Fracture mechanics of rate-and-state faults and fluid injection induced slip.

Abstract

Propagation of a slip transient on a fault with rate- and state-dependent friction resembles a fracture whose near tip region is characterized by large departure of the slip velocity and fault strength from the steady-state sliding. We develop a near tip solution to describe this unsteady dynamics, and obtain the fracture energy Gc, dissipated in overcoming strength-excursion away from steady state, as a function of the rupture velocity vr. This opens a possibility to model slip transients on rate-and-state faults as singular cracks characterized by approximately steady-state frictional resistance in the fracture bulk, and by a stress singularity with the intensity defined in terms of Gc(vr) at the crack tip. In pursuing this route, we develop and use an analytical equation of motion to study 1-D slip driven by a combination of uniform background stress and a localized perturbation of the fault strength with the net Coulomb force ΔT. In the context of fluid injection, ΔT is a proxy for the injection volume Vinj. We then show that, for ongoing fluid injection, the propagation speed of a transient induced on a frictionally stable fault is bounded by a large-time limiting value proportional to the injection rate dVinj/dt, while, for stopped injection, the maximum slip run-out distance is proportional to [Formula: see text]. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.