Seismic Performance Analysis of Concrete Gravity Dams [1st ed.] 9789811561931, 9789811561948

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Advanced Topics in Science and Technology in China 57

Gaohui Wang  Wenbo Lu  Sherong Zhang

Seismic Performance Analysis of Concrete Gravity Dams

Advanced Topics in Science and Technology in China Volume 57

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Gaohui Wang Wenbo Lu Sherong Zhang •

•

Seismic Performance Analysis of Concrete Gravity Dams

123

Gaohui Wang State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Wuhan, China

Wenbo Lu State Key Laboratory of Water Resources and Hydropower Engineering Science Wuhan University Wuhan, China

Sherong Zhang State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University Tianjin, China

ISSN 1995-6819 ISSN 1995-6827 (electronic) Advanced Topics in Science and Technology in China ISBN 978-981-15-6193-1 ISBN 978-981-15-6194-8 (eBook) https://doi.org/10.1007/978-981-15-6194-8 Jointly published with Zhejiang University Press The print edition is not for sale in China Mainland. Customers from China Mainland please order the print book from: Zhejiang University Press. © Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 This work is subject to copyright. All rights are reserved by the Publishers, 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 publishers, 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 publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain 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

Preface

In order to meet the ever-increasing demand for power, irrigation, drinking water, etc., numerous high concrete dams are being built or to be built and the majority of them are located in active seismic regions. Due to the low tensile resistance of concrete material, concrete dams will inevitably occur cracking damage under strong ground motions. Considering that the possible dam failure due to seismic activities could result in heavy loss of human life and substantial property damages, seismic safety evaluation of high dams remains a crucial problem in dam construction. To achieve a reasonable assessment of the seismic safety of dams, study on the cracking damage processes and potential failure modes of concrete dams subjected to strong earthquakes is indispensable and deserves more investigation and attention. This book addresses the challenges in approach and application of seismic performance evaluation of concrete gravity dams. Earthquake ground motion is a complex natural phenomenon associated with the abrupt energy release caused by the fault rupture, and it is influenced by many factors, such as earthquake source mechanism, propagation path of waves, and soil condition at the site. The seismic performance assessment of concrete dams under strong ground motions depends primarily on how accurate the constitutive models adopted in describing the structural behavior and in predicting possible future earthquake events at the precise site. The objectives of this book are aimed to evaluate the seismic performance of concrete gravity dams with consideration of the effects of strong motion duration, mainshock–aftershock seismic sequence, and near-fault ground motion. Both extended finite element method (XFEM) and concrete damaged plasticity (CDP) model are employed to characterize the mechanical behavior of concrete gravity dams under strong ground motions including the dam–reservoir–foundation interaction. In addition, the effects of the initial crack, earthquake direction, and cross-stream seismic excitation on nonlinear dynamic response and damage-cracking risk of concrete gravity dams to strong ground motions are discussed. This book is comprised of ten chapters. Chapter 1 provides an overview on the effects of strong earthquake ground motions on concrete dams. v

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Chapter 2 provides two fracture modeling approaches, i.e. XFEM and CDP model, to describe nonlinear dynamic response and seismic failure process of concrete gravity dams under strong ground motions. Chapter 3 deals with the numerical prediction of crack propagation in concrete gravity dams with single and multiple initial cracks. The effects of the initial crack position and length on the crack propagation and seismic response of dam–reservoir–foundation systems are studied. Chapter 4 generalizes five potential failure modes of concrete gravity dams by applying the incremental dynamic analysis method based on the XFEM. Chapter 5 proposes local and global damage indices to assess quantitatively the effects of strong motion duration on the accumulated damage of concrete gravity dams. The definition of single-component durations that exhibit the strongest influence on structural damage is determined. Chapter 6 proposes a general integrated duration definition for multi-component seismic excitations based on the existing concept of strong motion duration. Chapter 7 assesses the effects of aftershocks on concrete gravity dams and provides a quantitative description of the damage demands prior to and following the aftershocks. Chapter 8 examines the influence of earthquake direction on seismic performance of concrete gravity dams subjected to seismic sequences. Chapter 9 proposes a systematic approach for seismic performance evaluation of concrete gravity dams subjected to near-fault and far-fault ground motions based on the presented performance criteria. Chapter 10 establishes a three-dimensional model to obtain the more realistic seismic response of concrete gravity dams under strong ground motions. This chapter conducts a systematic study on the 3D seismic damage-cracking behavior of concrete gravity dams with all the following factors considered: contraction joint nonlinearity, cross-stream earthquake excitation, and dam–foundation–reservoir interaction. The authors gratefully appreciate the supports from the National Natural Science Foundation of China (No. 51939008) and the Technology and Industry for National Defense of China (No. JCKY2018110C162). Wuhan, China Wuhan, China Tianjin, China

Gaohui Wang Wenbo Lu Sherong Zhang

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . 1.1 Background . . . . . . . . . . . . . . . . . . . 1.2 Objective and Scope of This Research 1.3 Organization of the Book . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . .

2

Comparative Analysis of Nonlinear Seismic Response of Concrete Gravity Dams Using XFEM and CDP Model . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Method for Dynamic Failure Analysis of Concrete Dams Under Strong Earthquake . . . . . . . . . . . . . . . . . . . . 2.2.1 Prototype Observation . . . . . . . . . . . . . . . . . . . . 2.2.2 Model Test Method . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Numerical Simulation Method . . . . . . . . . . . . . . . 2.3 eXtended Finite Element Method (XFEM) . . . . . . . . . . . . 2.3.1 XFEM Approximation . . . . . . . . . . . . . . . . . . . . 2.3.2 Enrichment Functions . . . . . . . . . . . . . . . . . . . . . 2.3.3 Discrete Equations . . . . . . . . . . . . . . . . . . . . . . . 2.4 Concrete Damaged Plasticity (CDP) Model . . . . . . . . . . . 2.4.1 Damage Evolution . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Yield Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Flow Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Lagrangian Formulation for Dynamic Interaction of Dam-Reservoir-Foundation Systems . . . . . . . . . . . . . . . 2.6 Application of the Two Models in Concrete Gravity Dams 2.6.1 Description of Koyna Gravity Dam-ReservoirFoundation System . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 A Comparative Study on Seismic Nonlinear Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4

Seismic Cracking Analysis of Concrete Gravity Dams with Initial Cracks Using XFEM . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Validation Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Seismic Crack Propagation Analysis of Koyna Gravity Dam with Initial Crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Initial Cracking Models . . . . . . . . . . . . . . . . . . . . . 3.3.2 Seismic Crack Propagation Process with no Initial Crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Seismic Crack Propagation Process for Single Initial Cracking Models . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Seismic Crack Propagation Process for Multiple Initial Cracking Model . . . . . . . . . . . . . . . . . . . . . . 3.4 Seismic Crack Propagation Analysis of Guandi Gravity Dams with Initial Cracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 FEM Model and Material Properties . . . . . . . . . . . . 3.4.2 Initial Crack Position . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Crack Propagation Process of the Dam with no Initial Crack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Influence of Initial Crack Position . . . . . . . . . . . . . . 3.4.5 Influence of Initial Crack Length . . . . . . . . . . . . . . . 3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seismic Potential Failure Mode Analysis of Concrete Gravity Dam–Water–Foundation Systems Through Incremental Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Nonlinear Dynamic Response of Guandi Dam Under Design Peak Ground Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 FEM Model and Material Properties . . . . . . . . . . . . 4.2.2 Seismic Response and Crack Propagation Analysis . 4.3 Seismic Potential Failure Mode Analysis . . . . . . . . . . . . . . . 4.3.1 Database of as-Recorded Acceleration Records . . . . 4.3.2 Incremental Dynamic Analysis . . . . . . . . . . . . . . . . 4.3.3 Typical Failure Modes of the Guandi Gravity Dam for Each Record . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Generalization of Potential Failure Modes for Concrete Gravity Dams . . . . . . . . . . . . . . . . . . . . . 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Correlation Between Single Component Durations and Damage Measures of Concrete Gravity Dams . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Strong Motion Duration-Related Measure Used in this Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Definitions of Strong Motion Duration for Single Component Ground Motion . . . . . . . . . . . 5.2.2 Accelerogram Selection and Correction . . . . . . . . . . 5.2.3 Strong Motion Duration Prediction . . . . . . . . . . . . . 5.2.4 Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Seismic Accumulated Damage Indices . . . . . . . . . . . . . . . . . 5.4 Seismic Damage Analysis of Koyna Dam . . . . . . . . . . . . . . 5.4.1 Description of Koyna Gravity Dam Model Used for Evaluation . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Strong Motion Duration Effects on Accumulated Damage of Concrete Gravity Dams . . . . . . . . . . . . . 5.5 Correlation Study Between Strong Motion Durations and Damage Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Damage Measures of Local and Global Damage Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 Damage Measures of Peak Displacement and Damage Energy Dissipation . . . . . . . . . . . . . . . 5.5.3 Identifying the Influence of Single Component Duration on Damage Measures . . . . . . . . . . . . . . . . 5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integrated Duration Effects on Seismic Performance of Concrete Gravity Dams . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 A General Definition of Integrated Duration . . . . . . . . . . 6.2.1 Single Component Duration . . . . . . . . . . . . . . . 6.2.2 Integrated Duration of Multi-component Ground Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Database of as-Recorded Acceleration Records . . . . . . . . 6.3.1 Accelerogram Selection and Integrated Duration Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Relationship Between Integrated and Single Component Durations . . . . . . . . . . . . . . . . . . . . 6.4 Influence of Two-Component Ground Motions on Nonlinear Dynamic Response . . . . . . . . . . . . . . . . . . 6.4.1 Displacement Response . . . . . . . . . . . . . . . . . . 6.4.2 Stress Response . . . . . . . . . . . . . . . . . . . . . . . .

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6.4.3 Damage Dissipation Energy Response . . . . . . . 6.4.4 Damage Analysis . . . . . . . . . . . . . . . . . . . . . . 6.5 Correlation Between Integrated Durations and Damage Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

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Damage Demand Assessment of Concrete Gravity Dams Subjected to Mainshock-Aftershock Seismic Sequences . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Mainshock–Aftershock Seismic Sequences . . . . . . . . . . . . . . 7.2.1 Construction Method of Mainshock–Aftershock Seismic Sequences . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 As-Recorded Mainshock–Aftershock Seismic Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Correlation Between Ground Motion Characteristics of Mainshocks and Major Aftershocks . . . . . . . . . . . 7.3 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Koyna Dam–Reservoir–Foundation System . . . . . . . 7.3.2 Seismic Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Nonlinear Behavior of the Koyna Dam–Reservoir–Foundation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Structural Damage . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Displacement Response . . . . . . . . . . . . . . . . . . . . . 7.4.3 Damage Dissipated Energy . . . . . . . . . . . . . . . . . . . 7.5 Estimation of Damage Demands for Mainshock–Aftershock Seismic Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.1 Effects of as-Recorded Mainshock–Aftershock Seismic Sequences . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.2 Comparative Analysis of Damage Demands Between as-Recorded Seismic Sequences and Repeated Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Earthquake Direction Effects on Nonlinear Dynamic Response of Concrete Gravity Dams to Seismic Sequences . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Earthquake Incident Direction for Two-Dimensional Seismic Performance Analysis . . . . . . . . . . . . . . . . . . . 8.3 Finite Element Model . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Description of Finite Element Model of Dam-Foundation-Reservoir Systems . . . . . . 8.3.2 Input Ground Motions . . . . . . . . . . . . . . . . . .

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8.4

Effects of Earthquake Direction . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Direction Effects of Single Earthquake Events . . . . . 8.4.2 Direction Effects of Mainshock–Aftershock Seismic Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.3 Effects of Aftershock Polarity . . . . . . . . . . . . . . . . . 8.5 Influence of the Ground Motion Intensity on the Seismic Sequence Direction Effects . . . . . . . . . . . . . . . . . . . . . . . . . 8.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

Seismic Performance Evaluation of Dam-Reservoir-Foundation Systems to Near-Fault Ground Motions . . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Characteristics of Near-Fault Ground Motions . . . . . . . . . . . 9.2.1 Forward Directivity Effect . . . . . . . . . . . . . . . . . . . . 9.2.2 Fling Step Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.3 Hanging Wall Effect . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Near-Fault and Far-Fault Ground Motion Records Considered in This Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Seismic Performance Evaluation Methods . . . . . . . . . . . . . . 9.5 Near-Fault Ground Motion Effects on Seismic Performance of Concrete Gravity Dams Using Linear and Nonlinear Evaluation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 Seismic Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.2 Seismic Performance Evaluation Using Linear Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.3 Seismic Performance Evaluation Using Nonlinear Dynamic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Nonlinear Dynamic Response of Concrete Gravity Dams Subjected to Near-Fault and Far-Fault Ground Motions . . . . . 9.6.1 Nonlinear Displacement Response . . . . . . . . . . . . . . 9.6.2 Seismic Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6.3 Damage Energy Dissipation . . . . . . . . . . . . . . . . . . 9.6.4 Identifying the Influence of Near-Fault Ground Motions on Seismic Damage of Dams . . . . . . . . . . . 9.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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10 Deterministic 3D Seismic Damage Analysis of Guandi Concrete Gravity Dam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Material Properties of Mass Concrete and Contraction Joint Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Material Properties of Mass Concrete . . . . . . . . . . . 10.2.2 Contraction Joint Nonlinearity . . . . . . . . . . . . . . . . . 10.3 3D Lagrangian Finite Element Formulation . . . . . . . . . . . . . 10.4 Validation Test for 3D Model . . . . . . . . . . . . . . . . . . . . . . . 10.5 3D Guandi Gravity Dam-Reservoir-Foundation System . . . . . 10.5.1 Introduction to Guandi Gravity Dam . . . . . . . . . . . . 10.5.2 3D Finite Element Model . . . . . . . . . . . . . . . . . . . . 10.6 Nonlinear Seismic Behavior . . . . . . . . . . . . . . . . . . . . . . . . 10.6.1 Seismic Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.2 Maximum Stream Displacement . . . . . . . . . . . . . . . 10.6.3 Contact Behavior of Contraction Joints . . . . . . . . . . 10.7 Evaluation of the Key Factors Affecting Damage-Cracking Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.1 Discussion of Results from 3D Dam-Reservoir-Foundation Model . . . . . . . . . . . . . . 10.7.2 Comparisons of 3D and Quasi-3D Analysis Results for Representative Monoliths . . . . . . . . . . . . 10.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Principal Symbols and Abbreviations

Symbols B ¼ rw Bef b bj C Cc Cf E f H hs K Kc Kf Kf M Mf Mc n Rf Rc
S Sf
t ui

Matrix of derivatives of extended shape functions wri Strain–displacement matrix of the fluid element Body force vector per unit mass Vector of corresponding additional degrees of freedom for modeling crack faces (not crack tips) Damping matrix Damping matrix of the coupled system Elasticity matrix consisting of diagonal terms Elastic tensor External load vector Matrix consisting of interpolation functions of the fluid element Vector consisting of interpolation functions of the free surface fluid element Stiffness matrix Stiffness matrix of the coupled system Stiffness matrix of the fluid system System stiffness matrix including the free surface stiffness Mass matrix Mass matrix of the fluid system Mass matrix of the coupled system External unit vector to C Time-varying nodal force vector for the fluid system Time-varying nodal force vector of ground acceleration
Deviatoric part of the effective stress tensor r Stiffness matrix of the free surface of the fluid system Applied traction force vector on the Neumann boundary Ct Classical degrees of freedom for node i.

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xiv

u_
u [u] Uf Usf Uc U_ U_ c €f U €c U € u x x* r C11 C22, C33 and C44 DP&A DILi DIG E E0 EH Ei Fy Ed G Fl1 ðxÞ and Fl2 ðxÞ Fl (r, h) Gf H(x) H(t) I I0 I0H I0V I0H1 and I0H2
I1
J2 JI K1  I K2  I

Principal Symbols and Abbreviations

Velocity Applied displacement vector on the Dirichlet boundary Cu Jump in the displacement Nodal displacement vector Vertical nodal displacement vector Vector of the displacement of the coupled system Nodal velocity vector Vector of the velocity of the coupled system Nodal acceleration Vector of the acceleration of the coupled system Acceleration Sample gauss point Closest point to x Cauchy stress tensor Bulk modulus of fluid Rotation constraint parameter Park and Ang index Local damage index for crack path i Global damage index Elasticity modulus Initial (undamaged) elastic stiffness of the material Hysteretic energy Damage dissipation energy at the crack path i Elastic strength Damage dissipated energy Scalar plastic potential function Asymptotic crack-tip enrichment functions Crack-tip enrichment functions Fracture energy Heaviside function Husid diagram as a function of time t Set of all nodes in the mesh Arias intensity Arias intensities of the horizontal component Arias intensities of the vertical component Arias intensities of the two horizontal ground motions First effective stress invariant Second effective deviatoric stress invariant Set of nodes whose shape function support is cut by a crack Set of nodes whose shape function support contains the first crack tip in their influence domain Set of nodes whose shape function support contains the second crack tip in their influence domain

Principal Symbols and Abbreviations

Kc Li M M0 Mw N Ni(x) P Px, Py and Pz P0 Pz R R′
Sij Tp T0 TB TU TE TS TS(70%) TS(90%) TH TV TI T H1 and T H2 TBI TUI TSI TBH TBV Un Wx Wy Wz a b bi1 and bi2 c0 l2 cl1 k and ck

xv

Strength ratio of concrete under equal biaxial compression to triaxial compression Total length to which crack path i is expected to grow Mainshock magnitude Aftershock magnitude Moment magnitude Number of seismic events Shape function associated with node i Pressure Corresponding rotational stresses Pressure value at zero opening Rotational stress parameter Correlation coefficient Source distance Effective deviatoric stress tensor Predominant period Total duration of the record Bracketed duration Uniform duration Effective duration Significant duration Time interval between 15 and 85% of the Husid diagram Time interval between 5 and 95% of the Husid diagram Strong motion durations of the horizontal component Strong motion durations of the vertical component Integrated duration Strong motion durations of two perpendicular horizontal components Integrated bracketed duration Integrated uniform duration Integrated significant duration Bracketed duration of the horizontal component Bracketed duration of the vertical component Normal component of the interface displacement Rotation about the axis x Rotation about the axis y Rotation about the axis z Ground acceleration Constant Length of the edges of the quadrilateral constant strain elements beside node i on the upstream surface of the dam Initial contact distance Vector of corresponding additional degrees of freedom which are related to the modeling of crack tips

xvi

d dt dc g fc0 ft h jt, jc lDi m0i n nA and nB p
p
q l ufn v yi (r, h) pffiffi r sin h=2 a and b m w wri 3 C Cu Ct q
r ^
max r rb0 rc0
c r
t r rt0 e ee ep

Principal Symbols and Abbreviations

Scalar stiffness degradation variable Tension damage Compression damage Acceleration due to gravity Compressive strength of the concrete Tensile strength of the concrete Depth of water Tensile damage variable Compressive damage variable Length of the damage path in crack path i Westergaard virtual mass Unit outward normal to the crack at x* Index sets of the nodes of superposed element A and element B Normal contact pressure Effective hydrostatic pressure Mises equivalent effective stress Coefficient of friction Normal component of the free surface displacement Volume Distance from node i to the water surface Local polar coordinate system with its origin at the crack tip Discontinuous across the crack plane, whereas the last three functions are continuous Dimensionless material constants Poisson’s ratio Dilation angle measured in the p–q plane at high confining pressure Extended shape functions Parameter that defines the rate at which the function approaches the asymptote defined by w Boundary Dirichlet boundary Neumann boundary Initial mass density Effective stress
Algebraically maximum eigenvalue of r Concrete strength under equal biaxial compression Initial compressive yield stress Effective compressive cohesion stresses Effective tensile cohesion stresses Uniaxial tensile stress at failure Total strain tensor Elastic strain Plastic strain

Principal Symbols and Abbreviations

~epc ~ept eel ev k_

Equivalent compressive plastic strain Equivalent tensile plastic strain Elastic strain Volumetric strain Nonnegative function referred to as the plastic consistency parameter Crack normal opening Crack tangential sliding Weight density of fluid Mass density of the fluid Mass density of water Subdomain element A Subdomain element B Viscous damping ratio Cohesive traction applied on the discontinuity surface

dn dt cw qf qw XA XB f sc

Abbreviations CDP CMOD COD COSMOS CRCM DCR DDA DE-BE DEM DI DP FBG FCM-VSRF FEM IDA LEFM MDOF MFCM NLFM NPSBFEM3D OMFCM PEER PGA

xvii

Concrete damaged plasticity Crack mouth opening displacement Crack opening displacement Consortium of Organizations for Strong Motion Observation Systems Coaxial rotating crack model Demand–capacity ratio Discontinuous deformation analysis Distinct element–boundary element Distinct element method Damage index Drucker−Prager Fiber Bragg grating Fixed crack model with a variable shear resistance factor Finite element method Incremental dynamic analysis Linear elastic fracture mechanics Multi-degree of freedom Multidirectional fixed crack model Nonlinear fracture mechanics 3D nonlinear polyhedron scaled boundary finite element Orthogonal multi-fixed crack model Pacific Earthquake Engineering Research Center Peak ground acceleration

xviii

PGD PGV PUM RC RCC RFPA SDOF SMD SPH XFEM

Principal Symbols and Abbreviations

Peak ground displacement Peak ground velocity Partition of unity method Reinforced concrete Roller-compacted concrete Rock failure process analysis Single degree of freedom Strong motion duration Smoothed particle hydrodynamics Extended finite element method

Chapter 1

Introduction

1.1 Background Dams are important lifeline engineering, which has contributed to the development of civilization for a long time. In order to meet the ever-increasing demand for flood control, hydropower, irrigation and drinking water etc., the majority of high dams have been built, are being built or to be built in the southwest region of China with active seismic activities. Table 1.1 shows some typical high dam projects, in which the height of the dam is from 100 to 250 m. The design peak ground acceleration (PGA) is also given in Table 1.1. It can be found that the design PGA for some dams is very high. The seismic safety problem of high dams is very outstanding. The earthquake is a devastating natural disaster. Due to the outburst of strong earthquakes like Wenchuan earthquake in 2008 (8.0 M w ), Haiti earthquake in 2010 (7.3 M w ), Tohoku earthquake in 2011(9.0 M w ), and Chile earthquake in 2015 (8.3 M w ), it seems that the earth has come into an era with more and stronger earthquakes. When subjected to strong ground motions, mass concrete dams are likely to experience cracking due to the low tensile resistance of concrete. Meanwhile, the potential crack initiation and propagation would adversely affect the static and dynamic performance of dams. As cracks penetrate deep inside a dam, its structural resistance may be considerably weakened, thereby increasing the risk of the dam failure and endangering the safety of the dam. However, the possible failure of dams retaining large quantities of water can cause a considerable amount of devastation in the downstream populated area during strong earthquakes. Hence, dams must be completely safe and stable. The seismic safety evaluation of high dams remains a crucial problem in dam construction. The prototype observation is a very useful method to acknowledge the dynamic and earthquake behavior of high dams to actual earthquakes. While there are many high concrete dams throughout the world, only some of them have experienced ground shaking induced structural damage. To name just a few, the Hsingfengkiang dam, China, 1962; Koyna dam, India, 1967; and Sefid-Rud dam, Iran, 1990 are the © Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_1

1

2 Table 1.1 Concrete gravity dams with the height from 100 to 250 m in the southwest region of China

1 Introduction Concrete gravity dam

Maximum height (m)

PGA (g)

Longtan

216.5

0.20

Huangdeng

203

0.251

Guandi

168

0.34

Xiangjiaba

162

0.222

Jinanqiao

160

0.399

Ahai

138

0.344

Kalasuke

121.5

0.21

Longkaikou

119

0.394

ones that have suffered from damage in earthquakes (Nuss et al. 2012), as shown in Fig. 1.1. The Hsinfengkiang dam is a concrete buttress dam with a crest length of 440 m, a crest width of 5 m, and a maximum structural height of 105 m, which was completed in 1962 located Guangdong Province, China. The magnitude M 6.1 Hsinfengkiang earthquake occurred on March 19, 1962 with the focal depth of 5 km. This earthquake is considered to be a reservoir triggered (Tsung-ho et al. 1976). A horizontal crack 82 m long on the monoliths 13# to 17# developed on the right side of the downstream face around the elevation of 108 m at which the slope changes abruptly. A few smaller cracks developed on the left side of the dam at the same elevation as the crack on the right side. The Koyna dam is a concrete gravity dam, which was built from 1954 to 1963 located in the southwestern region of India. The dam has a crest length of 853 m, a crest width of 14.8 m, a maximum structural height of 103 m, and a maximum base width of 70.2 m. A significant change of slope on the downstream face is 37 m below the dam crest. The Koyna earthquake occurred on December 11, 1967 with the epicenter 13 km from the dam with a focal depth of 8–13 km. The magnitude is M 6.5. The maximum accelerations were recorded at the foundation gallery in the stream direction of 0.49 g, cross-stream direction of 0.63 g, and cross-stream direction of 0.34 g. The Koyna earthquake has caused very serious structural damage to the dam, including horizontal cracks on the upstream and downstream faces of a number of non-overflow monoliths around the elevation at which the slope of the downstream face changes abruptly. Leakage was found in some of these monoliths near the changes in the slope of the downstream face, implying the complete penetration from the upstream face to the downstream face (Chopra and Chakrabarti 1973). The Sefid Rud Dam is a concrete buttress dam, which was built from 1956 until 1962. The project is located in Manjil in Gilan Province, northern Iran. The crest length of the dam is 425 m, the highest monolith is 106 m high. There are 23 buttresses, 14 m wide, with a web thickness of 5 m. The dam was originally designed to withstand a 0.25 g using the quasi-static method. An exceptionally strong ground motion with a magnitude of M 7.6 hit the area of the dam on June 20, 1990. Two strong aftershocks having magnitude in the 6.2–6.5 magnitude range occurred several hours

1.1 Background

3

(a)

(b)

(c) Fig. 1.1 Location of earthquake induced crack. a Hsinfengkiang dam; b Koyna dam; c Sefid Rud dam

4

1 Introduction

after the main shock. Damages to the dam structure consisted mainly of cracks along the horizontal construction joints and of spalling of concrete along the vertical joints between buttress heads (Ghaemmaghami and Ghaemian 2010). Following the earthquake, the most serious observed damage to the dam was horizontal cracks that appeared in the upper parts of the monoliths, especially in the highest monolith. A major crack ran almost the whole length of the dam at about 14 m below the crest. Leakage was reported through some of the cracks. Other damage included minor damage and displacement of all the gates, varying types of damage at the dam crest. Nonlinear dynamic response and damage propagation process of high concrete dams to strong ground motions are very complicated. Seismic safety evaluation of high dams remains a crucial problem in dam construction. The investigation and survey on the actual earthquake damage of high dams is an important way to analyze the seismic performance and failure pattern of high dams. However, there is just a little actual seismic damage of high dams to strong ground motions. The nonlinear dynamic response, damage mechanism, cracking process, potential failure mode, and seismic performance of high concrete dams under strong ground motions have not been further understanding. In the absence of monitoring data of actual dam damage process, dynamic model test and finite element method are the main means to understand the nonlinear dynamic response behavior and earthquake damage modes for high concrete dams, which are very important to dam seismic performance evaluation.

1.2 Objective and Scope of This Research This book addresses the challenges in approach and application of seismic performance evaluation of concrete gravity dams. The seismic performance assessment of concrete dams under strong ground motions depends primarily on how accurate the constitutive models adopted in describing the structural behavior and in predicting possible future earthquake events at the precise site. In fact, many nonlinear constitutive models have also been developed in order to forecast the nonlinear dynamic response of concrete dams under strong ground motions. There are based either on the discrete crack approach (Ingraffea and Saouma 1985; Ayari and Saouma 1990; Ahmadi et al. 2001; Omidi et al. 2013) or the smeared crack approach (Bhattacharjee and Léger 1994; Léger and Leclerc 1996; Ghaemian and Ghobarah 1999; Wang et al. 2000). In addition, other models, such as plastic-damage model (Lee and Fenves 1998; Omidi et al. 2013), rock failure process analysis (Zhong et al., 2011), distinct element method (Pekau and Cui 2004), discontinuous deformation analysis (Wang et al. 2006), mesh-free particle method called smoothed particle hydrodynamics (Das and Cleary 2013) and hybrid distinct element-boundary element (Mirzayee et al. 2011), are also used in some cases to analyze the seismic failure behavior of concrete dams. It is well known that the earthquake ground motion is a complex natural phenomenon associated with the abrupt energy release caused by fault rupture, and

1.2 Objective and Scope of This Research

5

it is influenced by many factors, such as earthquake source mechanism, propagation path of waves, soil condition at the site, and so on. Earthquake strong ground motion can be characterized by many different parameters including amplitude, frequency content and strong motion duration, each of which reflects some particular feature of the shaking. The most frequently used intensity parameters are the peak ground acceleration (PGA), peak ground velocity (PGV), strong motion duration (SMD) and spectral amplitude for different characteristic periods of the strong motion records. The importance of the amplitude and frequency content has been universally recognized. But strong motion duration is also one of the key intensity parameters that contribute to the seismic performance of structures. However, current approaches for earthquake-resistant design and structural analysis based on the response spectrum have not yet considered the influence of the ground motion duration. Earthquakes are usually part of a sequence of ground motions which can be defined as the foreshock, mainshock, and aftershock. Seismic sequences characterized by a mainshock followed by strong aftershocks in a short time have been observed in many areas. Most aftershocks are located over the full area of fault rupture and either occur along the fault plane itself or along other faults within the volume affected by the strain associated with the mainshock. Strong aftershocks are dangerous because they are usually unpredictable, and have the potential to cause additional structural damage (Li and Ellingwood 2007; Ruiz-García and Negrete-Manriquez 2011; Goda 2012; Salami et al. 2019). The structure already damaged from the mainshock and not yet repaired, which may be incapable of resisting the excitation of the strong aftershocks, may be collapsed or become completely unusable under mainshockaftershock seismic sequences (Li et al. 2014; Omranian et al. 2018; Shokrabadi et al. 2018; Shokrabadi and Burton 2018). This characteristic is very important and the influence of seismic sequences can’t be ignored. However, most structures designed according to the modern seismic codes only apply a single earthquake on structure modeling and analysis. The seismic performance of concrete gravity dams has been examined by the isolated ‘design earthquake’ without taking the influence of multiple earthquake phenomena into account. In this case, the structure may sustain damage in the event of the ‘design earthquake’, and this single seismic design philosophy does not take the effect of strong aftershocks on the accumulated damage of structures into account. However, in the real earthquake event, bigger earthquakes may trigger more and larger aftershocks and the sequences can last for years or even longer, the tremors always occurred repeatedly. So, this structure located in seismic regions is not only exposed to a single seismic event, but also to a seismic sequence. Therefore, it is of great importance and urgency to investigate the influence of as-recorded mainshockaftershock seismic sequences on the dynamic response and accumulated damage of concrete gravity dams. Recordings obtained in recent earthquakes revealed that seismic ground motions recorded within the near-fault region are quite different from the usual far-fault ground motions observed at large distance in many respects such as the period of earthquake continuity, peak ground acceleration, velocity and displacement, rupture directivity, fling step and pulse properties (Chopra and Chintanapakdee 2001). Forward directivity and fling effects have been identified by seismologists as the

6

1 Introduction

primary characteristics of near-fault ground motions (Mavroeidis and Papageorgiou 2003). Fault-normal components of ground motions often contain a large displacement and velocity pulses, which expose the structure to high input energy in the beginning of the earthquake. The pulses are strongly influenced by the rupture mechanism, the slip direction relative to the site, and the location of the recording station relative to the fault which is termed as ‘directivity effect’ due to the propagation of the rupture toward the recording site (Bray and Rodriguez-Marek 2004). Because of the unique characteristics of near-fault ground motion, the ground motions recorded in the nearfault region have the potential to cause considerable damage to structures. Therefore, structural response to near-fault ground motions has received much attention in recent years. The effects of near-fault ground motions on many civil engineering structures, such as buildings (Bhagat et al. 2018; Yaghmaei-Sabegh et al. 2019; Yang et al. 2019) and bridges (Ardakani and Saiidi 2018; Xiang and Alam 2019; Xin et al. 2019), have been investigated in many recent studies. It can be clearly seen from these studies that the near-fault ground motion has a significant influence on the nonlinear dynamic response of structures. Structures located within the near-fault region suffered more severe damage than those located in the far-fault zone. The related study is therefore a very important topic for the structural engineering. However, there is no sufficient research about the near-fault ground motion effects on the seismic performance and accumulated damage of concrete gravity dams. For these problems above, the objectives of this book are aimed to evaluate the seismic performance of concrete gravity dams with consideration of the effects of strong motion duration, mainshock-aftershock seismic sequence, and near-fault ground motion. Both extended finite element method (XFEM) and concrete damaged plasticity (CDP) model are employed to characterize the mechanical behavior of concrete gravity dams under strong ground motions including the dam-reservoirfoundation interaction. In addition, the effects of the initial crack, earthquake direction, and cross-stream seismic excitation on nonlinear dynamic response and damage-cracking risk of concrete gravity dams to strong ground motions are discussed.

1.3 Organization of the Book This book is comprised of ten chapters. In this chapter, the research background and objectives have been presented. An overview on the effects of strong earthquake ground motions on concrete dams is provided. Chapter 2 provides two fracture modelling approaches, i.e. XFEM and CDP model, to describe the nonlinear dynamic response and seismic failure process of concrete gravity dams under strong ground motions. The Lagrangian approach is used for the finite element modeling of the dam-reservoir-foundation interaction problem. The effects of different nonlinear approaches on the seismic response of the dam are compared and discussed.

1.3 Organization of the Book

7

The seismic crack propagation of concrete gravity dams with initial cracks at the upstream and downstream faces has rarely been studied during strong earthquakes. Chapter 3 deals with the numerical prediction of crack propagation in concrete gravity dams with single and multiple initial cracks. The crack progress of a scaled-down 1:40 model of a gravity dam with the initial notch in the upstream wall is simulated to verify the validity of the calculation model. The effects of the initial crack position and length on the crack propagation and seismic response of dam-reservoir-foundation systems are studied. Chapter 4 generalizes five potential failure modes of concrete gravity dams by applying the incremental dynamic analysis method based on the XFEM. Considering the uncertainty of the ground motion input, 40 as-recorded accelerograms with each scaled to 8 increasing intensity levels are selected as seismic excitations. Based on 320 numerical simulation results, typical failure processes are presented. Chapter 5 proposes local and global damage indices to quantitatively assess the effects of strong motion duration on the accumulated damage of concrete gravity dams. This chapter describes numerically the interdependency between single component durations and structural accumulated damage indices. The definition of single component durations that exhibit the strongest influence on structural damage is determined. Then, Chap. 6 proposes a general integrated duration definition for multi-component seismic excitations based on the existing concept of strong motion duration. The relationship between integrated and single horizontal or vertical durations is investigated. A series of nonlinear dynamic analyses is performed to quantify the effects of integrated duration and vertical seismic excitations on the nonlinear response of concrete gravity dam-reservoir-foundation systems. Chapter 7 assesses the effects of aftershocks on concrete gravity dam–reservoir– foundation systems and provides a quantitative description of the damage demands prior to and following the aftershocks. The correlation between ground motion characteristics (i.e. frequency content, strong motion duration, and amplitude) of the mainshocks and major aftershocks is discussed. Then, Chap. 8 examines the influence of earthquake direction on seismic performance of concrete gravity dams subjected to seismic sequences. Nonlinear dynamic analyses of the dam-reservoir-foundation system subjected to as-recorded mainshock-aftershock sequences are conducted to investigate the effects: (1) direction of single earthquake events; (2) direction of seismic sequences; (3) aftershock polarity; and (4) earthquake intensity. Chapter 9 deals with the characterization and modeling of near-fault and farfault ground motions. A systematic approach for seismic performance evaluation and assessment of the probable level of damage based on the proposed performance criteria is presented by using linear analysis results. To validate the presented seismic performance evaluation method, nonlinear dynamic damage analyses of the concrete dam under near-fault ground motions are conducted. Owing to the presence of contraction joints, the above-mentioned analyses that deal with the nonlinear dynamic response and seismic safety evaluation of concrete gravity dams are based on the two-dimensional model, with the underlying assumption that the monoliths behave independently during earthquake activities. Chapter 10 establishes a three-dimensional model to obtain the more realistic seismic response

8

1 Introduction

of concrete gravity dams. This chapter conducts a systematic study on the 3D seismic damage-cracking behavior of concrete gravity dams with all the following factors considered: contraction joint nonlinearity, cross-stream earthquake excitation, and dam-foundation-reservoir interaction.

References Ahmadi, M. T., Izadinia, M., & Bachmann, H. (2001). A discrete crack joint model for nonlinear dynamic analysis of concrete arch dam. Computers & Structures, 79(4), 403–420. Ardakani, S. M. S., & Saiidi, M. S. (2018). Simple method to estimate residual displacement in concrete bridge columns under near-fault earthquake motions. Engineering Structures, 176, 208–219. Ayari, M. L., & Saouma, V. E. (1990). A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks. Engineering Fracture Mechanics, 35(1–3), 587–598. Bhagat, S., Wijeyewickrema, A. C., & Subedi, N. (2018). Influence of near-fault ground motions with fling-step and forward-directivity characteristics on seismic response of base-isolated buildings. Journal of Earthquake Engineering 1–20. Bhattacharjee, S. S., & Léger, P. (1994). Application of NLFM models to predict cracking in concrete gravity dams. Journal of Structural Engineering, 120(4), 1255–1271. Bray, J. D., & Rodriguez-Marek, A. (2004). Characterization of forward-directivity ground motions in the near-fault region. Soil Dynamics and Earthquake Engineering, 24(11), 815–828. Chopra, A. K., & Chakrabarti, P. (1973). The Koyna earthquake and the damage to Koyna Dam. Bulletin of the Seismological Society of America, 63(2), 381. Chopra, A. K., & Chintanapakdee, C. (2001). Comparing response of SDF systems to near-fault and far-fault earthquake motions in the context of spectral regions. Earthquake Engineering and Structural Dynamics, 30(12), 1769–1789. Das, R., & Cleary, P. W. (2013). A mesh-free approach for fracture modelling of gravity dams under earthquake. International Journal of Fracture, 179(1–2), 9–33. Ghaemian, M., & Ghobarah, A. (1999). Nonlinear seismic response of concrete gravity dams with dam–reservoir interaction. Engineering Structures, 21(4), 306–315. Ghaemmaghami, A. R., & Ghaemian, M. (2010). Shaking table test on small-scale retrofitted model of Sefid-rud concrete buttress dam. Earthquake Engineering and Structural Dynamics, 39, 109–118. Goda, K. (2012). Nonlinear response potential of mainshock–aftershock sequences from Japanese earthquakes. Bulletin of the Seismological Society of America, 102(5), 2139–2156. Ingraffea, A. R., & Saouma, V. (1985). Numerical modeling of discrete crack propagation in reinforced and plain concrete. In Fracture mechanics of concrete: Structural application and numerical calculation (pp. 171–225). Netherlands: Springer. Lee, J., & Fenves, G. L. (1998). A plastic-damage concrete model for earthquake analysis of dams. Earthquake Engineering and Structural Dynamics, 27(9), 937–956. Léger, P., & Leclerc, M. (1996). Evaluation of earthquake ground motions to predict cracking response of gravity dams. Engineering Structures, 18(3), 227–239. Li, Q., & Ellingwood, B. R. (2007). Performance evaluation and damage assessment of steel frame buildings under main shock-aftershock earthquake sequences. Earthquake Engineering and Structural Dynamics, 36(3), 405–427. Li, Y., Song, R., & Van de Lindt, J. W. (2014). Collapse fragility of steel structures subjected to earthquake mainshock-aftershock sequences. Journal of Structural Engineering, 140(12), 4014095. Mavroeidis, G. P., & Papageorgiou, A. S. (2003). A mathematical representation of near-fault ground motions. Bulletin of the Seismological Society of America, 93(3), 1099–1131.

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Mirzayee, M., Khaji, N., & Ahmadi, M. T. (2011). A hybrid distinct element-boundary element approach for seismic analysis of cracked concrete gravity dam-reservoir systems. Soil Dynamics and Earthquake Engineering, 31(10), 1347–1356. Nuss, L. K., Matsumoto, N., & Hansen, K. D. (2012). Shaken but not stirred-earthquake performance of concrete dams (pp. 1511–1530). In USSD Proceedings. Omidi, O., Valliappan, S., & Lotfi, V. (2013). Seismic cracking of concrete gravity dams by plastic– damage model using different damping mechanisms. Finite Elements in Analysis and Design, 63, 80–97. Omranian, E., Abdelnaby, A. E., & Abdollahzadeh, G. (2018). Seismic vulnerability assessment of RC skew bridges subjected to mainshock-aftershock sequences. Soil Dynamics and Earthquake Engineering, 114, 186–197. Pekau, O. A., & Cui, Y. (2004). Failure analysis of fractured dams during earthquakes by DEM. Engineering Structures, 26(10), 1483–1502. Ruiz-García, J., & Negrete-Manriquez, J. C. (2011). Evaluation of drift demands in existing steel frames under as-recorded far-field and near-fault mainshock-aftershock seismic sequences. Engineering Structures, 33(2), 621–634. Salami, M. R., Kashani, M. M., & Goda, K. (2019). Influence of advanced structural modeling technique, mainshock-aftershock sequences, and ground-motion types on seismic fragility of low-rise RC structures. Soil Dynamics and Earthquake Engineering, 117, 263–279. Shokrabadi, M., Burton, H. V., & Stewart, J. P. (2018). Impact of sequential ground motion pairing on mainshock-aftershock structural response and collapse performance assessment. Journal of Structural Engineering, 144(10), 4018177. Shokrabadi, M., & Burton, H. V. (2018). Risk-based assessment of aftershock and mainshockaftershock seismic performance of reinforced concrete frames. Structural Safety, 73, 64–74. Tsung-ho, H., Hsueh-hai, L., Tu-hsin, H., & Cheng-jung, Y. (1976). Strong-motion observation of water-induced earthquakes at Hsinfengkiang reservoir in China. Engineering Geology, 10(2), 315–330. Wang, G., Pekau, O. A., Zhang, C., & Wang, S. (2000). Seismic fracture analysis of concrete gravity dams based on nonlinear fracture mechanics. Engineering Fracture Mechanics, 65(1), 67–87. Wang, J., Lin, G., & Liu, J. (2006). Static and dynamic stability analysis using 3D-DDA with incision body scheme. Earthquake Engineering and Engineering Vibration, 5(2), 273–283. Xiang, N., & Alam, M. S. (2019). Displacement-based seismic design of bridge bents retrofitted with various bracing devices and their seismic fragility assessment under near-fault and far-field ground motions. Soil Dynamics and Earthquake Engineering, 119, 75–90. Xin, L., Li, X., Zhang, Z., & Zhao, L. (2019). Seismic behavior of long-span concrete-filled steel tubular arch bridge subjected to near-fault fling-step motions. Engineering Structures, 180, 148– 159. Yaghmaei-Sabegh, S., Neekmanesh, S., & Ruiz-García, J. (2019). Evaluation of the coefficient method for estimation of maximum roof displacement demand of existing buildings subjected to near-fault ground motions. Soil Dynamics and Earthquake Engineering, 121, 276–280. Yang, D., Guo, G., Liu, Y., & Zhang, J. (2019). Dimensional response analysis of bilinear SDOF systems under near-fault ground motions with intrinsic length scale. Soil Dynamics and Earthquake Engineering, 116, 397–408. Zhong, H., Lin, G., Li, X., & Li, J. (2011). Seismic failure modeling of concrete dams considering heterogeneity of concrete. Soil Dynamics and Earthquake Engineering, 31(12), 1678–1689.

Chapter 2

Comparative Analysis of Nonlinear Seismic Response of Concrete Gravity Dams Using XFEM and CDP Model

2.1 Introduction The majority of high concrete dams are being built or to be built in countries with active seismic activities. However, concrete dams will inevitably occur cracking damage due to the low tensile resistance of concrete material under strong ground motions. The seismic safety evaluation of concrete dams has received considerable attention since the outburst of strong earthquakes. Seismic failure analysis of concrete dams is a complex problem associated with the highly nonlinear mechanical behavior of concrete material under strong ground motions. The linear elastic model in conjunction with criteria based on an allowable maximum tensile stress is commonly utilized in the seismic design and safety evaluation of dams (Chopra 1988). Complex nonlinear constitutive models are required in order to capture the concrete material’s behavior and assess the seismic safety of concrete dams in earthquake-prone areas. An investigation of the cracking mechanism and nonlinear dynamic response of concrete dams under strong earthquakes is critically important for a rigorous seismic safety evaluation, and nonlinear models simulating crack propagation within the dam body need to be employed. However, there is no unified fracture modelling approach to capture damage and failure in concrete dams. Different nonlinear models may lead to some differences in cracking behavior of concrete dams. Several material models have been introduced in order to model the nonlinear behavior of the concrete material. The available literature includes models based on the theories of hypoelasticity, hyperelasticity, plasticity, fracture mechanics, plastic-fracture, and continuum damage (Cervera et al. 1995). Different fracture methods with various material constitutive models will obtain different nonlinear behaviors, which may significantly influence on the dam safety evaluation. The present work will make use of both XFEM and CDP model to characterize the mechanical behavior of concrete gravity dams under strong ground motions. The seismic fracture response of concrete gravity dams is investigated © Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_2

11

12

2 Comparative Analysis of Nonlinear Seismic Response …

with considering the effects of dam-reservoir-foundation interaction. The Lagrangian approach is used for the finite element modeling of dam-reservoir-foundation interaction problem. For numerical application, seismic analyses of the Koyna gravity dam are performed by using the 1967 Koyna earthquake records. How the two models tackle the initiation and propagation of cracks in the dam body is investigated. The crack propagation processes and failure modes of the dam structures are compared.

2.2 Method for Dynamic Failure Analysis of Concrete Dams Under Strong Earthquake Due to the low tensile strength of concrete materials, concrete dams are likely to experience cracking. Hence, nonlinear dynamic analysis of concrete dams to earthquake loading will be inevitable. However, nonlinear dynamic response and failure processes of concrete dams subjected to strong ground motions are very complex. In the absence of monitoring data of the actual seismic crack processes of dams, the dynamic model test and finite element method are important means to understand the nonlinear dynamic behavior and damage pattern of high concrete dams under strong ground motions. This section mainly reviewed the dynamic analysis methods for concrete dams to strong earthquake loading. The model test, fracture mechanics, and damage mechanics methods are introduced emphatically. The advantages and disadvantages of these methods are discussed. At the same time, the latest dynamic methods for simulating the damage processes of concrete dams to strong earthquakes are reviewed.

2.2.1 Prototype Observation The prototype observation is a very direct method to understand the seismic performance of high dams to actual earthquakes. However, concrete dams have exhibited extremely well seismic performance, even when subjected to strong ground motions far in excess of their design. Hence, there are few concrete dams that have suffered earthquake failure or major damages. This section will review some concrete dams that have been reported earthquake-induced failure or major damages (Nuss et al. 2012), as summarized in Table 2.1.

2.2.2 Model Test Method The dynamic model test is an important method to understand the nonlinear dynamic response and seismic failure modes of the dam. The model test mainly includes the

Country

India

Taiwan, China

Japan

Dam

Koyna gravity dam

Shih Kang gravity dam

Uh gravity dam

14

21.4

103

Height (m)

Table 2.1 Damaged concrete dams under strong ground motions Crest feet (m)

34

357

853

Western Tottori Oct 6, 2000

Chi-Chi Sep 21, 1999

Koyna Dec 11, 1967

Event

7.3

7.6

6.5

Mag.

(continued)

Although the Uh gravity dam was subjected to strong ground motion, the only damage to the dam was cracking 10–30 mm wide on the spillway channel near the base of the downstream face

The fault rupture extended both upstream and downstream of the dam and caused extensive damage to bays 16–18. The ground movement led to a vertical differential movement of about 9 m in these bays (the left part of these bays raised about 11, and the right side raised about 2 m). There was also a diagonal horizontal offset through the dam of about 7 m, and the dam collapsed with uncontrolled release of water. This is the first concrete dam, which has failed due to an earthquake

Cracks mainly appeared in the non-overflow monoliths. 18 horizontal cracks developed on the upstream face and 7 cracks developed on the downstream face around the elevation at which the slope of the downstream face changes abruptly. Leakage was found in some of these monoliths near the changes in the slope of the downstream face, implying the complete penetration from the upstream face to the downstream face

Results

2.2 Method for Dynamic Failure Analysis of Concrete Dams … 13

Country

USA

China

Iran

Dam

Pacoima arch dam

Hsinfengkiang buttress dam

Sefid Rud buttress dam

Table 2.1 (continued) Height (m)

106

105

113

417

440

180

Crest feet (m)

Manjil Jun 21, 1990

Reservoir Mar 19,1962

Northridge Jan 17, 1994

Event

7.7

6.1

6.8

Mag.

Horizontal cracks appeared in the upper parts of the monoliths, especially in the highest monolith. A major crack ran almost the whole length of the dam at about 14 m below the crest. Leakage was reported through some of the cracks

A horizontal crack 82 m long on the monoliths 13# to 17# developed on the right side of the downstream face around the elevation of 108 m at which the slope changes abruptly. A few smaller cracks developed on the left side of the dam at the same elevation as the crack on the right side

The main damage is that the contraction joint between the arch dam and thrust block at the left abutment opened 50 mm. The thrust block and underlying rock mass may have moved away from the dam about 13 mm

Results

14 2 Comparative Analysis of Nonlinear Seismic Response …

2.2 Method for Dynamic Failure Analysis of Concrete Dams …

15

centrifuge test and shaking table test. With the extensive construction of high DAMS in the world, the model test technology for the dam has been developed rapidly. Many researchers have investigated the nonlinear dynamic response behavior and cracking failure processes of dams under strong earthquakes by using model tests. Chen et al. National Research Council (Dams, 1990a) employed the shaking table test to investigate the seismic failure process of the Koyna gravity dam under strong ground motions. Pekau et al. (1995) investigated the cracking process of the Koyna dam under simplified loading conditions on a shaking table. Tinawi et al. (2000) presented shake table tests to study the dynamic cracking and sliding response of concrete gravity dams, the experimental results have been compared with a simulation. Zhou et al. (2000) performed a series of dynamic experiments of high arch dams to investigate the seismic response and failure modes. Morin et al. (2002) conducted shake table tests to study the seismic behavior and the applicability of the joint model on a 3.4 m high post-tensioned gravity dam. Li et al. (2005) investigated the seismic response of the powerhouse monolith of the Three Gorges dam through the model test on a shaking table. Wang and Li (2006) carried out a seismic overloading model test to study the dynamic behavior of an arch dam with the height of 278 m in prototype. Ghaemmaghami and Ghaemian (2008, 2010) conducted a shaking table test to study the seismic failure process of the Sefid-Rud concrete dam under the strong earthquake of M 7.6, where the scale of the model is 1:30. Rochon-Cyr and Léger (2009) performed a series of shaking table sliding tests to investigate the dynamic sliding response of a 1.5 m high concrete gravity dam model including water uplift pressure. Zhong et al. (2011) investigated the dynamic response and failure modes of the Dagangshan arch dam based on the model test. Chen et al. (2013) studied the dynamic failure process of the Ahai concrete gravity dam used the shaking table model test, where the interaction between the reservoir water and dam is considered, and the foundation is assumed to be rigid. Resatalab et al. (2013) conducted an experimental study on seismic response behavior of concrete gravity dams on the shaking table with considering the interaction between the dam-foundation and reservoir. Aldemir et al. (2015) conducted a pseudo-dynamic testing to investigate the seismic cracking of a concrete gravity dam with a 1/75 scaled. Ro¸sca (2008) used the physical model to study the dynamic behavior and failure mechanism of concrete dams to strong ground motions. He thought that the simulation of boundary conditions is one major problem, and the simulation of material properties seems to be the most difficult and important for the small-scale modeling. Phansri et al. (2010) conducted two small-scale model tests on the shaking table to examine the seismic-induced damage of a concrete gravity dam. They simulated the two shaking table tests to study the crack/behavior of the two small-scale dams using the plasticdamage model. Wang et al. (2014) conducted a comparative model experiment test on the shaking table to study the seismic failure process of a concrete gravity dam with and without the reinforcement measure, and evaluate the effectiveness of the strengthening measure. Wang et al. (2019) conducted a dynamic fracture test for a small-scale model on the shaking table to investigate the dynamic characteristics and failure modes of a concrete gravity dam with the prototype height of 278 m. In their test, the Fiber Bragg Grating (FBG) strain sensor is employed to obtain the

16

2 Comparative Analysis of Nonlinear Seismic Response …

dynamic strain and residual strain. Rodríguez et al. (2020) compared the seismic performance of the Koyna dam using both the numerical method and shake table testing. They concluded that the scale model testing can provide invaluable insights into the nonlinear dynamic response and failure mechanisms of concrete gravity dams, which is even more important in terms of climate change to support capital planning and improve dam safety throughout the world. Although the dynamic model test can capture the dynamic response and failure process of concrete dams, the investment of the model test is large and the period is very long. Many issues need to be clarified. It is difficult to satisfy the similar rate requirements of the mechanical properties of materials, loads and boundary conditions at the same time. And there are still some technical problems, such as the method of overloading, similar criterion of failure test, and the change of material properties in the strength reserve method.

2.2.3 Numerical Simulation Method With the development of computer technology and numerical analysis, the application of nonlinear finite element methods provides a new way to study the dynamic response and failure processes of concrete dams under earthquake loads. The crack plays an important role in the dynamic response behavior of concrete dams. How to simulate crack propagation becomes an important problem. Over the past several decades, extensive research has been carried out and many crack models have been developed to simulate the nonlinear seismic response of concrete gravity dams. There are two traditional fracture models, namely, discrete crack approach (Hillerborg et al. 1976) and smeared crack approach (Rashid 1968). In the discrete crack model, fracture mechanics concepts are used to model the discrete cracking. The discontinuous displacement field at a crack is accounted for by introducing a discontinuity interface into the solid and describing its behavior by a discrete tractionseparation law (Lagier et al. 2011). In a finite element mesh, discontinuity interfaces are placed at element boundaries. Hence, they need remeshing algorithms to accommodate crack propagation (Ingraffea and Saouma 1985). This approach would be efficiently applied to problems where only a few well-defined fractures are encountered. There are two methods that can be used in the discrete crack model, i.e., the linear elastic fracture mechanics (LEFM) and nonlinear fracture mechanics (NLFM). When the applied loads are very slow and are also the impulsive loads, the fracture behavior of concrete structures seems to be adequately predicted by the LEFM model. However, in the intermediate range, from short-term static loading to seismicinduced strain rates, the NLFEM model appears to be more appropriate to describe the fracture process (Bhattacharjee and Leger 1993). Ingraffea (1990) employed the mixed-mode LEFM implemented within a discrete crack method to elucidate the crack initiation and trajectory of the Fontana dam. Ayari and Saouma (1990) developed an LEFM criterion with the discrete crack model for seismic analysis of concrete gravity dams. Bhattacharjee and Léger (1994) investigated the fracture propagation

2.2 Method for Dynamic Failure Analysis of Concrete Dams …

17

process of concrete gravity dams with initial cracks by using the discrete crack model based on the nonlinear fracture mechanics (NLFM). Ahmadi et al. (2001) presented a discrete crack joint model to investigate the nonlinear dynamic response of concrete arch dams. Shi et al. (2003) developed an extended fictitious crack model to analyze the multiple discrete cracking behavior in concrete dams. The original single-crack and multiple-crack problems are involved in the numerical modeling. Lohrasbi and Attarnejad (2008) investigated the crack propagation process of concrete gravity dams using the discrete crack method, and concluded that the discrete crack method can demonstrate the real crack and its opening, but it required an expense of time and money because of frequent meshing. Shi et al. (2014) presented a two-step approach for discrete crack analysis of concrete gravity dams to earthquake force. In the smeared crack model which is based on changes in the constitutive laws governing the behavior of concrete, cracking is modeled by modifying the strength and stiffness of concrete and by distributing or “smearing” the dissipated energy along the finite width of the localization band (Theiner and Hofstetter 2009; Markoviˇc et al. 2013). The structural integrity is evaluated on a local basis. El-Aidi and Hall (1989a, b) discussed the nonlinear dynamic response and seismic performance of concrete dams based the smeared crack approach. Bhattacharjee and Leger (1993) employed a nonlinear smeared fracture model to predict the failure process and energy response of Koyna gravity dams under strong ground motions. Ghaemian and Ghobarah (1999) used the smeared crack model to investigate the seismic cracking and response of concrete gravity dams. In their model, the staggered solution method is presented to consider the dam-reservoir interaction, and the crack propagation criterion is based on the nonlinear fracture mechanics. Lotfi and Espandar (2004) combined the discrete crack and non-orthogonal smeared crack technique to investigate the nonlinear seismic behavior of concrete arch dams. They found that the developed discrete crack and non-orthogonal smeared crack is a more rigorous, consistent and realistic approach. Calayir and Karaton (2005a) presented a co-axial rotating crack model (CRCM) to discuss the nonlinear fracture process of concrete gravity dams subjected to strong earthquakes with considering the effects of damreservoir interaction. Mirzabozorg and Ghaemian (2005) proposed a smeared crack approach to model the three-dimensional dynamic behavior of the Koyna gravity dams and Morrow Point arch dams. Hariri-Ardebili et al. (2013) proposed a coaxial rotating smeared crack model to study the seismic failure behavior of the Koyna gravity dam considering the fracture energy effects and the dam-reservoir and damfoundation interactions. Zhang et al. (2014) employed the smeared crack model to present the cracking characteristics of concrete gravity dams with longitudinal joints. Hariri-Ardebili and Seyed-Kolbadi (2015) assessed the seismic cracking of the Koyna gravity dam, Sefidrud buttress dam, and Dez arch dam using an improved 3D co-axial rotating smeared crack model. Their simulation results are reasonably matched with experimental tests. Hariri-Ardebili et al. (2016) investigated FEM-based parametric analysis of a typical concrete gravity dam. In their finite element model, a developed rotating smeared crack model is used to obtain the nonlinear dynamic response of the dam. Kong et al. (2017) used the co-axial rotating smeared crack model to study the seismic cracking behavior of the conventional reinforced concrete face

18

2 Comparative Analysis of Nonlinear Seismic Response …

slab and ductile fiber-reinforced cement-based composite face slab for concretefaced rockfill dams. Moradloo et al. (2018) employed a modified three-dimensional rotating smeared crack model to obtain the nonlinear behavior of concrete arch dams and evaluate the seismic fragility of dams through nonlinear incremental analysis. Alijani-Ardeshir et al. (2019) discussed the effects of three smeared crack models on seismic response of the Pine Flat dam, the three models are the multidirectional fixed crack model (MFCM), coaxial rotating crack model (CRCM), and orthogonal multi fixed crack model (OMFCM). Pirooznia (2019) investigated the isolation layer effects on the seismic improvement of concrete gravity dams considering the damreservoir interaction based on the smeared crack method. Their results revealed that the isolation layer can reduce the earthquake response and crack propagation process. Under the traditional finite element framework, the description of discontinuous displacement field is usually realized by coordinating the element boundary with discontinuous interface and setting double nodes in corresponding positions. The simulation of evolving discontinuous interface requires continuous remeshing. This will result in a large amount of pretreatment workload, which is not conducive to engineering applications. The extended finite element method (XFEM) (Belytschko and Black 1999; Moës et al. 1999; Stazi et al. 2003; Belytschko et al. 2009), which is based on the cohesive segments method (Remmers et al. 2008) in conjunction with the phantom node technique (Hansbo and Hansbo 2004; Song et al. 2006), can be used to simulate crack initiation and propagation along an arbitrary path, since the crack propagation is not tied to the element boundaries in a mesh. With this approach, it is not necessary to define the crack tip position, but it is possible to simply define a reference region in which the crack will propagate. The near-tip asymptotic singularity is not needed, and only the displacement jump across a cracked element is considered. Hence, the crack must propagate across an entire element at a time to avoid the need to model the stress singularity. The phantom node method describes discontinuity by superposing the phantom elements instead of introducing additional degrees of freedom, and it is easy to incorporate into conventional finite element codes. The XFEM is applied to dynamic problems. Pan et al. (2014) compared the seismic failure process of concrete gravity dams using different fracture approaches including the XFEM with a cohesive law, the crack band finite element method with a plastic-damage relation, and the Drucker-Prager elasto-plastic model. Wang et al. (2015) investigated the potential failure modes of the Guandi gravity dam based on the XFEM. They obtained the typical failure processes and five potential failure modes of concrete gravity dams through incremental dynamic analysis. Zhang et al. (2013) presented the XFEM to predict the seismic crack propagation process of concrete gravity dams with single and multiple initial cracks. Pirboudaghi et al. (2018) proposed an extended finite element-wavelet transform coupled procedure for seismic damage detection based system identification of concrete dams. The advantage of the structural health monitoring used the XFEM is that the whole dam structure is potentially under damage risk without predefined damage. Huang (2018) simulated the seismic crack propagation of concrete gravity dams using the XFEM. In his numerical framework, an incrementation-adaptive multi-transmitting boundary is employed to model the seismic wave propagation in the reservoir and foundation.

2.2 Method for Dynamic Failure Analysis of Concrete Dams …

19

Ma et al.(2019) investigated the seismic dynamic response and crack propagation process of the Koyna gravity dam with different initial crack lengths based on the XFEM. Concrete is a kind of quasi-brittle material, which behaves as linear elastic behavior under the action of the small ground motion. However, with the increase of ground motion load, the micro-cracks in concrete will gradually develop into macroscopic cracks. The nonlinear dynamic behavior analysis of concrete dams based on the plastic damage mechanics has a sufficient theoretical basis. The damage mechanics method has become an important means to reflect the nonlinearity of concrete materials. In order to describe the complex mechanical behavior of concrete material under earthquake conditions, a number of damage constitutive models have been developed, including the isotropic damage models (Lubliner et al. 1989; Mazars and Pijaudier-Cabot 1989; Lee and Fenves 1998a, b), anisotropic damage models (Dragon and Mroz 1979; Murakami and Ohno 1981), and the damage models (Cervera et al. 1995, 1996; Yazdchi et al. 1999) for concrete gravity dams under seismic loads. The concrete damaged plasticity (CDP) model which is developed by Lubliner et al. (1989) and modified by Lee and Fenves (1998a, b) offers a particularly interesting context where damage evolution can be simulated. This approach describing the nonlinear behavior of each compounding substance of a multiphase composite material is used for seismic cracking analysis of concrete dams. In this model, the uniaxial strength functions are factorized into two parts to represent the permanent (plastic) deformation and degradation of stiffness (degradation damage). It assumes that there are two main failure mechanisms of the concrete material, one for tensile cracking, and the other for compressive crushing. Lee and Fenves (1998a, b) used the modified plastic-damage constitutive model to evaluate the nonlinear seismic response of the Koyna dam under the 1967 Koyna earthquake. The rateindependent and strain softening effects have been considered. Sarkar et al. (2007) investigated the influence of the reservoir height and foundation modulus on the nonlinear seismic response of the Koyna gravity dam through the concrete damaged plasticity model. Omidi et al. (2013) employed the plastic-damage model to study the damping mechanism effects on the seismic cracking response of concrete gravity dams including the dam-reservoir interaction. Zhang and Wang (2013) discussed the effects of near-fault ground motions on the nonlinear dynamic response and accumulated damage of concrete gravity dams using the concrete damage plasticity model. Ghaedi et al. (2015) studied the size and shape effects of the gallery on seismic nonlinear dynamic response of roller compacted concrete gravity dams based on the concrete damaged plasticity model. Chen et al. (2016) presented a failure analysis approach for concrete arch dams based on the elastic strain energy criterion using the orthotropic damage mode. Yazdani and Alembagheri (2017) investigated the nonlinear seismic response of gravity dams under near-fault ground motions based on the plastic-damage method. Omidi and Lotfi (2017) presented a combined discrete crack and plastic-damage (DC-PD) method to investigate the seismic nonlinear response of concrete arch dams. In their technique, the discrete crack approach is used to model the joints, and the plastic-damage model is employed to study the damage process of arch dams. Khazaei Poul and Zerva (2018) conducted

20

2 Comparative Analysis of Nonlinear Seismic Response …

nonlinear time-domain dynamic analyses to evaluate the input motion mechanism effect on concrete gravity dams based on the concrete damage plasticity model. Chen et al. (2019) used the concrete damage plasticity model to investigate the seismic performance and failure modes of the Jin’anqiao concrete gravity dam. In their model, the viscous-spring boundary is employed to model the interaction between the dam and foundation. Zhao et al. (2019) investigated the seismic damage of concrete gravity dams using the concrete damaged plasticity constitutive model. The earthquake damage has been quantitatively assessed using electro-mechanical impedance measurements. Daneshyar and Ghaemian (2019) developed a new ratedependent anisotropic damage-plastic model to model the seismic nonlinear response of concrete arch dams with the coupled adhesive-frictional joint response. Pang et al. (2020) used the plastic-damage model to describe the seismic nonlinearity of concrete face slabs, and investigate the seismic fragility of concrete face rockfill dam. Lu et al. (2019) discussed the spatial variability effects of strength parameters on the seismic response characteristics of concrete gravity dams based on the concrete damage plasticity model. In addition, other models, such as the rock failure process analysis (RFPA), distinct element method (DEM), discontinuous deformation analysis (DDA), meshfree particle method called smoothed particle hydrodynamics (SPH) and hybrid distinct element-boundary element (DE-BE) et al., are also methods for simulation of concrete dams and their behavior. Zhong et al. (2011)employed the rock failure process analysis (RFPA) proposed by Tang and Kou (1998) to investigate the typical failure process and failure modes of concrete gravity dams considering the uncertainty in ground motion input and concrete material. Pekau and Cui (2004) conducted a comprehensive study on the nonlinear dynamic response behavior of the fractured Koyna dam subjected to strong ground motions using the distinct element method (DEM). Bretas et al. (2014) also used the DEM to evaluate the seismic safety of masonry gravity dams. Wang et al. (2006) used the discontinuous deformation analysis (DDA) to investigate the dynamic stability of a fractured concrete gravity dam under seismic ground motions. Das and Cleary (2013) explored a meshfree particle method called smoothed particle hydrodynamics (SPH) to model the seismic failure process of concrete gravity dams subjected strong ground motions. Mirzayee et al. (2011) proposed a new algorithm called the hybrid distinct elementboundary element (DE-BE) to study the nonlinear dynamic behavior of cracked concrete gravity dam-reservoir systems. Pan et al (2011) employed the Drucker– Prager (DP) elasto-plastic model to discuss the seismic crack process of concrete dam and compare with the extended finite element method (XFEM) and crack band finite element method. Chen et al. (2017) proposed a 3D nonlinear polyhedron scaled boundary finite element (NPSBFEM3D) for elasto-plastic analysis with the advantages of FEM, BEM and polyhedrons. The authors have successfully carried out seismic cracking analysis of concrete gravity dams with this method.

2.3 eXtended Finite Element Method (XFEM)

21

2.3 eXtended Finite Element Method (XFEM) In the standard FEM, cracks are required to follow element edges for the discontinuity modeling. In contrast, the crack geometry in the extended finite element method (XFEM) need not be aligned with the element edges and thus is independent of the background mesh. Such an independence is made by enriching the standard displacement-based finite element approximation with some pre-knowledge of the physics of crack. It is based on the partition of unity method (PUM) introduced by Melenk and Babuška (1996), which allows local enrichment functions to be easily incorporated into a finite element approximation. This enrichment function typically consists of some near-tip asymptotic functions that capture the singularity around the crack tip and a discontinuous function that represents the jump in displacement across the crack surface. By implementing the generalized Heaviside function (Moës et al. 1999), the method was further enhanced, avoiding taking into account the complicated mapping for arbitrary curved cracks.

2.3.1 XFEM Approximation The XFEM enriches a standard displacement based finite element approximation with discontinuous functions. The approximation for a displacement vector function u with the partition of unity enrichment (Fig. 2.1) in the XFEM takes the following form (Moës et al. 1999):

Fig. 2.1 Enriched nodes in the XFEM

22

2 Comparative Analysis of Nonlinear Seismic Response …

uxfem (x) =



ui Ni (x)

i∈I

+



b j N j (x)H (x)

j∈J







only Heaviside nodes

+

 k∈K 1



Nk (x)

 4 



ckl1 Fl1 (x)

l=1

+ 



Nk (x)

k∈K 2

 4  l=1

 ckl2 Fl2 (x)

(2.1) 

only crack - tip nodes

where x = {x, y} is the two-dimensional coordinate system, I is the set of all nodes in the mesh, N i (x) is the shape function associated with node i, ui are the classical degrees of freedom for node i. J ⊂ I is the set of nodes whose shape function support is cut by a crack, bj is the vector of corresponding additional degrees of freedom for modeling crack faces (not crack-tips). If the crack is aligned with the mesh, bj represent the opening of the crack, H(x) is the Heaviside function. K 1 ⊂ I and K 2 ⊂ I are the set of nodes whose shape function support contains the first and second crack tips in their influence domain, respectively. ckl1 and ckl2 are the vector of corresponding additional degrees of freedom which are related to the modeling of crack-tips, as the near-tip regions are enriched with four different crack functions. Fl1 (x) and Fl2 (x) are the asymptotic crack-tip enrichment functions. If there is no enrichment, then the above equation reduces to the classical finite element approximation ufem (x) = i ui Ni (x). The first term on the right-hand side of the above equation (Eq. (2.1)) is applied to all the nodes while the second term is only valid for nodes whose shape function support is cut by the crack interior, and the third (fourth) term is used only for nodes whose shape function support is cut by the crack tip.

2.3.2 Enrichment Functions To model the discontinuity in displacement field, the enrichment function H(x) which we refer to as a generalized Heaviside enrichment function is implemented in the simulation of powder-die contact surface. The function H(x) takes the value of +1 above the crack, and −1 below the crack. The function H(x) is given by

H (x) =

1 if (x − x∗ ) · n ≥ 0 −1 otherwise

(2.2)

where x is a sample gauss point, x* (lies on the crack) is the closest point to x (Fig. 2.2), and n is the unit outward normal to the crack at x*. Figure 2.2 illustrates the discontinuous jump function across the crack surface.

2.3 eXtended Finite Element Method (XFEM)

23

Fig. 2.2 Representation of normal and tangential coordinates for a smooth crack

In order to model the crack-tip and also to improve the representation of cracktip fields, crack-tip enrichment functions are used in the element which contains the crack tip. For an isotropic material, the crack-tip enrichment functions F l (r, θ ) which are also shown in Fig. 2.2 are given as  4 {Fl (r, θ )}l=1 =

√ θ √ θ √ θ √ θ r sin , r cos , r sin θ sin , r sin θ cos 2 2 2 2

(2.3)

where (r, θ ) is the local polar coordinate system with its origin at the crack tip, and √ θ = 0 is tangent to the crack at the tip. Note that the first function in Eq. (2.3) r sin θ 2, is discontinuous across the crack plane, whereas the last three functions are continuous. It bears emphasis that the near-tip discontinuity can be represented with other sets of functions, or even a single function which is discontinuous across the crack tip geometry. Multiple cracks can be treated in the above framework, by incorporating additional discontinuous and near-tip enrichment. The cohesive segments method (Remmers et al. 2008) in conjunction with phantom nodes proposed by Song et al. (2006) has been used in the framework of the XFEM to simulate the crack initiation and propagation along arbitrary, solutiondependent paths in the bulk materials for brittle or ductile fracture. The cohesive segments are not restricted to being located along element boundaries, but can be located at arbitrary locations and in arbitrary directions, allowing for the resolution of complex crack patterns. In this case the near-tip asymptotic singularity is not needed, and only the displacement jump across a cracked element, which is described using the phantom node method, is considered. Therefore, the crack has to propagate across an entire element at a time to avoid the need to model the stress singularity. Phantom nodes, which are superposed on the original real nodes, are utilized to represent the discontinuity of the cracked elements, as illustrated in Fig. 2.3 (Song et al. 2006). Propagation of a crack along an arbitrary path is made possible by the use of phantom nodes that initially have exactly the same coordinates as the real nodes and that are completely constrained to the real nodes up to damage initiation. In an uncrack element, each phantom node is completely constrained to their corresponding real nodes (n1 to n4 ). But when crossed by a crack at c , the element is partitioned into two subdomains, Ω A and Ω B . The discontinuity in the displacement

24

2 Comparative Analysis of Nonlinear Seismic Response …

Fig. 2.3 Representation of cracked elements by implementation of the phantom node method

is made possible by adding phantom nodes (n 1 to n 4 ) superimposed to the original nodes. The existing element is replaced by two sub-elements, referred to as element A and element B. Each sub-element is formed by a combination of some real nodes (the ones corresponding to the cracked part) and phantom nodes (the ones corresponding to the respective part of the original element). The two sub-elements are constituted by the nodes n 1 , n 2 , n3 and n4 (nA ) and n1 , n2 , n 3 , and n 4 (nB ). Each phantom node and its corresponding real node are no longer tied together and can move apart. Both elements are only partially active, the active part of element A is Ω A and the active part of element B is Ω B . This is represented numerically in the definition of the displacement field: the displacement of a point with coordinates x is computed by 

uA (x, t) = uAj (t)N j (x), x ∈ ΩA uB (x, t) = uBj (t)N j (x), x ∈ ΩB

(2.4)

The approximation of the displacement field is then given by: u(x, t) =



uAj (t)N j (x) H (− f (x)) +    j∈n A uA (x,t)



uBj (t)N j (x) H ( f (x))    j∈n B

(2.5)

uB (x,t)

where nA and nB are the index sets of the nodes of superposed element A and element B, respectively; f (x) is the signed distance measured from the crack. The crack normal opening δ n and the tangential sliding δ t are shown in the following equation:

2.3 eXtended Finite Element Method (XFEM)



25

δn = n[u] δt = [u] − nδn 

(2.6)

where [u] is the jump in the displacement given as [u] =

 j∈n A

N j uAj −



N j uBj

(2.7)

j∈n B

In order to control the magnitude of separation, the cohesive law is defined. A separation occurs when the cohesive strength of the cracked element is zero, after which the phantom and the real nodes move independently. This method which provides an effective and attractive engineering approach, has been used to simulate the initiation and growth of multiple cracks in solids by Remmers et al. (2008) and Song et al. (2006). The detail of the flowchart for crack propagation simulation can be found in references (Ye et al. 2012). In the XFEM, the mesh is not required to conform to the geometric discontinuities. Two signed distance functions per node are generally required to describe the crack location, including the location of crack tips, in a cracked geometry. The first signed distance function describes the crack surface, while the second is used to construct an orthogonal surface so that the intersection of the two surfaces gives the crack front. The first signed distance function is assigned only to nodes of elements intersected by the crack, while the second is assigned only to nodes of elements containing the crack tips.

2.3.3 Discrete Equations The proposed approach is based on an elastodynamics behavior for XFEM analysis of the two-dimensional dam section subjected to an earthquake. We write the strong form of the momentum conservation law in terms of the Cauchy stress tensor, for the current configuration described in Fig. 2.4, as follows: Fig. 2.4 Notations used for a two-dimensional domain

26

2 Comparative Analysis of Nonlinear Seismic Response …

∂σi j + ρbi − ρ u¨ i = 0 ∈ Ω ∂x j

(2.8)

where σ is the Cauchy stress tensor, ρ is the initial mass density, b is the body force vector per unit mass, u¨ is the acceleration. The boundary conditions are σi j n j = t¯i ∈ Γt

(2.9)

ui = u¯ i ∈ Γu

(2.10)

where n is the external unit vector to Γ , t¯ is the applied traction force vector on the Neumann boundary Γt , u¯ is the applied displacement vector on the Dirichlet boundary Γu . It can be noted that Γu ∩ Γt = Γ and  u ∪ Γt = ∅. The weak form of the momentum equation for dynamic problems in the current configuration is given by 

 ¨ ρ uδudΩ + Ω

 ˙ CuδudΩ +

Ω

 σδεdΩ +

Ω

 c

δ[u]dΓc =

Γc

 ρbδudΩ +

Ω

t¯δudΓt

Γt

(2.11) where t¯ is the normalized traction prescribed on Γt ; τc is the cohesive traction applied on the discontinuity surface; u˙ is the velocity; C is the damping matrix. In the XFEM, approximation (2.1) is utilized to calculate the displacement uh (x) for a typical point x in the dam section. Using the standard Bubnov-Galerkin procedure, the equilibrium discrete system of equations for a two-dimensional dam section subjected to an earthquake with XFEM obtained from Eq. (2.11) can be written as Mu¨ h + Cu˙ h + Kuh = f

(2.12)

where M is the mass matrix; C is the damping matrix; K is the stiffness matrix; f is the external load vector; uh = {u, a, c}T is the vector of nodal parameters, including displacements u, Heaviside and crack tip enrichment degrees of freedom a and c, respectively. Rayleigh damping assumption is used for material damping; thus viscous damping matrix is defined as C = αM + βK

(2.13)

where α and β are the constant factors determined by the given free-vibration frequencies of the dam structure to damping ratio. These matrices for an element e are defined as

2.3 eXtended Finite Element Method (XFEM)

⎡

27

Miuuj ⎢ Miej = ⎣ Miauj Micuj ⎡ Kiuuj ⎢ au e Ki j = ⎣ Ki j Kicuj

⎤ Miuaj Miucj ⎥ Miaaj Miacj ⎦ Micaj Miccj ⎤ Kiuaj Kiucj ⎥ Kiaaj Kiacj ⎦ Kicaj Kiccj

T  fie = fiu , fia , fic

(2.14)

(2.15)

(2.16)

The components of consistent mass matrix Mirsj (r, s = u, a, c), stiffness matrix rs Ki j (r, s = u, a, c) and force vector fir (r = u, a, c) include all parts of the classical FEM(uu ), Heaviside enrichment(aa ), orthotropic crack tip enrichment(cc ) and the coupled parts of XFEM approximation(ua, uc, ac ) are given by:  Mirsj =  Kirsj =  fir =

ρζir ζ js dΩ (r, s = u, a, c)

(2.17)

(Bir )T D(Bsj )dΩ (r, s = u, a, c)

(2.18)

Ω

Ωe



ψir tdΓ + Γt

ψir bdΩ (r = u, a, c)

(2.19)

Ωe

Where ⎧ ⎨ Ni r = u ζir = N H r = a (α = 1, 2, 3and4) ⎩ i Ni Fαi r = c ⎧ ⎨ Ni r = u ψir = Ni H r = a (α = 1, 2, 3 and 4) ⎩ Ni Fα r = c

(2.20)

(2.21)

and B = ∇ψ is the matrix of derivatives of extended shape functions ψir .

2.4 Concrete Damaged Plasticity (CDP) Model In order to describe the complex mechanical behavior of concrete material under earthquake conditions, a number of constitutive models have been developed,

28

2 Comparative Analysis of Nonlinear Seismic Response …

including the isotropic damage models (Lubliner et al. 1989; Mazars and PijaudierCabot 1989; Lee and Fenves 1998a, b), the anisotropic damage models (Dragon and Mroz 1979; Murakami and Ohno 1981), and the damage models (Cervera et al. 1995, 1996; Yazdchi et al. 1999) for concrete gravity dams under seismic loads. In this section, a basic constitutive model developed by Lubliner et al. (1989) and modified by Lee and Fenves (1998a, b) is presented. The model describing the nonlinear behavior of each compounding substance of a multiphase composite material is commonly used for seismic cracking analysis of concrete dams. In this model, the uniaxial strength functions are factorized into two parts to represent the permanent (plastic) deformation and degradation of stiffness (degradation damage). It assumes that there are two main failure mechanisms of the concrete material, one for tensile cracking, and the other for compressive crushing.

2.4.1 Damage Evolution In the incremental theory of plasticity, the total strain tensor, ε, is decomposed into the elastic part, εe , and the plastic part, εp , which for linear elasticity is given by: ε = εe + ε p

(2.22)

The state of the nonlinear local problem with variables {εe , εp , κ} is assumed to be known at time t. With this information, the stress tensor is given by σ = (1 − d)σ¯ = (1 − d)E 0 (ε − ε p ) and d = d(κ)

(2.23)

where E 0 is the initial (undamaged) elastic stiffness of the material, d is the scalar stiffness degradation variable, which can take values in the range from 0 (undamaged material) to 1 (fully damaged material). The damage associated with the failure mechanisms of the concrete (cracking and crushing) therefore results in a reduction in the elastic stiffness, which is assumed to be a function of a set of the internal variable κ consisting of tensile and compressive damage variables, i.e. κ = {κ t , κ c }. Damage functions in tension d t and in compression d c are nonlinear functions calculated by comparison of the uniaxial response with experimental data. Following the usual notions of continuum damage mechanics, the effective stress σ¯ is defined as σ¯ =

σ = E 0 (ε − ε p ) 1−d

(2.24)

Similarly, the first effective stress invariant I¯1 and the second effective deviatoric stress invariant J¯2 are defined in terms of the effective stress tensor. I¯1 = σ¯ ii

(2.25)

2.4 Concrete Damaged Plasticity (CDP) Model

29

1 J¯2 = S¯i j S¯i j 2

(2.26)

where S¯i j is the effective deviatoric stress tensor. The stress-cracking strain curves for uniaxial tension and the stress-crushing strain in uniaxial compression are needed to define elastic, plastic and damage behaviors, as shown Fig. 2.5. The stress-strain relations under uniaxial tension and compression loading are p

σt = (1 − dt )E 0 (εt − εt )

(2.27)

σc = (1 − dc )E 0 (εc − εcp )

(2.28)

Fig. 2.5 Response of concrete under a uniaxial tension and b uniaxial compression

30

2 Comparative Analysis of Nonlinear Seismic Response …

2.4.2 Yield Criterion The yield function proposed by Lubliner et al. (1989) and modified by Lee and Fenves (1998) is adopted. The Concrete Damaged Plasticity (CDP) model uses the yield condition to account for different evolution of strength under tension and compression. In terms of effective stresses, the yield function takes the following form F=

       1  q¯ − 3α p¯ + β ε˜ p σˆ¯ max − γ −σˆ¯ max − σ¯ c ε˜ cp ≤ 0 1−α

(2.29)

with

σbo σc0 − 1

α= 0 ≤ α ≤ 0.5, 2σbo σc0 − 1  p σ¯ c ε˜ c β =  p  (1 − α) − (1 + α), σ¯ t ε˜ t γ =

3(1 − K c ) , 2K c − 1

q¯ =

(2.31) (2.32)

σ¯ : I, 3

(2.33)

3¯ ¯ S: S 2

(2.34)

p¯ = − !

(2.30)

where α and β are dimensionless material constants, σ¯ˆ max is the algebraically maximum eigenvalue of σ¯ , σb0 is the concrete strength under equal biaxial compression, σc0 is the initial compressive yield stress, σ¯ c and σ¯ t are the effective compressive p p and tensile cohesion stresses respectively, ε˜ c and ε˜ t are the equivalent compressive and tensile plastic strains respectively, K c is the strength ratio of concrete under equal biaxial compression to triaxial compression, p¯ is the effective hydrostatic pressure, q¯ is the Mises equivalent effective stress, and S¯ is the deviatoric part of the effective stress tensor σ¯ . Typical yield surfaces in the deviatoric plane are shown in Figs. 2.6, and 2.7 shows the initial shape of the yield surface in the principal plane stress space.

2.4.3 Flow Rule The plastic strain rate is evaluated by the flow rule, which is defined by a scalar plastic potential function, G. During plasticity, the normality plastic flow rule is applied as

2.4 Concrete Damaged Plasticity (CDP) Model

31

Fig. 2.6 Yield surfaces in the deviatoric plane

Fig. 2.7 Initial yield function in plane stress space

ε˙ p = λ˙

∂G(σ¯ ) ∂ σ¯

(2.35)

where λ˙ is a non-negative function referred to as the plastic consistency parameter. A Drucker-Prager hyperbolic function is used as the plastic potential function

32

2 Comparative Analysis of Nonlinear Seismic Response …

G=

"

( σt0 tan ψ)2 + q¯ 2 − p¯ tan ψ

(2.36)

where ψ is the dilation angle measured in the p–q plane at high confining pressure; σt0 is the uniaxial tensile stress at failure; and  is a parameter, referred to as the eccentricity, that defines the rate at which the function approaches the asymptote defined by ψ (the flow potential tends to a straight line as the eccentricity tends to zero). This flow potential, which is continuous and smooth, ensures that the flow direction is defined uniquely.

2.5 Lagrangian Formulation for Dynamic Interaction of Dam-Reservoir-Foundation Systems In order to consider the reservoir effect on the behavior of the dam under strong ground motions, three approaches are generally used in the analyses of fluid-structure interaction problems. The simplest one is the added mass approach initially proposed by Westergaard (1933) (with added masses on the dam). Another approach is the Eulerian approach (Maity and Bhattacharyya 2003), in which the displacements are the variables in the structure and the pressure or velocity potential is the variables in the fluid. Since these variables in the structure and fluid are different in the Eulerian approach, a special-purpose computer program is required for the solution of coupled systems. The third way to represent the fluid-structure interaction is the Lagrangian approach (Wilson and Khalvati 1983; Calayir and Dumanoˇglu 1993), where the displacements are the variables for both the fluid and the structure) approaches. For that reason, Lagrangian displacement-based fluid elements can be easily incorporated into a general-purpose computer program for structural analysis, because special interface equations are not required. Dynamic response of fluid-structure systems using the Lagrangian approach has been investigated by many researchers (Calayir and Karaton 2005b; Bilici et al. 2009). The formulation of the fluid-solid system based on Lagrangian approach is given according to Refs (Wilson and Khalvati 1983; Calayir and Dumanoˇglu 1993). In this approach, displacements are selected as the variables in both fluid and structure domains. Fluid is assumed to be linearly elastic, inviscid, and irrotational. For a general two-dimensional fluid element, the stress-strain relationships can be written as:

#

#  C11 0 εv P = (2.37) WZ 0 C22 Pz where P is the pressure, C 11 is the bulk modulus of fluid and εv is the volumetric strain; W z is the rotation about the axis z, Pz and C 22 are the rotational stress and constraint parameter related with W z , respectively. Note that the rotation constraint parameter C 22 in the above stress–strain relationship of fluid is introduced to enforce

2.5 Lagrangian Formulation for Dynamic Interaction …

33

the irrotationality of fluid by penalty method. It should be as high as necessary to prevent fluid rotation but small enough to avoid causing numerical ill-conditioning in the assembled stiffness matrix. In the analysis, the effects of the small amplitude free surface waves, which are commonly referred to as the sloshing effects, are taken into account. The sloshing effects cause a pressure at the free surface of fluid, which is given by P = −γw u fn

(2.38)

where γ w is the weight density of fluid and ufn is the normal component of the free surface displacement. The free surface stiffness for fluid is obtained from the discrete form of Eq. (2.38). In this study, the equations of motion of the fluid system are obtained using energy principles. Using the finite element approximation, the total strain energy of the fluid system can be written as πe =

1 T U KfUf 2 f

(2.39)

where Uf is the nodal displacement vector, Kf is the stiffness matrix of the fluid system. Kf is obtained by the sum of the stiffness matrices of the fluid elements as follows ⎫ ⎬ K f = Kef $ eT e e (2.40) e K f = B f C f B f dV ⎭ V

where Cf is the elasticity matrix consisting of diagonal terms in Eq. (2.37). Bef is the strain-displacement matrix of the fluid element. An important behavior of fluid systems is the ability to displace without a change in volume. For reservoir and storage tanks, this movement is known as sloshing waves in which the displacement is in the vertical direction. The increase in the potential energy of the system because of the free surface motion can be written as πs =

1 T U S f Us f 2 sf

(2.41)

where Usf and Sf are the vertical nodal displacement vector and the stiffness matrix of the free surface of the fluid system, respectively. Sf is obtained by the sum of the stiffness matrices of the free surface fluid elements as follows ⎫ ⎬ S f = Sef $ T e (2.42) e S f = ρ f g hs hs dA ⎭ A

34

2 Comparative Analysis of Nonlinear Seismic Response …

where hs is the vector consisting of interpolation functions of the free surface fluid element. ρ f and g are the mass density of the fluid and the acceleration due to gravity, respectively. In addition, the kinetic energy of the system can be written as T =

1 ˙T ˙f U MfU 2 f

(2.43)

˙ and Mf are the nodal velocity vector and the mass matrix of the fluid system, where U respectively. Mf is also obtained by the sum of the mass matrices of the fluid elements as follows ⎫ ⎬ M f = Mef $ T e (2.44) e M f = ρ f H HdV ⎭ V

where H is the matrix consisting of interpolation functions of the fluid element. If Eqs. (2.39), (2.41) and (2.43) are combined using the Lagrange’s equations, the following set of equations is obtained ¨ f + K∗f U f = R f MfU

(2.45)

¨ f , U f , K∗ and Rf are the nodal acceleration, the nodal displacement, the where U f system stiffness matrix including the free surface stiffness and the time-varying nodal force vector for the fluid system, respectively. In the formation of the fluid element matrices, reduced integration orders are utilized. The equations of motion of the fluid system (Eq. (2.45)), have a similar form to those of the structure system. For obtaining the coupled equations of the fluidstructure system, it is required to determine the interface condition. Because the fluid is assumed to be inviscid, only the displacement in the normal direction to the interface is continuous at the interface of the system. Assuming that positive face is the structure and negative face is the fluid, the boundary condition at the fluid-structure interface is Un− = Un+

(2.46)

where U n is the normal component of the interface displacement (Akkas et al. 1979). Using the interface condition, the equations of motion of the coupled system to ground motions including damping effects are given by ¨ c + Cc U ˙ c + Kc Uc = Rc Mc U

(2.47)

where Mc , Cc and Kc are the mass, damping and stiffness matrices for the coupled ˙ c and U ¨ c are the vectors of the displacement, velocity, system, respectively. Uc , U acceleration of the coupled system, respectively. Rc is the time-varying nodal force vector of ground acceleration.

2.6 Application of the Two Models in Concrete Gravity Dams

35

2.6 Application of the Two Models in Concrete Gravity Dams 2.6.1 Description of Koyna Gravity Dam-Reservoir-Foundation System

0.4

Horizontal Component

Acceleration (g)

Acceleration (g)

Koyna concrete gravity dam in India, 103 m high and 70.2 m wide at its base, is selected for numerical application. The Koyna earthquake of magnitude 6.5 on the Richter scale on December 11, 1967, with maximum acceleration measured at the foundation gallery of 0.49 g and 0.34 g in horizontal and vertical direction, has caused very serious structural damage to the dam, including horizontal cracks on the upstream and downstream faces of a number of non-overflow monoliths around the elevation at which the slope of the downstream face changes abruptly (Chopra and Chakrabarti 1973). Leakage was observed in some of these monoliths near the changes in the slope of the downstream face, implying a complete penetration from the upstream face to the downstream face. This problem has been extensively analyzed by a number of investigators. In this section, dynamic response analyses of the Koyna dam are performed by using the XFEM and CDP model. The time history of the Koyna earthquake is shown in Fig. 2.8. Two-dimensional 4-node plane strain elements (CPE4R) with reduced integration and hourglass control are used to discretize the concrete dam. The mesh of the concrete dam is adequately refined at the base and near the change in the slope of the downstream face where crack growth is expected. The results of the mesh sensitivity analysis suggest that the mesh sizes along the base and near the change in the downstream slope are 1.0 m and 0.5 m, respectively. The element size for other parts is about 1.5 m. The finite element model of the dam-reservoir-foundation interaction system is given in Fig. 2.9a, and the dimensions of the dam are given in Fig. 2.9b. For the initial time step, nodal displacements on the left and right truncated boundary of the dam-reservoir-foundation system are assumed to be zero in the normal direction. In addition, the foundation base is fully constrained. In the sequent

0.2 0.0 -0.2 -0.4 0

2

4

6

Time (s) (a)

8

10

Vertical Component

0.4 0.2 0.0 -0.2 -0.4 0

2

4

6

8

10

Time (s) (b)

Fig. 2.8 Koyna earthquake on December 11, 1967. a Horizontal component; b vertical component

36

2 Comparative Analysis of Nonlinear Seismic Response …

Fig. 2.9 Finite element discretization for the dam- reservoir-foundation system of Koyna dam: a dam-reservoir-foundation system and b concrete gravity dam

dynamic analysis, all displacement constraints are released and the selected earthquake accelerations are applied to the foundation base as the input load. At the fluidsolid interface, the displacement in the normal direction to the interface is assumed to be continuous during the entire simulation. The foundation rock is assumed to be linearly elastic and massless. The massless foundation is used to avoid reflection of the outgoing waves. The reservoir water is assumed to be linearly elastic, irrotational, and inviscid. The material parameters for concrete, foundation rock, and water are listed in Table 2.2. The material parameters used in the CDP model for concrete is shown in Table 2.3. In order to consider strain rate effects of concrete material, a dynamic magnification factor of 1.2 is implemented to the tensile strength of concrete. To account for the energy dissipation in the dam-reservoir-foundation system, a Rayleigh damping ratio of 5% is applied to the natural frequencies of the first and second vibration modes of the entire system, which are 2.55 Hz and 6.13 Hz, respectively. Table 2.2 Material parameters for concrete, foundation rock, and water

Material name

Property name

Value

Unit

Concrete

Young’s modulus

31.0

GPa

Mass density

2643

kg/m3

Tensile strength

2.9

MPa

Compressive strength

24.1

MPa

Poisson’s ratio

0.2

–

Young’s modulus

21.6

GPa

Poisson’s ratio

0.2

–

Bulk modulus

2.07

GPa

Mass density

1000

kg/m3

Foundation rock Water

2.6 Application of the Two Models in Concrete Gravity Dams

37

Table 2.3 Material parameters used in the CDP model for concrete Concrete compression hardening and damage

Concrete tension stiffening and damage

Stress (MPa)

Crushing strain

Stress (MPa)

13

0

0

2.9

0

0

24.1

0.00016

0

2.76

0.000012

0.068

20.64

0.00054

0.244

2.30

0.000036

0.219

12.66

0.00132

0.541

1.57

0.000085

0.435

6.45

0.00288

0.756

0.94

0.000181

0.640

3.15

0.00599

0.876

0.54

0.000375

0.787

1.54

0.01221

0.938

0.31

0.000761

0.878

0.76

0.02464

0.969

0.19

0.001535

0.961

Damage

Cracking strain

Damage

The values of the mass and stiffness proportional damping coefficients used for both fluid and structure are then calculated to be α = 1.1317 and β = 0.001834.

2.6.2 A Comparative Study on Seismic Nonlinear Response Dynamic crack propagation processes of Koyna gravity dam under the 1967 earthquake including dam-reservoir-foundation interaction are conducted employing both the XFEM based on the cohesive segments method and the CDP model made in ABAQUS program. The integration time step used in the analysis is 0.01 s. For dynamic input, the transverse and vertical acceleration components of the 1967 Koyna earthquake are selected. The linear and nonlinear solutions obtained from the dynamic analysis of the dam-reservoir-foundation system are compared with each other. The cracking effects of the concrete material on the seismic response of the dam-reservoir-foundation system are examined. The static solutions of the dam due to its gravity loads and hydrostatic loads are taken as initial conditions in the dynamic analyses of the system. For previously evaluating the seismic performance and predicting the overstressed regions where cracking may occur in the dam body, the maximum and minimum principal stresses for the linear dynamic analysis case are shown in Fig. 2.10. The numeric values marked on these envelopes are given in terms of Pa. From the response results, it can be found that a larger tensile stress is observed at the dam heel and the upper part of the dam, especially near the change in the slope of the downstream face. The maximum tensile stress is 9.30 MPa on the downstream face at the elevation of the downstream slope change, which is approximately 3.2 times the tensile strength selected for the concrete material. These maximum tensile stress on the upstream face exceed 4.5 MPa, and exceed 7.0 MPa around at the dam heel. Compressive stresses also take larger values in the upper part of the upstream and downstream faces, especially around the elevation of the downstream slope change. The maximum

38

2 Comparative Analysis of Nonlinear Seismic Response …

Fig. 2.10 Envelopes of maximum (a) and minimum (b) principal stresses of Koyna dam for the linear dynamic analysis case

compressive stress is 11.55 MPa, which is smaller than the compressive strength of concrete material. In these overstressed regions, cracks in the dam body are expected to occur. Therefore, it can be stated that the linear time history analysis of the damreservoir-foundation system is insufficient, and the nonlinear time history analysis is required to further assess the dam damage and estimate the performance more accurately. The results corresponding to the linear dynamic response clearly indicate that significant nonlinear deformation of Koyna gravity dam should be expected for the 1967 Koyna earthquake. The seismic failure processes of Koyna dam during the Koyna earthquake are predicted using both the XFEM and CDP model. The crack propagation processes and final crack profile of Koyna dam obtained from the XFEM are shown in Fig. 2.11. As shown, smooth curvature discrete cracks penetrating the elements are obtained. The accumulated damage processes of Koyna dam during the Koyna earthquake as predicted using the CDP model are given in Fig. 2.12. The damage of a crack at an element integration point is indicated by shading the related area with red color. As shown, the crack propagation processes and failure modes are obtained. As observed by comparing Figs. 2.11 and 2.12, the crack propagation processes are more or less similar, with the time for two initial cracks beginning to propagate at the dam heel and around the elevation at which the slope of the downstream face changes abruptly. Subsequently, crack trajectories obtained from the XFEM and CDP model have some differences. For both the nonlinear constitutive models, the initial crack propagation in dam firstly occurs at the dam heel at the time t = 2.71 s, and

2.6 Application of the Two Models in Concrete Gravity Dams

39

Fig. 2.11 Crack propagation processes of Koyna gravity dam obtained from the XFEM at six selected times. a t = 2.71 s; b t = 3.87 s; c t = 3.92 s; d t = 4.25 s; e t = 4.27 s; f t = 4.48 s

other initial crack in the dam is observed at 3.87 s near the change in the slope of the downstream face. At these locations, stresses are concentrated and the tensile stresses take large values. After t = 3.92 s, there is some difference between the cracking propagation process from the XFEM and CDP model. For the XFEM technique, the initial crack near the change in the slope of the downstream face extends deeper inside of the dam, and propagates about two-third through the width of the dam section at t = 4.25 s. The crack trajectory curves down due to the compressive stresses resulting from rocking of the top block (Fig. 2.11c, d. After the time instant t = 4.25 s, the crack propagates horizontally toward to upstream face. At t = 4.48 s, the downstream crack extends completely to the upstream face at a height of 60.0 m above the base, penetrating the whole section of the dam. It can be noted that the crack propagation processes are mostly concentrated at the time from 3.87 to 4.48 s when the dynamic displacement response of the dam crest is larger, and the dam remains its overall safety. While, for the CDP model, initial crack begins to initialize near the middle

40

2 Comparative Analysis of Nonlinear Seismic Response …

Fig. 2.12 Crack propagation processes of Koyna gravity dam obtained from the CDP model at six selected times. a t = 2.71 s; b t = 3.87 s; c t = 3.92 s; d t = 4.21 s; e t = 4.67 s; f t = 5.56 s

of the upstream face (Fig. 2.12d) due to the vibration characteristics at t = 4.21. As the dam oscillates during the earthquake, these previously formed cracks at the upstream and downstream faces extend into the dam, penetrating the whole section of the dam. Based on the XFEM and CDP model, it can be found that the Koyna earthquake causes serious structural damage to the Koyna dam. The final crack profiles of Koyna gravity dam under Koyna ground motion predicted by the XFEM and CDP model are compared with the previous research results and model test. Figure 2.13 summarizes the final crack profiles obtained by different approaches. By comparing the current results with the Koyna dam prototype observation (Chopra and Chakrabarti 1973), the model test (Dams 1990b) and previous research results, it can be noted that the crack trajectories in the dam are different from the various fracture procedures. While, the finial crack profiles are

2.6 Application of the Two Models in Concrete Gravity Dams

41

42

2 Comparative Analysis of Nonlinear Seismic Response …

Fig. 2.13 Comparison of the final crack profile of Koyna gravity dam during 1967 Koyna earthquake obtained by different approaches. a Extended finite element method (XFEM); b Concrete damaged plasticity (CDP) model; c Experimental result (Dams 1990b); d Smeared crack model (Mirzabozorg and Ghaemian 2005); (e) Non-linear smeared fracture (Bhattacharjee and Leger 1993); f Smeared carck model considering fracture energy effects (Hariri-Ardebili et al. 2013); g Nonlinear fracture mechanics (Wang et al. 2000); h DruckerPrager elasto-plastic model(Pan et al. 2011); i Crack band finite element method (Pan et al. 2011); j Plastic-damage model (Lee and Fenves 1998a, b); k Plastic-damage model employing the damage-dependent damping mechanism (Omidi et al. 2013); l Continuum damage concrete model (Calayir and Karaton 2005b); m co-axial rotating crack model (Calayir and Karaton 2005a); n Damage rupture process (Chen et al. 2014); o Rock failure process analysis (Zhong et al. 2013); p Mesh-free approach (SPH) (Das and Cleary 2013)

1.5

XFEM CDP Linear

4 2

Displacement (cm)

Displacement (cm)

more or less similar. The failure mechanism is formed by two main damage zones, one at the base, and one in the upper part of the dam around the elevation at which the slope of the downstream face changes abruptly. The top cracking profiles are almost either nearly horizontal or sloping downward from the downstream face toward the upstream face. But in some analyses, cracks are predicted to initialize near the middle of the upstream face or the downstream face, and extend into the dam. From the Fig. 2.13, it may be concluded that both the XFEM and CDP model can predict effectively the crack propagation processes in concrete gravity dams under seismic conditions. The seismic response of the dam-reservoir-foundation system is investigated by comparison of the linear and nonlinear dynamic procedures. Figure 2.14 shows the time history graphs of the horizontal and vertical displacements of the dam crest (point P1) obtained from the linear elastic, XFEM, and CDP model. The positive directions of the horizontal and vertical displacement are in the downstream and upward directions, respectively. There is no cracking during the relatively small amplitude motion. Although cracking in the dam is firstly observed at 2.71 s around the dam heel, the depth of the crack propagation is smaller. Subsequently, other initial crack in the dam is observed at 3.87 s near the change in the slope of the downstream face, which extends deeper inside of the dam. The nonlinear displacement responses

0 -2 -4 0

2

4

6

8

10

XFEM CDP Linear

1.0 0.5 0.0 -0.5 -1.0 -1.5

0

2

4

6

Time (s)

Time (s)

(a)

(b)

8

10

Fig. 2.14 Comparison of the horizontal and vertical displacement histories of the point P1 at the dam crest from the different procedures. a Horizontal displacement; b vertical displacement

2.6 Application of the Two Models in Concrete Gravity Dams

43

XFEM CDP Linear

8 6 4 2 0 0

2

4

6

Time (s)

(a)

8

10

Minimum principal stress (MPa)

Maximum principal stress (MPa)

based on the XFEM and CDP before 3.87 s are almost coincident with those calculated from the linear elastic analysis. The subsequent displacements obtained from the linear and nonlinear solutions separately with each other as the cracks form and propagate in the dam. It can be seen from Fig. 2.14 that displacement responses are significantly different from the various procedures as the cracks propagate in the dam. The differences in the displacement amplitude, which are initially small, reach important levels as the cracks propagate deeper inside of the dam. The vibration periods of displacement response are also changed by the crack propagation, and a lengthening vibration period from the XFEM and CDP model is found, implying that the rigidity of the dam is gradually decreased due to concrete softening. It has been also found that after the strong earthquake, more significant residual displacements using the CDP model remain in the dam crest due to plastic strain during the cyclic loading. At all times, nonlinear response analyses from the two fracture procedures indicate that the dam-reservoir-foundation system remains stable. However, the final conclusions about the dynamic stability should be based on a separate rigid-body analysis of the block considering large displacements and water-fracture interaction mechanisms. Figure 2.15 shows the time history graphs of the maximum and minimum principal stresses occurred in the center of the element E1 located at the changes in the slope of the downstream face. It is seen from Fig. 2.15 that the stress responses obtained from different procedures are also significantly different. The maximum peak value of the maximum principal stresses for the linear case is larger than that in the nonlinear case. The maximum peak value of the maximum principal stresses for the linear case is 8.53 MPa. While, the maximum peak values of those for the two nonlinear cases are about the tensile strength of the concrete material (2.9 MPa). Figure 2.15a confirms that the tensile strength obtained from the XFEM is completely removed after cracking. In CDP model, the damage associated with the failure mechanisms of the concrete will result in a reduction of the elastic stiffness. Therefore, the tensile strength using the CDP model does not completely reduce to zero after damage

0 -2 -4 -6 -8 -10

XFEM CDP Linear

-12 -14 0

2

4

6

8

10

Time (s)

(b)

Fig. 2.15 Comparison of the maximum (a) and minimum (b) principal stress histories from the different procedures occurred in the center of the element E1 (near the changes in the slope of the downstream face)

2 Comparative Analysis of Nonlinear Seismic Response …

XFEM CDP Linear

8 6 4 2 0 0

2

4

6

8

10

Minimum principal stress (MPa)

Maximum principal stress (MPa)

44

0 -2 -4 XFEM CDP Linear

-6 0

2

4

6

Time (s)

Time (s)

(a)

(b)

8

10

Fig. 2.16 Comparison of the maximum (a) and minimum (b) principal stress histories from the different procedures occurred in the center of the element E2 (at the dam heel)

occurring. The minimum principal stress for the nonlinear cases generally takes larger peak values. The maximum peak values of the minimum principal stresses for the XFEM and the CDP model are 12.28 MPa and 14.55 MPa, respectively, which is smaller than the compressive strength of the concrete material. The time history graphs of the maximum and minimum principal stresses occurred in the center of element E2 located at the dam heel are given in Fig. 2.16. The variations in these stresses are similar to those of the element E1. After 2.71 s, the stress responses obtained from the linear and nonlinear solutions separately with each other as the cracks form and propagate in the dam. The XFEM technique based on the cohesive segments method in conjunction with the phantom node technique is used to model crack initiation and propagation along an arbitrary path. Therefore, the crack response behavior can be obtained based on the XFEM. The time history graphs of the crack opening displacement at the downstream and upstream faces near the elevation at which the slope of the downstream face changes abruptly are presented in Fig. 2.17. The peak value of crack opening displacement at the downstream end happens at 4.32 s, reaching 14.76 mm, and at the upstream end happens at 4.55 s, reaching 10.91 mm. As shown in Fig. 2.17, it is known that the crack opening displacement at the downstream end is dominant Fig. 2.17 Time history graphs of the crack opening displacement (COD)

16

14.76mm

14

COD (mm)

12

Downstream Upstream

10.91mm

10 8 6 4 Initial crack

2 0

Penetrated crack

-2 0

2

4

6

Time (s)

8

10

Fig. 2.18 Sliding displacement histories of the upper block of the dam after the formation of the penetrated crack

Sliding along the crack (mm)

2.6 Application of the Two Models in Concrete Gravity Dams

45

2 1.58mm

1 0 Penetrated crack

-1 -2 -3

-3.73mm

-4 0

2

4

6

8

10

Time (sec)

compared with that at the upstream end. The reason for this is mainly because the upstream-sloped crack, which increases the resistance against downstream sliding of the upper block, makes the upper block easier to rotate toward the upstream direction rather than downstream direction under seismic conditions. Figure 2.18 shows the histories of the sliding of the upper block of the dam after the formation of the penetrated crack obtained by the XFEM. As may be seen from Fig. 2.18, the maximum sliding displacement toward the downstream direction is 1.58 mm at 4.52 s, and toward the upstream direction is −3.73 mm at 4.75 s. It may be concluded that when the Koyna earthquake causes the penetrated crack damage to Koyna dam, the upper block remains stable against overturning, as the maximum sliding displacement of 3.73 mm is almost negligible, and the residual displacement is very small. It should be noted that these crack response behaviors can’t be obtained from the CDP model.

2.7 Conclusions In this study, nonlinear dynamic response and seismic failure processes of concrete gravity dams are investigated with considering the effects of damreservoir-foundation interaction. The Lagrangian approach is used for the finite element modeling of the dam-reservoir-foundation interaction problem. Two fracture modelling approaches, XFEM and CDP model, are compared for failure analyses of concrete gravity dams. The XFEM based on the cohesive segments method in conjunction with the phantom node technique can be used to model crack initiation and propagation along an arbitrary path. While, the CDP model including the strain hardening or softening behavior is presented to describe the accumulated damage processes of structures under strong ground motions. The Koyna gravity dam is selected as a numerical application for analyzing the failure processes using the two approaches. The effects of different nonlinear approaches on the seismic response of the dam are compared and discussed.

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Comparison of the results of the two different nonlinear approaches, the Koyna dam prototype observation, model test and those of available methods in the literature indicates that both the XFEM and the CDP model selected for concrete gravity dams can be used in the seismic failure analysis. The crack initiation obtained from the two procedures is more or less similar, with the same time for two initial cracks beginning to propagate at the dam heel and downstream face. While, the crack trajectories in the dam are different from the various fracture procedures. The failure mechanism is formed by two main damage zones, one at the base, and one in the upper part of the dam around the elevation at which the slope of the downstream face changes abruptly. For the XFEM technique, the initial crack near the change in downstream slope extends completely to the upstream face, penetrating the whole section of the dam. While, crack obtained from the CDP model is also predicted to initialize near the middle of the upstream face, these previously formed cracks at the upstream and downstream faces extend into the dam, which penetrates the whole monolith of the dam. Nonlinear dynamic response of the dam-reservoir-foundation system is investigated by comparison of the linear and nonlinear dynamic procedures. During the relatively small amplitude motion, nonlinear dynamic responses based on the XFEM and CDP model are almost coincident with those calculated from the linear elastic analysis. While, displacement and stress responses are significantly different from the various procedures as the cracks propagate in the dam. Significant residual displacements are predicted by the CDP model due to plastic strain during the cyclic loading, which haven’t been found in the XFEM. However, the XFEM can be used to predict opening and sliding displacements of the cracks. In order to capture the cracking mechanism and nonlinear dynamic response of concrete gravity dams under strong ground motions, appropriate nonlinear models simulating crack propagation are critically important for a rigorous seismic safety evaluation.

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Chapter 3

Seismic Cracking Analysis of Concrete Gravity Dams with Initial Cracks Using XFEM

3.1 Introduction Concrete gravity dams are distinguished from other concrete structures because of their size and their interactions with the reservoir and foundation. In practical service, concrete gravity dams normally might have well cracked at their base or at the upstream and downstream faces caused by internal and external temperature variations, shrinkage of the concrete, differential foundation settlement, previous earthquakes, or other reasons (Ingraffea 1990; Feng et al. 1996). These cracks with limited depth will possibly develop in the dam body or, through the monoliths under static or dynamic conditions. As a result, these existing cracks weaken the seismic capacity of concrete gravity dams mainly due to the nonlinear behavior, during strong ground motions. Hence, the real analytical challenge for the crack analysis of concrete gravity dams is to predict their propagation paths under seismic loading conditions. Then, countermeasures can be taken at an early stage to stem their further growth. Nonlinear response of cracked concrete gravity dams has been of great interest in engineering. Many studies (Ayari and Saouma 1990; Bhattacharjee and Léger 1994; Léger and Leclerc 1996; Wang et al. 2000; Ahmadi et al. 2001) focused mainly on the propagation of cracks in the dam, which is accompanied by opening and closing of the cracks, including shake table experiments (Hall 1988; Li et al. 2005; RochonCyr and Léger 2009). However, little efforts have been done for the case in which cracks are expected to appear at the upstream and downstream faces in non-overflow monoliths of the dam. In this case, the seismic response becomes more complex. Shi et al. (2003) used a well-quoted scale model of a concrete gravity dam to analyze multiple discrete cracks in concrete and obtain various kinds of cracking behaviors. Barpi and Valente (2000) employed the cohesive crack model to investigate the behavior of a concrete gravity dam of 103 m high with an initial crack in the upstream face. Their results showed that the initial notch in the upstream face served as the starting point of a crack that propagated toward the foundation during the loading process. Bolzon (2004) compared the merits of Linear Elastic Fracture © Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_3

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Mechanics (LEFM) and cohesive crack approach on the evaluation of safety against ultimate failure of large concrete gravity dams with an initial notch at the base. Batta and Pekau (1996) extended the two-dimensional boundary element procedure for analyzing the propagation of a single discrete crack to simultaneous multiple cracking in concrete gravity dams. Bhattacharjee and Léger (1994) considered both the coaxial rotating crack model (CRCM) and the fixed crack model with a variable shear resistance factor (FCM-VSRF) to study the nonlinear response of a model concrete gravity dam with initial notch on the upstream surface and a full-scale concrete gravity dam with the pre-assigned imperfection located on the upstream side at the elevation of the downstream slope change. Their results showed that the ultimate response of the full-scale dam was not sensitive to the depth of initial imperfection placed on the upstream side. Oliver et al. (2002) presented the strong discontinuity approach to observe the fracture process of a reduced model of a concrete gravity dam with an initial notch on the upstream surface. Tinawi et al. (2000) conducted the shake table experiment and numerical simulation on four 3.4-m-high plain concrete gravity dam models with initial notch to study their dynamic cracking and evaluate the seismic safety. Zhang et al. (2013) presented the extended finite element method (XFEM) to analyze the seismic crack propagation of concrete gravity dams with initial cracks at the upstream and downstream faces. Pekau and Cui (2004) used the distinct element method (DEM) to study the seismic behavior of the fractured Koyna dam during earthquakes. Their results showed that the safety of the dam was ensured if the crack shape was horizontal or upstream-sloped, and it was very dangerous if the crack slopes downstream. Javanmardi et al. (2005) combined the discrete crack model with a theoretical model for uplift pressure variations along a cracked dam to study the seismic stability of concrete gravity dams. Wang et al. (2006) studied the stability of a gravity dam on jointed rock foundation and the seismic stability of the fractured Konya gravity dam using 3D-discontinuous deformation analysis (3D-DDA). Pekau and Zhu (2006), Zhu and Pekau (2007) proposed a rigid model and a flexible FE model to study the seismic behavior of cracked concrete gravity dams. Mirzayee et al. (2011) proposed a hybrid distinct element-boundary element (DE-BE) approach for modeling the nonlinear seismic behavior of fractured concrete gravity dams considering dam-reservoir interaction effects. Shi et al. (2013) used the scaled boundary polygons coupled with the interface element to investigate the crack propagation in concrete gravity dams with a preset notch at the upstream face. Jiang et al. (2013) develop a dynamic contact model and a simplified reinforcing steel constitutive model to analyze the failure process of the cracked gravity dam with and without reinforcement. Cracking plays an important role in the concrete structural behavior, and the modeling of crack growth is a problem of great importance in the simulation of failure. In this chapter, the extended finite element method (XFEM), which is based on the cohesive segments method in conjunction with the phantom node technique, is used to study the crack propagation and nonlinear fracture behavior of concrete gravity dams with initial cracks under earthquake conditions. The XFEM can be used to simulate crack initiation and propagation along an arbitrary path, since the crack propagation is not tied to the element boundaries in a mesh. A scaled-down

3.1 Introduction

55

1:40 model of a gravity dam with an initial notch on the upstream wall is analyzed for accuracy verification. The Lagrangian approach is used for the finite element modeling of dam-reservoir-foundation interaction problem. Subsequently, seismic cracking analyses of Koyna gravity dam and Guandi gravity dam with initial cracks are performed. The Koyna dam with single and multiple initial cracks is investigated to evaluate the seismic crack propagation of concrete gravity dams with initial cracks. The influence of the initial crack position and length on the crack propagation process of Guandi gravity dams subjected to design earthquake is also discussed. The crack propagation process and failure modes of the dam with cracks are obtained.

3.2 Validation Test A scaled model of a concrete gravity dam tested by Carpinteri et al. (1992) is analyzed using the XFEM. The model, which contains a horizontal notch of 15 cm on the upstream face located at a quarter of the dam height, is loaded with an equivalent hydraulic load in order to induce a curved crack that propagates from the tip of the notch towards the downstream face, as shown in Fig. 3.1. Numerical simulation of this test was reported in several public actions using the FEM in combination with CCMs (Barpi and Valente 2000; Shi et al. 2003). Finite element model for the dam with the setup is shown in Fig. 3.2. The mesh of the dam is adequately refined at the lower portion of the dam, in which crack propagation is expected. The material properties of the model dam are: elasticity modulus E = 35,700 MPa, Poisson’s ratio v = 0.1, tensile strength σ u = 3.6 MPa, and fracture energy Gf = 184 N/m. The density of the material is assumed to be 2400 kg/m3 . Following an unsuccessful experimental attempt to simulate the selfweight condition, in which an unstable failure occurred along the base of the model, Fig. 3.1 Model test of the concrete gravity dam with the initial crack (Carpinteri et al. 1992)

56

3 Seismic Cracking Analysis of Concrete Gravity …

Fig. 3.2 Dam model, Scale 1:40, notch depth of 15 cm (dimensions in cm)

the repaired model as the second model has been tested without any adjustment of the self-weight condition. In the present study, only the second model is analyzed, and the predicted response of the single crack is compared with the documented experimental and discrete crack analysis results of Carpinteri et al. (1992). The crack mouth opening displacement (CMOD) at a rate of 1.2 µm/s is applied as the control parameter in the present nonlinear analyses performed using the XFEM. The hydraulic thrust was generated by means of a servo-controlled actuator with a 2000 kN capacity and applied to the upstream side. This force was distributed in four concentrated loads whose intensity is indicated in Fig. 3.3. This force is gradually increased until the failure of the dam. 1000

Applied force (kN)

Fig. 3.3 Total upstream face load versus CMOD displacement

Experimental result (Carpinteri, 1992) Cohesive crack model XFEM

800 600 400 200 0

0.0

0.1

0.2

0.3

0.4

CMOD (mm)

0.5

0.6

0.7

3.2 Validation Test

Numerical results from the XFEM procedure

57

Previous research results

Fig. 3.4 Numerical and experimental crack trajectories for the concrete gravity dam. a Numerical results from the XFEM procedure; b Previous research results (Carpinteri et al. 1992; Barpi and Valente 2000)

The relations between the total upstream face load and CMOD obtained from the XFEM, cohesive crack model (Barpi and Valente 2000)and experimental results (Carpinteri et al. 1992) are shown in Fig. 3.3. As is apparent from Fig. 3.3 that these curves are close to each other. The predicted peak load of the numerical simulation based on the XFEM agrees well with the experiment results. Figure 3.4 shows the computed and experimental crack trajectories. It can be noted that the occurring crack profile shows a good agreement with the experimental results of the model test. By comparing the current results with previous research results (Carpinteri et al. 1992; Barpi and Valente 2000), notice that the curved character of the crack trajectory is correctly captured by the XFEM, indicating that the XFEM procedure can predict effectively the crack propagation process in concrete gravity dams with initial cracks.

3.3 Seismic Crack Propagation Analysis of Koyna Gravity Dam with Initial Crack 3.3.1 Initial Cracking Models In this section, the dynamic cracking analysis of Koyna dam is performed by using the extended finite element method for the concrete material. The time history of the Koyna earthquake is shown in Fig. 2.8 (Chap. 2). Finite element model for the tallest section of the dam is shown in Fig. 3.5. The mesh of the dam is adequately refined near the changes in the slope of the downstream faces, in which crack propagation is expected. The reason for this is because damage due to tensile stresses is expected to initiate near stress concentrations in those zones. The foundation of the dam is taken as being rigid. Westergaard virtual mass (Westergaard 1933) is employed to include the hydrodynamic effect. The value of the Westergaard virtual mass m i at node i on the upstream surface of the dam is

58

3 Seismic Cracking Analysis of Concrete Gravity …

Fig. 3.5 Finite element model of Koyna dam

m i =

 7 hyi ρw (bi1 + bi2 ) 2 8

(3.1)

where h is the depth of water; yi is the distance from node i to the water surface, ρ w is the mass density of water; and bi1 and bi2 are the length of the edges of the quadrilateral constant-strain elements beside node i on the upstream surface of the dam. It should be noted that the seismic water pressure effects inside the cracks are not considered in the analysis. Further studies of the effect of seismic water pressure on the crack propagation and dynamic response of the dam are deemed necessary. In order to reveal the seismic behavior and the crack propagation process of the cracked concrete gravity dams, the Koyna concrete gravity dam with three different sets of initial cracks from the preassigned imperfection, located on the upstream and downstream faces at the elevation of the downstream slope change, is assumed as shown in Fig. 3.6. The initial crack at the base is also considered, but an initial crack modeled at this location did not propagate during seismic analysis. The depths of the initial cracks are all assumed to be 0.4 m. Their corresponding XFEM discretizations are depicted in Fig. 3.6, and titled as Case I for the profile with a horizontal crack at the upstream face (Crack C1), Case II for a horizontal crack at the downstream face (Crack C2), Case III for an upstream-sloped crack at the downstream face (Crack C3), Case IV for both the Crack C1 and Crack C2, Case V for both the Crack C1 and Crack C3. A coefficient of friction of 0.7 is assumed for all the cases to consider the effective interlock in the cracks, and the cohesion coefficient of the crack is set at zero. The material parameters and loadings are assumed as aforementioned. It is evident that the model for the actual cracking of the dam is more likely to be associated with crack C2 and crack C3. This is because the change in the slope of the downstream face provides a singular point for the first crack formation. However,

3.3 Seismic Crack Propagation Analysis of Koyna Gravity Dam with Initial Crack

59

Fig. 3.6 Details of Koyna dam with different initial cracks

the initial cracks are not solely stress-induced but may also arise due to a variety of other causes including shrinkage, temperature effects, etc. (Batta and Pekau 1996), the additional three fracture models are included in the following examination of the fracture process of Koyna dam.

3.3.2 Seismic Crack Propagation Process with no Initial Crack The crack propagation processes of the Koyna dam during the Koyna earthquake as predicted using the XFEM procedures is shown in Fig. 3.7. As shown, smooth curvature discrete cracks penetrating the elements are obtained. The fracture propagation processes can be described as follows: The initial crack in the dam is firstly observed at 3.87 s near the changes in the slope of the downstream face (Fig. 3.7a). At this location, stresses are concentrated and the tensile stresses take large values. As the vibration characteristics, the crack extends deeper inside of the dam. After a period of 0.4 s, i.e. at t = 4.27 s, the downstream crack propagates about three-fourth through the width of the dam section. The crack trajectory curves down due to the compressive stresses resulting from rocking of the top block (Fig. 3.7b–d). After the time instant t = 4.27 s, the crack propagates horizontally toward to upstream face. At t = 4.48 s, the downstream crack extends completely to the upstream face at a height of 56.7 m above the base, penetrating the whole section of the dam. It can be noted that the crack propagation process is mostly concentrated at the time from 3.87 to 4.48 s when the dynamic displacement response of the dam crest is larger, and the dam remains its overall safety.

60

3 Seismic Cracking Analysis of Concrete Gravity …

(a) t=3.87s

(b) t=4.00s

(c) t=4.27s

(d) t=4.48s

Fig. 3.7 Processes of Koyna dam crack propagation at four selected times. a t = 3.87 s; b t = 4.00 s; c t = 4.27 s; d t = 4.48 s

3.3.3 Seismic Crack Propagation Process for Single Initial Cracking Models Dynamic crack propagation and response analysis of Koyna gravity dam with signal initial crack under the 1967 earthquake are conducted employing the XFEM-based cohesive segments method. Results for seismic crack propagation with initial cracks C1, C2 and C3 considered separately are presented in Fig. 3.8, Figs. 3.9 and 3.10, respectively. Figure 3.8 shows the crack propagation processes of the Koyna dam with initial crack C1. As shown, it is known that the final cracking profile with initial crack C1 is quite different from those with the initial cracks C2 and C3. As the vibration characteristics, the initial crack propagation in the dam is firstly observed at 3.20 s near the initial crack C1. After a stretch of horizontal propagation, the crack profile gradually curves downward due to the increasing compressive stresses on the downstream side. At t = 4.49 s, the crack extends about five-sixth through the width of

(a) t=3.20s

(b) t=3.80s

(c) t=4.15s

(d) t=4.49s

Fig. 3.8 Crack propagation processes of Koyna dam for single initial crack C1(Case I) at four selected times. a t = 3.20 s; b t = 3.80 s; c t = 4.15 s; d t = 4.49 s

3.3 Seismic Crack Propagation Analysis of Koyna Gravity Dam with Initial Crack

(a) t=3.87s

(b) t=3.90s

(c) t=4.25s

61

(d) t=4.49s

Fig. 3.9 Crack propagation processes of Koyna dam for single initial crack C2(Case II) at four selected times. a t = 3.87 s; b t = 3.90 s; c t = 4.25 s; d t = 4.49 s

(a) t=3.87s

(b) t=4.00s

(c) t=4.27s

(d) t=4.49s

Fig. 3.10 Crack propagation processes of Koyna dam for single initial crack C3(Case III) at four selected times. a t = 3.87 s; b t = 4.00 s; c t = 4.27 s; d t = 4.49 s

the dam section, and then stops propagation. The final crack profile is presented in Fig. 3.8d, and no penetrating crack appears in this case. Dynamic crack propagation processes of Koyna dam with initial cracks C2 and C3 are shown in Figs. 3.9 and 3.10, respectively. The final cracking profiles for the initial cracks C2 and C3 models are more or less similar, with the initial cracks breaking through to the opposite face of the dam to cause complete rupture, but the crack trajectories are very different. The crack trajectory for the Case III is similar to the Case that the dam with no initial crack (Fig. 3.7), the reason for this is because the initial crack directions are similar. As the vibration characteristics, the initial crack propagation in the dam with initial cracks C2 and C3 also first occurs at 3.87 s near the discontinuity in the slope of the downstream face. After time t = 4.49 s, variation in this damage is insignificant level. In the absence of other cracking, the initial horizontal crack C2 of Fig. 3.9 propagates horizontally and emerges close to the upstream face at the elevation near the changes in the downstream slope. Similarly,

62

3 Seismic Cracking Analysis of Concrete Gravity …

Displacement (cm)

4 2 0 No initial crack Initial crack C1(Case I) Initial crack C2(Case II) Initial crack C3(Case III)

-2 -4 -6 0

2

4

6

8

10

Time(sec)

Fig. 3.11 Time history graphs of the horizontal displacements of the point p1 at the dam crest

when only initial crack C3 is considered (Fig. 3.10), the crack extends toward the upstream face along the initial crack direction. The time history graphs of the horizontal displacement at the point P1 on the dam crest for different crack models are given in Fig. 3.11, with positive displacement in the downstream direction. In addition to Case I, the curves of the horizontal displacement are basically similar in other cases. Although initial cracks near the changes in the slope of the downstream face cause different cracking profiles, there is only a slight difference in the horizontal displacement obtained with and without initial crack. It is also seen from this figure that crack propagation is not necessarily in phase with the displacement of the crest of the dam. Figures 3.12 and 3.13 show the time history graphs of the crack opening displacements, and the history of the sliding of the upper block of the dam after the formation of the penetrated crack. The results obtained from different crack models have some differences. These differences for the COD reach to an important level in point of amplitude and frequency content (especially between t = 3.20 and 4.50 s) as the cracks propagate in the dam. There is only crack opening/closing behavior in case I, because no penetrated crack occurred in the dam. From the time history graphs of the COD of Fig. 3.12, it is evident that the cracks remain more or less closed for almost the entire time. As may be seen from Fig. 3.13, the maximum sliding displacement toward the upstream direction is −3.88 mm at 4.58 s under Case III. The residual displacement for the crack C2 is 0.35 mm toward the downstream direction due to the water pressure, and the residual displacement for the crack C3 is −0.24 mm toward the upstream direction due to the upstream-sloped crack. It may be concluded that the upper block remains stable against overturning, as the residual displacement is almost negligible.

3.3.4 Seismic Crack Propagation Process for Multiple Initial Cracking Model The results of the seismic crack propagation processes with multiple cracking models are given in Figs. 3.14 and 3.15. As is to be expected, the above more complicated

3.3 Seismic Crack Propagation Analysis of Koyna Gravity Dam with Initial Crack

63

18 17.10mm

10.08mm

10

COD (mm)

COD (mm)

8 6 4 2

Downstream Upstream

15

Upstream

12 9 6

3.54mm

3

Initial crack

Initial crack

0

0 0

2

4

6

8

10

Penetrated crack

0

2

4

Time (sec)

6

8

10

Time (sec)

(a)

(b) 14 13.70mm

12

Downstream Upstream

COD (mm)

10 8.49mm

8 6 4 Initial crack

2 0

Penetrated crack

-2 0

2

4

6

8

10

Time (sec) (c)

Sliding along the crack (mm)

Fig. 3.12 Time history graphs of the crack opening displacement (COD) for single initial cracking models. a Case I; b Case II; c Case III 2 1.45mm

1

0.35mm

0

-0.01mm -0.24mm

-1 No initial crack Initial crack C2 (Case II) Initial crack C3 (Case III)

-2 -3

-3.28mm -3.89mm

-4 0

2

4

6

8

10

Time (sec)

Fig. 3.13 Sliding displacement histories of the upper block of the dam with single initial crack after the formation of the penetrated crack

cracking pattern associated with the multiple cracking model increases the computational effort. As shown, the crack propagation processes are more or less similar, with time for both initial cracks beginning to propagate. In both the multiple cracking models, the initial crack propagation in dam firstly occurs on the upstream face at the time t = 3.20 s. After a stretch of horizontal propagation, the initial downstream

64

3 Seismic Cracking Analysis of Concrete Gravity …

(a) t=3.20s

(b) t=3.87s

(c) t=4.00s

(d) t=4.49s

Fig. 3.14 Crack propagation processes of Koyna dam for multiple initial crack C1 and C2(Case IV) at four selected times. a t = 3.20 s; b t = 3.87 s; c t = 4.00 s; d t = 4.49 s

(a) t=3.20s

(b) t=3.87s

(c) t=4.15s

(d) t=4.46s

Fig. 3.15 Crack propagation processes of Koyna dam for multiple initial crack C1 and C3(Case V) at four selected times. a t = 3.20 s; b t = 3.87 s; c t = 4.15 s; d t = 4.46 s

crack begins to propagate toward the upstream face at the time t = 3.87 s. But crack trajectories obtained from single and multiple initial cracking models have some differences. These differences reach to an important level in point of processes as the cracks propagate in the dam. For single initial cracking models, initial cracks propagate through to the opposite face of the dam to cause serious damage. But the initial cracks at the downstream and upstream faces extend into the dam for multiple initial cracking models, nearly penetrating the whole section of the dam. The time history graphs of the COD cracked at both the upstream and downstream faces are given in Fig. 3.16, and show much more complexity due to the existence of multi-cracks. It is seen from Fig. 3.16 that the cracks also remain more or less closed for almost the entire time. Although the initial cracks have some effects on the final cracking profile of the dam, there is only a slight difference in the time history of the COD obtained with the multiple cracking models. Upstream crack C1 is first to propagate and experiences an increase in the magnitude of COD compared to the corresponding single crack model. This crack propagation is associated with

3.3 Seismic Crack Propagation Analysis of Koyna Gravity Dam with Initial Crack

65

12

12

11.47mm 8.75mm

8 6 4 2

12.27mm

10

Downstream Upstream

COD (mm)

COD (mm)

10

Initial crack

8 6 4 2

0

Downstream Upstream

8.38mm

Initial crack

0

Initial crack

Initial crack

-2

-2 0

2

4

6

8

10

0

2

4

6

8

10

Time (sec)

Time (sec) (a)

(b)

Fig. 3.16 Time history graphs of the crack opening displacement (COD) for multiple initial cracking models. a Case IV; b Case V

Sliding along the crack (mm)

relatively large crack opening displacement at approximately 4.17 s. After the time t = 4.49 or 4.46 s, the cracks do not propagate, but the crack opening displacement continues to increase. As shown in Fig. 3.16a, the peak of crack opening displacement at the downstream end happens at 4.54 s, reaching 11.47 mm, and at the upstream end happens at 4.29 s, reaching 8.75 mm. Figure 3.16b shows that the peak of crack opening displacement at the downstream end also happens at 4.54 s, reaching 12.27 mm, and at the upstream end happens at 4.29 s, reaching 8.75 mm. Figure 3.17 shows the sliding displacement history of the upper block of the dam. As may be seen from Fig. 3.17, the maximum sliding displacement toward the upstream direction is −2.28 mm at 4.54 s under Case V. 2 1.16mm

1 0.19mm

0 -0.18mm

Initial crack C1 and C2 (Case (IV) Initial crack C1 and C3 (Case V)

-1 -2

-2.28mm

0

2

4

6

8

10

Time (sec)

Fig. 3.17 Sliding displacement histories of the upper block of the dam with multiple initial crack

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3 Seismic Cracking Analysis of Concrete Gravity …

3.4 Seismic Crack Propagation Analysis of Guandi Gravity Dams with Initial Cracks 3.4.1 FEM Model and Material Properties The Guandi gravity dam is currently under construction in Southwest China. The dam is located in a strong earthquake region with the design peak ground acceleration (PGA) of 0.34 g. A typical non-overflow monolith of the dam, which is 142 m high with a 138 m deep reservoir, is employed to model its seismic damage process. Four-node plane strain quadrilateral isoparametric elements with 2 * 2 Gauss integration are utilized to discretize the rock foundation and dam structure as shown in Fig. 3.18. Foundation corresponding to twice the dam height from the dam heel to upstream, from the dam toe to downstream and from the dam bottom downward is modeled with massless foundation. Since the presented research is aimed at the seismic damage process of concrete gravity dams, the nonlinearity of the foundation rock is not considered. In addition, Lagrangian approach is used for the finite element modeling of dam-reservoir-foundation interaction problem. The material parameters of the fluid are assumed as aforementioned. The energy dissipation of the monolith is considered by the Rayleigh damping method with 5% damping ratio. The traditional massless foundation approach is utilized herein to account for the dam-foundation interaction. Applied loads include self-weight of the dam, hydrostatic, uplift, hydrodynamic, and earthquake forces. Static solutions of the dam due to its gravity loads and hydrostatic loads are taken as initial conditions in the dynamic analyses of the system. Three indices of concrete are employed, i.e. C15, C20, and C25. The material properties are listed in Table 3.1. The tensile strength is taken as 10% of its compressive counterpart. The elasticity modulus and Poisson’s ratio of the foundation rock are taken as 21.6 GPa and 0.20, respectively. To account for the effect of strain rate, modulus and strength of the dam and modulus of the foundation rock are increased

Dam-reservoir-foundation system Fig. 3.18 Finite element meshes of the dam-reservoir-foundation system

Dam

3.4 Seismic Crack Propagation Analysis of Guandi Gravity Dams …

67

Table 3.1 Material properties of the dam Concrete

Modulus (GPa)

Poisson’s ratio

Density (kg/m3 )

Compressive strength (MPa)

Tensile strength (MPa)

Fracture energy (N/m)

C15

56.0

0.167

2552

14.53

1.45

205

C20

57.6

0.167

2552

19.38

1.94

257

C25

58.8

0.167

2552

21.45

2.15

300

by 30% according to the Code for Seismic Design of Hydraulic Structures in China. Both stream and vertical directions are subjected to earthquake excitation.

3.4.2 Initial Crack Position In order to predict the locations of potential cracking, stress analysis of the intact Guandi gravity dam subjected to the recorded Koyna earthquake with the design peak ground acceleration (PGA) of 0.34 g as well as the static loads (concrete dead weight plus reservoir hydrostatic pressure) is first performed. Envelope of the resulting principal tensile stresses for the dam is presented in Fig. 3.19. It can be seen from that the zones of high tensile stress exceed the tensile strength of concrete are mainly observed on the downstream surface (near the change in downstream slope) and the upstream surface (near the slope change at two heights of 8 and 48 m above the base, the dam heel and the upper part of the upstream surface). On the slope change and the dam heel, due to the stress concentration, the stress singularity results in a high computed tensile stress almost three times the tensile strength of concrete. Fig. 3.19 Envelope of principal tensile stresses for seismic analysis without cracks

68

3 Seismic Cracking Analysis of Concrete Gravity …

Based on the above, the Guandi concrete gravity dam with six different sets of small initial cracks from the pre-assigned imperfection, located on the upstream and downstream faces, is assumed as shown in Fig. 3.20. The initial crack at the dam heel is also considered, but an initial crack modeled at this location did not propagate during seismic analysis. The seismic performance and crack propagation process of the cracked concrete gravity dams are investigated for each of these six models of cracking. In order to examine the influence of the initial crack position on the crack propagation trajectory, the depths of the initial cracks are all assumed to be 0.4 m, which is introduced separately on the downstream and the upstream faces of the dam. Their corresponding XFEM discretizations are depicted in Fig. 3.18, and titled as Case I for an intact profile with no initial crack, Case II an upstream-sloped crack at the downstream face (Crack C1), Case III for the profile with a horizontal crack at the upstream face near the change in the slope of the face at a height of 8 m above the base (Crack C2), Case IV for a horizontal crack at the upstream face near the slope change at a height of 48 m above the base (Crack C3), Case V, VI and VII for a horizontal crack on the upstream face at the a height of 123.35 m, 110 m and 95 m above the base (Crack C4, Crack C5 and Crack 6), respectively. A coefficient of friction of 0.7 is assumed for all the cases to consider the effective interlock in the cracks, and the cohesion coefficient of the crack is set at zero. It is evident that the model for the actual cracking of the dam is more likely to be associated with crack C1, C2 and crack C3. This is because the change in the slope of the downstream and upstream faces provides a singular point for the first crack formation. However, the initial cracks are not solely stress-induced but may also arise due to a variety of other causes including shrinkage, temperature effects, etc., the additional three fracture models are included in the following examination of the fracture process of the dam. Fig. 3.20 Details of Koyna dam with different initial cracks

3.4 Seismic Crack Propagation Analysis of Guandi Gravity Dams …

(a) t=4.18s

(b) t=4.24s

(c) t=4.55s

69

(d) t=5.56s

Fig. 3.21 Crack propagation processes of the dam with no initial crack (Case I) at four selected times. a t = 4.18 s; b t = 4.24 s; c t = 4.55 s; d t = 5.56 s

3.4.3 Crack Propagation Process of the Dam with no Initial Crack In order to investigate the influence of initial cracks on the seismic performance and crack propagation of concrete gravity dams, dynamic crack process and response analysis of the intact Guandi gravity dam under the 1967 earthquake with the design peak ground acceleration (PGA) of 0.34 g are firstly conducted employing the XFEMbased cohesive segments method. Figure 3.21 shows the crack propagation processes of the intact dam (Case I) as predicted using the XFEM procedures. As shown, no penetrating crack appears in this case, and the failure mechanism is formed of two main damage zones, one near the dam heel and one at the change in the downstream slope. An initial crack in the dam is predicted to initially occur near the changes in the slope of the downstream face at 4.18 s. At this location, stresses are concentrated and the tensile stresses take large values. As the vibration characteristics, the crack extends deeper inside of the dam at approximately a 45° angle to the vertical. The crack trajectory curves down due to the compressive stresses resulting from rocking of the top block. Furthermore, an initial crack in the dam heel is observed at 4.24 s, which is probably due to stress concentration. It can be noted that the crack at the slope change stops expanding after 5.56 s, and the crack extends into the dam about 10 m.

3.4.4 Influence of Initial Crack Position Seismic crack propagation analyses of the dam with initial cracks C1–C6 considered separately are presented in Figs. 3.22, 3.23, 3.24, 3.25, 3.26 and 3.27, respectively. It can be seen from that the initial crack positions have significant influence on the seismic performance and crack propagation processes of concrete gravity dams, which will cause more severe damage to the dam body than the intact dam profile.

70

3 Seismic Cracking Analysis of Concrete Gravity …

(a) t=3.42s

(b) t=4.24s

(c) t=4.60s

(d) t=4.63s

Fig. 3.22 Crack propagation processes of the dam for single initial crack C1 (Case II) at four selected times. a t = 3.42 s; b t = 4.24 s; c t = 4.60 s; d t = 4.63 s

(a) t=4.26s

(b) t=4.61s

(c) t=4.67s

(d) t=5.00s

Fig. 3.23 Crack propagation processes of the dam for single initial crack C2 (Case III) at four selected times. a t = 4.26 s; b t = 4.61 s; c t = 4.67 s; d t = 5.00 s

(a) t=4.21s

(b) t=4.62s

(c) t=4.66s

(d) t=4.87s

Fig. 3.24 Crack propagation processes of the dam for single initial crack C3 (Case IV) at four selected times. a t = 4.21 s; b t = 4.62 s; c t = 4.66 s; d t = 4.87 s

In some cases, cracks extend completely to the opposite face, penetrating the whole section of the dam and separating the crest from the upper part of the dam. Figure 3.22 shows the crack propagation processes of the Guandi gravity dam with initial crack C1. As shown, the crack propagation processes for the Case II are more or less similar to the Case I that the dam with no initial crack as shown in Fig. 3.21. But smooth curvature discrete cracks penetrating the elements are obtained in the Case II. At t = 3.42 s, the initial crack C1 near the changes in the slope of the

3.4 Seismic Crack Propagation Analysis of Guandi Gravity Dams …

(a) t=4.24s

(b) t=4.26s

(c) t=4.40s

71

(d) t=4.83s

Fig. 3.25 Crack propagation processes of the dam for single initial crack C4 (Case V) at four selected times. a t = 4.24 s; b t = 4.26 s; c t = 4.40 s; d t = 4.83 s

(a) t=4.24s

(b) t=4.26s

(c) t=4.30s

(d) t=4.81s

Fig. 3.26 Crack propagation processes of the dam for single initial crack C5 (Case VI) at four selected times. (a) t = 4.24 s; (b) t = 4.26 s; (c) t = 4.30 s; (d) t = 4.81 s

(a) t=4.24s

(b) t=4.26s

(c) t=4.30s

(d) t=4.68s

Fig. 3.27 Crack propagation processes of the dam for single initial crack C6 (Case VII) at four selected times. a t = 4.24 s; b t = 4.26 s; c t = 4.30 s; d t = 4.68 s

downstream face is beginning to propagate almost perpendicular to the downstream surface. With the on-going acceleration excitation, the crack extends deeper inside of the dam. The crack trajectory curves down due to the compressive stresses resulting from rocking of the top block (Fig. 3.22a–c). After a period of 1.18 s, i.e. at t = 4.60 s, the downstream crack propagates about four-fifth through the width of the dam section (Fig. 3.22c). After the time instant t = 4.60 s, the crack propagates

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horizontally toward to upstream face. At t = 4.48 s, the downstream crack extends completely to the upstream face at a height of 116.2 m above the base, penetrating the whole section of the dam (Fig. 3.22d). Dynamic crack propagation processes of the dam with initial cracks C2 and C3 are shown in Figs. 3.23 and 3.24, respectively. The crack propagation processes and the final cracking profiles for the initial cracks C2 and C3 models are more or less similar, in which a crack is observed to initially occur near the change in the slope of the downstream face and then extends into the dam, and three damage zones (the change in downstream and upstream slopes and near the dam heel) are clearly identified. For the initial crack C2 model (Case III), the initial crack C2 breaks through to the base of the dam to cause complete rupture (Fig. 3.23c). In addition, one crack develops near the change in downstream slope and another crack extends near the change in the upstream slope (Fig. 3.23). For the initial crack C3 model (Case IV), the initial crack C3 at the change in the slope of the upstream face continues to grow downwards toward downstream in a slightly inclined direction (about 10° to the horizontal) with the continuous vibration of the dam. The crack propagates up to about 27.8 m and then stops propagation (Fig. 3.24d). The crack propagation depth at this location for Case IV is longer than the Case III. The results of the seismic crack propagation processes of the dam with initial cracks C4, C5, and C6 are given in Figs. 3.25, 3.26 and 3.27. As shown, it is known that the final cracking profiles with initial cracks C4, C5, and C6 are quite different from those with the initial cracks C1, C2, and C3. The final cracking trajectories for the initial cracks C4, C5 and C6 models are more or less similar, with the initial cracks breaking through to the opposite face of the dam to cause serious damage. For the initial crack C4 model (Case V), a crack in the upper of the dam upstream face propagates downwards toward downstream in a slightly inclined direction and finally reaches the downstream face, penetrating the whole section of the dam (Fig. 3.25). In Case VI (the initial crack C5 model), the initial crack C5 approximately horizontal toward the downstream face, separates the crest from the upper part of the dam (Fig. 3.26). For the initial crack C5 model (Case VII), the initial crack propagation in the dam is firstly observed at 4.26 s near the initial crack C5 due to the vibration characteristics. After a stretch of horizontal propagation, the crack profile gradually curves downward due to the increasing compressive stresses on the downstream side. At t = 4.68 s, the crack extends about five-sixth through the width of the dam section, and then stops propagation. The final crack profile is presented in Fig. 3.27d, and no penetrating crack appears in this case.

3.4 Seismic Crack Propagation Analysis of Guandi Gravity Dams …

73

3.4.5 Influence of Initial Crack Length The finite element model (Fig. 3.18) with initial cracks at the downstream face (Crack C1) and the upstream face near the slope change at a height of 48 m above the base (Crack C3) is analyzed with four values of initial crack lengths, 0.2 m, 0.4 m, 1.0 m and 2.0 m, to study the sensitivity of the predicted response to this initial parameter. Finial failure patterns of the dam with different initial crack lengths are shown in Figs. 3.28 and 3.29. A comparison of horizontal displacement time history of the dam crest with that of no initial crack is shown in Fig. 3.30, with positive displacement in the downstream direction. The influence of initial crack lengths on the crack propagation trajectory can be addressed by comparing Figs. 3.21d, 3.28 and 3.29. It can be found that the initial crack length has some influence on the crack propagation depths. When the initial crack length at the downstream face is 0.2 m, there is no penetrating crack. With the increase of the initial crack length to 0.4 m, the downstream crack extends completely to the upstream face, penetrating the whole section of the dam. The ultimate failure profiles are very similar for the initial crack length of 0.4 m, 1.0 m and 2.0. However,

(a) Length=0.2m

(b) Length=0.4m

(c) Length=1.0m

(d) Length=2.0m

Fig. 3.28 Final crack profiles of the dam with different initial crack lengths at the downstream face: a length = 0.2 m; b length = 0.4 m; c length = 1.0 m; b length = 2.0 m

(a) Length=0.2m

(b) Length=0.4m

(c) Length=1.0m

(d) Length=2.0m

Fig. 3.29 Final crack profiles of the dam with different initial crack lengths at the upstream face near the slope change at a height of 48 m above the base: a length = 0.2 m; b length = 0.4 m; c length = 1.0 m; d length = 2.0 m

74 6

Displacement (cm)

Fig. 3.30 Time history graphs of the horizontal displacements of the dam crest with initial cracks at a the downstream face; b the upstream face near the slope change at a height of 48 m above the base

3 Seismic Cracking Analysis of Concrete Gravity … No initial carck Length=0.4m Length=2.0m

4 2 0 -2 -4 0

2

4

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6

8

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5

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4 3 2 1 0 -1 -2

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6

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(b)

there is a significant impact on the horizontal displacement response of the dam with different initial crack lengths at the downstream face as shown in Fig. 3.30a. As observed by comparing Figs. 3.21d and 3.29, it can be found that the position of the initial crack has significant influence on the crack propagation process of concrete gravity dams. While the crack trajectories are very similar for different initial crack lengths located in the upstream face near the slope change at a height of 48 m above the base, the reason for this is because the initial crack directions are similar. The crack propagation depths at the upstream face for the initial crack length of 0.2 m, 0.4 m, 1.0 m and 2.0 m are 22.75 m, 27.80 m, 28.63 m and 31.02 m, respectively. Although the initial cracks at the upstream face near the slope change cause different cracking depths, there is only a slight difference in the horizontal displacement obtained with different initial crack lengths.

3.5 Conclusions The objective of this study is to evaluate the influence of the initial crack position and length on the seismic performance and crack propagation of concrete gravity dams with considering the effects of dam-reservoir-foundation interaction. The reservoir water is modeled using two-dimensional fluid finite elements by the Lagrangian

3.5 Conclusions

75

approach. The extended finite element method (XFEM), which is based on the cohesive segments method in conjunction with the phantom node technique, is used to model the cracked concrete gravity dam and predict the crack propagation process. The performance of the XFEM procedure for the analysis of crack propagation in concrete gravity dams with initial cracks has been demonstrated in this work. For this purpose, cracking processes of a scaled-down 1:40 model of a gravity dam with an initial notch on the upstream wall loaded with an equivalent hydraulic load are analyzed for accuracy verification. The results show that the crack profile match well with the experimental results from the model test, indicating that the XFEM procedure can effectively capture the crack propagation processes and the crack trajectory in concrete gravity dams with initial cracks. Seismic cracking analysis of the cracked concrete gravity dam indicates that the initial cracks are important in the estimation of the seismic response and crack propagation process. The crack propagation processes for the multiple cracking models are considerably different those for the single initial crack models. In addition to single initial crack in the upstream face of the dam, other possible patterns of initial cracks, including multiple initial on both upstream and downstream face of the dam, result in nearly penetrating cracks in the dam. Seismic cracking analyses of the Guandi gravity dam with six different sets of small initial cracks at different locations along the upstream and downstream faces are performed. The results with and without initial cracks are compared, and significant differences in terms of the crack profile are observed, which indicate that the initial crack position has significant influence on the crack propagation process of concrete gravity dams. The cracked dam will cause more severe damage to the dam body than the intact dam profile. The critical cracking is found to be associated with fracture originating at the point of downstream slope change and penetrating the dam almost instantaneously to separate the crest from the upper part of the dam. Other possible patterns of initial cracks on the upstream face of the upper of the dam also result in a complete rupture. The influence of the initial cracks with different lengths at the downstream and upstream faces is also discussed. The results show that the initial crack length has some impact on the crack propagation depths and displacement response. The crack trajectories are very similar for cases with different initial crack lengths.

References Ahmadi, M. T., Izadinia, M., & Bachmann, H. (2001). A discrete crack joint model for nonlinear dynamic analysis of concrete arch dam. Computers & Structures, 79(4), 403–420. Ayari, M. L., & Saouma, V. E. (1990). A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks. Engineering Fracture Mechanics, 35(1–3), 587–598. Barpi, F., & Valente, S. (2000). Numerical simulation of prenotched gravity dam models. Journal of Engineering Mechanics, 126(6), 611–619.

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Batta, V., & Pekau, O. A. (1996). Application of boundary element analysis for multiple seismic cracking in concrete gravity dams. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 33(6), A277. Bhattacharjee, S. S., & Léger, P. (1994). Application of NLFM models to predict cracking in concrete gravity dams. Journal of Structural Engineering, 120(4), 1255–1271. Bolzon, G. (2004). LEFM and cohesive-crack approaches to safety evaluation of concrete gravity dams. In Computational Mechanics WCCM VI in conjunction with APCOM’04, Beijing (pp. 1–5). Carpinteri, A., Valente, S., Ferrara, G., & Imperato, L. (1992). Experimental and numerical fracture modelling of a gravity dams. In Fracture Mechanics of Concrete Structures, Proceedings of the First International Conference on Fracture Mechanics of Concrete Structures, Elsevier Applied Science, Breckenridge, CO (pp. 351–360). Feng, L. M., Pekau, O. A., & Zhang, C. H. (1996). Cracking analysis of Arch Dams by 3D boundary element method. Journal of Structural Engineering, 122(6), 691–699. Hall, J. F. (1988). The dynamic and earthquake behaviour of concrete dams: review of experimental behaviour and observational evidence. Soil Dynamics and Earthquake Engineering, 7(2), 58–121. Ingraffea, A. R. (1990). Case studies of simulation of fracture in concrete dams. Engineering Fracture Mechanics, 35(1–3), 553–564. Javanmardi, F., Léger, P., & Tinawi, R. (2005). Seismic structural stability of concrete gravity dams considering transient uplift pressures in cracks. Engineering Structures, 27(4), 616–628. Jiang, S., Du, C., & Hong, Y. (2013). Failure analysis of a cracked concrete gravity dam under earthquake. Engineering Failure Analysis, 33, 265–280. Léger, P., & Leclerc, M. (1996). Evaluation of earthquake ground motions to predict cracking response of gravity dams. Engineering Structures, 18(3), 227–239. Li, Q. S., Li, Z. N., Li, G. Q., Meng, J. F., & Tang, J. (2005). Experimental and numerical seismic investigations of the Three Gorges dam. Engineering Structures, 27(4), 501–513. Mirzayee, M., Khaji, N., & Ahmadi, M. T. (2011). A hybrid distinct element-boundary element approach for seismic analysis of cracked concrete gravity dam-reservoir systems. Soil Dynamics and Earthquake Engineering, 31(10), 1347–1356. Oliver, J., Huespe, A. E., Pulido, M. D. G., & Chaves, E. (2002). From continuum mechanics to fracture mechanics: the strong discontinuity approach. Engineering Fracture Mechanics, 69(2), 113–136. Pekau, O. A., & Cui, Y. (2004). Failure analysis of fractured dams during earthquakes by DEM. Engineering Structures, 26(10), 1483–1502. Pekau, O. A., & Zhu, X. (2006). Three-degree-of-freedom rigid model for seismic analysis of cracked concrete gravity dams. Journal of Engineering Mechanics, 132(9), 979–989. Rochon-Cyr, M., & Léger, P. (2009). Shake table sliding response of a gravity dam model including water uplift pressure. Engineering Structures, 31(8), 1625–1633. Shi, M., Zhong, H., Ooi, E. T., Zhang, C., & Song, C. (2013). Modelling of crack propagation of gravity dams by scaled boundary polygons and cohesive crack model. International Journal of Fracture, 183(1), 29–48. Shi, Z., Suzuki, M., & Nakano, M. (2003). Numerical analysis of multiple discrete cracks in concrete dams using extended fictitious crack model. Journal of Structural Engineering, 129(3), 324–336. Tinawi, R., Léger, P., Leclerc, M., & Cipolla, G. (2000). Seismic safety of gravity dams: From snake table experiments to numerical analyses. Journal of Structural Engineering, 126(4), 518–529. Wang, G., Pekau, O. A., Zhang, C., & Wang, S. (2000). Seismic fracture analysis of concrete gravity dams based on nonlinear fracture mechanics. Engineering Fracture Mechanics, 65(1), 67–87. Wang, J., Lin, G., & Liu, J. (2006). Static and dynamic stability analysis using 3D-DDA with incision body scheme. Earthquake Engineering and Engineering Vibration, 5(2), 273–283. Westergaard, H. M. (1933). Water pressures on dams during earthquakes. Transactions ASCE, 95(2), 418–433.

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Zhang, S., Wang, G., & Yu, X. (2013). Seismic cracking analysis of concrete gravity dams with initial cracks using the extended finite element method. Engineering Structures, 56, 528–543. Zhu, X., & Pekau, O. A. (2007). Seismic behavior of concrete gravity dams with penetrated cracks and equivalent impact damping. Engineering Structures, 29(3), 336–345.

Chapter 4

Seismic Potential Failure Mode Analysis of Concrete Gravity Dam–Water–Foundation Systems Through Incremental Dynamic Analysis

4.1 Introduction When subjected to strong ground motions, mass concrete dams are likely to experience cracking due to the low tensile resistance of concrete. Meanwhile, the potential crack initiation and propagation would adversely affect the static and dynamic performance of dams. As cracks penetrate deep inside a dam, its structural resistance may be considerably weakened, thereby endangering the safety of the dam. While there are many high concrete dams throughout the world, only some of them have experienced ground shaking induced structural damage. To name just a few, the Hsingfengkiang dam, China, 1962; Koyna dam, India, 1967; and Sefid-Rud dam, Iran, 1990 are the ones that have suffered from damage in earthquakes. The shaking table test, which can reproduce the seismic response of structures to seismic loadings, is one method to investigate the seismic failure process of high concrete dams. However, many issues need to be clarified for the model test. Among them, the problem of similarity relation is the most difficult, particularly for the seismic failure process of high concrete dams. Apart from the shaking table test, many nonlinear models have also been developed in order to assess the seismic safety of concrete dams. There are based either on the discrete crack approach (Ingraffea and Saouma 1985; Ayari and Saouma 1990; Ahmadi et al. 2001) or the smeared crack approach (Bhattacharjee and Léger 1994; Léger and Leclerc 1996; Ghaemian and Ghobarah 1999; Wang et al. 2000). In addition, other models, such as the plasticdamage model, extended finite element method (XFEM), discrete element method (DEM), discontinuous deformation analysis (DDA), are also used in some cases to analyze the seismic failure behavior of concrete dams. Without being exhaustive, some contributions to these methods and their applications in the seismic crack analysis of concrete dams are worth mentioning. Lee and Fenves (1998) developed a new plastic-damage constitutive model for earthquake analysis of concrete dams, and Long et al. (2009) used this model to study the seismic damage mechanics of the gravity dam and evaluate the effect of the reinforcement. © Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_4

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Calayir and Karaton (2005a, b) presented a continuum damage model and a co-axial rotating crack model for earthquake damage response analysis of concrete gravity dams with the effects of dam-reservoir interaction considered. Zhang et al. (2013a, b) investigated the influences of strong motion duration and mainshock-aftershock seismic sequences on the accumulated damage of concrete gravity dams using a concrete damage plasticity (CDP) model. Omidi et al. (2013) examined the seismic fracture responses of concrete gravity dams due to constant and damage-dependent damping mechanisms. They used a plastic-damage model to simulate the irreversible damage occurring in the fracturing process of concrete. Pan et al. (2011) compared the cracking process and profiles of concrete dams using the XFEM with cohesive constitutive relations, crack band finite element method with plastic-damage relations, and finite element Drucker-Prager Elasto-plastic model. Zhang et al. (2013c) presented the XFEM for analyzing the seismic crack propagation of concrete gravity dams with initial cracks at the upstream and downstream faces. Zhong et al. (2011) extended the Rock Failure Process Analysis (RFPA) to study the failure process of high concrete dams subjected to strong earthquakes. They presented the typical failure process and failure modes of concrete gravity dams with considering the uncertainty in the ground motion input and concrete material. Pekau and Cui (2004) used the DEM to study the seismic behavior of the fractured Koyna dam during earthquakes. Their results showed that the safety of the dam is ensured if the crack shape is horizontal or upstream-sloped, and it is very dangerous if the crack slopes downstream. Bretas et al. (2014) developed the DEM to investigate failure mechanisms in masonry gravity dams. Mirzayee et al. (2011) proposed a hybrid distinct element-boundary element approach to model the nonlinear seismic behavior of cracked concrete gravity dams considering dam-reservoir interaction effects. Wang et al. (2006) employed the DDA to study the seismic stability of the upper part of the fractured Koyna dam. Das and Cleary (2013) explored a mesh-free particle method called smoothed particle hydrodynamics (SPH) for the modeling of gravity dam failure subjected to fluctuating dynamic earthquake loads. Although all the aforementioned research investigated the failure process of dams under some specific seismic ground excitations, only a quite limited number of them have been performed to generalize the seismic failure modes of concrete dams, especially from a large and reliable database of ground motions. In this contribution, we analyze the complicated seismic failure process of the Guandi concrete dam located in China, which involves lots of mechanisms such as elastic deformation and initiation and propagation of cracks leading to ultimate failure. The XFEM, which was originally proposed by Belytschko and Black (1999), is employed to investigate the nonlinear dynamic behavior of concrete gravity dams. Moreover, the cohesive segments method (Remmers et al. 2008) in conjunction with the phantom node technique (Hansbo and Hansbo 2004; Song et al. 2006) is introduced to the XFEM framework in order to simulate crack initiation and propagation along arbitrary paths, This strategy provides great flexibility and versatility in the numerical modeling of discontinuities, since the finite element mesh conforming to cracks is not required and the remeshing during crack growth is avoided in this strategy. These advantages are attributed to the enrichment functions added to the standard finite element

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81

approximation, which is based on the partition of unity concept. Furthermore, the interaction between the impounded water and the dam-foundation system is also explicitly taken into account by modeling the reservoir water with two-dimensional fluid finite elements in the Lagrangian formulation. That is to say, the presented XFEM framework is applied in the fluid-solid coupled systems for solid (concrete dam) modeling. More importantly, the presented study also attempts to generalize the potential failure modes of concrete gravity dams from a large database of ground motions. Considering the uncertainty in the ground motion input, 40 as-recorded accelerograms with each scaled to 8 increasing intensity levels are selected as seismic excitations. Seismic cracking damage process and dynamic response of concrete gravity dams including the effect of dam-reservoir-foundation interaction are simulated through the incremental dynamic analysis (IDA) (Alembagheri and Ghaemian 2013a, b; Billah and Alam 2014; Nik Azizan et al. 2018; Sotoudeh et al. 2018; Chen et al. 2019) based XFEM. The typical failure process and potential failure modes of concrete gravity dams under strong earthquake ground motions are presented.

4.2 Nonlinear Dynamic Response of Guandi Dam Under Design Peak Ground Acceleration 4.2.1 FEM Model and Material Properties In this section, the seismic potential failure modes of the Guandi concrete gravity dam-reservoir-foundation system are studied. The Guandi gravity dam with a design PGA of 0.34 g is located on the Yalong River in the Sichuan Province of China. A typical non-overflow monolith with a height of 142 m is employed to model its seismic damage process. The finite element model of the dam-reservoir-foundation interaction system is shown in Fig. 4.1. It should be noted that the upstream face near the dam heel and the downstream face near the dam toe have been simplified as compared with Sect. 3.4.1. The Lagrangian approach is used for the finite element modeling of dam-reservoirfoundation interaction problem. For the initial time step, displacements of nodes on the left and right truncated boundary of the dam-reservoir-foundation system are assumed to be zero in the normal direction. In addition, the base of the foundation is fully constrained. For the sequent dynamic analysis, all displacement constraints are released, and the horizontal and vertical components of the selected earthquake accelerations are applied to the foundation base as the input loading. The material parameters of the fluid are assumed as aforementioned. The traditional massless foundation approach is utilized herein to account for the dam-foundation interaction. Since the presented research is aimed at the seismic damage processes of concrete gravity dams, nonlinearity of the foundation rock is not considered. The energy

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4 Seismic Potential Failure Mode Analysis of Concrete …

(a) Dam-reservoir-foundation system

(b) Guandi gravity dam

Fig. 4.1 Finite element meshes of the Guandi graivty dam-reservoir-foundation system. a Damreservoir-foundation system; b Guandi gravity dam

dissipation of the monolith is considered by the Rayleigh damping method with 5% damping ratio. Three indices of concrete are employed, i.e. C15, C20 and C25. The material properties of the dam concrete are listed in Table 3.1. The tensile strength is taken as 10% of its compressive counterpart. The elasticity modulus and Poisson’s ratio of the foundation rock are taken as 21.6 GPa and 0.20, respectively. To account for the effects of strain rate, modulus and strength of the dam and modulus of the foundation rock are increased by 30% according to the Code for Seismic Design of Hydraulic Structures in China. Both horizontal direction and vertical direction are subjected to earthquake excitation.

4.2.2 Seismic Response and Crack Propagation Analysis In this section, the effects of the concrete cracking damage on the seismic response of the dam-reservoir-foundation system under design peak ground acceleration (PGA) of 0.34 g are investigated by comparison of the linear and nonlinear dynamic solutions of the system. The linear solution is obtained by assuming the concrete to be linear elastic while the nonlinear dynamic solution of the dam is obtained from the XFEMbased cohesive segments method. Namely, the concrete cracking damage resulting from the seismic ground motion is considered in the nonlinear solution. Besides the effects of the concrete cracking damage, we also analyze and discuss the full process of dynamic cracking of the Guandi dam. The Koyna earthquake, which is scaled to have 0.34 g spectral acceleration in the stream direction, is used as seismic excitation. The implicit Newmark-β method is used in the incremental dynamic analysis for time stepping, which is unconditionally stable. That is to say, any time

4.2 Nonlinear Dynamic Response of Guandi Dam Under Design Peak …

83

step will lead to stable results. However, in order to ensure accurate time integration, sufficiently small time increment is needed. On the other hand, excessive time steps result in high burden and poor computational efficiency. In practice, an adequate balance between accuracy and efficiency can be obtained by choosing the following combination: the initial increment size and maximum increment size are 0.001 s and 0.01 s, respectively. Meanwhile, automatic time incrementation is used for the dynamic analysis to further improve the efficiency. Figure 4.2 compares the history of horizontal and vertical displacements at the dam crest obtained from the linear elastic method and the XFEM, respectively, when the Guandi dam is under the combined static and earthquake loads. The solid lines are the response of the dam using the XFEM, whereas the dashed lines are the dam response assuming the concrete is linear elastic. The positive directions of the horizontal and vertical displacement are in the downstream and upward directions, respectively. As can be seen in Fig. 4.2, the nonlinear dynamic response before cracking initiation (1.90 s) is coincident with the response calculated from the linear elastic analysis. This means that the maximum principal stress in the dam does not exceed the tensile strength of the concrete during the relatively small amplitude motion, and there is no cracking before t = 1.90 s. The subsequent displacements obtained from the linear and nonlinear solutions separately with each other as the cracks form and propagate in the dam. It is clear from Fig. 4.2 that the nonlinear response has a substantially different displacement history than the linear model after t = 3.67 s. The vibration periods of displacement response are also changed by the crack propagation, and a lengthened vibration period from the XFEM procedure is found. It implies that the crest displacements are dominated by rigid–body rocking of the upper portion of the dam after the formation of cracks near the change in the slope of the downstream face. At all times, the nonlinear response analysis shows that the dam remains stable. Figures 4.3 and 4.4 present the time history graphs of the crack opening displacements, and the history of the sliding of the upper block of the dam after the formation of the penetrated crack. As shown in Fig. 4.3, the peak of crack opening displacement at the downstream end happens at 4.32 s, reaching 1.79 cm, and at the upstream end happens at 3.92 s, reaching 0.77 cm. It can also be found from Fig. 4.3 that the crack opening displacement at the downstream end is dominant compared with

2.00cm

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Fig. 4.3 Time history graphs of the crack opening displacement (COD)

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Time (s) Fig. 4.4 Sliding displacement histories of the upper block of the dam after the formation of the penetrated crack

that at the upstream end. The reason for this is mainly because the upstream-sloped crack, which increases the resistance against downstream sliding of the upper block, makes the upper block easier to rotate toward the upstream direction rather than downstream direction under seismic conditions. As may be seen from Fig. 4.4, the maximum sliding displacement toward the downstream direction is 0.26 cm at 3.69 s, and toward the upstream direction is −2.08 cm at 3.92 s. It may be concluded that when the Koyna earthquake scaled to have 0.34 g spectral acceleration in the stream direction causes the penetrated crack damage to the dam, the upper block remains stable against overturning, as the maximum sliding displacement of 2.08 cm is almost negligible, and the residual displacement is very small. Crack propagation processes in the Guandi gravity dam at four selected times as predicted using the XFEM procedure are shown in Fig. 4.5. As shown, the smooth curvature discrete crack penetrating the elements is obtained. Damage initiates from

4.2 Nonlinear Dynamic Response of Guandi Dam Under Design Peak …

(a) t=1.90s

(b) t=2.59s

(c) t=3.67s

85

(d) t=3.98s

Fig. 4.5 Processes of the crack propagation in the Guandi gravity dam at four selected times. a t = 3.87 s; b t = 4.00 s; c t = 4.27 s; d t = 4.48 s (Amplification factor: 100)

regions with very high stress concentrations. An upstream-sloped in the dam is initiated at the discontinuity in the slope of the downstream face at about t = 1.90 s (Fig. 4.5a). At this location, stresses are concentrated and the tensile stresses take large values. As the vibration characteristics, the crack extends deeper inside of the dam. The initial crack propagates almost perpendicular to the downstream surface. The crack trajectory curves down due to the compressive stresses resulting from rocking of the top block (Fig. 4.5a, b). At t = 2.59 s, the upper crack propagates to about three-fifth through the thickness of the dam section (Fig. 4.5b). After the time instant t = 2.59 s, the crack propagates approximately horizontally toward the upstream face. At t = 3.67 s, the downstream crack extends completely to the upstream face at a height of 118.4 m above the base, penetrating the whole section of the dam (Fig. 4.5c). Because of the thrust of impounded water which is opposing the tendency of the top section to slide along the crack in the upstream direction, the computed crack profiles in the upper part of the dam can be considered neutral or favorable conditions to maintain stability.

4.3 Seismic Potential Failure Mode Analysis 4.3.1 Database of as-Recorded Acceleration Records In order to investigate the potential failure modes of concrete gravity dam-reservoirfoundation systems subjected to strong ground motions, 40 real earthquake records, which have been selected from the databases of the Consortium of Organizations for Strong Motion Observation Systems (COSMOS) (COSMOS 2019) and Pacific Earthquake Engineering Research Center (PEER) (PEER 2019) with a broad distribution of durations, are applied to the structure. The seismic sequences with different earthquake magnitudes (i.e. M w 6.0–7.8) that have occurred in the United States, Taiwan and India, are shown in Table 4.1. The data sample includes well-known earthquakes with strong seismic activity, such as Loma Prieta (1989), Northridge

Chi-Chi

Chi-Chi

Chi-Chi

Chi-Chi

14

15

Northridge

8

13

Northridge

7

12

Northridge

6

Northridge

Northridge

5

11

Northridge

4

Northridge

Northridge

3

Northridge

Northridge

2

10

Koyna

1

9

Earthquake

No.

20-09-1999

20-09-1999

20-09-1999

20-09-1999

17-01-1994

17-01-1994

17-01-1994

17-01-1994

17-01-1994

17-01-1994

17-01-1994

17-01-1994

17-01-1994

17-01-1994

11-12-1967

Date

32.0

8.9

7.9

8.3

17.9

29.4

8.6

7.1

12.9

8.6

18.4

15.7

35.8

12.5

13.0

Distance to fault (km)

Table 4.1 Earthquake records used in the failure mode analysis

Ilan, Taiwan #ILA067

Taichung, Taiwan #TCU050

Taichung, Taiwan #TCU072

Taichung, Taiwan #TCU078

Tarzana, CA—Cedar Hill #24436

Warm Springs #24272

Sylmar, CA—Jensen Filtration Plant #655

Newhall, CA—Los Angeles County Fire #24279

CA—White Oak Covenant Church #5303

Los Angeles Dam #2141

Los Angeles Mulholland Dr #5314

Epiphany Litheran Church #5353

Los Angeles Terrace #24592

Coldwater Canyon School #5309

Koyna Dam

Station location

7.6

7.6

7.6

7.6

5.3

6.7

6.7

6.7

6.7

6.7

6.7

6.7

6.7

6.7

6.5

Mw

90

0

360

0

90

90

22

360

180

334

35

196

180

180

0

Comp.

(continued)

195.70

127.50

360.10

301.80

365.30

221.20

560.30

578.20

467.90

419.10

641.90

404.20

310.10

313.30

464.78

PGA (cm/s2 )

86 4 Seismic Potential Failure Mode Analysis of Concrete …

Earthquake

Chi-Chi

Chi-Chi

Chi-Chi

Loma Prieta

Loma Prieta

Loma Prieta

Loma Prieta

Loma Prieta

Loma Prieta

Loma Prieta

Loma Prieta

Imperial Valley

Imperial Valley

Imperial Valley

Imperial Valley

No.

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Table 4.1 (continued)

15-10-1979

15-10-1979

15-10-1979

15-10-1979

18-10-1989

18-10-1989

18-10-1989

18-10-1989

18-10-1989

18-10-1989

18-10-1989

18-10-1989

20-09-1999

20-09-1999

20-09-1999

Date

5.2

9.8

5.6

12.9

2.8

16.9

2.8

22.7

6.3

11.9

15.9

17.2

31.1

3.2

37.2

Distance to fault (km)

El Centro, CA—Array Sta 5 #0952

Casa Flores Mexicali #6619

El Centro, CA—Differential Array #5165

El Centro, CA—Array Sta 7 #5028

Gilroy Array Sta 1, CA #47379

Coyote Lake Dam, CA #57217

Corralitos, CA #57007

Gilroy Array Sta 7 #57425

Gilroy Array Sta 3 # 47381

Santa Teresa Hills #57563

Capitola, CA #47125

South St and Pine Dr #47524

Chiayi, Taiwan #CHY086

Taichung, Taiwan #TCU076

Chiayi, Taiwan #CHY014

Station location

6.5

6.5

6.5

6.5

7.0

7.0

7.0

7.0

7.0

7.0

7.0

7.0

7.6

7.6

7.6

Mw

230

0

360

52

90

285

90

90

90

315

90

90

0

90

0

Comp.

(continued)

360.37

238.10

473.64

205.76

433.60

471.00

469.40

314.30

362.00

223.40

390.80

174.50

201.60

336.10

254.90

PGA (cm/s2 )

4.3 Seismic Potential Failure Mode Analysis 87

Earthquake

Imperial Valley

Imperial Valley

Imperial Valley

Petrolia

Parkfield

Superstition Hills

Kern County

San Simeon

Landers

Landers

No.

31

32

33

34

35

36

37

38

39

40

Table 4.1 (continued)

28-06-1992

28-06-1992

22-12-2003

21-07-1952

24-11-1987

28-09-2004

17-08-1991

15-10-1979

15-10-1979

15-10-1979

Date

10.0

28.6

14.8

36.2

13.0

14.0

11.7

21.8

8.8

21.7

Distance to fault (km) 6.5

6.5

Mw

Joshua Tree #22170

Whitewater Canyon #5072

Caltrans Bridge Grnds #37737

Lincoln School #1095

Westmorland, CA #11369

USGS Parkfield Dense #02

General Store #89156

7.3

7.3

6.5

7.5

6.6

6.0

6.0

Superstition Mtn, CA—Camera Site #0286 6.5

Holtville, CA—Post Office #5055

El Centro, CA—Array Sta 13 #5059

Station location

90

270

90

111

180

360

90

135

225

230

Comp.

278.40

124.92

175.00

175.95

203.56

170.00

488.70

182.19

242.96

131.07

PGA (cm/s2 )

88 4 Seismic Potential Failure Mode Analysis of Concrete …

4.3 Seismic Potential Failure Mode Analysis

89

(1994), and Chi-Chi (1999) events. Owing to the uncertainty of earthquake activities, the amplitude of earthquakes may vary over a wide range according to the seismic hazard analysis with a different occurrence probability. Eight levels of the acceleration amplitude are employed in the analysis, i.e. 0.2, 0.3, 0.34, 0.4, 0.50, 0.6, 0.7 and 0.8 g. By increasing the earthquake intensity, the structure is shifted from its initial elastic state into a series of successive inelastic states and finally to its collapse. In each seismic analysis first the static loads including the self-weight of the dam and the hydrostatic load on upstream face of the dam are applied, and then the two components of the selected earthquakes are uniformly applied at the base of the foundation.

4.3.2 Incremental Dynamic Analysis Failure mode analysis of concrete gravity dams-reservoir-foundation systems is carried out through nonlinear IDA based on XFEM. Final cracking profiles of the Guandi gravity dam under the 1967 Koyna record at different shaking intensity levels are shown in Fig. 4.6. The crack initiation occurs at different times and locations depending on the amplitude. When the dam is loaded with only static loads, stress level in the dam is relatively low, no visible crack is detected. For the seismic motions

(a) PGA=0.2g

(e) PGA=0.5g

(b) PGA=0.3g

(f) PGA=0.6g

(c) PGA=0.34g

(g) PGA=0.7g

(d) PGA=0.4g

(h) PGA=0.8g

Fig. 4.6 Final cracking profiles of the Guandi gravity dam subjected to Koyna record at various intensity levels. a PGA = 0.2 g, b PGA = 0.3 g, c PGA = 0.34 g, d PGA = 0.4 g, e PGA = 0.5 g, f PGA = 0.6 g, g PGA = 0.7 g, and h PGA = 0.8 g

90

4 Seismic Potential Failure Mode Analysis of Concrete …

associated with a PGA of 0.2 g, very minor damage is identified near the change in the downstream slope. With the increasing acceleration excitation, the downstream surface and upstream surface as well as the dam heel of the dam are characterized by high tensile stress and compressive stress. At the 0.30 g level, some moderate damage is identified, but it does not seem to reach a level that could compromise the integrity of the section. The upper crack propagates to about three-fifth through the thickness of the dam section. The results corresponding to the 0.34–0.80 g PGA level clearly indicate that significant damage is detected. At the 0.34 g level, the upper crack propagates completely to the upstream face, causing the dam head detached from the dam body. At the 0.6 g level, cracks appear not only at the dam heel and the change in the downstream slope, but also near the change in the slope of the upstream face. As the dam oscillates during an earthquake, these cracks extend into the dam. The case associated with a PGA of 0.70 g shows clear indications of significant strength degradation in the dam, with two cracking patterns that completely extend across the upper and middle sections. Typical damage processes of the Guandi gravity dam-reservoir-foundation system subjected to the Koyna acceleration time history with an amplitude of 0.7 g, about 2.0 times the design PGA, are plotted in Fig. 4.7. As shown, three damage zones (i.e. the change in the slope of the down face, the change in upstream slope, and the dam heel) are clearly identified and they correspond to the areas associated with the maximum tensile demands. At 1.84 s, the initial crack in the dam is firstly observed near the

(a) t=1.84s

(e) t=2.32s

(b) t=1.89s

(f) t=2.77s

(c) t=1.95s

(g) t=3.69s

(d) t=2.23s

(h) t=4.42s

Fig. 4.7 Typical damage processes of the Guandi gravity dam under Koyna acceleration time histories with an amplitude of 0.7 g. a t = 1.84 s, b t = 1.89 s, c t = 1.95 s, d t = 2.23 s, e t = 2.32 s, f t = 2.77 s, g t = 3.69 s, and h t = 4.42 s (Amplification factor: 100)

4.3 Seismic Potential Failure Mode Analysis

91

change in the slope of the down face (Fig. 4.7a). With the on-going acceleration excitation, the crack extends deeper inside of the dam. During the next seconds, this crack propagates quickly and finally to the upstream face at 1.95 s, penetrating the whole section of the dam (Fig. 4.7c). In addition, a crack develops in the dam heel at 2.23 s, which is probably due to stress concentration (Fig. 4.7d). After the time instant t = 2.32 s, a crack in the middle of the dam is initiated at the change in the slope of the upstream face (Fig. 4.7e) and the tensile stress is remarkably concentrated here. With the continuous vibration of the dam, this crack continues to grow downward toward downstream in a slightly inclined direction (about 10° to the horizontal). The crack propagates up to 27 m and then grows upward toward downstream at an angle of about 50° with respect to the dam bottom (Fig. 4.7f-g). At t = 4.42 s, the upstream crack extends completely to the downstream face, penetrating the whole section of the dam (Fig. 4.7h). This finally separates a major portion of the structure and causes catastrophic failure.

4.3.3 Typical Failure Modes of the Guandi Gravity Dam for Each Record In order to obtain the potential failure modes of concrete gravity dams, 40 real earthquake records are selected as earthquake excitation. Each record is scaled to 8 increasing intensity levels in the stream direction to generate eight groups of acceleration excitations. More than 320 cases were calculated in the present study. But only some typical results are shown in this section. Typical cracking profiles of the Guandi gravity dam for each record at a certain shaking intensity level are shown in Fig. 4.8. The deformations of the dam at the end of the earthquakes can also be observed in Fig. 4.8. It should be noted that the deformation has been magnified 100 times. These figures depict the damage predicted for different real ground motions considered in this study. From the numerical results, it can be found that the selected real strong motion records have significant influence on the crack propagation process and the finial cracking profile of concrete gravity dams, which may be mainly because they have a different intensity parameter, such as the peak ground acceleration (PGA), the strong motion duration (SMD) and the spectral amplitudes for different characteristic periods. In addition to the previously mentioned three damage zones (the dam neck, dam heel, and change in upstream slope), other two damage zones (the downstream face and concrete partition junction) are also detected. Top cracking profiles are almost either nearly horizontal or sloping downward from the downstream face toward the upstream face. It can also be found from Fig. 4.8 that for concrete gravity dams, the dam neck is vulnerable to damage due to stress concentration. At this location, penetrated cracks are detected even under some smaller ground motions. In some records, there are uncompleted cracks at the neck of the

92

4 Seismic Potential Failure Mode Analysis of Concrete … PGA=0.7g

(a) No. 1

PGA=0.4g

(b) No. 2

PGA=0.3g

PGA=0.4g

(f) No. 6

(g) No. 7

PGA=0.6g

(c) No. 3 PGA=0.8g

(h) No. 8 PGA=0.4g

PGA=0.5g

PGA=0.6g

(d) No. 4

(e) No. 5

PGA=0.2g

PGA=0.5g

(i) No. 9 PGA=0.3g

(j) No. 10

PGA=0.4g

PGA=0.5g

(k) No. 11

(l) No. 12

PGA=0.5g

PGA=0.3g

PGA=0.8g

PGA=0.5g

PGA=0.6g

(p) No. 16

(q) No. 17

(r) No. 18

(s) No. 19

(t) No. 20

PGA=0.6g

(u) No. 21

PGA=0.5g

(v) No. 22

(m) No. 13

PGA=0.7g

(w) No. 23

(n) No. 14

PGA=0.8g

(x) No. 24

PGA=0.3g

(o) No. 15

PGA=0.6g

(y) No. 25

Fig. 4.8 Typical cracking profiles for the Guandi gravity dam under real earthquake records at different shaking intensity levels (amplification factor: 100)

4.3 Seismic Potential Failure Mode Analysis PGA=0.6g

PGA=0.4g

(z) No. 26

(aa) No. 27

PGA=0.4g

(ee) No. 31 PGA=0.5g

(jj) No. 36

PGA=0.7g

(ff) No. 32 PGA=0.6g

(kk) No. 37

93

PGA=0.8g

PGA=0.5g

(bb) No. 28

(cc) No. 29

PGA=0.34g

(dd) No. 30

PGA=0.7g

PGA=0.4g

PGA=0.5g

(gg) No. 33

(hh) No. 34

(ii) No. 35

PGA=0.6g

(ll) No. 38

PGA=0.6g

(mm) No. 39

PGA=0.6g

(nn) No. 40

Fig. 4.8 (continued)

dam. But in some earthquake analyses, there is no cracking at the neck of the dam. With the increasing acceleration excitation, cracks are predicted to initialize near the middle of the upstream face or the downstream face, and multiple failure modes occur in the dam, which may be because that the downstream and upstream surfaces as well as the dam heel of the dam are characterized by high tensile stress under strong ground motions.

4.3.4 Generalization of Potential Failure Modes for Concrete Gravity Dams From the 320 numerical simulation results, five typical failure modes are obtained, as shown in Fig. 4.9. The first failure mode (Fig. 4.9a) is cracking that initiates at the change in downstream slope and propagates almost perpendicular to the downstream surface for a certain distance. Then the cracking propagates approximately horizontally toward the upstream face and separates the crest from the upper part of

94

4 Seismic Potential Failure Mode Analysis of Concrete … I

v iv II

II

(a) Failure mode I

(b) Failure mode II

III

(c) Failure mode III

(d) Failure mode iv

(e) Failure mode v

Fig. 4.9 Typical failure modes of concrete gravity dams under strong ground motions. a Failure mode I, b Failure mode II, c Failure mode III, d Failure mode iv, and e Failure mode v

the dam. The second failure mode (Fig. 4.9b) is cracking that initiates at the dam heel and progresses a certain distance from the upstream face to the downstream face. In the third failure mode (Fig. 4.9c), cracking in the middle of the dam are initiated at the changes in the slope of the upstream face and propagate toward downstream in a slightly inclined direction. Finally the cracking reaches the downstream face. These cracks finally separate a major portion of the structure and cause catastrophic failure. The fourth failure mode (Fig. 4.9d) is cracking that initiates from the downstream face and travels almost normal to the initiation surface. Then the cracking propagates across another crack initiated from the change in upstream slope and finally penetrates the whole section of the dam. In the fifth failure mode (Fig. 4.9e), crack begins to initialize near the upper of the upstream face, which is especially easy for the concrete partition junction. Then it propagates approximately horizontally toward the opposite face and finally reaches the downstream face, with a cracking pattern that extends completely across the upper section. The first two failure modes can be caused by relatively minor earthquakes. Since the water pounding function of the reservoir is retained to a great extent, no disastrous results would occur toward the downstream areas. These latter three failure modes require much stronger seismic excitations (maybe 1.5 times the design PGA or even greater than that), as compared to the former two failure modes. Although earthquake shock much stronger than the design value is of low probability, the experiences from the Hsinfengkiang gravity dam in China, Koyna gravity dam in India, and Sefid Rud dam in Iran show that these could happen. The possible failure of these modes of dams retaining large quantities of water will cause the most undesirable impact on the downstream populated area along with a considerable amount of devastation. This enlightens the importance for the dam designers and related researchers to obtain insights into fracture mechanisms of the dam under various dynamic load cases. Understanding the failure pattern can also be used to assist in improving dam design and provide more realistic failure scenarios for subsequent dam break flood modeling.

4.4 Conclusions

95

4.4 Conclusions Dam failure will lead to catastrophic consequences including loss of human life and property damage. The objective of this study is to predict the possible failure modes of concrete gravity dams with considering the effects of dam-reservoir-foundation interaction. The reservoir water is modeled using two-dimensional fluid finite elements by the Lagrangian approach. The extended finite element method (XFEM) based on the cohesive segments method in conjunction with the phantom node technique is presented to deal with the numerical prediction of crack propagation in concrete gravity dams. 40 as-recorded strong ground motion records considered in this study are used as seismic excitations. The crack propagation processes and potential failure modes of the Guandi gravity dam with considering the effects of dam-reservoir-foundation interaction are investigated by applying the IDA method based on the XFEM. Damage and cracking of concrete gravity dams in earthquakes are caused mainly by excessive stress. The selected real strong motion records have significant influence on the crack propagation processes and the finial cracking profile of concrete gravity dams. The dam neck is vulnerable to damage, in which penetrated cracks are detected even under some smaller ground motions. With the increasing acceleration excitations, multiple failure modes occur in the dam. Cracks at the dam neck, dam heel and abrupt change in slope of upstream face are most often observed. Based on the 320 numerical simulation results, five typical failure modes are obtained. Cracks may mainly occur in the following regions: the discontinuity in the slope of the downstream face, the change in upstream slope, the dam heel, the downstream face and the concrete partition junction. The obtained potential failure modes of the dam can be used to assist in improving dam design and provide more realistic failure scenarios for subsequent dam break flood modeling.

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Chapter 5

Correlation Between Single Component Durations and Damage Measures of Concrete Gravity Dams

5.1 Introduction As is well known, earthquake ground motion can be characterized by amplitude, frequency content and strong motion duration, each of which reflects some particular feature of the shaking. Amplitude is generally characterized by the peak ground acceleration (PGA), the peak ground velocity (PGV) and the peak ground displacement (PGD). The frequency content is generally described by the Fourier spectrum of the ground motion. Nonetheless, both amplitude and frequency distribution can be described by the widely accepted response spectrum (in terms of acceleration, velocity, or displacement). The importance of the amplitude and frequency content has been universally recognized. However, the conclusions with regard to the relevance of strong motion duration to structural response differ widely, ranging from null to significant, which remains a topic of considerable debate. This is mainly because the influence of strong motion duration on structural response and damage depend on many factors including the type of structure examined, the construction model, the other parameters used to characterize the ground motion, the measure of structural damage employed, and the large number of widely differing duration definitions that have been proposed (Bommer et al. 2004, 2006; Hancock and Bommer 2006). There are more than 30 different definitions of strong motion duration (Bommer and Martínez-Pereira 1999). While there is no unanimous view regarding which of the definitions of strong motion duration is to be preferred, which probably reflects the fact that different definitions may be more or less suitable for different applications. Although a large number of definitions of strong motion duration have been presented in the literature, the available definitions can be grouped into four different categories: (a) bracketed duration (Ambraseys and Sarma 1967; Bolt 1973); (b) uniform duration (Bommer et al. 2009); (c) effective duration (Bommer and Martínez-Pereira 1999); (d) significant duration (Trifunac and Brady 1975). Subsequently, several new definitions and prediction models of strong motion duration have been put forward. For © Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_5

99

100

5 Correlation Between Single Component Durations and Damage …

example, Taflampas et al. (2009) proposed a new definition of strong motion duration combining the alternative bracketed and significant duration definitions based on the time integral of the absolute ground velocity, and their presented bracketedsignificant duration was found to be well correlated with the strong motion part of the records. Montejo and Kowalsky (2008) proposed a procedure for estimation of frequency dependent strong motion duration based on the continuous wavelet transform and the decomposition of the earthquake record. Arjun and Kumar (2011) developed a neural network approach for estimation of strong motion duration based on earthquake records and site characteristics. Yaghmaei-Sabegh et al. (2014) presented a simple and effective empirical model for predicting the significant duration of ground motions based on recorded earthquake events in Iran. Experiences from a number of earthquakes show that a ground motion with moderate peak ground acceleration and a long duration may cause greater strength and stiffness degradation than a ground motion with a large acceleration and a small duration (Bommer and Martínez-Pereira 1999). The duration of strong motion may significantly affect the damage of structures and plays an important role in assessing the damage potential of earthquake ground motions. However, current approaches for the earthquake-resistant design and structural analysis based on the response spectrum have not yet considered the influence of the ground motion duration. There are many studies reporting that link structural damage to parameters related either directly or indirectly to strong motion duration. However, the relevance of strong motion duration to structural response remains an open question, with some research indicating no effect (Cornell 1997; Shome et al. 1998) and other research indicating a possible correlation (Reinoso et al. 2000; Hancock and Bommer 2004). At least part of the reason that researches have differing conclusions on the importance of strong motion duration is the use of different duration definitions, structural models, and damage metrics. For example, Hancock and Bommer (2006) presented a summary and critical review of the literature with regard to the influence of strong motion duration on structural demand, and concluded that those studies employing damage measures related to cumulative energy usually found a positive correlation between strong motion duration and structural damage, while those using damage measures, such as maximum response parameters, generally found little or no correlations between duration and damage. In order to investigate the influence of the strong motion duration on structural response and damage, a substantial amount of research has been carried out over the past decades. Mahin (1980) found that strong motion duration might play an important role in the inelastic deformation and energy dissipation demands of short period structures. Léger and Leclerc (1996) suggested that short duration analytic records should not be used as a substitute for other types of more appropriate records in the earthquake safety evaluation of concrete dams. Youd et al. (2001) clearly recognized that the strong motion duration has profound effects on the behavior of saturated soil. Kunnath and Chai (2004) found that the long duration will increase inelastic design base shear. Bommer et al (2004) showed that the duration of strong motion can make a significant influence on the strength degradation of masonry structures. Iervolino

5.1 Introduction

101

et al. (2006) addressed the question of which nonlinear demand measures are sensitive to ground motion duration by statistical analyses of several case studies. The results led to the conclusion that duration of ground motion does not have a significant influence on displacement ductility and cyclic ductility demand. Hancock and Bommer (2007) revealed that duration of strong motion has no influence on damage measures employing the peak response such as inter-storey drift, but if cumulative parameters are used to measure the damage, the duration of strong motion is found to have a significant influence on the inelastic structural response. Ruiz-García (2010) conducted a comprehensive analytical study to evaluate the influence of strong motion duration on the residual displacement demands of SDOF and MDOF systems. They found that long duration ground motions may lead to larger median residual displacement ratios for SDOF systems, and tend to increase residual drift demands in the upper stories of MDOF systems. Sarieddine and Lin (2013) discussed the correlations between the strong motion duration and structural damage. They emphasized that there is no correlation between the structural response and ground motion duration. Raghunandan and Liel (2013) suggested that the ground motion duration should be considered in the structural design and assessment of seismic risk. Because the ground motion duration is found to have a significant influence on the collapse risk of the analyzed RC buildings. Ou et al. (2014) examined the seismic behavior of RC bridge columns under long duration ground motions. Their result indicated that the column tested under long duration ground motions shows a similar peak strength but a lower ductility capacity. Chandramohan et al. (2015) isolated and quantified the influence of ground motion duration on the structural collapse capacity of a modern steel moment frame and an RC bridge pier. They thought the significant duration definition is the most suitable metric to describe the strong motion duration for structural analysis. Hou and Qu (2015) concluded that duration of spectrally matched ground motions does not have the effect on the central tendency of ductility demand, but it has a significant influence on the hysteretic energy dissipation demands. Khaloo et al. (2016) investigated the influence of reducing earthquake record duration on fragility curves of RC frames. They concluded that the seismic performance of structures is dependent on ground motion duration of records when the energy-based or combination indices are employed as the damage measures. Chandramohan et al. (2016) developed a procedure to compute the source-specific probability distribution of the strong motion duration, and evaluated the influence of hazard-consistent ground motion duration on the collapse risk of an eight-story RC moment frame building. Barbosa et al. (2016) evaluated the effects of ground motion duration on structural damage of steel moment resisting frame buildings. Their results indicated that strong motions duration has a significant influence on the deformations and measures when the spectral accelerations are large. Belejo et al. (2017) found that the strong motion duration has little effect on the displacement and drift responses of the plan-asymmetric RC building, but it considerably affects the damage predicted using the Park-Ang and Reinhorn and Valles damage indices. Tombari et al. (2017) employed a beam nonlinear Winkler foundation model to investigate the effects of ground motion duration and soil nonlinearity on the seismic performance of single piles based on the incremental dynamic analysis method. Their results showed that

102

5 Correlation Between Single Component Durations and Damage …

the long ground motion duration will exacerbate the effects of the cyclic degradation/hardening and the gapping. Bravo-Haro and Elghazouli (2018) examined the influence of ground motion duration on the nonlinear dynamic response of steel moment frames considering the cyclic degradation effects. They found that long duration ground motions will increase the probability of collapse of steel moment frames, and considerably reduce the structural collapse capacity up to 40%. Pan et al. (2018) investigated the effects of strong motion duration on the seismic performance and collapse rate of three low-rise light-frame wood houses. Kiani et al. (2018) examined the role of the conditioning intensity measure in the influence of ground motion duration on the dynamic response of building structures. They found that ground motion duration considerably affects the structural response in terms of cumulative absolute velocity and spectral acceleration. Other conditioning intensity measures, such as the peak ground acceleration and velocity, spectrum intensity, and spectral acceleration, are not substantially affected by ground motion duration. Samanta and Pandey (2018) studied the effects of strong motion duration on the seismic performance of a fifteen storied building structure. They concluded that ground motion duration decreases the peak floor acceleration and average floor spectral acceleration only at higher hazard. Zhang et al. (2018) concluded that the ground motion duration has a significant influence on the seismic performance of high-rise intake towers in terms of the seismic displacement along the main stream. Molazadeh and Saffari (2018) investigated the destructive effects of strong motion duration on ductility and hysteretic energy dissipation demands of SDOF systems. Their results showed that the strong motion duration has a significant influence on the pinching-degrading behavior of SDOF systems with short periods. Kabir et al. (2019) evaluated the seismic fragility of a multi-span RC bridge subjected to near-fault, far-field and long duration ground motions. Their results showed that failure probabilities of bridge piers and isolation bearings are dominated by long duration ground motions than those of near-fault and far-fault ground motions. Kiani et al. (2019) examined the importance of ground motion duration on the risk-based structural responses, and thought the ground motion duration based on the definition of significant duration even in case of shallow events is an important parameter which should be considered in ground motion selection. Greco et al. (2019) discussed the correlation between the ground motion duration and damping reduction factor using the random vibration theory. Their results indicated that the damping reduction factor is sensitive to the ground motion duration, where the value of the damping reduction factor will diminish with the increase of effective duration values. Pan et al. (2019) studied the effects of long duration ground motions on the seismic performance and collapse capacity of a mid-rise wood frame building through incremental dynamic analysis method. Their results indicated that long duration ground motions will reduce the median collapse capacity by 18%, and increase the estimated median Park and Ang damage index by 36%. Pan et al. (2020) explored the seismic damage of four representative light-frame wood houses under long duration earthquakes, and developed the fragility curves for conventional low-rise light-frame wood buildings.

5.1 Introduction

103

It should be noted that few studies have focused their attention on the nonlinear dynamic response and seismic damage of concrete gravity dams subjected to earthquake motions with different strong motion durations. For example, Zhang et al. (2013a) investigated the effects of strong motion duration on the dynamic response and accumulated damage of concrete gravity dams based on the definition of significant duration. Their result showed that strong motion duration is insignificant to peak displacement response assessment. While studies employing damage measures using local and global damage indices showed that strong motion duration is positively correlated to the accumulated damage for events with similar response spectrum. Wang et al. (2018) investigated the strong duration effects on the nonlinear dynamic response of a dam-reservoir-foundation system. Their results indicated that the larger is the ground motion intensity, the more pronounced is the ground motion duration effects on dam responses. Xu et al. (2018) investigated the influence of strong motion duration on the seismic performance of high concrete-faced rockfill dams based on elastoplastic analysis. They found that the strong motion duration was positively correlated with the displacement and plastic shear strain, but weakly correlated with face-slab damage index. The objective of this chapter is to provide a method for quantifying the interrelationship between strong motion durations and damage measures of concrete gravity dams. 20 as-recorded accelerograms with a wide range of durations, which are scaled and matched to match a 5% damped target spectrum, are selected in this study. Three different definitions of significant duration, bracketed duration and uniform duration are presented for measuring strong motion durations. Local damage index, global damage index, peak displacement, and damage energy dissipation are employed as the measures of structural damage. A Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior is selected for the concrete material. Nonlinear dynamic response and seismic damage analyses of Koyna gravity dam under different strong motion durations are conducted to furnish the structural damage status. The interrelationships between the different strong motion durations and the damage measures are given.

5.2 Strong Motion Duration-Related Measure Used in this Study 5.2.1 Definitions of Strong Motion Duration for Single Component Ground Motion Any attempt to study on the correlation between strong motion durations and structural damage levels immediately faces the problem that there is currently no universally accepted definition of strong motion duration. Several researches in the past have been conducted for the quantification of strong motion duration (Shoji et al. 2005; Bommer et al. 2009; Taflampas et al. 2009; Arjun and Kumar 2011), and

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5 Correlation Between Single Component Durations and Damage …

there are more than 30 different definitions of strong motion duration (Bommer and Martínez-Pereira 1999) based on one component of ground motions. There is no clear consensus as to which of the multiple definitions of duration is to be preferred, which probably reflects the fact that different definitions may be more or less suitable for different applications. In the past, a number of researchers had proposed procedures to compute strong motion duration of an earthquake record. In general, the available definitions can be classified into four different groups: (a) Bracketed duration (T B ) (Ambraseys and Sarma 1967; Bolt 1973) in which the duration is defined as the time interval between the first and the last exceedances of a particular threshold of acceleration (usually 0.05 g); (b) Uniform duration (T U ) (Bommer et al. 2009), which rather than a continuous time window is defined as the sum of time intervals during which the record exceeds a particular acceleration threshold; (c) Effective duration (T E ) (Bommer and Martínez-Pereira 1999) that defines the duration of strong motion as the time interval between two particular thresholds of the Arias intensity, and; (d) Significant duration (T S ) (Trifunac and Brady 1975), it is defined to be the interval between the time at which a given percentage of Arias intensity of the record is reached. Most of the proposed definitions are applied directly to recordings of the ground motion, but a few apply one of these generic definitions to dynamic response of structures. Within the four generic definitions, distinction, which is related to whether the thresholds of acceleration or energy are absolute values or defined relative to the maximum value attained in the accelerogram, can also be found. Absolute definition includes bracketed duration (T B ), uniform duration (T U ) and effective duration (T E ), and relative definition contains significant duration. Among different seismic parameters, attention is focused on those which have a high level of correlation with the examined damage indices. The definition of effective duration is not considered in this study because it is very difficult to ascertain the particular thresholds of the Arias intensity for the effective duration. Therefore, the bracketed duration, the uniform duration, and the significant duration according to Trifunac/Brandy are chosen in this study. The uniform duration only considers the intervals for which the ground acceleration is above the threshold, which differs from the bracketed duration, therefore uniform duration is always shorter than bracketed duration for a given acceleration record, as shown in Fig. 5.1. For these two definitions, the absolute threshold such as 0.05 g or 0.10 g can be used. It is well known that the destructiveness of a seismic excitation can be described using several intensity parameters. The Arias intensity (Arias 1970) is an energyrelated seismic index which is designed to reflect the total energy content of a seismic excitation, and is defined by the following relation:

Absolute acceleration (g)

Absolute acceleration (g)

Acceleration (g)

5.2 Strong Motion Duration-Related Measure Used in this Study 0.3 0.2 0.1 0.0 -0.1 -0.2 -0.3

105 Acceleration record

0

2

4

6

Time (s)

8

10

(a) A natural accelerogram 0.3 0.2

Accelaration record Bracketed duration (TB )

Absolute threshold 0.05g

0.1

TB=3.76s

0.0 0

2

4

Time (s)

6

8

10

(b) The diagram of bracketed duration 0.3

Accelaration record Uniform duration (TU )

0.2

Absolute threshold 0.05g TU=2.36s

0.1 0.0 0

2

4

Time (s)

6

8

10

(c) The diagram of uniform duration

Fig. 5.1 Diagram of bracketed and uniform durations of a natural accelerogram

π I0 = 2g

T0 a 2 (t)dt

(5.1)

0

where, I 0 is the Arias intensity, T 0 is the total duration of the record and a is the ground acceleration. Trifunac and Brady (1975) have defined the significant duration of strong ground motion as the time interval between 5 and 95% of the Arias intensity. For this definition, the Husid diagram (Husid 1969) is used. The Husid diagram is the time history of the seismic energy content scaled to the total energy content and it is given by H (t) =

π 2g

t 0

a 2 (t)dt I0

(5.2)

where, a is the ground acceleration and H(t) is the Husid diagram as a function of time t. The Husid diagram of a natural accelerogram is shown in Fig. 5.2. In this figure strong motion duration after Tricunac/Brandy can be computed easily.

106

5 Correlation Between Single Component Durations and Damage …

gravity dams

Acceleration (g)

0.3

0.0

-0.3

0

10

20

Arias intensity (%)

100

85%

80

40

Time (s)

50

60

95%

T70%

60

T90%

40 20 0

30

5%

H(t) T70%=18.73s T90%=26.04s

15%

0

10

20

30

40

Time (s)

50

60

Fig. 5.2 Husid diagram of a natural accelerogram

Because the thresholds of Arias intensity used in this study are relative to the total Arias intensity of the record, the symbol T S (significant duration) is used, with the subscript indicating the relative threshold. Two definitions of T S(70%) (15–85%) (Takizawa and Jennings 1980) and T S(90%) (5–95%) (Trifunac and Brady 1975) are used, as shown in Fig. 5.2. The first strong motion duration is defined as the time interval between 15 and 85% of the Husid diagram and the second strong motion duration is defined as the time interval between 5 and 95% of the Husid diagram. The former definition is intended to capture the energy from the body waves whereas the latter includes the full wave train. The T S is defined by the following relation TS = T2 − T1 

H (T1 ) = 15% or H (T2 ) = 85%



H (T1 ) = 5% H (T2 ) = 95%

(5.3)

(5.4)

where, T S is the significant duration of ground motion, T 2 is the time at the 85% or 95% of the Husid diagram and T 1 is the time at the 15% or 5% of the Husid diagram.

5.2 Strong Motion Duration-Related Measure Used in this Study

107

5.2.2 Accelerogram Selection and Correction In order to identify the relationship between the accumulated damage and strong ground motion duration, 20 real earthquake records used in this study have been selected from the databases of the COSMOS (COSMOS 2019) and PEER (PEER 2019) with a broad distribution of durations. Table 5.1 shows the data of the acceleration time history with different earthquake magnitudes (i.e. M w 6.0–7.8) that have occurred in the United States, Taiwan and India. The data sample includes worldwide well-known earthquakes with strong seismic activity, such as the Loma Prieta (1989), Northridge (1994), and Chi-Chi (1999) events. For the purpose of analyzing strong motion duration effects on nonlinear demand, it is necessary to minimize the influence of the spectral amplitude and other factors. The ground motion records are normalized to have the same peak ground acceleration (PGA) equal to 0.3 g. Besides, the accelerograms are scaled and matched to the target spectrum at a given damping level using the SeismoSignal. The SeismoSignal uses wavelets to adjust the accelerograms to match the response spectra, while minimizing changes to the other ground motion characteristics. The adjusted accelerograms have a good match on average to the target spectrum, which ensures that the main difference between the records is the strong motion duration. The modified records with different range durations are illustrated in Fig. 5.3, and the corresponding response spectrum is shown in Fig. 5.4.

5.2.3 Strong Motion Duration Prediction In order to develop vector predictions of duration in conjunction with other groundmotion parameters related to amplitude and energy content. Three different levels of peak ground acceleration (PGA) are considered for the input motions: 0.25, 0.30 and 0.35 g. Among different strong motion durations, attention is focused on those which have a high level of correlation with the examined damage measures. Therefore, the definitions of the significant, bracketed, and uniform duration are used in this study. According to these definitions, strong motion durations for all seismic excitations described in Table 5.1 are calculated, as shown in Table 5.2. The duration parameters of the non-modified real accelerograms are also given in Table 5.2. It can be seen from Table 5.2 that these earthquakes with larger PGA will increase absolute measures like bracketed duration (T B ) and uniform duration (T U ) whereas the relative measures [e.g. significant duration: T S(70%) (15–85%) and T S(90%) (5–95%)] are not influenced by the increased amplitude.

Earthquake

Koyna

Northridge

Northridge

Loma Prieta

Chi-Chi

Petrolia

Northridge

Loma Prieta

Chi-Chi

Landers

Northridge

Loma Prieta

Superstition Hills

Kern County

Landers

San Simeon

Parkfield

No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

28-09-2004

22-12-2003

28-06-1992

21-07-1952

24-11-1987

18-10-1989

17-01-1994

28-06-1992

20-09-1999

18-10-1989

17-01-1994

17-08-1991

20-09-1999

18-10-1989

17-01-1994

17-01-1994

11-12-1967

Date

14

14.8

10.0

36.2

13.0

11.9

8.6

28.6

7.9

15.9

18.4

11.7

8.3

17.2

15.7

35.8

13.0

Distance to fault (km)

Table 5.1 Strong motion database (non-modified records)

USGS Parkfield Dense #02

Caltrans Bridge Grnds #37737

Joshua Tree #22170

Lincoln School #1095

Westmorland, CA #11369

Santa Teresa Hills #57563

Los Angeles Dam #2141

Whitewater Canyon #5072

Taichung, Taiwan #TCU072

Capitola, CA #47125

Los Angeles Mulholland Dr #5314

General Store #89156

Taichung, Taiwan #TCU078

South St and Pine Dr #47524

Epiphany Litheran Church #5353

Los Angeles Terrace #24592

Koyna Dam

Station location

6.0

6.5

7.3

7.5

6.6

7.0

6.7

7.3

7.6

7.0

6.7

6.0

7.6

7.0

6.7

6.7

6.5

Mw

360

90

90

111

180

315

334

270

360

90

35

90

0

90

196

180

0

Comp.

(continued)

170.00

175.00

278.40

175.95

203.56

223.40

419.10

124.92

360.10

390.80

641.90

488.70

301.80

174.50

404.20

310.10

480.20

PGA (cm/s2 )

108 5 Correlation Between Single Component Durations and Damage …

Earthquake

Imperial Valley

Northridge

Chi-Chi

No.

18

19

20

Table 5.1 (continued)

20-09-1999

17-01-1994

15-10-1979

Date

8.9

12.5

9.8

Distance to fault (km)

Taichung, Taiwan #TCU050

Coldwater Canyon School #5309

Casa Flores Mexicali #6619

Station location

7.6

6.7

6.5

Mw

0

180

0

Comp.

127.50

313.30

238.10

PGA (cm/s2 )

5.2 Strong Motion Duration-Related Measure Used in this Study 109

110

5 Correlation Between Single Component Durations and Damage … 1

2

3

0.6 g

7

13

11

15

14

18

17

16

6

10

9

8

12

5

4

20

19

20 s

Fig. 5.3 Acceleration time histories for the modified strong motion records used in this study. For ground motion information see Table 5.1

gravity dams

3.0

Amplification factor

2.5 2.0 1.5 1.0 0.5 0.0 0

1

2

Period (s)

3

4

Fig. 5.4 Acceleration spectrum for scaled earthquake records

5.2.4 Correlation Analysis Figure 5.5 shows the correlation between total duration and different duration definitions of the modified records with a PGA of 0.30 g, and Fig. 5.6 illustrates a case of correlation between significant duration (15–85% Arias intensity) and other different duration definitions of the modified records with a PGA of 0.30 g. As shown, it is known that although durations calculated using different definitions are generally poorly correlated with the total duration, there is an approximate correlation between

Northridge

Northridge

Loma Prieta

Chi-Chi

Petrolia

Northridge

Loma Prieta

Chi-Chi

Landers

Northridge

Loma Prieta

Superstition Hills

Kern County 54.22

Landers

2

3

4

5

6

7

8

9

10

11

12

13

14

15

40.00

59.82

25.00

26.55

56.55

40.00

39.82

25.00

10.00

60.00

40.00

20.00

20.00

10.00

Koyna

1

T 0 (s)

Earthquake

No.

21.48

13.86

8.82

6.60

4.06

23.59

15.24

8.48

4.46

2.00

18.73

13.00

7.14

5.49

26.08

28.86

17.04

9.32

6.67

31.36

23.55

13.16

7.62

3.26

26.04

23.70

10.12

10.27

31.44

33.84

23.24

16.28

7.02

43.04

30.52

14.62

9.28

3.76

31.31

33.18

13.74

14.31

31.10

32.98

23.20

15.18

6.66

40.18

25.02

14.46

8.56

3.70

31.28

25.98

11.12

12.03

6.92

PGA = 0.25 g

PGA = 0.35 g

36.68

35.34

23.24

19.46

9.01

49.16

30.56

14.62

9.28

5.14

31.33

33.22

16.58

16.21

8.98

14.14

8.50

7.44

6.62

3.08

20.00

12.38

5.74

3.76

2.36

12.24

10.60

6.22

4.82

2.62

11.88

6.44

5.76

5.74

2.43

16.84

10.53

4.88

3.12

1.90

10.05

8.08

5.12

3.72

2.16

PGA = 0.25 g

PGA = 0.30 g

6.92

PGA = 0.30 g

5.02

T S(90%)

T S(70%)

3.08

Uniform duration T U (s)

Bracketed duration T B (s)

Significant duration T S (s)

Table 5.2 Strong motion durations obtained from modified records

(continued)

16.48

10.74

8.78

7.60

3.62

22.58

14.40

6.62

4.44

2.74

14.27

12.74

7.20

5.94

3.11

PGA = 0.35 g

5.2 Strong Motion Duration-Related Measure Used in this Study 111

Earthquake

San Simeon

Parkfield

Imperial Valley

Northridge

Chi-Chi

No.

16

17

18

19

20

Table 5.2 (continued)

50.00

21.86

16.95

20.00

25.00

T 0 (s)

17.62

8.20

6.65

6.41

25.77

15.86

10.56

11.63

33.52

18.82

16.27

16.58

32.55

18.80

15.69

14.86

9.14

PGA = 0.25 g

PGA = 0.35 g

34.02

19.04

16.69

18.68

11.66

18.61

6.30

7.02

5.93

3.28

16.05

5.06

5.87

4.81

2.39

PGA = 0.25 g

PGA = 0.30 g

10.97

PGA = 0.30 g

10.19

T S(90%)

T S(70%)

5.86

Uniform duration T U (s)

Bracketed duration T B (s)

Significant duration T S (s)

20.51

7.66

8.03

6.99

4.09

PGA = 0.35 g

112 5 Correlation Between Single Component Durations and Damage …

Strong motion duration (s)

5.2 Strong Motion Duration-Related Measure Used in this Study

113

TS(70%)(15~85%) TS(90%)(5~95%) TB (0.05g) TU (0.05g)

40 30 20 10 0

0

10

20

30

40

Total duration (s)

50

60

Strong motion duration (s)

Fig. 5.5 Correlation between total duration and different definitions of duration (PGA = 0.3 g)

TS(90%)(5~95%) TB (0.05g) TU (0.05g)

40 30 20 10 0

0

5

10

15

20

Significant duration TS(70%) (15~85%) (s)

25

Fig. 5.6 Correlation between significant duration [T S(70%) (15–85%)] and different definitions of duration (PGA = 0.3 g)

significant duration [T S(70%) (15–85%)] and other different definitions of duration for these modified records used in this study. This is because the records have been scaled to have the same PGA, and have been matched to the target spectrum at a given damping level.

5.3 Seismic Accumulated Damage Indices We evaluate the effects of mainshock-aftershock seismic sequences on accumulated damage based on the ultimate state of the dam. As a new indicator that means the soundness of a dam against crack penetration failure, both local and global damage indices are proposed to assess the accumulated damage of structures quantitatively. In this model, the global damage is obtained as a weighted average of the local damage at the ends of each element, with the dissipated energy as the weighting function. The local damage index (Fig. 5.7) is given by the following relation:

114

5 Correlation Between Single Component Durations and Damage …

The length of the residual path in crack path 1 where cracking did not occur

lD1 L1

The length of the residual path in crack path 2 where cracking did not occur

lD2

L2

Fig. 5.7 Establishment of the crack paths

 D I Li =

l Di Li

 (5.5)

where, DI Li is the local damage index for crack path i, L i is the total length to which crack path i is expected to grow, and lDi is the length of the damage path in crack path i. The damage of a crack at an element integration point is indicated by shading the related area with red color. As shown in Fig. 5.7, crack paths along the damaged elements are obtained. The residual crack paths are established a priori, and assumed to propagate approximately horizontally toward the opposite face, with a cracking pattern that extends completely across the section. In the present case, the global damage index is a weighted average of the local damage indices and the damage dissipation is chosen as the weighting function. The global damage index is given by D IG =

n i=1 D I Li E i  n i=1 E i

(5.6)

where, DI G is the global damage index, DI Li is the local damage index, E i is the damage dissipation energy at the crack path i (the energy dissipated in the whole (or partial) model by damage), n is the number of crack paths at which the local damage is computed.

5.4 Seismic Damage Analysis of Koyna Dam

115

5.4 Seismic Damage Analysis of Koyna Dam 5.4.1 Description of Koyna Gravity Dam Model Used for Evaluation The Koyna concrete gravity dam in India, 103 m high, and 70.2 m wide at its base, which is one of a few concrete dams that have experienced a destructive earthquake, is selected as an application. Finite element model for the tallest section of the dam is shown in Fig. 5.8. The mesh of the dam is adequately refined at the base and near the changes in the slope of the downstream face, in which the crack propagation is expected. The reason is that damage due to tensile stresses is expected to initiate near stress concentrations in those zones. The foundation of the dam is taken as being rigid. The material parameters of the Koyna dam concrete are as follows: the elasticity modulus E = 3.1 × 104 MPa, the Poisson’s ratio ν = 0.2, the mass density ρ = 2643 kg/m3 , the fracture energy is 250 N/m. The tensile and compressive strength of the dam are 2.9 and 24.1 MPa, respectively. A dynamic magnification factor of 1.2 is considered for the tensile strength to account for strain rate effects. The energy dissipation of the monolith is considered by the Rayleigh damping method with 5% damping ratio. The maximum reservoir water level of 96.5 m is considered. Applied

Fig. 5.8 Finite element model of Koyna dam

116

5 Correlation Between Single Component Durations and Damage …

loads include self-weight of the dam, hydrostatic, uplift, hydrodynamic, and earthquake forces. The static solution of the dam due to its gravity loads and hydrostatic loads is taken as initial conditions in the dynamic analyses of the system. Westergaard virtual mass (Westergaard 1933) is employed to include the hydrodynamic effect.

5.4.2 Strong Motion Duration Effects on Accumulated Damage of Concrete Gravity Dams Earthquakes often lead to stiffness and strength deterioration of structures. For two earthquake ground motions with similar spectral amplitude but of different duration, the motion of longer duration would be expected to more damaging. Hence, the duration of earthquake ground motion should be considered an important parameter in addition to the maximum amplitude and frequency content for adequately characterizing the effect of earthquake ground motion on seismic damage of structures. In order to investigate the effects of strong motion duration on the accumulated damage of concrete gravity dams, the dynamic damage analyses of Koyna gravity dam under selected real earthquakes are conducted employing the Concrete Damaged Plasticity (CDP) model developed by Lubliner et al. (1989) and modified by Lee and Fenves (1998) (see Zhang et al. 2013b) for a detailed description of the constitutive model). The integration time step used in the analysis is 0.01 s. Only the one component (horizontal) of the seismic input is considered in these analyses, which are conducted considering 20 different earthquake records, with records selected to represent a wide range of intensities from relatively weak motions to very strong shaking. These records are modified to match a 5% damped target spectrum. The accumulated damage profiles of Koyna dam during the modified real accelerograms with a PGA of 0.3 g are shown in Fig. 5.9. These figures depict the damage predicted for different range durations of real ground motions considered in this study. The shaded area related to red color indicates those elements that experienced some level of tensile damage over the duration of the analysis. As shown, the crack propagation process and failure modes are obtained. From the cracking profiles shown in Fig. 5.9a–t, it can be observed that the failure mechanism is formed of two main damage zones, one at the base and one in the upper part of the dam. In almost all the analyses, the cracking is always initiated at the dam heel which may be due to stress concentration, and then progresses a long way from the upstream face to the downstream face. These cracking profiles in the upper part of the dam are always initiated near the discontinuity in the slope of the downstream face. Top cracking profiles are almost either nearly horizontal or sloping downward from the downstream face toward the upstream face at approximately a 45° angle to the vertical. The crack trajectory curves down due to the compressive stresses resulting from rocking of the top block. But in some analyses, cracks are predicted to initialize near the middle of the upstream face or the downstream face, and extend into the dam. Because of the thrust of impounded water which is opposing the tendency of the top section to

5.4 Seismic Damage Analysis of Koyna Dam TS (70%)=3.08s TS (90%)=5.02s TB=6.92s TU=2.62s

(a) No. 1 TS (70%)=2.00s TS (90%)=3.26s TB=3.76s TU=2.36s

(f) No. 6 TS (70%)=4.06s TS (90%)=6.67s TB=7.02s TU=3.08s

(k) No. 11 TS (70%)=5.86s TS (90%)=10.19s TB=10.97s TU=3.28s

(p) No. 16

TS (70%)=5.49s TS (90%)=10.27s TB=14.31s TU=4.82s

TS (70%)=7.14s TS (90%)=10.12s TB=13.74s TU=6.22s

117 TS (70%)=13.00s TS (90%)=23.70s TB=33.18s TU=10.60s

(b) No. 2

(c) No. 3

(d) No. 4

TS (70%)=4.46s TS (90%)=7.62s TB=9.28s TU=3.76s

TS (70%)=8.48s TS (90%)=13.16s TB=14.62s TU=5.74s

TS (70%)=15.24s TS (90%)=23.55s TB=30.52s TU=12.38s

(g) No. 7 TS (70%)=6.60s TS (90%)=9.32s TB=16.28s TU=6.62s

(l) No. 12 TS (70%)=6.41s TS (90%)=11.63s TB=16.58s TU=5.93s

(q) No. 17

(h) No. 8

(i) No. 9

TS (70%)=18.73s TS (90%)=26.04s TB=31.31s TU=12.24s

(e) No. 5 TS (70%)=23.59s TS (90%)=31.36s TB=43.04s TU=20.00s

(j) No.10

TS (70%)=8.82s TS (90%)=17.04s TB=23.24s TU=7.44s

TS (70%)=13.86s TS (90%)=28.86s TB=33.84s TU=8.5s

TS (70%)=21.48s TS (90%)=26.08s TB=31.44s TU=14.14s

(m) No. 13

(n) No. 14

(o) No. 15

TS (70%)=6.65s TS (90%)=10.56s TB=16.27s TU=7.02s

TS (70%)=8.20s TS (90%)=15.86s TB=18.82s TU=6.30s

TS (70%)=17.62s TS (90%)=25.77s TB=33.52s TU=18.61s

(r) No. 18

(s) No. 19

(t) No. 20

Fig. 5.9 Cracking profiles for Koyna dam under modified real accelerations with a PGA of 0.30 g (for ground motion information see Table 5.1)

118

5 Correlation Between Single Component Durations and Damage …

slide along the crack in the upstream direction, the computed crack profiles in the upper part of the dam can be considered neutral or favorable conditions to maintain stability. For the seismic motions associated with a short duration, the actual response of the dam will exhibit some tensile cracking, and some small damage is identified. But it will not drastically affect the results of the dynamic behavior of the dam. On the other hand, the cases associated with a moderate duration, the moderate damage is found, but it does not seem to reach a level that could compromise the integrity of the section. However, the results corresponding to the input motions with a long duration clearly show indications of significant strength degradation in the dam, with a cracking pattern that extends completely across the upper section. Longer duration will lead to greater accumulate damage to which aseismic design of the dam should be given attention.

5.5 Correlation Study Between Strong Motion Durations and Damage Measures The influence of strong motion duration on nonlinear structural response, however, remains a topic of much debate and universal conclusions are unlikely to reached since the resolution of the issue is complicated by the variety of definitions of duration and the variety of structural behavior, as well as the difficulty of decoupling the specific effect of duration from other features of the ground motion. In order to analysis the interrelationships between the different strong motion durations and the damage measures, both relative (15–85% significant duration and 5–95% significant duration) and absolute (0.05 g bracketed duration and 0.05 g uniform duration) definitions are used to determine the influence of ground motion duration on different damage measures such as peak displacement, local damage index, global damage index and damage energy dissipation. The seismic response analyses are carried out by scaling each input record, to progressively increase the intensity of ground shaking by increments of about 0.05 g. Real earthquake records are scaled to different intensity levels in order to produce responses ranging from elastic to large nonlinear responses of the dam. A further aspect which has been taken into consideration is the expected damage potential of strong motion duration on concrete gravity dams to be analyzed.

5.5.1 Damage Measures of Local and Global Damage Indices After the nonlinear dynamic response analyses of the examined concrete gravity dam for all the selected accelerograms at different intensity levels, the peak displacement and damage energy dissipation are obtained, and the local and global damage indices

5.5 Correlation Study Between Strong Motion Durations …

119

are computed according to Eqs. (5.5) and (5.6) for each seismic excitation. The damage index values for each used accelerogram are given in Table 5.3. The influence of strong motion duration on the damage of concrete gravity dams is illustrated by using different symbols for different levels of duration on plots of average spectral accelerations versus damage indices. Correlations are also made between strong motion duration and peak displacement and damage energy dissipation. As mentioned above, the failure mechanism is formed by two main damage zones, one at the base and one in the upper part of the dam. Hence, two local damage indices are calculated. To analyze the effects of strong motion duration on the accumulated damage of concrete gravity dams, Figs. 5.10, 5.11 and 5.12 are generated by plotting the accumulated damage of the dam imparted by the 20 records for a given level of intensity in terms of local and global damage indices. Trend lines (straight lines) for each level of intensity are displayed with the aim of identifying a general tendency (if any). This also applies to the other figures of this type in the article. However, S-from trend lines are fitted to the plots to show the general trends for the correlation between strong motion duration and local damage index of the dam heel. In some cases, the S-form trend lines are also used to identify the correlation between the uniform duration and damage measures. The trend lines show that, as would be expected, the local and global damage indices of the examined dam during the modified real accelerograms with longer duration are generally greater than that under shorter events for the same level of spectral acceleration. It can also be found that the ground motions with greater peak ground acceleration (PGA) would cause greater damage to concrete gravity dams than smaller events. However, the correlation is relatively weak with significant overlap between uniform duration and damage measures with different PGA (Fig. 5.10d, 5.11d, and 5.12d). The damage demand examined by the significant duration (15–85% significant duration and 5–95% significant duration) is proportional to the peak ground acceleration of ground motions. Results from the bracketed duration and uniform duration measures are not very similar. This is because the relative measures (significant duration) are not influenced by the increased amplitude. As can be seen from Figs. 5.10, 5.11 and 5.12, studies employing damage measures using local and global damage indices show that strong motion durations calculated from different definitions (bracketed duration, uniform duration and significant duration) are all positively correlated to the accumulated damage for events with similar response spectrum. Damage measures such as the local damage index for the dam upper zone and global index for the dam are consistently greater for ground motions with longer duration. While, the accumulated damage on the dam heel is not very sensitive to strong motion duration. The accumulated damage for the upper zone of the dam is more sensitive to ground motion duration, which gives more importance to the dissipated energy during the hysteretic behavior of the structure since the high seismic response zone is mainly located in the upper zone of the dam. After the long duration earthquake, more significant accumulated damage remains in the upper zone of the dam due to plastic strain during cyclic loadings.

The upper part of the dam

Global damage index

Northridge

Loma Prieta 0.20

Chi-Chi

Petrolia

Northridge

Loma Prieta 0.17

Chi-Chi

Landers

Northridge

Loma Prieta 0.13

Superstition 0.16 Hills

Kern County

3

4

5

6

7

8

9

10

11

12

13

14

0.20

0.05

0.23

0.17

0.10

0.09

0.20

0.19

0.14

Northridge

2

0.08

Koyna

0.23

0.22

0.17

0.08

0.26

0.22

0.22

0.14

0.14

0.24

0.27

0.25

0.19

0.09

0.27

0.27

0.22

0.11

0.31

0.25

0.25

0.17

0.17

0.28

0.31

0.28

0.22

0.14

0.36

0.23

0.17

0.02

0.69

0.38

0.25

0.18

0.05

0.58

0.40

0.26

0.08

0.08

0.64

0.44

0.28

0.15

1.00

0.63

0.42

0.30

0.10

0.90

0.61

0.48

0.26

0.21

0.90

0.55

0.41

0.21

1.00

0.86

0.64

0.38

0.13

1.00

0.79

0.65

0.32

0.28

0.25

0.18

0.14

0.04

0.35

0.22

0.19

0.12

0.08

0.29

0.25

0.21

0.12

0.08

0.34

0.28

0.20

0.10

0.44

0.32

0.27

0.18

0.13

0.40

0.36

0.31

0.21

0.12

(continued)

0.43

0.34

0.27

0.14

0.48

0.40

0.35

0.23

0.16

0.46

0.44

0.38

0.25

0.18

PGA (0.25 g) PGA (0.30 g) PGA (0.35 g) PGA (0.25 g) PGA (0.30 g) PGA (0.35 g) PGA (0.25 g) PGA (0.30 g) PGA (0.35 g)

The dam heel

Local damage index

1

No. Earthquake

Table 5.3 Damage index values (for ground motion information see Tables 5.1 and 5.2)

120 5 Correlation Between Single Component Durations and Damage …

The upper part of the dam

Global damage index

Parkfield

Imperial Valley

Northridge

Chi-Chi

17

18

19

20

0.22

0.16

0.14

0.14

San Simeon 0.20

16

0.22

Landers

0.26

0.19

0.17

0.20

0.25

0.25

0.31

0.22

0.22

0.23

0.28

0.30

0.40

0.34

0.21

0.24

0.30

0.59

0.75

0.44

0.43

0.31

0.32

0.90

1.00

0.67

0.55

0.55

0.54

1.00

0.27

0.20

0.16

0.17

0.23

0.31

0.39

0.25

0.24

0.23

0.27

0.42

0.50

0.34

0.31

0.32

0.35

0.48

PGA (0.25 g) PGA (0.30 g) PGA (0.35 g) PGA (0.25 g) PGA (0.30 g) PGA (0.35 g) PGA (0.25 g) PGA (0.30 g) PGA (0.35 g)

The dam heel

Local damage index

15

No. Earthquake

Table 5.3 (continued)

5.5 Correlation Study Between Strong Motion Durations … 121

5 Correlation Between Single Component Durations and Damage …

0.3

Local damage index

Local damage index

122

0.2

0.1

0.0

PGA=0.30g PGA=0.25g PGA=0.35g 0

5

10

15

20

0.3

0.2

0.1

0.0

25

Duration (s)

PGA=0.30g PGA=0.25g PGA=0.35g 0

5

0.3

0.2

0.1

0.0

PGA=0.30g PGA=0.25g PGA=0.35g 0

10

20

30

40

15

20

Duration (s)

25

30

35

(b) Significant, TS (90%) (5-95%)

Local damage index

Local damage index

(a) Significant duration, TS (70%) (15-85%)

10

0.3

0.2

0.1

0.0

50

PGA=0.30g PGA=0.25g PGA=0.35g 0

5

10

Duration (s)

15

20

25

Duration (s)

(c) Bracketed duration, TB (0.05g)

(d) Uniform duration, TU (0.05g)

1.0 0.8 0.6 0.4

PGA=0.30g PGA=0.25g PGA=0.35g

0.2 0.0

0

5

10

15

20

Local damage index

Local damage index

Fig. 5.10 Influence of strong motion duration on the local damage index measure for the dam heel. a T S(70%) (15–85%); b T S(90%) (5–95%); c T B (0.05 g); d T U (0.05 g) 1.0 0.8 0.6 0.4

0.0

25

PGA=0.30g PGA=0.25g PGA=0.35g

0.2 0

5

10

(a) Significant duration, TS (70%) (15-85%)

25

30

35

1.0

0.8 0.6 0.4

PGA=0.30g PGA=0.25g PGA=0.35g

0.2 0

10

20

30

40

Duration (s)

(c) Bracketed duration, TB (0.05g)

50

Local damage index

Local damage index

20

(b) Significant, TS (90%) (5-95%)

1.0

0.0

15

Duration (s)

Duration (s)

0.8 0.6 0.4

PGA=0.30g PGA=0.25g PGA=0.35g

0.2 0.0

0

5

10

15

20

25

Duration (s)

(d) Uniform duration, TU (0.05g)

Fig. 5.11 Influence of strong motion duration on the local damage index measure for the upper part of the dam. a T S(70%) (15–85%); b T S(90%) (5–95%); c T B (0.05 g); d T U (0.05 g)

5.5 Correlation Study Between Strong Motion Durations … 0.5

0.4 0.3 0.2

PGA=0.30g PGA=0.25g PGA=0.35g

0.1 0.0

0

5

10

15

20

Global damage index

Global damage index

0.5

123

0.4 0.3 0.2

0.0

25

PGA=0.30g PGA=0.25g PGA=0.35g

0.1

0

5

10

Duration (s)

(a) Significant duration, TS (70%) (15-85%)

25

30

35

0.5

0.4 0.3 0.2

PGA=0.30g PGA=0.25g PGA=0.35g

0.1

0

10

20

30

Duration (s)

40

(c) Bracketed duration, TB (0.05g)

50

Global damage index

Global damage index

20

(b) Significant, TS (90%) (5-95%)

0.5

0.0

15

Duration (s)

0.4 0.3 0.2

PGA=0.30g PGA=0.25g PGA=0.35g

0.1 0.0

0

5

10

15

Duration (s)

20

25

(d) Uniform duration, TU (0.05g)

Fig. 5.12 Influence of strong motion duration on the global damage index measure for the dam. a T S(70%) (15–85%); b T S(90%) (5–95%); c T B (0.05 g); d T U (0.05 g)

5.5.2 Damage Measures of Peak Displacement and Damage Energy Dissipation To analyze the effects of strong motion duration on the damage of concrete gravity dams, Fig. 5.13 is generated to identify whether the peak displacement response of the dam is related to strong motion duration, and Fig. 5.14 are generated by plotting the damage energy dissipation of the dam imparted by the 20 records for a given level of intensity. From Fig. 5.13, it can be observed that there is no significant relationship between any of the three duration definitions (bracketed duration, uniform duration, and significant duration) under consideration and the damage measure based on the peak displacement of the structure. However, the results from the damage energy dissipation measure are similar to that from the local and global index measures. Stronger duration dependence might be found for higher loading levels, which would cause greater deformation and damage energy dissipation in the dam. From Fig. 5.14, it can also be noticed that the bracketed and uniform durations significantly increase the scatter of damage measures around the trend lines.

124

5 Correlation Between Single Component Durations and Damage … 6

5 4 3 2

PGA=0.30g PGA=0.25g PGA=0.35g

1 0 0

5

10

15

Duration (s)

20

Peak displacement (cm)

Peak displacement (cm)

6

5 4 3 2

PGA=0.30g PGA=0.25g PGA=0.35g

1 0

25

0

10

15

20

Duration (s)

25

30

35

(b) Significant, TS (90%) (5-95%)

(a) Significant duration, TS (70%) (15- 85%) 6

6

5 4 3 2

PGA=0.30g PGA=0.25g PGA=0.35g

1 0 0

10

20

30

Duration (s)

40

Peak displacement (cm)

Peak displacement (cm)

5

5 4 3 2

PGA=0.30g PGA=0.25g PGA=0.35g

1 0

50

0

(c) Bracketed duration, TB (0.05g)

5

10

15

20

Duration (s)

25

(d) Uniform duration, TU (0.05g)

80

PGA=0.30g PGA=0.25g PGA=0.35g

60 40 20 0

0

5

10

15

20

25

Damage energy dissipation (kN.m)

Damage energy dissipation (kN.m)

Fig. 5.13 Influence of strong motion duration on peak displacement of the dam. a T S(70%) (15– 85%); b T S(90%) (5–95%); c T B (0.05 g); d T U (0.05 g) 80

PGA=0.30g PGA=0.25g PGA=0.35g

60 40 20 0

0

5

10

Duration (s)

40 20 0

0

10

20

30

Duration (s)

(c) Bracketed duration, TB (0.05g)

40

50

Damage energy dissipation (kN.m)

Damage energy dissipation (kN.m)

PGA=0.30g PGA=0.25g PGA=0.35g

60

20

25

30

35

(b) Significant, TS (90%) (5-95%)

(a) Significant duration, TS (70%)(15-85%) 80

15

Duration (s)

80

PGA=0.30g PGA=0.25g PGA=0.35g

60 40 20 0

0

5

10

15

20

25

Duration (s)

(d) Uniform duration, TU (0.05g)

Fig. 5.14 Influence of strong motion duration on the damage energy dissipation measure for the dam. a T S(70%) (15–85%); b T S(90%) (5–95%); c T B (0.05 g); d T U (0.05 g)

5.5 Correlation Study Between Strong Motion Durations …

125

5.5.3 Identifying the Influence of Single Component Duration on Damage Measures The above analyses show that strong motion duration has significant influence on the local damage of the dam upper part, the global damage, and the damage energy dissipation. Hence, Fig. 5.15 mainly shows the comparison of the correlations between strong motion duration and these damage measures during the modified real accelerograms with a PGA of 0.3 g. The trend lines in Fig. 5.15 show that the events with longer duration generally cause greater damage on the dam than the shorter events for the same level of spectral acceleration. The findings do indicate that the seismic performance of concrete gravity dams would be improved by taking account of the expected duration of earthquake ground motion. The comparison of the scatter of the observations around the trend lines illustrated in Fig. 5.15 indicates that the significant duration obtained based on the time between 15 and 85% of the Arias intensity, is the duration measure which slightly more correlates with accumulated damage. This is to be expected, as this measure is the best indication to assess the potential damage energy of earthquake ground motion, as noted earlier. However, duration measures with 5–95% significant duration, 0.05 g bracketed duration and 0.05 g uniform duration generally increase the scatter of the damage measures around the trend lines. In order to justify this assertion and emphasize the grade of interrelation 0.5

Global damame index

Local damame index

1.0 0.8 0.6 0.4

TS(70%) (15~85%) TS(90%) (5~95%) TB (0.05g) TU (0.05g)

0.2 0.0

0

10

20

30

0.4 0.3 0.2

0.0

40

TS(70%) (15~85%) TS(90%) (5~95%) TB (0.05g) TU (0.05g)

0.1

0

10

Duration (s)

(a) The local damage index measure for the dam upper part Damage energy dissipation (kN.m)

20

30

40

Duration (s)

(b) The global damage index measure

30

20 TS(70%) (15~85%) TS(90%) (5~95%) TB (0.05g) TU (0.05g)

10

0

0

10

20

30

40

Duration (s)

(c) Damage energy dissipation measure

Fig. 5.15 Comparison of the correlations between strong motion duration with different definitions and a the local damage index measure for the dam upper part; b the global damage index measure; c damage energy dissipation measure

126

5 Correlation Between Single Component Durations and Damage …

between strong motion duration and damage measures, the correlation coefficient (R) has been used, which is defined by the following relation: N

¯ i − y¯ ) (xi − x)(y  N ¯ 2 ¯ )2 i=1 (x i − x) i=1 (yi − y

R =  N

i=1

(5.7)

where x i and x¯ are the actual and its average values; yi and y¯ are the predicted and its average values; and N denotes the number of data in the analysis. The values (R) of correlation coefficients between strong motion durations with different definitions and damage measures are tabulated in Table 5.4. Correlation coefficients between absolute durations with different thresholds (0.05 and 0.10 g bracketed durations, 0.05 and 0.10 g uniform durations) and damage measures are also compared in Table 5.4. Through the correlation coefficients presented in Table 5.4, it can be seen that the strong motion duration as defined by Trifunac and Brady has a very high correlation with accumulated damage and damage energy dissipation. This is due to the fact that their definition does take into account the seismic energy content. The two kinds Table 5.4 Values (R) of correlation coefficient between strong motion duration and damage measures Damage measures The local damage index measure for the dam upper part

Duration measures

PGA(0.25 g)

PGA(0.30 g)

PGA(0.35 g)

T S(70%) (15–85%)

0.942

0.980

0.940

T S(90%) (5–95%)

0.894

0.938

0.939

T B (0.05 g)

0.884

0.926

0.896

T U (0.05 g)

0.831

0.916

0.886

T B (0.10 g)

0.851

0.926

0.887

T U (0.10 g)

0.766

0.843

0.815

0.908

0.929

0.888

0.892

0.917

0.886

T B (0.05 g)

0.872

0.909

0.877

T U (0.05 g)

0.814

0.872

0.860

T B (0.10 g)

0.522

0.371

0.307

The global damage index T S(70%) (15–85%) measure for the dam T S(90%) (5–95%)

The damage energy dissipation measure for the dam

The value (R) of correlation coefficient

T U (0.10 g)

0.476

0.345

0.285

T S(70%) (15–85%)

0.920

0.930

0.913

T S(90%) (5–95%)

0.880

0.913

0.898

T B (0.05 g)

0.865

0.881

0.884

T U (0.05 g)

0.823

0.813

0.828

T B (0.10 g)

0.486

0.429

0.437

T U (0.10 g)

0.447

0.374

0.382

5.5 Correlation Study Between Strong Motion Durations …

127

of significant durations (T S(70%) (15–85%) and T S(90%) (5–95%)) provide almost the same interrelation grade between the examined damage measures. It must be pointed out that the duration measure predicted by the 15–85% significant duration has shown a slightly higher correlation with accumulated damage when compared with the 5– 95% significant duration. However, both of them have a higher correlation when compared with the absolute duration. Compare the correlations between damage measures and absolute durations with different thresholds (0.05 and 0.10 g), it can be seen that there is a very high correlation between damage measures and absolute duration with 0.05 g threshold. On the other hand, a very poor correlation can be observed between damage measures and absolute duration with 0.10 g threshold. Among the examined definitions of strong motion duration, the 15–85% significant duration has the strongest correlation with the local damage indices. The analyses presented in this chapter show that for ground motions with comparable modified real records, those with longer duration or greater magnitude generally cause greater damage, as measured by local damage index and global damage index, in concrete gravity dams. This is simply an empirical verification of expected structural behavior, which suggests that shorter strong motion duration records should not be used as the seismic motion input in the earthquake safety evaluation of concrete gravity dams. It should be noted that the correlation grade between the examined strong motion durations and the damage indices presented in this study is valid for the specific case of spectrum compatible accelerograms as presented in Sect. 5.2. Further investigations will be carried out using the abundant strong motion records.

5.6 Conclusions Researchers have shown increasing interest in relating the structural damage caused by earthquakes to parameters associated with ground motion duration. In this chapter, a methodology for quantifying the interrelationship between strong motion durations and damage measures of concrete gravity dams is presented. The questions which definition of the strong motion duration is the most useful indicator of earthquake damage potential and which damage measure is the most useful index of the structural performance are evaluated. The nonlinear dynamic response and seismic damage process of concrete gravity dams during ground motions with different durations are conducted according to the Concrete Damaged Plasticity (CDP) model. The local damage index, global damage index, peak displacement response and damage energy dissipation are considered as the damage measures. 20 real earthquake records with a wide range of durations, which are scaled to match the target spectrum at a given damping level, are considered in this study. The definitions of significant duration, bracketed duration and uniform duration are used for characterizing the strong motion duration. From the calculated durations with different definitions, it can be found that durations are generally poorly correlated

128

5 Correlation Between Single Component Durations and Damage …

with the total duration. However, there is an approximate correlation between significant duration [T S(70%) (15–85%)] and other different definitions of duration for these modified records. The results show that, for concrete gravity dams, the influence of strong motion duration (measured by different definitions) depends on both the peak ground acceleration and the damage measure employed. Although measure using peak response is predominantly used in design and assessment applications because of their conceptual simplicity, the damage measure based on the peak displacement response exhibits a poor correlation with the duration of the ground motion. However, strong motion duration has been found to be significant to the cumulative damage of the dam. Damage measures such as local damage index, global damage index and damage energy dissipation are consistently greater for ground motions with longer duration. Among the examined definitions of strong motion duration, the 15–85% significant duration has the strongest correlation with the accumulated damage, as this duration definition is intended to assess the potential damage energy of earthquake ground motions. T S(70%) (15–85%) displays the highest correlation coefficient with the local damage index for the dam upper part. Good correlation can be observed between damage measures and absolute duration with 0.05 g threshold, whereas absolute duration with 0.10 g threshold provides poor or fair correlation with damage measures. The influence of duration depends on a number of different factors including the definition of strong motion duration, damage measure, strong motion record, and structural model. These promising results are the starting point for further exploration, of more seismic records and of other types of dams.

References Ambraseys, N. N., & Sarma, S. K. (1967). The response of earth dams to strong earthquakes. Geotechnique, 17(3), 181–213. Arias, A. (1970). A measure of earthquake intensity. Seismic Design for Nuclear Power Plants RJ Hanson, 438–483. Arjun, C. R., & Kumar, A. (2011). Neural network estimation of duration of strong ground motion using Japanese earthquake records. Soil Dynamics and Earthquake Engineering, 31(7), 866–872. Barbosa, A. R., Ribeiro, F. L. A., & Neves, L. A. C. (2016). Influence of earthquake groundmotion duration on damage estimation: application to steel moment resisting frames. Earthquake Engineering & Structural Dynamics. Belejo, A., Barbosa, A. R., & Bento, R. (2017). Influence of ground motion duration on damage index-based fragility assessment of a plan-asymmetric non-ductile reinforced concrete building. Engineering Structures, 151, 682–703. Bolt, B. A. (1973). Duration of strong ground motion. In Proceedings 5th World Conference on Earthquake Engineering (pp. 1304–1313), Rome, Italy. Bommer, J. J., Hancock, J., & Alarcón, J. E. (2006). Correlations between duration and number of effective cycles of earthquake ground motion. Soil Dynamics and Earthquake Engineering, 26(1), 1–13.

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Lubliner, J., Oliver, J., Oller, S., & Onate, E. (1989). A plastic-damage model for concrete. International Journal of Solids and Structures, 25(3), 299–326. Mahin, S. A. (1980). Effects of duration and aftershocks on inelastic design earthquakes. Istanbul, 5, 677–680. Molazadeh, M., & Saffari, H. (2018). The effects of ground motion duration and pinching-degrading behavior on seismic response of SDOF systems. Soil Dynamics and Earthquake Engineering, 114, 333–347. Montejo, L. A., & Kowalsky, M. J. (2008). Estimation of frequency-dependent strong motion duration via wavelets and its influence on nonlinear seismic response. Computer-Aided Civil and Infrastructure Engineering, 23(4), 253–264. Ou, Y., Song, J., Wang, P., Adidharma, L., Chang, K., & Lee, G. (2014). Ground motion duration effects on hysteretic behavior of reinforced concrete bridge columns. Journal of Structural Engineering, 140(3), 4013065. Pan, Y., Ventura, C. E., & Finn, W. D. L. (2018). Effects of ground motion duration on the seismic performance and collapse rate of light-frame wood houses. Journal of Structural Engineering, 144(8), 4018112. Pan, Y., Ventura, C. E., Finn, W. D. L., & Xiong, H. (2019). Effects of ground motion duration on the seismic damage to and collapse capacity of a mid-rise woodframe building. Engineering Structures, 197, 109451. Pan, Y., Ventura, C. E., & Tannert, T. (2020). Damage index fragility assessment of low-rise lightframe wood buildings under long duration subduction earthquakes. Structural Safety, 84, 101940. PEER. (2019). Pacific Earthquake Engineering Research Center, http://peer.berkeley.edu/peer_g round_motion_database/. Raghunandan, M., & Liel, A. B. (2013). Effect of ground motion duration on earthquake-induced structural collapse. Structural Safety, 41, 119–133. Reinoso, E., Ordaz, M., & Guerrero, R. U. L. (2000). Influence of strong ground-motion duration in seismic design of structures (p. 1151). Ruiz-García, J. (2010). On the influence of strong-ground motion duration on residual displacement demands. Earthquakes and Structures, 1(4), 327–344. Samanta, A., & Pandey, P. (2018). Effects of ground motion modification methods and ground motion duration on seismic performance of a 15-storied building. Journal of Building Engineering, 15, 14–25. Sarieddine, M., & Lin, L. (2013). Investigation correlations between strong-motion duration and structural damage. Structures Congress, 10, 2926–2936. Shoji, Y., Tanii, K., & Kamiyama, M. (2005). A study on the duration and amplitude characteristics of earthquake ground motions. Soil Dynamics and Earthquake Engineering, 25(7), 505–512. Shome, N., Cornell, C. A., Bazzurro, P., & Carballo, J. E. (1998). Earthquakes, records, and nonlinear responses. Earthquake Spectra, 14(3), 469–500. Taflampas, I. M., Spyrakos, C. C., & Koutromanos, I. A. (2009). A new definition of strong motion duration and related parameters affecting the response of medium-long period structures. Soil Dynamics and Earthquake Engineering, 29(4), 752–763. Takizawa, H., & Jennings, P. C. (1980). Collapse of a model for ductile reinforced concrete frames under extreme earthquake motions. Earthquake Engineering & Structural Dynamics, 8(2), 117– 144. Tombari, A., Naggar, M. H. E., & Dezi, F. (2017). Impact of ground motion duration and soil nonlinearity on the seismic performance of single piles. Soil Dynamics and Earthquake Engineering, 100, 72–87. Trifunac, M. D., & Brady, A. G. (1975). A study on the duration of strong earthquake ground motion. Bulletin of the Seismological Society of America, 65(3), 581–626. Wang, C., Hao, H., Zhang, S., & Wang, G. (2018). Influence of ground motion duration on responses of concrete gravity dams. Journal of Earthquake Engineering, 1–25. Westergaard, H. M. (1933). Water pressures on dams during earthquakes. Trans. ASCE, 98, 418–432.

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Xu, B., Wang, X., Pang, R., & Zhou, Y. (2018). Influence of strong motion duration on the seismic performance of high CFRDs based on elastoplastic analysis. Soil Dynamics and Earthquake Engineering, 114, 438–447. Yaghmaei-Sabegh, S., Shoghian, Z., & Neaz Sheikh, M. (2014). A new model for the prediction of earthquake ground-motion duration in Iran. Natural Hazards, 70(1), 69–92. Youd, T. L., Idriss, I. M., Andrus, R. D., Arango, I., Castro, G., Christian, J. T., et al. (2001). Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils. Journal of Geotechnical and Geoenvironmental Engineering, 127(10), 817–833. Zhang, S., Wang, G., Pang, B., & Du, C. (2013a). The effects of strong motion duration on the dynamic response and accumulated damage of concrete gravity dams. Soil Dynamics and Earthquake Engineering, 45, 112–124. Zhang, S., Wang, G., & Sa, W. (2013b). Damage evaluation of concrete gravity dams under mainshock–aftershock seismic sequences. Soil Dynamics and Earthquake Engineering, 50, 16–27. Zhang, H. Y., Zhang, L. J., Wang, H. J., & Guan, C. N. (2018). Influences of the duration and frequency content of ground motions on the seismic performance of high-rise intake towers. Engineering Failure Analysis, 91, 481–495.

Chapter 6

Integrated Duration Effects on Seismic Performance of Concrete Gravity Dams

6.1 Introduction Ground motions induced by earthquake events contain three translational components, which can be directly recorded by strong-motion seismometers. When time history analyses are performed to evaluate the seismic performance of important infrastructures (e.g. high dams, bridges and tall buildings), the effects of ground motion components should be considered, and as-recorded accelerograms including multiple components are usually selected as the seismic excitation. For concrete gravity dams, both the vertical and stream components of earthquake ground motions are usually considered in two-dimensional models (Calayir and Karaton Calayir and Karaton 2005; Omidi et al. 2013; Zhang et al. 2013a, b; Hariri-Ardebili and Saouma 2015; Wang et al. ; Hariri-Ardebili et al. 2016a, b), whereas stream, cross-stream and vertical motions are usually selected as seismic excitations for three-dimensional analyses (when required) (Wang et al. 2012; Arici et al. 2014). On the other hand, the seismic response analysis of arch dams is, in general, conducted based on threedimensional models, in which three components of earthquake ground motions are applied simultaneously (Engineering Manual 1110-2-6051 2003; Hariri-Ardebili and Kianoush 2014; Hariri-Ardebili et al. 2016a, b). Earthquake ground motions can be characterized by three main parameters (i.e. amplitude, frequency content, and duration). As one of the major characteristics of ground motions, the effects of strong motion duration on seismic demands imposed on structures have been widely studied (Bommer et al. 2004; Raghunandan and Liel 2013; Zhang et al. 2013a, b; Ou et al. 2014; Song et al. 2014; Chandramohan et al. 2015; Hou and Qu 2015; Wang et al. 2015a, b, c; Kiani et al. 2018; Molazadeh and Saffari 2018; Pan et al. 2018; Samanta and Pandey 2018; Zhang et al. 2018; Kabir et al. 2019). A common argument is that the degree of influence of duration on structural damage depends on several factors including the definition of strong

© Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_6

133

134

6 Integrated Duration Effects on Seismic Performance …

motion duration, the type of structure examined, the strong motion record selected as seismic excitations, and the demand measures used to quantify the damage (Hancock and Bommer 2006). An important issue encountered in the duration effect analysis is to determine the strong motion duration of ground motions. As summarized in Ref (Bommer and Martínez-Pereira 1999), more than 30 different strong motion duration definitions have been presented in the literature and without being exhaustive, some contributions are worth mentioning. There are four typical and widely used definitions of strong motion duration, i.e. (a) bracketed duration (Ambraseys and Sarma 1967; Bolt 1973); (b) uniform duration (Bommer et al. 2009); (c) effective duration (Bommer and Martínez-Pereira 1999), and; (d) significant duration (Trifunac and Brady 1975), and then classified by whether the amplitude or energy thresholds used for their measurement are absolute or relative to the peak value in the recording. Subsequently, several new definitions and prediction models of strong motion duration have been put forward. Subsequently, several new definitions and prediction models of strong motion duration have been put forward (Kempton and Stewart 2006; Bommer et al. 2009; Taflampas et al. 2009; Yaghmaei-Sabegh et al. 2014). It should be emphasized that all the aforementioned duration definitions can only determine the strong motion duration based on one component of ground motions, either horizontal seismic excitation or vertical one. However, multiple components of earthquake ground motions are usually selected as seismic excitations in practice. To account for the duration contributions of all ground motion components, Wang et al. (2015a, b, c) proposed a concept of integrated duration based on the integrated Husid diagram. Nonetheless, this definition of integrated duration can only calculate the significant duration of multi-component ground motions. This study aims to answer the question how to predict the integrated duration when selecting multiple components of ground motions for structural response analysis. For this purpose, a general concept of integrated duration is proposed based on the existing definitions of strong motion duration. Integrated Bracketed duration, integrated uniform duration, and integrated significant duration are chosen as the duration measures. The peak displacement, maximum principal stress, damage dissipation energy, and local damage index are adopted as the seismic demands. The relationship between integrated and single horizontal or vertical durations is investigated based on 20 as-recorded accelerograms with a wide range of duration. A series of nonlinear dynamic analyses is performed to quantify the effects of integrated duration and vertical seismic excitations on the nonlinear response of concrete gravity dam-reservoir-foundation systems. The results reveal the correlation between different integrated durations and damage measures.

6.2 A General Definition of Integrated Duration

135

6.2 A General Definition of Integrated Duration 6.2.1 Single Component Duration As mentioned above, the most widely used measures for the strong motion duration based on one component of ground motions can be classified into four categories: (a) bracketed duration (T B ) (Ambraseys and Sarma 1967; Bolt 1973); (b) uniform duration (T U ) (Bommer et al. 2009); (c) effective duration (T E ) (Bommer and MartínezPereira 1999); (d) significant duration (T S ) (Trifunac and Brady 1975). In this study, the definition of effective duration is not considered since it is very difficult to obtain the particular thresholds of the Arias intensity for each record. The bracketed duration (T B ) and uniform duration (T U ) belong to the class of absolute duration definitions. One specific acceleration threshold (i.e. 0.05 g) is considered for both the absolute duration definitions in this study. In contrast, the significant duration (T S ) is a relative duration concept in the sense that the significant duration is unaffected by the scaling of ground motion records.

6.2.2 Integrated Duration of Multi-component Ground Motions In seismic performance analysis, multiple components of ground motions are usually chosen as seismic excitations for structures. In order to bridge the gap between strong motion duration and multi-component excitations, a general definition of integrated duration is proposed based on the existing concepts of strong motion duration. As well known, the destructiveness of ground motions can be characterized by several intensity parameters. The Arias intensity I 0 is a popular energy-related seismic intensity metric reflecting the total energy content of a ground motion. With the Arias intensity being selected as the weighting function, the integrated duration is proposed to be a weighted average of the corresponding single component duration. Take two-component excitations for example, the proposed integrated duration (T I ) can be defined as TI =

T H × I0H + T V × I0V I0H + I0V

(6.1)

where I0H and I0V are the Arias intensities of horizontal and vertical components, respectively. T H and T V are the strong motion durations of horizontal and vertical components, respectively. Note that T H and T V can be calculated based on any aforementioned duration definitions. For three-component excitations, the integrated duration (T I ) can also be easily obtained as follows

136

6 Integrated Duration Effects on Seismic Performance …

TI =

T H1 × I0H1 + T H2 × I0H2 + T V × I0V I0H1 + I0H2 + I0V

(6.2)

where T H1 and T H2 are the strong motion durations of two perpendicular horizontal components; I0H1 and I0H2 are the Arias intensities of the two horizontal ground motions. In this chapter, we focus on two-component ground motions (with horizontal and vertical components) since the seismic response of concrete gravity dams is investigated based on a 2D model. According to Eq. (6.1) and single component duration definitions, integrated bracketed duration (TBI ), integrated uniform duration (TUI ), and integrated significant duration (TSI ) can be obtained, serving as a unified duration measure of two-component ground motions. For example, the integrated bracketed duration (TBI ) can be calculated by the following relation TBI =

TBH × I0H + TBV × I0V I0H + I0V

(6.3)

where TBH and TBV are the bracketed duration of horizontal and vertical components, respectively. For illustrative purpose, the entire calculation process of the integrated bracketed duration is shown in Fig. 6.1 for an as-recorded accelerogram.

Fig. 6.1 Illustration of the integrated bracketed duration

6.3 Database of as-Recorded Acceleration Records

137

6.3 Database of as-Recorded Acceleration Records 6.3.1 Accelerogram Selection and Integrated Duration Prediction This study focuses on how to determine the integrated durations and their effects on the nonlinear dynamic demands imposed to concrete gravity dams. For this purpose, as-recorded acceleration time histories with two components are needed for performing nonlinear dynamic analyses. In this contribution, a total of 20 real earthquake records from around the world, covering a broad range of duration, are used with each of which containing two accelerograms (horizontal and vertical components). The relevant information of these earthquakes, obtained from the database provided by the Consortium of Organizations for Strong Motion Observation Systems (COSMOS) (COSMOS 2019), is summarized in Table 6.1. This information contains the magnitude, the epicenter distance, the total duration T 0 , and the peak ground acceleration (PGA). In order to isolate and quantify the influence of duration on the nonlinear dynamic response of concrete gravity dams, it is necessary to minimize the effects of PGA, spectral amplitude and other ground motion characteristics. All horizontal accelerograms are normalized to have a PGA of 0.3 g, and the PGA of vertical accelerograms is scaled to 0.2 g (two thirds of the horizontal PGA). The spectral acceleration of all horizontal ground motions is scaled and adjusted to have a good match on average to the target spectrum (as shown in Fig. 6.2) by using wavelets. Vertical accelerograms are also adjusted along with horizontal components. By doing so, the major difference between these records is ensured to be the strong motion duration. Based on the aforementioned definitions, both the single component and integrated strong motion durations are calculated for all seismic excitations listed in Table 6.1, which are summarized in Table 6.2.

6.3.2 Relationship Between Integrated and Single Component Durations In order to study whether the integrated durations have similar duration distribution as their corresponding single component durations, the relationship between integrated and single component durations is investigated in this section. Furthermore, the correlation between horizontal and vertical component durations is also analyzed. To measure the linear correlation between strong motion durations, the Pearson correlation coefficient is calculated. Based on the single component durations listed in Table 6.2, relationship between horizontal and vertical component durations is shown in Fig. 6.3. The correlation coefficients are also provided in this figure for each duration definition. As can

138

6 Integrated Duration Effects on Seismic Performance …

Table 6.1 List of as-recorded earthquake ground motions with two components (non-modified records) No. Earthquake

Date

Station location

M w Distance T 0 (s) Original record to fault PGA(cm/s2 ) (km) Horizontal Vertical

1

Koyna

11-12-1967 Koyna Dam

6.5

13.0

10.00

480.20

333.20

2

Northridge

17-01-1994 Los Angeles Terrace #24592

6.7

35.8

20.00

310.10

131.90

3

Northridge

17-01-1994 Epiphany 6.7 Litheran Church #5353

15.7

20.00

404.20

409.52

4

Loma Prieta 18-10-1989 South St and Pine Dr #47524

7.0

17.2

40.00

174.50

193.21

5

Chi-Chi

20-09-1999 Taichung, Taiwan #TCU078

7.6

8.3

60.00

301.80

170.37

6

Petrolia

17-08-1991 General Store 6.0 #89156

11.7

10.00

488.70

164.30

7

Northridge

17-01-1994 Los Angeles Mulholland Dr #5314

6.7

18.4

25.00

641.90

331.40

8

Loma Prieta 18-10-1989 Capitola, CA #47125

7.0

15.9

39.82

390.80

500.10

9

Chi-Chi

20-09-1999 Taichung, Taiwan #TCU072

7.6

7.9

40.00

360.10

276.00

10

Landers

28-06-1992 Whitewater Canyon #5072

7.3

28.6

56.55

124.92

110.97

11

Northridge

17-01-1994 Los Angeles Dam #2141

6.7

8.6

26.55

419.10

316.50

12

Loma Prieta 18-10-1989 Santa Teresa Hills #57563

7.0

11.9

25.00

223.40

205.02

13

Superstition 24-11-1987 Westmorland, 6.6 Hills CA #11369

13.0

59.82

203.56

187.63

14

Kern County

21-07-1952 Lincoln 7.5 School #1095

36.2

54.22

175.95

102.85

15

Landers

28-06-1992 Joshua Tree #22170

7.3

10.0

40.00

278.40

177.73

16

San Simeon 22-12-2003 Caltrans Bridge Grnds #37737

6.5

14.8

25.00

175.00

86.65

(continued)

6.3 Database of as-Recorded Acceleration Records

139

Table 6.1 (continued) No. Earthquake

Date

Station location

M w Distance T 0 (s) Original record to fault PGA(cm/s2 ) (km) Horizontal Vertical

17

Parkfield

28-09-2004 USGS Parkfield Dense #02

6.0

18

Imperial Valley

15-10-1979 Casa Flores Mexicali #6619

6.5

19

Northridge

17-01-1994 Coldwater 6.7 Canyon School #5309

20

Chi-Chi

20-09-1999 Taichung, Taiwan #TCU050

7.6

14

20.00

170.00

86.00

9.8

16.95

238.10

327.70

12.5

21.86

313.30

256.25

8.9

50.00

127.50

85.95

Amplification factor

3.0 Target spectrum Adjusted spectrum

2.5 2.0 1.5 1.0 0.5 0.0 0

1

2

3

4

Period (s) Fig. 6.2 Acceleration spectrum for scaled earthquake records

be seen, the horizontal component duration calculated using five definitions under consideration is positively related to the corresponding vertical duration. In general, this means that the longer the horizontal duration is, the larger the vertical duration is. It can also be seen that the significant duration measure (TS(5−95%) ) gives much higher correlation coefficient as compared with the uniform duration definition. Figure 6.4 depicts the correlation between integrated durations calculated using different definitions and their corresponding single component durations for horizontal and vertical accelerograms. The values (R) of correlation coefficient are summarized in Table 6.3. In order to investigate the influence of the PGA of vertical

Vertical component

Integrated duration (s)

3.08

5.49

7.14

13.00

18.73

2.00

4.46

8.48

15.24

23.59

4.06

6.60

8.82

13.86

21.48

5.86

6.41

6.65

8.20

17.62

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

18.40

7.00

5.71

5.83

5.05

21.58

10.50

9.98

6.24

3.75

20.33

15.34

5.56

5.04

2.24

15.83

9.42

6.42

5.69

2.42

25.77

15.86

10.56;

11.63

10.19

26.08

28.86

17.04

9.32

6.67

31.36

23.55

13.16

7.62

3.26

26.04

23.7

10.12

10.27

5.02

33.52

18.82

16.27

16.58

10.97

31.44

33.84

23.24

16.28

7.02

43.04

30.52

14.62

9.28

3.76

31.31

33.18

13.74

14.31

6.92

18.61

6.30

7.02

5.93

3.28

14.14

8.50

7.44

6.62

3.08

20.00

12.38

5.74

3.76

2.36

12.24

10.60

6.22

4.82

2.62

9.51

6.62

8.26

8.58

7.79

22.28

20.26

11.38

6.38

4.21

21.20

11.05

6.02

5.12

3.34

18.46

13.12

4.84

7.05

3.84

9.33

5.86

8.09

7.20

6.75

22.50

15.42

11.02

7.30

4.09

20.14

13.42

6.30

5.56

3.78

17.11

8.90

5.54

7.42

3.37

18.17

11.20

12.96

14.76

13.17

26.34

33.58

15.92

10.74

7.59

31.36

24.59

10.64

8.76

6.96

25.63

23.10

10.70

11.98

5.58

20.87

11.52

15.38

19.72

14.23

29.86

39.24

17.34

11.52

8.04

24.01

20.19

11.54

10.26

5.06

32.77

13.48

7.84

14.62

7.94

5.00

3.56

5.62

6.52

3.74

9.66

6.44

5.62

3.12

2.06

7.66

3.66

4.3

3.28

1.64

7.92

2.80

2.22

3.00

2.66

17.63

8.28

7.31

7.71

6.73

21.51

16.30

10.10

6.48

3.96

21.69

14.73

6.70

5.08

2.60

18.53

13.36

6.74

7.00

3.59

20.37

6.84

6.16

7.36

6.69

22.72

11.62

12.04

6.48

4.63

20.66

15.24

5.72

5.26

3.6

15.99

11.02

6.36

8.31

2.95

26.62

16.26

11.33

13.65

12.02

26.38

30.20

17.86

9.75

7.38

29.45

23.23

12.84

7.79

4.15

25.52

24.38

10.26

11.43

5.29

31.17

16.83

15.99

18.18

12.44

30.91

36.00

21.17

15.17

7.36

37.83

28.57

13.52

9.70

4.21

31.78

29.68

12.54

14.45

7.39

16.08

5.55

6.58

6.23

3.49

12.62

7.68

6.80

5.80

2.74

16.62

10.73

5.22

3.55

2.11

10.86

9.21

5.41

4.01

2.64

H H H H H V V V V v I I I I I Ts(15−85%) Ts(5−75%) Ts(5−95%) TB(0.05g) TU(0.05g) Ts(15−85%) Ts(5−75%) Ts(5−95%) TB(0.05 g) TU(0.05 g) Ts(15−85%) Ts(5−75%) Ts(5−95%) TB(0.05 g) TU(0.05 g)

Horizontal component

No. Single component duration (s)

Table 6.2 Strong motion durations obtained from modified records

140 6 Integrated Duration Effects on Seismic Performance …

Vertical component duration (s)

6.3 Database of as-Recorded Acceleration Records 40

TS(15-85%)

35

TS(5-95%)

141

TS(5-75%) TB(0.05g)

30

R=0.946

TU( 0.05g)

25

R=0.774

20 15

R=0.887

10 R=0.897 5 0

R=0.637

0

10

20

30

40

50

Horizontal component duration (s)

Fig. 6.3 Correlation between horizontal and vertical component durations

accelerograms on the correlation between integrated and single component durations, the vertical accelerograms are also scaled to have the same PGA with that of horizontal components. The corresponding correlation coefficients are also tabulated in Table 6.3. As shown, the integrated durations predicted by the proposed general definition are positively correlated with their corresponding single component durations (both horizontal and vertical components). Overall, the correlation coefficients for the horizontal component are higher than those of the vertical component. This is because that the Arias intensity is selected as the weighting function. Due to the seismic characteristics of the selected records, the average value of the Arias intensity for horizontal accelerations is greater than that of vertical accelerations. In addition, it can be seen that the difference of the correlation coefficient between horizontal and vertical components relies on the adopted duration definition. More specifically, the correlation difference is small for significant and bracketed durations, whereas uniform duration gives much larger correlation difference. When the PGA of vertical accelerograms is changed from two thirds of the horizontal PGA to full horizontal PGA, a certain decline in the correlation coefficient between integrated and horizontal durations is observed, whereas the correlation coefficient between integrated and vertical durations slightly increases.

6.4 Influence of Two-Component Ground Motions on Nonlinear Dynamic Response In order to identify the effects of integrated duration and two-component seismic excitations on the structural response, the Koyna concrete gravity dam is selected as the representative numerical example. In order to model the dam-reservoirfoundation interaction system, the Lagrangian finite element formulation is utilized

6 Integrated Duration Effects on Seismic Performance …

25

Single component duration (s)

Single component duration (s)

142 Horizontal component Vertical component

20

R=0.988

15 10 R=0.924

5 0

5

10

15

20

Integrated duration (s)

20

10

Horizontal component Vertical component

25 20 15

R=0.948

10 R=0.995

5 0

5

10

15

20

Integrated duration (s)

0

25

30

40

5

10

15

Integrated duration (s)

20

Horizontal component Vertical component

30

R=0.989

20 10

R=0.853

0

(c) Significant duration ( TS(5 -95%) ) Single component duration (s)

R=0.885

5

(b) Significant duration ( TS(5 - 75%) ) Single component duration (s)

Single component duration (s)

30

R=0.990

15

(a) Significant duration ( TS(15 -85%) ) 35

Horizontal component Vertical component

25

10

20

30

Integrated duration (s)

40

(d) Bracketed duration ( TB(0.05g) )

Horizontal component Vertical component

25 20 15

R=0.997

10 5 0

R=0.672

0

5

10

Integrated duration (s)

15

20

(e) Uniform duration ( TU(0.05g) )

Fig. 6.4 Correlation between integrated durations and single component durations for five duration definitions: a significant duration (TS(15−85%) ); b significant duration (TS(5−75%) ); c significant duration (TS(5−95%) ); d bracketed duration (TB(0.05 g) ); e uniform duration (TU(0.05 g) )

to take into account the fluid-solid interaction. In this formulation, the displacements are supposed to be the unknown variables for both the water and dam/foundation domains. The Concrete Damaged Plasticity (CDP) model including the strain hardening/softening behavior is employed to capture crack initiation and propagation in the dam body. The geometry and finite element (FE) discretization of the Koyna dam–reservoir–foundation system are illustrated in Sect. 2.5 (Chap. 2). The material parameters for concrete, foundation rock, and water are the same as Table 2.1. Firstly, the influence of vertical component ground motions on nonlinear dynamic response of the Koyna gravity dam-reservoir-foundation system under typical earthquakes is investigated. The response history of the Koyna dam subjected to two representative earthquakes, i.e. Loma Prieta #47524 (No. 4) and Kern County #1095 (No.

6.4 Influence of Two-Component Ground Motions on Nonlinear Dynamic Response

143

Table 6.3 Values (R) of correlation coefficients between integrated durations and single component durations Correlation coefficients

The PGA of vertical accelerograms is scaled to two thirds of the PGA of horizontal components

The PGA of vertical accelerograms is the same with that of horizontal components

Horizontal component

Vertical component

Horizontal component

Vertical component

I Ts(15−85%)

0.988

0.924

0.980

0.959

I Ts(5−75%) I Ts(5−95%) I TB(0.05 g) I TU(0.05 g)

0.990

0.885

0.985

0.958

0.995

0.948

0.989

0.982

0.989

0.853

0.973

0.896

0.997

0.672

0.991

0.723

14), are selected for examination, since the vertical component of Loma Prieta #47524 earthquake increases the structural demands, while that of Kern County #1095 earthquake reduces the demands. The examined responses include displacement, stress, dissipation energy and crack patterns of the dam body. Subsequently, the influence of vertical seismic excitations on the seismic performance of Koyna concrete gravity dam-reservoir-foundation system is quantified by using 20 as-recorded seismic ground motions.

6.4.1 Displacement Response

4

Dam crest

Displacement (cm)

Displacement (cm)

The horizontal displacement histories at the crest of the dam subjected to two representative earthquakes are shown in Fig. 6.5. Both the results for single and twocomponent earthquake excitations are presented. Here, the positive and negative signs of the displacement value represent the downstream and upstream directions, respectively. It is evident that although the maximum absolute displacement is slightly increased (Fig. 6.5a) or reduced (Fig. 6.5b) when both the horizontal and vertical

2 0 -2 Horizontal Horizontal+Vertical

-4 0

10

20

Time (s)

(a)

30

40

4

Dam crest

2 0 -2 Horizontal Horizontal+Vertical

-4 0

5

10

15

20

25

Time (s)

(b)

Fig. 6.5 Horizontal displacement histories at the crest of the dam under two representative ground motions. a Loma Prieta #47524; b Kern County #1095

144

6 Integrated Duration Effects on Seismic Performance …

excitations are considered, the overall displacement histories for two-component excitations almost coincide with that when only horizontal component is considered. The displacement response processes are less likely to be affected by the vertical excitations when the PGA of vertical accelerations is scaled to be two thirds of horizontal PGA.

6.4.2 Stress Response

Horizontal Horizontal+Vertical

2 1 0 -1

Dam heel

0

10

20

30

40

Maximum principal stress (MPa)

Time (s)

2 Dam heel

1 Horizontal Horizontal+Vertical

-1 0

5

10

15 Time (s)

3 Horizontal Horizontal+Vertical

2 1

Near the change in downstream slope

0 -1

0

10

20

20

25

(b)

30

40

Time (s)

(a)

3

0

Maximum principal stress (MPa)

3

Maximum principal stress (MPa)

Maximum principal stress (MPa)

Figure 6.6 shows the maximum principal stress history at the dam heel and near the change in the slope of the downstream face of the dam under two representative ground motions. It can be seen that the vertical ground motion has significant influence on the response history of maximum principal stress. At the beginning, the dynamic stress responses obtained from two-component excitations are close to those under horizontal ground motions alone. The subsequent stress responses obtained from the single and two-component seismic excitations deviate from each other. Overall, the stress response under two-component excitations is slightly smaller than that subjected to single-component excitations.

3 Near the change in downstream slope

2 1 0

Horizontal Horizontal+Vertical

-1 0

5

10

15

20

25

Time (s)

Fig. 6.6 Maximum principal stresses at the dam heel and near the change in downstream slope of the dam under two representative ground motions. a Loma Prieta #47524; b Kern County #1095

25 20

Horizontal Horizontal+Vertical

15 10 5 0

0

10

20 Time (s)

30

40

Damage dissipation energy (kN.m)

Damage dissipation energy (kN.m)

6.4 Influence of Two-Component Ground Motions on Nonlinear Dynamic Response

145

25 20 Horizontal Horizontal+Vertical

15 10 5 0

0

5

(a)

10

Time (s)

15

20

25

(b)

Fig. 6.7 Damage dissipation energy of the dam under two representative ground motions. a Loma Prieta #47524; b Kern County #1095

6.4.3 Damage Dissipation Energy Response Figure 6.7 shows the damage-induced energy dissipation curves for the entire dam body subjected to single and two-component ground motions. The dash lines represent the dissipated energy of the dam subjected to both horizontal and vertical accelerations, whereas the solid lines denote that under the horizontal excitations alone. As can be seen from Fig. 6.7, the vertical seismic excitation has a certain influence on the damage dissipation energy. The final damage dissipation energy is 23.56 kNm for the two-component Loma Prieta (#47524) earthquake, whereas a value of 21.15 kNm is obtained when only the horizontal component is considered. On the other hand, the final damage dissipation energy obtained from the Kern Count record (#1095) is 23.55 and 18.99 kNm for single and two-component excitations, respectively.

6.4.4 Damage Analysis Seismic damage profiles of Koyna dam resulted from the two representative ground motions are depicted in Fig. 6.8. Both the damage profiles for single and twocomponent earthquake excitations are presented for comparison purpose. The contour value between 0 and 1 indicates the concrete damage status ranging from intact to fully damaged material. One can see that although the vertical excitation does not significantly affect the dynamic displacement response, the finial cracking profile may be changed a lot by the vertical excitation. It should be noted that the inclination of the cracking profile could affect the stability of the separated upper block of the dam body when penetrated cracks are formed under strong ground motions.

146

6 Integrated Duration Effects on Seismic Performance … Horizontal and vertical

Horizontal

(a)

Horizontal

Horizontal and vertical

(b)

Fig. 6.8 Cracking profiles of dam body under two representative ground motions. a Loma Prieta #47524; b Kern County #1095

6.4.4.1

Identifying the Influence of Vertical Seismic Excitations

To quantify the influence of vertical seismic excitations on the nonlinear response of Koyna concrete gravity dam-reservoir-foundation system, a series of nonlinear dynamic analyses are carried out, with the dam-reservoir-foundation system subjected to the 20 as-recorded seismic ground motions. Note that each ground motion includes both the horizontal and vertical components. For comparison purpose, the nonlinear response of the dam-reservoir-foundation system subjected to horizontal excitations alone is also examined. Three engineering demand parameters are considered in this study, these being peak displacement, damage dissipation energy, and local damage index. The local damage index is defined as the ratio of the length of a cracking path to the total cross-sectional length along the path. The results of maximum horizontal displacements at the crest, damage dissipation energy, and local damage index are compared in Fig. 6.9 for single (horizontal

6.4 Influence of Two-Component Ground Motions on Nonlinear Dynamic Response 7

Single component (H) Two components (H+V)

6

Displacement (cm)

147

5 3.73 cm

4 3.63 cm

3 0

5

10

15

20

No.

Damage dissipation energy (kN.m)

(a) 40

Single component (H) Two components (H+V)

30

15.34 kN.m

20

10

0

14.40 kN.m

0

5

10

15

20

No.

(b)

Local damage index

1.0 0.8 0.6

0.49

0.4

0.48

0.2 0.0

Single component (H) Two components (H+V) 0

5

10

15

20

No.

(c) Fig. 6.9 Effects of vertical seismic excitations on the nonlinear dynamic response of Koyna concrete gravity dam: a maximum absolute horizontal displacements at dam crest; b damage dissipation energy; c local damage index for the upper part

148

6 Integrated Duration Effects on Seismic Performance …

excitation alone) and two-component (horizontal and vertical excitations) ground motions. The black solid and magenta dashed lines represent the average response of the dam under single and two-component seismic excitations, respectively. It is very interesting to see that the vertical ground motions do not always increase the seismic demands. As can be further seen, the nonlinear response of the dam is mainly dominated by the horizontal excitations. The average values of the maximum horizontal displacement (Fig. 6.9a), damage dissipation energy (Fig. 6.9b), and local damage index measure (Fig. 6.9c) predicted by using two-component seismic excitations are higher than those with horizontal excitations. For example, the average local damage index for the upper part of the dam under two-component seismic excitations is 0.49, while the corresponding value for horizontal accelerograms is 0.48. In this case, the vertical excitations only increase this structure demand very slightly. It should be noted that the observation on the average demand increase due to vertical excitations is obtained from the response of the Koyna gravity dam subjected to a specific set of earthquake ground motion. Thus, it might not apply to other gravity dams and ground motions.

6.5 Correlation Between Integrated Durations and Damage Measures In the literature, many studies have been conducted concerning the effects of strong motion duration on the nonlinear dynamic response of concrete gravity dams (Ou et al. 2014; Song et al. 2014). However, most of the past studies are based on horizontal seismic excitations and the corresponding single component durations. Now we have a general definition of integrated duration that accounts for the duration contributions from all components of ground motions. This section aims to quantify the correlation between the general integrated duration and seismic demands of Koyna concrete gravity dam-reservoir-foundation system, considering both the horizontal and vertical ground motions. To the best knowledge of the authors, this study presents the first reference in this respect. In order to present a comprehensive study on the effects of integrated duration, we consider five integrated durations including both relative (15–85, 5–75 and 5– 95% significant durations) and absolute (0.05 g bracketed and uniform durations) definitions and three damage measures in terms of peak displacement, damage dissipation energy and local damage index. The correlation between employed integrated durations and damage measures is shown as data pairs in Figs. 6.10, 6.11 and 6.12. Straight trend line, least-squares fitted to the data points, is displayed for each pair of integrated duration definition and damage measure, aiming at identifying the possible tendency. As can be seen from Figs. 6.10, 6.11 and 6.12, integrated durations based on different definitions are all positively correlated with the adopted damage measures. To wit, the nonlinear dynamic response of the Koyna dam under two-component

6.5 Correlation Between Integrated Durations and Damage Measures 7

7 TsI(15-85%)

I TB(0.05g)

I Ts(5 -75%)

6

I Ts(5 -95%)

Displacement (cm)

Displacement (cm)

149

R=0.783

5

R=0.689 R=0.790

4 3 2

6

I TU(0.05g)

R=0.778

5

R=0.701

4 3 2

0

10

20

30

0

40

10

Integrated duration (s)

20

30

40

Integrated duration (s)

(a)

(b)

40 35

R=0.882

30

R=0.840

25

R=0.809

20 15 10

TsI(15- 85 %) I Ts(5 - 75%)

5 0

I Ts(5 -95%)

0

10

20

30

40

Damage dissipation energy (kN.m)

Damage dissipation energy (kN.m)

Fig. 6.10 Correlation between integrated duration and peak displacement at the dam crest: a relative durations; b absolute durations 40 35 30 R=0.803

25

R=0.836

20 15 10 I TB(0.05g)

5 0

I TU(0.05g)

0

10

20

30

40

Integrated duration (s)

Integrated duration (s)

(a)

(b)

Fig. 6.11 Correlation between integrated duration and damage dissipation energy: a relative durations; b absolute durations R=0.885

0.8

1.0 R=0.812

Damage index

Damage index

1.0

R=0.858

0.6 0.4 0.2

TsI(15-85%) I Ts(5 -75%)

0.0 10

20

30

Integrated duration (s)

(a)

0.8

R=0.867

0.6 0.4 0.2 I TB(0.05g)

0.0

I Ts(5 -95%)

0

R=0.864

40

I TU(0.05g)

0

10

20

30

40

Integrated duration (s)

(b)

Fig. 6.12 Correlation between integrated duration and local damage index: a relative durations; b absolute durations

150

6 Integrated Duration Effects on Seismic Performance …

seismic excitations with longer integrated duration is in general larger than that under shorter earthquake events for the same level of PGA. The correlation coefficients R between integrated durations and damage measures are also given in Figs. 6.10, 6.11 and 6.12. It is found that 15–85% integrated signifI ) has the strongest correlation with the adopted damage icant duration (Ts(15−85%) measures among the examined five integrated duration definitions. But there is no homogeneous trend for other four integrated duration definitions. For peak displacement demand (as shown in Fig. 6.10), 5–75% integrated significant duration I ) exhibits a higher correlation compared with 5–95% integrated significant (Ts(5−75%) I duration (Ts(5−95%) ). Furthermore, the correlation coefficient obtained from 0.05 g I integrated uniform duration (TU(0.05g) ) is higher than that of 0.05 g integrated brackI eted duration (TB(0.05g) ). However, an opposite tendency is observed for damage dissipation energy (Fig. 6.11) and local damage index (Fig. 6.12) demands: 5–95% I ) shows slightly higher correlation than 5– integrated significant duration (Ts(5−95%) I 75% integrated significant duration (Ts(5−75%) ) and 0.05 g integrated bracketed duraI I tion (TB(0.05g) ) is better than 0.05 g integrated uniform duration (TU(0.05g) ) in terms of the degree of correlation. Another interesting observation is that the correlation coefficients for peak displacement measure are lower than those for damage dissipation energy and local damage index. It means that the integrated duration could affect the accumulative damage more than the peak displacement response. For comparison purpose, the correlation between horizontal durations and damage measures under horizontal seismic excitations alone is provided in Fig. 6.13. It can be seen from Fig. 6.13a that the peak displacement is mildly-to-weakly correlated with horizontal durations from a statistical point of view. The correlation coefficients obtained from horizontal seismic excitations are lower than those from twocomponent ground motions. In addition, the slope of trend lines between peak displacements and horizontal durations is very gentle. The maximum slopes of the trend lines, which represent the degree of influence, are 0.049 and 0.165 for single and two-component seismic excitations, respectively. This observation indicates a weaker influence of horizontal duration on peak displacement demand, as compared with that of integrated duration under two-component seismic excitations. On the other hand, the other damage measures such as damage dissipation energy and local damage index are considerably greater for ground motions with longer duration. Correlation coefficients between horizontal duration and these two damage measures (damage dissipation energy and local damage index) are slightly higher than those of integrated duration (Fig. 6.13b–c) under both the horizontal and vertical excitations. This is because that the vertical excitations may increase or reduce the damage measures, which could affect the correlation between integrated durations and damage measures. It is also interesting to find that among the examined horizontal duration definitions, the significant horizontal duration associated with 15–85% of the Arias intensity exhibits the strongest correlation with the employed damage measures. This

6.5 Correlation Between Integrated Durations and Damage Measures

Displacement (cm)

7

151

H Ts(15 -85%)

H Ts(5 - 75%)

6

H Ts(5 - 95%) H TB(0.05g)

5

H TU(0.05g)

R=0.540

R=0.629 R=0.669 R=0.650

4 R=0.626

3 2

0

10

20

30

40

Damage dissipation energy (kN.m)

Horizontal duration (s) (a) 40 35

R=0.930

30 25

R=0.913

R=0.861

20

R=0.813

15

R=0.881

10

H Ts(5 - 75%) H Ts(5 - 95%)

5 0

H Ts(15 -85%)

H TB(0.05g) H TU(0.05g)

0

10

20

30

40

Horizontal duration (s) (b) R=0.980

Damage index

1.0

R=0.938

0.8

R=0.916

R=0.926

R=0.928

0.6

H Ts(15 -85%)

0.4

H Ts(5 - 75%)

0.2

H Ts(5 - 95%) H TB(0.05g)

0.0

H TU(0.05g)

0

10

20

30

40

Horizontal duration (s) (c) Fig. 6.13 Correlation between horizontal duration and damage measures under single horizontal seismic excitations: a peak displacement; b damage dissipation energy; c Local damage index

152

6 Integrated Duration Effects on Seismic Performance …

observation is consistent with what we found for the integrated duration. On the other hand, the 5–75% significant horizontal duration has the weakest correlation with damage measures among the examined three significant duration definitions.

6.6 Conclusions Most previous studies with respect to the influence of strong motion duration on the nonlinear dynamic response of structures are based on horizontal seismic excitations and the corresponding single component durations. In contrast, this study investigates the integrated duration effects on concrete gravity dam-reservoir-foundation systems subjected to both horizontal and vertical ground motions. The novelty of this work lies in the proposal of a general duration definition to take into account the duration contributions of all ground motion components. The unified integrated duration can be calculated based on any existing concept of strong motion duration. In this study, we consider integrated bracketed, uniform, and significant durations to measure durations for two-component ground motions. 20 as-recorded earthquake records with a wide range of durations are applied to Koyna dam-reservoir-foundation system, in order to quantify the influence of vertical excitation and integrated durations. The following conclusions can be drawn from the study: (1) The horizontal duration computed by the selected duration definitions is positively correlated to the corresponding vertical duration. Moreover, integrated durations are also positively correlated with both the horizontal and vertical durations. The correlation coefficients between integrated and horizontal durations are larger than those between integrated and vertical durations. (2) The displacement response is very slightly affected by vertical excitations, whereas vertical excitations have a certain influence on the history of maximum principal stress and damage dissipation energy. The cracking profile may also be changed by the vertical motions. It is also found that the vertical motions do not always increase the seismic demands such as peak displacement, accumulated local damage, and dissipation energy. (3) Nonlinear dynamic response of the Koyna dam under two-component seismic excitations with longer integrated duration is in general greater than that under ground motions with shorted integrated duration. 15-85% integrated significant duration has the strongest correlation with the examined damage measures among the five integrated duration definitions. (4) Although horizontal duration is mildly-to-weakly correlated with peak displacement under single seismic excitations, the slope of trend lines between horizontal durations and peak displacements is very gentle. Compared with the horizontal duration, the integrated duration exhibits higher correlation and more significant influence on the peak displacement demand of the Koyna concrete gravity dam subjected to two-component ground motions.

6.6 Conclusions

153

Based on the results of this investigation, it is suggested that the effects of integrated duration should be taken into account for seismic performance assessment of concrete gravity dams.

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Kempton, J. J., & Stewart, J. P. (2006). Prediction equations for significant duration of earthquake ground motions considering site and near-source effects. Earthquake Spectra, 22(4), 985–1013. Kiani, J., Camp, C., & Pezeshk, S. (2018). Role of conditioning intensity measure in the influence of ground motion duration on the structural response. Soil Dynamics and Earthquake Engineering, 104, 408–417. Molazadeh, M., & Saffari, H. (2018). The effects of ground motion duration and pinching-degrading behavior on seismic response of SDOF systems. Soil Dynamics and Earthquake Engineering, 114, 333–347. Omidi, O., Valliappan, S., & Lotfi, V. (2013). Seismic cracking of concrete gravity dams by plastic– damage model using different damping mechanisms. Finite Elements in Analysis and Design, 63, 80–97. Ou, Y., Song, J., Wang, P., Adidharma, L., Chang, K., & Lee, G. (2014). Ground motion duration effects on hysteretic behavior of reinforced concrete bridge columns. Journal of Structural Engineering, 140(3), 4013065. Pan, Y., Ventura, C. E., & Finn, W. D. L. (2018). Effects of ground motion duration on the seismic performance and collapse rate of light-frame wood houses. Journal of Structural Engineering, 144(8), 4018112. Raghunandan, M., & Liel, A. B. (2013). Effect of ground motion duration on earthquake-induced structural collapse. Structural Safety, 41, 119–133. Samanta, A., & Pandey, P. (2018). Effects of ground motion modification methods and ground motion duration on seismic performance of a 15-storied building. Journal of Building Engineering, 15, 14–25. Song, R., Li, Y., & van de Lindt, J. W. (2014). Impact of earthquake ground motion characteristics on collapse risk of post-mainshock buildings considering aftershocks. Engineering Structures, 81, 349–361. Taflampas, I. M., Spyrakos, C. C., & Koutromanos, I. A. (2009). A new definition of strong motion duration and related parameters affecting the response of medium-long period structures. Soil Dynamics and Earthquake Engineering, 29(4), 752–763. Trifunac, M. D., & Brady, A. G. (1975). A study on the duration of strong earthquake ground motion. Bulletin of the Seismological Society of America, 65(3), 581–626. Wang, G., Wang, Y., Lu, W., Zhou, C., Chen, M., & Yan, P. (2015a). XFEM based seismic potential failure mode analysis of concrete gravity dam–water–foundation systems through incremental dynamic analysis. Engineering Structures, 98, 81–94. Wang, G., Wang, Y., Lu, W., Zhou, W., & Zhou, C. (2015b). Integrated duration effects on seismic performance of concrete gravity dams using linear and nonlinear evaluation methods. Soil Dynamics and Earthquake Engineering, 79, 223–236. Wang, G., Zhang, S., Zhou, C., & Lu, W. (2015c). Correlation between strong motion durations and damage measures of concrete gravity dams. Soil Dynamics and Earthquake Engineering, 69, 148–162. Wang, H., Feng, M., & Yang, H. (2012). Seismic nonlinear analyses of a concrete gravity dam with 3D full dam model. Bulletin of Earthquake Engineering, 10(6), 1959–1977. Yaghmaei-Sabegh, S., Shoghian, Z., & Neaz Sheikh, M. (2014). A new model for the prediction of earthquake ground-motion duration in Iran. Natural Hazards, 70(1), 69–92. Zhang, H. Y., Zhang, L. J., Wang, H. J., & Guan, C. N. (2018). Influences of the duration and frequency content of ground motions on the seismic performance of high-rise intake towers. Engineering Failure Analysis, 91, 481–495. Zhang, S., Wang, G., Pang, B., & Du, C. (2013a). The effects of strong motion duration on the dynamic response and accumulated damage of concrete gravity dams. Soil Dynamics and Earthquake Engineering, 45, 112–124. Zhang, S., Wang, G., & Yu, X. (2013b). Seismic cracking analysis of concrete gravity dams with initial cracks using the extended finite element method. Engineering Structures, 56, 528–543.

Chapter 7

Damage Demand Assessment of Concrete Gravity Dams Subjected to Mainshock-Aftershock Seismic Sequences

7.1 Introduction In the performance-based design of concrete dams, the dams are designed to meet the normal operating requirement when subjected to frequent earthquakes, to undergo repairable damage during a design basis earthquake, and to prevent uncontrollable failure during a calibrated earthquake (Chinese 2011). In China, these earthquake loadings, without exception, are specified in the current seismic codes as single events (Chinese 2001). However, earthquakes, in general, do not occur as a single event but as a series of shocks. A large mainshock usually triggers numerous aftershocks in a short period. For example, the 2008 Wenchuan earthquake had a mainshock measuring 8.0 M w followed by approximately five aftershocks of magnitude greater than 6.0 (Zhai et al. 2013). Mainshock–aftershock seismic sequences have also been observed in many dam projects, as shown in Table 7.1 (Alliard 2006). When a dam has been damaged by a mainshock, strong aftershocks may cause additional cumulative damage to the dam before it is repaired, increasing the risk of a major damage or collapse. Thus, mainshock–aftershock seismic sequences represent a realistic situation that requires special treatment in the seismic design. The seismic performance of structures that are subjected to multiple earthquakes has gained a great deal of attention from researchers. Several investigations have been conducted to study the damage potential of aftershocks. Those studies vary in several aspects: the type of structures (reinforced concrete buildings (Liolios et al. 2015; Zafar and Andrawes 2015), reinforced concrete containments (Zhai et al. 2015, 2017), bridges (Jeon et al. 2016), etc.), model representation (single-degree-offreedom (Hatzigeorgiou and Beskos 2009; Goda 2012)to multi-degree-of-freedom (Liolios et al. 2015; Zafar and Andrawes 2015)), generation of mainshock–aftershock seismic sequences (as-recorded sequences (Zafar and Andrawes 2015), artificial records (Goda and Taylor 2012; Han et al. 2015), actual records with scaling (Hatzigeorgiou 2010a; Hatzivassiliou and Hatzigeorgiou 2015), etc.), and objective (seismic demand (Hatzigeorgiou 2010b; Goda and Salami, 2014), life-cycle cost © Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_7

155

156

7 Damage Demand Assessment of Concrete Gravity …

Table 7.1 Mainshock-aftershock sequences recorded in the dam projects (Alliard 2006) Name

Country

Year of Year Mainshock Largest Largest Type impounding of magnitude aftershock aftershock main magnitude delay shock

Koyna

India

1962

1967

6.3

5.1

10 months Concrete gravity

Kremasta

Greece

1965

1966

6.2

5.5

Several months

1959

1962

6.1

5.3

1 year 1/2 Buttress

Kariba

Zimbabwe 1958

1963

6.0

5.8

2 Days

Arch

Oroville

USA, Ca.

1967

1975

5.7

5.2

1 day

Earth-filled

Aswan

Egypt

1964

1981

5.6

4.6

9 months

Earth and rock filled

Lake Mead (Hoover dam)

USA, Co.

1935

1938

5.0

4.0

2h

Arch

Benmore

New Zealand

1964

1966

5.0

4.4

1 year

Earth-filled

Marathon

Greece

1929

1938

5.0

–

–

Concrete gravity

Monteynard

France

1962

1963

4.9

4.5

–

Arch

Bhatsa

India

1977

1983

4.9

3.9

4 months

Masonry gravity

Nurek

Tadjikistan 1972

1972

4.6

4.3

Several hours

Earth-filled

Hsinfengkiang China

Rockfilled

(Liek Yeo and Allin Cornell 2009), risk assessment (Song et al., 2014), vulnerability assessment (Li et al. 2014; Raghunandan et al. 2015), etc.). Without being exhaustive, some studies on the aftershock effects on the seismic performance of structures are worth mentioning. Salami et al. (2019) quantified the influence of real mainshock-aftershock sequences on the seismic fragility of a 2strory RC structure. They found that considering aftershocks will increase the probability of exceedance of extensive and complete damage up to 10% for the crustal ground motions and 5% for the inslab and interface records. Shokrabadi and Burton (2018) quantified the impact of aftershock and mainshock-aftershock on the seismic risk of three reinforced concrete moment frame structures. Their results showed that both the increased post-mainshock seismic hazard as well as the reduction in the structural capacity have a significant influence on the seismic hazard. Shokrabadi et al. (2018) evaluated the influence of mainshock-aftershock ground motion pairing on the structural response and collapsed performance of five ductile reinforced concrete frames with varying heights. Their results showed that the mainshock-aftershock may overestimate or underestimate the seismic demand and risk relative to the use of more-appropriate mainshock-aftershock record pairs. Hosseinpour and Abdelnaby (2017) concluded that the earthquake direction, aftershock polarity, and vertical component can have a significant influence on the nonlinear dynamic behavior of RC

7.1 Introduction

157

building structures subjected to multiple earthquakes. Zhai et al. (2015) explored the seismic response of RC containment building subjected to as-records mainshockaftershock seismic sequences, their results indicated that aftershocks have a significant influence on the dynamic response of RC buildings in terms of maximum top response and accumulated damage. Ruiz-García et al. (2014) evaluated the effects of mainshock-aftershock seismic sequences on the dynamic response of RC framed-buildings located in soft-soil sites. Their results showed that the relationship between the period of the building after the mainshock and the predominant period of the aftershock has a significant influence on the seismic response of RC buildings to aftershock ground motions. Silwal and Ozbulut (2018) examined the aftershock collapse performance of steel frame buildings with and without superelastic viscous dampers subjected to mainshock-aftershock seismic sequences. Ruiz-García et al. (2018) explored the effects of as-recorded mainshock-aftershock sequences on the seismic response of three-dimensional steel moment-resisting buildings in terms of lateral interstory drift demands. Song et al. (2016) proposed a framework to examine the effects of aftershock ground motions on the seismic loss of steel buildings. The uncertainty in earthquake ground motions, structural model, damage and loss was considered by using the Monte Carlo Simulation with Latin Hypercube Sampling. Amiri and Bojórquez (2019) quantified the residual displacement ratios of structures as bi-linear SDOF systems under mainshock-aftershock seismic sequences. The effects of ground motion characteristics of seismic sequences such as site condition, magnitude, epicentral distance, and duration have been considered. Rinaldin et al. (2017) investigated the effects of repeated seismic sequences on SDOF systems with hysteretic or damped dissipative behavior. They concluded that the seismic design codes should consider the influence of mainshock-aftershock seismic sequences on structural response. Yaghmaei-Sabegh and Ruiz-García (2016) investigated the nonlinear dynamic response of SDOF systems subjected to asrecorded Varzaghan-Ahar seismic sequences in terms of constant-ductility strength reduction factor and inelastic displacement ratios, and thought that it is not reasonable to repeat the mainshock as the aftershock. Zhai et al. (2014) investigated the effects of mainshock-aftershock ground motions on the ductility demand, normalized hysteretic energy and damage index of inelastic SDOF structures, and found that the aftershock has a more significant influence on the normalized hysteretic energy and damage index than on ductility demand. Furtado et al. (2018) assessed the seismic vulnerability of undamaged and damaged structures with and without infill masonry walls under mainshock-aftershock sequences. They found that aftershocks will cause higher seismic vulnerability to the damaged RC structures than the undamaged structures. Morfidis and Kostinakis (2017) explored the role of masonry infills on the damage response of 3D RC buildings with different heights, structural systems and distribution of masonry infills subjected to seismic sequences, and found that seismic sequences has larger influence on the structural damage for the infilled buildings than that for bare structures. Tesfamariam et al. (2015) studied the seismic vulnerability of RC buildings with unreinforced masonry infill walls subjected to mainshock-aftershock seismic sequences. Their results showed that the mainshockaftershock seismic sequences will increase the seismic demands when compared

158

7 Damage Demand Assessment of Concrete Gravity …

with single mainshock ground motions. Omranian et al. (2018) performed a cloud analysis method to study the seismic vulnerability of RC skew bridges subjected to as-recorded mainshock-aftershock sequences. The effects of the skew angle of the deck and direction of the seismic excitation on the fragility curves have been discussed. They thought it was unconservative if only the mainshocks are considered. Pang and Wu (2018) investigated the seismic fragility of multispan RC bridges subjected to mainshock-aftershock sequences, and found that aftershocks can be harmful to both bridge components and system. Shin and Kim (2017) explored the effects of frequency contents of aftershock ground motions on nonlinear dynamic response of RC bridge columns, and demonstrated that the frequency contents of aftershocks have great influence on the seismic performance of RC columns. Dong and Frangopol (2015) performed a framework for risk and resilience assessment of highway bridges subjected to mainshock and aftershock sequences. The effects of the uncertainties associated with seismic scenarios and consequence evaluation were incorporated within their framework. Their results showed that the strong aftershocks have a significant influence on the repair loss and residual functionality of bridges. Fakharifar et al. (2015) evaluated the efficacy of three types of repair jackets on mainshock-damaged RC bridge columns subjected to aftershock attacks with various intensities using the incremental dynamic analyses method, and found the three repair jackets can effectively improve the seismic performance and collapse capacity of bridges by approximately 20% under severe aftershocks. Konstandakopoulou and Hatzigeorgiou (2017) evaluated the seismic performance of water and wastewater steel tanks subjected to as-recorded and artificial seismic sequences. They thought the single earthquake records would lead to underestimate the seismic demands of the steel tanks in terms of bearing capacity and deformation. Singh et al. (2018) employed a unidirectional shake table to investigate the seismic behavior of the damaged tunnel subjected to aftershock ground motions, and found that the damaged tunnel is more vulnerable to the low frequency aftershocks. Sun et al. (2020) evaluated the effects of mainshock-aftershock seismic sequences on the nonlinear dynamic response of hydraulic arched tunnels using the lining local damage index and lining global damage index. Their results showed that seismic sequences have a negative influence on the seismic performance of the tunnel, and will cause relatively severe cumulative damage in comparison with single mainshock ground motions. Yu et al. (2019) concluded that strong aftershocks have a significant influence on the seismic performance and floor acceleration response spectrum of the AP1000 nuclear island building and will aggravate the potential cumulative damage. Zhao et al. (2020) thought the aftershocks have only a minor impact on the seismic behavior of isolated AP1000 nuclear island building because of the isolation systems. Concrete gravity dams located in earthquake-prone regions are not only exposed to a single seismic event but also to a sequence of seismic shocks. Strong aftershocks have the potential to cause additional cumulative damage to the mainshockdamaged dams. Despite the fact that this problem has been qualitatively acknowledged, nonlinear demands of concrete gravity dams (Oudni and Bouafia 2015; Wang et al. 2015a; Alembagheri, 2016; Hariri-Ardebili et al. 2016a, b) are mainly based

7.1 Introduction

159

on a single and rare design earthquake. To the best of our knowledge, only a few researchers have evaluated the effect of mainshock–aftershock seismic sequences on the nonlinear behavior of dams. Alliard and Léger (2008) studied the earthquake safety evaluation of concrete gravity dams considering the aftershocks, they found that strong aftershocks can cause additional damage and sliding displacements to concrete gravity dams. Xia et al. (2010) employed a fully coupled method to analyze the response of the earth embankment subjected to repeated earthquakes. Zhang et al. (2013) examined the effects of as-recorded mainshock–aftershock seismic sequences on the accumulated damage of concrete gravity dams. Their results indicated that mainshock-aftershock seismic sequences have a significant influence on the accumulated damage of concrete gravity dams. Pang et al. (2020) discussed the effects of mainshock-aftershock seismic sequences on the probability of the high concrete face rockfill dam based on the vertical deformation and damage index, and concluded that strong aftershocks will significantly increase the fragility of the mainshock-damaged concrete face rockfill dam. It should be noted that most of the aforementioned studies were focused on the effects of seismic sequences (as-recorded sequences, artificial sequences, repeated sequences, etc.) on the seismic demands of reinforced concrete buildings. The limited works (Alliard and Léger 2008; Xia et al. 2010; Zhang et al. 2013a) mentioned above considered only the influence of the mainshock–aftershock seismic sequences on concrete gravity dams and the effect of the damage due to mainshock on the damage potential of aftershocks is not well understood. Besides, they did not provide statistical information about the seismic demands of concrete gravity dams subjected to single seismic events (both mainshocks and aftershocks) and mainshock–aftershock seismic sequences. Furthermore, it is interesting to know whether the repeated earthquake approach can be used to estimate the seismic performance of concrete gravity dams that are subjected to mainshock–aftershock seismic sequences. The objective of this study is to understand the effects of the as-recorded mainshock–aftershock seismic sequences on the damage demands of concrete gravity dam–reservoir–foundation systems. To achieve this, 20 as-recorded mainshock– aftershock seismic sequences are considered in this investigation. The objectives of the current research are as follows: (a) to investigate the correlation between the ground motion characteristics (i.e. frequency content, strong motion duration, and amplitude) of the mainshocks and the major aftershocks, (b) to study the differences in the nonlinear response of concrete gravity dam–reservoir–foundation systems subjected to single mainshocks, single aftershocks, and mainshock–aftershock seismic sequences, (c) to quantify the effects of aftershocks on the damage demands of concrete gravity dams, and (d) to compare the damage demands in terms of local and global damage indices between the as-recorded seismic sequences and the repeated earthquakes.

160

7 Damage Demand Assessment of Concrete Gravity …

7.2 Mainshock–Aftershock Seismic Sequences 7.2.1 Construction Method of Mainshock–Aftershock Seismic Sequences At present, the most widely used construction methods of mainshock–aftershock seismic sequences for the structural seismic response analysis can be classified into three categories: (a) as-recorded sequences (Ruiz-Garc I A and Negrete-Manriquez 2011; Efraimiadou et al. 2013); (b) repeated sequences (Hatzigeorgiou and Beskos 2009; Hatzigeorgiou and Liolios 2010a); (c) artificial sequences(Hatzigeorgiou and Liolios 2010b; Moustafa and Takewaki 2011). The as-recorded mainshock-aftershock seismic sequence is the first choice to investigate the effects of the seismic sequence on nonlinear dynamic response of structures. However, there are few records of as-recorded mainshock-aftershock seismic sequences which are exactly in line with the actual research need. Due to the large difference in the spectral characteristics between the mainshock and the aftershock, it is uncertain whether the artificial seismic sequence can reflect the seismic characteristics of the real seismic sequence. When an as-recorded single earthquake is combined to form a mainshock-aftershock earthquake sequence (i.e. repeated sequences), it is often necessary to determine the relationship of the magnitude and peak acceleration between the mainshock and aftershock. Hatzigeorgiou and Beskos (2009) employed the well-known Gutenberg-Richter Law (Gutenberg and Richter 1965) to express the relationship of magnitudes between mainshocks and aftershocks. The Gutenberg-Richter Law is often used to describe the relationship between the magnitude and total number of earthquakes in any given region and time period, which can be expressed as N = 10b(M−M0 ) or log(N ) = b(M − M0 )

(7.1)

where N is the number of seismic events with a given magnitude range; M is the magnitude of the mainshock; M 0 is the magnitude of the aftershock; b is the constant, which is typically equal to 1.0. It can be seen from Eq. (7.1) that when the mainshock magnitude of a given earthquake event is M, there will be 2 earthquakes with the aftershock magnitude M 0 = M − 0.3010(log(2) ≈ 0.3010), and 3 earthquakes with the aftershock magnitude M 0 = M − 0.4771(log(3) ≈ 0.4771). For example, for the given mainshock with M = 7.0, there will be 2 earthquakes with the aftershock magnitude M 0 = 7.0 − 0.3010 ≈ 6.7, and 3 earthquakes with the aftershock magnitude M 0 = 7.0 − 0.4771 ≈ 6.5. When the correlation of the magnitude between the mainshock and aftershock is obtained, the relationship of the peak ground acceleration (PGA) between the mainshock and aftershock can be calculated by using the well-known Joyner–Boore (Joyner and Boore 1982) attenuation relation, which is given by

7.2 Mainshock–Aftershock Seismic Sequences

log(PGA) = 0.49 + 0.23(M − 6) − log

161



 R 2 + 82 − 0.0027 R 2 + 82

(7.2)

Where PGA is expressed in gravitational acceleration, g; R is the source distance, in km; M is the magnitude. This equation can be combined with Eq. (7.1) to calculate the peak ground accelerations for 1, 2, and 3 earthquake events. According to Eqs. (7.1) and (7.2), irrespectively of source distance and magnitude of seismic events, the ratios between the peak ground accelerations (PGA) for the above-mentioned cases can be expressed as PGA(2−E V E N T S) PGA(M−0.3010) = PGA(1−E V E N T S) PGA(M) =

√ R 2 +82 −0.0027 R 2 +82 √ √ 100.49+0.23(M−6)−log R 2 +82 −0.0027 R 2 +82

100.49+0.23(M−0.3010−6)−log

√

.

(7.3)

.

(7.4)

= 0.8526 PGA(3−E V E N T S) PGA(M−0.4771) = PGA(1−E V E N T S) PGA(M) =

√ R 2 +82 −0.0027 R 2 +82 √ √ 100.49+0.23(M−6)−log R 2 +82 −0.0027 R 2 +82

100.49+0.23(M−0.4771−6)−log

√

= 0.7767 According to Eqs. (7.3) and (7.4), when the PGA of the mainshock is Ag,max , there will be 2 earthquakes with the aftershock PGA equal to 0.8526 · Ag,max , and 3 earthquakes with the aftershock PGA equal to 0.7767 · Ag,max .

7.2.2 As-Recorded Mainshock–Aftershock Seismic Sequences In order to investigate the nonlinear behavior of the mainshock-damaged concrete gravity dams subjected to strong aftershocks, seismic sequences including the mainshock and one major aftershock are needed for performing the nonlinear dynamic analyses. In this study, as-recorded mainshock–aftershock seismic sequences are selected according to the following criteria: (a) the magnitude of the mainshocks is equal to or greater than 5.5 and that of the major aftershocks is equal to or greater than 4.0, (b) accelerograms are recorded at stations, which are located in free fields or lowrise buildings, and (c) the predominant period (T p ) of the mainshocks is less than 0.4 s, which corresponds to the typical dam sites. With these criteria, 20 as-recorded mainshock–aftershock seismic sequences shown in Table 7.2, which were recorded at the same station and in the same direction, are selected from the strong motion database of the COSMOS (COSMOS 2019). The data sample includes well-known earthquakes with strong seismic activities, such as the Mammoth Lakes (1980), Kozani

Seismic sequences

Mammoth Lakes

Mammoth Lakes

Chalfant Valley

Chalfant Valley

Chalfant Valley

Chalfant Valley

Coalinga

Imperial Valley

Kozani

Kozani

Whittier Narrows

No.

1

2

3

4

5

6

7

8

9

10

11

24400

ITSAK

ITSAK

5055

CHP

54171

54171

54428

54428

54099

54099

Station location

270

90

0

315

0

270

180

360

270

180

90

Comp.

1987-10-01(14:42:20)

6.1(Mw )

5.3(ML )

1995-05-17(04:14:00)

5.3(ML ) 6.1(ML )

1995-05-17(04:14:00) 1995-05-13(08:47:00)

6.1(ML )

5.0(ML )

1979-10-15(23:19:35) 1995-05-13(08:47:00)

6.5(Mw )

1979-10-15(23:16:53)

5.3(Mw )

1983-07-25(22:31:39)

5.8(ML ) 6.0(Mw )

1986-07-31(07:22:40) 1983-07-22(02:39:54)

6.4(ML )

5.8(ML )

1986-07-31(07:22:40) 1986-07-21(14:42:26)

6.4(ML )

1986-07-21(14:42:26)

5.6(ML )

1986-07-21(14:51:09)

5.6(ML ) 6.4(ML )

1986-07-21(14:51:09) 1986-07-21(14:42:26)

6.4(ML )

5.7(ML )

1986-07-21(14:42:26)

6.1(ML )

1980-05-25(20:35:48)

5.7(ML )

1980-05-25(16:33:44)

6.1(ML )

1980-05-25(20:35:48)

Mag

1980-05-25(16:33:44)

Date

Table 7.2 List of mainshock-aftershock seismic sequences considered in this investigation

14.2

12.1

19.5

12.1

19.5

12.3

8.8

12.7

13.4

15.5

23.7

15.5

23.7

27.9

18.5

27.9

18.5

3.4

9.1

3.4

9.1

R (km)

399.10

119.26

136.00

126.19

211.03

246.06

209.40

521.20

350.10

121.44

169.00

179.66

249.10

101.54

394.60

156.56

435.80

490.54

392.09

338.87

402.19

Recorded PGA (cm/s2 )

0.20

0.14

0.20

0.22

0.20

0.22

0.22

0.22

0.14

0.24

0.36

0.34

0.24

0.12

0.24

0.12

0.20

0.14

0.14

0.16

0.22

Predominant period (s)

(continued)

7.94

5.63

7.72

5.41

5.84

12.84

13.22

2.77

9.01

17.18

17.04

14.16

12.76

11.16

8.16

7.66

7.26

3.54

8.94

3.54

8.96

Duration (5–95%) (s)

162 7 Damage Demand Assessment of Concrete Gravity …

Seismic sequences

Whittier Narrows

Whittier Narrows

Whittier Narrows

Whittier Narrows

Whittier Narrows

Cape Mendocino /Petrolia

Cape Mendocino /Petrolia

Cape Mendocino /Petroli

Cape Mendocino /Petroli

No.

12

13

14

15

16

17

18

19

20

Table 7.2 (continued)

1586

1583

1585

1585

24402

24402

24401

24401

24400

Station location

270

360

360

270

90

0

360

270

360

Comp.

7.0(Mw ) 6.6(Ms )

1992-04-26(07:41:00)

6.6(Ms )

1992-04-25(18:06:04)

7.0(Mw )

1992-04-26(07:41:00)

6.6(Ms )

1992-04-26(07:41:00) 1992-04-25(18:06:04)

7.0(Mw )

6.6(Ms )

1992-04-26(07:41:00) 1992-04-25(18:06:04)

7.0(Mw )

1992-04-25(18:06:04)

5.3(Mw )

1987-10-04(10:59:38)

5.3(Mw ) 6.1(Mw )

1987-10-04(10:59:38) 1987-10-01(14:42:20)

6.1(Mw )

5.3(Mw )

1987-10-04(10:59:38) 1987-10-01(14:42:20)

6.1(Mw )

1987-10-01(14:42:20)

5.3(Mw )

1987-10-04(10:59:38)

5.3(Mw ) 6.1(Mw )

1987-10-01(14:42:20)

1987-10-04(10:59:38)

5.3(Mw ) 6.1(Mw )

1987-10-04(10:59:38) 1987-10-01(14:42:20)

Mag

Date

45.3

35.1

47.1

32.7

33.3

26.5

33.3

26.5

18.2

19.4

18.2

19.4

15.1

15.5

15.1

15.5

16.3

14.2

16.3

R (km)

228.40

261.50

271.00

280.10

431.40

471.00

344.20

317.60

187.90

157.90

266.00

299.30

193.40

183.80

137.20

136.50

308.60

420.10

333.30

Recorded PGA (cm/s2 )

0.36

0.2

0.38

0.4

0.34

0.24

0.30

0.16

0.14

0.22

0.14

0.10

0.28

0.12

0.30

0.12

0.16

0.18

0.14

Predominant period (s)

10.78

16.19

9.75

15.06

6.83

10.42

6.76

10.65

3.04

8.1

2.14

4.54

2.76

7.34

3.74

11.44

6.2

7.14

5.18

Duration (5–95%) (s)

7.2 Mainshock–Aftershock Seismic Sequences 163

7 Damage Demand Assessment of Concrete Gravity … 150

200 Time gap (10 s)

1980/05/25 20:35:48

0

-400 0

5

10

15 20 Time (s)

25

30

Kozani seismic sequence Station: ITSAK-Comp.:90

50

Time gap (10 s)

0 -50 -100 -150

35

0

5

10

15

400

Time gap (10 s)

0

0

5

10

1987/10/04 10:59:38

-200

15

20

25

Time (s)

(c)

30

35

40

30

35

40

Cape Mendocino/Petrolia seismic sequence Station: 1585-Comp.:270

200 Time gap (10 s)

0 1992/04/25 18:06:04

Acceleration (cm/s2)

Whittier Narrows seismic sequence Station: 24402 -Comp.:90

100

-100

25

(b)

1987/10/01 14:42:20

Acceleration (cm/s2)

(a)

200

20

Time (s)

-200 -400

45

1992/04/26 07:41:00

-200

100

1983/07/25 22:31:39

Acceleration (cm/s2)

Mammoth Lakes seismic sequence Station: 54099 Convict Creek-Comp.:90

1980/05/25 16:33:44

Acceleration (cm/s2)

400

1983/07/22 02:39:54

164

0

5

10

15

20

25

30

35

40

45

50

55

Time (s)

(d)

Fig. 7.1 Four representative as-recorded mainshock–aftershock seismic sequences: a Mammoth Lakes, Station: 54099-Comp. 90, b Kozani, Station: ITSAK-Comp. 90, c Whittier Narrows, Station: 24402-Comp. 90, and d Cape Mendocino/Petrolia, Station: 1585-Comp. 270

(1995), Whittier Narrows (1987), and Cape Mendocino/Petrolia (1992) events. For each of the 20 sequential ground motion records, the time gap between the mainshock and the aftershock seismic events is set to be 10 s as illustrated in Fig. 7.1, which shows the aforementioned four representative mainshock–aftershock seismic sequences. This gap has zero acceleration ordinates and is adequate to allow the structure to cease moving after the previous seismic event. It should be noted that the selected aftershock records might be greater than the typical aftershock records that are actually observed in the field. This is because the ground motion database, such as COSMOS, lists only the stronger aftershock records. Therefore, the results presented in this study should be interpreted cautiously. The most important characteristics that describe an earthquake ground motion are the maximum absolute amplitude, frequency content, and strong motion duration. These characteristics of the seismic sequences used in this study are listed in Table 7.2. The peak ground acceleration (PGA) is selected as the amplitude of the accelerogram. The predominant period (T p ), which is a measure of the frequency content of the ground motion, is defined as the period at which the maximum spectral acceleration occurs in an acceleration response spectrum calculated at 5% damping. Various definitions (Wang et al. 2015b, 2016) of strong motion duration have been proposed; however, the use of the significant duration seems more appropriate and justified because the ground motion records are required to be scaled for analysis, and the significant duration is not affected by scaling (Zhang et al. 2013b; Wang et al. 2015c). In this study, significant duration T 90 % (5–95%), which is defined as the time interval between 5% and 95% of the Arias intensity, is selected to measure the duration of ground motions.

7.2 Mainshock–Aftershock Seismic Sequences

165

7.2.3 Correlation Between Ground Motion Characteristics of Mainshocks and Major Aftershocks In order to investigate the similarity between the ground motion characteristics of the selected aftershock accelerations and their corresponding mainshock time-histories, the following parameters are calculated for each ground motion: (a) the predominant period (T p ), (b) the strong motion duration (T 90 % ), and (c) the peak ground acceleration (PGA). For the purpose of illustration, the elastic spectra of the four typical seismic sequences at a viscous damping ratio of ζ = 5% are presented in Fig. 7.2, and the corresponding power amplitude spectra are shown in Fig. 7.3. The predominant periods (T p ) of the mainshocks and major aftershocks are also indicated in Fig. 7.2. It can be clearly observed that the predominant periods and power amplitudes of the mainshocks and their corresponding aftershocks are significantly different, which means that the mainshock and the major aftershock have different frequency contents. Thus, it may not be appropriate to assume that the mainshock–aftershock seismic sequences have identical frequency content (Zhai et al. 2013). 0.6

1.6

Spectral acceleration (g)

Spectral acceleration (g)

1.8 Mainshock

1.4

Aftershock

1.2 1.0 0.8 0.6 0.4 0.2 0.0

0.5

Mainshock Aftershock

0.4 0.3 0.2 0.1 0.0

0

2

4

0

Period (s)

(a) 1.4

Spectral acceleration (g)

Spectral acceleration (g)

4

(b)

1.0 Mainshock

0.8

Aftershock

0.6 0.4 0.2 0.0

2

Period (s)

0

2

Period (s)

(c)

4

1.2

Mainshock

1.0

Aftershock

0.8 0.6 0.4 0.2 0.0

0

2

4

Period (s)

(d)

Fig. 7.2 Elastic pseudo-acceleration response spectra of four typical seismic sequences (5%). a Mammoth Lakes, Station: 54099-Comp. 90, b Kozani, Station: ITSAK-Comp. 90, c Whittier Narrows, Station: 24402-Comp. 90, and d Cape Mendocino/Petrolia, Station: 2585-Comp. 270

166

7 Damage Demand Assessment of Concrete Gravity … 0.12 Mainshock Aftershock

0.15

Power amplitude

Power amplitude

0.18

0.12 0.09 0.06 0.03

Mainshock Aftershock

0.08

0.04

0.00

0.00 0.1

1

0.1

10

Frequency (Hz)

1

(a)

(b) 0.28

0.12 Mainshock Aftershock

Power amplitude

Power amplitude

10

Frequency (Hz)

0.08

0.04

0.24

Mainshock Aftershock

0.20 0.16 0.12 0.08 0.04

0.00

0.00 0.1

1

Frequency (Hz)

(c)

10

0.1

1

10

Frequency (Hz)

(d)

Fig. 7.3 Power amplitude spectra of four typical mainshock–aftershock sequences: a Mammoth Lakes, Station: 54099-Comp. 90, b Kozani, Station: ITSAK-Comp. 90, c Whittier Narrows, Station: 24402-Comp. 90, and d Cape Mendocino/Petrolia, Station: 2585-Comp. 270

The correlation between the three major characteristics of the mainshocks and their corresponding aftershocks is quantified in Fig. 7.4a (predominant period), Fig. 7.4b (strong motion duration), and Fig. 7.4c (peak ground acceleration, PGA). The correlation coefficient for the predominant period is 0.30, indicating that the predominant periods of the mainshock ground motions and that of the aftershock ground motions are weakly correlated from a statistical point of view. Based on this observation, it can be concluded that the simulation approach of repeating the mainshock as an aftershock may not be appropriate. A much higher correlation coefficient (0.74) is obtained for the significant duration than the predominant period, meaning that the strong motion duration of the mainshocks is mildly correlated with that of the corresponding aftershocks. Furthermore, it is observed that, on an average, the strong motion duration of the mainshocks is approximately 28.6% longer than that of the corresponding aftershocks. In addition, it can be clearly observed from Fig. 7.4c that the PGA of the mainshocks follows an approximately linear trend with respect to that of the major aftershocks (i.e. the PGA of the major aftershocks increases with an increase in the PGA of the mainshocks). For the selected seismic sequences, it was observed that, on an

7.2 Mainshock–Aftershock Seismic Sequences

167

T90% of aftershock (s)

Tp of aftershock (s)

0.4

0.3

0.30

0.2

0.1

0.0 0.0

0.1

0.2

0.3

20 18 16 14 12 10 8 6 4 2 0

0.74

0

0.4

2

4

Tp of mainshock (s)

(a)

PGA of aftershock (cm/s 2)

6

8 10 12 14 16 18 20

T90% of mainshock (s)

(b) 600 500 400 300 200

0.64

100 0

0

100

200

300

400

500

600

PGA of mainshock (cm/s2)

(c) Fig. 7.4 Relationship between characteristic parameters of mainshocks and their corresponding aftershocks. a Predominant period, b strong motion duration, and c peak ground acceleration

average, the PGA of the mainshock ground motions is 13.2% larger than that of their major aftershocks. It should be noted that the correlation phenomena quantified in this study are specific to the selected 20 as-recorded seismic sequences. Further investigations will be carried out by using abundant as-recorded seismic sequences.

7.3 Finite Element Model 7.3.1 Koyna Dam–Reservoir–Foundation System In order to quantify the influence of the major aftershocks on the nonlinear dynamic response of the mainshock-damaged concrete gravity dams, the Koyna concrete gravity dam is selected as a representative numerical example. The geometry and finite element (FE) discretization of the Koyna dam–reservoir–foundation system are

168

7 Damage Demand Assessment of Concrete Gravity …

illustrated in Sect. 2.5 (Chap. 2). The material parameters for concrete, foundation rock, and water are the same as Table 2.1.

7.3.2 Seismic Input A set of 20 as-recorded seismic sequences with one major aftershock is considered as the seismic input, as summarized in Table 7.2. The mainshocks are scaled to have a PGA of 0.40 g. The aftershock accelerograms are adjusted along with their corresponding mainshock accelerogram. Thus, all the seismic sequences are multiplied by appropriate factors. For example, the aforementioned four typical sequential ground motions are multiplied by 0.976 (Mammoth Lakes, Station: 54099-Comp. 90), 2.885 (Kozani, Station: ITSAK-Comp. 90), 2.485 (Whittier Narrows, Station: 24402-Comp. 90), and 1.236 (Cape Mendocino/Petrolia, Station: 2585-Comp. 270). In order to investigate the influence of the aftershocks on the damage demands of the mainshock-damaged dam, repeated earthquakes (i.e. back-to-back approach) are also considered as the seismic input. The back-to-back approach assumes that the features of the ground motion, such as the frequency content and strong motion duration of the mainshocks and aftershocks, are the same. The amplitude (i.e. PGA) of the mainshock is multiplied by a scaling factor (0.8526 (Hatzigeorgiou and Beskos 2009) or 1.0) to obtain the PGA of the aftershock.

7.4 Nonlinear Behavior of the Koyna Dam–Reservoir–Foundation System In this section, the nonlinear dynamic behavior of the concrete gravity dam–reservoir–foundation system subjected to the four representative seismic sequences is discussed. This study focuses on the following design parameters: structural damage, displacement response, and damage dissipated energy.

7.4.1 Structural Damage The damage profiles of the Koyna dam–reservoir–foundation system subjected to both single seismic events (mainshock or aftershock) and mainshock–aftershock seismic sequences are shown in Fig. 7.5. The contour values shown in Fig. 7.5 are calculated using the CDP model, and they indicate the damage variable of the concrete. In the CDP model, the damage variable of the concrete is determined by using the corresponding tensile and compressive strains, and it ranges from 0

7.4 Nonlinear Behavior of the Koyna Dam–Reservoir–Foundation System Mainshock 1980-05-25 (16:33:44)

Aftershock 1980-05-25 (16:33:44)

169

Mainshock–aftershock seismic sequence

(a) Mainshock 1995-05-13 (08:47:00)

Aftershock 1995-05-17 (04:14:00)

Mainshock–aftershock seismic sequence

(b) Mainshock 1987-10-01 (14:42:20)

Aftershock 1987-10-04 (10:59:38)

Mainshock–aftershock seismic sequence

(c) Mainshock 1992-04-25 (18:06:04)

Aftershock 1992-04-26 (07:41:00)

Mainshock–aftershock seismic sequence

(d)

Fig. 7.5 Damage profiles of the Koyna dam under single seismic events and seismic sequences. a Mammoth Lakes, Station: 54099-Comp. 90, b Kozani, Station: ITSAK-Comp. 90, c Whittier Narrows, Station: 24402-Comp. 90, and d Cape Mendocino/Petrolia, Station: 2585-Comp. 270

170

7 Damage Demand Assessment of Concrete Gravity …

(intact material) to 1 (fully damaged material). This figure depicts the damage of the dam–reservoir–foundation system due to the four representative ground motions considered in this study. It is evident that the aftershocks influence the accumulated damage of the post-mainshock concrete gravity dams significantly. In some cases, the results corresponding to the mainshock–aftershock ground motions clearly show a significant degradation in the strength of the dam, which is indicated by a crack that extends completely across the upper section. In general, it is observed that the seismic sequences do not lead to changes in the damage pattern of the dam during the aftershocks. In other words, if the dam suffers damage during the mainshock, it is likely that the damage accumulates sequentially during the aftershock. It is also observed that a significant difference exists in the damage profile of the upper part between the single mainshock and aftershock events. Such a difference may be contributed to the distinctive ground motion characteristics (i.e. amplitude, frequency content, and strong motion duration) between the mainshock and aftershock motions. Not only a single mainshock event can cause serious damage to the dam, but also a single aftershock event has the potential to cause extensive structural damage. In some cases, a single aftershock event can cause more damage to the dam than a single mainshock event. It is concluded that seismic sequences can lead to a higher accumulated damage to concrete gravity dams; hence, the seismic design of concrete gravity dams should be given more attention.

7.4.2 Displacement Response The time history of the horizontal displacements at the crest of the dam, which is subjected to the four representative sequential ground motions, is shown in Fig. 7.6 with the positive displacement toward the downstream direction. The displacement response of the dam subjected to single aftershock events is also illustrated in Fig. 7.6. For comparison, the starting time of the single aftershock event is adjusted to match the starting time of the aftershock in the seismic sequence. It is observed from Fig. 7.6 that the dam is excited in a different manner for each individual seismic event, and the nonlinear response that is obtained from the seismic sequences has a substantially different displacement history than those obtained from the single aftershocks. The maximum upstream horizontal displacements (indicated by negative values in Fig. 7.6) corresponding to the seismic sequences are greater than that corresponding to the single mainshocks. This is because that the examined dam exhibits residual displacements, which are accumulated during earthquakes, and therefore, the maximum displacements appear to increase during seismic sequences when compared to single mainshocks. This means that mainshock–aftershock seismic sequences require increased displacement demands when compared to single mainshocks. Seismic sequences have a significant influence on the residual displacements in addition to the maximum displacements. In some cases, single aftershocks

7.4 Nonlinear Behavior of the Koyna Dam–Reservoir–Foundation System

171

4

Displacement (cm)

Displacement (cm)

Seismic sequence Single aftershock Static loading

4 2 0 -2

0

5

10

15

20

25

0 -2 -4

Aftershock

Gap (10 s)

Mainshock -4

Seismic sequence Single aftershock Static loading

2

30

35

5

10

15

20

(a)

30

35

40

(b) 4

6 Seismic sequence Single aftershock Static loading

4

Displacement (cm)

Displacement (cm)

25

Time (s)

Time (s)

2 0 -2 -4

0 -2 -4

5

10

15

20

25

30

35

40

45

0

5

10

15

Aftershock

Gap (10 s)

Mainshock -6

0

Seismic sequence Single aftershock Static loading

2

Aftershock

Gap(10s)

Mainshock -6

Aftershock

Gap(10s)

Mainshock 0

20

25

30

35

40

45

50

55

Time (s)

Time (s)

(c)

(d)

Fig. 7.6 Time histories of horizontal displacement at crest of dam for typical seismic sequences. a Mammoth Lakes, Station: 54099-Comp. 90, b Kozani, Station: ITSAK-Comp. 90, c Whittier Narrows, Station: 24402-Comp. 90, and d Cape Mendocino/Petrolia, Station: 2585-Comp. 270

may induce residual displacements toward the downstream direction, unlike the corresponding mainshocks, which induce displacements in the upstream direction. However, in most of the cases, seismic sequences generally lead to a higher and more intense response when compared to the worst single seismic event.

7.4.3 Damage Dissipated Energy Another critical parameter is the damage dissipated energy (E d ), which can be computed by numerical quadrature according to the following equation.  dt Ed = v

1 el ε : E: εel dddv 2

(7.5)

0

where d t is the current damage level, E is the elastic tensor, εel is the elastic strain, and v is the volume. This parameter is useful to evaluate the potential damage that the structure has sustained. Figure 7.7 shows the damage-induced dissipated energy curves of the Koyna dam subjected to sequential and single seismic events. The solid lines represent the energy dissipated during the mainshock–aftershock seismic sequences, whereas the dashed lines denote the energy dissipated during the single aftershock ground motions. For comparison, the starting time of the single aftershock

7 Damage Demand Assessment of Concrete Gravity … 30

Seismic sequence Single aftershock

25

27.8 KN.m

20 12.9 KN.m

15 10 5 0 -5

0

5

10

Aftershock

Gap (10 s)

Mainshock 15

20

25

30

35

Damage dissipated energy (KN.m)

Damage dissipated energy (KN.m)

172

30

Seismic sequence Single aftershock

25

6.2 KN.m

20 15

9.2 KN.m

10 5 0 -5

5

10

Time (s)

15

20

37.7 KN.m

5

10

15

Aftershock

Gap (10 s) 20

25

Time (s)

(c)

30

35

40

45

Damage dissipated energy (KN.m)

Damage dissipated energy (KN.m)

69.1 KN.m

0

30

35

40

(b)

Seismic sequence Single aftershock

Mainshock

25

Time (s)

(a)

80 70 60 50 40 30 20 10 0 -10

Aftershock

Gap (10 s)

Mainshock 0

35

Seismic sequence Single aftershock

30 25

12.26 KN.m

19.8 KN.m

20 15 10 5 0 -5

Mainshock 0

5

Gap (10 s)

Aftershock

10 15 20 25 30 35 40 45 50 55

Time (s)

(d)

Fig. 7.7 Damage dissipated energy curves of the dam for typical seismic sequences. a Mammoth Lakes, Station: 54099-Comp. 90, b Kozani, Station: ITSAK-Comp. 90, c Whittier Narrows, Station: 24402-Comp. 90, and d Cape Mendocino/Petrolia, Station: 2585-Comp. 270

is adjusted to be the same as that of the aftershock in the seismic sequence. It is evident that more energy is dissipated during the seismic sequences than during the corresponding mainshocks. In some cases, the energy dissipation induced by the single aftershock is larger than that induced by the mainshock–aftershock seismic sequence. It is also interesting to observe that the energy dissipated during the single aftershock ground motions is higher than the additional energy dissipated during the seismic sequences. This means that the mainshock-damaged condition will strongly influence the subsequent nonlinear dynamic behavior.

7.5 Estimation of Damage Demands for Mainshock–Aftershock Seismic Sequences As described in Sect. 7.4, the typical seismic sequences require the increased capacity to withstand nonlinear demands (i.e. damage accumulation, residual displacement,

7.5 Estimation of Damage Demands for Mainshock–Aftershock Seismic Sequences

173

and damage dissipated energy) when compared to the corresponding single mainshocks. This section will examine the estimation of damage demands for both the asrecorded seismic sequences and repeated earthquakes. In order to quantify the structural damage demand of the concrete gravity dam under investigation, the damage index (DI) and damage dissipated energy are computed.

7.5.1 Effects of as-Recorded Mainshock–Aftershock Seismic Sequences The damage demands of the concrete gravity dam subjected to mainshock–aftershock seismic sequences can be characterized by the additional damage due to the aftershock ground motions with respect to the mainshock ground motions. Figure 7.8 shows the local and global damage indices corresponding to the selected 20 asrecorded mainshock–aftershock seismic sequences. The damage level for the single mainshocks and single aftershocks is indicated in this figure. The mean values of damage indices for the single and sequential seismic events are also indicated in Fig. 7.8. It can be observed that in any as-recorded seismic sequences, strong aftershocks cause increased damage both in the local and global levels. This implies that strong aftershocks influence the accumulated damage significantly during multiple seismic events. However, it should be emphasized that aftershock risks are not always high for all situations. The ground motion database COSMOS lists only the major aftershock records, and thus the selected mainshock–aftershock records are demanding or more critical cases with respect to the other typical cases. As shown in Fig. 7.8, the seismic sequences increase the damage indices (both the local and global indices) when compared to the single mainshock ground motions. On an average, the global index of the dam corresponding to the as-recorded seismic sequences is 1.41 times of that corresponding to the single mainshocks. The local damage indices of the upper part and heel of the dam subjected to the mainshock– aftershock seismic sequences appear to increase by 45% and 25%, respectively, with respect to that obtained for the corresponding single mainshocks. The mean values of the additional damage indices of the upper part of the dam, heel of the dam, and entire dam corresponding to the as-recorded mainshock–aftershock seismic sequences are 0.24, 0.04, and 0.09, respectively. This indicates that the additional damage caused by the aftershocks is more pronounced for the upper part of the dam, and the accumulated damage of the heel of the dam is not very sensitive to the seismic sequences. From Fig. 7.8, it can be observed that in some cases, the damage index corresponding to the single strong aftershocks may be larger than that corresponding to the single mainshocks, which implies that a single aftershock event may cause more damage to the dam than a single mainshock event. This is because the mainshock and the corresponding aftershock have significantly different ground motion characteristics. In some seismic sequences, although the magnitude of the mainshock is greater

174

7 Damage Demand Assessment of Concrete Gravity …

Fig. 7.8 Damage indices of the dam for typical seismic sequences. a Local damage index for the upper part of the dam, b local damage index for the dam heel, and c global damage index for the whole dam

than that of the major aftershock, the intensity of the major aftershock (measured by the PGA) is greater than that of the corresponding mainshock. Figure 7.9 shows the ratios of the additional damage demands induced by the aftershock of as-recorded mainshock–aftershock seismic sequences (DIas ) to those of the undamaged dam subjected to the single aftershocks (DIas). The additional damage index depends not only on the level of damage following the mainshock but also on the ground motion characteristics of the aftershock. It is interesting to observe that for all the ratios lower than 1.0, strong aftershocks will cause greater damage

7.5 Estimation of Damage Demands for Mainshock–Aftershock Seismic Sequences

175

1.0 Upper part; Mean=0.39 Dam heel; Mean=0.22 Global; Mean=0.31

ΔDIas/DIas

0.8 0.6 0.4 0.2 0.0

0

2

4

6

8

10

12

14

16

18

20

No.

Fig. 7.9 Ratios of additional damage indices of the mainshock-damaged dam subjected to aftershocks (DIas ) to damage indices of the undamaged dam subjected to single aftershocks (DIas )

to the undamaged dam than to the mainshock-damaged dam, as shown in Fig. 7.9. Especially, the local damage index ratio and the global index ratio shown in Fig. 7.9 are lower than 0.5 for most seismic sequence ground motions. This may be because the downstream and upstream surfaces of the upper part of the dam as well as the heel of the dam are characterized by high tensile stress under strong ground motions. The initial damage always appears in these high-stress areas and quickly extends to the inside of the dam. After the crack propagates to a certain depth, the development of the damage slows down even under the same loading condition. Hence, strong aftershocks will cause a smaller additional damage to the mainshock-damaged dam than when they are applied to the undamaged dam. It should also be noted that this observation might be specific to the selected strong aftershock records, dam types, and modeling assumptions adopted in the structural model as well as the damage measures. When moderate or small aftershocks, which may not cause damage to the undamaged dam, are selected as the seismic input, the relevant conclusion may not be applicable. The mean ratios of the local damage indices of the upper part and heel of the dam are 0.39 and 0.22, respectively, whereas the mean ratio of the global damage index is 0.31. This means that the structural damage induced by the mainshock–aftershock seismic sequences is not a linear superposition of the single mainshock and single aftershock. On an average, the additional damage indices of the mainshock-damaged dam subjected to aftershocks decreased by approximately 60% with respect to the undamaged dam subjected to the corresponding single aftershocks. The ratios of the additional damage dissipated energy of the mainshock-damaged dam subjected to aftershocks (DDEas ) to that of the undamaged dam subjected to single aftershocks (DDEas ) are also computed for each as-recorded mainshock– aftershock ground motion, as shown in Fig. 7.10. The mainshock–aftershock seismic sequences strongly affect damage dissipated energy, in addition to the aforementioned damage indices. It is obvious that all the ratios in Fig. 7.10 are lower than

176

7 Damage Demand Assessment of Concrete Gravity … 1.0 Mean=0.59

ΔDDEas/DDEas

0.8 0.6 0.4 0.2 0.0

0

2

4

6

8

10

12

14

16

18

20

No. Fig. 7.10 Ratios of additional damage dissipated energy of the mainshock-damaged dam subjected to aftershocks (DDEas ) to that of the undamaged dam subjected to single aftershocks (DDEas )

1.0, which also implies that strong aftershocks will cause greater damage to the undamaged dam than to the mainshock-damaged dam.

7.5.2 Comparative Analysis of Damage Demands Between as-Recorded Seismic Sequences and Repeated Earthquakes In order to identify the influence of ground motion characteristics of aftershocks on the damage demands of the mainshock-damaged dam, the earthquake accelerograms of aftershocks are constructed by using different methods. The as-recorded mainshock–aftershock seismic sequences presented in Sect. 7.2.1 are considered as the reference Case 1. For comparison, the PGA of the aftershock of the asrecorded seismic sequences is also scaled to have the same value of 0.34 g (with a scaling factor of 0.8526 (Hatzigeorgiou and Beskos 2009)), namely, Case 2. Additionally, earthquake accelerograms of the mainshocks are simply repeated to form the earthquake accelerograms of the aftershock. In this way, the mainshock–aftershock seismic sequences are modeled by using back-to-back identical accelerograms, namely, repeated earthquakes. Two different levels of PGA are considered for the aftershock ground motion: 0.4 g (without scaling the mainshock to obtain the aftershock) and 0.34 g for Case 3 and Case 4, respectively. Table 7.3 summarizes the cases for each seismic sequence considered in this study. The PGA ratio for the seismic sequences is defined as the ratio of the PGA of the aftershock (PGAas ) to the PGA of the mainshock (PGAms ). The analyses described in Sects. 7.4 and 7.5.1 are with respect to Case 1. Figure 7.11 shows the additional damage index for the upper part of the dam, heel of the dam, and entire dam that are subjected to both the as-recorded seismic sequences and the repeated earthquakes. Table 7.4 summarizes the mean values of the

7.5 Estimation of Damage Demands for Mainshock–Aftershock Seismic Sequences

177

Table 7.3 List of the computed cases and information of mainshock-aftershock seismic sequences considered in this investigation Description As-recorded seismic sequences

Repeated seismic sequences

Case

Number of records

PGA Mainshock (g)

Aftershock (g)

Ratio (PGAas /PGAms )

Case 1

20

0.40

Adjusting along with the corresponding mainshock

The same with the non-modified records

Case 2

20

0.40

0.34

0.8526

Case 3

20

0.40

0.40

1.0

Case 4

20

0.40

0.34

0.8526

damage indices corresponding to the mainshocks and the additional damage indices corresponding to the aftershocks for the upper part of the dam, heel of the dam, and entire dam. The increasing damage index ratio is defined as the ratio of the additional damage indices of the mainshock-damaged dam subjected to aftershocks (DIas ) to the damage indices of the undamaged dam subjected to single mainshocks (DIms ). It can be observed that the selection of the aftershock ground motions influences the damage demands of the concrete gravity dam significantly. The damage demands triggered by the mainshocks are larger than those triggered by the aftershocks are. It can be observed from the results of Case 1 and Case 2 that the mean values of the additional damage indices corresponding to the as-recorded aftershocks are approximately the same, especially for the local damage index of the upper part of the dam. This means that when the as-recorded mainshock–aftershock seismic sequences are selected as the seismic input, the aftershocks can also be scaled to have the same PGA based on an empirical PGA ratio, which is derived using the ratio of the empirical attenuation functions (Hatzigeorgiou and Beskos 2009) (e.g., a PGA ratio of 0.8526 for the aftershocks). It can be observed from the results of Case 3 and Case 4 that the repetition of the identical earthquake ground motions (Case 3) triggers slightly more additional damage demands of the dam at the end of the same earthquake ground motion (Case 4). It can be observed that the smaller the PGA of the aftershocks in the repeated approach, the lower the additional damage indices. Comparing the damage demands of the as-recorded seismic sequences (Case 1 and Case 2) and repeated earthquakes (Case 3 and Case 4), the additional damage indices corresponding to the aftershocks are more pronounced when the aftershocks are as recorded with respect to the mainshocks. An important finding for the performance assessment of the concrete gravity dam subjected to a mainshock–aftershock scenario is that the damage demands computed from the repeated seismic sequences are, in general, smaller than that computed from the as-recorded seismic sequences. This means that the use of repeated earthquakes tends to underestimate the amplitude of the damage demands, especially when the PGA of the aftershocks of the repeated seismic sequences is scaled with a PGA ratio of 0.8526 (Case 4).

178

7 Damage Demand Assessment of Concrete Gravity … Case 1 Case 2 Case 3 Case 4

Additional damage index

0.6 0.5

Mean=0.240 Mean=0.244 Mean=0.198 Mean=0.111

0.4 0.3 0.2 0.1 0.0 0

2

4

6

8

10

12

14

12

14

16

18

20

No.

(a)

Additional damage index

0.18

Case 1 Case 2 Case 3 Case 4

0.15 0.12

Mean=0.040 Mean=0.046 Mean=0.035 Mean=0.015

0.09 0.06 0.03 0.00 -0.03 0

2

4

6

8

10

16

18

20

No.

(b) Additional damage index

0.25

Case 1 Case 2 Case 3 Case 4

0.20

Mean=0.088 Mean=0.092 Mean=0.074 Mean=0.038

0.15 0.10 0.05 0.00 0

2

4

6

8

10

12

14

16

18

20

No.

(c)

Fig. 7.11 Additional damage index caused by different seismic sequence cases. a Upper part of the dam, b dam heel, and c entire dam

It should be noted that the approach of using the mainshock as an aftershock, has been found in (Li and Ellingwood 2007; Ruiz-García and Negrete-Manriquez 2011; Goda 2015) to overestimate the drift demands of the frame structures when compared to the as-recorded mainshock–aftershock seismic sequences. From these studies, one may naturally expect the same outcome for concrete dams and conclude

0.539

0.539

0.539

0.539

Case 2

Case 3

Case 4

DIms

0.111

0.198

0.244

0.240

DIas

20.6

36.7

45.3

44.5

DIas /DIms (%)

Local damage index for the upper part of the dam

Case 1

Case

0.198

0.198

0.198

0.198

DIms

0.015

0.035

0.046

0.040

DIas

7.6

17.7

23.2

20.2

DIas /DIms (%)

Local damage index for the dam heel

0.280

0.280

0.280

0.280

DIms

0.038

0.074

0.092

0.088

DIas

13.6

26.4

32.9

31.4

DIas /DIms (%)

Global damage index for the dam

Table 7.4 Average values of damage indices under mainshocks and additional damage indices under aftershocks

7.5 Estimation of Damage Demands for Mainshock–Aftershock Seismic Sequences 179

180

7 Damage Demand Assessment of Concrete Gravity …

that it is conservative (or safe) to use repeated earthquakes of this kind. However, the presented study, which is specific to the concrete gravity dams, suggests that repeated earthquakes of this kind should be used with more caution. The underlying reason for this observation may be attributed to the fact that concrete gravity dams are massive concrete structures. The structural characteristics, seismic failure modes, and damage measures of concrete gravity dams are quite different from those of the frame structures. According to the results of the study, once a crack propagates to a certain depth in the dam body (mainshock-damaged dam), strong ground motions, which have the same frequency content as that of the mainshock, tend to slow down subsequent damage development when compared to the as-recorded aftershocks. In addition, it should be noted that the observation of this chapter might be specific to the selected strong aftershock records, dam types, modeling assumptions as well the damage measures. Comparing Case 2 and Case 4, the additional damage indices in the upper part of the dam, heel of the dam, and entire dam computed from the as-recorded seismic sequences are larger by approximately 54.5%, 67.4%, and 58.7%, respectively, than the corresponding additional damage indices calculated from the repeated earthquakes.

7.6 Conclusions This study presents the damage demand assessment for the concrete gravity dam– reservoir–foundation systems subjected to as-recorded and artificial mainshock– aftershock seismic sequences. The main innovation of this work is the quantification of the effects of aftershocks directly into the damage demands of the mainshockdamaged dam. For this purpose, a set of 20 as-recorded mainshock–aftershock earthquake ground motions is considered in this study, and four approaches are employed to form the mainshock–aftershock seismic sequences. The following conclusions are drawn from this investigation: (1) Although the strong motion duration and PGA amplitude of the mainshocks and the major aftershocks considered in this investigation are correlated in an approximately linear fashion, the frequency content of the mainshocks, which is measured by using the predominant period of the ground motion, is weakly correlated with their corresponding frequency content of the aftershocks. Thus, it can be concluded that the simulation approach of repeating the mainshock as an aftershock is not appropriate. (2) There exists a significant contrast in the damage profile between a single mainshock event and a single aftershock event because of their different ground motion characteristics. However, the damage induced by the mainshock propagates sequentially during the aftershock. (3) Mainshock–aftershock seismic sequences lead to an increase in the accumulated damage of the concrete gravity dam. Strong aftershocks will cause greater

7.6 Conclusions

181

damage demands to the undamaged dam than to the mainshock-damaged dam. The additional damage indices of the mainshock-damaged dam that is subjected to aftershocks decrease by approximately 60% with respect to the undamaged dam that is subjected to only the aftershocks. (4) The aftershock ground motions selected by using different approaches influence the damage demands of the concrete gravity dam–reservoir–foundation system significantly. The as-recorded aftershocks cause a greater additional damage to the mainshock-damaged dam than the artificial aftershocks of the repeated approach. Repeated earthquakes tend to underestimate the level of damage demands, especially for a PGA ratio of 0.8526. When the as-recorded mainshock–aftershock seismic sequences are selected as the seismic input, the as-recorded aftershock accelerograms can be adjusted along with their corresponding mainshocks or scaled to have the same PGA by using an empirical PGA ratio.

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Chapter 8

Earthquake Direction Effects on Nonlinear Dynamic Response of Concrete Gravity Dams to Seismic Sequences

8.1 Introduction Historical earthquakes have shown that a large mainshock can usually trigger numerous aftershocks within a short period of time. For example, the 2010 Chile earthquake had a mainshock measuring 8.8 M w followed by 306 aftershocks with the magnitude greater than 5.0, and 21 aftershocks with the magnitude greater than 6.0 (Ruiz-García and Negrete-Manriquez 2011). This means that man-made civil engineering structures (e.g., concrete gravity dams) in the seismically active region are not exposed to a single seismic event, but to a sequence of seismic shocks consisting of foreshock, mainshock, and aftershock. However, the modern performance-based assessment methodology for evaluation of concrete gravity dams is only based on a single earthquake event in current seismic codes [e.g. in China (Chinese 2011)]. The phenomenon of multiple earthquakes has not been considered adequately. It has been recognized that strong aftershocks have the potential to cause additional cumulative damage to the mainshock-damaged structures. Despite the fact that the influence of mainshock-aftershock seismic sequences on the nonlinear dynamic response of structures has been qualitatively acknowledged (Fakharifar et al. 2015; Jeon et al. 2016; Song et al. 2016; Konstandakopoulou and Hatzigeorgiou 2017; Moshref et al. 2017; Rinaldin et al. 2017; Shin and Kim 2017; Zhai et al. 2017), nonlinear dynamic response analysis and seismic performance evaluation of concrete gravity dams are mainly based on a single earthquake event (Zhang et al. 2013b; Hariri-Ardebili and Saouma 2015; Wang et al. 2015; Hariri-Ardebili et al. 2016; Soysal et al. 2016; Bybordiani and Arıcı 2017; Yazdani and Alembagheri 2017). To the best of our knowledge, only a few researchers have investigated the influence of strong aftershocks on the seismic demands of dams (Alliard and Léger 2008; Xia et al. 2010; Zhang et al. 2013a; Wang et al. 2017a). In addition, these studies all revealed that strong aftershocks have a significant influence on the nonlinear seismic demands of dams. Thus, ground accelerations of mainshock-aftershock sequences represent a real situation that requires special treatment in the dam seismic design. © Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_8

185

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8 Earthquake Direction Effects on Nonlinear Dynamic Response …

The time history analysis method has been widely used to evaluate the seismic performance of dams. When as-recorded ground motion accelerograms are selected as the seismic input for two-dimensional analyses of concrete gravity dams, one horizontal seismic component is generally applied to the foundation base in the upstream-downstream direction. The downstream-upstream direction has not been considered. However, previous studies indicate that the orientation of the seismic input with regard to the principal structural axes has a significant influence on the structural response. Changing the orientation of the seismic input may lead to a quite different structural response, which can radically alter the analysis results in terms of the damage level and damage characteristics. Rigato and Medina (2007) examined the influence of the earthquake direction on seismic demands for inelastic single-story structures subjected to bi-directional ground motions. They concluded that applying bi-directional ground motions only along the principal axes of structures would underestimate the inelastic peak deformation demand. Hosseinpour and Abdelnaby (2017) investigated the performance of the irregular structures subjected to seismic sequences in different directions. Their results indicated that changing the earthquake direction will significantly affect the residual drifts in most cases. Hatzivassiliou and Hatzigeorgiou (2015) examined the effect of seismic sequence direction incident on the nonlinear response of building structures for different siting configurations. Ruiz-García and Aguilar (2015) studied the effect of aftershock direction (aftershock polarity) on the aftershock collapse potential. Their observation showed that the aftershock direction has a significant influence not only on the aftershock collapse capacity but also in the aftershock capacity against demolition. Morfidis and Kostinakis (2017) employed 12 different incident angles to account for the influence of earthquake direction on the dynamic response of RC buildings with masonry infills to seismic sequences. They found that it is of great importance to account for the direction of the seismic motion. Raghunandan et al. (2015) mentioned that when the residual drift resulting from a mainshock is high, the direction of the aftershock with respect to the mainshock is important. Kostinakis et al. (2015) investigated the impact of the seismic excitation angle on the damage level of 3D multi-story RC buildings. They proposed that the common practice of applying the seismic ground motions along the structural axes can lead to significant underestimation of structural damage. However, the aforementioned studies are aimed at the reinforced concrete building structures. Despite the significance of the incidence directions of the ground motion records, few studies have focused their attention on the nonlinear response of concrete gravity dam-reservoir-foundation systems subjected to seismic sequences in different incidence directions. The seismic sequence direction may influence the cumulative damage processes of the dams, which will lead to different failure mechanisms. The objective of this chapter is to better understand differences in structural response and damage on concrete gravity dams when subjected to mainshock-aftershock seismic sequences with different incidence directions. To accomplish this purpose, two seismic incident directions (i.e. the upstream-downstream and downstream-upstream directions) are applied along horizontal axes of the two-dimensional model. Nonlinear dynamic

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187

response of the concrete gravity dam-reservoir-foundation system subjected to asrecorded mainshock-aftershock sequences is conducted. The effects of direction of single earthquake events, direction of seismic sequences, aftershock polarity are investigated. The influence of the intensity of ground motions on the seismic sequence direction effects is also discussed.

8.2 Earthquake Incident Direction for Two-Dimensional Seismic Performance Analysis The length of the dam axis of concrete gravity dams is generally very long. In order to adapt the deformation requirements of the foundation and minimize the cracking caused by the shrinkage, concrete gravity dams are constructed as individual monoliths that are separated by contraction joints. Owing to the presence of contraction joints, most of the nonlinear dynamic response analyses of concrete gravity dams are through two-dimensional (2D) model (Wang et al. 2017b). When the time history analysis method is selected to assess the seismic performance of concrete gravity dams based on the two-dimensional model, earthquake accelerations (artificial or as-recorded) are applied to the foundation base as the input load. However, due to the uncertainty of the location of the epicenter of the next earthquake, different incidence directions of the selected strong ground motion records should be considered in order to assess the maximum structural demands. Hence, for two-dimensional seismic performance analysis of concrete gravity damreservoir-foundation systems, two earthquake incidence directions should be considered. Figure 8.1 shows the configurations of two incident directions for the twodimensional model of concrete gravity dams. One is the upstream-downstream direction. Another one is the downstream-upstream direction).

(a)

(b)

Fig. 8.1 Two siting configurations of earthquake direction for the concrete gravity dam-reservoirfoundation systems based on two-dimensional model: a the upstream-downstream direction, and b the downstream-upstream direction

188

8 Earthquake Direction Effects on Nonlinear Dynamic Response …

8.3 Finite Element Model 8.3.1 Description of Finite Element Model of Dam-Foundation-Reservoir Systems In order to evaluate the influence of the earthquake direction on the nonlinear dynamic response of concrete gravity dams to mainshock-aftershock seismic sequences, the Koyna concrete gravity dam is selected as a representative numerical example. The finite element (FE) discretization of the Koyna dam–reservoir–foundation system is illustrated in Sect. 2.5. The foundation rock is assumed to be massless to avoid wave propagation effects when applying free field earthquake records at the foundation base. The reservoir water is assumed to be linearly elastic, irrotational, and inviscid. The energy dissipation of the dam-reservoir-foundation system is considered by the Rayleigh damping method with 5% damping ratio. Applied loads include the selfweight of the dam, hydrostatic, uplift, hydrodynamic, and earthquake forces. The static solutions of the dam due to its gravity loads and hydrostatic loads are taken as initial conditions in the dynamic analyses of the system. For the initial time step, the nodal displacements on the left and right truncated boundary of the dam–reservoir–foundation system are assumed as zero in the normal direction. In addition, the foundation base is fully constrained. In the sequent dynamic analysis, all the displacement constraints are released, and the selected earthquake accelerations are applied to the foundation base as the input load. At the fluid– solid interface, the displacement in the direction normal to the interface is assumed continuously during the entire simulation.

8.3.2 Input Ground Motions In order to obtain the nonlinear behavior of concrete gravity dams subjected to seismic sequences by time history analysis method, four as-recorded mainshockaftershock earthquake records, namely, Mammoth Lakes (1980), Kozani (1995), Whittier Narrows (1987), and Cape Mendocino/Petrolia (1992) events, are selected from the database provided by the COSMOS (COSMOS 2019). The details of these ground motion records are listed in Table 8.1. Each selected mainshock–aftershock seismic sequence is recorded at the same station and in the same direction. For the comparison purpose, mainshock accelerograms of aforementioned seismic sequences are scaled to have the same PGA of 0.40 g. The aftershock accelerograms are adjusted along with their corresponding mainshock accelerograms. Thus, aforementioned four typical sequential ground motions are multiplied by 0.976 (Mammoth Lakes seismic sequences), 2.885 (Kozani seismic sequences), 2.485 (Whittier Narrows seismic sequences), and 1.236 (Cape Mendocino/Petrolia seismic sequences). The scaled mainshock-aftershock seismic records with different durations are illustrated in Fig. 8.2. Every sequential ground motion is constructed as a

Seismic sequences

Mammoth Lakes

Kozani

Whittier Narrows

Cape Mendocino/Petrolia

No.

1

2

3

4

1585

24402

ITSAK

54099

Station location

270

90

90

90

Comp.

7.0(Mw ) 6.6(Ms )

1992-04-26 (07:41:00)

5.3(Mw )

1987-10-04 (10:59:38) 1992-04-25 (18:06:04)

6.1(Mw )

5.3(ML )

1995-05-17 (04:14:00) 1987-10-01 (14:42:20)

6.1(ML )

5.7(ML )

1980-05-25 (20:35:48) 1995-05-13 (08:47:00)

6.1(ML )

Mag

1980-05-25 (16:33:44)

Date

Table 8.1 List of mainshock-aftershock seismic sequences considered in this investigation

33.3

26.5

18.2

19.4

12.1

19.5

3.4

9.1

R (km)

344.20

317.60

187.90

157.90

119.26

136.00

338.87

402.19

Recorded PGA (cm/s2 )

0.30

0.16

0.14

0.22

0.14

0.20

0.16

0.22

Predominant period (s)

6.76

10.65

3.04

8.1

5.63

7.72

3.54

8.96

Duration (5–95%) (s)

8.3 Finite Element Model 189

190

8 Earthquake Direction Effects on Nonlinear Dynamic Response … 400

Mammoth Lakes seismic sequence

Kozani seismic sequence

2

Acceleration (cm/s )

2

Time gap (10 s)

1980/05/25 16:33:44

1980/05/25 20:35:48

0 -200 -400 0

5

10

15

20

25

30

200 Time gap (10 s)

0 -200 -400

0

35

1983/07/25 22:31:39

200

1983/07/22 02:39:54

Acceleration (cm/s )

400

5

10

15

20

Time (s)

35

40

Cape Mendocino/Petrolia seismic sequence

400

2

Acceleration (cm/s )

Whittier Narrows seismic sequence

-400 0

5

10

1987/10/04 10:59:38

-200

15

20

25

30

35

40

200 Time gap (10 s)

0 -200 -400

45

Time (s)

(c)

1992/04/26 07:41:00

Time gap (10 s)

0

1992/04/25 18:06:04

200

1987/10/01 14:42:20

2

Acceleration (cm/s )

30

(b)

(a)

400

25

Time (s)

0

5

10

15

20

25

30

35

40

45

50

55

Time (s)

(d)

Fig. 8.2 Four as-recorded mainshock–aftershock seismic sequences: a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

unique seismic record where between mainshock-aftershock seismic events a time gap of ten seconds is applied. This gap has zero acceleration ordinates and is adequate to allow the structure to cease moving after the previous seismic event.

8.4 Effects of Earthquake Direction In order to see the seismic performance of concrete gravity dams subjected to ground motions in different directions, different sequences are employed and applied in both upstream-downstream and downstream-upstream directions. The effects of direction of single earthquake events, direction of seismic sequences, and aftershock polarity on the nonlinear dynamic response of concrete gravity dams to strong ground motions are evaluated. It should be noted that applying aftershocks without their mainshock to the dam is aimed to observe the influence of the aftershock on the accumulated damage of the mainshock-damaged dams.

8.4.1 Direction Effects of Single Earthquake Events Figure 8.3 shows the final damage profile of the Koyna gravity dam subjected to single mainshock and aftershock events with different incidence directions. Figure 8.3 clearly shows the differences between the damage characteristics of the Koyna dam

8.4 Effects of Earthquake Direction Mainshock Upstreamdownstream direction

191

Mainshock Downstreamupstream direction

Aftershock Upstreamdownstream direction

Aftershock Downstreamupstream direction

Aftershock Upstreamdownstream direction

Aftershock Downstreamupstream direction

(a) Mainshock Upstreamdownstream direction

Mainshock Downstreamupstream direction

(b) Mainshock Upstreamdownstream direction

Mainshock Downstreamupstream direction

Aftershock Upstreamdownstream direction

Aftershock Downstreamupstream direction

(c) Mainshock Upstreamdownstream direction

Aftershock Upstreamdownstream direction

Mainshock Downstreamupstream direction

Aftershock Downstreamupstream direction

(d)

Fig. 8.3 Damage profiles of the Koyna dam under single seismic events in different incidence directions. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

192

8 Earthquake Direction Effects on Nonlinear Dynamic Response …

when it was subjected to the selected as-record records applied along the upstreamdownstream and downstream-upstream directions. Changing the earthquake direction significantly affects the damage propagation processes of the upper part of the dam. The accumulated damage on the heel is not very sensitive to the earthquake incidence direction. Although the cracking profiles in the upper part of the dam are initiated at the change in the slope of the downstream face in most analyses, the crack propagation direction and crack length in the subsequent analysis are significantly different when subjected to different earthquake directions. In some stations, cracks are predicted to initialize near the middle of the upstream face and extend into the dam toward the downstream face when subjected to ground motions in the upstreamdownstream direction. However, this cracking path of the dam will be completely changed when subjected to the same ground motions in the downstream-upstream direction. It is also observed from Fig. 8.3 that there is a significant difference in the damage profile of the upper part of the dam under the single seismic events. This may be because that the selected single ground motions have different ground motion characteristics (i.e. frequency content, peak ground acceleration, and strong motion duration). In some cases, the single aftershock ground motions can also cause serious damage to the dam with the formation of the penetrated crack. This means that the strong aftershock ground motions have the potential to cause additional damage to the dam and cannot be simply repeated by the mainshocks. The time history of the horizontal displacements at the crest of the dam subjected to the single mainshock ground motions with two incidence directions is shown in Fig. 8.4. The horizontal displacement response of the dam subjected to single aftershock events with two incidence directions is also illustrated in Fig. 8.5. The positive displacement is assumed toward the downstream direction. The initial displacement is 0.29 cm, which is caused by the static loads. It can be observed from Figs. 8.4 and 8.5 that the earthquake direction has a significant influence on the nonlinear displacement response of the dam. In most cases, changing the earthquake direction will affect the direction of the maximum horizontal displacements (indicated by the positive and negative values in Figs. 8.4 and 8.5). In some stations, the nonlinear displacement response in two directions is not significantly different at the beginning, but the difference increases under the subsequent seismic input. In some cases, the upstream-downstream incidence direction may induce residual displacements toward the downstream direction, and the downstream-upstream incidence direction may induce residual displacements toward the upstream direction. The differences between the total residual displacements are more than 2.35 cm for two earthquake directions (see Fig. 8.5c). However, in some cases, the residual displacements are toward the same direction under the two earthquake directions.

8.4 Effects of Earthquake Direction

193 Upstream-downstream direction Downstream-upstream direction

3

Displacement (cm)

Displacement (cm)

3 2 1 0 -1 -2 -3

Upstream-downstream direction Downstream-upstream direction

-4 0

3

6

2 1 0 -1 -2 -3 -4

9

12

Time(s)

15

0

5

Time(s)

(a) Upstream-downstream direction Downstream-upstream direction

3 2 1 0 -1 -2 -3 5

10

15

Time(s)

Upstream-downstream direction Downstream-upstream direction

3

-4 0

15

(b) 4

Displacement (cm)

Displacement (cm)

4

10

2 1 0 -1 -2 -3 -4

20

0

5

10

(c)

15

20

Time(s)

25

(d)

4

4

Upstream-downstream direction Downstream-upstream direction

3 2 1 0 -1 -2 -3

Upstream-downstream direction Downstream-upstream direction

3

Displacement (cm)

Displacement (cm)

Fig. 8.4 Horizontal displacements of the dam crest under single mainshock events in different incidence directions. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

-4

2 1 0 -1 -2 -3 -4

0

3

6

0

9

5

Time(s)

15

(b) 5

Upstream-downstream direction Downstream-upstream direction

Upstream-downstream direction Downstream-upstream direction

4

Displacement (cm)

Displacement (cm)

(a) 5 4 3 2 1 0 -1 -2 -3 -4 -5

10

Time(s)

3 2 1 0 -1 -2 -3

0

5

10

Time(s)

(c)

15

-4

0

5

10

15

20

Time(s)

(d)

Fig. 8.5 Horizontal displacements of the dam crest under single aftershock events in different incidence directions. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

194

8 Earthquake Direction Effects on Nonlinear Dynamic Response …

8.4.2 Direction Effects of Mainshock–Aftershock Seismic Sequences Figures 8.6 and 8.7 show the final damage profiles of the Koyna dam subjected to the as-recorded mainshock-aftershock seismic sequences with two earthquake incidence directions. As shown, it can be found that the earthquake direction has a significant influence on the damage propagation path and failure mechanism of the upper part of the dam to seismic sequence. The more serious damage the single aftershock events with different directions cause to the dam, the greater impact on the final damage the mainshock-aftershock seismic sequence direction has, such as the Mammoth Lakes and Whittier Narrows seismic sequences. The same seismic sequence with different incidence directions will cause more or less similar damage profile and damage level to the dam. By comparing Fig. 8.3 (single seismic events) with Figs. 8.6 and 8.7 (mainshockaftershock seismic events), it can be noted that the damage level of the upper part of

(a)

(b)

(c)

(d)

Fig. 8.6 Damage profiles of the Koyna dam under the selected mainshock-aftershock seismic sequences in the upstream-downstream direction. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

(a)

(b)

(c)

(d)

Fig. 8.7 Damage profiles of the Koyna dam under the selected mainshock-aftershock seismic sequences in the downstream-upstream direction. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

8.4 Effects of Earthquake Direction

195

4

4

Upstream-downstream direction Downstream-upstream direction Static loading

2

Displacement (cm)

Displacement (cm)

the dam subjected to the single mainshock ground motions is smaller in comparison to that subjected to mainshock-aftershock seismic sequences. Strong aftershock ground motions can cause significant additional damage to the mainshock-damaged dam. Although there are different failure modes of the dam when subjected to single mainshock and single aftershock, the seismic sequences do not lead to changes in the damage pattern of the dam during the aftershocks in general. Results of this study indicate that considering just a mainshock to evaluate the structural response in different directions may cause an underestimation in the difference between structural demands in different directions. Figure 8.8 shows the horizontal displacement time history of the dam crest to the mainshock-aftershock seismic sequences with two incidence directions. It is obvious that the mainshock-aftershock seismic sequence direction has a significant influence on the peak displacement demands. For example, the maximum positive and negative horizontal displacements of the crest dam under the Mammoth Lakes seismic sequences in the upstream-downstream direction are 3.70 cm and −2.73 cm, respectively. However, the maximum positive and negative displacements of the crest dams to the Mammoth Lakes seismic sequences in the downstream-upstream directions are 3.00 cm and −3.73 cm, respectively. Residual displacements are accumulated during the mainshock-aftershock seismic sequences. However, due to the influence of the mainshock-damaged, the residual displacements are always toward the upstream direction under the two earthquake directions.

0 -2 -4

5

Aftershock

Gap (10 s)

Mainshock

0

10

15

20

25

30

Upstream-downstream direction Downstream-upstream direction Static loading

2 0 -2 -4

35

5

10

15

Displacement (cm)

Displacement (cm)

4

Upstream-downstream direction Downstream-upstream direction Static loading

2 0 -2 -4 -6

0

5

10

Aftershock

Gap(10s)

Mainshock

15

20

25

Time (s)

(c)

25

30

35

40

(b)

(a)

4

20

Time (s)

Time (s) 6

Aftershock

Gap(10s)

Mainshock

0

30

35

40

45

Upstream-downstream direction Downstream-upstream direction Static loading

2 0 -2 -4 -6

Gap (10 s)

Mainshock

0

5

10 15

20

Aftershock

25 30 35 40 45

50 55

Time (s)

(d)

Fig. 8.8 Time histories of horizontal displacement at the dam crest under mainshock-aftershock seismic sequences with different incidence directions. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

196

8 Earthquake Direction Effects on Nonlinear Dynamic Response …

8.4.3 Effects of Aftershock Polarity Previous studies have shown that the mainshock or the aftershock accelerograms in a sequence could have the opposite as-recorded value. This means that the mainshockaftershock could have different polarity (Raghunandan et al. 2012; Ruiz-García and Aguilar 2015). To investigate the effects of aftershock polarity on the nonlinear dynamic response in this study, the aftershock ground motions followed by the mainshocks are assumed to have the same incidence direction (i.e. positive polarity) and the opposite incidence direction (i.e. negative polarity) with the corresponding mainshock ground motions. Figure 8.9 shows the damage profiles of the dam under the mainshock-aftershock seismic sequences with considering the negative polarity of aftershocks. These results are compared with the cases when the mainshock and aftershock are in the same direction (Fig. 8.6). Findings indicate that when the single aftershock ground motions cause small damage to the undamaged dam, the aftershock polarity has a slight effect on the damage propagation process and damage demands of the dam. Unlike the direction effects of mainshock-aftershock seismic sequences, the aftershock polarity will not significantly change the damage pattern of the dam in general. This is because that the dam suffers the mainshocks with the same direction, and it is likely that the mainshock-damaged accumulates sequentially during the aftershock with different polarity. Figure 8.10 shows the horizontal displacement response of the crest dam under the selected mainshock-aftershock seismic sequences with different polarity for the aftershocks. In general, there is no significant difference between the displacement responses of the dam. However, maximum displacement demands are affected by aftershock polarity. In some stations (Fig. 8.10a), the aftershock earthquake ground motion with the negative polarity tends to move the dam to the opposite direction of the original post-mainshock residual displacement. This means that the aftershock polarity may lead to a recentering behavior.

(a)

(b)

(c)

(d)

Fig. 8.9 Damage profiles of the Koyna dam under the selected mainshock-aftershock seismic sequences with considering the negative polarity of aftershocks. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

2 0 -2

0

5

Aftershock

Gap (10 s)

Mainshock

-4

10

15 20 Time (s)

197

4

Upstream-downstream direction Downstream-upstream direction Static loading

4

Displacement (cm)

Displacement (cm)

8.5 Influence of the Ground Motion Intensity on the Seismic …

25

30

Upstream-downstream direction Downstream-upstream direction Static loading

2 0 -2 -4

35

5

10

15

(a) Displacement (cm)

Displacement (cm)

2 0 -2

0

5

10

15

20

30

35

40

25

Upstream-downstream direction Downstream-upstream direction Static loading

2 0 -2 -4

Aftershock

Gap(10s)

Mainshock

-6

25

(b) 4

Upstream-downstream direction Downstream-upstream direction Static loading

-4

20

Time (s)

6 4

Aftershock

Gap(10s)

Mainshock

0

30

35

40

-6

0

5

10

15

Aftershock

Gap (10 s)

Mainshock

45

20

Time (s)

(c)

25

30

35

40

45

50

55

Time (s)

(d)

Fig. 8.10 Time histories of horizontal displacement at the dam crest with considering the aftershock polarity effects. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

8.5 Influence of the Ground Motion Intensity on the Seismic Sequence Direction Effects In order to investigate the influence of the intensity of ground motions on the damage characteristics of the dam under seismic sequences in different incidence directions, as-recorded mainshock-aftershock seismic sequences are scaled to different intensity levels to produce response ranging from small to large nonlinear response of the dam. For this purpose, the nonlinear dynamic response analyses are carried out by scaling each real mainshock-aftershock record, to progressively increase the intensity of ground motions by increments of about 0.1 g. Hence, the mainshock accelerograms of the aforementioned seismic sequence are scaled to have the PGA of 0.3 g, 0.4 g, and 0.5 g, respectively. The aftershock accelerograms are adjusted along with their corresponding mainshock accelerograms. It should be noted that the nonlinear dynamic responses of the dam under seismic sequences with the mainshock PGA of 0.4 g are shown in Sect. 8.4.2. Figure 8.11 and Fig. 8.12 show the damage profiles of the Koyna dam subjected to seismic sequences in two directions with the mainshock PGAs of 0.3 g and 0.5 g, respectively. Comparing Figs. 8.6 and 8.7 with Figs. 8.11 and 8.12, it can be seen that the intensity of ground motions has a significant influence on the seismic sequence direction effects. When the mainshock PGA of seismic sequences is not high (i.e. 0.3 g), there is a slight difference between the damage demands and damage profiles for the dam subjected to seismic sequences in two incidence directions. In most cases, cracks in the upper part of the dam are initiated at the downstream slope change discontinuity and extend into the dam toward the upstream face when subjected to

198

8 Earthquake Direction Effects on Nonlinear Dynamic Response … Downstreamupstream direction

Upstreamdownstream direction

(a)

(b) Downstreamupstream direction

Upstreamdownstream direction

Downstreamupstream direction

Upstreamdownstream direction

Upstreamdownstream direction

(c)

Downstreamupstream direction

(d)

Fig. 8.11 Damage profiles of the Koyna dam subjected to mainshock-aftershock seismic sequences in different incidence directions with the mainshock PGA of 0.3 g. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia Downstreamupstream direction

Upstreamdownstream direction

(a) Upstreamdownstream direction

(b) Downstreamupstream direction

(c)

Downstreamupstream direction

Upstreamdownstream direction

Upstreamdownstream direction

Downstreamupstream direction

(d)

Fig. 8.12 Damage profiles of the Koyna dam subjected to mainshock-aftershock seismic sequences in different incidence directions with the mainshock PGA of 0.5 g. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

8.5 Influence of the Ground Motion Intensity on the Seismic …

199

two earthquake directions with the mainshock PGA of 0.3 g. However, as the PGA of the seismic sequences increases, the difference between the damage characteristics increases, and the structural demands also increase. This indicates that the damage demand and failure mechanism of the concrete gravity dam are more sensitive to the earthquake directions when subjected to seismic sequences with a higher PGA. In order to quantify the structural damage demands of the concrete gravity dams subjected to different incidence directions, the local damage index (DI), which is defined as the ratio of the length of a cracking path to the total cross-sectional length along the path, is computed. Figure 8.13 shows the local damage index of the upper part of the dam subjected to single mainshock events and mainshock-aftershock seismic sequences in different incidence directions. As shown, local damage indices of the examined dam during the selected as-recorded mainshock-aftershock accelerograms with large PGA are generally greater than those under small events. It can also be found that earthquake direction causes different damage demands to the dam. The difference between structural damage demands in different directions increases with the increase of the PGA. However, it should be noted that when strong ground motions (i.e. PGA=0.5 g) cause very serious damage to the dam, such as the penetrated crack,

Damage index

1.0

Upstream-downstream direction Downstream-upstream direction Kozani Mammoth Lakes

Whittier Narrows

Cape Mendocino/Petrolia

0.5

0.0 0.3g

0.4g 0.5g

0.3g 0.4g

0.5g

0.3g 0.4g 0.5g

0.3g 0.4g 0.5g

Damage index

(a)

1.0

Upstream-downstream direction Downstream-upstream direction Kozani Mammoth Lakes

Whittier Narrows

Cape Mendocino/Petrolia

0.5

0.0 0.3g

0.4g 0.5g

0.3g 0.4g

0.5g

0.3g 0.4g 0.5g

0.3g 0.4g 0.5g

(b) Fig. 8.13 Local damage index for the upper part of the dam subjected to single mainshock events and mainshock-aftershock seismic sequences in different incidence directions. a Single mainshock ground motions; b mainshock-aftershock seismic sequences

200

8 Earthquake Direction Effects on Nonlinear Dynamic Response …

Additional damage indices

0.5 0.4

Upstream-downstream direction Downstream-upstream direction Mammoth Lakes

Kozani

Whittier Narrows

Cape Mendocino/Petrolia

0.3 0.2 0.1 0.0

0.3g

0.4g 0.5g

0.3g

0.4g 0.5g

0.3g

0.4g 0.5g

0.3g

0.4g 0.5g

Fig. 8.14 Additional local damage index for the upper part of the dam caused by mainshockaftershocks seismic sequences

the local damage index cannot be used to evaluate the earthquake direction effects on the structural damage demands for the dam. Figure 8.14 shows the additional local damage index for the upper part of the dam caused by the aftershock ground motions. It is obvious that mainshock-aftershock seismic sequences cause an increment of the local damage index in comparison with single mainshock events. However, the influence degree of the mainshock-aftershock seismic sequences on the structural damage demands depends on the intensity of the selected ground motions. Weak aftershock ground motions have less effect on structural damage demands of the dam than strong aftershocks, which will lead to little additional damage to concrete gravity dams. In general, strong aftershock ground motions have a significant influence on the seismic performance of the dam. However, if strong mainshock ground motions have led to serious damage to the dam, the strong aftershocks may also cause little accumulated damage to the dam. Figures 8.15 and 8.16 show the time history of the horizontal displacements at the crest dam to different PGAs. It is obvious that seismic sequences, earthquake directions, and PGA strongly affect the nonlinear dynamic response behavior of the dam. As it can be seen in Fig. 8.15, the nonlinear dynamic responses in two directions are not significantly different when subjected to seismic sequences with the PGA of 0.3 g. However, the difference, especially for the residual displacements, significantly increases under the high PGA of 0.5 g (Fig. 8.16). It can also be found that the residual displacements are accumulated during the seismic sequences. Figure 8.17 shows the maximum positive and negative horizontal displacements of the dam crest subjected to mainshock-aftershock seismic sequences with different PGAs. Figure 8.18 illustrates the residual displacements for sequence ground motions with different PGAs. It can be seen from Figs. 8.17 and 8.18 that the earthquake direction has a significant influence on the maximum horizontal displacement and residual displacements. The calculated maximum horizontal displacements and residual displacements are all becoming more sensitive to the earthquake direction with the increase of the PGA. For example, maximum horizontal displacements of the dam subjected to the Kozani seismic sequence in the upstream-downstream and downstream-upstream directions with the mainshock PGA of 0.5 g are −6.12 cm and

8.5 Influence of the Ground Motion Intensity on the Seismic … 4

Upstream-downstream direction Downstream-upstream direction Static loading

2

Displacement (cm)

Displacement (cm)

4

0 -2 -4

0

5

Aftershock

Gap (10 s)

Mainshock

10

15

20

25

30

35

2 0 -2 -4 -6 0

5

10

Aftershock

Gap(10s)

Mainshock

15

20

25

Upstream-downstream direction Downstream-upstream direction Static loading

2 0 -2 -4

5

10

30

35

40

45

Aftershock

Gap(10s)

Mainshock

0

15

20

25

30

35

40

Time (s) (b)

4

Upstream-downstream direction Downstream-upstream direction Static loading

Displacement (cm)

Displacement (cm)

Time (s) (a) 4

201

Upstream-downstream direction Downstream-upstream direction Static loading

2 0 -2 -4

5

10

15

Aftershock

Gap (10 s)

Mainshock

0

20

25

30

35 40

45

50 55

Time (s)

Time (s) (c)

(d)

Fig. 8.15 Horizontal displacement of the crest dam subjected to mainshock-aftershock seismic sequences in different incidence directions with the mainshock PGA of 0.3 g. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia 6

Upstream-downstream direction Downstream-upstream direction Static loading

2

Displacement (cm)

Displacement (cm)

4

0 -2 -4 0

5

Aftershock

Gap (10 s)

Mainshock

10

15

20

25

30

Upstream-downstream direction Downstream-upstream direction Static loading

4 2 0 -2 -4

0

35

5

10

15

20

Upstream-downstream direction Downstream-upstream direction Static loading

0 -2 -4 -6 0

5

10

Aftershock

Gap(10s)

Mainshock

15

20

25

Time (s)

(c)

30

35

40

(b) 4 Displacement (cm)

Displacement (cm)

(a) 2

25

Time (s)

Time (s) 4

Aftershock

Gap(10s)

Mainshock

-6

Upstream-downstream direction Downstream-upstream direction Static loading

2 0 -2 -4 -6

35

40

45

0

5

10

15

Aftershock

Gap (10 s)

Mainshock

-8 30

20

25

30

35

40

45

50

55

Time (s)

(d)

Fig. 8.16 Horizontal displacement of the crest dam subjected to mainshock-aftershock seismic sequences in different incidence directions with the mainshock PGA of 0.5 g. a Mammoth Lakes, b Kozani, c Whittier Narrows, and d Cape Mendocino/Petrolia

202

8 Earthquake Direction Effects on Nonlinear Dynamic Response …

Maximum displacement (cm)

6 4

0.3g 0.4g

0.5g

0.3g 0.4g

0.3g 0.4g 0.5g

0.5g

0.3g 0.4g 0.5g

2 0 A

-2 -4 -6

Kozani

Mammoth Lakes

-8

Upstream-downstream direction Downstream-upstream direction

Whittier Narrows

Cape Mendocino/Petrolia

Fig. 8.17 Maximum horizontal displacement of the crest dam under different intensity levels of ground motions

Residual displacement (cm)

0.5 0.0

0.3g 0.4g 0.5g

0.3g 0.4g

0.3g 0.4g 0.5g

0.5g

0.3g 0.4g 0.5g

A

-0.5 -1.0 -1.5

Mammoth Lakes

Kozani

-2.0

Whittier Narrows

-2.5 -3.0 -3.5

Upstream-downstream direction Downstream-upstream direction

Cape Mendocino/Petrolia

Fig. 8.18 Residual displacement of the crest dam under different intensity levels of ground motions

4.26 cm, respectively. And the residual displacements are −3.12 cm and −0.34 cm, respectively. It can also be found that the ground motions with greater PGA would cause greater residual displacement to the dam than smaller events. Changing in the damage, maximum displacement, and residual displacement demands with the earthquake direction shows different performances in different directions. This might be mainly due to the distinctive variations and degradation of the structural properties (i.e. strength, stiffness, and damping) in different directions. Therefore, it is necessary to include the effects of earthquake direction on the nonlinear dynamic behavior when evaluating the seismic performance of concrete gravity dams subjected to strong mainshock-aftershock seismic sequences.

8.6 Conclusions The present study investigated the nonlinear dynamic behavior of the twodimensional concrete gravity dam–reservoir–foundation systems subjected to single seismic events and mainshock-aftershock seismic sequences in different directions. The main innovation of this work is to evaluate the earthquake direction effects on

8.6 Conclusions

203

the structural demands of the dam based on the two-dimensional model. For this purpose, two seismic incident directions (i.e. as-recorded acceleration time history and opposite direction of the as-recorded acceleration time history) are applied along horizontal axes of the two-dimensional model. Nonlinear dynamic response history analyses are conducted to investigate the effects of direction of single earthquake events, direction of seismic sequences, and aftershock polarity. The influence of the intensity of ground motions on the direction effects of seismic sequences is also discussed. Based on the results, the following conclusions may be drawn: 1. Changing the earthquake direction of single seismic events or mainshockaftershock seismic sequences can significantly affect the damage, maximum displacement and residual displacement demands of the dam. The more different damage the single seismic events with different directions cause to the dam, the greater impact on the final damage the direction of mainshock-aftershock seismic sequences has. The application of earthquake records along the horizontal axes in the upstream-downstream direction may lead to significant underestimation of seismic damage. 2. In general, the aftershock polarity will not significantly change the damage pattern of the dam. In some cases, the aftershock earthquake ground motion with the negative polarity tends to move the dam to the opposite direction of the original post-mainshock residual displacement, which means that the aftershock polarity may lead to a recentering behavior. 3. The intensity of ground motions has a significant influence on the seismic sequence direction effects. When the mainshock PGA of seismic sequences is not high, there is a slight difference between the damage demands and damage profiles for the dam subjected to two incidence directions. However, as the PGA of the seismic sequences increases, the damage propagation processes, damage demands, maximum displacement, and residual displacements are becoming more sensitive to the earthquake direction. 4. The influence degree of the mainshock-aftershock seismic sequences on the additional damage demands depends on the intensity of the selected ground motions. Weak aftershock ground motions have less effect on structural damage demands of the dam than strong aftershocks. In general, strong aftershock ground motions will significantly increase the accumulated damage of the dam. However, if strong mainshock ground motions have led to serious damage to the dam, the strong aftershocks may also cause little accumulated damage to the dam. The aforementioned conclusions are obtained from the nonlinear dynamic response of the Koyna gravity dam subjected to four specific mainshock-aftershock seismic sequences. Thus, these conclusions may not apply to all gravity dams and ground motions. To better assess the earthquake direction effects, further study using seismic fragility analysis, abundant strong motion records, and more incident angles will be undertaken in the future.

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8 Earthquake Direction Effects on Nonlinear Dynamic Response …

References Alliard, P., & Léger, P. (2008). Earthquake safety evaluation of gravity dams considering aftershocks and reduced drainage efficiency. Journal of Engineering Mechanics, 134(1), 12–22. Bybordiani, M., & Arıcı, Y. (2017). The use of 3D modeling for the prediction of the seismic demands on the gravity dams. Earthquake Engineering & Structural Dynamics. Chinese, S. (2011). Code for design of seismic of hydropower projects. Beijing: Chinese Electric Power Press. COSMOS. (2019). Strong Motion Virtual Data Center, http://strongmotioncenter.org/vdc/scripts/ default.plx. Fakharifar, M., Chen, G., Sneed, L., & Dalvand, A. (2015). Seismic performance of post-mainshock FRP/steel repaired RC bridge columns subjected to aftershocks. Composites Part B Engineering, 72, 183–198. Hariri-Ardebili, M. A., & Saouma, V. (2015). Quantitative failure metric for gravity dams. Earthquake Engineering and Structural Dynamics, 44(3), 461–480. Hariri-Ardebili, M. A., Seyed-Kolbadi, S. M., & Kianoush, M. R. (2016). FEM-based parametric analysis of a typical gravity dam considering input excitation mechanism. Soil Dynamics and Earthquake Engineering, 84, 22–43. Hatzivassiliou, M., & Hatzigeorgiou, G. D. (2015). Seismic sequence effects on three-dimensional reinforced concrete buildings. Soil Dynamics and Earthquake Engineering, 72, 77–88. Hosseinpour, F., & Abdelnaby, A. E. (2017). Effect of different aspects of multiple earthquakes on the nonlinear behavior of RC structures. Soil Dynamics and Earthquake Engineering, 92, 706–725. Jeon, J., DesRoches, R., & Lee, D. H. (2016). Post-repair effect of column jackets on aftershock fragilities of damaged RC bridges subjected to successive earthquakes. Earthquake Engineering and Structural Dynamics, 45(7), 1149–1168. Konstandakopoulou, F. D., & Hatzigeorgiou, G. D. (2017). Water and wastewater steel tanks under multiple earthquakes. Soil Dynamics and Earthquake Engineering, 100, 445–453. Kostinakis, K., Morfidis, K., & Xenidis, H. (2015). Damage response of multistorey r/c buildings with different structural systems subjected to seismic motion of arbitrary orientation. Earthquake Engineering and Structural Dynamics, 44(12), 1919–1937. Morfidis, K., & Kostinakis, K. (2017). The role of masonry infills on the damage response of R/C buildings subjected to seismic sequences. Engineering Structures, 131, 459–476. Moshref, A., Khanmohammadi, M., & Tehranizadeh, M. (2017). Assessment of the seismic capacity of mainshock-damaged reinforced concrete columns. Bulletin of Earthquake Engineering, 15(1), 291–311. Raghunandan, M., Liel, A. B., & Luco, N. (2015). Aftershock collapse vulnerability assessment of reinforced concrete frame structures. Earthquake Engineering and Structural Dynamics, 44(3), 419–439. Raghunandan, M., Liel, A. B., Ryu, H., Luco, N., & Uma, S. R. (2012). Aftershock fragility curves and tagging assessments for a mainshock-damaged building. In Proceedings of the 15th World Conference on Earthquake Engineering, Lisbon. Rigato, A. B., & Medina, R. A. (2007). Influence of angle of incidence on seismic demands for inelastic single-storey structures subjected to bi-directional ground motions. Engineering Structures, 29(10), 2593–2601. Rinaldin, G., Amadio, C., & Fragiacomo, M. (2017). Effects of seismic sequences on structures with hysteretic or damped dissipative behaviour. Soil Dynamics and Earthquake Engineering, 97, 205–215. Ruiz-García, J., & Aguilar, J. D. (2015). Aftershock seismic assessment taking into account postmainshock residual drifts. Earthquake Engineering and Structural Dynamics, 44(9), 1391–1407. Ruiz-García, J., & Negrete-Manriquez, J. C. (2011). Evaluation of drift demands in existing steel frames under as-recorded far-field and near-fault mainshock-aftershock seismic sequences. Engineering Structures, 33(2), 621–634.

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Shin, M., & Kim, B. (2017). Effects of frequency contents of aftershock ground motions on reinforced concrete (RC) bridge columns. Soil Dynamics and Earthquake Engineering, 97, 48–59. Song, R., Li, Y., & Van de Lindt, J. W. (2016). Loss estimation of steel buildings to earthquake mainshock-aftershock sequences. Structural Safety, 61, 1–11. Soysal, B. F., Binici, B., & Arici, Y. (2016). Investigation of the relationship of seismic intensity measures and the accumulation of damage on concrete gravity dams using incremental dynamic analysis. Earthquake Engineering and Structural Dynamics, 45(5), 719–737. Wang, G., Wang, Y., Lu, W., Yan, P., Zhou, W., & Chen, M. (2017a). Damage demand assessment of mainshock-damaged concrete gravity dams subjected to aftershocks. Soil Dynamics and Earthquake Engineering, 98, 141–154. Wang, G., Wang, Y., Lu, W., Yu, M., & Wang, C. (2017b). Deterministic 3D seismic damage analysis of Guandi concrete gravity dam: A case study. Engineering Structures, 148, 263–276. Wang, G., Wang, Y., Lu, W., Zhou, C., Chen, M., & Yan, P. (2015). XFEM based seismic potential failure mode analysis of concrete gravity dam–water–foundation systems through incremental dynamic analysis. Engineering Structures, 98, 81–94. Xia, Z., Ye, G., Wang, J., Ye, B., & Zhang, F. (2010). Fully coupled numerical analysis of repeated shake-consolidation process of earth embankment on liquefiable foundation. Soil Dynamics and Earthquake Engineering, 30(11), 1309–1318. Yazdani, Y., & Alembagheri, M. (2017). Nonlinear seismic response of a gravity dam under nearfault ground motions and equivalent pulses. Soil Dynamics and Earthquake Engineering, 92, 621–632. Zhai, C., Zheng, Z., Li, S., & Pan, X. (2017). Damage accumulation of a base-isolated RCC building under mainshock-aftershock seismic sequences. KSCE Journal of Civil Engineering, 21(1), 364– 377. Zhang, S., Wang, G., & Sa, W. (2013a). Damage evaluation of concrete gravity dams under mainshock–aftershock seismic sequences. Soil Dynamics and Earthquake Engineering, 50, 16–27. Zhang, S., Wang, G., & Yu, X. (2013b). Seismic cracking analysis of concrete gravity dams with initial cracks using the extended finite element method. Engineering Structures, 56, 528–543.

Chapter 9

Seismic Performance Evaluation of Dam-Reservoir-Foundation Systems to Near-Fault Ground Motions

9.1 Introduction Ground motion records obtained in recent major strong earthquakes, such as Loma Prieta (1989), Northridge (1994), Kobe (1995), Kocaeli (1999), and Chi-Chi (1999), revealed unique characteristics of ground motions in a near-fault area. The seismic ground motions recorded within the near-fault region of an earthquake at stations located toward the direction of the fault rupture are significantly different from the usual far-fault ground motions observed at a large distance (Chopra and Chintanapakdee 2001). Forward directivity and fling effects have been identified by seismologists as the primary characteristics of near-fault ground motions (Mavroeidis and Papageorgiou 2003). The fault-normal components of ground motions often contain large displacements and velocity pulses. Such a pronounced pulse does not exist in far–fault ground motions. The pulses are strongly influenced by the rupture mechanism, the slip direction relative to the site, and the location of the recording station relative to the fault which is termed as ‘directivity effect’ due to the propagation of the rupture toward the recording site (Wang et al. 2002; Somerville 2003; Bray and Rodriguez-Marek 2004). Because of the unique characteristics of near-fault ground motion, the ground motions recorded in the near-fault region, which expose the structure to high input energy in the beginning of the earthquake (Liao et al. 2004), have the potential to cause a large response and considerable damage to structures. Therefore, structural response to near-fault ground motions has received much attention in recent years. The effects of near-fault ground motions on many civil engineering structures, such as buildings and bridges, have been investigated in many recent studies. Xiang and Alam (2019) evaluated the seismic vulnerability of double-column bridge bents retrofitted with different braces under near-fault and far-field ground motions. Xin et al. (2019) investigated the seismic behaviors of long-span concrete-filled steel tubular arch bridges under near-fault fling-step motions, and the effects of different components in fling-step motions on the seismic response of the bridge are conducted © Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_9

207

208

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

by the parametric analysis. Ma et al. (2019) developed a probabilistic seismic demand model to evaluate the seismic performance of regular continuous bridges subjected to pulse-like near-fault ground motions. Their results showed that the near-fault ground motions can cause more serious damage to the bridge. Kabir et al. (2019) assessed the seismic vulnerability of a multi-span bridge subjected to near-fault, far-fault, and long duration ground motions. They thought the failure probabilities of the bridge system were dominated by the long duration ground motions than those of nearfault and far-fault ground motions. Ardakani and Saiidi (2018) developed a simple empirical method to evaluate the residual displacements of concrete bridge columns subjected to near-fault ground motions. Hedayati Dezfuli et al. (2017) concluded that near-fault ground motions will cause more damage to the bridge structure than far-fault ground motions in terms of maximum lateral displacement, generated shear force, residual deformation, and energy dissipation capacity of the bridge bearings, duck, and piers. Yang et al. (2017) demonstrated that the seismic demands of the seismically isolated bridge located in the vicinity of a surface fault rupture or crossing a fault rupture zone will be significantly underestimated when the high-pass filtered ground motion is utilized. Li et al. (2017) evaluated the seismic response of superspan cable-stayed bridges built in the forward region, middle region, and backward region relative to fault rupture. Their results showed that the bridge located in the middle region will experience a larger response than that in the forward region and backward region. Yang et al (2019) proposed an intrinsic length scale significance to analyze the dimensional response of bilinear SDOF systems subjected to nearfault ground motions. Manafpour and Kamrani Moghaddam (2019) investigated the effects of seismic sequences on the dynamic response of RC SDOF systems subjected to near-fault and far-fault ground motions. Both the pulse-like and no-pulse motions were considered in the near-fault ground motions. Du et al. (2020) investigated the seismic performance of bucking-restrained braced RC frame structures subjected to near-fault ground motions with forward directivity and fling-step effects. Their results indicated that near-fault ground motions with forward-directivity and flingstep effects will produce larger maximum interstory drift ratio and story drift than non-pulse-like near-fault ground motions. Bilgin and Hysenlliu (2020) predicted the nonlinear displacement demands of low and mid-rise masonry buildings subjected to near-fault and far-fault ground motions. They concluded that the near-fault ground motions have significantly more damage potential on masonry structures than farfault ground motions. Bhagat et al. (2018) investigated the nonlinear seismic response of base-isolated buildings subjected to near-fault ground motions with fling-step and forward-directivity characteristics. Behesthi Aval et al. (2018) discussed the seismic performance of tunnel form buildings subjected to near-fault and far-fault ground motions through incremental dynamic analysis method. They found that the probability of reaching structural elements to preliminary damage levels under near-fault ground motions was increased up to 20% when compared with far-fault ground motions. Cao et al. (2016) investigated the effects of wave passage on torsional response of elastic buildings under near-fault pulse-like ground motions. A simplified pulse model is used to represent the main features of near-fault ground motions which will cause large torsional response to the buildings. Tajammolian et al. (2016)

9.1 Introduction

209

investigated the effects of mass eccentricity on the seismic response of isolated structures under near-fault ground motions. Eslami et al. (2016) conducted a numerical investigation on the seismic retrofitting of RC buildings subjected to near-fault ground motions using the carbon fiber-reinforced polymer sheets. They concluded that the retrofitting scheme can substantially improve the seismic performance of RC buildings under impulsive ground motions. Beiraghi et al. (2016a) examined the seismic behavior of RC wall tall buildings subjected to forward directivity nearfault and far-fault ground motions, and concluded that near-fault ground motions will produce considerably larger seismic demands (i.e. curvature ductility, interstory drift and displacement) as compared with the far-fault ground motions. They also found that the near-fault motion pulse will transfer more energy quantity to the RC core-wall buildings (Beiraghi et al. 2016b). Sun et al. (2020) compared the far-fault and near-fault ground motion effects on the probabilistic seismic response of arched hydraulic tunnels, and found that the near-fault ground motions with flingstep effects can cause higher probability of exceedance to the arched hydraulic tunnel than other types of ground motions. Konstandakopoulou et al. (2019) investigated the nonlinear dynamic behavior of 3D offshore platforms including the pile-soilstructure interaction effects under near-fault ground motions. They found that nearfault ground motions from reverse or oblique reverse faults will cause more intense structural response as compared with ground motions that correspond to strike-slip faults. Chen et al. (2020) examined the elastoplastic dynamic response of intake tower structures subjected to near-fault ground motions with forward-directivity and fling-step effects. Their results showed that the near-fault ground motions can lead to great nodal displacement of intake tower structures. It can be clearly seen from these studies that the importance of near-fault ground motion effects on the nonlinear dynamic response of structures has been highlighted. Aseismic design of structures should be given attention to the characteristics of near-fault ground motions due to their impulsive effects on structures. It should be noted that few studies have focused their attention on the nonlinear dynamic response and seismic damage of concrete gravity dams subjected to nearfault ground motions. For example, Akköse and Sim¸ ¸ sek (2010) studied the seismic response of a concrete gravity dam subjected to near-fault and far-fault ground motions including dam-water-sediment-foundation rock interaction. They found that plastic deformations in the dam subjected to near-fault ground motion are greater than those subjected to far-fault ground motion. Bayraktar et al. (2009; 2010) examined the effects of near-fault and far-fault ground motions on the nonlinear response of gravity dams. The results revealed that there are more seismic demands on displacements and stresses when the dam is subjected to near-fault ground motion. Yazdani and Alembagheri (2017a, b) investigated nonlinear seismic response analyses and seismic vulnerability assessment of gravity dams located in near-fault areas by proposing a probabilistic seismic demand model for gravity dams considering near-field earthquake ground motions. Although previous studies provided some information on the effects of near-fault ground motions on the response of dams, there is no sufficient research about the near-fault ground motion effects on the seismic damage of concrete gravity dams. Zou et al (2019) explored the seismic slope stability of a high rockfill

210

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

dam considering strain softening subjected to pulse-like ground motions. The results showed that the pulse-like ground motion has a significant impact on sliding displacement of the rockfill dam. Gorai and Maity (2019) compared the effects of near-fault and far-fault ground motions on the seismic performance of concrete gravity dams in terms of demand capacity ratio, cumulative inelastic duration, and spatial extent of overstress region. The main objective of this chapter is to investigate and compare the dynamic behavior of concrete gravity dams subjected to near-fault and far-fault ground motion excitations with considering the effects of dam-reservoir-foundation interaction. The Concrete Damage Plasticity (CDP) model which includes the strain hardening or softening behavior is adopted to study the seismic response of concrete gravity dams under earthquake conditions. The 1979 Imperial Valley, 1989 Loma Prieta, 1994 Northridge, and 1999 Chi-Chi earthquake records which display ground motions with an apparent velocity pulse are selected to represent the near-fault ground motion characteristics. In this study, the term “near-fault ground motion” is referred to the ground motion record obtained in the vicinity of a fault with the apparent velocity pulse (pulse duration larger than 1.0 s), and the peak ground velocity/peak ground acceleration (PGV/PGA) value which is larger than 0.1 s. The earthquake ground motions recorded at the same site from other events that the epicenter far away from the site are employed as the far-fault ground motions, which are used to compare with near-fault ground motions. The Lagrangian approach is used for the finite element modeling of dam-reservoir-foundation interaction problem. The Koyna gravity dam is employed as a numerical application. Nonlinear seismic damage analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. The influence of near-fault ground motions on the dynamic response and seismic damage of concrete gravity dams is examined.

9.2 Characteristics of Near-Fault Ground Motions It is well known that the earthquake is a complex natural phenomenon associated with the abrupt energy release caused by the fault rupture. There are many factors that affect the types of ground motions at a site, such as the underlying soil condition at the site, earthquake source mechanism, the magnitude of the earthquake, the distance from the earthquake, propagation path of waves, and topographic features. A nearfault ground motion is one that is experienced near the rupturing fault line. When a site lies within the near-fault region (usually less than 10 km), a unique set of factors controls the motion that is recorded, which will be different from those observed further away from the seismic source. The characteristics of near-fault ground motions are linked to the fault geometry and the orientation of the traveling seismic waves. The most primary characteristics of near-fault ground motions concerning the field of structural and civil engineering are the impulsive characteristic of the velocity (i.e. the forward directivity effect) and displacement ground motions affecting at long periods (i.e. fling step effect), which

9.2 Characteristics of Near-Fault Ground Motions

211

have caused severe structural damage in recent major earthquakes. Another feature is the hanging wall/footwall effect. Although the near-fault ground motion has the typical characteristic of a short duration, high amplitude pulse, these phenomena are not always observed, which are based on the focal mechanism and the direction of the fault rupture. This means that not all sites within the near-fault region will experience the high amplitude pulse-like behavior during the earthquake.

9.2.1 Forward Directivity Effect One of the critical factors affecting ground motion in the near field area is the direction in which rupture progresses from the hypocenter along the zone of rupture. An earthquake is a shear dislocation that begins at a point on a fault and spreads throughout the fault plane at a velocity that is almost equal to the shear wave velocity. The rupture velocity is generally slightly less than the shear wave velocity. If a site is located at one end of a fault and the rupture propagates from the other end. The rupture velocity is on the average 80% of the shear wave velocity. (Near-fault ground motions and structural design issues.) Figure 9.1 shows the forward directivity phenomenon. When the fault ruptures toward the site A, the shear wave energy will arrive at this site within a short time frame (almost the same time). Because of this, the seismic energy from each fault segment arrives together at site A, and accumulates in front of the propagating rupture, which is expressed in the forward directivity region as a relatively short duration record containing large velocity amplitude. However, the seismic energy will be distributed when arrives at Site B over a longer period of time, resulting in a longer duration record with lower velocity amplitudes. This can be explained by other scientific phenomena such as the sonic boom or the Doppler effect, which is essentially the same principle and may be thought of accordingly. Forward directivity effects can be classified as forward, reverse, or neutral, as shown in Fig. 9.2. When the rupture propagates toward the site and the angle between the fault and the direction from the hypocenter to the site is reasonably small, this site is likely to generate the forward directivity effects. This is because that the rupture often propagates at a velocity close to the velocity of shear wave radiation, energy is accumulated in front of the propagating rupture and is expressed in the forward directivity region as a large velocity pulse (Somerville et al. 1997). Forward directivity effects can be presented both for strike-slip and dip-slip events. In strikeslip events, forward directivity conditions are typically largest for sites near the end of the fault when the rupture front is moving towards the site and slip vector points toward the site as well. In dip-slip events, forward directivity conditions occur at sites located in the up-dip projection of the fault plane (Bray and Rodriguez-Marek 2004). This means that the rupture direction is aligned up on the fault plane and the slip vector points upwards as well. The conditions that lead to high forward directivity can be summarized as follows (Somerville 2005):

212

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

Forward

R

up tu

re

D

ire

Fa

Neutral

ct

ul

t

io

n

Fig. 9.1 Effects of accumulation of seismic energy

Reverse

Neutral

Fig. 9.2 Defining a site as forward, reverse, or neutral directivity

9.2 Characteristics of Near-Fault Ground Motions

213

• The smaller the angle between the direction of the rupture propagation and the direction of the seismic waves travelling from the fault to the site, the higher the forward directivity effects. • The larger the fraction of the fault rupture surface that lies between the hypocenter and the site, the higher the forward directivity effects. • Forward directivity does not exist if the slip is concentrated near one end of the fault where the site is located, even if these geometrical conditions are satisfied. If the rupture propagates away from the site, this site is likely to demonstrate reverse directivity, and the ground motion is characterized by long duration and low amplitude at long periods. When the rupture propagation is neither predominantly towards nor away from the site, this means that the site is located close to the epicenter of the strike-slip faulting and located off the end of the up-dip projection of reverse faults. In this condition, the site experiences the neutral directivity. The phrase “directivity effects” usually refers to “forward directivity effects”, as this case is expected to result in ground motions that are more critical to engineering structures.

9.2.2 Fling Step Effect The fling step effects are the consequences of a permanent ground displacement due to the static deformation field of the earthquake, occurring over a discrete time interval of several seconds as the fault slip is developed (Stewart et al., 2002). This effect is observed close to the fault and can be significant when excessive tectonic deformations occur due to large slip on the fault plane (as shown Fig. 9.3). For a strike-slip fault, the offset is partitioned primarily on the fault parallel component. For a dip-slip fault, the offset is partitioned chiefly on the fault normal and vertical components. Pulses from the fling step effects have different characteristics than those from forward directivity effects. The forward directivity effect is a dynamic phenomenon that produces no permanent ground displacement and hence two-sided velocity pulses. Whereas the fling step effect is characterized by a unidirectional large amplitude velocity pulse and a discrete step in the displacement time history. The effects of both fling step and forward directivity can be superimposed on one another in the fault normal component of a dip-slip earthquake, whereas the parallel component of the fault will show neither effects. In general, the fault normal and fault parallel components show similar patterns in the far-field ground motion. However, the near-fault ground motion can show a substantial difference.

9.2.3 Hanging Wall Effect In the near-fault earthquake, there are not only the forward directivity effect and the fling step effect, but also the hanging wall effect. Since the sites located on the

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9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

Velocity (cm/s)

200 150 100 50 0 -50 -100 -150 -200

0

5

10

15

20

25

30

35

40

45

50

55

35

40

45

50

55

Displacement (cm)

Time (s) 200 150 100 50 0 -50 -100 -150 -200 0

5

10

15

20

25

30

Time (s)

Fig. 9.3 Typical velocity and displacement time history curves of 1999 Kocaeli earthquake with fling step effect

hanging wall of a dip-slip fault are generally closer to the fault than those located on the foot wall at the same closest distance, the ground motions of the hanging wall are larger than those located on the foot wall at the same closest distance. This is the hanging wall effect of the near-fault ground motion, as shown in Fig. 9.4. Abrahamson and Somerville (1996) observed that the peak horizontal accelerations on the hanging wall sites were about 50% greater than those located on the foot wall over a distance range of 10–20 km during the 1994 Northridge earthquake. Hangingwall effects have also been observed in some reverse dip-slip faulting earthquakes of the past and can be expected in future reverse events.

Fig. 9.4 Hanging wall effect of near-fault ground motions

9.3 Near-Fault and Far-Fault Ground Motion Records Considered in This Study

215

9.3 Near-Fault and Far-Fault Ground Motion Records Considered in This Study One of the most important characteristics of near-fault events concerning the field of structural and civil engineering is the impulsive character of the velocity and displacement ground motions affecting at long periods and thereby having a severe influence on the structures. The selection of ground motion is one of the important parts of seismic evaluation of gravity dams. In this study, 10 as-recorded near-fault ground records are selected as the input ground motion from the 1979 Imperial Valley, 1989 Loma Prieta, 1994 Northridge, and 1999 Chi-Chi earthquakes. These records, which display ground motions with an apparent velocity pulse, are selected to represent the near-fault ground motion characteristics. The velocity pulse duration in the near-fault ground motions is larger than 1.0 s. In addition, the ratio of the peak ground velocity (PGV) to the peak ground acceleration (PGA) of the near-fault ground motions is larger than 0.1 s. On the contrary, another set of ground motion records, recorded at the same site condition from the same earthquake events with epicenter far away from the site, is employed to represent the characteristics of farfault ground motion. The properties of these records are depicted in Table 9.1. The ground motion records are obtained from the databases of the COSMOS (COSMOS 2019) and PEER (PEER 2019). As a typical example, Fig. 9.5 shows the acceleration, velocity and displacement time histories of the fault normal component of the near-fault and far-fault ground motions. Figure 9.6 shows the acceleration response spectrum with damping ratio 5% for selected near-fault and far-fault ground motion records in the Northridge earthquake. As shown in Fig. 9.5, it can be seen from that there is a distinct difference between the velocity pulse of ground motions recorded at near-fault and far-fault regions. The near-fault ground motion possesses a significantly long period pulse in the acceleration time history that is consistent with velocity and displacement histories. The long period response of the near-fault ground motion is more excessive than the far-fault ground motion. The near-fault and far-fault ground motion records are normalized to have the peak ground acceleration (PGA) equal to 0.3 g. In these analyses, only the first 15 s of the Northridge, Imperial Valley, and Loma Prieta earthquake records and the first 40 s of the Chi-Chi earthquake records are considered. Figure 9.7 presents acceleration time history for scaled near-fault and far-fault ground motion records. Figure 9.8 presents velocity time history for scaled near-fault and far-fault ground motion records.

9.4 Seismic Performance Evaluation Methods A systematic and rational methodology for seismic performance assessment and qualitative damage estimation using standard results from linear time-history analysis is presented. The performance evaluation and assessment of the probable level of

Ground motion

Near-fault

Far-fault

Near-fault

Far-fault

Near-fault

Far-fault

Near-fault

Far-fault

Near-fault

Far-fault

Near-fault

No.

1

2

3

4

5

6

7

8

9

10

11

Loma Prieta 1989

Imperial Valley 1979

Imperial Valley 1979

Imperial Valley 1979

Imperial Valley 1979

Northridge 1994

Northridge 1994

Northridge 1994

Northridge 1994

Northridge 1994

Northridge 1994

Earthquake

6.3

21.8

8.8

21.7

5.2

17.9

8.6

29.4

8.6

18.4

7.1

Distance to fault (km)

5.3

6.7

6.7

6.7

6.7

6.7

Mw

6.5

Gilroy Array Sta 3 # 47381

6.5

Superstition Mtn, CA 6.5 - Camera Site #0286

Holtville, CA - Post Office #5055

El Centro, CA - Array 6.5 Sta 13 #5059

El Centro, CA - Array 6.5 Sta 5 #0952

Tarzana, CA - Cedar Hill #24436

Los Angeles Reservoir #2141

Warm Springs #24272

Sylmar, CA - Jensen Filtration Plant #655

Los Angeles, CA Fire Station 108 #5314

Newhall, CA–Los Angeles County Fire #24279

Station location

Table 9.1 Properties of selected near-fault and far-fault ground motions considered in this investigation

90

135

225

230

230

90

64

90

22

35

360

Comp.

362.00

182.19

242.96

131.07

360.37

365.30

317.6

221.20

560.30

576.93

578.20

PGA (cm/s2 )

43.80

8.65

51.90

12.70

95.89

11.80

44.54

13.40

77.23

29.75

94.70

PGV (cm/s)

(continued)

0.121

0.047

0.214

0.096

0.266

0.032

0.140

0.061

0.138

0.052

0.164

PGV/PGA (s)

216 9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

Ground motion

Far-fault

Near-fault

Far-fault

Near-fault

Far-fault

Near-fault

Far-fault

Near-fault

Far-fault

No.

12

13

14

15

16

17

18

19

20

Table 9.1 (continued)

Chi-Chi 1999

Chi-Chi 1999

Chi-Chi 1999

Chi-Chi 1999

Chi-Chi 1999

Chi-Chi 1999

Loma Prieta 1989

Loma Prieta 1989

Loma Prieta 1989

Earthquake

31.1

3.2

37.2

7.9

32.0

8.9

16.9

2.8

22.7

Distance to fault (km)

7.6

6.5

6.5

6.5

Mw

Chiayi, Taiwan #CHY086

Taichung, Taiwan #TCU076

Chiayi, Taiwan #CHY014

Taichung, Taiwan #TCU072

7.6

7.6

7.6

7.6

Ilan, Taiwan #ILA067 7.6

Taichung, Taiwan #TCU050

Coyote Lake Dam, CA #57217

Corralitos, CA #57007

Gilroy Array Sta 7 #57425

Station location

0

90

0

90

90

90

285

90

90

Comp.

201.60

336.10

254.90

466.90

195.70

142.70

471.00

469.40

314.30

PGA (cm/s2 )

17.9

59.00

22.90

70.80

11.40

32.40

37.50

47.50

16.30

PGV (cm/s)

0.089

0.176

0.090

0.152

0.058

0.227

0.079

0.101

0.052

PGV/PGA (s)

9.4 Seismic Performance Evaluation Methods 217

218

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation … Near-fault

Acceleration (g)

Acceleration (g)

0.6 0.3 0.0 -0.3 -0.6

0

3

6

9

12

0.6

Far-fault

0.3 0.0 -0.3 -0.6

0

15

3

6

Velocity (cm/s)

Velocity (cm/s)

50 0 -50

0

3

6

9

15

12

0 -50

-100

50

Displacement (cm)

Displacement (cm)

15

50

0

3

6

3

6

Time (s)

25 0 -25 -50

12

100

100

-100

9

Time (s)

Time (s)

0

3

6

9

12

15

9

12

Time (s)

15

50 25 0 -25 -50

0

9

12

15

Time (s)

Time (s)

(a) Near-fault ground motion

(b) Far-fault ground motion

Fig. 9.5 Sample of acceleration, velocity, and displacement time histories for a near-fault ground motion recorded at Newhall station, and b far-fault ground motion recorded at Los Angeles station in Northridge earthquake

2.5

Response Acceleration (g)

Fig. 9.6 Acceleration response spectrum with damping ratio 5% for selected near-fault and far-fault ground motions

2.0

Near-fault Far-fault

1.5 1.0 0.5 0.0 0

1

2

Period (s)

3

4

damage are formulated based on the demand-capacity ratios for stresses, the cumulative duration of stress excursions beyond the tensile strength of the concrete and the spatial extent of overstressed regions. This evaluation is applied to the damage control range of strains shown in Fig. 9.9.

0.6 g

9.4 Seismic Performance Evaluation Methods

219

1

2

3

4

5

6

7

8

9

10

11

12

15

14

13

17

16

20

19

18

20 s

Fig. 9.7 Acceleration time histories for the scaled near-fault and far-fault ground motions used in this study. For ground motion information see Table 9.1

1

2 3

7

8

13

14

4

120 cm/s

9

10

15

5

6

11

12

16

18

17

20

19

20 s

Fig. 9.8 Velocity time histories for the scaled near-fault and far-fault ground motions used in this study. For ground motion information see Table 9.1

The demand-capacity ratio (DCR) for concrete gravity dams is defined as the ratio of the calculated maximum principal stress to tensile strength of the concrete. The tensile strength of the plain concrete used in this definition is the static tensile strength characterized by the uni-axial splitting tension tests or from f t = 1.7 f c2/3

(9.1)

Demand-Capacity Ratio

220

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation … 2 T=0.24s

1 0 -1 -2 0.0

0.24

0.48

0.72

0.96

(a) Time (s)

Cumulative Inelastic Duration (s)

Duration=0.4s

1.44

Stress

0.5 0.4

1.20

Significant damage Assess using nonlinear analysis

3.4fc

0.1 0.0 0.0

1.7fc

1.92

Damage Control Region

/ 2/3

B Apparent Tensile Strength

0.3 0.2

1.68

/ 2/3

A

Low to moderate damage Assess using linear analysis

Demand-Capacity Ration (DCR)

(b)

2.0

Strain

(c)

Fig. 9.9 Illustration of seismic performance and damage criteria (Ghanaat 2004)

proposed by Raphael (1984), where f c is the compressive strength of the concrete. The maximum permitted DCR for the linear analysis of dams is 2. This corresponds to a stress demand twice the static tensile strength of the concrete. As illustrated in the stress-strain curve in Fig. 9.9c, the stress demand associated with a DCR of 2 corresponds to the so called “apparent dynamic” tensile strength of the concrete, a quantity proposed by Raphael for evaluation of the results of linear dynamic analysis. The cumulative inelastic duration of stress excursions is defined as the total duration of the stress excursions above a stress level associated with a DCR ≥ 1. The higher the cumulative duration, the higher is the possibilities for more damage. The sinusoidal stress history with five stress cycles is shown in Fig. 9.9a. The sinusoidal cycle duration of the stress excursion above the tensile strength is equal to T/3, where T is the period of the sinusoid. The total inelastic duration for all five stress excursions (shaded area) amounts to 5T/3. Considering that the period of the signal is 0.24 s, the cumulative inelastic duration of stress excursions is 0.4 s. The cumulative duration for a DCR of 2 is assumed zero. For gravity dams a lower cumulative duration of 0.3 s (in Fig. 9.10) is assumed, mainly because gravity dams resist loads by cantilever mechanism only, as opposed to arch dams that rely on both the arch and cantilever actions.

9.4 Seismic Performance Evaluation Methods 0.5 Cumulative Inelastic Duration (s)

Fig. 9.10 Seismic performance threshold curves for concrete gravity dams

221

0.4 0.3

Significant damage Assess using nonlinear analysis

0.2 0.1 0.0

Low to moderate damage Assess using linear analysis 2.0

1.0

Demand-Capacity Ration (DCR)

The seismic performance and probable level of damage of concrete gravity dams are evaluated on the basis of the demand-capacity ratios, the cumulative inelastic duration and the spatial extent of overstressed regions described above. Three performance levels are considered (Ghanaat 2004): (1) Minor or no damage. The dam response is assumed to be elastic if the demand capacity ratio (DCR) ≤ 1. The dam is considered to behave in the elastic range with little or no possibility of damage. (2) Acceptable level of damage. If the estimated DCR > 1, the dam will exhibit a nonlinear response in the form of cracking and joint opening. If the estimated DCR < 2, the overstressed regions are limited to 15 percent of the dam crosssection surface area, and the cumulative duration of stress excursion also falls below the performance curve given in Fig. 9.10, the level of nonlinear response or cracking can be considered acceptable with no possibility of failure. (3) Severe damage. The damage is considered as severe if the DCR > 2, or the cumulative overstress duration for all DCR values between 1 and 2 falls above the performance curves as shown in Fig. 9.10. In these situations, nonlinear time history analysis may be required to further investigate the performance of the dam.

9.5 Near-Fault Ground Motion Effects on Seismic Performance of Concrete Gravity Dams Using Linear and Nonlinear Evaluation Methods Due to the unique characteristics of the near-fault ground motions and their potential to cause severe damage to structures, the interest on the near-fault effect on structural response has increased. Earthquake engineers have been considering methods

222

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

to incorporate near-fault effects in engineering design (Mavroeidis and Papageorgiou 2003). The seismic safety evaluation of high dams subjected to near-fault ground motions remains a crucial problem in dam construction. In this study, a set of selected near-fault and far-fault ground motion records is used to examine the near-fault ground motion effects on seismic performance of concrete gravity dams with considering the effects of dam-reservoir-foundation interaction. Only the horizontal component of the seismic input is considered in this analysis. A 5% damping ratio has been assumed in all dynamic analyses. The integration time step used in the time history analysis is 0.005 s. The geometry and finite element (FE) discretization of the Koyna dam–reservoir–foundation system are illustrated in Sect. 2.5 (Chap. 2). The material parameters for concrete, foundation rock, and water are the same as Table 2.1. It is known that seismic performance assessment of concrete gravity dams has become significantly important in view of the observed lack of seismic resistance of dams during strong earthquakes. Due to the severe damage effects of impulsive type motions on structures, satisfactory seismic performance of concrete gravity dams located in the near-fault region is necessary because the release of the impounded large quantity of water can cause a considerable amount of devastation in the downstream populated areas. The state-of-the-art for evaluating seismic response of concrete gravity dams has progressively moved from elastic static analysis to elastic dynamic, nonlinear static and finally nonlinear dynamic analysis. The traditional seismic performance evaluation method is based on linear theory. It is assumed that the tensile stresses should be less than the dynamic tensile strength of the concrete material. However, in practice up to five stress excursions above the tensile strength of the concrete material has been considered acceptable based on engineering judgment and other considerations (USACE, 2003). To overcome the above shortcomings, a new performance evaluation approach mainly based on the demand-capacity ratios (DCR) and cumulative overstress duration, was proposed by Ghanaat (2002, 2004). Yamaguchi et al. (2004) used this method to evaluate the seismic performance of concrete gravity dams. Sevim (2011) investigated the effect of material properties on the seismic performance of arch dam-reservoir-foundation interaction systems based on the Lagrangian approach using demand-capacity ratios.

9.5.1 Seismic Input A type of 8 records from Table 9.1 is selected as the input ground motion for seismic performance of concrete gravity dams. The assembled database can be investigated in two sub-data sets. The first set which displays ground motions with an apparent velocity pulse is selected to represent the near-fault ground motion characteristics. On the contrary, the second set of four ordinary ground motion records is employed to represent the characteristics of far-fault ground motion. Informations pertinent to the ground motion data sets, including closest fault distance, station, component of earthquake and peak ground acceleration (PGA), peak ground velocity (PGV), and

9.5 Near-Fault Ground Motion Effects on Seismic Performance of Concrete …

223

the ratio of PGV to PGA, are presented in Tables 9.2 and 9.3. The ground motion records are obtained from the databases of the COSMOS (COSMOS 2019) and PEER (PEER 2019). The near-fault and far-fault ground motion records are normalized to have the peak ground acceleration (PGA) equal to 0.30 g. In the analyses, only the first 15 s of the earthquake records are considered. Two different levels of peak ground acceleration (PGA) are considered for the input motions: 0.20 and 0.30 g.

9.5.2 Seismic Performance Evaluation Using Linear Dynamic Analysis The seismic performance of Koyna dam is firstly evaluated by using the linear time history analysis results for both near-fault and far-fault ground motions scaled to 0.20 and 0.30 g. The response of the dam has been determined in terms of the response parameters such as the demand-capacity ratios (DCR), cumulative overstress duration and overstressed areas. The maximum principle tensile stress histories for both near-fault and far-fault earthquake records with a PGA level of 0.20 g are plotted by displaying the demandcapacity ratios (DCR) in Figs. 9.11 and 9.12. Figure 9.13 presents the corresponding performance evaluation curves for both near-fault and far-fault earthquakes at the 0.20 g level. Figure 9.14 shows the overstressed regions of the dam in terms of the DCR values for near-fault ground motions scaled to 0.20 g. The shaded areas indicated that the concrete material regions where the computed DCR values exceeded 1.0. It is clear from Fig. 9.11 and Fig. 9.13a that the dam subjected to far-fault ground motions with a PGA level of 0.20 g is considered to behave in the elastic range with little or no possibility of damage, because the maximum principle tensile stresses are almost less than the tensile strength of the concrete material (2.9 MPa). It can be seen from Fig. 9.12 that the maximum principal stress peaks in excess of the tensile strength of the concrete material vary from 4 to 7 cycles for different near-fault earthquake records with a PGA level of 0.20 g. Figure 9.13b shows that the cumulative overstress durations for DCR = 1 are over than 0.3 s for all cases, but most of the resulting cumulative duration curves are located within the zone of acceptable performance, and the areas of overstressed regions associated with DCR > 1 represent only 2.5, 2.0, 5.5, and 1.2% of the total section area (Fig. 9.14). It is therefore concluded that the actual seismic performance of the dam subjected to near-fault ground motions at the 0.20 g level is likely to exhibit some tensile cracking but the global consequences of the resulting damage are expected to be minor. The damage is considered as an acceptable level. Based on these results, it can be concluded that the results from the linear time history analysis still provide sufficient information to characterize the response of the dam for both near-fault and far-fault ground motions with a PGA level of 0.20 g.

Earthquake

Northridge

Imperial Valley

Loma Prieta

Kobe

No.

1

2

3

4

1995

1989

1979

1994

Year

1.0

2.8

5.2

8.6

Distance to fault (km)

6.5

6.7

Mw

JMA station

6.9

Corralitos, CA #57007 6.5

El Centro, CA - Array Sta 5 #0952

Sylmar, CA - Jensen Filtration Plant #655

Station location

Table 9.2 Properties of selected near-fault ground motions considered in this investigation

0

90

230

22

Comp.

805.45

469.40

360.37

560.30

PGA (cm/s2 )

81.3

47.50

95.89

77.23

PGV (cm/s)

0.101

0.101

0.266

0.138

PGV/PGA (s)

224 9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

Earthquake

Northridge

Imperial Valley

Loma Prieta

Kobe

No.

1

2

3

4

1995

1989

1979

1994

Year

22.5

16.9

21.8

29.4

Distance to fault (km)

Kakogawa

Coyote Lake Dam, CA #57217

Superstition Mtn, CA-Camera Site #0286

Warm Springs #24272

Station location

Table 9.3 Properties of selected far-fault ground motions considered in this investigation

6.9

6.5

6.5

6.7

Mw

0

285

135

90

Comp.

246.58

471.00

182.19

221.20

PGA (cm/s2 )

18.74

37.50

8.65

13.40

PGV (cm/s)

0.076

0.079

0.047

0.061

PGV/PGA (s)

9.5 Near-Fault Ground Motion Effects on Seismic Performance of Concrete … 225

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation … (a) Northridge #24272

6 DCR=2 4 DCR=1

2 0 0

3

6

9

12

15

Time (s)

Max. Principal Stress (MPa)

Max. Principal Stress (MPa)

226

(b) Imperial Valley #0286

6 DCR=2 4 DCR=1

2 0 0

3

6

4 DCR=1

2 0 0

3

6

12

15

(b) (c) Loma Prieta #57217

12

9

15

Time (s)

Max. Principal Stress (MPa)

Max. Principal Stress (MPa)

(a) DCR=2

6

9

Time (s)

(d) Kobe #Kakogawa

DCR=2

6 4

DCR=1

2 0 0

3

6

9

12

15

Time (s)

(c)

(d)

4

DCR=1

2 0 0

3

6

9

12

15

Max. Principal Stress (MPa)

Time (s)

Max. Principal Stress (MPa)

(a) Northridge #655

DCR=2

6

(b) Imperial Valley #0952

6 DCR=2 4 DCR=1

2 0 0

3

6

6 4 2 0

3

6

9

Time (s)

(c)

12

15

(b) (c) Loma Prieta #57007

DCR=1

0

9

Time (s)

(a) DCR=2

12

15

Max. Principal Stress (MPa)

Max. Principal Stress (MPa)

Fig. 9.11 Time histories of maximum principal tensile stresses for far-fault ground motions with a PGA level of 0.20 g. a Northridge #24272, b Imperial Valley #0286, c Loma Prieta #57217, and d Kobe # Kakogawa

(d) Kobe #JMA

DCR=2

6 4

DCR=1

2 0 0

3

6

9

12

15

Time (s)

(d)

Fig. 9.12 Time histories of maximum principal tensile stresses for near-fault ground motions with a PGA level of 0.20 g. a Northridge #655, b Imperial Valley #0952, c Loma Prieta #57007, and d Kobe # JMA

Figure 9.15 and Fig. 9.16 display the maximum principle tensile stress histories for both near-fault and far-fault earthquake records with a PGA level of 0.30 g. The corresponding performance evaluation curves are shown in Fig. 9.17. The overstressed regions computed using the linear time history analyses in terms of the DCR values for near-fault ground motions scaled to 0.30 g are shown in Figs. 9.18

0.4 Northridge Imperail Valley Loma Prieta Kobe Target

0.3

0.2

0.1

0.0 1.0

1.2

1.4

1.6

1.8

Demand-Capacity Ration (DCR)

(a) Far-fault earth quakes

2.0

Cumulative Overstress Duration (s)

Cumulative Overstress Duration (s)

9.5 Near-Fault Ground Motion Effects on Seismic Performance of Concrete …

227

0.4 Northridge Imperail Valley Loma Prieta Kobe Target

0.3

0.2

0.1

0.0 1.0

1.2

1.4

1.6

1.8

2.0

Demand-Capacity Ration (DCR)

(b) Near-fault earth quakes

Fig. 9.13 Performance assessment curves for Koyna dam subjected to near-fault and far-fault earthquakes with a PGA level of 0.20 g

Fig. 9.14 Overstressed regions for Koyna dam under near-fault ground motions with a PGA level of 0.20 g. a Northridge #655, (b) Imperial Valley #0952, c Loma Prieta #57007, and d Kobe # JMA

and 9.19. The shaded areas indicated that the concrete material regions where the computed DCR values exceeded 1.0. It can be seen from Figs. 9.15, 9.16a and 9.18 that the dam subjected to farfault earthquake records with a PGA level of 0.30 g suffers an acceptable level damage with no possibility of failure as the estimated DCR < 2, most of the resulting cumulative duration curves are located within the zone of acceptable performance, and the overstressed regions associated with DCR > 1 are less than 15% of the total section area. Therefore, some tensile cracking damage around the neck of the dam is expected but it will not drastically affect the resulting dynamic behavior. It is clear from Fig. 9.16 that the maximum principal stress peaks in excess of the tensile strength of the concrete material vary from 7 to 13 cycles for different nearfault earthquake records with a PGA level of 0.30 g. Some values of the maximum principal stress are over than DCR = 2 (3–5 cycles) for all near-fault earthquakes. The results in Fig. 9.17b show that the stress demand-capacity ratios exceed 2 and the cumulative inelastic duration is substantially greater than the acceptance level. It means that the near-fault ground motions with a PGA level of 0.30 g will cause

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

10

(a) Northridge #24272

8 DCR=2

6 4

DCR=1

2 0 0

3

6

9

12

15

Max. Principal Stress (MPa)

Max. Principal Stress (MPa)

228

10

(b) Imperial Valley #0286

8 DCR=2

6 4

DCR=1

2 0 0

3

6

(a) 10

(c) Loma Prieta #57217

8 DCR=2

6 4

DCR=1

2 0 0

3

6

9

12

15

Time (s)

9

12

15

Max. Principal Stress (MPa)

Max. Principal Stress (MPa)

Time (s)

(b)

10

(d) Kobe #Kakogawa

8 6 4

DCR=2

DCR=1

2 0 0

Time (s)

3

6

9

12

15

Time (s)

(c)

(d)

(a) Northridge #655

8 6

DCR=2

4

DCR=1

2 0 0

3

6

9

12

15

Max. Principal Stress (MPa)

10

10

(b) Imperial Valley #0952

8 6 4

DCR=2

DCR=1

2 0

0

3

6

(a)

10

(c) Loma Prieta #57007

8 6

DCR=2

4

DCR=1

2 0 0

3

6

9

12

15

Time (s)

Time (s)

9

12

15

Max. Principal Stress (MPa)

Max. Principal Stress (MPa)

Max. Principal Stress (MPa)

Fig. 9.15 Time histories of maximum principal tensile stresses for far-fault ground motions with a PGA level of 0.30 g. a Northridge #24272, b Imperial Valley #0286, c Loma Prieta #57217, and d Kobe # Kakogawa

(b)

10

(d) Kobe #JMA

8 6 4

DCR=2

DCR=1

2 0

0

3

6

9

Time (s)

Time (s)

(c)

(d)

12

15

Fig. 9.16 Time histories of maximum principal tensile stresses for near-fault ground motions with a PGA level of 0.30 g. a Northridge #655, b Imperial Valley #0952, c Loma Prieta #57007, and d Kobe # JMA

a considerable damage on the dam body as the performance curve is above the acceptance curve. Therefore, it can be stated that the linear time history analysis of the dam is insufficient, and the nonlinear time history analysis is required to estimate the performance more accurately.

0.4 Northridge Imperail Valley Loma Prieta Kobe Target

0.3

0.2

0.1

0.0 1.0

1.2

1.4

1.6

1.8

Demand-Capacity Ration (DCR)

(a) Far-fault earth quakes

2.0

Cumulative Overstress Duration (s)

Cumulative Overstress Duration (s)

9.5 Near-Fault Ground Motion Effects on Seismic Performance of Concrete …

229

1.2 Northridge Imperail Valley Loma Prieta Kobe Target

1.0 0.8 0.6 0.4 0.2 0.0 1.0

1.2

1.4

1.6

1.8

2.0

Demand-Capacity Ration (DCR)

(b) Near-fault earth quakes

Fig. 9.17 Performance assessment curves for Koyna dam subjected to near-fault and far-fault earthquakes with a PGA level of 0.30 g

Fig. 9.18 Overstressed regions for Koyna dam under far-fault ground motions with a PGA level of 0.30 g. a Northridge #24272, b Imperial Valley #0286, c Loma Prieta #57217, and d Kobe # Kakogawa

Fig. 9.19 Overstressed regions for Koyna dam under near-fault ground motions with a PGA level of 0.30 g. a Northridge #655, b Imperial Valley #0952, c Loma Prieta #57007, and d Kobe # JMA

230

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

Based on these results, it can be concluded that there are more seismic performance demands for the dam subjected to near-fault ground motions. The nonlinear analysis is required for near-fault ground motions at the 0.30 g level to further assess the dam damage.

9.5.3 Seismic Performance Evaluation Using Nonlinear Dynamic Analysis According to the proposed performance criteria, the results corresponding to the 0.30 g PGA level clearly indicated significant nonlinear deformation should be expected for near-fault ground motions. The nonlinear analysis must be carried out for seismic performance assessment of the dam. To validate this aspect of the proposed damage criteria, nonlinear dynamic damage analyses of the selected concrete dam under near-fault ground motions are conducted employing the Concrete Damaged Plasticity (CDP) model with the strain hardening or softening behavior. In order to study the influence of near-fault ground motions on the seismic performance of concrete gravity dams, nonlinear seismic analyses of concrete gravity dams subjected to far-fault ground motions are also performed. Seismic damage profiles of the Koyna gravity dam during the real near-fault and far-fault ground motions with a PGA of 0.3 g are shown in Figs. 9.20 and 9.21, respectively. The shaded area related with red color indicates those elements that experienced some level of tensile damage. The figures depict the damage predicted for real ground motions considered in this study. From the cracking profiles shown in Figs. 9.20 and 9.21, it can be observed that the failure mechanism is formed of two main damage zones, one at the base and one in the upper parts of the dam (downstream face or upstream face). Two damage zones are clearly identified and they correspond to the areas associated with the maximum tensile demands predicted

Fig. 9.20 Cracking profiles of Koyna dam under near-fault ground motions with a PGA level of 0.30 g. a Northridge #655, b Imperial Valley #0952, c Loma Prieta #57007, and d Kobe # JMA

9.5 Near-Fault Ground Motion Effects on Seismic Performance of Concrete …

231

Fig. 9.21 Cracking profiles of Koyna dam under far-fault ground motions with a PGA level of 0.30 g. a Northridge #24272, b Imperial Valley #0286, c Loma Prieta #57217, and d Kobe # Kakogawa

by the previous linear analyses. It can be also seen from Figs. 9.20 and 9.21 that asrecorded near-fault ground motions have significant influence on the seismic damage of concrete gravity dams. For the far-fault ground motions associated with a PGA level of 0.30 g, some moderate damage is identified (Fig. 9.21) but it does not seem to reach a level that could compromise the integrity of the section. On the other hand, the results corresponding to the input near-fault ground motions associated with a PGA level of 0.30 g clearly show indications of significant strength degradation in the dam, with a cracking pattern that extends completely across the upper section. Comparison of the dam crest horizontal displacement histories from the nonlinear analyses of the concrete gravity dam subjected to near-fault and far-fault ground motion indicates that a remarkable upstream deviation appears in the dam response under some near-fault ground motion cases, and there is a little, if any, residual deformation of the dam under far-fault ground motions compared with the initial displacement when imposing the seismic load. The maximum residual displacement of about 1.98 cm occurs under the near-fault ground motion recorded at Corralitos, CA #57007 station in the Loma Prieta earthquake, with respect to the equivalent deformation caused by the static loads.

9.6 Nonlinear Dynamic Response of Concrete Gravity Dams Subjected to Near-Fault and Far-Fault Ground Motions Due to the unique characteristics of the near-fault ground motions and their potential to cause severe damage to structures, the interest on the near-fault effect on structural response has increased. Earthquake engineers have been considering methods to incorporate near-fault effects in engineering design (Mavroeidis and Papageorgiou

232

9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

2003). In this thesis, a set of selected near-fault and far-fault ground motion records (as shown Table 9.1) is used to examine the near-fault ground motion effects. Nonlinear seismic analyses of dam-reservoir-foundation systems subjected to both near-fault and far-fault ground motions are performed. The influence of near-fault and far-fault ground motions on the dynamic response and seismic damage of concrete gravity dams is studied and discussed. Dynamic damage analysis of the selected concrete dam is conducted employing the Concrete Damaged Plasticity (CDP) model with the strain hardening or softening behavior. The integration time step used in the nonlinear analysis is 0.005 s.

9.6.1 Nonlinear Displacement Response Two sets of analyses, namely the near-fault case and far-fault case, are conducted to study the influence of near-fault and far-fault ground motions on the seismic response of dam-reservoir-foundation systems. Each set contains 10 as-recorded ground motion records. Figure 9.22 shows the time histories of horizontal displacements at the dam crest obtained from nonlinear analyses for near-fault and farfault ground motions, with positive displacement in the downstream direction. It is clear from Fig. 9.22 that the non-linear response obtained from near-fault ground motions has a substantially different displacement history than those obtained from far-fault ground motions. The crest horizontal displacement values for near-fault ground motions are greater than those for far-fault ground motions although the peak ground acceleration of near-fault and far-fault records are the same. Comparison of the dam crest horizontal displacement histories from the nonlinear analyses of the dam-reservoir-foundation system subjected to near-fault and farfault ground motion indicates that a remarkable upstream deviation appears in the dam response under some near-fault ground motion cases, and there is a little, if any, residual deformation of the dam under far-fault ground motions compared with the initial displacement when imposing the seismic load. The maximum residual displacement of about 3.75 cm occurs under the near-fault ground motion recorded at Taichung, Taiwan #TCU076 station in Chi-Chi earthquake, with respect to the equivalent deformation caused by the static loads. It is also seen from Fig. 9.22 that plastic deformations in the dam subjected to near-fault ground motions are larger than those subjected to far-fault ground motions.

9.6.2 Seismic Damage Seismic damage profiles of the Koyna gravity dam during the real near-fault and far-fault ground motions (Northridge earthquake, Imperial Valley earthquake, Loma Prieta earthquake, Chi-Chi earthquake) with a PGA of 0.3 g including dam-reservoirfoundation interaction are shown in Figs. 9.23, 9.24, 9.25 and 9.26, respectively.

No.1ñNear-fault No.2ñFar-fault

3 0 -3 -6

0

3

6

9

12

15

6

No.3ñNear-fault No.4ñFar-fault

3 0 -3 -6 0

3

6

9

12

Displacement (cm)

6

Displacement (cm)

Displacement (cm)

9.6 Nonlinear Dynamic Response of Concrete Gravity Dams Subjected …

15

233

6

No. 5ñNear-fault No. 6ñFar-fault

3 0 -3 -6 0

3

6

Time (s)

Time (s)

9

12

15

Time (s)

Displacement (cm)

Displacement (cm)

(a) 6

No. 7ñNear-fault No. 8ñFar-fault

3 0 -3 -6

0

3

6

9

12

15

6

No. 9ñNear-fault No. 10ñFar-fault

3 0 -3 -6

0

3

6

Time (s)

9

12

15

Time (s)

No. 11ñNear-fault No. 12ñFar-fault

3 0 -3 0

3

6

9

12

15

No. 15ñNear-fault No. 16ñFar-fault

3 0 -3 -6

0

8

16

24

Time (s)

32

No. 13ñNear-fault No. 14ñFar-fault

3 0 -3 -6 0

3

6

40

6

No. 17ñNear-fault No. 18ñFar-fault

3 0 -3 -6 0

8

16

9

12

15

Time (s)

(c) Displacement (cm)

6

6

24

Time (s)

32

Displacement (cm)

-6

Time (s) Displacement (cm)

Displacement (cm)

Displacement (cm)

(b) 6

40

6

No. 19ñNear-fault No. 20ñFar-fault

3 0 -3 -6

0

8

16

24

32

40

Time (s)

(d) Fig. 9.22 Time histories of horizontal displacements at the crest of the dam subjected to near-fault and far-fault ground motions from the a Northridge, b Imperial Valley, c Loma Prieta, and d Chi-Chi earthquakes. For ground motion information see Table 9.1

The shaded area related with red color indicates those elements that experienced some level of tensile damage over the duration of the analysis. The figures depict the damage predicted for real ground motions considered in this study. From the cracking profiles shown in Figs. 9.23, 9.24, 9.25 and 9.26, it can be observed that as-recorded near-fault ground motions have significant influence on the seismic damage of concrete gravity dams. In some cases, the results corresponding to the input motions with near-fault ground motions clearly show indications of significant strength degradation in the dam, with a cracking pattern that extends completely across the upper section. It can also be seen from Figs. 9.23, 9.24, 9.25 and 9.26 that the failure mechanism is formed by two main damage zones, one at the base and one in the upper parts of the dam. In almost all the analyses, the cracking is always first initiated at the dam heel, and then progresses a long way from the upstream face to the downstream face.

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9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

No. 5

No. 3

No. 1

(a) No. 2

No. 4

No. 6

(b) Fig. 9.23 Cracking profiles of Koyna dam under the Northridge earthquake: a near-fault ground motions b far-fault ground motions No. 7

No. 9

(a)

No. 8

No. 10

(b)

Fig. 9.24 Cracking profiles of Koyna dam under the Imperial Valley earthquake: a near-fault ground motions b far-fault ground motions

9.6 Nonlinear Dynamic Response of Concrete Gravity Dams Subjected … No. 13

No. 11

(a)

No. 12

235 No. 14

(b)

Fig. 9.25 Cracking profiles for Koyna dam under the Loma Prieta earthquake: a near-fault ground motions b far-fault ground motions

Fig. 9.26 Cracking profiles of Koyna dam under the Chi-Chi earthquake: a near-fault ground motions b far-fault ground motions

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9 Seismic Performance Evaluation of Dam-Reservoir-Foundation …

Cracking profiles in the upper part of the dam are always initiated at the point of slope discontinuity on the downstream face. Top cracking profiles are almost either nearly horizontal or sloping downward from the downstream faces towards the upstream faces. But in some analyses, cracks are predicted to initialize near the middle of the upstream face or the downstream face, and extend into the dam. Because of the thrust of impounded water which is opposing the tendency of the top section to slide along the crack in the upstream direction, the computed crack profiles in the upper part of the dam can be considered neutral or favourable conditions to maintain stability.

9.6.3 Damage Energy Dissipation

No. 1 No. 2 No. 3 No. 4 No. 5 No. 6

40 30 20 10 0

0

3

40

6

9

12

15

3

40 30 20 10 0

0

3

6

9

(a)

(b)

10

0

No. 7 No. 8 No. 9 No. 10

50

Time (s)

20

0

60

Time (s)

No. 11 No. 12 No. 13 No. 14

30

Damgage Energy Dissipation (KN.m)

50

6

Time (s)

(c)

9

12

15

Damgage Energy Dissipation (KN.m)

Damgage Energy Dissipation (KN.m)

Damgage Energy Dissipation (KN.m)

Figure 9.27 shows the energy dissipation curves of the dam under near-fault and farfault ground motions. The damage energy dissipation capacity of the dam increases when subjected to near-fault ground motions. The cumulative damage energy dissipation of the dam for near-fault ground motions is 4.68 times that for far-fault ground motions, on average. This demonstrates that near-fault ground motion will cause

100

12

15

No. 15 No. 16 No. 17 No. 18 No. 19 No. 20

80 60 40 20 0

0

10

20

Time (s)

30

40

(d)

Fig. 9.27 Damage energy dissipation curves of the dam for near-fault and far-fault ground motions. a Northridge earthquakes, b Imperial Valley earthquakes, c Loma Prieta earthquakes, and d Chi-Chi earthquakes

9.6 Nonlinear Dynamic Response of Concrete Gravity Dams Subjected …

237

more severe damage to the dam body than far-fault ground motion. As can be seen in Fig. 9.27, the amount of the damage can also be assessed by the damage energy dissipation.

9.6.4 Identifying the Influence of Near-Fault Ground Motions on Seismic Damage of Dams The absolute maximum horizontal displacements obtained from the nonlinear analyses for both near-fault and far-fault ground motions are given in Fig. 9.28. It can be seen from Fig. 9.28 that the values of maximum horizontal displacements for the dam under near-fault ground motions are generally greater than those subjected to far-fault ground motions. In order to analyze the effects of near-fault ground motion on seismic damage of concrete gravity dams, Figs. 9.29, 9.30 and 9.31 are generated by plotting the accumulated damage of the dam imparted by the 20 records for a given level of intensity in terms of the local and global damage indices. Trend lines are displayed with the aim of identifying an average value for each case. From Figs. 9.29, 9.30 and 9.31, it can be observed that studies employing damage measures using local and global damage indices show that near-fault ground motion may have a significant influence on the accumulated damage. The global index of the dam for near-fault ground motions is 1.89 times that for far-fault ground motions, on average. It can also be seen from Figs. 9.29-9.31 that the upper zone of concrete gravity dams is more vulnerable to near-fault earthquakes in comparison to a corresponding far-fault ground motion. Damage measures such as the local damage index Near-fault Far-fault

Displacement (cm)

7 5

6

Average of 5.06cm

3

5 1

4

1.74cm 2

11

7 8

4

0

2

4

Average of 3.32cm 6

8

15 17

13

9

6

3 2

19

10

12

14

16

10

12

14

16

No.

18

20

18

20

Fig. 9.28 Absolute maximum horizontal displacements at crest of the dam under near-fault and far-fault ground motions. For ground motion information see Table 9.1

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Local damage index

1.0

Average of 0.84

1

19

9

13

11

0.8

3

15

7

5

0.6

8

4

0

2

Average of 0.40

4

6

16

14

12

0.4 0.2

Near-fault Far-fault

0.44

6

2

17

10

8

10

No.

12

14

16

18

20

18

20

Fig. 9.29 Influence of near-fault and far-fault ground motions on the local damage index measure for the upper part of the dam (near the changes in the slope of the downstream face). For ground motion information see Table 9.1

Local damage index

0.25

5 1

0.20

0.07

19

12

9

3

0.15

15

Average of 0.18

7

13

8

16

0.10

18

0.05 0.00

20

17

14

0

6

2

4

2

4

Average of 0.11

6

8

11

Near-fault Far-fault

10

10

No.

12

14

16

18

20

Fig. 9.30 Influence of near-fault and far-fault ground motions on the local damage index measure for the dam heel. For ground motion information see Table 9.1

for the upper zone of the dam are consistently greater for near-fault ground motions. While, the accumulated damage on the dam heel is not very sensitive to near-fault ground motions. The local damage index under near-fault ground motion for the upper part of the dam is 0.84, and for the dam heel is 0.18, on average. The accumulated damage for the upper zone of the dam is more sensitive to near-fault ground motion, which gives more importance to the dissipated energy during the hysteretic behavior of the structure since the high seismic response zone is mainly located in the upper zone of the dam.

9.7 Conclusions

Global damage index

0.4

239

1

5

7

15

9

3

0.3

19 17

13

Average of 0.34

0.16

11

8

12

16 14

0.2 2

6 4

0.1 0

2

4

18

Average of 0.18

6

8

Near-fault Far-fault

10

10

No.

20

12

14

16

18

20

Fig. 9.31 Influence of near-fault and far-fault ground motions on the global damage index measure for the dam. For ground motion information see Table 9.1

9.7 Conclusions The purpose of this study was to analytically evaluate the near-fault and far-fault ground motion effects on nonlinear dynamic response and seismic damage of concrete gravity dams with considering the effects of dam-reservoir-foundation interaction. The reservoir water is modeled using two-dimensional fluid finite elements by the Lagrangian approach. The Koyna gravity dam is chosen for analysis. 20 asrecorded near-fault and far-fault strong ground motion records considered in this study are used as seismic excitations. Nonlinear seismic analyses of concrete gravity dams under earthquake conditions are performed according to the Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior. It is concluded from the study that the nonlinear response obtained from nearfault ground motions has a substantially different displacement history than those obtained from far-fault ground motions. The crest horizontal displacement values for near-fault ground motions are greater than those for far-fault ground motions. A comparison of the dam crest horizontal displacement history from the nonlinear analyses of the dam-reservoir-foundation system subjected to near-fault and far-fault ground motion indicates that a remarkable upstream deviation appears in the dam response under some near-fault ground motion cases. The performed seismic damage analyses show that accumulated damage of dams under consideration is found to be significantly affected by near-fault ground motion. The upper zone of concrete gravity dams is more vulnerable to near-fault earthquakes in comparison to a corresponding far-fault ground motion. In some cases, the results corresponding to the input motions with near-fault ground motions clearly show indications of significant strength degradation in the dam, with a cracking pattern that extends completely across the upper section.

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According to this study, near-fault earthquake ground motions have remarkable effects on the nonlinear dynamic response and accumulated damage of concrete gravity dams due to their impulsive effects on structures. Near-fault ground motions have the potential to cause more severe damage to the dam body than far-fault ground motions. The effects of near-fault ground motions on concrete gravity dams should be taken into account to obtain more realistic results.

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Chapter 10

Deterministic 3D Seismic Damage Analysis of Guandi Concrete Gravity Dam

10.1 Introduction During the recent decades, the growing demand for green energy has boosted the construction of high concrete dams, many of which are located in seismically active regions. For instance, tens of concrete dams over 150 m in height are either being built or planned in Southwest China, with the design peak ground acceleration value up to 0.56 g. The seismic safety of concrete dams is one of the most important issues in the engineering field since earthquake activities may impair the proper functioning of these critical infrastructures and trigger catastrophic failure that results in heavy loss of human life and property. One of the major reasons for seismic damage and failure of such structures is the initiation, growth and coalescence of cracks in concrete (Mridha and Maity 2014). Due to the growing concern on the seismic safety of concrete dams, nonlinear numerical models, which can predict crack initiation and propagation through the dam body, have attracted great research interest in the community of dam engineering and been widely used for evaluating the seismic performance of concrete dams. These models can be grouped into two families: continuum crack approaches with no intention to capture individual cracks such as smeared crack approach (Bhattacharjee and Léger 1994; Léger and Leclerc 1996) and plastic-damage model (Lee and Fenves 1998a, b; Omidi et al. 2013), and discrete crack approaches aimed at resolving individual cracks, including the fracture mechanics approach (Ayari and Saouma 1990) and extended finite element method (XFEM) (Zhang et al. 2013a, b; Wang et al. 2015a, b). While discrete crack approaches provide an explicit representation of discontinuous displacement fields, they need to keep track of the evolution of individual cracks, therefore imposing significant challenges to finite element (FE) implementations, especially in three dimensional cases. On the other hand, the continuum crack models treat cracks as the ultimate consequence of damage accumulation in

© Zhejiang University Press and Springer Nature Singapore Pte Ltd. 2021 G. Wang et al., Seismic Performance Analysis of Concrete Gravity Dams, Advanced Topics in Science and Technology in China 57, https://doi.org/10.1007/978-981-15-6194-8_10

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10 Deterministic 3D Seismic Damage Analysis …

the constitutive relations with strain softening. While discrete crack models can be regarded as more accurate modeling techniques than continuum methods, continuum crack approaches are computationally very attractive and better suited for complex engineering problems (Wang and Waisman 2016). In order to meet the deformation requirements of the foundation and to minimize the cracking caused by shrinkage, concrete gravity dams are constructed as individual monoliths that are separated by contraction joints. Owing to the presence of contraction joints, most of the analyses that deal with the nonlinear dynamic response and seismic safety evaluation of concrete gravity dams are through either two dimensional (2D) (Huang and Zerva 2013; Omidi et al. 2013; Alembagheri and Ghaemian 2013a; Alembagheri and Seyedkazemi 2015) or quasi three dimensional (3D) (Pan et al. 2011; Mridha and Maity 2014) models, with the underlying assumption that the monoliths behave independently during earthquake activities. The tallest monolith of concrete gravity dams, usually located on the valley bottom, is often selected for dynamic analysis since this monolith is the most critical part of dam structures. Based on 2D or quasi-3D simulations, many factors which may influence the dynamic behavior of concrete gravity dams have been studied, including the input excitation mechanism, strong motion duration, near-fault ground motions, aftershocks, reservoir length, to name just a few(Zhang and Wang 2013; Wang et al. 2015a, b, 2016, 2017). However, three dimensional analyses are required in order to obtain a more realistic seismic response of concrete gravity dams. The reasons are threefold. First, monoliths of a concrete gravity dam have different heights and cross-sections. Such difference leads to distinct periods of vibration and damage characteristics during seismic events. For instance, the Koyna earthquake caused varying degrees of damage to different monoliths of the Koyna dam (Chopra and Chakrabarti 1973), including horizontal cracks on the downstream face of monoliths 13–18 and 25–30 and on the upstream face of monoliths 10–18 and 24–30. Second, the contraction joints are expected to open/close and slide cyclically when subjected to severe earthquake ground motions. The nonlinear interaction between concrete monoliths would result in the redistribution of stresses in dam bodies and thus may influence the pattern and degree of the damage-cracking of concrete gravity dams. When high concrete gravity dams are built in narrow valleys, vast height variations exist between adjacent monoliths and dam foundations are usually tilted in the cross-stream direction. Under cross-stream seismic excitations, these factors would further increase the nonlinear response of contraction joints of dams, which may in turn affect the overall seismic performance of concrete gravity dams significantly. Last, gravity dam-foundation systems generally undergo significant dynamic forces (from reservoirs) when subjected to earthquakes, which may lead to crack initiation and propagation in dam bodies. In addition, the dynamic interaction between the dam and foundation can also affect the system response through the reflection and radiation of seismic waves. However, the significance of the dam-foundation-reservoir interaction can only be partially considered by the widely used 2D or quasi-3D models, in which the cross-stream interaction is completely neglected.

10.1 Introduction

245

Up to now, 3D finite element analyses accounting for the effects of contraction joints (Feng et al. 2011; Hariri-Ardebili et al. 2013; Omidi and Lotfi 2013; Wang et al. 2013; Alembagheri and Ghaemian 2013b, 2015; Hariri-Ardebili and Kianoush 2014) are mainly carried out in reference to arch dams and there are only a few studies on the 3D dynamic response of concrete gravity dams. Azmi and Paultre (2002) studied the influence of contraction joints opening-closing as well as shear sliding on the seismic behavior of Outardes 3 gravity dam comprised of 19 monoliths. Wang et al. (2012a, b) employed a 3D model to analyze the earthquake response of a concrete gravity dam based on the linear material model of mass concrete. In their study, dynamic contact between monoliths was taken into account. The results showed that increasing the connection between the monoliths can enhance the aseismic capacities of the dam. In order to investigate the nonlinear seismic response of a typical gravity dam as accurate as possible, Hariri-Ardebili et al. (2016) modeled one of the non-overflow monoliths in 3D geometry with three times of the actual thickness of the monolith and only the results at the middle section were extracted. Arici et al. (2014) and Yilmazturk et al. (2015) conducted seismic response analyses of a roller compacted concrete (RCC) gravity dam including 3D dam-reservoir-foundation interaction. By comparing the results with those from 2D analyses, they found that the 3D behavior of the dam is substantially different from that obtained from the idealized 2D analyses. They emphasized the importance and necessity of full 3D analyses for gravity dams, especially when they are built in relatively narrow canyons. In this contribution, a systematic study has been conducted on the 3D seismic damage-cracking behavior of concrete gravity dams with all the following factors considered: contraction joint nonlinearity, cross-stream earthquake excitation, and dam-foundation-reservoir interaction. The effects of the cross-stream seismic excitation and contraction joints on the cracking characteristics of a practical gravity dam have been investigated. To this end, Guandi concrete gravity dam, built in the highly seismic zone of China, is considered. The Concrete Damaged Plasticity (CDP) model (Lubliner et al. 1989; Lee and Fenves 1998a, b) including strain hardening/softening behavior is used to capture crack initiation and propagation in the dam body. The joint nonlinearity associated with opening and slipping of contraction joints is modeled using two different surface-to-surface contact models (soft and hard formulations) so that the effects of joint infills can be quantified. The Lagrangian approach is used for the modeling of the dam-reservoir-foundation interaction. The proposed model is first validated against the experimental cracking results of the Koyna concrete gravity dam. Then a comprehensive investigation of the seismic cracking characteristics of the Guandi concrete gravity dam-foundation-reservoir system is carried out based on 3D nonlinear dynamic analyses. Several case studies are conducted to investigate the influence of the cross-stream seismic excitation and contraction joints on nonlinear dynamic responses of the Guandi gravity dam.

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10 Deterministic 3D Seismic Damage Analysis …

10.2 Material Properties of Mass Concrete and Contraction Joint Nonlinearity Two sources of nonlinearity are involved in the dynamic behavior of concrete gravity dams: material nonlinearity due to concrete cracking and contact nonlinearity owing to the opening/closure and sliding of contraction joints. Numerical models for both sources of nonlinearity are detailed in this section. FE analyses presented in this work are performed using the general-purpose commercial software ABAQUS/Standard V 6.11(Version 2011).

10.2.1 Material Properties of Mass Concrete In general, both the degradation of stiffness (damage) due to micro-cracking and unrecoverable deformation (plasticity) are exhibited by concrete materials. Therefore, a proper constitutive model for concrete should address the two physically distinct behaviors. The Concrete Damaged Plasticity (CDP) model, proposed by Lubliner et al. (1989) and modified by Lee and Fenves (1998a, b), offers a particularly efficient context where damage evolution and plastic deformation can be modeled simultaneously. In this model, uniaxial strength functions are factorized into two parts to represent the permanent (plastic) deformation and degradation of stiffness (damage). Two main failure mechanisms of the concrete material are assumed in the CDP model: one is tensile cracking and the other is compressive crushing. Accordingly, different strength and post-peak behaviors of concrete can be taken into account for tension and compression. This approach, which can efficiently describe complex mechanical behavior of concrete under cyclic loadings, is selected in this study for the seismic cracking analysis of concrete dams. The interested reader is referred to (Zhang et al. 2013a, b) for more details concerning the constitutive model, including the damage evolution, the yield criterion, and the flow rule.

10.2.2 Contraction Joint Nonlinearity Concrete gravity dams are constructed as individual monoliths which are separated by contraction joints. The contraction joints are expected to open/close and slide cyclically during severe earthquake ground motions. The presence of these weak planes between monoliths may significantly affect the dynamic behavior of concrete gravity dam-reservoir-foundation systems. In order to model the joint behavior, a surface-to-surface contact model is used in the present study. The interaction between contacting surfaces consists of two components: normal interaction due to loads perpendicular to surfaces in contact, and tangential one, referring to possible relative sliding between two adjacent surfaces.

10.2 Material Properties of Mass Concrete and Contraction Joint Nonlinearity

247

Shear keys are not considered in contraction joints. To quantify the effect of joint infill, two different contact formulations are adopted in this study to describe the normal behavior, i.e. hard and soft contact models as shown in Fig. 10.1. We define the clearance as the normal separation between two surfaces. In hard contact formulation, the contact constraint is applied when the clearance becomes zero. There is no limit on the magnitude of contact pressure that can be transferred by the contact surfaces. The surfaces start to separate when the contact pressure becomes zero or negative, in which case the contact constraint is removed. Thus, a dramatic change in contact pressure may occur when the contact condition changes from “open” (a positive clearance) to “close” (zero clearance). On the other hand, the normal stress is an exponential function of the clearance in the soft contact formulation, which is suited to describe the contact behavior of soft, thin layer of grouting materials between the contraction joint surfaces. The adopted exponential function is given as follows:  p=

0, P0 exp(1)−1



1−

c c0

  exp 1 −

c c0



 c ≥ c0 − 1 , c < c0

(10.1)

where c0 is the initial contact distance, p is the normal contact pressure, P0 is the pressure value at zero opening. In this model, the surfaces begin to transmit normal pressure once the distance between them, measured in the normal direction, reduces to the initial contact distance c0 . For each joint, the initial contact distance c0 = 1 mm and the pressure value P0 = 50 MPa at zero opening are selected (Chen et al. 2012; Wang et al. 2012a, b). In addition to determining whether contact occurs at a particular point, the relative sliding of the contact surfaces is also calculated. When surfaces are in contact, they usually transfer not only normal pressure but also shear forces. Thus, the shear forces that resist the relative sliding of the surfaces should be taken into consideration. In this study, the Coulomb friction model is employed to characterize the frictional

Fig. 10.1 Contact pressure-clearance relationships for hard and soft contact models

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10 Deterministic 3D Seismic Damage Analysis …

behavior between the surfaces. The tangential motion is zero until the shear traction reaches a critical value, which depends on the normal contact pressure as follows τcrit = μp

(10.2)

where μ is the coefficient of friction and p is the contact pressure between the two surfaces. This equation gives the limiting frictional shear stress for the contacting surfaces.

10.3 3D Lagrangian Finite Element Formulation The adopted finite element formulation (Wilson and Khalvati 1983; Calayir and Dumanoˇglu 1993) for a three dimensional fluid-solid coupled system is based on the Lagrangian approach. In this approach, displacements are selected to be the unknown variables for both the fluid and structure domains. Fluid is assumed to be linearly elastic, inviscid, and irrotational. The stress-strain relationships for a general three-dimensional fluid element read: ⎫⎧ ⎫ ⎧ ⎫ ⎧ C11 0 0 0 ⎪ P ⎪ ⎪ ⎪ εv ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎨ ⎬ ⎪ ⎬⎪ ⎬ ⎨ ⎪ Wx Px 0 C22 0 0 = (10.3) ⎪ Wy ⎪ ⎪ P ⎪ ⎪ 0 0 C33 0 ⎪ ⎪ ⎪ ⎪ ⎩ ⎩ ⎭ ⎪ ⎭⎪ ⎭ ⎩ y⎪ Pz Wz 0 0 0 C44 where P is the pressure, C 11 is the bulk modulus of fluid, εv is the volumetric strain; W x , W y and W z are the rotations with respect to the Cartesian axis x, y, z, respectively, Px , Py and Pz are the corresponding rotational stresses, C 22 , C 33 and C 44 are the constraint parameters. Note that the rotation constraint parameters in the above stress–strain relationships are introduced to enforce the irrotationality of fluid by means of a penalty method. It should be as high as necessary to prevent fluid rotation but small enough to avoid causing numerical ill-conditioning in the assembled stiffness matrix. In the analysis, the effect of the small amplitude free surface waves, which is commonly referred to as the sloshing effect, is taken into account. The sloshing effect causes a pressure at the free surface of fluid, which is given by P = −γw u fn

(10.4)

where γ w is the weight density of fluid and ufn is the normal component of the free surface displacement. The free surface stiffness for fluid is obtained from the discrete form of Eq. (10.4). Detailed formulation on the Lagrangian finite element formulation for the simulation of the dam-reservoir-foundation system can be found in Ref. Calayir and Dumanoˇglu (1993).

10.4 Validation Test for 3D Model

249

10.4 Validation Test for 3D Model In order to validate the effectiveness of the numerical framework, a quasi 3D model of a single monolith is established to analyze the cracking behavior of Koyna concrete gravity dam under the 1967 Koyna earthquake. Three components of the Koyna earthquake are shown in Fig. 10.2. Only the stream and vertical components of the seismic ground motions are considered in the validation test, which is consistent with the seismic input for the model test reported in (Mridha and Maity 2014). The geometric characteristics and FE mesh of the quasi 3D model are shown in Fig. 10.3. The material parameters for the Koyna dam-reservoir-foundation system are listed in Table 2.2 (Chap. 2). The tensile and compressive strength of concrete are 2.9 and 24.1 MPa, respectively. The fracture energy is 250 N/m. In order to avoid wave propagation effects when applying free field earthquake records at the foundation base, the foundation rock is assumed to be massless. The reservoir water is assumed to be linearly elastic, inviscid, and irrotational. The rotation constraint parameter of the fluid is assumed to be 1000 times of its bulk modulus (Akkose et al. 2008). A dynamic magnification factor of 1.2 is considered for the tensile strength to account for strain rate effects. The energy dissipation of the dam-reservoir-foundation system is considered by the Rayleigh damping method with 5% damping ratio. Transmitting boundaries have been used at the truncated boundary of the reservoir. It should be noted that the wave absorption at the reservoir bottom has not been considered. Component L

0.2 0.0 -0.2 -0.4 0

Component T

0.4

Acceleration(g)

Acceleration(g)

0.4

0.2 0.0 -0.2 -0.4

2

4

6

8

10

0

2

4

Time (s)

8

10

Time (s) (b)

(a) 0.4

Acceleration (g)

6

Component V

0.2 0.0 -0.2 -0.4 0

2

4

6

8

10

Time (s) (c)

Fig. 10.2 Koyna earthquake on December 11, 1967. a Component L, b Component T, and c Component V. (L: stream direction, T: cross-stream direction, and V: vertical direction)

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10 Deterministic 3D Seismic Damage Analysis …

Fig. 10.3 Geometry and finite element discretization for the Koyna dam-reservoir-foundation system. a Quasi 3D model of the dam-reservoir-foundation system, and b enlarged plot of the dam body

For the initial time step, the nodal displacements on the truncated boundary of the reservoir and foundation are assumed to be zero in the normal direction. In addition, the bottom boundary of the foundation is fully constrained. After the static analysis, all the displacement constraints are released, and the stream and vertical components of the Koyna earthquake accelerations are applied to the base of the foundation as the input loading. Figure 10.4 compares the final cracking profile of Koyna dam obtained from the quasi-3D numerical simulation with that from the model test (Mridha and Maity 2014). The damage zone, which indicates the cracking profiles, is shaded in red color. As can be clearly seen, the numerical cracking profile matches reasonably well with the experimental results. It can be concluded that the presented numerical framework can predict effectively the crack propagation process in concrete gravity dams under seismic loadings. It should be noted that the presented test does not consider the effect of contraction joints and a better validation may be pursued if the experimental data for the full 3D model with multiple monoliths become available.

10.5 3D Guandi Gravity Dam-Reservoir-Foundation System 10.5.1 Introduction to Guandi Gravity Dam Guandi hydropower station (see Fig. 10.5), which is a roller compacted concrete (RCC) dam, is located on the Yalong River in the Sichuan Province of China. The crest length of the dam is 467 m, the highest monolith is 168 m high, and the normal depth of reservoir water is 164 m. The maximum thickness of the dam base is 153.2 m

10.5 3D Guandi Gravity Dam-Reservoir-Foundation System

251

Fig. 10.4 Final failure mode of Koyna dam under the 1967 earthquake given by a three dimensional finite element meshes; b experimental results from the model test with full reservoir. The elasticity modulus, density, tensile, and compressive strength of the model test are 203.68 MPa, 2578 kg/m3 , 0.19023 MPa and 0.01869 MPa, respectively (Mridha and Maity 2014)

Fig. 10.5 Site photos of the Guandi hydropower project: a upstream side; b downstream side

while the thickness at the crest of the dam is 20 m. The dam was built with 22 contraction joints, with the space between each other being approximately 20 m. These contraction joints form a set of 23 monoliths. The basic material parameters for the Guandi gravity dam-reservoir-foundation system are listed in Table 10.1. It should be noted that three indices of concrete are employed, i.e. C15, C20 and C25. However, only C20 concrete is employed for the

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Table 10.1 Dynamic material parameters for the Guandi gravity dam-reservoir-foundation system

Material

Modulus (GPa)

Poisson’s ratio

Density (kg/m3 )

Concrete

57.6

0.167

2552

Foundation rock

21.6

0.2

Massless (assumption)

Reservoir water

2.07 (Bulk modulus)

–

1000

whole dam in this Chapter due to the complexity of the 3D dam-reservoir-foundation system. The dynamic tensile and compressive strength of concrete are 1.94 MPa and 19.38 MPa, respectively (obtained by applying a dynamic magnification factor of 1.3 to the static strength). The fracture energy is 257 N/m. The uniaxial tension and compression stress-strain behavior used in the CDP model were obtained from the concrete experiments conducted for the Guandi gravity dam. These stress-strain curves, which define the nonlinear behavior of concrete, are tabulated in Table 10.2. The material parameters for the reservoir water are assumed to be the same with those used in the validation test. The traditional massless foundation approach is utilized here to avoid wave propagation effects when applying free field earthquake records at the foundation base. In this model, only the stiffness of the foundation medium is considered. It should be noted that the massless foundation model may overestimate the nonlinear dynamic response of concrete dams in comparison with massed foundation model (Hariri-Ardebili and Mirzabozorg 2013; Hariri-Ardebili et al. 2016). The material damping for the dam-reservoir-foundation system is considered via the Rayleigh damping assumption with 5% damping ratio in the analysis. The value of the damping ratio is selected according to the current seismic codes in China. We should mention that this value may be overestimated as the nonlinear processes in the dam will produce additional damping. While transmitting boundaries are used at Table 10.2 Uniaxial tension and compression behavior used in the CDP model Compression hardening and damage

Tension stiffening and damage

Stress (MPa)

Crushing strain

Damage

Stress (MPa)

Cracking strain

Damage

15.50

0

0

1.94

0

0

19.38

0.00007

0

1.90

0.000003

0.057

17.35

0.00024

0.228

1.74

0.000010

0.170

11.87

0.00057

0.505

1.41

0.000024

0.346

6.65

0.00124

0.724

1.00

0.000051

0.545

3.43

0.00259

0.856

0.66

0.000104

0.713

1.72

0.00528

0.927

0.41

0.000212

0.829

0.86

0.01067

0.963

0.26

0.000428

0.901

0.43

0.02143

0.981

0.16

0.000859

0.944

0.22

0.04297

0.991

0.10

0.001721

0.968

10.5 3D Guandi Gravity Dam-Reservoir-Foundation System

253

the truncated boundary of the reservoir, we do not consider the wave absorption at the reservoir bottom. The Guandi gravity dam is located in a highly seismic region with a design peak ground acceleration (PGA) of 0.34 g, and found on very dense soil and soft rock with shear wave velocity more than 500 m/s. The static solution of the dam-reservoirfoundation system is taken as the initial condition in the nonlinear dynamic analysis. The static loads considered here are the body self-weight, the hydrostatic pressure of the impounded water, and the uplift pressure. The dynamic loads include earthquake excitations in three directions and the hydrodynamic pressure. Due to the lack of real earthquake records from a location close to the dam, three seismic records from similar sites (i.e. 1967 Koyna #Koyna dam, 1994 Northridge #5353 and 1989 Loma Prieta #57563) are selected as the earthquake excitation for the 3D seismic analysis of the Guandi gravity dam. All acceleration components are scaled by the same factor such that the PGA along the stream direction is 0.34 g. After analyzing the results, we found that although the selected three seismic records lead to differences in the damage-cracking pattern and response level, the observations about the effects of the cross-stream seismic excitation and contraction joints on the cracking characteristics of the Guandi gravity dam are more or less the same for the three earthquakes. For clarity, we only discuss the results from the Koyna earthquake in the following.

10.5.2 3D Finite Element Model The finite element discretization of the Guandi gravity dam-reservoir-foundation system, together with the layout of 22 contraction joints, is shown in Fig. 10.6. The interaction between the impounded water and the dam-foundation system is explicitly taken into account by modeling the reservoir water with three dimensional fluid elements in the Lagrangian formulation. The foundation extends to a distance of 168 m (the height of the tallest monolith) in downward, upstream, downstream, leftward, and rightward directions. The solid domain (dam body and foundation rock) is discretized with eight-node solid elements whereas eight-node Lagrangian fluid elements are adopted for the modeling of reservoir water. A relatively fine mesh is used for the entire dam. The model consists of 189,411 elements and 223,017 nodes, among them 59,465 elements are used for the dam, and 36,175 elements are used for the reservoir domain. For the initial time step, the displacements of nodes on the truncated boundary of the three-dimension dam-reservoir-foundation system are assumed as zero in the normal direction. In addition, the base of the foundation is fully constrained. In the subsequent nonlinear dynamic analysis, all displacement constraints are released, and three components of the selected earthquake accelerations are applied to the foundation base as the input loading. The implicit Newmark-β time integration method is applied to conduct the seismic response analysis. The initial increment size and maximum increment size are 0.001 s and 0.01 s, respectively.

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Fig. 10.6 Finite element model of the Guandi dam-foundation-reservoir system: a geometric configuration of the coupled system; b mesh for the dam body and foundation; c layout of contraction joints

10.6 Nonlinear Seismic Behavior

255

10.6 Nonlinear Seismic Behavior Nonlinear dynamic analysis is performed based on the established three-dimensional FE model, in which the effects of concrete cracking, contraction joint nonlinearity and dam-reservoir-foundation interaction are taken into account. Furthermore, we also investigate the potential influence of joint grouting materials on the dynamic response of the Guandi dam by using both hard and soft pressure-clearance relationships. The following performance criterion has been used to evaluate the seismic performance: (1) No damage: from the initial intact state to some minor cracks (in numerical simulation this corresponds to a small damage area with a low damage value). The dam is considered to behave in the elastic range with little or no possibility of damage; (2) Slight damage: from a few minor cracks to cracks penetrating the one-third width of the dam section. The level of nonlinear response or cracking can be considered acceptable with no possibility of failure; (3) Moderate damage: the crack depth is from one-third to two-third of the dam section width. The dam can be easily repaired without affecting the dam operation; (4) Severe damage: crack depth is from two-third of the dam section width to almost perforation. This damage state is associated with extensive damages requiring immediate retrofit and rehabilitation actions.

10.6.1 Seismic Damage The final damage profiles of the Guandi gravity dam are compared in Fig. 10.7 for hard and soft contact formulations, where the serial number for each monolith (1–23) is also given for better understanding. It can be seen in Fig. 10.7 that the final damage profiles from both contact models are quite similar to each other. As can also be seen in Fig. 10.7, cracks mainly develop in the following regions: the discontinuity in the slope of the downstream face (monoliths 5–10, 16–20), the junction of the pier and spillway sill (monoliths 11–15), the dam heel (monoliths 12–15), and the upstream face (monoliths 8–10). In the simulation, the gates of the crest spillway have not been modeled, and the piers are modeled as freestanding cantilevers, using the constitutive model for mass concrete. Due to the cross-stream movement of the dam, severe damage is localized in the piers. The actual damage level is expected to be smaller since there are gates as well as traffic beams on the top of the piers that can enhance the stiffness. In addition, piers are reinforced concrete structures and the adopted material model could overestimate the damage of piers. Based on the above mentioned performance criteria, the Koyna earthquake causes moderate damage to the middle non-overflow and spillway monoliths.

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Fig. 10.7 Final damage profiles of Guandi concrete dam: a upstream side, hard contact; b upstream side, soft contact; c downstream side, hard contact; d downstream side, soft contact

10.6.2 Maximum Stream Displacement The distribution of the maximum stream displacements along the crest is shown in Fig. 10.8 for hard and soft contact formulations, where the positive displacement is in the downstream direction. As can be seen, while the maximum positive displacements of each monolith from the hard contact formulation are slightly larger than those from the soft one, the hard contact model leads to smaller maximum displacements in the upstream direction. Overall, the difference in the maximum stream displacements along the crest is minor between hard and soft contact models. For non-overflow Positive-Hard contact Negative-Hard contact Positive-Soft contact Negative-Soft contact

Displacement (mm)

60 40 20 0 -20 -40 0

2

4

6

8

10

12

14

16

18

20

Monolith number Fig. 10.8 Maximum positive and negative stream displacements along the dam crest

22

24

10.6 Nonlinear Seismic Behavior

257

monoliths (1–9, 17–23), the maximum stream displacements on the dam crest are closely related to the height of monoliths: the maximum positive displacement for non-overflow monoliths from the hard contact formulation is 39.3 mm at monolith 9, with a height of 142 m. For overflow monoliths, the maximum positive displacement from the hard contact formulation is 54.4 mm at monolith 11, whereas the maximum displacement in the upstream direction is relatively small. This is because that the structural feature of piers limits the upstream movement.

10.6.3 Contact Behavior of Contraction Joints Envelopes of the resulting contact pressure on 22 contraction joints based on hard and soft contact formulations are presented in Fig. 10.9. As can be seen, the envelopes of the contact pressure resulted from the two contact models are quite close to each other.

Fig. 10.9 Envelopes of contact pressure of 22 contraction joints using a hard contact formulation and b soft contact formulation (unit: Pa)

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10 Deterministic 3D Seismic Damage Analysis …

Fig. 10.10 Envelopes of contraction joint opening displacement for representative joints: a J3; b J9; c J10 (unit: m)

Great contact pressure on contraction joints is generated by the dynamic interaction between monoliths. The zones of high contact pressure are mainly located on the dam crest and the spillway sill (near the junction of the pier and spillway). The maximum contact pressure from the hard contact formulation is 6.40 MPa, arising on J15. The above analyses indicate that the material properties of the joint infill have limited influence on the nonlinear dynamic response of the Guandi dam. It is also found that the major conclusions drawn from the following case studies are not affected by the adopted contact model. Therefore, for clarity, the following results that consider contraction joint nonlinearity are all based on the hard contact formulation. Envelopes of opening displacement for three representative contraction joints J3, J9, and J10 are depicted in Fig. 10.10. It can be found that the maximum opening displacement appears on the dam crest. Figure 10.11 shows the time history of the opening and sliding displacements of the three contraction joints (J3, J9 and J10) on the dam crest. As can be seen in Fig. 10.11, the opening and sliding displacements of J10 is significantly larger than those of J3 and J9. This can be explained by the presence of piers in the overflow monoliths which reduce the cross-stream stiffness.

10.7 Evaluation of the Key Factors Affecting Damage-Cracking Characteristics In this section, four different cases are investigated in order to obtain insight into the effects of contraction joints and cross-stream excitation on the seismic damagecracking behavior of the concrete gravity dam. The Guandi gravity dam-reservoirfoundation system presented in Sect. 10.5 is taken as the reference Case A. The basic features of the four simulation cases are summarized as follows: (1) Case A: 3D dam-reservoir-foundation model which considers material nonlinearity in terms of concrete damage-cracking, joint nonlinearity in terms of contraction joint opening and sliding, and three-component ground motion including stream, cross-stream and vertical components.

10.7 Evaluation of the Key Factors Affecting Damage-Cracking Characteristics 70

J3 J9 J10

60

Contraction joint openting (mm)

259

50 40 30 20 10 0 0

2

4

6

8

10

6

8

10

Time (s)

(a) Contraction joint sliding (mm)

35

J3 J9 J10

30 25 20 15 10 5 0 -5

0

2

4

Time (s)

(b) Fig. 10.11 Displacement histories of three representative contraction joints (J3, J9, and J10) on the dam crest: a opening displacement; b sliding displacement

(2) Case B: same with Case A except that the dam body is modeled as a whole without contraction joints. (3) Case C: same with Case A except that only stream and vertical seismic excitations are considered. (4) Case D: quasi-3D model is used for representative monoliths (monoliths 9, 11, and 16) where material nonlinearity and two-component seismic excitation including stream and vertical components are considered. It should be noted that in Case D the quasi-3D meshes for monoliths 9, 11 and 16 are the same with the meshes used in Case A for those monoliths. All analyses are performed on a PC with an Intel(R) Core (TM) i7-4770 CPU at 3.40 GHz and 16 GB RAM. The CPU times for Case A, Case B, Case C, and Case D (monoliths 9) are 321,552 s, 5,292 s, 176,736 s, and 711 s, respectively.

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10 Deterministic 3D Seismic Damage Analysis …

10.7.1 Discussion of Results from 3D Dam-Reservoir-Foundation Model Figure 10.12 compares the final damage-cracking patterns of the Guandi gravity dam for Cases A, B, and C. Note that the damage profile shown in Fig. 10.12a is the same as that in Fig. 10.7a. As can be seen from Fig. 10.12, both the contraction joints and cross-stream seismic excitation have a significant influence on the cracking behavior of the dam body. The damage area for Case B in which the dam body is modeled as a whole is smaller in comparison to the damage zone for reference Case A. This is because that the existence of contraction joints could reduce the integral rigidity of the dam body and thus leads to larger nonlinear demands. Severe damage region for Case B appears primarily in the piers on the spillway sections due to the cross-stream movement of the dam. By comparing Fig. 10.12a, c, it can also be found that the damage level for Case C (without cross-stream seismic excitation) is significantly lower than that of reference Case A. There is almost no damage in the piers of the overflow monoliths in Case C,

Fig. 10.12 Comparison of seismic damage-cracking behaviors for: a Case A; b Case B (no contraction joint); c Case C (no cross-stream seismic excitation). The figures in the left column are views from the upstream side whereas those in the right column are views from the downstream side

10.7 Evaluation of the Key Factors Affecting Damage-Cracking Characteristics

261

which implies that the damage of piers in Case A is mainly resulted from the crossstream seismic excitation. This is expected since the piers have larger stiffness in the stream direction than that in the cross-stream direction. The damage on the upstream face of monoliths 8–10 occurring in reference Case A is not observed in Case C. This means that dynamic interaction between monoliths caused by the cross-stream ground motion could cause significant damage to the dam.

10.7.2 Comparisons of 3D and Quasi-3D Analysis Results for Representative Monoliths The results from the 3D dam-reservoir-foundation FE model (Cases A, B, and C) are compared with the results from quasi-3D models for three representative monoliths (Case D). Figures 10.13, 10.14 and 10.15 depict the damage-cracking behaviors of three representative monoliths (non-overflow monolith 9, overflow monolith 11, and middle spillway monolith 16) for all four cases. It can be seen that the damage pattern in reference Case A is significantly different from that of other cases. Compared with quasi-3D modeling (Case D), more severe damage is observed when considering the contraction joints and cross-stream seismic excitation (Case A), especially in overflow monolith 11. This observation indicates the importance of the full three dimensional modeling for the seismic safety assessment of concrete gravity dams. In addition, it can also be observed that the damage-cracking behavior for Case C is quite close to that from quasi-3D modeling (Case D), implying that the dynamic interaction between monoliths is mainly caused by the cross-stream excitation. Figure 10.16 compares the time history of the stream displacement on the dam crest for four simulation cases. Due to hydrostatic pressure, initial stream displacement exists with the maximum value occurring in Case D and the minimum value occurring in Case B for each representative monolith. As shown in Fig. 10.16,

Fig. 10.13 Seismic damage characteristics of non-overflow monolith 9: a reference Case A; b Case B (no contraction joint); c Case C (no cross-stream seismic excitation); d Case D (quasi-3D model for single monolith)

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10 Deterministic 3D Seismic Damage Analysis …

Fig. 10.14 Seismic damage characteristics of overflow monolith 11: a reference Case A; b case B (no contraction joint); c Case C (no cross-stream seismic excitation); d Case D (quasi-3D model for single monolith)

Fig. 10.15 Seismic damage characteristics of middle spillway monolith 16: a reference Case A; b Case B (no contraction joint); c Case C (no cross-stream seismic excitation); d Case D (quasi-3D model for single monolith)

the dynamic responses in the stream direction almost coincide with each other before 4.0 s and then start to deviate from each other. However, Case D shows a similar behavior to Case C during the entire dynamic response process. In Case A, the residual plastic displacements on the dam crest are −7.14 mm, 22.7 mm, and −11.2 mm for representative monoliths 9, 11 and 16, respectively, which are higher than those in other cases. The nonlinear displacement response analysis shows that the Guandi dam remains stable during the selected seismic event. However, the final conclusions about the dynamic stability of the Guandi dam should be based on a continuous analysis of the post-cracking dam under new ground motions. The cross-stream displacement time history of the three representative monoliths is also compared in Fig. 10.17 for all cases, where the positive displacement is in the leftward direction. Although the three-component ground motion is applied as the input loading for Cases A and B, the cross-stream displacement in Case

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A is substantially higher than that in Case B. This means that the contract joint has significant influence on the nonlinear dynamic response along the cross-stream direction. Although the cross-stream seismic excitation is not considered in Case C, small cross-stream displacement occurs due to the dynamic interaction between monoliths. What can be concluded with the comparisons presented in the subsection is that contraction joints and cross-stream seismic excitation play a role of great importance in the seismic performance of the concrete gravity dam. Performing quasi-3D or 2D analyses, in which the aforementioned two factors cannot be appropriately captured, may significantly underestimate the damage-cracking risk of concrete gravity dams when subjected to strong ground motions, which is non-conservative for the seismic design of concrete gravity dams. It is worth noting that the obtained conclusions are based on the deterministic analyses using three real earthquake records. The influence of contraction joints and cross-stream seismic excitation on the dynamic response of concrete gravity dams depends on a variety of factors including the ground motion input and site conditions. To better assess such influence and in the spirit of performance based earthquake engineering (Hariri-Ardebili and Saouma 2016a, b), seismic fragility analysis using abundant strong motion records is planned as future work.

10.8 Conclusions In this contribution, a comprehensive study of the seismic damage-cracking behavior of the Guandi concrete gravity dam is presented based on the three dimensional dynamic nonlinear finite element model. All of the following important factors are taken into account: the interaction of dam-reservoir-foundation, the opening/closing and sliding of contraction joints, and the cross-stream seismic excitation. Comparisons are made between the results from both the hard contact formulation and exponential contact model. The effectiveness of the numerical framework which considers the dam-reservoir-foundation interaction is first validated against the experimental results of the Koyna concrete gravity dam. Then case studies are conducted in order to characterize the effects of contraction joints and cross-stream ground motion on the seismic performance of the Guandi concrete gravity dam. The following conclusions can be drawn based on the analysis results: (1) The type of selected contact model has limited influence on the nonlinear dynamic response of Guandi dam. (2) Nonlinear dynamic responses are closely related to the height and structural feature of monoliths. Large damage appears primarily in the middle monoliths of the river bed. Higher strength concrete can be used in these regions to minimize the expected seismic damage and improve the safety of Guandi dam. (3) Contraction joints are expected to open/close and slide repeatedly during strong ground motions. The existence of contraction joints could reduce the integral

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rigidity of the monolithic model, and thus lead to larger nonlinear demands in the three dimensional dam-reservoir-foundation system. Dynamic interaction between monoliths caused by the cross-stream ground motion could cause significant damage to the dam. (4) Damage-cracking level from the three-dimensional model with the contraction joints and cross-stream seismic excitation considered is much severer than the quasi-3D results. Hence, the quasi-3D or 2D analyses may significantly underestimate the damage-cracking risk of concrete gravity dams when subjected to strong ground motions, which is non-conservative for the seismic design of concrete gravity dams. The observation indicates the importance of three-dimensional modeling for the seismic safety evaluation. The aforementioned conclusions are obtained from the response of the Guandi gravity dam subjected to three specific earthquake ground motions. Thus, these conclusions may not apply to all gravity dams and ground motions. Further study using incremental dynamic analysis, richer ground motion database and reinforcement concrete material model for the piers will be undertaken in the future.

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