Shear vibration of inhomogeneous earth dams in rectangular canyons

Abstract

Analytical solutions for shear vibrations of earth dams in the critical upstream-downstream direction have been presented. Both the inhomogeneity of the cyclic shear modulus and the effect of the usually neglected abutment constraint have been taken into account in formulations. Some evidence is presented which shows that the mean shear modulus over a horizontal plane at a given depth from the crest of the dam varies with the square-root of that depth, rather than linearly or with 2/3 power of depth as it has been assumed in previous studies. The constraining effect of the abutments of the embankment is idealized by considering a rectangular valley cross section. It is shown that, unlike the homogeneous case, valley shape couples analytically with the inhomogeneity of shear modulus. Solution for free vibrations are then presented in the form of mode shapes, frequencies, and modal participation factors. In the limit L/h→∞, where L is the crest length and h is the embankment height, the plane strain condition is obtained. Since the plane strain idealization is usually made in practice, comparisons are made with this limit case to estimate the extent of the error made by one dimensional simplification.