A frequency-dependent absorbing boundary condition for numerically solving u-U elastic wave equations in layered and fluid-saturated porous media

Abstract

An accurate absorbing boundary condition (ABC) is proposed to incorporate in the frequency-domain finite element simulation for numerically solving u-U elastic wave equations in horizontally multilayer fluid-saturated porous media. The u-U elastic wave equations are first discretized only along the depth direction in which the material properties are heterogeneous, analytical method using in the remaining coordinate direction. A general eigenvalue problem on the horizontal wavenumber is then solved with the frequency as known parameter. Dynamic stiffness on the artificial boundary of finite domain is finally obtained as ABC based on the solution to the above eigenvalue problem. The proposed ABC is mathematically derived without introducing any approximate assumptions, and the only approximation comes from the finite-element discretization of the fluid-saturated porous medium in the depth direction. The proposed ABC can also be coupled seamlessly with the finite element method (FEM). Numerical examples of wave radiation problems are given to demonstrate the effectiveness of the proposed ABC and its coupling with FEM. Finally, a practical application of proposed ABC to assess the topography effects of the fluid-saturated porous basin-type site is presented to show that the proposed ABC can also be used to solve wave scattering problems in geotechnical earthquake engineering.