“Bristle-State” Friction: Modeling Slip Initiation and Transient Frictional Evolution From High-Velocity Earthquake Rupture Experiments

Fracture mechanics theory and seismological observations suggest that slip-rate is constantly changing during earthquake rupture, including dramatic acceleration from static conditions to high velocity sliding followed by deceleration and arrest. This slip history is partly determined by a complex frictional evolution, including overcoming peak friction, rapid weakening, and re-strengthening (or healing). Recent experimental developments have allowed friction evolution measurements under realistic slip histories reaching high co-seismic slip-rates of meters per second. Theoretical work has focused on describing the observed steady-state weakening at these high-velocities, but the transient behavior has only been fit by direct parameterizations without state variable dependence, needed to simulate arbitrary slip-histories. Commonly used forms of rate-state friction (RSF) are based on low-velocity, step-change experiments and have been shown to not fit the entire frictional evolution using a single set of realistic parameters. Their logarithmic form precludes zero fault slip-rate, assuming it is never truly static, thus does not capture slip initiation phenomena that might contribute to nucleation behavior. Inverting high slip-rate and friction data from different types of experiments, we show that RSF can work by using parameter ranges far from typical low-velocity values. In comparison, we introduce “bristle-state” friction (BSF) models, developed by control-system engineers to predict the transient frictional evolution during arbitrary stressing, especially reversals through static conditions. Although BSF models were also designed for low-velocities, we show that their form provides advantages for fitting frictional evolution measurements under high slip-rate, long-displacement, non-trivial slip histories, especially during the initial strengthening stage.