UCLA

A simplified analytical solution is derived for the dynamic response of a flexible vertical retaining wall supported on a rotationally compliant footing, subjected to vertically-propagating harmonic S-waves under plane-strain conditions. The wall retains a semi-infinite, homogeneous viscoelastic soil layer of constant thickness and material properties. The proposed solution is based on the Veletsos-Younan simplifying assumption of zero vertical normal stresses in the soil, and negligible variation of vertical displacements with horizontal distance from the wall. A modified integration technique is employed, inspired by the seminal work of Vlasov and Leontiev, which simplifies the analysis by suppressing the vertical coordinate and transforming the governing partial differential equation into an ordinary one that admits an elementary solution. Both cantilever and top-hinged walls are studied. Closed-form solutions are derived for lateral soil displacements, dynamic soil pressures, and equivalent Winkler springs connecting the wall to the far-field soil. It is shown that for cantilever conditions even a small amount of wall flexibility leads to a strong reduction in soil thrust, while the rotation at the wall base causes an additional decrease in thrust. The predictions of the method are in good agreement with available solutions, while new results for combined wall flexibility and rotational compliance are presented. The proposed approach offers a simpler alternative to the complex elastodynamic solutions of Veletsos and Younan.