Lateral response of dams in semi-elliptical rigid canyons

Abstract

An analytical closed-form solution is developed for the lateral response of earth and rockfill dams built in semi-elliptical canyons. The dam is idealized as a linearly hysteretic elastic body deforming only in shear, whereas the canyon is assumed to be rigid. The solution for the dam response is given in terms of prolate spheroidal radial and angular functions of the first kind and zero order. Results are presented for natural frequencies, modal displacement shapes, participation factors, and response to transient and steady-state harmonic base excitation for various dam length-to-height ratios. Comparisons are made of the effects of the length-to-height ratio and the canyon shape on the response of dams built in semi-elliptical and rectangular canyons. A subsequent study (Dakoulas, P. & Hsu, C.H., Response of earth dams in semi-elliptical flexible canyons to oblique SH waves, Report, Rice University, Houston, Texas, 1993) extends this model to a semi-elliptical canyon consisting of flexible elastic rock, subjected to obliquely incident harmonic SH waves.