Microphysically derived expressions for rate-and-state friction parameters, a, b, and Dc

Abstract

Rate-and-state friction (RSF) laws are extensively applied in fault mechanics but have a largely empirical basis reflecting only limited understanding of the underlying physical mechanisms. We recently proposed a microphysical model describing the frictional behavior of a granular fault gouge undergoing deformation in terms of granular flow accompanied by thermally activated creep and intergranular sliding at grain contacts. Numerical solutions reproduced typical experimental results well. Here we extend our model to obtain physically meaningful, analytical expressions for the steady state frictional strength and standard RSF parameters, a, b, and Dc. The frictional strength contains two components, namely, grain boundary friction and friction due to intergranular dilatation. The expressions obtained for a and b linearly reflect the rate dependence of these two terms. Dc scales with slip band thickness and varies only slightly with velocity. The values of a, b, and Dc predicted show quantitative agreement with previous experimental results, and inserting their values into classical RSF laws gives simulated friction behavior that is consistent with the predictions of our numerically implemented model for small departures from steady state. For large velocity steps, the model produces mixed RSF behavior that falls between the Slowness and Slip laws, for example, with an intermediate equivalent slip(-weakening) distance d0. Our model possesses the interesting property not only that a and b are velocity dependent but also that Dc and d0 scale differently from classical RSF models, potentially explaining behaviour seen in many hydrothermal friction experiments and having substantial implications for natural fault friction.