A microphysical model of rock friction and the brittle-ductile transition controlled by dislocation glide and backstress evolution

Rate- and state-friction (RSF) is an empirical framework that describes the complex velocity-, time-, and slip-dependent phenomena observed during frictional sliding of rocks and gouge in the laboratory. Despite its widespread use in earthquake nucleation and recurrence models, our understanding of RSF, particularly its time- and/or slip-dependence, is still largely empirical, limiting our confidence in extrapolating laboratory behavior to the seismogenic zone. While many microphysical models have been proposed over the past few decades, none have explicitly incorporated the effects of strain hardening, anelasticity, or transient elastoplastic rheology. Here we present a new model of rock friction that incorporates these phenomena directly from the microphysical behavior of lattice dislocations. This model of rock friction exhibits the same logarithmic dependence on sliding velocity (strain rate) as RSF and displays a dependence on the internal backstress caused by long-range interactions among geometrically necessary dislocations (GNDs). Changes in the backstress (internal stress) evolve exponentially with plastic strain of asperities and are dependent on both the current backstress and previous deformation, which give rise to phenomena consistent with interpretations of the "critical slip distance, " "memory effect, " and "evolution effect " of RSF. The rate dependence of friction in this model is primarily controlled by the evolution of backstress and temperature. We provide several analytical predictions for RSF-like behavior and the "brittle-ductile " transition based on microphysical mechanisms and measurable parameters such as the GND density and strain-dependent hardening modulus.