A note on the seismic response of rigid cantilever retaining walls

The elasticity based dynamic response of retaining walls, attached to a semi-infinite elastic backfill stratum, has yet to be solved exactly. There are three analytical approximation approaches in the literature to simplify the equations of motion. The solutions based on these approaches can be numerically implemented. However, the frequency range for which these solutions may provide accurate results has not yet been established. In this paper, the exact frequency equation and frequency spectra for the problem under free vibration are presented first, and the three simplified equations of motion are then reviewed. Next, the exact frequency spectra are then used to assess the frequency range of applicability of the three approximation approaches. It is concluded that for all practical values of Poissonʹs ratio, all three approaches provide a reasonable approximation to the exact solution in the low frequency range of the first mode. The first mode response of the horizontal and rocking impedance functions, for the rigid retaining wall are then derived, based on the simplified equations of motion, and the numerical data are presented for the low frequency range identified.