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;
Rate and state frictional parameters are typically determined using two types of experimental protocols: velocity steps and slide‐hold‐slide events. Here we take a new approach by examining the frictional response to controlled, harmonic oscillations in load point velocity. We present a Matlab graphical user interface software package, called RSFitOSC, that allows users to easily determine frictional parameters by fitting oscillation events using the rate and state friction equations. We apply our new methods to a set of ice‐rock friction experiments conducted over a temperature range of −16.4°C to −2°C, and described in a companion paper: McCarthy et al. (2021,
- NSF-PAR ID:
- 10363356
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geochemistry, Geophysics, Geosystems
- Volume:
- 23
- Issue:
- 2
- ISSN:
- 1525-2027
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract 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. -
Basal slip along glaciers and ice streams can be significantly modified by external time-dependent forcing, although it is not clear why some systems are more sensitive to tidal stresses. We have conducted a series of laboratory experiments to explore the effect of time varying load point velocity on ice-on-rock friction. Varying the load point velocity induces shear stress forcing, making this an analogous simulation of aspects of ice stream tidal modulation. Ambient pressure, double-direct shear experiments were conducted in a cryogenic servo-controlled biaxial deformation apparatus at temperatures between −2°C and −16°C. In addition to a background, median velocity (1 and 10 μm/s), a sinusoidal velocity was applied to the central sliding sample over a range of periods and amplitudes. Normal stress was held constant over each run (0.1, 0.5 or 1 MPa) and the shear stress was measured. Over the range of parameters studied, the full spectrum of slip behavior from creeping to slow-slip to stick-slip was observed, similar to the diversity of sliding styles observed in Antarctic and Greenland ice streams. Under conditions in which the amplitude of oscillation is equal to the median velocity, significant healing occurs as velocity approaches zero, causing a high-amplitude change in friction. The amplitude of the event increases with increasing period (i.e. hold time). At high normal stress, velocity oscillations force an otherwise stable system to behave unstably, with consistently-timed events during every cycle. Rate-state friction parameters determined from velocity steps show that the ice-rock interface is velocity strengthening. A companion paper describes a method of analyzing the oscillatory data directly. Forward modeling of a sinusoidally-driven slider block, using rate-and-state dependent friction formulation and experimentally derived parameters, successfully predicts the experimental output in all but a few cases.more » « less
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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
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Abstract This letter compares the predictions of two expressions proposed for the porosity evolution in the context of rate and state friction. One (Segall & Rice, 1995,
https://doi.org/10.1029/95jb02403 ) depends only on the sliding velocity; the other (Sleep, 1995,https://doi.org/10.1029/94jb03340 ) depends only on the state variable. Simulations of both are similar for velocity stepping and slide‐hold‐slide experiments. They differ significantly for normal effective stress jumps at constant sliding velocity. Segall and Rice (1995,https://doi.org/10.1029/95jb02403 ) predicts no change in the porosity; Sleep (1995,https://doi.org/10.1029/94jb03340 ) does. Simulation with a spring‐block model indicates that the magnitude of rapid slip events is essentially the same for the two formulations. Variations of porosity and induced pore pressure near rapid slip events are similar and consistent with experimental observations. Predicted porosity variations during slow slip intervals and the time at which rapid slip events occur are significantly different. The simulation indicates that changes in friction stress due to pore pressure changes exceed those due to rate and state effects.
