Dilatancy and Compaction of a Rate-and-State Fault in a Poroelastic Medium: Linearized Stability Analysis

Faults in the crust at seismogenic depths are embedded in a fluid-saturated, elastic, porous material. Slip on such faults may induce transient pore pressure changes through dilatancy or compaction of the gouge or host rock. However, the poroelastic nature of the crust and the full coupling of inelastic gouge processes and the host rock have been largely neglected in previous analyses. Here, we present a linearized stability analysis of a rate-and-state fault at steady-state sliding in a fully-coupled poroelastic solid under in-plane and anti-plane sliding. We further account for dilatancy of the shear zone and the associated pore pressure changes in an averaged sense. We derive the continuum equivalent of the analysis by Segall and Rice (1995, https://doi.org/10.1029/95jb02403), and highlight a new parameter regime where dilatancy stabilization can act in a highly diffusive solid. Such stabilization is permitted since the time scale of flux through the shear zone and diffusion into the bulk can be very different. A novel aspect of this study involves analyzing the mechanical expansion of the shear layer causing fault-normal displacements, which we describe by a mass balance of the solid constituent of the gouge. This effect gives rise to a universal stabilization mechanism in both drained and undrained limits. The importance of the mechanism scales with shear-zone thickness and it is significant for wider shear zones exceeding approximately 1 cm. We hypothesize that this stabilization mechanism may alter and delay an ongoing shear localization process.