Abstract:

A system of equations describing wave propagation in a unique class of inhomogeneous porous media is presented. The specific porous medium considered consists of an elastic matrix whose pores are filled with a viscous compressible fluid. The two components, solid and fluid, are microscopically homogeneous but the porous medium is inhomogeneous because the unperturbed porosity varies with position. Volume-averaging theorems are used to construct the general equations which form the basis for the analysis. It is shown that, in general, the presence of a porosity gradient introduces new coupling terms between the fluid and solid phases in the equations of motion. Since inhomogeneity usually implies anisotropy the problem is further specialized for the case of transverse anisotropy. It is further assumed that the wave propagates in the direction of the porosity gradient, which is a principal direction of the anisotropy. The equations are compared to recent work describing rigid framed grounds with exponential porosity profiles. [Work supported by ONR and USDA ARS National Sedimentation Laboratory.]