Estimation of time-variable friction parameters using machine learning

Abstract

SUMMARY The laboratory-derived rate- and state-dependent friction (RSF) law governs rock friction. Although a number of studies have investigated the RSF friction parameters, they are not fully understood yet within a physical framework. In this study, we estimated the variation of RSF parameters during stick-slip cycles, in order to have insights into the temporal variation of fault conditions during slipping, which may help understand the relation between the change in friction parameters and the generation of gouge particles. To get a more refined understanding of the evolution of RSF parameters, we estimated these parameters for each of the hundreds of stick-slip events that occurred on laboratory faults during an experiment. We used experiment data for which the gouge particles were removed from the laboratory faults at the beginning of each experiment; this procedure made possible to evaluate the influence of the gouge layer evolution on the variation of the RSF parameters. Since the amount of data was very large, we adopted a random forest (RF) machine learning approach for data analysis. The RF model was trained on simulated friction data and then applied to the experiment stick-slip event data to estimate the RSF parameters. To generate simulated friction data of stick-slip events, a one-degree-of-freedom spring-slider model governed by the RSF law was assumed. From plots of friction change as a function of displacement, some representative features were extracted to account for the RSF parameters and were used as input to the RF algorithm. Using the RF approach, we captured the variation of the RSF parameters a, $b - a$ and ${D}_{\mathrm{c}}\ $defined in the RSF law. The results show that during a first transient phase, the parameter a becomes smaller, while parameters $b - a$ and ${D}_{\mathrm{c}}$ become larger, as the gouge layer becomes thicker. The variation of the RSF parameters becomes less pronounced during the following steady-state phase. These results suggest that the variation of RSF friction parameters may be related to the evolution of the gouge layer.