Fracture mechanics of rate-and-state faults and fluid injection induced slip
Dmitry Garagash
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 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 Δ T . In the context of fluid injection, Δ 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 /d t , while, for stopped injection, the maximum slip run-out distance is proportional to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>V</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">inj</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">total</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.