Approximate analytical/numerical solutions for the seismic response of rigid walls retaining a transversely isotropic poroelastic soil

Abstract

Three approximate analytical solutions for the problem of the seismic response of two rigid cantilever walls retaining a transversely isotropic poroelastic soil layer over bedrock are presented under conditions of plane strain and time harmonic ground motion. These approximate solutions come as a result of various reasonable simplifications concerning various response quantities of the problem, which reduce the complexity of the governing equations of motion. The method of solution in all the cases is the same with that used for obtaining the exact solution of the problem, i.e., expansion of response quantities in the frequency domain in terms of sine and cosine Fourier series along the horizontal direction and solution of the resulting system of ordinary differential equations with respect to the vertical coordinate in conjunction with the boundary conditions. The first approximate solution is obtained on the assumption of neglecting all the terms of the equations of motion associated with the fluid acceleration. The second approximate solution is obtained on the assumption that the fluid displacements are equal to the corresponding solid displacements. The third approximate solution is obtained as the sum of the second approximate solution for the whole domain plus a correction inside a boundary layer at the free soil. All three approximate solutions are compared with respect to their accuracy against the exact solution and useful conclusions pertaining the approximate range of the various parameters, like porosity, permeability and anisotropy indices, for minimization of the approximation error are drawn.