This paper analyzes the effects of pore pressure rate for a spring - block system that is a simple model of a laboratory experiment. Pore pressure is increased at a constant rate in a remote reservoir and slip is governed by rate and state friction. The frequency of rapid slip events increases with the increase of a nondimensional pressure rate that is the ratio of the time scale of frictional sliding to that for pressure increase. As the pressure rate increases, the more rapid increase of pore pressure on the slip surface quickly stabilizes slip events due to rate and state friction. Rate and state and pressure rate effects interact in a limited range of pressure rate and diffusivity. This range includes pressure rates and diffusivities representative of recent laboratory experiments.

Fluid-fault interactions result in many two-way coupled processes across a range of length scales, from the micron scale of the shear zone to the kilometer scale of the slip patch. The scale separation and complex coupling render fluid-fault interactions challenging to simulate and may ultimately limit our understanding of experimental data and induced seismicity. Here we present spectral boundary-integral solutions for in-plane interface sliding and opening in a poroelastic solid. We solve for fault slip in the presence of rate-and-state frictional properties, inelastic dilatancy, injection, and the coupling of a shear zone and a diffusive poroelastic bulk. The shear localization zone is treated as having a finite-width and non-constant pore pressure, albeit with a simplified mathematical representation. The dimension of the 2D plane strain problem is reduced to a 1D problem resulting in increased computational efficiency and incorporation of small-scale shear-zone physics into the boundary conditions. We apply the method to data from a fault injection experiment that has been previously studied with modeling. We explore the influence of inelastic dilatancy, bulk poroelastic response, and bulk diffusivity on the simulated fault slip due to the injection. Dilatancy not only alters drastically the stability of fault slip but also the nature of pore pressure evolution on the fault, causing significant deviation from the standard square-root-of-time diffusion. More surprisingly, varying the bulk’s poroelastic response (by using different values of the undrained Poisson’s ratio) and bulk hydraulic diffusivity can be as critical in determining rupture stability as the inelastic dilatancy.

This letter compares the predictions of the two expressions that have been proposed for the porosity evolution in the context of rate and state friction. One depends only on the sliding velocity; the other depends only on the state variable. The predictions of the two expressions are similar for simulations of velocity stepping and slide-hold-slide experiments but differ significantly for normal effective stress jumps at constant sliding velocity. The formulation that depends only on the velocity predicts no change in the porosity; the other does. A simulation with a spring-block model indicates that the magnitude of rapid slip events is essentially the same for the two models. Variations of porosity and induced pore pressure near rapid slip events are similar and consistent with experimental observations. Predicted porosity variations during slow slip intervals and the time at which rapid slip events occur are significantly different.