Dynamic response of rigid walls retaining steel strip-reinforced soil to earthquake forces

The dynamic pressures induced by earthquake forces on a pair of rigid walls retaining steel strip-reinforced elastic soil over bedrock, are investigated through an analytical/numerical solution procedure under plane strain conditions. The reinforced soil is treated as an elastic continuum consisting of two phases: the elastic soil matrix in plane strain and the horizontally arranged steel strips under axial deformation. Thus, there are three governing equations of motion in terms of displacements: two for the elastic soil matrix and one for the elastic steel strips, coupled through interaction forces. Assuming time harmonic seismic excitation and expanding the displacements in Fourier sine and cosine series with respect to the horizontal coordinate, one can reduce the governing system of partial differential equations of motion to ordinary ones with respect to the vertical coordinate. Solving this system, the seismic pressure on the wall as well as the shear force and bending moment at the wall base are determined analytically. The response to transient earthquake forces is obtained numerically through Fourier synthesis. The employment of the solution to obtain results for the special case of the unreinforced soil and the comparison of those results against existing ones in the literature serve to verify that solution. Parametric studies are then presented for the assessment of the effects of soil reinforcement on the seismic response of the wall-soil system.