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

Abstract

Fracture mechanics theory and seismological observations suggest that slip-rate isconstantly changing during earthquake rupture, including dramatic acceleration fromstatic conditions to high velocity sliding followed by deceleration and arrest. This sliphistory is partly determined by a complex frictional evolution, including overcomingpeak friction, rapid weakening, and re-strengthening (or healing). Recent experimentaldevelopments have allowed friction evolution measurements under realistic slip historiesreaching high co-seismic slip-rates of meters per second. Theoretical work has focusedon describing the observed steady-state weakening at these high-velocities, but thetransient behavior has only been fit by direct parameterizations without state variabledependence, needed to simulate arbitrary slip-histories. Commonly used forms ofrate-state friction (RSF) are based on low-velocity, step-change experiments and havebeen shown to not fit the entire frictional evolution using a single set of realisticparameters. Their logarithmic form precludes zero fault slip-rate, assuming it is never trulystatic, thus does not capture slip initiation phenomena that might contribute to nucleationbehavior. 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-velocityvalues. In comparison, we introduce “bristle-state” friction (BSF) models, developedby control-system engineers to predict the transient frictional evolution during arbitrarystressing, especially reversals through static conditions. Although BSF models werealso designed for low-velocities, we show that their form provides advantages for fittingfrictional evolution measurements under high slip-rate, long-displacement, non-trivial sliphistories, especially during the initial strengthening stage.