls. ACI J 79(4):257–269 29. Farrar CR, Baker WE (1993) Experimental assessment of low-aspect-ratio, reinforced concrete shear wall stiffness. Earthq Eng Struct Dyn 22:373–387 30. Beko A, Rosko P, Wenzel H, Pegon P, Markovic D, Molina FJ (2015) RC shear walls: full-scale cyclic test, insights and derived analytical model. Eng Struct 102:120–131 31. https://www.vce.at/iris/pdf/irisbook/iris_chapter10.pdf 32. Brun M, Labbe P, Bertrand D, Courtois A (2011) Pseudo-dynamic tests on low-rise shear walls and simplified model based on the structural frequency drift. Eng Struct 33:796–812 33. Rama Rao GV, Gopalakrishnan N, Jaya KP, Muthumani K, Reddy GR, Parulekar YM (2014) Studies on nonlinear behavior of shear walls of medium aspect ratio under monotonic and cyclic loading. J Perform Constr Facil ASCE 30(1) 34. Whyte CA, Stojadinovic B (2013) Effect of ground motion sequence on response of squat reinforced concrete shear walls. J Struct Eng ASCE 35. DOI 10.1061/(ASCE)ST.1943–541X.0000912 36. Wilson EL, Der Kiureghian A, Bayot EP (1981) A replacement for the SRSS method in seismic analysis. Earthq Eng Struct Dyn 9:187–194 37. Der Kiureghian A (1981) A response spectrum method for random vibration analysis of MDF systems. Earthq Eng Struct Dyn 9:419–435 38. ASCE/SEI 7-10 (2010) Minimum design loads for buildings and other structures. American Society of Civil Engineers, Virginia 39. ASCE/SEI 4-16 (2017) Seismic analysis of safety-related nuclear structures. American Society of Civil Engineers, Virginia 40. IS 1893 (Part 1) (2016) Criteria for earthquake resistant design of structures, part 1 general provision and buildings. Bureau of Indian Standards, New Delhi 41. International Association for Earthquake Engineering, Regulations for Seismic Design—A World List, 1996 42. International Association for Earthquake Engineering, Regulations for Seismic Design–A World List 1996—Supplement, 2000 43. UBC (1997) Structural design requirements. In: International conference of building officials, vol 2, California, USA 44. Comite Europeen de Normalisation CEN (2004) Eurocode 8—Design of structures for earthquake resistance. Part-1. General rules, seismic actions and rules for buildings. European Committee for Standardization, Brussels. 45. Standards New Zealand (2004) NZS 1170–5 (S1): structural design actions—Part 5: earthquake actions—New Zealand. Wellington, NZ 46. Standard No. 2800 (2007) Iranian code of practice for seismic resistant design of buildings. BHRC Publication No. S-465, Tehran 47. The Government of the Republic of Turkey (2007) Specification for buildings to be built in seismic Zzones. Ministry of Public Works and Settlement, Government of the Republic of Turkey 48. SNI-02-1726-2002 (2002) Seismic resistance design standard for buildings. Ministry of Public Work, Indonesian National Standardization Agency 49. Caltrans (2013) Caltrans seismic design criteria version 1.7. Sacramento. California Department of Transportation, CA 50. Lopez OA, Cruz M (1996) Number of modes for the seismic design of buildings. Earthq Eng Struct Dyn 25:837–855

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51. Mehr M, Zaghi AE (2016) Seismic response of multi-frame bridges. Bull Earthq Eng 14(4):1219–1243 52. https://doi.org/10.1007/s10518-016-9882-y 53. Masoud M (2015) Seismic transverse response of multi-frame bridges. Doctoral Dissertation, University of Connecticut. https://digitalcommons.uconn.edu/dissertations/762.

Effect of pH on Compressibility Behaviour of Cement-Treated Soil Suresh Kommu and SS Asadi

Abstract To enrich the performance of structures, the stability of underlying soils must be checked. The stability of soil may change due to discharge of pollutants into water bodies without adequate treatment which causes momentous changes in the behaviour of water and further leads to changes in the pH of water. In the present study the black cotton soil has been treated with ordinary Portland cement of 53-grade and Portland slag cement with different percentages (3, 6 and 9%), and laboratory tests such as Atterberg limits, compaction, UCS, CBR and consolidation have been performed. This paper attempts to assess the effect of pH (pH = 5, 7 and 9) levels on curing time (7, 14 and 28 days) behaviour of cement-treated soil. Test results have shown that there is an increase in OMC which leads to decrease in MDD. The UCS and CBR strengths of soil got increased due to the addition of cement; besides that, there is a reduction in the compressibility with the addition of cement content which were cured for ages (7, 14 and 28 days). Keywords pH · Compressibility · Strength characteristics and curing time

Notations Cc k Mv Cv

Compression index Permeability Coefficient of volume compressibility Coefficient of consolidation.

S. Kommu (B) Department of Civil Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, Andhra Pradesh 522502, India e-mail: [email protected] Department of Civil Engineering, VNR Vignana Jyothi Institute of Engineering and Technology, Hyderabad, Telangana 500090, India SS Asadi Department of Civil Engineering, Vignan’s Foundation for Science Technology and Research, Deemed to Be University, Guntur, Andhra Pradesh 522213, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_63

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1 Introduction Generally, industries are the main source for human life and developing countries. Because of the increase in the industrial activities, the waste which has been released from these industries causes enormous changes. In most of the developed countries, among 70% of solid and liquid wastes are dumped into water bodies without appropriate treatment due to which the ground water is getting polluted. The contaminated water contains heavy metals which create problems in environment due to which the pH of water may vary. If the pH level of water is 7 it comes under alkaline water. The change in the pH of water may affect the soil which leads to geotechnical problems. The reduction in the strength properties may be found, because of the mineralogical changes in the behaviour of soil. Mostly, expansive soils are the most problematic soils that exert pressure on the foundation or basement which results in lateral moment of the structure. These soils become sticky when they absorb water and become hard and brittle when they are in dry state. It can be avoided by improving the properties of soil which further increases the strength, stiffness, and so on. To accomplish higher strength, stabilization can be used by adding different additives. In the present study two different types of cements, namely ordinary Portland cement and Portland slag cement, have been used. The technical information about cement-treated soil mixtures have been carried out from various research works, in which study [1] revealed that the maximum dry density has been decreased with the increase in the OMC with the addition of cement. The results that are obtained from [2] using lime and cement have concluded that cement treatment is more efficient than lime treatment in improving the values of CBR. Paper [3] shows that the unconfined compressive strength increases with the increase in the amount of cement content and for mixtures with 0% cement. The CBR values for unsoaked specimens are greater than those of soaked specimens. However, the CBR for soaked specimens are higher than those of unsoaked specimens. Paper [4] shows the investigation of stabilized soil by mechanical means such as chemical stabilization or vibration and compaction by using cement. Properties of stabilized sand were evaluated, and the curing periods with variations in cement content were quantified in [5]. The compression index (C c ) for cement-treated soils was found to be decreased when compared to the untreated soil samples with increase in the curing ages as mentioned in [6]. In this investigation the effect of acids and alkalis separately by varying pH (pH=5, pH=7 and pH=9) levels and curing time behaviour of black cotton soil when treated with different proportions of OPC and PSCon behaviour and strength characteristics of soils can be found by performing a series of UCS, CBR and consolidation tests.

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2 Aim of the Study The aim of this research was to establish the effect of acidic and alkaline nature on curing time behaviour of cement-treated soil.

3 Objectives of the Study • To analyse the properties such as consistency limits, grain size distribution and standard proctor test of black cotton soil before and after stabilization with two different types of cement (OPC and PSC). • To assess the behavioural changes and strength characteristics of treated soils which were cured under different pH (pH = 5, 7 and 9) levels. • To evaluate the effect of pH (pH = 5, 7 and 9) and curing time on various parameters such as coefficient of consolidation, compressibility, coefficient of volume compressibility and permeability of untreated and treated soil. • A comparative study is made between the soil treated with ordinary Portland cement and Portland slag cement which were cured under varied pH conditions. The soil treated with cement (OPC, PSC) which yields more strength is considered to be best suited for construction purposes.

4 Materials Used 4.1 Cement In the present study the ordinary Portland cement and Portland slag cement was purchased from a cement company in Hyderabad. The ordinary Portland cement (OPC) of 53-grade is a type of hydraulic cement, which has been used worldwide and Portland slag cement (PSC) is an intimate mixture of OPC and granulated slag cement.

4.2 Black Cotton Soil The black cotton soil which was collected from Medchal Road, Ranga Reddy district, Telangana state of India at a depth of 0.3 m was blackish grey colour. Before conducting the laboratory experiments the soil was oven dried and later, the index and engineering properties of soil has been determined as per the Indian standards (Table 1).

792 Table 1 Properties of black cotton (BC) soil

S. Kommu and SS Asadi S. No.

Property

BC soil

1

Specific gravity

2.6

2

Gravel size (%)

0

3

Sand size (%)

5

4

Silt size (%)

33

5

Clay size (%)

62

6

Liquid limit (LL) (%)

62

7

Plastic limit (PL) (%)

37.3

8

Plasticity index (PI) (%)

24.7

9

Classification [3]

CH

10

pH

7.82

11

Organic content (%)

10.8

12

Optimum moisture content (%)

19.8

13

Maximum dry density (g/cc)

1.48

14

Unconfined compressive strength (kg/cm2 )

1.74

15

California bearing ratio test (%)

3.74

5 Laboratory Mix Design In the present study, the chosen black cotton soil was mixed in dry condition with ordinary Portland cement (53-grade) and Portland slag cement individually with various percentages (3, 6 and 9%).

6 Methodology 6.1 Laboratory Experiments Various tests were carried out in the laboratory, and the index and engineering properties of the soil samples have been determined as per the Indian standard specifications. The specific gravity of the chosen soil was dogged by using density bottle based on [7]. The grain size distribution of the soils has been strong-minded as per [8] and the soil classification is based on [9]. The casagrande liquid limit apparatus was used to determine the liquid limit of untreated and various soil–cement mixes, and plastic limit test has been conducted using rolling thread method as outlined in [10]. The standard proctor test was conducted to determine the direction of OMC and MDD of the soil according to IS:2720-Part7 [11]. The organic matter of the chosen soil can be determined using [12] and the pH of the soil can be found using [13].

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Fig. 1 UCS specimens under testing

(a) Before curing

6.1.1

(b) After curing

Unconfined Compressive Strength

Preparation of Specimen The soil sample which was sieved through 425 µ sieve was mixed with various percentages (3, 6 and 9%) of cement at required OMC. Later, the design mix has been compacted in the compaction mould. Further, the sample was ejected from the mould and checked for required dimensions (38 mm diameter and 76 mm height) as per the standards. For each cement content, nine set of specimens have been prepared for chosen soil with ordinary Portland cement and Portland slag cement separately. The specimens were wrapped in a polythene cover for one day and later, and the specimens were directly immersed in water at three different pH levels (pH = 5, 7 and 9) for curing ages of 7, 14 and 28 days. Test Procedure The unconfined compressive strength was determined as per [14] by placing the uncured and cured cylindrical-shaped specimens on the base plate, and without any stress application on the sample, the load frame has been fixed. Later, by adjusting the dial gauge and proving readings to zero at a strain rate of 1.5 mm/min, the proving ring readings are to be noted for regular intervals of dial gauge readings. The UCS specimens under testing can be shown in Fig. 1.

6.1.2

California Bearing Ratio Test

California bearing ratio test is most important for pavements because the thickness of pavement depends upon CBR value of soil as per IRC.

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6.1.3

S. Kommu and SS Asadi

Preparation of Specimen

Unsoaked Specimen The soil–cement mix at optimum moisture content for various percentages (3, 6 and 9%) of cement was compacted by placing a spacer disc at the bottom of the CBR mould in five equal layers. The excess soil is trimmed off by removing the collar. Later, the spacer disc was removed by reversing the mould with the addition of surcharge loads on the top of the soil specimen. Soaked Specimen The soil sample was prepared by compacting the design mix in CBR mould. Before performing the test, the porous plate was placed on the top of the soil sample along with a filter paper in addition of surcharge loads. Later, the mould containing soil is engrossed in water at three different pH (pH = 5, 7 and 9) levels for curing period of 7, 14 and 28 days. Test Procedure The CBR mould is placed on the testing machine and the plunger is brought in contact with the soil sample. The proving ring and dial gauge readings are set to zero. The CBR value can be found as per [15] at a penetration rate of 1.25 mm/min. The specimen under testing was shown in Fig. 2. Fig. 2 CBR specimen under testing

Effect of pH on Compressibility Behaviour of Cement-Treated Soil

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Consolidation Test

Preparation of Specimen The test specimens were prepared by compacting the soil–cement mixture with different cement percentages (3, 6 and 9%) in standard proctor compaction mould at obtained optimum moisture content on non-treated and cement-treated soils. After completion of compaction the specimens were extracted from the compaction mould as per the required dimensions (2 cm height and 10 cm diameter) and the excess soil was trimmed off. The consolidation ring containing soil sample was placed in consolidation cell by providing the porous stones on the top and bottom of the specimen along with a filter paper which was placed between the porous stones and specimen. Now, the consolidation cell is adjusted in a suitable position in the loading device. Test Procedure The consolidation test was carried out according to IS 2720-15 [16] at a pressure increment of 0.25, 0.5, 1.0 and 2.0 kg/cm2 by varying pH (pH = 5, 7 and 9) levels. For each load increment the corresponding dial gauge readings are taken using time (minutes) sequence of 0.00, 0.25, 1.00, 4.00, 9, 16, 25, 36, 49, 64, 81, 100 and 1440.

6.2 Analysis of Test Results 6.2.1

Effect of Cement on Engineering Properties

Atterberg limits The liquid limit (LL) and plastic limit (PL) of black cotton soil increase with the increase in the cement contents, and the drop in the plasticity index (PI) was found with the increase in the cement contents (Figs. 3, 4, and 5).

6.2.2

Compaction Characteristics

The increase in the addition of cement decreases the maximum dry density with the increase in the corresponding values of optimum moisture content (Figs. 6 and 7).

6.2.3

Strength Characteristics

The unconfined compressive strength and California bearing ratio values increases when black cotton soil is treated with ordinary Portland cement and Portland slag cement individually with the increase in the cement content (Table 2).

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Fig. 3 Variation of liquid limit for black cotton soil when treated with ordinary Portland cement (OPC) and Portland slag cement (PSC) individually

Fig. 4 Variation of plastic limit for black cotton soil when treated with ordinary Portland cement (OPC) and Portland slag cement (PSC) individually

6.2.4

Influence of Curing Time

The effect of curing time for 7, 14 and 28 days on various cement contents (3, 6 and 9%) was studied. The strength of soil–cement mixes has been increased with the curing ages. This gain in strength may continue for years which further increase the UCS and CBR values. The UCS and CBR specimens at the time of curing are shown in Fig. 8.

Effect of pH on Compressibility Behaviour of Cement-Treated Soil

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Fig. 5 Variation of plasticity index for black cotton soil when treated with ordinary Portland cement (OPC) and Portland slag cement (PSC) individually

Fig. 6 Variation of OMC for black cotton soil treated with OPC and PSC separately

7 Effect of pH and Curing Time on Strength Characteristics The UCS and CBR strengths of black cotton soil increase with an increase in curing periods/days (Figs. 9, 10, 11, 12, 13, and 14).

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Fig. 7 Variation of MDD for black cotton soil treated with OPC and PSC separately

Table 2 UCS and CBR values of BC soil treated with OPC and PSC Cement content (%)

BC + OPC CBR (%)

BC + PSC UCS (kg/cm2 )

CBR (%)

UCS (kg/cm2 )

3

9.3

4.2

7.2

3.7

6

14.5

7.1

13.8

4.8

9

21.7

8.3

19.6

7.2

(a) UCS samples at the time of curing

(b) CBR samples at the time of curing

Fig. 8 Curing of UCS and CBR specimens when BC soil treated with OPC and PSC under different pH [pH = 5 (acid), pH = 7 (neutral) and pH = 9 (base)] levels

Effect of pH on Compressibility Behaviour of Cement-Treated Soil Fig. 9 Variations in the unconfined compressive strength of black cotton soil treated with cement (OPC, PSC) which were cured under different acid (pH = 5) for curing ages of 7, 14 and 28 days

Fig. 10 Variations in the unconfined compressive strength of black cotton soil treated with cement (OPC, PSC) which were cured under different base (pH = 9) for curing ages of 7, 14 and 28 days

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Fig. 11 Variations in the unconfined compressive strength of black cotton soil treated with cement (OPC, PSC) which were cured under different neutral (pH = 7) for curing ages of 7, 14 and 28 days

Fig. 12 Variations in the CBR values of black cotton soil treated with cement (OPC, PSC) which were cured under different acid (pH = 5) for curing ages of 7, 14 and 28 days

7.1 Effect of pH and Curing Time on Consolidation Parameters The black cotton soil when treated with ordinary Portland cement and Portland slag cement separately under different pH (pH = 5, 7 and 9) levels, the coefficient of consolidation and compressibility decreases with the increase in the cement contents

Effect of pH on Compressibility Behaviour of Cement-Treated Soil

801

Fig. 13 Variations in the CBR values of black cotton soil treated with cement (OPC, PSC) which were cured under different base (pH = 9) for curing ages of 7, 14 and 28 days

Fig. 14 Variations in the CBR values of black cotton soil treated with cement (OPC, PSC) which were cured under different neutral (pH = 7) for curing ages of 7, 14 and 28 days

and curing ages. Whereas on the other side the coefficient of volume compressibility and permeability increases with curing ages and decreases with the addition of cement content.

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8 Discussions • The liquid limit and plastic limit values of black cotton soil increase after addition of various percentages (3, 6 and 9%) of cements; besides that, the drop in the plasticity index values was observed with the addition of cement contents. The reduction in the plasticity index was due to cementitious links between the soil particles and calcium silicates and aluminate hydration products as per the previous study [2]. However, the decrease in the plasticity index values increases the workability of soils and also improves the volume change characteristics. • According to Fig. 6, the maximum OMC is required to stabilize the black cotton soil with ordinary Portland cement compared with Portland slag cement, and Fig. 7 illustrates that the maximum MDD is attained for BC + OPC when compared to BC + PSC. The increase in the optimum moisture content was because of cement which consists of fine particles in it. With the increase in the fine particles the surface area is going to be increased which further needs a supplementary quantity of water and the decrease in the maximum dry density with the addition of cement was due to phenomenon of flocculation and agglomeration of fine-grained soil. Similar results have been observed in [17]. • According to Figs. 11, 12, 13 and 14, the maximum UCS and CBR values are accomplished for black cotton soil when treated with OPC compared to PSC. This indicates that the increase in the CBR value increases the bearing capacity of the soil and there is a decrease in the total thickness of the pavement. The increase in the strength with the increase in the percentages of cement was due to earlier hydrations reactions and formation of secondary cementitious products as studied from [18]. The UCS and CBR strengths got increased when the black cotton soil is treated with ordinary Portland cement under pH = 7 (neutral) and the same soil when treated with Portland slag cement the UCS and CBR strengths got increased in pH = 9 (base) compared with pH = 7 (neutral) and pH = 5 (acid). This is because of slag cement which acts as excellent resistance to alkali and sulphate attacks. • According to Tables 3, 4, 5, 6, 7 and 8, the coefficient of consolidation decreases with the increase in the percentages of cement and curing ages. Similarly, the compression index got decreased with the increase in the cement contents and curing ages. This is because of the effect of cement content which affects the structuration of the soil and makes the stabilized soil to become stiffer as studied in [6]. Besides that, the coefficient of volume compressibility increases with the increase in the curing ages and decreases with the addition of cement content and similarly the permeability of black cotton soil decreases with the increase in the cement content and increases with the increase in the curing ages. This is due to the decrease in the voids present in the soil particles with the increase in the cement content which improves the bonding between the cement and soil particles. • The black cotton soil when treated with ordinary Portland cement under pH = 7 (neutral) gives best results than the soil–cement (OPC) mixes which were cured

Effect of pH on Compressibility Behaviour of Cement-Treated Soil

803

Table 3 Variation in consolidation parameters (C v , M v , C c , k) with the effect of acid (pH = 5) and curing time when black cotton soil treated with OPC Cement content

Curing period in days

Acid C v (m2 /s)

M v (m2 /kN)

Cc

k (m/s)

4.5 × 10–4

0.037

0.73

1.67E−05

10–4

BC + OPC 3

7

3

14

4.4 ×

0.043

0.69

1.85E−05

3

28

4.1 × 10–4

0.051

0.64

2.09E−05

6

7

3.9 × 10–4

0.025

0.68

9.75E−06

6

14

3.7 × 10–4

0.030

0.64

1.11E−05

6

28

3.3 × 10–4

0.039

0.61

1.4E−05

9

7

3.0 × 10–4

0.019

0.61

6.27E−06

9

14

2.9 × 10–4

0.026

0.59

8.06E−06

28

2.7 ×

0.031

0.53

8.99E−06

BC + OPC

BC + OPC

9

10–4

Table 4 Variation in consolidation parameters (C v , M v , C c , k) with the effect of base (pH = 9) and curing time when black cotton soil treated with OPC Cement content

Curing period in days

Acid C v (m2 /s)

M v (m2 /kN)

Cc

k (m/s)

4.4 × 10–4

0.035

0.72

1.61E−05

10–4

BC + OPC 3

7

3

14

4.4 ×

0.042

0.68

1.89E−05

3

28

4.1 × 10–4

0.049

0.63

2.06E−05

6

7

3.9 × 10–4

0.023

0.68

9.2E−06

6

14

3.8 × 10–4

0.026

0.65

1.01E−05

6

28

3.5 × 10–4

0.035

0.62

1.3E−05

7

3.1 × 10–4

0.016

0.62

5.6E−06

10–4

0.022

0.60

7.26E−06

0.028

0.55

8.68E−06

BC + OPC

BC + OPC 9 9

14

3.0 ×

9

28

2.9 × 10–4

under pH = 5 (acid) and pH = 9 (base) compared to Portland slag cement and the same soil when treated with Portland slag cement under pH = 9 (base) gives best results than the soil–cement (PSC) mixes which were cured under pH = 5 (acid) and pH = 7 (neutral) compared to ordinary Portland cement. This is because of slag cement which acts as excellent resistance to alkali and sulphate attacks.

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Table 5 Variation in consolidation parameters (C v , M v , C c , k) with the effect of neutral (pH = 7) and curing time when black cotton soil treated with OPC Cement content

Curing period in days

Acid C v (m2 /s)

M v (m2 /kN)

CcCc

k (m/s)

4.5 × 10–4

0.038

0.74

1.67E−05

10–4

BC + OPC 3

7

3

14

4.3 ×

0.048

0.68

2.02E−05

3

28

4.0 × 10–4

0.056

0.63

2.24E−05

6

7

3.8 × 10–4

0.026

0.69

1.01E−06

6

14

3.5 × 10–4

0.034

0.64

1.22E−05

6

28

3.1 × 10–4

0.042

0.60

1.43E−05

9

7

2.8 × 10–4

0.021

0.60

6.51E−06

9

14

2.6 × 10–4

0.027

0.57

7.56E−06

28

2.5 ×

0.031

0.52

7.75E−06

BC + OPC

BC + OPC

9

10–4

Table 6 Variation in consolidation parameters (C v , M v , C c , k) with the effect of acid (pH = 5) and curing time when black cotton soil treated with PSC Cement content

Curing period in days

Acid C v (m2 /s)

M v (m2 /kN)

Cc

k (m/s)

4.4 × 10–4

0.034

0.72

1.5E−05

10–4

BC + OPC 3

7

3

14

4.3 ×

0.040

0.70

1.7E−05

3

28

4.1 × 10–4

0.051

0.68

2.1E−05

6

7

4.0 × 10–4

0.019

0.70

9.2E−06

6

14

3.9 × 10–4

0.022

0.65

1.2E−05

6

28

3.4 × 10–4

0.028

0.63

1.5E−05

7

3.1 × 10–4

0.016

0.62

5.9E−06

10–4

0.022

0.60

6.6E−06

0.028

0.55

8.1E−06

BC + OPC

BC + OPC 9 9

14

3.0 ×

9

28

2.9 × 10–4

9 Conclusions • The liquid limit and plastic limit of two different types of soils increase with increase in cement content and the plasticity index of BC soil decreases with

Effect of pH on Compressibility Behaviour of Cement-Treated Soil

805

Table 7 Variation in consolidation parameters (C v , M v , C c , k) with the effect of base (pH = 9) and curing time when black cotton soil treated with PSC Cement content

Curing period in days

Acid C v (m2 /s)

M v (m2 /kN)

Cc

k (m/s)

4.2 × 10–4

0.042

0.72

1.8E−05

10–4

BC + OPC 3

7

3

14

4.1 ×

0.048

0.69

1.97E−05

3

28

3.9 × 10–4

0.051

0.67

9.99E−05

6

7

3.7 × 10–4

0.027

0.69

1.05E−06

6

14

3.4 × 10–4

0.031

0.63

1.05E−05

6

28

3.0 × 10–4

0.036

0.60

1.08-05

9

7

2.9 × 10–4

0.016

0.60

4.64E−06

9

14

2.5 × 10–4

0.024

0.57

6E−06

28

2.3 ×

0.036

0.54

8.28E−06

BC + OPC

BC + OPC

9

10–4

Table 8 Variation in consolidation parameters (C v , M v , C c , k) with the effect of neutral (pH = 7) and curing time when black cotton soil treated with PSC Cement content

Curing period in days

Acid C v (m2 /s)

M v (m2 /kN)

Cc

k (m/s)

4.2 × 10–4

0.035

0.70

1.5E−05

10–4

BC + OPC 3

7

3

14

4.0 ×

0.044

0.68

1.8E−05

3

28

3.9 × 10–4

0.052

0.62

2E−05

6

7

4.0 × 10–4

0.024

0.69

9.6E−05

6

14

3.9 × 10–4

0.031

0.62

1.2E−05

6

28

3.7 × 10–4

0.040

0.59

1.5E−05

7

3.0 × 10–4

0.020

0.64

6E−06

10–4

0.026

0.58

7.5E−06

0.032

0.54

8.6E−06

BC + OPC

BC + OPC 9 9

14

2.9 ×

9

28

2.7 × 10–4

increase in percentage of OPC and PSC cement separately, which is favourable since it increases the workability of soils. • The optimum moisture content values of treated soil samples were increased continuously for all percentages of cement than that of untreated soil samples. Besides that, there is a slight decrease in MDD with the increase in the percentages of cement.

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• The UCS and CBR strengths were more pronounced in ordinary Portland cement of 53-grade than Portland slag cement. The unconfined compressive strength has increased from 1.7 to 8.3 kg/cm2 for black cotton soil when treated with OPC. The CBR values when treated with OPC (53-grade) got increased from 3.74 to 21.7% for black cotton soil. • The maximum improvement in the strength can be observed with the addition of cement under curing period of 28 days. Based on UCS and CBR results, it has been concluded that the black cotton soil when treated with Portland slag cement was effective than ordinary Portland cement when cured under pH = 5 (acid) and pH = 9 (base) and the same soil when cured under pH = 7 (neutral), the ordinary Portland cement was effective than Portland slag cement. • The reduction in the permeability, compression index, coefficient of consolidation and coefficient of volume compressibility was observed with the increase in the cement content. The BC + OPC when cured under pH = 7 (neutral) improve the properties of soil compared to pH = 5 (acid) and pH = 9 (base). BC + PSC when cured under base improves the parameters of consolidation than that of BC + OPC.

10 Recommendations • The leakage of effluent into subsoil directly affects the use and stability of the supported structure. Disposal of wastes from industries and accidental spillage of chemicals during the course of industrial operations are the major sources which affects the pH of water. In this investigation, an attempt is made to find out the behavioural changes and strength characteristics of stabilized soils, when cured under different pH levels (pH = 5, pH = 7 and pH = 9). • The ordinary Portland cement which has been used in the present study is highly recommended where fast pace of construction is required and requires minimum curing period of 7 days because of its fast increase in strength in the earlier days. When exposed to hot and dry weather conditions the minimum curing period of 10 days are required. Hence, ordinary Portland cement can be preferred, where faster removal of framework or faster work rate is required. Also OPC can resist against sulphates, alkalies, chlorides and chemicals. But compared to Portland slag cement, the ordinary Portland cement has lower resistance to attacks against chemicals. • The Portland slag cement which has been used in the present study is used in virtually all concrete applications such as concrete pavements, wastewater treatment and marine applications, structures and foundations. It is also used in nonconcrete applications such as soil–cement and hazardous waste solidification. Also, the use of slag cement reduces the emission of greenhouse gases. Slag cement improves compressive and flexural strength, but reduces permeability and provides resistance to corrosion and chloride intrusion. It has the ability to mitigate moderate-to-severe sulphate attack and higher alkali cements.

Effect of pH on Compressibility Behaviour of Cement-Treated Soil

807

References 1. Teja PRK, Study on the curing time effect on UCC strength and variation in engineering properties of cement treated soils. In: 50th Indian geotechnical conference, 17–19 December 2015, Pune, Maharashtra, India 2. Bekki H, Djilaili Z et al (2015) Durability of treated silty soil using lime and cement in road construction—a comparative study. Online J Sci Technol 5(2) 3. Promputthangkoon P, Karnchanachetanee B (2013) Geomaterial prepared from waste tyres, soil and cement. Panu Promputthangkoon and Bancherd Karnchanachetanee/Procedia—Soc Behav Sci 91:421–428 4. Bahar R, Benazzoug M et al (2004) Performance of compacted cement-stabilized soil. Cement Concr Compos 26(2004):811–820 5. AlAghbari MY, Dutta RK, Suitability of desert sand cement mixes for base courses in highway pavements. ejge paper 2005 0558 6. Ho M-H, Chan C-M (2011) Some mechanical properties of cement stabilized Malaysian soft clay. Int J Civ Environ Struct Constr Architect Eng 5(2):201 7. IS 2720-Part 3 (1980) Determination of specific gravity. Bureau of Indian Standards, New Delhi, India 8. IS 2720-Part 4 (1985) Grain size analysis. Bureau of Indian Standards, New Delhi, India 9. IS 1498 (1970) Classification and identification of soils for general engineering purposes. Bureau of Indian Standards, New Delhi, India 10. IS 2720-Part 5 (1985) Determination of liquid limit and plastic limit of soils. Bureau of Indian Standards, New Delhi, India 11. IS 2720-Part 7 (1980) Determination of water content-dry density relation using light compaction. Bureau of Indian Standards, New Delhi, India 12. IS 2720-Part 22 (2010) Determination of organic matter of soils. Bureau of Indian Standards, New Delhi, India 13. IS 2720-Part 26 (1997) Determination of pH value of soils. Bureau of Indian Standards, New Delhi, India 14. IS 2720-Part 10 (1991) Determination of unconfined compressive strength of soils. Bureau of Indian Standards, New Delhi, India 15. IS 2720-Part 16 (2002) Laboratory determination of CBR. Bureau of Indian Standards, New Delhi, India 16. IS 2720-15 (1965) Method of test for soils, Part XV Determination of consolidation properties. Bureau of Indian Standards, New Delhi, India 17. Sarkar G, Rafiqulislam MD et al (2012) Study on the geotechnical properties of cement based composite fine-grained soil. Int J Adv Geotech Eng 01(02). ISSN 2319-5347 18. Bushra I, Robinson RG (2010) Strength behaviour of cement stabilised marine clay cured under stress. Indian Geotech conference-2010

Simplified Grid Strut and Tie Model Approach for Shear Walls Kannan C Bhanu, N. Ganesan, and P. V. Indira

Abstract Conventional strut and tie model for certain structural elements are not well established. Alternative methods that evolved later are inappropriate for general practice. A new simplified grid strut and tie method is introduced in this paper. For checking the effectiveness and reliability of the proposed method, a model of slender shear wall with staggered openings was developed and compared with the experimental and numerical analysis available in the literature. Results were promising as it predicted the failure modes satisfactorily. Keywords Grid strut and tie model · Shear wall · Staggered openings

1 Introduction Strut and tie method is a well-accepted method for the analysis and design of structural elements belonging to both Bernoulli region and disturbed region. Shear wall is one of the structural elements which can be analysed and designed using strut and tie method. Shear walls with staggered openings are general in modern buildings. These openings which are provided for several purposes reduce the seismic performance of the shear wall. Strut and tie model for certain structural elements, like deep beams, solid shear walls, squat shear wall with openings and so on, are established by the past researchers [1, 2]. However, it is difficult to develop a model for certain structural elements like slender shear walls with regular and staggered openings. Some studies are available on the new approaches like grid strut and tie method, nonlinear truss modelling, macro modelling and so on [3–5]. K. C Bhanu (B) · N. Ganesan · P. V. Indira National Institute of Technology Calicut, Kozhikode, Kerala, India e-mail: [email protected] N. Ganesan e-mail: [email protected] P. V. Indira e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_64

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Fig. 1 Strut and tie model for shear wall with staggered openings. Source Yanez et al. [2]

In this paper, a simplified grid strut and tie model is introduced for the twodimensional analysis of slender shear walls with staggered openings. The model is created by considering all the reinforcement provided in the structural element as tie members and the concrete present between these reinforcements as struts. Effective strength of struts, ties and nodes is obtained as specified in the conventional strut and tie method. Unlike conventional strut and tie model for shear walls as shown in Fig. 1, more number of nodes are considered as supports in this method. Owing to this, the effect of all the vertical reinforcements embedded into the foundation are effectively considered in the model. Since the model will be having a significant number of elements and supports, numerical analysis may be used for the analysis of the grid strut and tie model developed in this manner. This grid strut and tie model was tried in the case of a slender shear wall with staggered openings and validated using the experimental results of Marius [6].

2 Development of Grid Strut and Tie Model In conventional strut and tie method, reinforcement provided in the tension zone and the concrete in the compression load path are considered as tie members and struts, respectively, as shown in Fig. 2. In the proposed grid strut and tie method, all the reinforcement bars were considered to model the grid. Bars along the thickness were bundled for two-dimensional analysis. Reinforcing bars near edges or opening sides were considered as a single element with total cross-sectional area, located at the centroid of the reinforcing bars. Area of each member was taken as the corresponding

Simplified Grid Strut and Tie Model Approach for Shear Walls

811

Fig. 2 Conventional strut and tie model for continuous deep beam

area of bars including the effective area of concrete in tension. Members were divided at the point of intersections and those intersections were considered as nodes. Nodes were connected diagonally to make the struts. Strut orientation was selected in accordance with the direction of lateral load. The width of struts was calculated depending on the width of bearing plates, width of tie members and inclination of strut with the tie member to which it is connected. The depth of the strut was considered as the thickness of the structural element. Support reactions were applied at the bottom end nodes of members corresponding to reinforcement bars continuing into the foundation. Lateral loads were applied at the corresponding nodes. The grid model developed was analysed using STAAD software. The calculated member forces were compared with its strengths in order to verify whether the load applied is causing any failure. Strength of a tie member was calculated as the product of yield stress and area of the corresponding reinforcement bars. Strength of struts was considered as in Eq. 1 (ACI 318-14 [7]). Strength of strut = 0.85 f c βs ws b

(1)

where f c is the cylinder strength of concrete, β s is the strut efficiency factor, ws is the width of the strut and b is the depth of the strut. Value of β s corresponding to bottle-shaped strut without adequate crack control reinforcement (Table 1) was adopted since no strut in the proposed grid strut and tie model will be having web reinforcement across it. The strength of the node was calculated using a nodal zone coefficient of 0.6 since every node was anchoring more than one tie. Loads were increased until there is yielding of any tie member or crushing of struts or nodes. Hence the model was used to predict the initial behaviour of the structural element.

812

K. C Bhanu et al.

Table 1 Strut efficiency factors as per ACI 318-14 Type of strut

Efficiency factor (β s )

Prismatic strut

1.00

Bottle-shaped strut with at least 0.3% effective web reinforcement

0.75

Bottle-shaped strut without or less than 0.3% web reinforcement

0.60λ

Struts located in tension members or tension zones of members

0.40

Struts in all other cases

0.60λ

Note λ = 1 for normal-weight concrete; 0.85 for sand lightweight concrete; 0.75 for all lightweight concrete

An attempt was made to develop a grid strut and tie model for slender shear wall with staggered openings studied by Marius [6].

3 Details of Specimen Specimen SW67 was selected for the validation of the grid model. Figure 3 shows the dimensional details and Fig. 4 shows the reinforcement details of the specimen.

Dimensions are in centimeters Fig. 3 Details of specimen SW67. Source Marius [6]

Simplified Grid Strut and Tie Model Approach for Shear Walls

813

Fig. 4 Reinforcement details of specimen SW67. Source Marius [6]

where α = 18° for the specimen SW67.

4 Analysis of Specimen As specified in the above procedure, all the longitudinal and transverse reinforcements were considered for the grid model. Reinforcement bars near openings and edges were bundled to their respective centroids. Diagonal struts were modelled depending on the direction of the lateral force applied. Figure 5 shows the grid

(a)

(b)

Fig. 5 Loading direction and grid model of specimen a SW6 and b SW7

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K. C Bhanu et al.

model of the specimen SW6 and SW7 which were modelled to study the effect of concentrated lateral force at top. Strength of each members was calculated as explained in section “Development of grid strut and tie model” in order to check for failure. Strength of tie members with four numbers, 6 mm diameter steel wires = 43.66 kN. Strength of tie members with two numbers 6 mm diameter steel wires = 21.83 kN. Strength of strut members varies depending on the inclination. Nodal strength with an efficiency coefficient 0.6 was also calculated and checked for nodal failure. First, a trial lateral load of 30 kN was applied and checked for the failure of members. From this preliminary analysis, it was clear that yielding stress of vertical reinforcement provided near the edges will be occurring first at the top level of opening provided at the bottom storey (Fig. 6). Stress in horizontal tie members near opening was close to yielding stress and this suggested the yielding stress of those horizontal tie members will be the second stage of failure. This predicted failure pattern was the same as that shown in the experiment by Marius [6]. The load was increased until the stress in vertical tie members reached yield stress and all other members were checked for failure. It was observed that at a lateral force of 45 kN, vertical bars yielded. Marius [6] conducted numerical analysis using BIOGRAF 02

2

2

2

1

1 2 1 1. 2.

(a) Yielding of vertical bars near opening

(b)

Yielding of horizontal bars

Fig. 6 Member forces of grid strut and tie model of a SW6 and b SW7

Simplified Grid Strut and Tie Model Approach for Shear Walls

815

Fig. 7 Failure modes of SW6 predicted by numerical study. Source Marius [6]

software which also showed similar yielding pattern that of grid analysis (Fig. 7). Along with lateral force, a constant load of 50 kN was applied axially in the experimental and numerical analysis. Owing to the effect of axial load, tension on vertical bars reduced, thereby increasing the lateral load capacity. In the numerical analysis conducted by Marius [6], the lateral load corresponding to the yielding of vertical reinforcement was 76.65 kN. The effect of axial load was not considered in the grid strut and tie analysis, hence showing a lower lateral load capacity.

5 Conclusion A simplified grid strut and tie method was proposed and the same was used to model slender shear wall with staggered openings. The model was validated using the results available in the literature. Such models will be useful in the case of structures where it is difficult to visualise the load path.

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References 1. Taylor CP, Cote PA, Wallace JW (1998) Design of slender reinforced concrete walls with openings. Struct J 95(4):420–433 2. Yanez FV, Park R, Paulay T (1992) Seismic behaviour of walls with irregular openings. In: Earthquake engineering tenth world conference. Balkema-Rotterdam, pp 3303–3308 3. Yun YM, Kim BH (2008) Two-dimensional grid strut-tie model approach for structural concrete. J Struct Eng 134(7):1199–1214. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:7(1199) 4. Park H, Eom T (2007) Truss model for nonlinear analysis of RC members subject to cyclic loading. J Struct Eng 133(10):1351–1363. https://doi.org/10.1061/(ASCE)0733-944 5(2007)133:10(1351) 5. Wang JY, Sakashita M, Kono S, Tanaka H, Lou WJ (2010) Behavior of reinforced concrete structural walls with various opening locations: experiments and macro model. J Zhejiang Univ Sci A 11(3):202–211. https://doi.org/10.1631/jzus.A0900400 6. Marius M (2013) Seismic behaviour of reinforced concrete shear walls with regular and staggered openings after the strong earthquakes between 2009 and 2011. Eng Fail Anal 34:537–565. https:// doi.org/10.1016/j.engfailanal.2013.05.014 7. American Concrete Institute (2014) Building Code Requirements for Structural Concrete (ACI 318-14): Commentary on Building Code Requirements for Structural Concrete (ACI 318R-14): an ACI report. American Concrete Institute. ACI

Analysis of RC Buildings by Metamodel Approaches Deepak Sahu, Pradip Sarkar, and Robin Davis

Abstract Response of RC structures is very complex and dynamic in nature because of the vulnerabilities that exist in geometry, material properties and loading. To represent the random dynamic responses accurately, stochastic analysis is chosen here. The stochastic analysis can be done by two types of methods, like statistical and the non-statistical approaches. In non-statistical approach a relationship is developed between the input and random output or responses. Computationally efficient, simplified methods are required as an alternative to Monte–Carlo simulation which is considered as an accurate method for stochastic analysis. The present study is an evaluation of the different non-statistical metamodel-based approaches such as high-dimensional model representation and using design of experiments approaches like central composite design, Box–Behnken design and full factorial design for the representation of the response surface. The effectiveness of high-dimensional model representation over conventional response surface metamodel approaches is discussed in the present study with regard to two contexts, namely free vibration response and nonlinear time history responses of RC frames. The seismic fragilities obtained using high-dimensional model representation are compared with established metamodel approaches for effectiveness and computational efficiency. It is found that the use of high-dimensional model representation yields fairly accurate results with even less computational effort. Keywords Stochastic analysis · HDMR · RSM

D. Sahu (B) · P. Sarkar · R. Davis Department of Civil Engineering, National Institute of Technology Rourkela, Rourkela 769008, India e-mail: [email protected] P. Sarkar e-mail: [email protected] R. Davis e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_65

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1 Introduction Prediction of structural behaviour in the case of unexpected loadings, such as earthquakes, cyclones, tsunamis and hurricanes, is very complex and difficult, since inconsistency existed in both the nature of loading and structural resistance [1]. To address this problem stochastic approach can be used to predict the response of the structure for these catastrophic events in a probabilistic manner. Monte-Carlo simulation (MCS) is a leading technique [2], which consists of large number of sampling process to obtain the responses, but becomes computationally affluent for problems having small probabilities among the commonly used statistical approaches [3]. Apart from statistical approach, the response of the structure is evaluated at some particular set of random parameters in the case of non-statistical method. A functional relationship is generated between the input and output variables known as a metamodel [4]. Response surface method (RSM) [5] is the most broadly used nonstatistical approach, which forms the metamodel. The selection of sampling points for the functional evaluation of the responses in RSM can be done by different techniques for design of experiments (DOE) such as central composite design (CCD) [6] and Box–Behnken design (BBD) [7]. A high-dimensional model representation (HDMR) [8] applied in different fields as method for stochastic analysis was introduced recently, to represent the response surface in terms of a metamodel for the study of structural behaviour [9] HDMR is used recently. The focus of this work is to scrutinize the effectiveness of the recently introduced HDMR method, to problems involving free vibration analysis of concrete buildings, with reference to established response surface methods.

2 Review of Metamodel-Based Approaches The present study considers the problem to obtain the random natural frequency for stochastic analysis of a RC symmetric bare framed building. Stochastic analysis of the selected problems requires the evaluation of metamodel using each method, HDMR, and RSM using different sampling techniques such as CCD and BBD. This section provides a review of the above methods.

2.1 RSM Approaches The RSM metamodel can be represented by its general form as shown in Eq. (1) y = f (xi ) + ε

(1)

Analysis of RC Buildings by Metamodel Approaches

819

Here, y represents the response (output), x i represents the input variables, and ε represents the error in estimation and can be neglected in the case of computer analysis [10]. The response surface input variables are the parameters whose uncertainty or randomness can cause uncertainty in the output or response. A second-order (quadratic) function is selected in the present study to evaluate the response. The form of such a function is shown in Eq. (2). y = β0 +

k 

βi xi +

i=1

k 

βii xi2 k +

i=1

k k−1  

βi j xi x j

(2)

i=1 j=1

where β is unknown coefficients, and k is the total number of input variables. To determine the unknown constants (β), the design of experiments should be carried out at the selected sampling points to obtain the response. Then, a functional relationship is established between the random input parameters and output responses which is called a metamodel. The different design methods implemented in this work are CCD, and BBD gives a different combination of the input variables. Details on these sampling methods can be found in the literature [11, 12].

2.2 HDMR Metamodel Approach HDMR method is used to incarnate the probability analysis of a system which needs a huge computational cost and effort. In other words, tedious processes like the MCS can be carried out on this compact model effectively and efficiently [13]. The input variables and the output function in HDMR can be conveniently represented as the N-dimensional vector x = {x 1 , x 2 , …, x N } and f (x), respectively. The value of N can vary up to the order of 100–1000 or more. Similar to other response surface methods, the effect of input variables on the output function can be independent and/or correlated. HDMR expresses the output f (x) as a hierarchical correlated function expansion in terms of the input variables as in Eq. (3). f (x) = f 0 +

N 

f i (xi ) +

i=1

+







  f i1 i2 xi1 , xi2

1 2.5

R. Sahu and U. K. Dewangan

Effect of Shear Span to Depth Ratio in Strut …

891

Fig. 10 Inclined strut member

Fig. 11 Arch action

Fig. 12 Two-panel strut member

6 Results and Conclusions In this paper, shear span to depth ratio is taken as an effective parameter to analyze deep beam by STM. Flexure strain variation is nonlinear which deviates from Bernoulli’s hypothesis. Flexural strength is decreasing with an increase in shear span of the deep beam was observed.

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Effectiveness factor in strength formula for strut member in STM depends on the shear span to depth ratio. That is, by decreasing the shear span to depth ratio effectiveness factor is increasing. The increase in shear span to depth ratio, decreases the Percentage of load distribution in horizontal tie member. While in the case of vertical tie member, the load distribution percentage increases with the increase of shear span to depth ratio. In STM, three types of failure criteria observed are the following: S. No.

Failure criteria

Failure mode

1

(a/d) < 1

The crack will be the reason for failure

2

1 < (a/d) < 2.5

After the development of crack, internal strength tries to form arch action, because of that the structure is still able to sustain more load

3

2.5 < (a/d) < 6

Due to longer shear span to depth ratio, the structure is unable to develop arch action and failure occurred

4

(a/d) > 6

Flexural failure occurred

Hence, the STM is effective and efficient to use for the beam having a/d in between 1 and 2.5. The above result is validated by using the FEM, in which stress flow is clearly visible and the flow path is as per the arrangement of Strut-and-Tie member.

References 1. Foster SJ, Malik AR (2002) Evaluation of efficiency factor models used in strut- and-tie modeling of nonflexural members. J Struct Eng 128(5):569–577 2. El-Metwally S, Chen WF (2017) Structural concrete: strut-and-tie models for unified design. CRC Press 3. Ahmed M, Yasser A, Mahmoud H, Ahmed A, Abdulla MS, Nazar S (2013) Load transfer mechanism based unified strut-and-tie modeling for design of concrete beams. Int J Civil Environ Struct Constr Archit Eng 7(3) 4. El-Metwally S, Chen WF (2011) Understanding structural engineering: from theory to practice. CRC Press 5. Shariat M, Eskandari-Naddaf H, Tayyebinia M, Sadeghian M (2018) Sensitivity analysis of reinforced concrete deep beam by STM and FEM (Part III). Mater Today: Proc 5(2):5529–5535 6. Victoria M, Querin OM, Martí P (2011) Generation of strut-and-tie models by topology design using different material properties in tension and compression. Struct Multi Optim 44(2):247– 258 7. Hwang SJ, Lee HJ (2002) Strength prediction for discontinuity regions by softened strut-and-tie model. J Struct Eng 128(12):1519–1526 8. Raj JL, Rao GA (2015) Shear strength of RC deep beam panels–a review. Int J Res Eng Technol 3(16):89–103 9. Niranjan BR, Patil SS (2012) Analysis and design of deep beam by using strut and tie method. IOSR J Mech Civil Eng IOSR-JMCE. ISSN, 2278-1684 10. Patil SS (2013) Analysis of deep beam using CAST software and compression of analytical strains with experimental strain results. Glob J Res Eng 12(4-J)

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11. Wang W, Jiang DH, Hsu CTT (1993) Shear strength of reinforced concrete deep beams. J Struct Eng 119(8):2294–2312 12. Foster SJ, Gilbert RI (1998a) Experimental studies on high-strength concrete deep beams. Struct J 95(4):382–390 13. Brown MD, Sankovich CL, Bayrak O, Jirsa JO, Breen JE, Wood SL (2006) Design for shear in reinforced concrete using strut-and-tie models (No. FHWA/TX-06/0-4371-2) 14. Arabzadeh A, Rahaei AR, Aghayari R (2009) A simple strut-and-tie model for prediction of ultimate shear strength of RC deep beams 15. Rao GA, Sundaresan R (2012) Evaluation of size effect on shear strength of reinforced concrete deep beams using refined strut-and-tie model. Sadhana 37(1):89–105 16. He ZQ, Liu Z, John Ma Z (2012) Investigation of load-transfer mechanisms in deep beams and corbels. ACI Struct J-Am Concr Inst 109(4):467 17. Chae HS, Yun YM (2016) Strut-tie models and load distribution ratios for reinforced concrete beams with shear span-to-effective depth ratio of less than 3 (II) validity evaluation. J Korea Concr Inst 28(3):267–278 18. Russo G, Somma G, Angeli P (2004) Design shear strength formula for high strength concrete beams. Mater Struct 37(10):680–688 19. Yap WT (2012) Strut and tie modelling of reinforced concrete short span beams. In: 1st civil and environmental engineering student conference, pp 25–26 20. Ahmad SH, Lue DM (1987) Flexure-shear interaction of reinforced high strength concrete beams. Struct J 84(4):330–341 21. Birrcher D, Tuchscherer R, Huizinga M, Bayrak O, Wood SL, Jirsa JO (2009) Strength and serviceability design of reinforced concrete deep beams (No. FHWA/TX-09/0-5253-1)

Optimal Design Techniques of Composite Payload Adapter for a Typical Launch Vehicle V. Pavithra and Gangadhar Ramtekkar

Abstract Composite materials made with the objective of getting a more desirable combination of properties are extensively used in weight-sensitive structures due to its very high strength to weight ratio and relatively high stiffness to weight ratio. A payload adapter forms an interface between the payload or the satellite and the launch vehicle core. The importance of weight savings in the payload adapter is that any reduction in its mass can help in a corresponding increase in the satellite mass since the sensitivity is 1:1. This is due to the positioning of the payload adapter near the satellite. This paper deals with the optimal design of a lightweight Composite Payload Adapter in three different configurations with a maximum mass advantage which at the same time should be able to withstand the loads acting on them during the flight. The design options studied were: monocoque, stringer-stiffened, and sandwich-structured construction. In monocoque construction, a metallic skinned structure made out of aluminium and also layered composite skinned structure made out of M55J/M18 prepreg laminates are considered for the study. The sandwich constructions are studied with metallic face sheets and layered composite face sheets in combination with a hexagonal aluminium honeycomb core. The study of stringerstiffened construction was conducted by comparing the structure having the stringers and the shell made of aluminium with that made of M55J/M18 laminates. The optimum design out of these cases studied was arrived at. Static, buckling and free vibration analyses of all the cases were carried out using the general-purpose finite element software MSC. NASTRAN. Keywords Composite · Laminate · Monocoque · Stringer-stiffened · Sandwich · Payload adapter

V. Pavithra (B) · G. Ramtekkar Civil Engineering, National Institute of Technology Raipur, Raipur, India e-mail: [email protected] G. Ramtekkar e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_71

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1 Introduction Any design which satisfies a set of design specifications while providing the best quality and performance is called an optimal design. It involves the determination of the design parameters which controls the shape, material properties and dimensions of the structure [1]. Thus, the theory of optimal design and its implications have a key role in the design of weight-sensitive applications like aerospace structures. The existing experience shows that direct substitution of carbon-epoxy composites for traditional ring-stiffened aluminium aerospace-framed structures results in usually 10–20% weight reduction accompanied by considerable cost savings [2]. There is a strong need in the aerospace industry to reduce the cost and improve the effectiveness of launching satellites into the orbit. The primary objective of a launch vehicle is to place as much as payload as possible into earth orbit at the lowest cost. Minimising the structural mass is crucial in many ways––it helps to increase payload mass and thus reduce the launch cost [3]. The objective of structural design is to achieve minimum weight with maximum safety so as to increase the economy of a space mission, at the same time, it should be able to withstand the loads acting on them during the flight. One of the ways to reduce the mass of the launch vehicle is to use composites in its components. So, this paper deals with the design and analysis of a lightweight Composite Payload Adapter (CPLA). Figure 1 shows the exploded view of a launch vehicle showing a payload adapter (PLA). Payloads, such as spacecraft, which are mounted on launch vehicles, are subject to severe vibrations during flight [4]. The payload adaptor must have high stiffness and a high natural frequency in order to prevent dynamic coupling between the satellite and the launch vehicle dynamics. Detailed ground tests, static and dynamic, are performed to make sure its structural safety.

Fig. 1 Exploded view of a launch vehicle. Source https://www.quora.com

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The PLA is a primary structure of a launcher providing the interface to the spacecraft [5, 6]. It is designed to support the payload during flight, transmit any loads induced by it back to the launch vehicle and facilitate power and signal connections between the spacecraft and the payload (United Launch Alliance, 2013). Optimization of this structure is of much importance as it is positioned towards the top of the launch vehicle because any mass saved in the PLA leads to a corresponding increase in the satellite mass in the ratio 1:1. In [7], the design of the monocoque and stringer-stiffened structure of PLA has been discussed. This paper extends the study by comparing it with the sandwich-structured PLA, which is a very lightweight design method.

2 Structural Configuration of PLA The functional requirement of the PLA involves connecting the satellite and the launch vehicle of two different diameters. Hence, the PLA is to be designed in the shape of a truncated cone. The structure has a diameter of 937 mm at the fore end and 1370 mm at the aft end (Fig. 2). The total height of the structure is 1040 mm. Two metallic rings attached to the cone at the either ends act as interface attachment rings. The fore end joins with the satellite and the aft end flange with the launch vehicle core. The structure is to be designed in such a way that it is safe in strength, stiffness and buckling consideration also should have the least possible mass. Thus, optimization by investigating the best possible shape and material orientation of the three chosen configurations, namely, monocoque, stringer-stiffened and sandwich structure is performed.

3 Design Specifications A structure is designed in such a way that it is able to take the design loads for its entire life span for which it is designed. In the case of a launch vehicle structure, it should be able to take the loads acting on them during the entire journey of the flight. Table 1 gives the design loads for PLA and Table 2 gives the satellite mass and inertia. A design safety factor of 1.25 shall be provided over the design load. The stiffness constraint given is that the lateral and axial frequency of PLA in base fixed configuration (Aft end of PLA has all D.O.F. arrested) with satellite mass and inertia simulated shall not be less than 15 Hz and 30 Hz, respectively [7]. This is done to avoid any chances of dynamic coupling because, in case of such a vibration, the dynamic response of the launch vehicle becomes the input to the satellite. So if their frequencies are not well-separated, their transmissibility values can couple resulting in rapid fatigue failures [8]. So the natural frequencies of both the satellite and the launch vehicle must be separated with an octave apart (means to double) to prevent coupling, i.e. the frequencies are separated by a ratio of more

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Fig. 2 Configuration of payload adapter

Table 1 Design loads on PLA

Mass of the payload (Satellite)

3500 kg

Axial load

300.43 kN

Lateral load

128.76 kN

Equivalent axial load (E.A.L.)

1255.3 kN

Bending Moment

327.04 kNm

Source Pavithra et al. [7] Table 2 Satellite details

Mass of the satellite

3500 kg

Height of satellite C.G. above its base

1.5 m

Moment of inertia about axial direction

1500 kg m2

Moment of inertia about lateral direction

3000 kg m2

Source Pavithra et al. [7]

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than 2:1. Here, the PLA is designed for a launch vehicle with a fundamental natural frequency of vibration as 7.5 Hz in the lateral mode and 15 Hz in the axial mode. Hence, the above frequency constraints must be satisfied to be safe in free vibration. In the case of a buckling analysis, the buckling load factor with a knockdown factor (K.D.F) of 0.6 and a design safety factor of 1.25 should be greater than one [7]. The K.D.F. is applied to compensate for the material and fabrication imperfections. Here, the buckling load factor is the ratio of the critical buckling load to the applied load and when this ratio is greater than 1, the structure is safe in buckling. The strength constraint is satisfied if the maximum stress generated in the structure is within the yield strength value of the material. A structure which satisfies all the three design constraints and has a mass within 25 kg can be taken as the optimum structure. E.A.L. = Axial Load ±

2M R

(1)

4 Construction Methodologies Adopted The design strategy adopted here is design through analysis. It is basically an optimization method by mass minimization technique. Three configurations studied are monocoque, stringer-stiffened and sandwich structure. For each case, three types of analysis are carried out, i.e. static, buckling and free vibration. The best laminate sequence for structural stability is arrived at through an iterative process. The stiffness of the structure is checked by conducting free vibration analysis after simulating the satellite mass and inertia at the fore end of the payload adapter as the frequency is directly related to the stiffness. The buckling strength is verified from the buckling analysis by applying the E.A.L. [Eq. (1)] at the fore end nodes of the PLA. The maximum stress and deformation in the structure is determined after carrying out static analysis.

4.1 Monocoque Construction Different options of monocoque construction, which is basically a single shell structure, are attempted. The first option considered is with a metallic skin alone made out of aluminium, the thickness of which is fixed by an iterative process. The thickness is varied starting from 1 mm. The second option considered is with a layered composite made of M55J/M18 prepreg laminates which are a laminate made of carbon fibres and epoxy resin, each layer being 0.1 mm thick. The optimum number of layers and ply orientation for the layered composite is arrived by an iterative process. The material properties of aluminium and M55J/M18 prepreg are given in Tables 3 and 4.

900 Table 3 Material properties of aluminium sheet

Table 4 Material properties of M55J/M18 Prepreg laminate

V. Pavithra and G. Ramtekkar Density of the material

2700 kg/m3

Elastic modulus

68.9 GPa

Poisson’s ratio

0.33

Shear modulus

25.89 GPa

Longitudinal elastic modulus (E 1 )

264.78 GPa

Transverse elastic modulus (E 2 )

5.952 GPa

Poisson’s ratio

0.346

Shear modulus (G12 = G13 = G23 )

4.415 GPa

Density of the material

1750 kg/m3

Longitudinal tensile strength

1326.9 MPa

Longitudinal compressive strength

724 MPa

Transverse tensile strength

21.78 MPa

Transverse compressive strength

117.43 MPa

In-plane shear strength

74.85 MPa

4.2 Stringer-Stiffened Construction In stringer-stiffened structure which consists of a thin shell stiffened by uniformly spaced longitudinal stringers, both aluminium and laminate version was tried. In this first case, both the stringers and the shell were made of aluminium. Here, the number of stringers and the thickness of the shell were iteratively changed to reach the minimum mass structure. Later, it was replaced with laminate and different thickness and layup of the laminate layers were tried to reach the optimum design. The stringers are provided with a hat section whose cross-sectional details are as shown in Fig. 3.

Fig. 3 Cross-sectional dimensions of the stringer. Source Pavithra et al. [7]

Optimal Design Techniques of Composite Payload … Table 5 Material properties of hexagonal aluminium honeycomb core

901

Density

36 kg/m3

Transverse shear modulus

225.6 MPa

Compressive strength

2.1 MPa

Compressive modulus

540 MPa

4.3 Sandwich-Structured Construction Two types of sandwich construction were studied––one with an aluminium sheet as the skin and the other with composite skin of M55J/M18 laminates. Hexagonal aluminium honeycomb was used as the core for both. The properties of aluminium honeycomb core are given in Table 5.

5 Finite Element Modelling A finite element model of the PLA structure was created using MSC PATRAN. The geometry of PLA in the form of a truncated cone is obtained. 2-D shell elements and 1-D beam elements were used to model the structures. The discretized model of monocoque PLA with a rigid link attached on the top is given in Fig. 4 and the finite element models of stringer-stiffened and sandwich PLA are given in Figs. 5 and 6. MSC. PATRAN was used as the preprocessor and the post-processor and MSC. NASTRAN was used as the solver.

6 Finite Element Analysis The boundary conditions for different analysis were given and the corresponding loads were also applied as in Table 1. Static, free vibration and buckling analyses were performed using MSC. NASTRAN [9].

6.1 Free Vibration Analysis In the free vibration analysis, all the aft end nodes are fixed, i.e. all the degrees of freedom of the nodes are arrested and the fore end nodes are rigidly linked to the centre of gravity (C.G.) of the satellite as in Fig. 4. A mass of 3500 kg is mounted at the C.G. of the satellite. Here, mode shapes and the corresponding frequencies are obtained as the output.

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Fig. 4 Discretized model of monocoque PLA with rigid link mounted on the top. Source Pavithra et al. [7]

6.2 Static Analysis Static analysis was carried out to estimate the maximum stress acting on the structure under the applied design loads. It also gives the maximum displacement in the structure under a set of given loads. In this analysis also, the aft end nodes are completely restrained and the fore end nodes are rigidly linked to a single master node at the satellite C.G. as in Fig. 4. The design loads are then applied at this master node. The stresses in each layer of the composite laminate were obtained.

Optimal Design Techniques of Composite Payload …

Fig. 5 Finite element model of stringer-stiffened PLA. Source Pavithra et al. [7]

Fig. 6 Finite element model of sandwich-structured PLA

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6.3 Buckling Analysis Buckling analysis is done by applying E.A.L. uniformly on all the nodes at the fore end. In the analysis, the buckling load factor is obtained. These factors are the eigenvalues of the instability problem, and when multiplied by the external loads give the buckling condition for the system. To ensure that any imperfection in the laminated shell will have no essential influence on the buckling load, K.D.F. is applied.

7 Optimum Design and Results The optimum structure of PLA in each of the three configurations studied was found out. It was found that composite structures weigh less compared to the metallic ones, which equally satisfy the design constraints. Among the three, sandwich- and stringer-stiffened weigh less compared to the monocoque construction. The free vibration and buckling analysis results which also satisfies the strength constraints are tabulated, and the contour plots are also shown in all the cases studied.

7.1 Monocoque Design Metallic Monocoque Structure. In the monocoque structure made of aluminium sheet, the thickness of the skin is varied from 1 mm and it is found that a minimum of 6 mm-thick aluminium sheet is required for satisfying the design constraints. Then, the mass of the structure obtained is 62.35 kg. The results of free vibration and buckling analysis are shown in Tables 6 and 7. The free vibration modes and the first buckling mode of the structure are shown in Figs. 7 and 8. Here, the minimum frequency in the lateral mode of free vibration is obtained as 18.15 Hz and in the axial mode is 98.48 Hz. The buckling load factor after applying Table 6 Results of free vibration analysis of metallic monocoque structure

Modes

Natural frequency (Hz)

Remarks

Mode 1

18.15

Lateral mode

Mode 2

18.15

Lateral mode

Mode 3

52.54

Torsional mode

Mode 4

95.40

Lateral mode

Mode 5

95.40

Lateral mode

Mode 6

98.48

Axial mode

Mode 7

245.80

Shell mode

Mode 8

245.80

Shell mode

Mode 9

257.38

Shell mode

Mode 10

257.38

Shell mode

Optimal Design Techniques of Composite Payload … Table 7 Results of buckling analysis of metallic monocoque structure

905

Modes

Buckling load factor Load factor Applying K.D.F.

Applying F.O.S.

Mode 1

2.17

1.74

1.04

Mode 2

2.17

1.74

1.04

Mode 3

2.65

2.12

1.27

Mode 4

2.65

2.12

1.27

Mode 5

3.42

2.73

1.64

Mode 6

3.42

2.73

1.64

Mode 7

3.60

2.88

1.73

Mode 8

3.60

2.88

1.73

Mode 9

4.34

3.47

2.08

Mode 10

4.34

3.47

2.08

F.O.S. and K.D.F. is obtained as 1.04 and the stresses obtained are also less than the strength of the material. Here, the maximum stress (Fig. 9) acting on the structure is less than the strength of the material. Composite Monocoque Structure. In the monocoque structure made of M55J/M18 prepreg laminates, the number of layers as well as the orientation was iterated to arrive at the optimum design. The optimum design was arrived at by using 45 laminate layers each 0.1 mm thick, in the following orientation: [0/0/90/90/0/90/0/-90/0/45/0/-45/0/90/0/-90/0/-45/45/0/90/0/45/0/90/0/45/45/0/-90/0/90/0/-45/0/45/0/-90/0/90/0/90/90/0/0]. The mass of the PLA designed

(a) Lateral Mode Fig. 7 Free Vibration modes of metallic monocoque structure

(b) Torsional Mode

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(c) Axial Mode

(d) Shell Mode

Fig. 7 (continued)

Fig. 8 First Buckling mode of metallic monocoque structure. Source Pavithra et al. [7]

was 30.31 kg. Even though the mass of composite monocoque PLA is almost 50% less compared to that of the metallic one, it couldn’t meet the design mass constraints. The results of free vibration and buckling analysis are shown in Tables 8 and 9. The free vibration modes and the first buckling mode of the structure are shown in Figs. 10 and 11.

Optimal Design Techniques of Composite Payload …

907

Fig. 9 Maximum stress distribution of the metallic monocoque PLA Table 8 Results of free vibration analysis of composite monocoque structure

Modes

Natural frequency (Hz)

Remarks

Mode 1

22.62

Lateral mode

Mode 2

22.62

Lateral mode

Mode 3

36.81

Torsional mode

Mode 4

69.43

Lateral mode

Mode 5

69.43

Lateral mode

Mode 6

123.04

Axial mode

Mode 7

278.70

Shell mode

Mode 8

278.70

Shell mode

Mode 9

291.26

Shell mode

Mode 10

291.26

Shell mode

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V. Pavithra and G. Ramtekkar

Table 9 Results of buckling analysis of composite monocoque structure

Modes

Buckling load factor Load factor Applying K.D.F.

Applying F.O.S.

Mode 1

2.08

1.67

1.01

Mode 2

2.08

1.67

1.01

Mode 3

2.39

1.91

1.15

Mode 4

2.39

1.91

1.15

Mode 5

3.03

2.43

1.46

Mode 6

3.03

2.43

1.46

Mode 7

3.70

2.96

1.77

Mode 8

3.70

2.96

1.77

Mode 9

3.70

2.96

1.78

Mode 10

3.70

2.96

1.78

Here also, the lateral and axial mode of free vibration have frequencies more than 15 Hz and 30 Hz, respectively, and the buckling load factor obtained is also greater than 1. The stresses obtained in all the 45 layers of the laminated shell are within the specified limit (Fig. 12). But, the mass of the structure is more than 25 kg.

(a) Lateral Mode

(b)TorsionalMode

Fig. 10 Free vibration modes of composite monocoque structure

Optimal Design Techniques of Composite Payload …

(c) Axial Mode Fig. 10 (continued)

Fig. 11 First buckling mode of composite monocoque structure

909

(d) Shell Mode

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V. Pavithra and G. Ramtekkar

Fig. 12 Stress distribution of layer 1 of laminated monocoque PLA

7.2 Stringer-Stiffened Design Metallic Stringer-Stiffened Structure. In the stringer-stiffened structure made of aluminium sheet, the thickness of the shell is varied from 1 mm and it is found that a minimum of 4 mm-thick aluminium sheet stiffened by 48 numbers of stringers are required for satisfying the design constraints. Then, the mass of the structure obtained is 55.10 kg. The results of free vibration and buckling analysis are shown in Tables 10 and 11. The free vibration modes and the first buckling mode of the structure are shown in Figs. 13 and 14. Here, the minimum frequency in the lateral mode of free vibration is obtained as 16.77 Hz and in the axial mode is 93.11 Hz. The buckling load factor after applying F.O.S. and K.D.F. is obtained as 1.03 and the stresses obtained are also less than the Table 10 Results of free vibration analysis of metallic stringer-stiffened structure

Modes

Natural frequency (Hz)

Remarks

Mode 1

16.77

Lateral mode

Mode 2

16.77

Lateral mode

Mode 3

43.09

Torsional mode

Mode 4

79.08

Lateral mode

Mode 5

79.08

Lateral mode

Mode 6

93.11

Axial mode

Mode 7

292.59

Shell mode

Mode 8

292.59

Shell mode

Mode 9

293.34

Shell mode

Mode 10

293.34

Shell mode

Optimal Design Techniques of Composite Payload … Table 11 Results of buckling analysis of metallic stringer-stiffened structure

911

Modes

Buckling load factor Load factor Applying K.D.F.

Applying F.O.S.

Mode 1

2.15

1.72

1.03

Mode 2

2.15

1.72

1.03

Mode 3

2.82

2.26

1.35

Mode 4

2.82

2.26

1.35

Mode 5

3.07

2.46

1.47

Mode 6

3.07

2.46

1.47

Mode 7

3.85

3.08

1.85

Mode 8

3.85

3.08

1.85

Mode 9

4.93

3.95

2.37

Mode 10

4.93

3.95

2.37

strength of the material. The maximum stress (Fig. 15) acting on the structure is also less than the strength of the material. But, the mass of the structure is much more than the limit. Composite Stringer-Stiffened Structure. In the stringer-stiffened structure made of M55J/M18 prepreg laminates, the number of layers as well as the orientation was iterated to arrive at the optimum design. The optimum design was arrived at by using 1.5 mm-thick laminated shell stiffened uniformly by using 64 numbers of laminated stringers. The optimum orientation of the laminated shell

(a) Lateral Mode

(b) Torsional Mode

Fig. 13 Free vibration modes of metallic stringer-stiffened structure

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V. Pavithra and G. Ramtekkar

(c) Axial Mode

(d) Shell Mode

Fig. 13 (continued)

Fig. 14 First buckling mode of metallic stringer-stiffened structure. Source Pavithra et al. [7]

Optimal Design Techniques of Composite Payload …

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Fig. 15 Stress distribution of metallic stringer-stiffened PLA

is [0/-60/0/-90/-90/90/60/0/60/90/-90/-90/0/-60/0] and that of the stringers is [0/45/0/45/0/90/90/0/45/0/-45/0]. The mass of the PLA designed was 21.79 kg. It is found that the mass of composite monocoque PLA is much less compared to that of the metallic one, still, it couldn’t meet the mass constraints. The results of free vibration and buckling analysis are shown in Tables 12 and 13 and the contours are given in Figs. 16 and 17. Table 12 Results of free vibration analysis of composite stringer-stiffened structure

Modes

Natural frequency (Hz)

Remarks

Mode 1

16.88

Lateral mode

Mode 2

16.88

Lateral mode

Mode 3

21.77

Torsional mode

Mode 4

42.36

Lateral mode

Mode 5

42.36

Lateral mode

Mode 6

97.73

Axial mode

Mode 7

393.20

Shell mode

Mode 8

393.20

Shell mode

Mode 9

393.26

Shell mode

Mode 10

393.26

Shell mode

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Table 13 Results of buckling analysis of composite stringer-stiffened structure

Modes

Buckling load factor Load factor Applying K.D.F.

Applying F.O.S.

Mode 1

2.15

1.72

1.03

Mode 2

2.15

1.72

1.03

Mode 3

2.82

2.26

1.35

Mode 4

2.82

2.26

1.35

Mode 5

3.07

2.46

1.47

Mode 6

3.07

2.46

1.47

Mode 7

3.85

3.08

1.85

Mode 8

3.85

3.08

1.85

Mode 9

4.93

3.95

2.37

Mode 10

4.93

3.95

2.37

In this case also, the lateral and axial mode of free vibration have frequencies more than 15 Hz and 30 Hz, respectively, and the buckling load factor obtained is also greater than 1. The stresses (Fig. 18) obtained in all the layers of the laminated shell and the stringers are within the specified limit. Here, the mass of the structure is less than 25 kg and hence meets all the design constraints including the mass criterion.

(a) Lateral Mode

(b) Torsional Mode

Fig. 16 Free vibration modes of laminated stringer-stiffened structure

Optimal Design Techniques of Composite Payload …

(c) Axial Mode

915

(d) Torsional Mode

Fig. 16 (continued)

Fig. 17 First buckling mode of laminated stringer-stiffened structure

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Fig. 18 Stress distribution of layer 1 of laminated stringer-stiffened PLA

7.3 Sandwich-Structured Design Metallic-Skinned Sandwich Structure. In the sandwich-structured construction made of aluminium skin and aluminium honeycomb core, the optimum design was obtained when 2.5 mm-thick aluminium sheet was given on either side of 10 mmthick core. The mass of the structure obtained is 53.35 kg. The results of free vibration and buckling analysis are shown in Tables 14 and 15. The free vibration modes and the first buckling mode of the structure are shown in Figs. 19 and 20. Here, the minimum frequency in the lateral mode of free vibration is obtained as 16.59 Hz and in the axial mode is 90 Hz. The buckling load factor after applying Table 14 Results of free vibration analysis of metallic-skinned sandwich structure

Modes

Natural frequency (Hz)

Remarks

Mode 1

16.59

Lateral mode

Mode 2

16.59

Lateral mode

Mode 3

47.98

Torsional mode

Mode 4

87.36

Lateral mode

Mode 5

87.36

Lateral mode

Mode 6

90.00

Axial mode

Mode 7

393.36

Shell mode

Mode 8

393.36

Shell mode

Mode 9

430.18

Shell mode

Mode 10

430.18

Shell mode

Optimal Design Techniques of Composite Payload … Table 15 Results of buckling analysis of metallic-skinned sandwich structure

917

Modes

Buckling load factor Load factor Applying K.D.F.

Applying F.O.S.

Mode 1

4.86

3.89

2.33

Mode 2

4.86

3.89

2.33

Mode 3

5.10

4.08

2.45

Mode 4

5.10

4.08

2.45

Mode 5

5.70

4.56

2.74

Mode 6

5.70

4.56

2.74

Mode 7

6.84

5.47

3.28

Mode 8

6.84

5.47

3.28

Mode 9

8.14

6.51

3.90

Mode 10

8.14

6.51

3.90

(a) Lateral Mode

(b) Torsional Mode

(c) Axial Mode Fig. 19 Free vibration modes of metallic-skinned sandwich PLA

(d) Shell Mode

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Fig. 20 First buckling mode of metallic-skinned sandwich PLA

F.O.S. and K.D.F. is obtained as 2.33. The maximum stress (Fig. 21) acting on the structure is also less than the strength of the material. But, the mass of the structure is much more than the limit. Laminate-Skinned Sandwich Structure. In the sandwich-structured construction made of M55J/M18 laminate skin and aluminium honeycomb core, the optimum design was obtained when 15 laminate layers where used on either side of 10 mmthick core. The optimum orientation of the shell is obtained as [0/90/0/90/0/90/ 0/90/0/90/0/90/0/90/0/90/0/90/0/90/0/90/0/90/0/90/0/90/0/90/0]. The mass of the designed structure is 21.59 kg. The results of free vibration and buckling analysis are shown in Tables 16 and 17. The free vibration modes and the first buckling mode of the structure are shown in Figs. 22 and 23. In this case also, the lateral and axial mode of free vibration have frequencies more than 15 Hz and 30 Hz, respectively, and the buckling load factor obtained is also greater than 1. The stresses acting anywhere on the structure are within the specified limit (Fig. 24). Here, the mass of the structure is less than 25 kg and hence meets all the design constraints including the mass criterion.

Optimal Design Techniques of Composite Payload …

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Fig. 21 Stress distribution on the skin of metallic-skinned sandwich PLA Table 16 Results of free vibration analysis of laminate-skinned sandwich structure

Modes

Natural frequency (Hz)

Remarks

Mode 1

15.36

Torsional mode

Mode 2

18.17

Lateral mode

Mode 3

18.17

Lateral mode

Mode 4

30.31

Lateral mode

Mode 5

30.31

Lateral mode

Mode 6

100.54

Axial mode

Mode 7

319.13

Shell mode

Mode 8

319.13

Shell mode

Mode 9

355.45

Shell mode

Mode 10

355.45

Shell mode

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Table 17 Results of buckling analysis of laminate-skinned sandwich structure

Modes

Buckling load factor Load factor Applying K.D.F.

Applying F.O.S.

Mode 1

2.78

2.22

1.33

Mode 2

2.78

2.22

1.33

Mode 3

2.88

2.30

1.38

Mode 4

2.88

2.30

1.38

Mode 5

3.54

2.83

1.70

Mode 6

3.54

2.83

1.70

Mode 7

4.45

3.56

2.14

Mode 8

4.45

3.56

2.14

Mode 9

5.14

4.11

2.47

Mode 10

5.14

4.11

2.47

8 Conclusion Three different configurations of PLA were studied. It was found that the use of composites resulted in more than 50% mass reduction in all three configurations compared to the metallic version. The sandwich structure and stringer-stiffened structures made of composites were found to save 29% and 28% weight, respectively, compared to the laminated monocoque structure. Even though both these structures were found to be effective in saving mass, sandwich structure is mostly preferred due to its ease of manufacturing compared to stringer-stiffened.

(a) Torsional Mode

(b) Lateral Mode

Fig. 22 Free vibration modes of laminate-skinned sandwich structured PLA

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(d) Shell Mode

Fig. 22 (continued)

Fig. 23 First buckling mode of laminate-skinned sandwich structured PLA

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Fig. 24 Stress distribution in layer 1 of laminated sandwich structure

Thus, the directional property of composites is utilised here. The weight savings achieved by converting a sheet-like monocoque structure into a stiffened and a sandwich structure is shown. This establishes the role of composites in economizing space missions.

References 1. Vasiliev VV, Morozov EV (2001) Mechanics and analysis of composite materials. Elsevier, UK 2. Vasiliev VV, Razin AF (2006) Anisogrid composite lattice structures for spacecraft and aircraft applications. Compos Struct 76:182–189 3. Devika V, Mathai A, Ramanujan J (2013) Finite element analysis of interface ring of a rocket launcher. ISSN: 23198753. www.ijirset.com 4. Thomas GR., Fadick CM. Fram BJ (2005) Launch vehicle payload adapter design with vibration isolation features. https://doi.org/10.1117/12.597776 5. Razin AF, Vasiliev VV (2004) Development of composite Anisogrid spacecraft attach fitting.https://www.escm.eu.org/docs/eccm/C202 6. Guerrera A, Verbaro A, Chiarelli MR (2014) Reverse engineering and structural analysis of the ariane payload adapters 7. Pavithra V, Balamurali AG, Ramtekkar G (2019) Optimal design and analysis of a stringerstiffened composite payload adapter. ISSN: 2395-0056 8. Steinberg DV (2000) Vibration analysis for electronic equipment 9. MSC. Nastran Manuals

Nonlinear Static Analysis of a Rectangular Cable Supported Submerged Floating Tunnel (SFT) as an Alternate Crossing for Waterway Md. Hafizur Rahman and Chhavi Gupta

Abstract A buoyant-rectangular cable supported Submerged Floating Tunnel (SFT) can often be used as a waterway crossing even over the vast length and depth following the Archimedes’ principle. The interaction between buoyancy and selfweight controls the static and dynamic behavior of the tunnel. For SFT, weight to buoyancy ratio must be equal or less than one (W /B ≤ 1), so that the tunnel tube can float, where the cable curbs the upward thrust confirming its position, and hence 0.8565 is chosen. Here, SFT is modeled in ANSYS based on the environmental parameters of the Qian Dao Lake (China), where self-weight, hydro-static pressure, vehicular load, and water pressure to the tunnel are considered during nonlinear static analysis. Consequently, it has been observed that the deformations and stresses are in the permissible limit, where maximum equivalent strain exceeds the allowable limit due to its high slenderness, and the maximum strain occurred only at the cable joints. Keywords Buoyancy · Archimedes’ principle · Static behavior · Upward thrust

1 Introduction Modern science is nothing but a skilled magician owing to its deeds and documentaries. With the racing era of modern science and technology, structural engineering is going ahead to rescue the new challenges. The waterway crossing is one of them and usually, bridge is used but submerged floating tunnel (SFT) can be used for coming out of this challenge [1]. Though immersed tunnel, undersea tunnel and bridge of long span has been being used for decades ago, now the curious concentrations are focused on the submerged floating tunnel as it is the new one and it gets the popularity day by day due to its interests. The SFT can easily solve the concerning environmental problems, involves lesser project costs, and can be introduced for its anti-vibrational Md. Hafizur Rahman (B) · C. Gupta Sharda University, Greater Noida, Uttar Pradesh, India e-mail: [email protected] C. Gupta e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_72

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behaviors [2]. It was first patented in Norway in the nineteenth century but it got the advanced achievements in the recent few years due to the complexity of analysis and invasions. Several proposals have been made but SFT has never been built (as of 2016) and several proposals have been presented by different entities [1, 3].

2 Modeling A rectangular SFT, a simple tubular segment having a horizontal axis of symmetry, is placed at 65 ft below the Still Water Level (SWL) because only light water vehicles are allowed to pass over the tunnel. It is located at 200 ft above the lake-bed and is anchored to lake-bed with steel cables to fix it in its position shown in Fig. 1. The SFT is planned to carry the vehicles only. In the SFT, vehicles are allowed to move in one direction. The carriageway used for the vehicles in the SFT is confirmed in accordance with the AASHTO [4]. The major details of the SFT are tabulated in Table 1.

Fig. 1 Schematic diagram of SFT

Nonlinear Static Analysis of a Rectangular Cable Supported … Table 1 Details of SFT tube

925

Type

Magnitude

Length

300 ft (6 @ 50 ft)

Height

22 ft

Width

34 ft

Horizontal Slab

1.5 ft (thickness)

Vertical wall

2.5 ft (thickness)

Carriage way

12.25 ft

3 Methodology In this study, the loads like self-weight, hydrostatic load, vehicle load, and static water load that can be statically induced on the SFT are only considered. The vehicle load is confirmed as per AASHTO (see Sect. 3) for HS 20 with the 100% intensity [4]. FEA-based software ANSYS is used for the analysis of the SFT.

3.1 Structural Scheme Assuming the cables lined at 45°, cables linked to body (X and Z = 0), high strength pre-cast concrete (M50), body-o-body fixed at internal rigid joints and constrained at both ends with connections, the SFT tube is generalized as Fig. 2. The whole SFT of some 300 ft (total length) is divided into six modules (M-1 and M-2) with 50 ft of each. Different supporting conditions for each module have been set that all DOFs are restrained at both ends (M-1) to ignore the large deformations which are assumed as the most realistic boundary condition constraining the rotation of SFT at the boundary. The module (M-2) is rigidly supported to the M-1 with the help of a rigid joint at both ends since the joints deserve the full authentication not to permit the water inside the tunnel and the adjacent joints are designed for the connection of full strength. The stability of SFT is ensured by the adequate anchoring configuration (steel cables) fixed at lake-bed and linked to the SFT with the help of spherical hinges in which displacement in X-and Y-directions is equal to 0. Totally

Fig. 2 Structural scheme of SFT

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Table 2 Characteristic parameters

Table 3 Material identification

Parameter

Magnitude

Unit

Density of water

63.99

lb/ft3

Maximum current velocity

0.328

ft/s

Maximum wave height

3.282

ft

Maximum wave period

2.3

s

Maximum wavelength

27.07

ft

Environmental temperature

20–21.4

°C

Material

Density (ρ) (pcf)

Concrete (pre-cast)

150

Steel (cable)

490

Young’s modulus (E) (psi) 106

Poisson’s ratio (ν)

4.821 × 0.2

29 × 106

0.3

thee pairs of inclined steel cables are configured at 45° for the single module before the net buoyancy. It is worthy to note that the soil’s properties are ignored here for the simplification of the analysis.

3.2 Parametric Characterization Useful data are taken from the Chinese team which was used for the prototype at Qian Dao Lake (China) (Tables 2 and 3).

3.3 Loading Condition The loads generated from the gravity, buoyancy, and vehicles are tabulated in Table 4 that describes the floating condition. Table 4 Characteristic loads for SFT Characteristic

Self-weight

Live load

Buoyant load

Residual buoyant

Total (kip)

11,174.5

1127.58

14,361.6

2059.52

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3.4 Static Structural Analysis It represents the response of the structure which is affected by the static loads such as self-weight, dry ballast load, and hydrostatic pressure. It also describes the stresses, strains, and displacements and different forces owing to the loads except inducing much inertia and the effects of damping. The global nodal displacement can be gained by the following equation: P =kd

(1)

The global load vector is then written as P = P k −P o

(2)

where Pk Matrix of load acting on node. Po Matrix of distributed load acting on element fixed end. These analyses are worked out for the maximum water level of some 307 ft including the tidal growth (20 ft). It is mainly done with a view to justify the static displacement in global X-, Y-, and Z-direction. In this case, ocean loading like wave loading is not considered. In this step, only water pressure on the top plate, buoyant, and vehicle pressure on the bottom plate and hydrostatic pressure on the vertical plate of the tunnel tube is accounted for (Fig. 3).

Fig. 3 Static load pattern

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4 Results and Discussions The static structural analysis is done under static loads named self-weight, hydrostatic load, vehicle load, and static water load. Figure 4 and its corresponding Table 5 show that the maximum deformation under service condition is about 3.5501 (total) at 150 ft which satisfies the ultimate deformation of 4.5 stated as L/800 for the vehicular load (see Sect. 2, AASHTO). The peak deformation is in downward direction due to the huge water pressure on SFT’s top, where the negative deformation represents the direction only. In the case of longitudinal direction (Z), the maximum deformation is at L/4 due to the changing of slope (Fig. 5). In stress and strain analysis depicted in Fig. 6, the maximum von Mises stress is 1.03 × 105 psi that satisfies the concrete stress level. It is mainly highlighted since it describes the criterion of the maximum distortion energy suggesting the yielding condition of the ductile materials while the invariant of second deviatory stress is critical. The equivalent tensile stress or von Mises stress is utilized to guess the yielding state owing to the uniaxial tensile stress and it is greater than the maximum principal stress of some 57,709 psi as the maximum principal stress explains the failure state when it is greater than the ultimate tensile or yield strength. From Fig. 6, it has been seen that the maximum shear stress is 59,436 psi, which also satisfies the

Total Static Deformation 4.5

Deformation (in)

4

3.55

3.5

2.8897

2.8897

3 2.5 2

1.5573

1.5573

1.5 1 0.5 0 0

50

100

150

200

250

300

Length (ft) Fig. 4 Total static deformation

Table 5 Static deformation Deformation

Total ()

Maximum (in)

3.55

Minimum (in)

0

Directional (X ) 0.0506 −0.0507

Directional (Y ) 0 – 3.549

Directional (Z ) 0.4132 −0.4127

Nonlinear Static Analysis of a Rectangular Cable Supported …

929

Fig. 5 Static deformations

Static Strain

Static Stress

Maximum Minimum

Minimum

85000

Magnitude(in/in)

Magnitude(psi)

Maximum

35000 -15000 -65000

Particular Stress

0.025

-0.025

Particular Strain

Fig. 6 Static stress (left) and strain (right)

failure condition because the material will not fail until the peak shear stress exceeds the shear stress at yield. In addition to the shear stress, the maximum von Mises, principal strain, and shear strain are 0.019906, 0.01199, and 0.02475, whereas the minimum values are 0.000013, −0.000003, and 0.0000115, respectively, but the allowable strain should be less than 0.003. The von Mises, principal and shear strains are too high at cable joints due to the high buoyancy force. These high margins of strains can be resisted using the hydro-pneumatic damper, which maintains the large axial strains resembling the

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Md. Hafizur Rahman and C. Gupta Directional Normal Strain

Minimum Maximum Z Y X -20000

-10000

0

10000

Directional Strain

Directional Stress

Directional Normal Stress

Minimum Maximum Z Y X

20000 -0.004

Magnitude

-0.002

0 0.002 Magnitude

0.004

Fig. 7 Directional normal stress (left) and strain (right)

effect of well pump and booster pump. Another cable configuration can also be introduced like tying the cable over the periphery of the tunnel tube to reduce the strains’ intensity. Figure 7 represents that the maximum normal stress and strain occur in the longitudinal direction (Z) and their magnitudes are 18,152 psi and 0.002953, respectively, where the corresponding minimum values s are −17,730 psi and − 0.002916, where the negative sign indicates the opposite direction only.

5 Conclusion SFT, which has the characteristics of tunneling and marine engineering, is complex in some disciplinary areas. It is too important to build the prophases of researches for widening the aspects of crossing projects. This paper analyzed the static behaviors of the SFT under service loads and it has been seen that. • The maximum deformation under service loads satisfies the maximum deformation for vehicular loads specified in the AASHTO. • The maximum equivalent tensile stress or Vov Mises stress and normal stress (in all directions) induced in the SFT are under the satisfaction where the von Mises, principal strain and shear strain are high only at cable joints.

References 1. Jakobsen B (2010) Design of the submerged floating tunnel operating under various conditions. Procedia Eng 4:71–79. https://doi.org/10.1016/j.proeng.2010.08.009 2. Man-Sheng D, Xue-Fei T, Yuan Z, Fei T (2016) Vibration control of the submerged floating tunnel under combined effect of internal wave and ocean current. Procedia Eng 166:160–170. https://doi.org/10.1016/j.proeng.2016.11.579 3. Zhang K, Xiang Y, Du Y (2010) Research on tubular segment design of submerged floating tunnel. Procedia Eng 4:199–205. https://doi.org/10.1016/j.proeng.2010.08.023 4. AASHTO LRFD BRIDGE (2012) Standard specifications of highway bridges. American Association of State Highway and Transportation Officials, 17th ed, Washington.

Nonlinear Finite Element Analysis of Plain Footing Rakhi Elizabeth Thankachan, Bennet Kuriakose, and Jitin Jacob

Abstract Plain foundations are shallow foundations which are widely used in construction industry. In traditional analysis of plain footing, the finite element analysis is carried out as plain strain problems in different soil models. In the case of 3D problems, the combined effect of nonlinear behaviour of soil and soil-structure interaction under footing is not accounted for. In this paper, the nonlinear analysis of plain footing is performed by using 3D stress elements and considered the interaction between the soil surface and the bottom of the foundation, that is, the distribution of contact pressure under the plain footing along with the material and geometric nonlinearities. A three-dimensional model of the plain footing having dimensions 0.6 m x 0.6 m x 0.05 m, resting on very soft clay, is considered and the rigorous analysis of the same is performed. The finite element model of the plain footing is developed by using the popular package ABAQUS. The validation of the model is performed by making use of the results from an experimental study available in the literature. A parametric study is also carried out to asses the performance of the footing under the variations of four different soil parameters, viz, elastic modulus, Poisson’s ratio, friction angle and cohesion intercept. Although the elastic properties of the soil have no influence on the bearing capacity of the footing, this is demonstrated for purely of academic interests. Keywords Plain footing · Nonlinear analysis · Finite element analysis · Contact pressure

1 Introduction The finite element analysis of plain footings is usually performed with various assumptions, in which the soil is considered as weightless, homogeneous, and isotropic material and the interface between the soil and footing is restrained against

R. E. Thankachan (B) · B. Kuriakose · J. Jacob Department of Civil Engineering, St. Joseph’s College of Engineering and Technology, Palai, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_73

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horizontal movements (rigid contact). The soil–structure interaction (contact pressure distribution) is an important factor that significantly influence the response of the superstructure. The distribution of contact pressure under rigid and flexible footings is different for cohesive and non-cohesive soils. Generally, for design purpose, the reaction of soil under the footing is averaged as uniform pressure, despite of the fact that the distribution of the same is practically non-uniform. In the past, a simplified interaction model known as Winkler model is developed, for the computer-aided numerical methods, to avoid the tedious process for developing solutions by the continuum analysis. The Winkler model, is similar to a medium, consists of infinite number of elastic, identical, independent springs. But the model was incapable of simulating the continuity of the soil medium. Later, the Winkler model is modified by interconnecting the elastic springs by structural elements and thereby modeling the continuity of the soil medium and the model is known as Pasternak model. However, in these models, it is assumed that the foundation is fixed to the natural foundation, the soil. Recently, it is realized that the soil–structure interaction (SSI) altered the response of the superstructure because of the rigidity of the structure and softness of the natural deposit. In the present study, the soil is treated as continuum half-space model and is assumed as homogeneous, isotropic and weightless. At the contact interface, a mechanical contact is defined between the footing surface and the soil surface using penalty method with the allowance of an elastic slip. A uniform contact pressure is considered at the interface between soil and the footing which is characterized by the coefficient of interface friction. It is noteworthy to review some of the previous studies on the behaviour of plain footings based on experimental [1–5] and numerical [4, 6–10, 11] procedures. In 1972, Brand et al. compared the performance of grouped pile foundations and spread footing in order to study the settlement and load-carrying capacities of both foundations [1]. Branko studied the long-term settlement of shallow foundation on frozen soil due to creep and consolidation [2]. Omar et al. performed laboratory model tests for the ultimate bearing capacity of the strip and square foundations resting on sand, which is reinforced by using geogrids [5]. Garbin et al. presented the design, construction and quality control of mass stabilization program, a dry soil mixing technique to increase the shear strength and to decrease the compressibility of organic clay insitu [3]. Zhu studied the bearing capacity of the strip footing on two-layer clay soil by finite element method. The soil is discretized with eight-node plain strain quadrilateral element. The footing is considered as rigid footing and the soil–footing interface is restrained in order to prevent horizontal movement at the interface. Tresca failure criterion is used to model soil as an elastic-perfectly plastic material and the soil is considered as a weightless material [8]. Konapure and Vivek compared the analysis of combined rectangular footing by Winkler’s model and finite element method [7]. Elshesheny et al. performed the finite element analysis of square footing resting on geosynthetic-reinforced soil employing Drucker–Prager’s model for soil [6]. Vilas and Moniuddin performed the two-dimensional finite element analysis of square footing to study the bearing capacity. The Mohr–Coulomb failure criterion is used for the material model [10]. Requena et al. predicted the settlement of footing

Nonlinear Finite Element Analysis of Plain Footing

933

on sandy soil using finite element method exercising Drucker–Prager’s yield criterion for soil. The footing is considered as rigid and the interaction between soil and footing is taken into account [9]. El-kady and Badrawi conducted experimental and numerical studies on isolated plain and folded footings. The Mohr–coulomb model is used to define the sand as an elasto-plastic material with reduced integration and hourglass control [4]. Namdar conducted a numerical investigation on soil-concrete foundation interaction and concluded that the application of soil-structure interaction on numerical model has an important effect and it improves the accuracy of the model [11]. In the literature, various aspects of nonlinear analysis of plain footing is observed, however, a rigorous analysis employing all the nonlinearities is not found to the knowledge of the authors. In this paper an exhaustive analysis of plain footing resting on uniformly distributed nonlinear half-space continuum is performed using a finite element model developed in ABAQUS [8]. The Mohr-Coulomb soil model is used for the analysis and is descretized with 8 noded 3D stress elements. The material and geometric nonlinearities involved in the behaviour of soil as well as contact pressure developed between the footing and the soil is also considered in the present model. The developed model is validated with experimental results presented in Brand et al. A detailed parametric study is also carried out to understand the effect of soil parameters like modulous of elasticity, Poisson’s ratio, friction angle and cohesion intercept. This study can form as a calibration model for the future numerical studies on plain footings.

2 Finite Element Analysis Procedure This section explains about the development of the finite element model of the footing. The soil is modeled as a continuum half-space and the decretization of which is performed by using 8 noded linear brick elements. The footing is also modeled using an 8-noded brick element mesh. Invoking the symmetry, one fourth of the system is only taken into consideration in the numerical model. The boundaries of the model are applied with symmetric boundary restrains. The other sides of the soil are considered to be extended up to a minimum of 1.5 times the width of the footing, and applied with restraint along two directions except the vertical. The bottom of the soil is applied with a restraint along all the three directions [12]. A three-dimensional Mohr–Coulomb material model is used for modelling the nonlinear behaviour of the soil medium, the yield surface of which is represented in Fig. 1. The Mohr-Coulomb model describes a linear relationship between normal and shear stresses (or maximum and minimum principal stresses) at failure. The yield surface shown in Fig. 1 is characterized in the principal effective stress plane by the following function [13]: F = σ  1 − σ  3 − 2c cosϕ  − (σ  1 − σ  3 ) sinϕ . Where c is the cohesion and ϕ  is the friction angle of the soil. The soil is considered as a homogeneous isotropic material and these idealizations show some variations from the actual experimental results. The three dimensional Mohr–Coulomb criterion is often expressed as

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Fig. 1 Mohr-Coulomb failure surface (Potts and Zdrakovi´c [13])

  σ1 + σ2 σ1 − σ2 = sin(ϕ) + cos(ϕ) ± 2 2   σ2 − σ3 σ2 + σ3 ± = sin(ϕ) + c cos(ϕ) 2 2   σ3 − σ1 σ3 + σ1 ± = sin(ϕ) + c cos(ϕ) 2 2 where σ 1 = Maximum principal stress σ 2 = Intermediate stress σ 3 = Minimum principal stress Φ = Angle of internal friction.

3

Validation Example

Validation of the method used for the present study is done using the experimental results obtained from the field experimental investigation done by Brand et al. In order to check the applicability of the developed finite element procedure and to validate the same, a square plain footing of plan dimensions 0.6 m x 0.6 m and thickness 0.05 m resting on uniform clayey soil at a depth 1.5 m from the ground level is considered [1]. The schematic representation of the plain footing under consideration is presented in Fig. 2. The shear strength of the soil above the base of the footing is neglected and is replaced by an equivalent surcharge [14]. The properties of the soil stratum are presented in Table 1. The concrete for plain footing pad is modelled as a linear elastic

Nonlinear Finite Element Analysis of Plain Footing

935

Fig. 2 Schematic representation of plain footing model 0.6 m x 0.6 m x 0.05 m resting on uniform soil stratum

material with Young’s modulus (Ec ) of 30 GPa and Poisson’s ratio (µc ) 0.15. The interaction between bottom surface of the footing and the soil surface is modelled by the penalty method in which an elastic slip (relative motion between two surfaces) is permitted between the two surfaces. The magnitude of maximum elastic slip in terms of fraction of characteristic surface dimension is limited to a value of 0.005. The frictional coefficient for the contact surfaces is 0.45 and the shear stresses are kept unlimited. A surcharge load of 150 kN is provided on the surface of the plain footing, which is equivalent to the maximum safe bearing capacity of clayey soil in general. The finite element model of the soil-footing system discretized with 8 noded 3D stress elements is shown in Fig. 3. The mesh of the soil stratum is refined under the plain footing, because a significant settlement occurs in this region. The method is validated with the study of Brand et al. on spread footing in soft Bangkok clay. The dimensions of the plain footings used for the experiment were 0.6 m × 0.6 m, 0.675 m × 0.675 m, 0.75 m × 0.75 m, 0.9 m × 0.9 m, 1.05 m × 1.05 m. The depth of the foundation was 1.5 m in all cases. For the present study and validation, the load-settlement graph for 0.6 m × 0.6 m plain footing having ultimate bearing capacity 60 kN/m2 is selected and the analysis is carried out using the properties of Bangkok clay [1, 15]. In order to validate the method, the elastic and shear strength parameters of the clay are determined theoretically. The available properties of the Bangkok clay from the soil tests [1, 15] were. • • • • •

Liquid limit = 80 Plastic limit = 40 Plasticity index = 40 Sensitivity = 5 Average undrained shear strength, obtained from Vane shear test,

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Fig. 3 Finite element model of the plain footing 0.6 m x 0.6 m x 0.05 m on soil stratum

Cu(VST) = 24 kN/m2 . Corrected value, C = 20 kN/m2 . The elastic properties (E and μ) are computed from the linear analysis of plain footing. The friction angle is obtained from the equation of coefficient of lateral pressure [14], k = 1 − sinφ; μ = 1 − sin(φ) 1−μ 0.43 = 1 − sin(φ) 1 − 0.43 φ = 14.23◦ where k = coefficient of lateral pressure μ = Poisson’s ratio  = Angle of internal friction. The shear strength parameter, cohesion intercept is determined from the Mohr circle. From the undrained cohesion intercept, the effective overburden pressure can

Nonlinear Finite Element Analysis of Plain Footing

937

be determined from the following equation [14], C = 0.11 + 0.0037 PI σ 20 = 0.11 + 0.0037 × 40 σ σ = 77.52 kN/m2 where C = Undrained cohesion intercept σ = Effective overburden pressure PI = Plasticity index. The effective overburden pressure (σ ) is taken as the maximum principal stress (σ 1 ) and the minimum principal stress (σ 3 ) is obtained from the equation [14],   14.23 σ3 = 77.52 × tan2 45 − 2 σ3 = 47 kN/m2 Using the maximum and minimum principal stresses, the Mohr circle is plotted and the shear strength of the soil (τ ) and the stress at the oblique plain (σ  ) are determined from the Mohr circle [14]. From the Mohr circle, the shear strength of the soil, τ = 18 kN/m2 and the stress at the oblique plain, σ ´ = 58 kN/m2 . τ = c + σ  tan(φ) c = τ −σ  tan(φ) c = 18 − 58 tan(14.23) = 3291 Pa. ≈ 4 kPa The properties of the Bangkok clay determined are listed in Table 1. The Bangkok clay is unsaturated low plasticity clay having very low stiffness and hence the water content of the clay is near to its liquid limit. The clay is very sensitive and has very low salt content. Since the shear strength is very low, the Bangkok clay shows the properties in between solid and fluid [14]. The sensitivity of the clay is 5 and is in the range of sensitive clays (4–8). Since sensitivity is the measure of the ability to resist shear stress on the soil [14], the

938 Table 1 Properties of the soil

R. E. Thankachan et al. Properties

Magnitude

Elastic modulus (E)

4 MPa

Poisson’s ratio (μ)

0.43

Friction angle (φ)

14

Dilation angle (ѱ)

0

Cohesion (c)

4 kPa

Bangkok clay is sensitive to disturbances and its properties change considerably even with slight deformations. The finite element analysis of plain footing is carried out and the displacement contours are shown in Fig. 4. The maximum settlement attained through the consolidation of soil is 62 mm. In the experiment result, conducted by Brand et al. the settlement was 40 mm. The difference in settlement is due to the fact that in the numerical analysis, the soil is assumed as homogeneous and isotropic. The red contour shows the lateral displacement of the soil surface with a minimum upward displacement of 16 mm and the deep blue contour shows the maximum settlement of 62 mm under the maximum load 68 kN. The slight lateral movement is due to the fact that the surface to surface contact of the plain footing and the soil is not rigid and is modelled using the penalty method which allows an elastic slip. The comparison between the results from the present study and experimental results are shown in Fig. 5. The ultimate load is defined as the point where the load-settlement graph becomes practically linear. An automatic load increment strategy is employed for the analysis with an initial step size of 1 kN and a maximum load step of 10 kN, which is executed via static general procedure. The ultimate load carrying capacity of the footing from the present study (59 kN) is compared with the value obtained from the experimental investigation (60 kN) reported by Brand et al. is compared in Fig. 4 and is found to be in good agreement, with a percentage variation of 1.68% from the actual field experimental

Fig. 4 Displacement contour of plain footing under maximum load 68 kN

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Fig. 5 Comparison of load-settlement graphs obtained from the field experiment and FEA

result. There is a slight difference in the curvatures of the graph, which perhaps of the fact that in the present model the presence of pore water is neglected and the soil is assumed as homogeneous and isotropic. In the load- settlement graph, the ultimate load is defined as the point where the load settlement graph becomes practically linear [15].

4 Parametric Study Since the finite element analysis of the plain footing is validated by considering all the nonlinearities, a study on the influence of soil parameters in Mohr-Coulomb soil model on the bearing capacity of the plain footing is essential for the further studies on shallow foundations in clayey soils. A detailed parametric study is carried out in order to understand the effect of soil parameters on the ultimate bearing capacity of plain footing. The elastic properties (E and μ) and shear strength parameters (C and φ) of soil are studied and the ultimate bearing capacities are compared. The values of each parameter are varied keeping the other parameters same in all cases.

4.1 Effect of Elastic Modulus Elastic modulus of the soil is the measure of its stiffness. The modulus of elasticity together with the Poisson’s ratio defines the linear part of the load–displacement graph. The comparison of load–displacement graph for plain footing for soil with different elastic moduli (10MPa, 8 MPa, 6 MPa, 4 MPa, and 2 MPa) is shown in Fig. 6.

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Fig. 6 Effect of elastic modulus of clay on the ultimate bearing capacity of the plain footing

When, the elastic modulus increases from 2 to 4 MPa, the ultimate bearing capacity increases from 59 to 60 kPa. The bearing capacity reduces to 59 kPa at elastic modulus 6 MPa and 8 MPa. It further reduces to 52 kPa at elastic modulus 10 MPa. It can be seen that the variation of bearing capacity of the clayey soil remains almost constant for varying elastic moduli except at E = 10 MPa. As the elastic modulus increases, clay shows a nonlinearly elastic behaviour. This reduces the settlement of foundation in the clay. Although the ultimate bearing capacity of the clay is almost constant for varying elastic moduli, the settlement decreases as the elastic moduli increases.

4.2 Effect of Poisson’s Ratio Poisson’s ratio defines the linear part of the load-settlement graph together with elastic modulus. It is seen that the effect of poisons ratio on the computed ultimate stresses is not significant. In the present study, the variation of Poisson’s ratio does not show much effect on the ultimate bearing capacity of the plain footing. In all cases the bearing capacity of the footing is 60 kN. The value of Poisson’s ratio 0.49 has chosen instead of 0.5, because the value 0.5 is suitable only for a perfectly incompressible material deformed elastically at small strains.

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Fig. 7 Effect of Poisson’s ratio of clay on the ultimate bearing capacity of the plain footing

4.3 Effect of Angle of Internal Friction The friction angle is a shear strength parameter, the definition of which is derived from the Mohr–Coulomb failure criteria and is used to describe the friction shear resistance. For normally consolidated clay, the friction angle ranges from 5° to 20° [16]. When the friction angle decreases, the plasticity index increases and hence the clay will act like a fluid and hence the shear strength decreases. In Fig. 8, as φ increases, the resistance to inter-particle slip increases and hence the shear strength of the clay increases, this will further increase the ultimate bearing capacity of the footing and hence the bearing capacity increases with increase in

Fig. 8 Effect of internal friction angle of clay on the ultimate bearing capacity of the plain footing

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internal friction angle. The ultimate bearing capacities for the friction angles, 8°, 10°, 12°, 14°, 16° are 38 kN, 42 kN, 51 kN and 65 kN respectively.

4.4 Effect of Cohesion Cohesion provides the shear strength to the soil and it describes the non-frictional part of the shear resistance which is independent of the normal stress. Figure 9 shows the effect of cohesion of soil on the ultimate bearing capacity of plain footing. As the value of cohesion increases from 4 to 10 kPa, the soil changes its state from liquid to semi-solid and then to solid. The strength of the soil increases as the shear strength increases and hence the bearing capacity of the footing increases. In Fig. 9, at C = 2 kPa, the shear strength of the soil is very low, because the clay is at its liquid limit (Casagrande). The soil reaches its ultimate bearing strength at 23 kPa at which the clay undergoes shear failure. After the shear failure, the settlement increases gradually up to 160 mm. At C equals 4 kPa, the soil is slightly plastic and the shear failure occurs at 61 kPa, after which the settlement reduces to 70 mm. Further increase in cohesion increases the bearing capacity and reduces the settlement. In this study, it is observed that the ultimate bearing capacity of the plain footing reduces in low bearing soil and the shallow plain foundations can be used only for soils having adequate shear strength.

Fig. 9 Effect of Cohesion intercept of clay on the ultimate bearing capacity of the plain footing

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5 Conclusion In this study, the continuum half-space model of plain shallow foundation is created using the ABAQUS, and the method is validated using the results from literature. The consideration of all nonlinearities makes the result more accurate and the ultimate bearing capacity values are near to the actual field result. The study gives the following conclusions: • The ultimate bearing capacities obtained from the field experimental study and the present study are 60 kN and 59 kN respectively. The percentage difference between the results from field experimental study and the present study is 1.68%. From this it can be concluded that the present study resembles the field experimental study very closely, that is the method gives a realistic result. This study can be used as a base for future studies about shallow foundations. • In the parametric study, as the stiffness of the soil alone increases, keeping the shear strength same, the bearing capacity of the plain footing is almost constant. , and hence the ultimate bearing capacity of the plain footing increases only if the shear strength of the soil is increased. However, the settlement decreases as the elastic modulus increases. • The variation in poisons ratio has no effect on the ultimate bearing capacity of the plain footing. Thus it can be concluded that the variation in the elastic properties of the soil has very less effect in improving the ultimate bearing capacity of the plain footing. • As the value of shear strength parameters increases, the ultimate bearing capacity of the plain footing increases and its value is very low (23 kPa) in soil having very low shear strength. • The conclusion from this study is that the method used in the present study can be used to simulate an actual field experiment and is very useful for the parametric study and the designing of new shallow foundations techniques.

References 1. Brand EW, Muktabhant C and Taechanthummarak A (1972) Load Test on Small Foundations in Soft Clay. Proceedings, Specialty Conference on Performance of Earth and Earth Supported Structures, ASCE. vol 1, Part 2, pp 903–928 2. Branko L (1983) Shallow foundations on frozen soil: Creep Settlement. J Geotech 109(11):1434. https://doi.org/10.1061/(ASCE)0733-9410 3. Garbin EJ, Mann J, McIntosh KA, Desai KR (2011) Mass stabilization for settlement Control of Shallow Foundations on Soft Organic Clayey Soils. Geo-Front ASCE. https://doi.org/10. 1061/41165(397)78 4. El-kady MS and Badrawi EF (2017) Performance of isolated and folded footing. JCDE 4:150– 157. https://doi.org/10.1016/j.jcde.2016.09.001 5. Omar MT, Das BM, Puri VK, Yen SC (1993) Ultimate bearing capacity of shallow foundations on sand with geogrid reinforcement. Can Geotech J 30(3):545–549. https://doi.org/10.1139/ t93-046

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6. Elshesheny A, Nagy N, Badawy A (2014) Finite element analysis of square footing resting on geosynthetic reinforced soil. Proceedings of the 10th ICCAE-10 conference 27–29 May 2014. https://doi.org/10.21608/ICCAE.2014.44109 7. Konapure CG and Vivek B (2013) Analysis of combined rectangular footing by Winkler’s model and Finite element method. IJEIT 3(5). ISSN 2277-3754 8. Zhu M (2004) Bearing capacity of strip footing on Two-Layer clay soil by finite element method. ABAQUS user’s conference, Department of civil and Environmental engineering, University of Michigan, Ann Arbor. https://doi.org/10.1016/j.compgeo.2015.05.018 9. Requena J, Ayuso J, Jimenez JR and Francisco A (2015) Prediction of footings settlement on sands by finite element method. Construction Engineering Area, University of Cordoba, Spain 10. Vilas, Moniuddin K (2015) Finite element analysis of soil bearing capacity using PLAXIS. Int J Eng Technol 4(06). ISSN: 2278-0181 11. Namdar A (2016) A numerical investigation on soil-concrete foundation interaction. Procedia Structural Integrity 2:2803–2809 12. Cook RD, Malkus DS, Plesha EM, Witt JR (2010) Concepts and applications of finite element analysis 13. Potts DM, Zdravkovi´c L (1999) Finite element analysis in geotechnical engineering: Theory. Thomas Telford Publishing, London. 14. Arora KR (2008) Soil mechanics and foundation engineering 15. Das BM (2011) Principles of foundation Engineering. Global Engineering, USA 16. Bowles JE (1997) Foundation analysis and design. McGraw-Hill, Singapore

Soil–Structure Interaction Analysis of Tall Steel Chimney Subjected to Wind Load Anjaly Mohan, Binny Lizia Jose, and Bennet Kuriakose

Abstract Chimneys are tall structures having phenomenal sensitivity to wind loads. Generally, computational analysis of tall structures is carried out without considering the effect of soil beneath, which in turn results in incorrect prediction when compared to the real response. This paper presents finite element modelling of a steel chimney on annular foundation subjected to wind load considering soil–structure interaction. The study reiterates the necessity of considering the effect of soil while reckoning the response of tall structures. Keywords Chimney · Soil structure interaction · Wind load · Finite element modelling

1 Introduction Chimneys are provided in concordance to industries for ventilation of hot flue gases or smoke to the atmosphere. Both steel and concrete chimneys are used in practice depending upon the specific usage and concerns. Steel chimneys are generally provided with a height of 50 m and above. Chimneys are subjected to heavy wind loads necessitating a numerical study for designing and assessing the serviceability. In conventional civil engineering analysis, the superstructure is analysed by treating it as independent from foundation and soil medium, assuming a fixity at its base. Therefore, an analysis scheme is necessitated which considers structure–foundation– soil as a single system and in the literature it is termed as Soil–Structure Interaction (SSI) analysis. SSI consideration provides rigour in the analysis procedure so as to assess the behaviour of the chimney more accurately, duly taking into account the flexibility of the soil on which it is founded. Few studies are reported in the literature considering the SSI of chimney subjected to wind loads, prominent ones being Bolisetti et al. [1], Chmielewski et al. [2], Jayalekshmi et al. [3], Liang et al. [4], Navarro [5] and Papadopoulos et al. [6]. A. Mohan (B) · B. L. Jose · B. Kuriakose Department of Civil Engineering, St. Joseph’s College of Engineering and Technology, Palai, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_74

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These studies consider soil as a finite continuum Luco [10]. A fore mentioned studies showed that the base moment of the chimney on soft soil increases up to ~10% due to the effect of along-wind load. The bending moment is considerably reduced in the annular raft foundation of tall chimneys due to flexibility of the foundation soil under along-wind load [7]. Wind force is considered as dominant load criteria in the design of tall steel chimneys, considering the along-wind and cross-wind actions. Few studies such as Tsukagoshi et al. [8], Vickery and Basu [9] and Wootton [7] throw light in this regard. Although the aforementioned studies provide abundant results and interpretation, more percipience is required because of the complexity of the problem. In this paper, finite element modelling of a steel chimney on ring foundation subjected to wind load considering SSI is presented. The numerical model of the chimney is developed by employing the popular ABAQUS package. Along-wind loads are estimated by using a simplified analytical scheme. Serviceability of the chimney is assessed through the deflection produced due to along-wind loads. This study proves the importance of consideration of foundation soil and its interaction with the chimney in the analysis procedures.

2 Modelling Considerations Along-wind load effects are caused by the ‘drag’ component of the wind force on the chimney, whereas across-wind loads are caused by the corresponding ‘lift’ component of the wind force on the chimney. The drag component thus causes direct buffeting action and the lift component is associated with the phenomenon of vortex shedding, which is the reason for the oscillation of chimney in a direction perpendicular to the direction of wind flow. There are generally two methods for estimating along-wind load and across-wind loads for chimneys such as simplified method and random response method [6]. The static force due to along wind acting at the midpoint of the k th zone shall be calculated from the formula [9] Pst,k = Cqk h k dk

(1)

where Pst,k is the static wind load acting at the midpoint, qk is the static wind pressure, dk is the external diameter of chimney, h k is the height of the kth zone strip and C is the shape factor for chimney. The finite element modelling of the steel chimney was carried out using the commercial finite element software ABAQUS. The steel chimney was modelled with 4-node doubly curved shell elements with reduced integration. For the threedimensional modelling of the ring foundation, 6-node linear brick elements with reduced integration were used. The soil stratum was modelled using 8-node hexagonal elements. In the present model, the soil and the chimney are assumed to

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exhibiting Hookean behaviour owing to the fact that the study is of preliminary nature. The horizontal movements at the interface between the soil and the structure are restrained for the analysis and the interface friction is neglected.

3 Numerical Example In order to portrait the suitability of the present model and the importance of SSI in the analysis procedure, a numerical example is presented. A tall steel chimney of 72 m height is considered with a uniform shell thickness of 20 mm. Height of the flare is considered to be 0.33 times that of the height of the chimney. The diameter of the flare is considered to be 1.6 times that of the diameter of the cylindrical part. The diameter of the cylindrical part of the chimney and the diameter of flare were 3 m and 4.8 m, respectively. Chimney was considered to be resting on an annular foundation of 700 mm depth, the outer diameter and inner diameter of which being 6.5 m and 4.5 m, respectively. Soil is considered to be a single homogeneous block of 19.5 m depth. Lateral boundary of the soil block is placed at a distance of 3 times the width of the foundation. The schematic representation of the elevation of the tall steel chimney and the ring foundation are depicted in Fig. 1. The chimney shell was discretized using shell elements of size 0.15 m. For the discretization of the ring foundation bias property was applied and the smallest element has a size of 0.15 m, whereas the maximum size is 0.3 m. The soil stratum is also discretized using elements of varying sizes, the mesh being coarse near the regions where stress gradients are expected to be low. The bottom of the soil medium is restrained for displacements in all the three directions whereas the lateral boundary of the soil stratum is restrained for the horizontal displacements. The finite element model of the steel chimney with a flexible base is shown in Fig. 2. The material properties of the steel chimney and foundation are presented in Table 1. To study the effect of SSI, four different types of soil were considered, viz., hard soil/rock (S1), dense soil (S2), medium soil (S3) and loose soil (S4). They were defined with their modulus of elasticity and Poisson’s ratio. Properties of these different soil types are given in Table 2. A rigid supported chimney is also considered in order to compare the results for the different soil types. A basic wind speed of 30 m/s was considered for the current study. The along-wind load calculated was given as point loads on the steel chimney at an equal interval of 8 m as only the global response of the structure was considered. The maximum deflection at the top of the steel chimney produced by the wind load without taking into account the dynamic factors calculated as acting on the circular cross section shall not be greater than h/200, i.e. 360 mm, where h is the unsupported height of the chimney. The lateral deflection of the chimney was obtained and it was observed that for the various soil types, S1, S2, S3 and S4 are presented in Table 3. There were 2.07%, 5.89%, 18.2% and 55.1% variation, respectively, for S1, S2, S3 and S4, when compared to the lateral deflection obtained for rigid base. This indicates that as the rigidity of the soil is decreased (i.e. soil become more soft),

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Fig. 1 Schematic diagram of a elevation of tall steel chimney b plan view of the annular foundation

there is a considerable increase in the deflection of the chimney. This shows the importance of the SSI scheme to be considered in the analysis, especially when the engineering problem needs to account for stringent consideration of serviceability. The contour of lateral deflection for soil type S1 is shown in Fig. 3.

4 Conclusions The effect of soil–structure interaction was studied on a tall steel chimney found on a ring foundation subjected to along-wind load. A finite element model of the steel chimney–foundation–soil system was developed by using ABAQUS. To examine the variation of response of chimney with soil stiffness, different soil parameters

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Fig. 2 Finite element model of steel chimney with a flexible base Table 1 Material properties

Steel chimney Concrete annular foundation

Elastic modulus

200 × 106 kN/m2

Poisson’s ratio

0.3

Elastic modulus

2.36 × 106 kN/m2

Poisson’s ratio

0.3

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Table 2 Properties of soils Soil type

Nomenclature

Elastic modulus, E (kN/m2 )

Poisson’s ratio, ν

Hard soil/rock

S1

7,650,000

0.3

Dense soil

S2

1,920,000

0.3

Medium soil

S3

446,000

0.35

Loose soil

S4

108,000

0.4

Fig. 3 Contour of lateral deflection of steel chimney resting on soil type S1

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Table 3 Deflection of steel chimney (mm) for different soil conditions Rigid base

S1

S2

S3

S4

79.25

80.89

83.92

93.67

122.90

were selected. The lateral deflection of chimney corresponding to these various soil parameters was compared with that of the rigid base chimney. It was observed that for the various soil types, S1, S2, S3 and S4 there was 2.07%, 5.89%, 18.2% and 55.1% variation, respectively, from the lateral deflection obtained for the rigid base. This study proved the significance of soil–structure interaction analysis of tall chimney subjected to wind loads. A study of the chimney considering the material and geometric nonlinearities is underway.

References 1. Bolisetti C, Whittaker AS, Coleman JL (2018) Linear and nonlinear soil-structure analysis of building and safety-related nuclear structures. Soil Dyn Earthq Eng 107:218–233. https://doi. org/10.1016/j.soildyn.2018.01.026 2. Chmielewski T, Górski P, Beirow B, Kretzschmar J (2005) Theoretical and experimental free vibration of tall industrial chimney with flexibility of soil. Eng Struct 27:25–34. https://doi. org/10.1016/j.engstruct.2004.08.009 3. Jayalekshmi BR, Jisha SV, Shivashankar R (2015) Wind load analysis of tall chimneys with piled raft foundation considering the flexibility of soil. Int J Adv Struct Eng 7:95–115 4. Liang J, Han B, Todorovska MI, Trifunac MD (2017) 2D Dynamic structure-soil-structure interaction for twin buildings in layered half space I: incident SH-waves. Soil Dyn Earthq Eng 102:172–194. https://doi.org/10.1016/j.soildyn.2017.08.017 5. Navarro C (1992) Influence of soil flexibility on the seismic behavior of of chimneys. Soil Dyn Earthq Eng 11:403–409. https://doi.org/10.1016/0267-7261(92)90004-W 6. Papadopoulos M, Beeumen RV, Francois S, Degrande G (2018) Model characteristics of structures considering dynamic soil-structure interaction effects. Soil Dyn Earthq Eng 105:114–118. https://doi.org/10.1016/j.soildyn.2017.11.012 7. Wootton LR (1969) The oscillation of larger circular stack in wind. P I Civil Eng 43:573–598. https://doi.org/10.1680/iicep.1969.7314 8. Tsukagoshi H, Tamura Y, Sasaki A, Kanai H (1993) Responses analyses on along-wind and across wind vibrations of tall building in time domain. J Wind Eng Ind Aerod 46–47:497–506. https://doi.org/10.1016/0167-6105(93)90317-H 9. Vickery BJ, Basu RI (1983) Across wind vibration of structures of circular cross section Part I—development of a mathematical model for two-dimensional conditions. J Wind Eng Ind Aerod 12:49–98. https://doi.org/10.1016/0167-6105(83)90080-6 10. Luco JE (1986) Soil- structure interaction effects on the seismic response of tall chimneys. Soil Dyn Earthq Eng 5:170–177. https://doi.org/10.1016/0267-7261(86)90020-5

Investigation of the Suitability of Water Demand Studies as an Indicator of Incompatibility Between Binders and Superplasticizers A. K. Swathy Krishna, T. K. Sreeranjini, and P. L. Vijayakumari

Abstract Use of superplasticizers (SP) in concrete production has advantages that are manifold, leading to improved performance in many characteristics including strength and durability. The use of SP ensures maximum workability with reduced water demand, heat of hydration, segregation, and bleeding. However, since most of the concrete mixtures used today included many additional ingredients especially in the binder phase, it is essential that the compatibility between ingredients and chemical admixtures is well established beforehand. In this study, the possibility of using a simple test such as the water demand variation with SP dosage, using Vicat’s apparatus, as an indicatory test to identify any incompatibility is explored. The experimental program consisted of studies on pastes composed of 2 brands of Portland Pozzolana Cement (PPC) with two major families of superplasticizers, viz., Sulphonated Naphthalene Formaldehyde (SNF), and Polycarboxylate Ether (PCE). Both SPs showed different trends in characteristics like water demand, workability, fluidity of paste, mixing time at the same SP dosage (solid content). PCE showed a trend of decrease in water demand whereas in case of SNF water demand decreased initially and later increased at slightly higher dosages of SP indicating that overdosing greatly affects the cement–superplasticizer interaction in SNF. The effect of the addition of more pozzolanic materials to fly ash based PPC, for increasing the sustainability potential was analyzed by replacing PPC with 5% and 10% of fly ash and Coconut Shell Ash (CSA). It was found that at different SP dosages, the water demand decreased considerably at initial dosages compared to the reference mix. The results from studies with SNF concluded that incompatibility exists irrespective of the cement brand. To understand the relation of incompatibility with a change in mixing method, hand mix was replaced by cake mixer, also different mixing pans were used and the graphs were compared. The experiment clarifies that although the A. K. Swathy Krishna (B) · T. K. Sreeranjini B. Tech, Jawaharlal College of Engineering and Technology (JCET), APJ Abdul Kalam Technological University, Thiruvananthapuram, Kerala, India e-mail: [email protected] P. L. Vijayakumari Department of Civil Engineering, Jawaharlal College of Engineering and Technology (JCET), Palakkad, Kerala, India © Springer Nature Singapore Pte Ltd. 2021 R. M. Singh et al. (eds.), Advances in Civil Engineering, Lecture Notes in Civil Engineering 83, https://doi.org/10.1007/978-981-15-5644-9_75

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trend of water demand–SP dosage graph (in percentage) remains the same, workability and water demand changed with the change in mixing. Though validation of these results has not been done with standard tests such as Marsh cone and minislump tests, the study leads to the conclusion that the water demand studies could be considered an indicative qualifier to identify compatibility issues and can be used complementing the standard tests which would provide quantitative evidence of the SP saturation dosage. Keywords Superplasticizer · Pozzolanic materials · Compatibility · Water demand

1 Introduction The studies and advancement of cement are being progressing all over the world because cement has an inevitable role in modern construction as well as environment. The amount of water in concrete is of major concern because of the fact that over use of water can reduce the strength of the structure. To reduce water without compromising the workability, superplasticizers are being widely used. Due to the physical and chemical variations of different families of SP, the reaction characteristic also varies. Hence, it is required to understand the incompatibility problems of cement and different families of SP. Similarly, there can be incompatibility while adding pozzolanic materials to a cement paste as the size variation of these particles can cause a change in water demand. In view of this, two abundantly available pozzolanic materials in India, namely fly ash and coconut shell ash (CSA) are used for the water demand study with variation in SP dosage. Understanding the influence of water demand with and without these pozzolanic materials is important in modern construction as these materials are now widely used with the view of reducing carbon dioxide emission and use the waste byproducts. Even without the addition of mineral admixtures, a change in the mixing process can influence the compatibility of cement and SP. So a cake mixer is introduced to analyze how the change in speed and uniformity in mixing can influence water demand compared to hand mix at different SP dosages. Because of these reasons, a study of cement–super plasticizer interaction is done using Vicat’s apparatus consistency test instead of standard tests to determine incompatibility related to water demand.

2 Experimental Program 2.1 Methodology Consistency test using Vicat’s apparatus is the basic test performed in the study. In addition to that solid content of SP was determined and amount of water was

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corrected so that SP dosage is in terms of solid content percentage. Data of water demand for different experiments were plotted as a graph and analyzed.

2.2 Solid Content Determination of SP The solid content determinations of superplasticizers (SP), viz., Sulphonated Naphthalene Formaldehyde (SNF) and Polycarboxylate Ether (PCE) were conducted as specified in “ASTM C494/C494M-99ae1-Standard specification for chemical admixtures for concrete”. 30 g of sand was taken in a jar and dried in oven for 17 h at 105 °C and weighed as m1 . 4 mL of SP was added over sand and weight was taken as m2 . This was dried at 105 °C for 17 h and weighed as m3 . Then the solid content is determined as m5 × 100/m4 , where m4 = m2 − m1 and m5 = m3 − m1 .

3 Water Demand Test It is expected that the water demand of the cement decreases during the addition of superplasticizers. Water demand test was done to understand the trend in reduction as well to ascertain whether the water demand change is indicative of the compatibility between cement and SP. Consistency test was conducted to determine the amount of water required for different mixes and hence to obtain the water demand variation. Correction was done for the water demand considering the liquid content of SP. Thus SP dosage was calculated as the percentage of solid content as mentioned in Table 1. The amount of percentage solid content of superplasticizer was determined as described above. SP dosage of 0.05, 0.1, 0.2%, 0.3, 0.4, 0.5, 0.7, 1, 1.3, 1.5% were taken for experiment. The amount of SP is calculated as follows: Weight of solid content of SP, W = weight of cement × percentage of SP used. Weight of SP, W sp = W /percentage solid content (Tables 2 and 3). Table 1 Observations of solid content determination of SP

Sample 1 (SNF)

Sample 2 (PCE)

m1

49.165

57.15

m2

53.505

61.47

m3

50.343

58.47

m4

4.34

4.31

m5

1.178

1.32

Solid content for SNF = m5 × 100/m4 = 1.178 × 100/4.34 = 27.14% Solid content for PCE = m5 × 100/m4 = 1.32 × 100/4.31 = 30.78%

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Table 2 Weight of SNF used with respect to percentage solid content in water demand test Weight of percentage by solid content/cement content

Weight of solid content of superplasticizer, W (g)

Weight of superplasticizer used (g) (SNF)

0

0

0

0.05

0.15

0.552689757

0.2

0.6

2.210759027

0.3

0.9

3.316138541

0.4

1.2

4.421518055

0.5

1.5

5.526897568

0.7

2.1

7.737656595

1

3

11.05379514

1.3

3.9

14.36993368

1.5

4.5

16.5806927

Table 3 Weight of PCE used with respect to percentage solid content in water demand test Weight of percentage by solid content/cement content

Weight of solid content of superplasticizer, W (g)

Weight of superplasticizer used (g) (PCE)

0

0

0

0.05

0.15

0.487329435

0.2

0.6

1.949317739

0.3

0.9

2.923976608

0.4

1.2

3.898635478

0.5

1.5

4.873294347

0.7

2.1

6.822612086

1

3

9.746588694

1.3

3.9

12.6705653

1.5

4.5

14.61988304

Consistency test using Vicat’s apparatus was carried out as specified in IS: 4031Part4-1988. Pastes were prepared using 300 g of cement with different water percentages for each SP dosage and were filled in Vicat’s mould. “Mix 1” denotes paste with SNF and “mix 2” with PCE. Plunger was gently lowered on the surface of the paste and reading was noted for different percentages of water. The percentage of water at which plunger penetrates to a depth of 5–7 mm from the bottom was determined by a trial, which denotes standard consistency value (Fig. 1). Tests were repeated by replacing cement with Pozzolanic materials, viz., coconut shell ash (CSA) and fly ash. “Mix 3” and “mix 4” by replacing cement with 5% of CSA with SNF and PCE, respectively. In order to understand the variation of water demand with addition of more CSA, again test was conducted on “mix 5” and “mix 6” by replacing 10% cement with CSA with SNF and PCE, respectively.

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Fig. 1 Water demand test with SP using Vicat’s apparatus

Experiments were again conducted by replacing 5 and 10% of cement with fly ash instead of CSA. “Mix 7” and “mix 8” denotes a combination of 5% fly ash with SNF and PCE, respectively. Again “mix 9” and “mix 10” were prepared with 10% of fly ash with the addition of SNF and PCE, respectively. The next experiment was conducted with “mix 11”, where second brand PPC was analyzed at different PCE dosages. “Mix 12” was prepared by mixing first brand PPC with PCE using a cake mixer with a gauging time of 5 minutes (Fig. 2; Table 4). Graphs were plotted showing the variation of cement–superplasticizer interaction from the results of all the tests, where X-axis indicates the water demand and Y-axis indicate SP dosage.

4 Material Study • A material study was conducted for the following materials: • Portland Pozzolana Cement (PPC): first brand PPC, second brand PPC (Table 5). • Pozzolanic materials: coconut shell ash (CSA), fly ash (Table 6).

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Fig. 2 Mixing of paste using cake mixer

Table 4 Specification of mix

Type of mix

Composition of mix

Mix 1

First brand PPC, SNF, hand mix

Mix 2

First brand PPC, PCE, hand mix

Mix 3

First brand PPC, SNF, 5% CSA, hand mix

Mix 4

First brand PPC, PCE, 5% CSA, hand mix

Mix 5

First brand PPC, SNF, 10% CSA, hand mix

Mix 6

First brand PPC, PCE, 10% CSA, hand mix

Mix 7

First brand PPC, SNF, 5% fly ash, hand mix

Mix 8

First brand PPC, PCE, 5% fly ash, hand mix

Mix 9

First brand PPC, SNF, 10% fly ash, hand mix

Mix 10

First brand PPC, PCE, 10% fly ash, hand mix

Mix 11

Second brand PPC, PCE, hand mix

Mix 12

First brand PPC, PCE, machine mix using cake mixer

• Superplasticizer: Sulphonated Naphthalene Formaldehyde (SNF), Polycarboxylate Ether (PCE) (Table 7).

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Table 5 Properties of Portland Pozzolana cement Cement

First brand PPC

Second brand PPC

Fineness (%)

9

6

Standard consistency

33.3% (hand mix)

31% (hand mix)

Initial setting time

32.67% (machine mix)

30% (machine mix)

2 h 5 min

1 h 55 min

Final setting time

5 h 20 min

4 h 10 min

Specific gravity

3.35

3.04

Soundness (mm)

1

0.5

Table 6 Properties of Pozzolanic materials Pozzolanic material

Fly ash

Fineness as per IS:4031-part1-1996 (90 µm) (%)

28

70

Fineness modulus as per IS:1727 (300 and 150 µm)

0.81

0.89

Table 7 Properties of superplasticizers

CSA

SP

SNF

PCE

Solid content (%)

27.14

30.78

Viscosity (visual observation)

Less

High

5 Results Figure 3 shows the variation of water demand with SP dosage for mix 1 and mix 2. In mix 1 water demand decreases up to 1% SP dosage and then it starts to increase, while mix 2 shows decreasing water demand with all dosages of SP. At every SP Water demand graph at different dosage of SPs Water demand (%)

36 32 28 mix 1 (SNF) mix 2 (PCE)

24 20 0

0.2 0.3 0.5 0.7

1

1.3 1.5

2

2.5

SP dosage (%) Fig. 3 Water demand–SP dosage graph at different dosages of SP

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dosage, the water demand of mix 2 was less than that of mix 1. Comparing mixes 1 and 2 initially, they had only a slight variation in water demand at the same SP dosage. But from 0.3% SP dosage onwards, mix 2 showed high reductions in water demand. At very high SP dosages, water demand tends to show minor variations at adjacent points in case of both mixes 1 and 2. Figure 4 indicates water demand variation of mix 1, 3, and 5. Water demand trend of mix 3 and 5 are similar to that of mix 1 but the ratio or point at which mix 3 and 5 show similarity with mix 1 varies. Depression at mix 3 and 5 occurred earlier at a point of 0.4% SP dosage. Variations of water demand of mix 2, 4, 6 are shown in Fig 5 and they show similar trends at different ratios as that of Fig 4. Water demand started to be constant for mix 4 and 6 from 0.7% SP dosage. Figures 6 and 7 depict that the water demand trend of mix 7, 8, 9, 10 shows great depression only at initial one or two points. Later the values tend to be constant. Analyzing Fig 6, it is clear that the trend of mix 7 and 9 is not exactly similar to mix 1 even though all mixes are having SNF. Mix 7 and 9 are pastes with SNF, but compared to mix 1, 3 and 5 they show only a very slight increase in value at overdosage. Without the addition of SNF, the water demand of mix 7 and 9 was higher than mix 1. But at 0.2 and 0.3% SP dosage, the water demand of mix 7 and 9 decreased than that of mix 1 at a considerable level. At 0.5% SP, mix 7 and mix 9 had a slight increase in water demand, but that rise is very minute. Then the graph has a small decrease which turns to be constant afterward. Figure 7 shows the water demand trends of mix 2, 8, 10 are decreasing with SP dosage. While mix 2 has a gradual decrease till 1% SP, mix 8 has significant depression at only at 0.2 and 0.3%., later the variation is minimum. In the case of mix 10, there is a large depression at 0.2% which is very much higher than the corresponding point of mix 2, and variation turns minor from that point onwards. Water demand graph comparing with and with out CSA using SNF

Water demand (%)

38 36 34 32 mix 1 (0%CSA)

30

mix 3(5% CSA)

28

mix 5 (10% CSA)

26 24 0

0.2

0.3

0.4

0.5

0.7

1

1.3

1.5

SP dosage (%)

Fig. 4 Water demand–SP dosage graph at different dosages of SNF with and without CSA

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Water demand graph comparing with and with out CSA using PCE 38

Water demand (%)

36 34 32 30

mix 2 (0% CSA)

28

mix 4 (5%) CSA

26

mix 6 (10% CSA)

24 22 20 0

0.2

0.3

0.5

0.7

1

1.3

SP dosage (%)

Fig. 5 Water demand–SP dosage graph at different dosages of PCE with and without CSA

Water demand graph comparing with and with out fly ash using SNF

Water demand (%)

36 34 32 30

mix 1 (0% fly ash) mix 7 (5% fly ash)

28

mix 9 (10% fly ash)

26 24

0

0.2

0.3

0.5

0.7

1

1.3

1.5

SP dosage (%)

Fig. 6 Water demand–SP dosage graph at different dosages of SNF with and without fly ash

While mix 8 has higher values than mix 2, mix 10 has almost the same values of mix 2 at overdosage of SP. In Fig 8, both mix 2 and mix 11 show gradual depression in values. The values of mix 11 are less than that of mix 2 and as the SP dosage increases the values of mix 11 start to decreases more than mix 2 at corresponding points. Figure 9 shows the values of mix 12 are lower than mix 2 at corresponding points. The trend of mix 12 is much deeper than mix 2.

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Water demand graph comparing with and with out fly ash using PCE 36

Water demand (%)

34 32 30 28

mix 2(0% fly ash) mix 8(5% fly ash)

26

mix 10(10% fly ash)

24 22 20

0

0.2

0.3

0.5

0.7

1

1.3

SP dosage (%)

Fig. 7 Water demand–SP dosage graph at different dosages of PCE with and without fly ash

Water demand graph on change in cement brand

Water demand (%)

35 30 25 20 mix 2 (first brand PPC)

15

mix 11 (second brand PPC)

10 5 0

0

0.2

0.3

0.5

0.7

1

SP dosage (%)

Fig. 8 Water demand–SP dosage graph at different dosages of SP with hand mix on first brand of PPC and second brand of PPC

6 Discussion 6.1 Mix 1 From the experiments, it was understood that the reaction on adding SP is fast in the case of SNF and has easy workability. When SNF is added, initially the water demand is decreasing. Then it is interesting to note that at a very high dosage of SP the trend reverses or the water demand increases. The normal dosage of SNF is 0.162–0.4071% (0.6–1.5 L/100 kg cement). But from 1.3% dosage (with no additives) and 0.5% (with

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Water demand graph on change in mixing method at different PCE dosage Water demand (%)

35 30 25 20 mix 2 (hand mix)

15

mix 12 (machine mix)

10 5 0

0

0.1

0.2

0.3

0.4

0.5

0.7

1

SP dosage (%)

Fig. 9 Water demand–SP dosage graph at different dosages of SP with hand mix and machine mix

the addition of CSA and fly ash) it is showing a reversing trend. So overdosing greatly affects the cement–superplasticizer interaction in SNF. For higher dosage, it showed segregation due to incompatibility. Cement was settled at a lower level, which may be the reason for the penetration problem and high water demand for SNF (Fig. 10). Fig. 10 Segregation at overdosage of SNF

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(1)

(2)

(3)

(4)

Fig. 11 Different stages of hand mixing with the addition of PCE showing workability issues

6.2 Mix 2 A clear trend of decreasing water demand with an increase in SP dosage was shown by the PCE mix. Normally recommended dosage rate of PCE is 0.1539–0.369% (0.50–1.2 L/100 kg of binders). But graphs show it does not show much variation with the over dosage of PCE [1]. The viscous PCE imparts fluidizing characteristics on paste. Cement–superplasticizer interaction is not immediate in the case of PCE mix. Hence there is a workability problem. Figure 11 shows the 4 stages of hand mixing with the workability problem when PCE is used. There is no clue of consistency with respect to workability at the initial stage and it took 10–11 m to show real nature, reaction, and workability. So there is a wastage of time and usage of more water can happen easily by mistake.

6.3 Mix 3, 4, 5, 6 Coconut shell ash has a fineness of 70% which implies larger particles and voids. Hence, it adsorbs a large amount of water. Coconut shell is well known for its adsorption property and used for water purification. As the percentage of CSA increased the water required also increased. The fineness of fly ash is 28%, which is also greater than cement particles. This results in adsorption and increase in water demand compared to the mix without Pozzolanic materials. As the SP dosage becomes very high, the water demand starts to become constant.

6.4 Mix 7, 8, 9, 10 At 0% SP dosage, the water demand was high on addition of fly ash compared to mix without fly ash. Then water demand shows a large depression with very next SP dosage of 0.2% and the magnitude of the dip is high for 10% fly ash compared to 5%

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fly ash. The smooth spherical surface of fly ash can be the reason for the immediate reaction and dip at initial points [2]. This implies that workability decrease and water demand increase with the addition of fly ash alone, while vice versa happens with the addition of fly ash and SP together in a mix [3]. After the great dip point, water demand is reducing only slightly with fly ash added mix and reaches to the point where water demand is almost constant. On the other hand, mix without fly ash is showing a gradual reduction in water demand from the beginning itself. Fly ash added mixes 7.9 imply an overdosage of SP at an early point of 0.5% while mix 1 which is without fly ash can withstand overdosage up to 1.3% when SNF is added. For mix 10 from 0.5% SP dosage onwards, the water demand requirement turns to be almost the same with that of mix 2. This is an indication of reduced incompatibility, fast reaction of SP with fly ash added mix, and its fast reach to maximum water reduction and optimum point of SP dosage. Hence, the addition of the pozzolanic material and fly ash can also solve the compatibility problem to certain limits [4].

6.5 Mix 11 A second brand PPC was introduced to check whether only the first brand PPC has some incompatibility with the PCE. There is a reduction in water demand for second brand PPC as it is finer than the first brand PPC. Second brand PPC has lesser lumps and voids demanding less water [2]. But PCE has a slight workability problem and took more time for proper reaction with second brand PPC also irrespective of the brand of cement.

6.6 Mix 12 Time taken to show required consistency value for all mix (mixing + time taken for the needle to penetrate) were 10–11 m for hand mixing (5 m gauging) and 3–5 m for machine mixing (3 m gauging). In the case of hand mix, the attempt to reduce time resulted in getting reading below 5 mm and mostly zero, even for a very slight increase in the amount of water. Mixing with cake mixer resulted in the easy breaking of layer hindrance and good hydration. Thus the problem of taking more time for hydration in case of hand mixing can be solved by introducing a machine mixer. The workability problem due to incompatibility can be solved by effective mixing using a machine mixer.

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7 Conclusions • PCE shows a trend of decreasing water demand on increasing the dosage of SP. So PCE does not show much variation with the increase in SP dosage. • SNF shows a trend of decreasing water demand initially and later it increases due to overdosage of SP. So overdosage greatly affects the cement–superplasticizer interaction in SNF. • There is a chance of segregation at overdosage of SNF. • More effective mixing was required in PCE than SNF for workability, as cement– superplasticizer interaction is delayed. This may lead to wastage of time and use of more water. • Water demand increases with usage of CSA and fly ash as their particle size increases compared to cement, resulting in larger voids in between and more adsorption and water demand. But there is a considerable reduction in water demand with the use of fly ash and superplasticizer together. There is an indication of faster reaction and quick overdosing due to the addition of pozzolanic materials. • Mixing with a cake mixer can cause easy breaking of layer hindrance and good hydration. Thus the problem of taking more time for hydration in case of PCE hand mixing can be solved by introducing a machine mixer. The water demand can also be reduced by the machine mixing method. • Water demand reduces with the use of finer cement. The incompatibility problem of taking more time for proper reaction takes place in the PCE mix irrespective of the brand of cement used. • Since the experiments conducted show enough indication of incompatibility, Vicat’s apparatus consistency test can also be used as a compatibility test.

References 1. Kannan Rajkumar PR, Ravichandran PT, Ravi JK, Krishnaraj L (2016) Investigation on the compatibility of cement paste with SNF and PCE based superplasticizers. Indian J Sci Technol 9(34) 2. Tiji KJ, Liji AM (2016) Compatibility study of an admixture with different cement brands of varying chemical composition for SCC. Int J Eng Res Technol 5(09) 3. Vanissorn V, Prinya C, Seksun R, Vanchai S (2015) Influence of fly ash fineness on water requirement and shrinkage of blended cement mortars. KKU Eng J 4. Winnefeld F, Zingg A, Holzer L, Pakusch J, Becker S (2009) Theettringite-superplasticizer interaction and its impact on the ettringite distribution in cement suspensions, conference paper, ResearchGate