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

• Published in: Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2021-05, Vol.379 (2196), p.20200129-20200129
• Main Author: Garagash, Dmitry I
• Format: Article
• Language: English
• ISSN: 1364-503X; 1471-2962
• DOI: 10.1098/rsta.2020.0129

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 , dissipated in overcoming strength-excursion away from steady state, as a function of the rupture velocity . 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 ( ) 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 Δ . In the context of fluid injection, Δ is a proxy for the injection volume . 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 /d , 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'.