Dynamic and Transient Infinite Elements (eBook)

Preamble 6
Acknowledgements 9
Contents 10
Nomenclature 14
Subscripts 15
Superscripts 15
1 Introduction 16
2 Theory of Two-Dimensional Dynamic Infinite Elements for Simulating Wave Propagation Problems in Infinite Media 22
2.1 Formulation of Two-Dimensional Dynamic Infinite Elements and Wave Input Method 24
2.1.1 Formulation of Two-Dimensional Dynamic Infinite Elements 26
2.1.2 Wave Input Method for Simulating Wave Scattering Problems in Infinite Media 32
2.2 Incident P-wave and SV-wave Reflection Characteristics on a Fixed Boundary 34
2.3 Formulation of Generalized Stresses on the Wave Input Boundary 38
2.3.1 SV-wave Incidence 39
2.3.2 P-wave Incidence 41
2.4 Verification of the Proposed Computational Model for Simulating Wave Scattering Problems in Infinite Media 43
2.4.1 Wave Reflection on the Surface of an Elastic Half-Plane 45
2.4.2 Wave Scattering on the Surface of a Semi-circular Canyon 47
2.4.3 Wave Scattering on the Surface of an Embankment Dam 50
3 Application of Two-Dimensional Dynamic Infinite Elements: Simulation of Dynamic DamWaterFoundation Interaction Problems 53
3.1 Simulation of Dynamic Gravity DamWaterFoundation Interaction Systems 53
3.1.1 Computational Model of a Concrete Gravity Dam--Water--Foundation System Including Reservoir Bottom Sediments 54
3.1.1.1 Computational Simulation of the Water Region 56
3.1.1.2 Computational Simulation of the Solid Region 57
3.1.1.3 Determination of the Coupling Force between the Water and the Solid Regions 58
3.1.2 Effects of Reservoir Bottom Sediments on the Dynamic Response of Concrete Gravity Dams due to Unit Harmonic Wave Incidences 61
3.1.2.1 Effects of Sediment Thickness on the Dynamic Response of Concrete Gravity Dams due to Unit Harmonic Wave Incidences 63
3.1.2.2 Effects of Sediment Elastic Properties on the Dynamic Response of Concrete Gravity Dams due to Unit Harmonic Wave Incidences 66
3.1.2.3 Effects of Poisson's Ratios of the Sediment on the Dynamic Response of Concrete Gravity Dams due to Unit Harmonic Wave Incidences 68
3.1.2.4 Effects of the Sediment Damping Coefficients on the Dynamic Response of Concrete Gravity Dams due to Unit Harmonic Wave Incidences 70
3.1.3 Transient Response of Concrete Gravity Dams due to Earthquake Wave Incidences 70
3.1.3.1 Selection of an Earthquake for the Transient Response of Concrete Gravity Dams due to Earthquake Wave Incidences 73
3.1.3.2 Transient Seismic Response of a Concrete Gravity Dam--Water--Foundation System Including Reservoir Bottom Sediment Effects 74
3.2 Simulation of Dynamic Embankment DamWaterFoundation Interaction Systems 79
3.2.1 Effects of Impervious Member Types on the Dynamic Response of an Embankment Dam--Foundation System 83
3.2.2 Effects of Reservoir Bottom Sediments on the Dynamic Response of an Embankment Dam--Foundation System 90
4 Application of Two-Dimensional Dynamic Infinite Elements: Simulation of Wave Scattering Effects under Different Canyon Topographical and Geological Conditions 99
4.1 Simulation of Infinite Domain of a Canyon 101
4.2 Effects of Canyon Topographical Conditions on the Ground Motions due to Harmonic Wave Incidences 109
4.2.1 Free-Field Motions along V-shaped Canyons due to Harmonic Wave Incidences 109
4.2.2 Free-Field Motions along Trapezoidal Canyons due to Harmonic Wave Incidences 113
4.3 Effects of Canyon Geological Conditions on Ground Motions due to Harmonic Wave Incidences 115
4.4 Effects of Canyon Topographical Conditions on Ground Motions due to Seismic Wave Incidences 118
4.4.1 Free-Field Motions along V-shaped Canyons due to Seismic Wave Incidences 120
4.4.2 Free-Field Motions along Trapezoidal Canyons due to Seismic Wave Incidences 123
4.5 Effects of Canyon Geological Conditions on Ground Motions due to Seismic Wave Incidences 129
5 Theory of Three-Dimensional Dynamic Infinite Elements for Simulating Wave Propagation Problems in Infinite Media 133
5.1 Coupled Computational Model for Simulating Three-Dimensional Wave Propagation Problems in Infinite Foundations of Structures 135
5.2 Formulation of Three-Dimensional Dynamic Infinite Elements 137
5.2.1 Mapping Functions of Three-Dimensional Dynamic Infinite Elements 138
5.2.2 Displacement Shape Functions of Three-Dimensional Dynamic Infinite Elements 139
5.2.3 Mass and Stiffness Matrices of Three-Dimensional Dynamic Infinite Elements 145
5.3 Verification of Three-Dimensional Dynamic Infinite Elements 148
6 Application of Three-Dimensional Dynamic Infinite Elements: Simulation of Dynamic StructureFoundation Interaction Problems 154
6.1 Numerical Simulation of Plate Foundation Vibration on a Visco-elastic Half-Space 154
6.1.1 Dynamic Response of a Square Plate on a Visco-elastic Half-Space under Harmonic Loading 155
6.1.1.1 Effects of Material Damping on the Complex Compliance of the Plate 157
6.1.1.2 Effects of Material Damping on the Distribution of Wave Motion in the near Field 160
6.1.2 Dynamic Response of a Square Plate on a Layered Visco-elastic Half-Space under Harmonic Loading 162
6.2 Numerical Simulation of the Dynamic Response of a Framed StructureRaft FoundationUnderlying Soil/Rock System 169
6.2.1 Numerical Simulation of a Three-Dimensional Framed Structure--Raft Foundation--Underlying Soil/Rock System 173
6.2.1.1 Numerical Simulation of a Three-Dimensional Framed Structure 174
6.2.1.2 Numerical Simulation of a Raft Foundation 174
6.2.1.3 Numerical Simulation of an Infinite Soil/Rock Medium 175
6.2.1.4 Coupling Equation of the Framed Structure--Raft Foundation--Underlying Soil/Rock System 175
6.2.2 Effects of Raft Foundation Flexibility on the Dynamic Response of a Three-Dimensional Framed Structure 176
6.2.3 Effects of Underlying Soil/Rock on the Dynamic Response of a Three-Dimensional Framed Structure 180
7 Theory of Transient Infinite Elements for Simulating Pore-Fluid Flow and Heat Transfer in Porous Media of Infinite Domains 186
7.1 Fundamental Theory of Transient Infinite Elements for Simulating Pore-Fluid Flow Problems in Fluid-Saturated Porous Media of Infinite Domains 187
7.1.1 Derivation of the Hydraulic Head Distribution Functions of Transient Infinite Elements 187
7.1.2 Derivation of the Property Matrices of Two-Dimensional Transient Infinite Elements for Simulating Pore-Fluid Flow Problems 193
7.1.2.1 The First Category of Two-Dimensional Transient Infinite Elements 194
7.1.2.2 The Second Category of Two-Dimensional Transient Infinite Elements 196
7.1.2.3 The Third Category of Two-Dimensional Transient Infinite Elements 197
7.1.2.4 The Fourth Category of Two-Dimensional Transient Infinite Elements 198
7.1.2.5 Two-Dimensional Transient Bi-infinite Elements 199
7.2 Fundamental Theory of Transient Infinite Elements for Simulating Heat Transfer Problems in Fluid-Saturated Porous Media of Infinite Domains 201
7.2.1 Derivation of the Heat Transfer Functions of Transient Infinite Elements 201
7.2.2 Derivation of the Property Matrices of Two-Dimensional Transient Infinite Elements for Simulating Heat Transfer Problems 203
7.3 Verification of Transient Infinite Elements for Simulating Pore-Fluid Flow and Heat Transfer Problems in Fluid-Saturated Porous Media of Infinite Domains 207
7.3.1 Verification of Transient Infinite Elements for Simulating a Pore-Fluid Flow Problem in the Fluid-Saturated Porous Medium of an Infinite Domain 207
7.3.2 Verification of Transient Infinite Elements for Simulating a Heat Transfer Problem in the Fluid-Saturated Porous Medium of an Infinite Domain 208
8 Theory and Application of Transient Infinite Elements for Simulating Contaminant Transport Problems in Fractured Porous Media of Infinite Domains 213
8.1 Coupled Computational Method of Finite Elements and Transient Infinite Elements for Simulating Transient Contaminant Transport Problems in Fractured Porous Media of Infinite Domains 214
8.1.1 Upwind Finite Element Formulation of the Problem 215
8.1.1.1 Spatial Discretization of the Problem 216
8.1.1.2 Temporal Discretization of the Problem 218
8.1.1.3 Weighting and Shape Functions of the Upwind Finite Element 219
8.1.2 Fundamental Formulas of Mapped Transient Infinite Elements for Simulating Transient Contaminant Transport Problems 222
8.1.3 Verification of the Coupled Computational Method of Upwind Finite Elements and Transient Infinite Elements 229
8.2 Parametric Study of Transient Contaminant Transport Problems in Fractured Porous Media of Infinite Domains 232
8.2.1 Effects of the Leakage between a Porous Block and a Fissured Network on Contaminant Concentration Distributions in the Fractured Porous Medium 233
8.2.2 Effects of Medium Porosities on Contaminant Concentration Distributions in the Porous Block and Fissured Network 240
8.2.3 Effects of Pore-Fluid Advection on Contaminant Concentration Distributions in the Porous Block and Fissured Network 244
8.2.4 Effects of Solute Dispersion on Contaminant Concentration Distributions in the Porous Block and Fissured Network 249
Summary Statements 255
References 258
Index 266