Diffraction of SH-waves by surface or sub-surface topographies with application to soil-structure interaction on shallow foundations

Seismic response of local sites is a significant problem that has been broadly researched for decades. It is an essential step in evaluating maximum intensity of earthquake effects for a specified local site that might happen in the future considering the effects of local topography or various massive artificial structures nearby, so it is crucial to seismic hazard, risk analysis, and earthquake microzonation. Seismic waves can be categorized into body waves and surface waves. Among the three types of body waves: P-, SV-, and SH-waves, the response of SH-waves, is restrained to the out-of-plane unidirection, thus is the most fundamental one and studied in this dissertation.;The objectives of this dissertation are: first, to explore diffraction of incident plane or cylindrical SH-waves by various topographies or underground irregularities; secondly, to investigate the Soil-Structure Interaction (SSI) effects. Two-dimensional plane strain models studied are as diverse as ground surface irregularities (e.g., hills, canyons, canyons), geotechnical engineering (e.g., tunnels, underground cavities, excavations, foundations), and Soil-Structure Interaction models with non-, rigid, or flexible foundations. Although the geometries adopted in those models are relatively much simpler than the ones by numerical methods, the analytical solutions gained by these simple models are indispensable in verifying solutions by various numerical methods (e.g., Finite Element Method; Boundary Element Method). All the models attempted are sitting or encased in an elastic half-space. All the materials appeared are isotropic, homogeneous, and perfectly elastic.;Wave function expansion method is used for solving all the mathematical models in an analytical scheme. The model is computed by mathematically assembling different segments together on their interfaces adjacent to each other. Finally, the problem is reduced to solving a series of infinite linear equations. The governing finite linear equation systems after truncation via this way are always ill-conditioned that require carefully coped with to ensure the accuracy of solutions.;With the analytical solution attained, the response of displacement and stress along the free ground surface are discussed. Displacement and stress residues are calculated to verify the validity of those numerical results. Great effects on dynamic stress concentration and motion nearby due to the existence of those irregularities are observed, evaluated, and analyzed.