Scattering Of Elastic Spherical Waves By 3D Sedimentary Basin And Mountain Embedded In A Layered Site

“The Belt and Road Initiative” promotes the construction of major infrastructure projects in the countries and regions along the routes.However,these areas are mostly distributed with sedimentary basins and mountains.More seriously,there have been frequent earthquakes along the routes in recent years,most of which are shallow earthquakes which usually causes severe damage.This geologically active sites are extremently unfavorable to the construction of the project.In the previous studies of the dynamic responses around local irregularities,the seismic source is usually assumed to be plane waves.This assumption is relatively reasonable when the hypocentral distance is large.However,for the shallow earthquakes with the smaller hypocentral distance,the curvature of the incident path cannot be ignored,so it is more reasonable to use spherical waves to simulate the source.Whereas the research on the scattering of spherical waves by local irregularities is very few in recent years,so that it can not provide more accurate and reliable directive data for seismic design issues.In view of this situation,the indirect boundary element method(IBEM)combined with the exact dynamic stiffness matrices of the layered viscoelastic half-space corresponding to the anti-symmetric cylindrical SH-waves and to the symmetric cylindrical P-and SVwaves,is proposed to investigate the dynamic responses of local irregularities embedded in a layered half-space under the incident spherical wave.The detailed work is as follows:Firstly,the exact dynamic stiffness matrices of the layered viscoelastic half-space corresponding to the anti-symmetric cylindrical SH-waves and to the symmetric cylindrical P-and SV-waves are established in the cylindrical coordinate system,and they can be directly used to solve the free-field responses under the incident spherical wave.In this way,the advantages of the stiffness matrices of the layered half-spcae in solving the problem involved with the layered half-space can be fully utilized.Secondly,taking the Green’s functions for uniformly distributed load applied on the inclined plane as a kernel,the scattered fileds in the closed domain and open domain can be constructed.These Green’s functions are widely adaptablefor complex and irregular boundaries with the merits of high accuracy,good stability and convergence.Thirdly,the proposed method is verified by comparing the degenerated results with those from several published papers.Finally,numerical calculations are performed to study the scattering of spherical P-,SV-and SH-waves by a three-dimensional sedimentary basin(mountain)embedded in a homogeneous and single-layered halfspace,and the effects of geometric parameters of irregularities,hypocentral locations and dynaic characteristics of external half-space on the ground motion are discussed.The results show that the depth of basin,the height of mountain,the hypocentral locations,the shear-wave velocity ratio between the bedrock and single rock layer and the frequency of incident wave all have obvious effects on the ground motion near the irregularities;A amount of seismic energy is concentrated into the sedimentary basin and the mountain,forming obvious “focusing effect” on the surface;There is an essential difference in the scattering effect of layered half-space and homogeneous halfspace.In the layered site,the ground motion near irregularities is determined by the dynamic characteristic of both the upper layer and the irregularities and the dynamic interaction between them.