On the response of a poro-elastic bed to water waves

The problem of the response of a porous elastic bed to water waves is treated analytically on the basis of the three-dimensional consolidation theory of Biot (1941). Exact solutions for the pore-water pressure and the displacements of the porous medium are obtained in closed form for the case of waves propagating over the poro-elastic bed. The theoretical results indicate that the bed response to waves is strongly dependent on the permeability k and the stiffness ratio G/K’ , where G is the shear modulus of the porous medium and K’ is the apparent bulk modulus of elasticity of the pore fluid. The earlier solutions for pore-water pressure by various authors are given as the limiting cases of the present solution. For the limits G/K′ → 0 or k → ∞, the present solution for pressure approaches the solution of the Laplace equation by Putnam (1949). For the limit G/K′ → ∞, the present solution approaches the solution of the heat conduction equation by Nakamura et al. (1973) and Moshagen & Tørum (1975). The theoretical results are compared with wave tank experimental data on pore-water pressure in coarse and fine sand beds which contain small amounts of air. Good agreement between theory and experiment is obtained.