Response of Dams in Semielliptical Canyons to Oblique SH Waves

Abstract

A new analytical solution is developed for steady-state lateral response of earth and rockfill dams built in semielliptical canyons and subjected to obliquely incident harmonic SH waves. The dam is idealized as a linearly hysteretic elastic body deforming only in shear, while the supporting canyon is modeled as an elastic rock half-space. The solution accounts in a rigorous way for the wave reflection and diffraction phenomena associated with the presence of the dam-filled canyon. The response of the dam and the canyon is expressed in terms of prolate radial and angular wave spheroidal functions. Representative results elucidate the importance of the effects of the dam-to-canyon material impedance, the canyon geometry, the angle of incidence, and the excitation frequency on the dam response. Comparisons are made with the response of the dam to “rigid-base” synchronous excitation. The developed solution offers a useful practical tool for parametric studies and preliminary design calculations, as the semielliptical shape can approximate reasonably well the geometry of several actual canyons.