Seismic Antiplane Response of Gaussian-Shaped Alluvial Valley

In this study, a direct time-domain numerical approach named the half-plane Boundary Element Method (BEM) is proposed based on the half-space Green’s functions for analyzing seismic Gaussian-shaped alluvial valley subjected to propagating obliquely incident SH-waves. In the use of the method, the meshes were only concentrated around the interface of the basin. First, the problem is decomposed into two parts including a half-plane Gaussian-shaped feature and a closed filled alluvium. Then, the method was applied to each part to obtain the considered matrices. Finally, by satisfying the boundary/continuity conditions at the interface, the coupled equation was transiently solved to determine the boundary values. All ground surface responses were also obtained in a secondary solution as internal points. After implementing the method in a general algorithm, several practical examples were analyzed to validate the responses. An advanced numerical study was performed to sensitize the surface motion of Gaussian-shaped alluvial valleys with variable shape/impedance ratios as synthetic seismograms and Three-Dimensional (3D) amplification patterns. Moreover, to complete the time-domain results, the transient response of the internal domain of the alluvium as well as the surrounding bed rock was shown by the snapshots views. In the following, the sensitivity analysis was carried out to obtain the seismic amplification pattern of the surface by considering the key parameters including impedance and shape ratios, incident wave angle, and response frequency. Finally, by collecting the maximum amplification of different scenarios and applying linear fit to the obtained values, the results were summarized as a series of linear equations and tables. The results showed that the mentioned factors were very effective in the seismic response of the surface. The results of the present study can be used to complete the accuracy of existing codes around the subject of near-filed site effects.