Abstract

Flow through a porous material will drive mechanical deformation when the fluid pressure becomes comparable to the stiffness or strength of the solid skeleton. This has applications ranging from hydraulic fracture for the recovery of shale gas, where fluid is injected at high pressure, to the mechanics of biological cells and tissues, where the solid skeleton is very soft. Both biological materials and geological ones can accommodate large deformations, but they do so very differently: Biological materials typically have a fibrous microstructure that stretches elastically, whereas geological materials often have a frictional, granular microstructure that fails plastically. Here, we consider some consequences of this distinction in the context of large poromechanical deformation driven by fluid injection. We motivate the problem with an experiment: Fluid injection into a packing of soft particles. Using high-resolution imaging, we measure the full deformation field and we study the dynamic interplay between grain-scale rearrangements and the macroscopic response. We show that the deformation involves a complex combination of rearrangement, shear failure, and the quasi-reversible storage and release of elastic energy. We then develop a mathematical model by posing this problem in a large-deformation framework and incorporating frictional shear failure. We show that this model successfully captures certain macroscopic (continuum-scale) aspects of our experiments. We also compare the large-deformation model with the predictions of linear poroelasticity to highlight the importance of volume conservation.