1 Solid Continuum Mechanics 3 --
1.3 Continuum Problem 7 --
2 Finite Element Method 13 --
2.1 Overview of FEM 14 --
2.2 Discretization of Function 17 --
2.3 Formulation of FEM 19 --
2.4 Major Numerical Techniques Used in FEM 23 --
2.4.1 Shape function 23 --
2.4.2 Isoparametric element 24 --
2.4.3 Gauss integral 25 --
2.5 Algorithm Used to Solve A Matrix Equation of FEM 26 --
2.5.1 Direct solvers 27 --
2.5.2 Iterative solvers 28 --
2.5.3 Algorithms used to solve a non-linear equation 30 --
3 Stochastic Modeling 33 --
3.1 Formulation of A Stochastic Variational Problem 34 --
3.2 Analysis Methods of A Stochastic Variational Problem 37 --
3.2.1 Bounding medium analysis 37 --
3.2.2 Spectral method 39 --
II Strong Ground Motion 43 --
4 The Wave Equation for Solids 45 --
4.1 Basics of the Wave Equation 46 --
4.2 Analytic Solutions of Particular Wave Problems 50 --
4.2.1 Out-of-plane shear wave 51 --
4.2.2 In-plane wave 55 --
4.2.3 Plane wave in three-dimensional setting 58 --
4.3 Numerical Analysis of the Wave Equation 60 --
4.3.1 Algorithms used for time integration 61 --
4.3.2 Stability of time integration 63 --
5 Analysis of Strong Ground Motion 65 --
5.1 Stochastic Modeling of Underground Structures 66 --
5.2 Bounding Medium Theory 67 --
5.3 Singular Perturbation Expansion 70 --
5.4 Formulation of Macro-Micro Analysis Method 72 --
5.5 Verification of Macro-Micro Analysis Method 75 --
5.5.1 Validation of bounding medium theory 75 --
5.5.2 Validation of singular perturbation expansion 79 --
5.5.3 Validation of macro-micro analysis method 83 --
6 Simulation of Strong Ground Motion 89 --
6.1 Summary of Macro-Micro Analysis Method 91 --
6.2 VFEM for Macro-Analysis and Micro-Analysis 92 --
6.2.2 VFEM for macro-analysis 94 --
6.2.3 VFEM for micro-analysis 98 --
6.2.4 Link from macro-analysis to micro-analysis 101 --
6.3 Simulation of Actual Earthquakes 102 --
6.3.2 Comparison of synthesized waveform with observed waveform 107 --
6.3.3 Distribution of simulated strong ground motion 108 --
6.3.4 The comparison of three-dimensional analysis and one-dimensional analysis 113 --
7 Elasto-Plasticity and Fracture Mechanics 121 --
7.1 Numerical Analysis of Failure 121 --
7.2 Elasto-Plasticity 123 --
7.3 Fracture Mechanics 126 --
8 Analysis of Faulting 131 --
8.1.3 Bounding medium approximation 138 --
8.1.4 Formulation of NL-SSFEM 140 --
8.2 Numerical Algorithms of NL-SSFEM 142 --
8.2.1 Matrix Jacobi method 142 --
8.2.2 Standardized KL expansion 143 --
8.2.3 Numerical perturbation during analysis of stochastic model 144 --
8.3 Validation of NL-SSFEM Simulation 146 --
8.4 Example of Fault Simulation of NL-SSFEM 150 --
9 Simulation of Faulting 159 --
9.1 Problem Setting for Fault Simulation 160 --
9.1.2 Output results 162 --
9.2 Reproduction of Model Experiments 163 --
9.2.1 Simulation of two-dimensional model experiment 163 --
9.2.2 Simulation of three-dimensional model experiment 168 --
9.3 Simulation of Actual Faults 179 --
9.3.1 Simulation of the Nojima Fault 179 --
9.3.2 Parametric study of stochastic parameters 186 --
9.3.3 Simulation of the Chelungpu Fault 189 --
10 BEM Simulation of Faulting 195 --
10.1 Problem Setting for Fault Simulation 196 --
10.1.1 Perturbation expansion of field variables with respect to crack extension 198 --
10.1.2 Crack driving forces 199 --
10.1.3 Solution of crack path problem 202 --
10.2 Formulation of Boundary Element Method 204 --
10.3 Verification of Analysis Method 206 --
10.3.1 Use of analytic solution 206 --
10.3.2 Use of numerical computation 209 --
10.4 Reproduction of Model Experiments 215 --
10.4.1 Simulation of model experiment of [Bray et al. (1994)] 216 --
10.4.2 Simulation of model experiment of [Tani (1994)] 217 --
IV Advanced Topics 221 --
11 Integrated Earthquake Simulation 223 --
11.1 System of Integrated Earthquake Simulation 224 --
11.3 Construction of Computer Model 228 --
11.3.1 Construction of ground structure model 229 --
11.3.2 Construction of residential building model 232 --
11.4 Example of Integrated Earthquake Simulation 235 --
11.4.2 Strong ground motion simulation 236 --
11.4.3 Structure response simulation 240 --
12 Unified Visualization of Earthquake Simulation 243 --
12.1 System for Unified Visualization 245 --
12.1.2 Mediator maker 249 --
12.2 IES for Unified Visualization 250 --
12.3 Example of Unified Visualization 255 --
13 Standardization of Earthquake Resistant Design 259 --
13.1 Standardization of Description Style 260 --
13.2 Description of Flow Chart in Terms of Object 261 --
13.2.1 Reconstruction of a flow chart for general earthquake resistant designs 262 --
13.2.2 Reconstruction of a flow chart for actual earthquake resistant design code 267 --
13.3 Example of Standardization 271 --
Appendix A Earthquake Mechanisms 279 --
A.1 Plate Tectonics and Active Faults 279 --
A.2 Earthquake as Wave Propagation 284 --
A.2.1 Determination of input strong ground motion according to earthquake scenario 285 --
A.2.2 Soil-structure interaction 287 --
Appendix B Analytical Mechanics 289 --
Appendix C Numerical Techniques of Solving Wave Equation 293 --
C.1 Explicit Method and Implicit Method 294 --
C.2 Analysis of Wave Equation Using FEM 296 --
C.3 Absorption Boundary 299 --
Appendix D Unified Modeling Language 303.
