Shock−wave propagation in fluid−saturated porous media

Mechanical constitutive relations for fluid−saturated porous rocks as previously formulated by Morland and Garg within the theory of interacting continua (TINC) have been generalized to include thermodynamic effects. The model is developed by defining effective stress tensors and effective densities in terms of the partial stress tensors, partial densities, and actual volume fractions occupied by each component. It is postulated that the constitutive law for each component as a single continuum relates effective pressure to effective deformation. Relative motion between the constituents is allowed through a simple Darcy−type law. The governing conservation equations together with the constitutive relations for a binary mixture are solved numerically using a so−called ’’leap−frog’’ finite−difference technique. The model is applied to study shock−wave propagation in a mixture of tuff and water.