Compressional wave propagation in liquid and/or gas saturated elastic porous media

Abstract

Concepts from the theory of interacting continua are employed to develop constitutive relations for liquid and/or gas saturated elastic porous media. The model is formulated by defining intrinsic stress tensors and densities in terms of the partial stress tensors, partial densities, and actual volume fractions occupied by each component. It is assumed that the constitutive law for each component as a single continuum relates intrinsic pressure to intrinsic deformation. Relative motion between the constituents is allowed through simple Darcy-type expressions. The governing equations together with the constitutive relations are used to investigate the propagation of both harmonic and transient pulses. In general three modes of wave propagation exist. In the case of a transient pulse, these modes lead to a three-wave structure. Laplace transform techniques are used to derive closed-form solutions for transient loading for two limiting values of viscous coupling (i.e., weak viscous coupling, strong viscous coupling). Strong viscous coupling results in the coalescence of the three wave fronts into a single front. Solutions for the general case of transient loading are obtained by numerical inversion of the Laplace transforms.