Plane-Strain Instability of Saturated Porous Media

Abstract

Herein, we investigate the plane-strain instability of rectangular blocks that are made of porous materials saturated with a fluid. We model the material behavior with rate-type constitutive equations, and study the instability generated by the interaction of nearly incompressible solid and fluid constituents. Our investigation, although it applies to a broad range of materials, is limited to hypoelastic and elastoplastic models. Elastoplastic models are found to undergo two-phase instability even though the solid phase remains stable. Two-phase instability is more likely to occur in contractant hardening materials than in dilatant materials. Its emergence is triggered by the solid-fluid interaction, and is delayed by the grain-fluid compressibility. Two-phase instability also takes place in dilatant materials, but is less catastrophic than in contractant materials. The present analysis is useful for distinguishing the physical from the artificial origins of instabilities, which is an important issue in the numerical solutions of soil-liquefaction problems.