Seismic analysis of rigid walls retaining a cross-anisotropic poroelastic soil layer over bedrock

The dynamic response of rigid walls retaining a cross-anisotropic poroelastic soil layer over bedrock to seismic horizontal excitation is determined analytically under conditions of plane strain. The problem is treated as a special case of that of a pair of rigid walls with a large separation distance. Use is made of Biot's anisotropic poroelastodynamic theory. Assuming time harmonic excitation, one is able to achieve an exact u-p formulation of the problem in the frequency domain. Expansion of the displacements and the pore-water pressure in terms of Fourier sine and cosine series along the horizontal direction, reduces the partial differential equations of motion in the frequency domain into a system of three ordinary differential equations, which can be easily solved analytically. Thus, closed form expressions for the seismic soil pressure, the distance from the base of the point of application of the resultant seismic pressure and the base shear force and bending moment are obtained. From the above cross-anisotropic poroelastic solution its special cases of isotropic poroelastic solution and cross-anisotropic elastic solution are obtained and compared with the corresponding existing analytical solutions for validation purposes. Finally, parametric studies are performed in order to assess the effect of cross-anisotropy on the seismic response of the wall-soil system.