Earthquake Engineering for Concrete Dams Analysis, Design, and Evaluation

A comprehensive guide to modern-day methods for earthquake engineering of concrete dams

Earthquake analysis and design of concrete dams has progressed from static force methods based on seismic coefficients to modern procedures that are based on the dynamics of dam–water–foundation systems. Earthquake Engineering for Concrete Dams offers a comprehensive, integrated view of this progress over the last fifty years. The book offers an understanding of the limitations of the various methods of dynamic analysis used in practice and develops modern methods that overcome these limitations. 

This important book:

• Develops procedures for dynamic analysis of two-dimensional and three-dimensional models of concrete dams
• Identifies system parameters that influence their response
• Demonstrates the effects of dam–water–foundation interaction on earthquake response
• Identifies factors that must be included in earthquake analysis of concrete dams
• Examines design earthquakes as defined by various regulatory bodies and organizations
• Presents modern methods for establishing design spectra and selecting ground motions
• Illustrates application of dynamic analysis procedures to the design of new dams and safety evaluation of existing dams. 

Written for graduate students, researchers, and professional engineers, Earthquake Engineering for Concrete Dams offers a comprehensive view of the current procedures and methods for seismic analysis, design, and safety evaluation of concrete dams.

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.

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

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