Analytical Solution for Wave-Induced Seabed Response in a Soil-Water Two-Phase Mixture

Abstract

The dynamic response of the seabed to ocean surface waves is treated analytically on the basis of an elastic wave theory in a soil-water mixture. The seabed is modeled as the aggregate of a poro-elastic soil-skeleton with air-containing pore-water, from which a general solution is presented for a homogeneous bed of infinite thickness. Two kinds of compressive waves and one shear wave are shown to exist in the seabed and their phases and attenuation characteristics are clarified. Based on the propagation of these elastic waves, exact solutions for the dynamic response in pore-water pressure and displacements of porous soil-skeleton are derived in physically lucid form. It is found that the relative motion between the soil and water is produced by the second compressive wave, but not from other elastic waves. The present solution is shown to include the well-known quasi-static solution given by Yamamoto et al. (1978), as a limiting case. By comparing the present dynamic solution with that of quasi-static state, two important nondimensional parameters are presented to discuss the applicability of each solution.