Constitutive laws for high‐velocity frictional sliding and their influence on stress drop during unstable slip

Abstract

The Dieterich‐Ruina state‐variable friction laws do a good job describing results of rock friction experiments, and fault models based on them are able to mimic natural seismicity in many respects. To be useful for modeling earthquakes, high velocities must be successfully modelled. Ruina gave a formula for steady state frictional strength with a constant (usually negative) slope on a logarithmic plot that does not agree with recent observations of friction of a variety of materials at velocities greater than 30 to 100 μms−1. This steady state function, termed the “log‐linear function,” with inertia neglected, does not recover from instability and, consequently, cannot give predictions of stress drop or peak velocities during unstable slip. Adding inertia yields stress drops that are too large to match experimental observations. This paper explores the consequences for unstable slip when inertia is considered and when the steady state function is altered at high velocity. Two steady state functions are considered: one that has no dependence on velocity at high slip velocity (“zero‐slope”) and one that has a positive velocity dependence at high velocity (“positive‐slope”). Inclusion of inertia and use of these modified steady state functions improve the results of simulations in terms of qualitatively reproducing many aspects of unstable sliding, but the positive‐slope function yields the best quantitative agreement with experimental observations. Use of the modified steady state functions predicts that stress drop during unstable sliding should decrease with increasing loading velocity and at sufficiently high load point velocity there will be a transition to stable sliding, a result that is observed experimentally.