On the microphysical foundations of rate-and-state friction

The rate-and-state formulation of friction is well established as a phenomenological yet quantitative description of friction dynamics, in particular the onset of stick-slip instabilities arising from an oscillatory bifurcation. We first discuss the physical origins of two theories for the derivation of friction coefficients used in rate-and-state models, both derived from thermally activated rate processes. Secondly, we propose a general expression for the state evolution law in the form of a first order kinetics which describes the relaxation to a velocity dependent equilibrium interfacial state phi(ss)(v) over a velocity dependent dynamic rejuvenation time-scale t(phi)(v). We show that the unknown relation phi(ss)(v), defined as the ratio of t(phi) to a constant interfacial stationary healing time-scale t(**), can be estimated directly from the experimental measurements of the steady-state friction coefficient and the critical stiffness for the onset of stick-slip behaviour of a spring-block system. Using a specific experimental dataset, we finally illustrate that this method provides the experimental measurements of the apparent memory length L-a(v)= v t(**) phi(ss)(v) and the constant characteristic relaxation time t(**) from which a constant intrinsic memory length L = V(*)t(**) can be defined once a slip rate of reference V. is chosen. As a result the complete state evolution law can be experimentally characterised. (C) 2011 Elsevier Ltd. All rights reserved.