Scattering Of Plane SV Waves By An Arbitrary Shape Underground Cavity

A lot of investigations of earthquake damage show that local site conditions can greatly affect the surface motion subjected to incident seismic waves .The effects represent primarily magnification and reduction, and consequently influence the distribution of earthquake damage .Site response analysis has been an attractive research topic in recent years. Theoretical analysis of this problem mainly relay on analytical method and numerical method. To analytical method ,there are already many analytical solutions. Analytical method only is used to regular shapes but generally site has irregular shapes, Hence, the investigation of numerical solution of scattering by irregular sites has important meaning on theory ,and it surely has distinct referenced value in practical project.The site have underground cavity is familiar to us in engineering .and sometimes it needs the sections of cavities be shapes besides circle. Based on this engineering background, numerical solution of incident SV waves by an underground cavity of arbitrary shape in a half-space are presented.In principle, the numerical method can resolve dynamic response problems of earthquake waves in various kinds of complex sites. The weighted residual method introduced in this paper for numerical solution of the scattering and diffraction of plane SV waves by a cavity of arbitrary shape.In this thesis, Fourier-Bessel series wave function expansion are used to solve this mixed-boundary problem. Very big circle are used to simulate the free boundary, Graf's addition theorem is used to convert the coordinates. Finally ,a set of infinite linear algebraic equations are reduced and numerical solutions are obtained by truncating the infinite equations.This paper presents the weighted residual method in solving numerically the two-dimensional scattering and diffraction of plane elastic SV waves by arbitrary shape underground cavity. The effects of the frequency of the incident waves, the shape of the cavity, the incident angle and the depth of cavity on displacement amplitude of ground surface are analyzed. Some beneficial conclusions are given in the end of the thesis.