Slide-Hold-Slide Protocols and Frictional Healing in Discrete Element Method (DEM) Simulations of Granular Fault Gouge

The empirical constitutive modeling framework of rate- and state-dependent friction (RSF) is commonly used to describe the time-dependent frictional response of fault gouge to perturbations from steady sliding. In a previous study (Ferdowsi & Rubin, 2020), we found that a granular-physics-based model of a fault shear zone, with time-independent properties at the contact scale, reproduces the phenomenology of laboratory rock and gouge friction experiments in velocity-step and slide-hold (SH) protocols. A few slide-hold-slide (SHS) simulations further suggested that the granular model might outperform current empirical RSF laws in describing laboratory data. Here, we explore the behavior of the same Discrete Element Method (DEM) model in SH and SHS protocols over a wide range of sliding velocities, hold durations, and system stiffnesses, and provide additional support for this view. We find that, similar to laboratory data, the rate of stress decay during SH simulations is in general agreement with the “Slip law” version of the RSF equations, using parameter values determined independently from velocity step tests. During reslides following long hold times, the model, similar to lab data, produces a nearly constant rate of frictional healing with log hold time, with that rate being in the range of ∼0.5 to 1 times the RSF “state evolution” parameter b. We also find that, as in laboratory experiments, the granular layer undergoes log-time compaction during holds. This is consistent with the traditional understanding of state evolution under the Aging law, even though the associated stress decay is similar to that predicted by the Slip and not the Aging law.