A 2.5D IBEM to investigate the 3D seismic response of 2D topographies in a multi-layered transversely isotropic half-space

Abstract

A two and half dimensional (2.5D) indirect boundary element method (IBEM) is developed to study the three dimensional (3D) seismic response of two dimensional (2D) topographies in a multi-layered transversely isotropic (TI) half-space, under obliquely incident qP-, qSV- and SH-waves. Based on the single-layer integral representation, the scattered fields are constructed by applying fictitious moving load on the boundary line elements, and the load densities are determined from the corresponding boundary conditions. The total wave fields can be obtained by superposition of the scattered fields and free fields solved by dynamic stiffness method. With aid of the dynamic 2.5D moving Green's functions (Ba et al. 2017b), this method has the merit of revealing the complex 3D wave-field characteristics, and the calculation domain being restricted to the cross section of topographies without the need of complex 3D discretization. The present formulations are validated by comparison with the published results, and by taking a semi-circular canyon as well as a semi-circular hill topographies as examples, selected numerical simulations are performed in both the frequency and time domains. Results show that the dynamic response for the TI medium differs remarkably from those for the isotropic case, simultaneously depending on incident angle and frequency of excitations. The amplification effects of the hill become prominent with the increase of Eh/Ev, with the displacement amplification more remarkable inside the hill region compared to that of the exterior region.