Rotatory and horizontal vibrations of a circular surface footing on a saturated elastic half-space

Abstract

The forced vibration of a liquid-filled, porous, elastic half-space produced by rotatory and horizontal oscillations of a circular surface footing is reduced to the solutions of Fredholm integral equations of the second kind. The circular footing is modeled by a pervious, weightless, rigid disk of negligible thickness. For a medium consisting of dense sand saturated by ground water, numerical solutions of the integral equations are obtained to reveal the variations of the impedance functions with the exciting frequency and the material parameters (permeability and Poisson's ratio). Comparison with the response of the dry soil is also discussed. In the rocking oscillation case, the presence of the ground water is found to influence the magnitude and shape of the impedance functions and may need to be considered in applicable soil-structure interaction problems. In the horizontal vibration case, however, marginal influence of the pore water is found to affect the response of the medium.