Wave propagation effects in a fluid-saturated porous solid

Abstract

Constitutive relations for a fluid-saturated elastic-plastic porous solid have been developed within the framework of the theory of interacting continua (TINC) by defining effective stress tensors and effective densities in the composite in terms of the actual volume fractions occupied by each component, partial stress tensors, and partial densities. The model is formulated by postulating that the constitutive law for each component as a single continuum relates effective stress tensor and effective deformation. In contradistinction to the classical homogenized models, TINC allows relative motion between the constituents. The governing conservation equations, together with the constitutive relations for a binary mixture, are solved by the Lax-Wendroff finite difference procedure. The model is applied to study finite-amplitude wave propagation in a porous tuff completely saturated with water. The results are compared with those obtained from a homogenized model. The present model predicts lower pressures and shock velocities than those given by the homogenized model.