(De)compaction of porous viscoelastoplastic media: Model formulation

Abstract

AbstractA nonlinear viscoelastoplastic theory is developed for porous rate‐dependent materials filled with a fluid in the presence of gravity. The theory is based on a rigorous thermodynamic formalism suitable for path‐dependent and irreversible processes. Incremental evolution equations for porosity, Darcy's flux, and volumetric deformation of the matrix represent the simplest generalization of Biot's equations. Expressions for pore compressibility and effective bulk viscosity are given for idealized cylindrical and spherical pore geometries in an elastic‐viscoplastic material with low pore concentration. We show that plastic yielding around pores leads to decompaction weakening and an exponential creep law. Viscous and plastic end‐members of our model are consistent with experimentally verified models. In the poroelastic limit, our constitutive equations reproduce the exact Gassmann's relations, Biot's theory, and Terzaghi's effective stress law. The nature of the discrepancy between Biot's model and the True Porous Media theory is clarified. Our model provides a unified and consistent formulation for the elastic, viscous, and plastic cases that have previously been described by separate “end‐member” models.