About the Author
ANIL K. CHOPRA is the Horace, Dorothy, and Katherine Johnson Professor Emeritus of Structural Engineering in the Department of Civil and Environmental Engineering, University of California at Berkeley. He served on the Berkeley faculty from 1969 to 2016.
Table of contents
Preface xiii
Acknowledgments xv
1 Introduction 1
1.1 Earthquake Experience: Cases with Strongest Shaking 1
1.2 Complexity of the Problem 6
1.3 Traditional Design Procedures: Gravity Dams 8
1.3.1 Traditional Analysis and Design 8
1.3.2 Earthquake Performance of Koyna Dam 9
1.3.3 Limitations of Traditional Procedures 9
1.4 Traditional Design Procedures: Arch Dams 11
1.4.1 Traditional Analysis and Design 11
1.4.2 Limitations of Traditional Procedures 12
1.5 Unrealistic Estimation of Seismic Demand and Structural Capacity 13
1.6 Reasons Why Standard Finite-Element Method is Inadequate 13
1.7 Rigorous Methods 14
1.8 Scope and Organization 16
Part I: Gravity Dams
2 Fundamental Mode Response of Dams Including Dam–Water Interaction 21
2.1 System and Ground Motion 21
2.2 Dam Response Analysis 22
2.2.1 Frequency Response Function 22
2.2.2 Earthquake Response: Horizontal Ground Motion 23
2.3 Hydrodynamic Pressures 24
2.3.1 Governing Equation and Boundary Conditions 24
2.3.2 Solutions to Boundary Value Problems 26
2.3.3 Hydrodynamic Forces on Rigid Dams 28
2.3.4 Westergaard’s Results and Added Mass Analogy 30
2.4 Dam Response Analysis Including Dam–Water Interaction 32
2.5 Dam Response 33
2.5.1 System Parameters 33
2.5.2 System and Cases Analyzed 34
2.5.3 Dam–Water Interaction Effects 34
2.5.4 Implications of Ignoring Water Compressibility 37
2.5.5 Comparison of Responses to Horizontal and Vertical Ground Motions 39
2.6 Equivalent SDF System: Horizontal Ground Motion 40
2.6.1 Modified Natural Frequency and Damping Ratio 40
2.6.2 Evaluation of Equivalent SDF System 42
2.6.3 Hydrodynamic Effects on Natural Frequency and Damping Ratio 43
2.6.4 Peak Response 45
Appendix 2: Wave-Absorptive Reservoir Bottom 46
3 Fundamental Mode Response of Dams Including Dam–Water–Foundation Interaction 49
3.1 System and Ground Motion 50
3.2 Dam Response Analysis Including Dam–Foundation Interaction 51
3.2.1 Governing Equations: Dam Substructure 51
3.2.2 Governing Equations: Foundation Substructure 52
3.2.3 Governing Equations: Dam–Foundation System 53
3.2.4 Dam Response Analysis 54
3.3 Dam–Foundation Interaction 54
3.3.1 Interaction Effects 54
3.3.2 Implications of Ignoring Foundation Mass 55
3.4 Equivalent SDF System: Dam–Foundation System 56
3.4.1 Modified Natural Frequency and Damping Ratio 56
3.4.2 Evaluation of Equivalent SDF System 57
3.4.3 Peak Response 59
3.5 Equivalent SDF System: Dam–Water–Foundation System 60
3.5.1 Modified Natural Frequency and Damping Ratio 60
3.5.2 Evaluation of Equivalent SDF System 61
3.5.3 Peak Response 62
Appendix 3: Equivalent SDF System 63
4 Response Spectrum Analysis of Dams Including Dam–Water–Foundation Interaction 65
4.1 Equivalent Static Lateral Forces: Fundamental Mode 66
4.1.1 One-Dimensional Representation 66
4.1.2 Approximation of Hydrodynamic Pressure 67
4.2 Equivalent Static Lateral Forces: Higher Modes 68
4.3 Response Analysis 70
4.3.1 Dynamic Response 70
4.3.2 Total Response 70
4.4 Standard Properties for Fundamental Mode Response 71
4.4.1 Vibration Period and Mode Shape 71
4.4.2 Modification of Period and Damping: Dam–Water Interaction 72
4.4.3 Modification of Period and Damping: Dam–Foundation Interaction 72
4.4.5 Generalized Mass and Earthquake Force Coefficient 74
4.5 Computational Steps 74
4.6 CADAM Computer Program 76
4.7 Accuracy of Response Spectrum Analysis Procedure 77
4.7.1 System Considered 77
4.7.2 Ground Motions 77
4.7.3 Response Spectrum Analysis 78
4.7.4 Comparison with Response History Analysis 79
5 Response History Analysis of Dams Including Dam–Water–Foundation Interaction 83
5.1 Dam–Water–Foundation System 83
5.1.1 Two-Dimensional Idealization 83
5.1.2 System Considered 84
5.1.3 Ground Motion 85
5.2 Frequency-Domain Equations: Dam Substructure 86
5.3 Frequency-Domain Equations: Foundation Substructure 87
5.4 Dam–Foundation System 88
5.4.1 Frequency-Domain Equations 88
5.4.2 Reduction of Degrees of Freedom 89
5.5 Frequency–Domain Equations: Fluid Domain Substructure 90
5.5.1 Boundary Value Problems 90
5.5.2 Solutions for Hydrodynamic Pressure Terms 91
5.5.3 Hydrodynamic Force Vectors 92
5.6 Frequency-Domain Equations: Dam–Water–Foundation System 93
5.7 Response History Analysis 94
5.8 EAGD-84 Computer Program 95
Appendix 5: Water–Foundation Interaction 96
6 Dam–Water–Foundation Interaction Effects in Earthquake Response 101
6.1 System, Ground Motion, Cases Analyzed, and Spectral Ordinates 101
6.1.1 Pine Flat Dam 101
6.1.2 Ground Motion 103
6.1.3 Cases Analyzed and Response Results 103
6.2 Dam–Water Interaction 105
6.2.1 Hydrodynamic Effects 105
6.2.2 Reservoir Bottom Absorption Effects 107
6.2.3 Implications of Ignoring Water Compressibility 108
6.3 Dam–Foundation Interaction 112
6.3.1 Dam–Foundation Interaction Effects 112
6.3.2 Implications of Ignoring Foundation Mass 112
6.4 Dam–Water–Foundation Interaction Effects 115
7 Comparison of Computed and Recorded Earthquake Responses of Dams 117
7.1 Comparison of Computed and Recorded Motions 117
7.1.1 Choice of Example 117
7.1.2 Tsuruda Dam and Earthquake Records 118
7.1.3 System Analyzed 119
7.1.4 Comparison of Computed and Recorded Responses 120
7.2 Koyna Dam Case History 122
7.2.1 Koyna Dam and Earthquake Damage 122
7.2.2 Computed Response of Koyna Dam 123
7.2.3 Response of Typical Gravity Dam Sections 126
7.2.4 Response of Dams with Modified Profiles 127
Appendix 7: System Properties 129
Part II: Arch Dams
8 Response History Analysis of Arch Dams Including Dam–Water–Foundation Interaction 133
8.1 System and Ground Motion 133
8.2 Frequency-Domain Equations: Dam Substructure 136
8.3 Frequency-Domain Equations: Foundation Substructure 137
8.4 Dam–Foundation System 138
8.4.1 Frequency-Domain Equations 138
8.4.2 Reduction of Degrees of Freedom 139
8.5 Frequency-Domain Equations: Fluid Domain Substructure 140
8.6 Frequency-Domain Equations: Dam–Water–Foundation System 142
8.7 Response History Analysis 143
8.8 Extension to Spatially Varying Ground Motion 144
8.9 EACD-3D-2008 Computer Program 146
9 Earthquake Analysis of Arch Dams: Factors to Be Included 149
9.1 Dam–Water–Foundation Interaction Effects 149
9.1.1 Dam–Water Interaction 150
9.1.2 Dam–Foundation Interaction 151
9.1.3 Dam–Water–Foundation Interaction 153
9.1.4 Earthquake Responses 153
9.2 Bureau of Reclamation Analyses 153
9.2.1 Implications of Ignoring Foundation Mass 156
9.2.2 Implications of Ignoring Water Compressibility 157
9.3 Influence of Spatial Variations in Ground Motions 158
9.3.1 January 13, 2001 Earthquake 159
9.3.2 January 17, 1994 Northridge Earthquake 160
10 Comparison of Computed and Recorded Motions 163
10.1 Earthquake Response of Mauvoisin Dam 163
10.1.1 Mauvoisin Dam and Earthquake Records 163
10.1.2 System Analyzed 165
10.1.3 Spatially Varying Ground Motion 166
10.1.4 Comparison of Computed and Recorded Responses 166
10.2 Earthquake Response of Pacoima Dam 168
10.2.1 Pacoima Dam and Earthquake Records 168
10.2.2 System Analyzed 171
10.2.3 Comparison of Computed and Recorded Responses: January 13, 2001 Earthquake 172
10.2.4 Comparison of Computed Responses and Observed Damage: Northridge Earthquake 172
10.3 Calibration of Numerical Model: Damping 174
11 Nonlinear Response History Analysis of Dams 177
Part A: Nonlinear Mechanisms and Modeling 178
11.1 Limitations of Linear Dynamic Analyses 178
11.2 Nonlinear Mechanisms 178
11.2.1 Concrete Dams 178
11.2.2 Foundation Rock 181
11.2.3 Impounded Water 181
11.2.4 Pre-Earthquake Static Analysis 181
11.3 Nonlinear Material Models 182
11.3.1 Concrete Cracking 182
11.3.2 Contraction Joints: Opening, Closing, and Sliding 183
11.3.3 Lift Joints and Concrete–Rock Interfaces: Sliding and Separation 184
11.3.4 Discontinuities in Foundation Rock 185
11.4 Material Models in Commercial Finite-Element Codes 185
Part B: Direct Finite-Element Method 186
11.5 Concepts and Requirements 186
11.6 System and Ground Motion 187
11.6.1 Semi-Unbounded Dam–Water–Foundation System 187
11.6.2 Earthquake Excitation 189
11.7 Equations of Motion 191
11.8 Effective Earthquake Forces 193
11.8.1 Forces at Bottom Boundary of Foundation Domain 193
11.8.2 Forces at Side Boundaries of Foundation Domain 194
11.8.3 Forces at Upstream Boundary of Fluid Domain 195
11.9 Numerical Validation of the Direct Finite Element Method 196
11.9.1 System Considered and Validation Methodology 196
11.9.2 Frequency Response Functions 199
11.9.3 Earthquake Response History 200
11.10 Simplifications of Analysis Procedure 201
11.10.1 Using 1D Analysis to Compute Effective Earthquake Forces 201
11.10.2 Ignoring Effective Earthquake Forces at Side Boundaries 203
11.10.3 Avoiding Deconvolution of the Surface Free-Field Motion 203
11.10.4 Ignoring Effective Earthquake Forces at Upstream Boundary of Fluid Domain 206
11.10.5 Ignoring Sediments at the Reservoir Boundary 207
11.11 Example Nonlinear Response History Analysis 211
11.11.1 System and Ground Motion 211
11.11.2 Computer Implementation 212
11.11.3 Earthquake Response Results 213
11.12 Challenges in Predicting Nonlinear Response of Dams 215
Part III: Design and Evaluation
12 Design and Evaluation Methodology 219
12.1 Design Earthquakes and Ground Motions 219
12.1.1 ICOLD and FEMA 220
12.1.2 U.S. Army Corps of Engineers (USACE) 221
12.1.3 Division of Safety of Dams (DSOD), State of California 221
12.1.4 U.S. Federal Energy Regulatory Commission (FERC) 221
12.1.5 Comments and Observations 221
12.2 Progressive Seismic Demand Analyses 224
12.3 Progressive Capacity Evaluation 226
12.4 Evaluating Seismic Performance 227
12.5 Potential Failure Mode Analysis 228
13 Ground-Motion Selection and Modification 231
Part A: Single Horizontal Component of Ground Motion 232
13.1 Target Spectrum 232
13.1.1 Uniform Hazard Spectrum 232
13.1.2 Uniform Hazard Spectrum Versus Recorded Ground Motions 232
13.1.3 Conditional Mean Spectrum 234
13.1.4 CMS-UHS Composite Spectrum 235
13.2 Ground-Motion Selection and Amplitude Scaling 239
13.3 Ground-Motion Selection to Match Target Spectrum Mean and Variance 241
13.4 Ground-Motion Selection and Spectral Matching 243
13.5 Amplitude Scaling Versus Spectral Matching of Ground Motions 247
Part B: Two Horizontal Components of Ground Motion 247
13.6 Target Spectra 247
13.7 Selection, Scaling, and Orientation of Ground-Motion Components 250
Part C: Three Components of Ground Motion 252
13.8 Target Spectra and Ground-Motion Selection 252
14 Application of Dynamic Analysis to Evaluate Existing Dams and Design New Dams 253
14.1 Seismic Evaluation of Folsom Dam 253
14.2 Seismic Design of Olivenhain Dam 257
14.3 Seismic Evaluation of Hoover Dam 261
14.4 Seismic Design of Dagangshan Dam 265
References 271
Notation 281
Index 291
