Site effects due to wave path inhomogeneity by BEM

The time-harmonic response of a multi-layered soil deposit resting on the elastic half-plane under the influence of incoming pressure and shear waves is numerically investigated by a hybrid boundary integral equation-plane wave decomposition method. The multi-layered deposit is finite-sized, with non-parallel layers and contains a free-surface relief, while the half-plane into which it is embedded is elastic, isotropic and inhomogeneous. Two basic types of material inhomogeneity are considered for the half-plane, namely a shear modulus that varies (a) quadratically and (b) exponentially with respect to the depth coordinate. In all cases, Poisson's ratio is fixed at one-quarter and conditions of plane strain are assumed to hold. This boundary-value problem is solved by using the direct boundary element method, while free-field motions in the surrounding inhomogeneous half-plane that include contributions of incident as well as of reflected waves, are computed by an analytical plane wave decomposition method. In order to handle both internal (the multi-layered region) and external (the half-plane domain) components of this problem, boundary conditions in the form of displacement and stress field continuity along the common interface between these two regions are imposed. Finally, a detailed simulation study of a complex geological region is conducted in the frequency domain, and the results clearly demonstrate the importance of local site effects on the propagation of obliquely incident waves following a wave path that is continuously inhomogeneous.