Friction modifies the quasistatic mechanical response of a confined, poroelastic medium

Abstract

The mechanical response of elastic porous media confined within rigid geometries is central to a wide range of industrial, geological, and biomedical systems. However, current models for these problems typically overlook the role of wall friction, and particularly its interaction with confinement. Here, we develop a theoretical framework to describe the interplay between the mechanics of the medium and Coulomb friction at the confining walls for slow, quasistatic deformations in response to two canonical uniaxial forcings: piston-driven loading (i.e., an imposed effective stress at the top boundary) and fluid-driven loading (i.e., an imposed fluid pressure at the top boundary) followed by unloading. We find that, during compression, the stress field evolves according to a quasistatic advection-diffusion equation, extending classical poroelasticity results. The magnitude of friction is controlled by a single dimensionless number proportional to the friction coefficient and the aspect ratio of the confining geometry. During decompression, a portion of the solid matrix remains stuck due to friction, leading to hysteresis and to the propagation of a slip front. In piston-driven loading, the frictional stress is directly coupled to the solid effective stress, leading to exponential damping of the loading and striking changes to the displacement field. However, this coupling limits the energy dissipated by friction. In fluid-driven loading, the pressure gradient locally adds energy, decoupling elastic energy storage and frictional energy dissipation. The displacement remains qualitatively unchanged but is quantitatively reduced due to large energy dissipation. In both cases, friction can have a substantial impact on the apparent mechanical properties of the medium.