3D dynamic responses of a 2D hill in a layered half-space subjected to obliquely incident plane P-, SV- and SH-waves

Abstract An indirect boundary element method (IBEM) is proposed to investigate the three-dimensional (3D) dynamic responses of a two-dimensional (2D) hill in a layered elastic half-space subjected to obliquely incident plane P-, SV-, and SH-waves. The proposed IBEM is characterized by adopting the full-space Green's function of moving distributed loads to construct the scattered field in the closed regions, while using the half-space Green's function of moving distributed loads to simulate the scattered field in the opened half-space region. This new method thus combines the merits of these two Green's function and is especially suitable for addressing 2.5D multi-domain coupled multilayered wave scattering problems with the advantages of singularity-free, low computational cost and flexibility. The accuracy and validity of the method is verified by comparing its results with a number of existing solutions. Numerical calculations are performed by taking semi-circular as well as semi-elliptical hills as examples, and the effects of the hill height, frequency of excitation, incident angle, and layering on the dynamic responses are analyzed in detail. It is found that the proposed method can treat the oblate as well as prolate hills, which demonstrate that the new IBEM has good adaptability to the shape of hills. In addition, numerical results show that significant focusing effects and standing-wave patterns are formed inside the hills under incident plane waves; the presence of the hill amplifies the ground motion significantly, which is highly related to the hill height, frequency of excitation, incident angle and dynamic characteristics of the site; And there exist pronounced dynamic interaction between the hill and the layer, which leads to the much more complex topographic effects.