Seismic response of the trapezoidal alluvial hill located on a circular cavity: Incident SH-wave.

A direct time-domain numerical approach named the half-plane boundary element method is proposed based on the half-space Green’s functions for seismic analysis of trapezoidal alluvial hill located on a circular cavity, subjected to propagating vertical incident SH-waves. To analyze the assumed model, a half plane time-domain Boundary Element Method (BEM) was used which can concentrate the meshes only around the boundary of desired features. First, the problem is decomposed into two parts including a pitted half-plane and a trapezoidal filled solid on the surface. Then, the influence coefficients of the matrices are obtained by applying the method to each part. By satisfying the boundary/continuity conditions on the interfaces, a coupled equation is formed to determine unknown boundary values in each time-step. After implementing the method in an advanced developed algorithm, its efficiency is investigated by solving some practical examples and compared with those of the published works. To complete the results, the sensitivity analysis was carried out to obtain the seismic response of hill by considering the key parameters including impedance and shape ratios. In the meantime, the effect of subsurface cavity on the amplification pattern of surface has been studied as well. The results showed that the impedance and shape ratios of the trapezoidal alluvial hill were very effective on the seismic response of surface. The results of the present study can be used by geotechnical engineers to completing and increasing the accuracy of existing codes around the subject of ground surface zonation in presence of different topographic features.