| Preamble | 6 |
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| Acknowledgements | 9 |
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| Contents | 10 |
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| Nomenclature | 14 |
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| Subscripts | 15 |
| Superscripts | 15 |
| 1 Introduction | 16 |
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| 2 Theory of Two-Dimensional Dynamic Infinite Elements for Simulating Wave Propagation Problems in Infinite Media | 22 |
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| 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 |
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| 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 |
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| 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 |
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| 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 |
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| 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
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