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
- Award ID(s):
- 2054439
- NSF-PAR ID:
- 10429770
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 119
- Issue:
- 30
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract 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. -
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Abstract In rate and state friction (RSF) theory, time‐dependent evolution (represented by the Aging law) and slip‐dependent evolution (represented by the Slip law) both succeed in explaining some features of the friction curves while failing in explaining others. Nevertheless, experimental results provided strong evidence for the two ideas and suggested that they are both critical components in friction evolution. Making a first attempt toward reconciling these two ideas, we developed a new friction model for RSF evolution assuming combined physical mechanisms that highlight asperities' plastic behavior: the time‐dependent growth of asperity contact area and the slip‐dependent enhancement (slip strengthening) of asperity intrinsic strength. Our model adopts a two‐scale mathematical structure developed by Li and Rubin (2017;
https://doi.org/10.1002/2017JB013970 ), where the specification of the surface distribution of asperity ensembles and their geometry facilitates the numerical construction of the state variable in the RSF equation. Results show that this new model's fit to the slide‐hold‐slide experiments is similar to the best fits of the Slip law, while it provides an improved physical picture; however, for velocity steps it fails to match the symmetry of step ups and downs, although the general fit is acceptable. By introducing two new parameters to specify the slip‐hardening mechanism, we allow the model to incorporate as a subset the pure time‐dependent model discussed in Li and Rubin (2017). Although failing to completely reconcile time‐ and slip‐dependent friction evolution, this study produced useful insights for future research; for example, a granular numerical description of the frictional surface might be convenient for modeling the physics of friction.
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2119462119
