2.5D scattering of obliquely incident seismic waves due to a canyon cut in a multi-layered TI saturated half-space

Abstract

This paper extends the two and a half-dimensional (2.5D) indirect boundary element method (IBEM) from the isotropic medium to the transversely isotropic (TI) saturated case, to study the three-dimensional (3D) scattering behavior of a two-dimensional (2D) geometric canyon cut in a multi-layered TI half-space. This method, conquering the drawbacks of both 2D and 3D simulations, can realistically assess the ground motion with less computation effort. The 3D exact stiffness matrix (Ba and Liang 2017) is adopted to solve the free-fields, through which the system with a great number of layers can be conveniently handled and the precision is not affected by layer's thickness. And the Green's functions for moving distributed loads in a multi-layered TI saturated half-space are derived in detail within the framework of Biot's theory (1962a, b), which is subsequently utilized to construct the scattered fields. The accuracy is illustrated by comparison with a verification example (Liang and Liu 2009) for a 2D isotropic case. The effects of some key parameters (anisotropy degree, incident angle, drainage condition, permeability and layering) on dynamic response are investigated through numerical implementations in frequency domain. The results show that material anisotropy has a noticeable influence on the displacement and pore pressure, and the influence becomes prominent for high incident frequency. The displacement amplitude is rather sensitive to permeability, whereas its distribution is hardly affected by permeability. Furthermore, the existence of layer complicates the scattering mechanics of layered system, heavily relating to material anisotropy.