Response of Earth Dams in Semicylindrical Canyons to Oblique SH Waves

Abstract

An analytical solution is developed for steady‐state lateral response of earth and rockfill dams built in semicylindrical 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 medium, representing a deformable rock half‐space. The solution accounts in a rigorous way for the complex wave reflection, transmission, and diffraction phenomena associated with the presence of the dam‐filled canyon. For the displacement fields in the dam and the canyon, closed‐form expressions are derived involving a series expansion in terms of spherical‐Bessel and Legendre functions. A parametric investigation elucidates the effects of the dam‐to‐canyon material impedance ratio, of the angle of incidence, and of the frequency of excitation on the response along the crest of the dam. Similarities and differences are noted and explained with the response of the dam to “rigid‐base”‐type (“synchronous”) excitation, as well as with the response of an alluvial semicylindrical valley to oblique SH waves.