Critical evaluation of state evolution laws in rate and state friction: Fitting large velocity steps in simulated fault gouge with time‐, slip‐, and stress‐dependent constitutive laws

Abstract

The variations in the response of different state evolution laws to large velocity increases can dramatically alter the style of earthquake nucleation in numerical simulations. But most velocity step friction experiments do not drive the sliding surface far enough above steady state to probe this relevant portion of the parameter space. We try to address this by fitting 1–3 orders of magnitude velocity step data on simulated gouge using the most widely used state evolution laws. We consider the Dieterich (Aging) and Ruina (Slip) formulations along with a stress‐dependent state evolution law recently proposed by Nagata et al. (2012). Our inversions confirm the results from smaller velocity step tests that the Aging law cannot explain the observed response and that the Slip law produces much better fits to the data. The stress‐dependent Nagata law can produce fits identical to, and sometimes slightly better than, those produced by the Slip law using a sufficiently large value of an additional free parameter c that controls the stress dependence of state evolution. A Monte Carlo search of the parameter space confirms analytical results that velocity step data that are well represented by the Slip law can only impose a lower bound on acceptable values of c and that this lower bound increases with the size of the velocity step being fit. We find that our 1–3 orders of magnitude velocity steps on synthetic gouge impose this lower bound on c to be 10–100, significantly larger than the value of 2 obtained by Nagata et al. (2012) based on experiments on initially bare rock surfaces with generally smaller departures from steady state.

Rate‐and‐State Model Casts New Insight into Episodic Tremor and Slow‐slip Variability in Cascadia

“…In this study we adopt the "slip-law," which is most consistent with laboratory experiments (e.g., Bhattacharya et al, 2015): In this study we adopt the "slip-law," which is most consistent with laboratory experiments (e.g., Bhattacharya et al, 2015):…”

Stability of faults with heterogeneous friction properties and effective normal stress

“…The transition under the aging law occurs at asperity sizes between two nucleation length scales L c and L ∞ , defined in Rubin and Ampuero (2005), and is broader at higher a/b because L c /L ∞ ∼ 1/(1 − a/b). However, the L ∞ length is irrelevant under the slip law (Ampuero and Rubin 2008), which is the state evolution law adopted here because it is more consistent with laboratory experiments with large velocity jumps, large enough to model the propagating front of slip transients (Bhattacharya et al 2015). Simulation results presented by Luo (2018) indicate that the width of the transition is more fundamentally affected by the range of scales of heterogeneity than by the choice of state evolution law.…”

“…The state variable θ evolves with time, as described by empirical evolution laws. Here we adopt the so-called "slip law", the state evolution law that is most consistent with laboratory experiments (Bhattacharya et al 2015):…”

An Effort to Reconcile Time‐ and Slip‐Dependent Friction Evolution

“…For the Slip law, recent results show that it unequivocally produces extraordinary good fits to velocity step experiments, but it is not able to match the SHS data to an acceptable extent (Bhattacharya et al, , ). It was also criticized for lacking a clear physical background in the construction of the state variable compared with the Aging law (e.g., Ikari et al, ), although various attempts have been made over the years to help the empirical law find proper physical basis (e.g., Aharonov & Scholz, ; Hatano, ; Sleep, ).…”

“…Simulations and inversions for velocity steps (data from Penn State University) and SHS (Beeler et al, , data) experiments are conducted using this new model. For SHS, two kinds of inversions are tried: only fitting the stress peaks and minima, a convenient approach in fitting SHS data (e.g., Beeler et al, ; Bhattacharya et al, ), and inverting the entire finite stress series from the start of the hold till the end of reslide, which is a more difficult approach but also has been adopted by many successful efforts (e.g., Marone, ; Marone & Saffer, ; Niemeijer et al, , ). Nevertheless, to the best of our knowledge, no previous studies have shown the result of fitting multiple finite SHS stress series together using the same parameters, and in the current study we made a first attempt.…”