Three simplified models for the analytic determination of the dynamic response of a crossanisotropic poroelastic half-plane to a load moving with constant speed on its surface are presented and compared against the corresponding exact model. The method of analysis of the exact and approximate models uses complex Fourier series to expand the load and the displacement responses along the horizontal direction of the steady-state motion and thus reduces the partial differential equations of the problem to ordinary ones, which are easily solved. The three simplified models are characterized by reasonable simplifying assumptions, which reduce the complexity of the exact model and facilitate the solution. In the first simplified model all the terms of the equations of motion associated with fluid acceleration are neglected. In the second simplified model, solid displacements are assumed to be equal to the corresponding fluid ones, while the third simplified model is the second one corrected with respect to the fluid pressure at the free boundary (top) layer. All three simplified models are compared with respect to their accuracy against the exact model and the appropriate range of values of the various significant parameters of the problem, like porosity, permeability, anisotropy indices, or load speed, for obtaining approximate solutions as close to the exact solution as possible is thoroughly discussed.

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.