Pore pressure evolution in deforming granular material: A general formulation and the infinitely stiff approximation

The physics of deformation of fluid-filled granular media controls many geophysical systems, ranging from shear on geological faults to landslides and soil liquefaction. Its great complexity is rooted in the mechanical coupling between two deforming phases: the solid granular network and the fluid-filled pore network. Often deformation of the granular network leads to pore fluid pressure (PP) changes. If the PP rises enough, the fluid-filled granular media may transition from a stress-supporting grain network to a flowing grain-fluid slurry, with an accompanying catastrophic loss of shear strength. Despite its great importance, the mechanisms and parameters controlling PP evolution by granular shear are not well understood. A formulation describing the general physics of pore fluid response to granular media deformation is developed and used to study simple scenarios that lead to PP changes. We focus on the infinitely stiff end-member scenario, where granular deformation is prescribed, and the PP responds to this deformation. This end-member scenario illustrates the two possible modes of pore fluid pressurization: (1) via rapid fluid flow when fluid drainage is good and (2) via pore volume compaction when drainage is poor. In the former case the rate of deformation controls PP evolution, while in the latter case, fluid compressibility is found to be an important parameter and the amount of pressurization is controlled by the overall compaction. The newly suggested fluid-induced mechanism (mechanism 1) may help explain observations of liquefaction of initially compact soils and shear zones.