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

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 G(c), dissipated in overcoming strength-excursion away from steady state, as a function of the rupture velocity v(r). 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 G(c)(v(r)) 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 Delta T. In the context of fluid injection, Delta T is a proxy for the injection volume V-inj. 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 dV(inj)/dt, while, for stopped injection, the maximum slip run-out distance is proportional to V-inj,total(2). This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.

Automated summary

The study develops a near tip solution to describe the unsteady dynamics of slip transients on rate- and state-dependent faults, and proposes using fracture energy to model these transients. It is shown that for faults induced by fluid injection, the propagation speed of a transient can be controlled by regulating the injection rate, and the maximum slip run-out distance is proportional to the total injection volume.