Dmitry Garagash

Propagation of a slip transient on a fault with rate-and-state dependent friction resembles a fracture which 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-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 by Gc(vr) at the crack tip. In pursuing this route, we develop and use an analytical equation of motion to study 1D slip driven by a combination of uniform background stress and a localized perturbation of the fault strength with the net Coulomb force ∆T. In the context of fluid injection, ∆T is a proxy for the injection volume Vinj. We then show that, for ongoing fluid injection, the maximum propagation speed of the transient induced on a frictionally-stable fault is bounded by a value proportional to Vinj(t), and, for stopped injection, the maximum slip run-out distance is proportional to the square of the total injected volume.