A Microphysical Interpretation of Rate-and-State Friction Behaviour: Insights from Discrete Element Modelling

Abstract:

For many years, empirical rate-and-state friction laws have been successfully applied to describe the transient frictional behaviour of fault zones, as observed in laboratory experiments and in nature. However, the rate-and-state friction parameters and equations are still poorly understood in terms of the underlying processes that operate at a micro-scale. Due to our lack of understanding, extrapolation of the frictional behaviour from sample-scale to the spatial and temporal scales of natural faults is non-trivial.

Several models have been proposed to explain the rate, temperature and stress dependence of the steady-state frictional strength of faults, based on microphysical processes operating at the grain-scale. These models were then extended to provide an explanation for transient frictional effects that are commonly observed in experiments in response to an instantaneous change in load point velocity. What these analytical models have in common is that they describe the interplay between time-dependent ductile and frictional processes, which provide a basis for extrapolation to natural conditions. At the same time, the models are limited due to oversimplification of the microstructure, e.g. a necessary assumption of the grain packing and the lack of a distributed grain size. By implementing the principles of these models into a Discrete Element formulation, many of the limitations can be circumvented to mimic more realistic fault zone geometries and microstructures.

We have developed a Discrete Element Model to study the interaction of pressure solution with local porosity and the effect on the transient and steady-state macroscopic frictional behaviour. It was found that the magnitude of slip events observed during simulations that showed velocity-weakening behaviour, is related to the pressure solution rate and degree of localisation. This has important implications for the expected magnitude of earthquakes generated at conditions favouring unstable sliding.