Contents

1 INTRODUCTION 9

1.1 TYPES OF DAMS 10

1.1.1 Embankment Dams 11

1.1.2 Concrete Arch and Dome Dams 13

1.1.3 Concrete Gravity and Gravity-Arch Dams 14

1.1.4 Concrete Slab and Buttress Dams 16

1.2 APPURTENANT FEATURES OF DAMS 16

1.3 SAFETY OF DAMS AND RESERVOIRS 18

1.4 HOW DAMS ARE BUILT 20

1.5 FAMOUS DAMS OF THE WORLD 21

1.6 POWER GENERATOR, FLOOD CONTROL AND IRRIGATION DAMS 25

1.6.1 Power Generator Dams 25

1.6.2 Flood Control Dams 26

1.6.3 Irrigation Dams 28

1.7 INSTRUMENTATIONS AND SURVEILLANCE OF DAMS . 28

1.7.1 Surveillance 28

1.7.2 Instrumentation 28

1.7.3 Instruments 30

1.8 ECOLOGICAL/ENVIRONMENTAL CONSIDERATION OF DAM OPERATION 33

1.9 THE HISTORY OF DAMS DESIGN 34

1.9.1 Irrigation Dams 35

1.9.2 Dams Designed for Water Supply 36

1.9.3 Flood Control Dams 38

1.9.4 Power Dams 39

1.9.5 The Moslem World 40

1.9.6 Development of the Modern Dams 42

1.10 BEAVERS 44

2 RESERVOIR 49

2.1 INTRODUCTION 49

2.2 GENERAL FORM OF RESERVOIR'S EQUATION OF MOTION 50

2.2.1 Velocity Field 50

2.2.2 System and Control Volume 52

2.2.3 Reynold's Transport Equation 53

2.2.4 Continuity Equation 56

2.2.5 Linear Momentum Equation 57

2.2.6 The Equation of the Motion 59

2.3 VISCOSITY 64

2.4 NAVIER-STOKES AND EULER EQUATIONS 65

2.5 COMPRESSIBLE FLUID 67

2.6 BOUNDARY-LAYER THEORY 71

2.7 IRROTATIONAL FLOW 74

2.8 RESERVOIR'S EQUATION OF MOTION 78

2.9 RESERVOIR BOUNDARY CONDITIONS 79

2.9.1 Dam-Reservoir Boundary Condition 80

2.9.2 Reservoir-Foundation Boundary Condition 81

2.9.3 Free Surface Boundary Condition 84

2.10 SOLUTION OF THE RESERVOIR EQUATION 86

2.11 RESERVOIR FAR-END TRUNCATED BOUNDARY CONDITION 93

3 FINITE ELEMENT MODELLING OF THE DAM-RESERVOIR SYSTEM 99

3.1 FINITE ELEMENT MODELLING OF THE STRUCTURE . 99

3.1.1 Single-Degree-Of-Freedom Systems 99

3.1.2 Multi-Degree-Of-Freedom System 101

3.2 COUPLING MATRIX OF THE DAM-RESERVOIR 106

3.3 FINITE ELEMENT MODELLING OF THE RESERVOIR . . 108 3.3.1 Truncated Boundary of the Reservoir's Far-End 110

3.4 EQUATION OF THE COUPLED DAM-RESERVOIR SYSTEM 111

4 DYNAMIC ANALYSIS OF DAM-RESERVOIR SYSTEM 113

4.1 INTRODUCTION 113

4.2 THE COUPLED DAM-RESERVOIR PROBLEM 115

4.3 DIRECT INTEGRATION OF THE EQUATION OF MOTION 115

4.4 USING NEWMARK-,3 METHOD FOR THE COUPLED EQUATIONS 117

4.5 STAGGERED DISPLACEMENT METHOD 118

4.5.1 Stability of the Staggered Displacement Method . . . .119

4.6 STAGGERED PRESSURE METHOD 121

4.6.1 Stability of the Staggered Pressure Method 122

4.7 MODIFIED STAGGERED PRESSURE METHOD 123

4.8 USING a-METHOD FOR THE COUPLED EQUATIONS . . 124 4.8.1 Staggered Displacement Method 124

4.9 SEISMIC ENERGY BALANCE 126

4.10 ACCURACY OF THE SOLUTION SCHEME 127

5 NONLINEAR FRACTURE MODELS OF CONCRETE GRAVITY DAMS 129

5.1 INTRODUCTION 129

5.2 A BRIEF STUDY OF NONLINEAR PARAMETERS 134

5.2.1 Finite element models of crack propagation 134

5.2.2 Discrete crack propagation model ,DCPM,( variable mesh) 135

5.2.3 Continuum crack propagation models (CCPM) 135

5.3 Constitutive models for crack propagation 136

5.3.1 Strength-based criteria 136

5.3.2 Fracture mechanics criteria 137

5.3.3 Shear resistance of fractured concrete 148

5.4 Post-fracture behaviour of concrete 149

5.5 Material parameters for fracture propagation analysis 150

5.5.1 Strength-of-material parameters 151

5.5.2 Linear elastic fracture mechanics parameters 153

5.5.3 Nonlinear fracture mechanics parameters 154

5.5.4 Shear resistance of fractured concrete 155

5.6 NONLINEAR MODELLING OF CONCRETE DAMS USING DAMAGE MECHANICS 156

5.6.1 NUMERICAL PROBLEMS RELATED TO STRAIN

SOFTENING 157

5.6.2 FUNDAMENTAL EQUATIONS OF DAMAGE MECHANICS 158

5.6.3 ISOTROPIC DAMAGE MODEL FOR CONCRETE . 159

5.6.4 ANISOTROPIC DAMAGE MODEL FOR CONCRETE160

5.6.5 EVALUATION OF DAMAGE VARIABLE 164

5.6.6 Damage evolution for concrete subjected to tensile strain 166

5.6.7 Opening and closing of the crack and initial damage . . 168

5.6.8 ANALYTICAL PROCEDURES IN A FINITE ELEMENT MODEL 168

5.7 CONSTITUTIVE MODEL FOR SMEARED FRACTURE ANALYSIS 170

5.7.1 Pre-fracture behaviour 170

5.7.2 Strain softening of concrete and the initiation criterion 170

5.7.3 Fracture energy conservation 172

5.7.4 Constitutive relationships during softening 173

5.7.5 Coaxial Rotating Crack Model (CRCM) 173

5.7.6 Fixed Crack Model With Variable Shear Resistance Factor (FCM-VSRF) 174

5.7.7 Closing and reopening of cracks 175

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