A microphysical model of rate- and state-friction controlled by dislocation glide and backstress (internal stress) evolution

Christopher A. Thom, Lars N. Hansen, David L. Goldsby, & Emily E. Brodsky

Published August 16, 2021, SCEC Contribution #11526, 2021 SCEC Annual Meeting Poster #158 (PDF)

Despite its widespread use in earthquake nucleation and recurrence models, our understanding of rate- and state-friction 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 viscous rheology, which lead to important differences in predicted frictional parameters at depth. Here we combine ideas from classical friction theory and elastoplastic contact mechanics with recent advances in our understanding of low-temperature plasticity and transient creep in geologic materials to produce a new model of rock friction. The model incorporates observations of scale-dependent strength, scale-dependent surface roughness, and the mechanics of transient rheology derived directly from the microphysical behavior of lattice dislocations. The model exhibits the same logarithmic dependence of friction on sliding velocity (strain rate) as rate- and state- friction and predicts a logarithmic dependence of friction on the internal backstress caused by long-range interactions among lattice dislocations. Changes in the backstress evolve exponentially with plastic strain of asperities and are dependent on both the current backstress and previous deformation, consistent with interpretations of the ‘critical slip distance,’ ‘memory effect,’ and ‘state variable’ in rate- and state- friction. This evolution results from anelastic effects caused by changes in the dislocation microstructures within asperities. The rate- and state- friction parameters a and b that determine fault stability are both controlled by the sliding velocity and the current backstress of asperities. We use the model to predict the temperature dependence of the base friction coefficient and rate- and state- friction parameters a, b, and Dc, and find remarkable quantitative agreement with previously published friction data for olivine-rich rocks from experiments spanning a temperature range of 1000°C. This framework provides an interpretation of rate- and state- friction parameters based on microphysical deformation mechanisms (dislocation glide and backstress) and measurable material properties such as scale-dependent yield strength, the strain-dependent work-hardening modulus, and the dislocation density within asperities.

Citation
Thom, C. A., Hansen, L. N., Goldsby, D. L., & Brodsky, E. E. (2021, 08). A microphysical model of rate- and state-friction controlled by dislocation glide and backstress (internal stress) evolution. Poster Presentation at 2021 SCEC Annual Meeting.

Related Projects & Working Groups
Fault and Rupture Mechanics (FARM)