Granular origins of rate- and state-dependent friction

Rate- and State-Dependent Friction (RSF) laws are among the most commonly used constitutive relations for describing the time-dependent frictional response of fault gouge to perturbations. The RSF laws are (mostly) empirical, and several versions of them with one or more state variables have been developed over the last five decades. Among the better known are the Aging and Slip laws. Despite its popularity, the micromechanical origins of RSF is a matter of much debate. Although the Slip law is more successful, none of the existing laws can predict all important and robust features of available lab data (Bhattacharya et al., 2017; Kato and Tullis, 2001). This shortcoming, coupled with their empirical nature, makes extrapolating the existing RSF constitutive laws to deformation in the Earth highly problematic.

In this work, we use a granular-physics-based model to explore the extent to which RSF behavior can be explained by the response of a granular gouge layer with time-independent properties at the contact scale. We have thus far examined the behavior for slip histories for which abundant lab data are available. These include velocity-stepping and slide-hold-slide tests. We find that the granular model (1) mimics the Slip law for those loading protocols where the Slip law accurately models laboratory data (velocity-step tests and the hold portions of slide-hold-reslide tests), and (2) deviate from the Slip law under conditions where the Slip law fails to match laboratory data (the reslide portions of slide-hold-reslide tests), in the proper manner to better match those lab data. A more careful comparison of simulated slide-hold-slide and normal-stress-step experiments with lab data is underway. We have further measured the "granular temperature" of the sheared gouge. We have found that if this temperature is normalized by the pressure times the activation volume for grain rearrangements (akin to the classical atomistic-scale explanation of the RSF "direct effect"), it produces a direct effect (RSF a) estimate that seems consistent with simulations, and is in the ballpark of lab data. Further, this normalized temperature is almost constant for a range of slow shear rates, consistent with rock lab observations of the direct effect and with previous measurements of the effective temperature of granular materials.