Slide‐Hold‐Slide Protocols and Frictional Healing in Discrete Element Method (DEM) Simulations of Granular Fault Gouge. Issue 12 (20th December 2021) - Ferdowsi, Behrooz; Rubin, Allan M.
Abstract: 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. Plain Language Summary: Numerical models of fault slip (earthquakes, earthquake nucleation, landslides, etc.) require "constitutive equations" that describe the time‐varying frictional strength of the fault. But despite being studied since Da Vinci, there is no consensus concerning the physics that underlies friction. Laboratory experiments have shown that frictional strength depends upon both the rate of fault slip, and a more nebulous property termed the fault "state". Conventional wisdom is that variations in "state" are generated by time‐dependent plastic flow or chemistry at microscopic contact points within the fault. Because faults in the Earth are invariably filled by fragmented rock (gouge), here we explore an alternative model in which variations in friction derive simply from granular rearrangements in a gouge layer, with no rate‐ or state‐dependence at individual grain/grain contacts. Previously, we showed that this model accurately described laboratory experiments in which a gouge layer was subjected to large variations in slip rate. Here we test the same model in "slide‐hold‐slide" protocols, long used to measure the amount of frictional strengthening that occurs during fault "holds". The study has broad implications for our understanding of the origins of transient friction on faults, an insight needed for improving geological hazard assessment. Key Points: We ran DEM simulations of a sheared granular layer with time‐independent contact‐scale properties in slide‐hold‐slide protocols The slide‐hold simulations with different model stiffnesses mimic the stress decay response of laboratory friction data As with lab data, the peak stress upon resliding increases linearly with log hold time, with a slope close to the rate‐state " b "