Dynamic response of anchored retaining walls on a compliant foundation

A simplified analytical solution is derived for the dynamic response of a flexible retaining wall constrained by a cable anchor installed at an arbitrary elevation along its height. The wall retains a linear viscoelastic homogeneous backfill of constant properties on a compliant foundation soil, and is excited by vertically-propagating harmonic S-waves under plane strain conditions. The simplifying assumptions of zero dynamic vertical normal stresses in the backfill and zero variation of vertical displacements with horizontal distance from the wall, originally adopted by Matsuo & Ohara 1960 and by Veletsos & Younan 1994, are employed. A closed-form solution based on a modified Vlasov-Leontiev formulation is derived, and an extensive parametric investigation is performed for exploring the effect of wall-soil interaction on seismic response. Simple expressions are obtained for wall deflections, soil thrusts, anchor and base shear forces, and base moments. The ratio of shear modulus between foundation and backfill controls the response of the system in conjunction with soil-wall relative stiffness. Results elucidate the importance of kinematic constraints on wall response. These aspects cannot be captured by conventional design methods based on limit state analysis which neglect kinematics and soil-structure interaction.