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

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Authors

Dmitry Garagash 

Abstract

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.

DOI

https://doi.org/10.31223/osf.io/wsgz2

Subjects

Earth Sciences, Engineering, Environmental Sciences, Geophysics and Seismology, Oil, Gas, and Energy, Physical Sciences and Mathematics, Physics

Keywords

equation of motion, fault rate-state friction, fluid injection-induced slip, fracture mechanics, rupture fronts

Dates

Published: 2020-07-08 10:43

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License

GNU Lesser General Public License (LGPL) 2.1

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