Rate and state dependent friction and the stability of sliding between elastically deformable solids

We study the stability of steady sliding between elastically deformable con tinua using rate and state dependent friction laws. That is done for both e lastically identical and elastically dissimilar solids. The focus is on lin earized response to perturbations of steady-state sliding, and on studying how the positive direct effect (instantaneous increase or decrease of shear strength in response to a respective instantaneous increase or decrease of slip rate) of those laws allows the existence of a quasi-static range of r esponse to perturbations at sufficiently low slip rate. We discuss the phys ical basis of rate and state laws, including the likely basis for the direc t effect in thermally activated processes allowing creep slippage at asperi ty contacts, and estimate activation parameters for quartzite and granite, Also, a class of rate and state laws suitable for variable normal stress is presented. As part of the work, we show that compromises from the rate and state framework for describing velocity-weakening friction lead to paradox ical results, like supersonic propagation of slip perturbations, or to ill- posedness, when applied to sliding between elastically deformable solids. T he case of sliding between elastically dissimilar solids has the inherently destabilizing feature that spatially inhomogeneous slip leads to an altera tion of normal stress, hence of frictional resistance. We show that the rat e and state friction laws nevertheless lead to stability of response to suf ficiently short wavelength perturbations, at very slow slip rates. Further, for slow sliding between dissimilar solids, we show that there is a critic al amplitude of velocity-strengthening above which there is stability to pe rturbations of all wavelengths. (C) 2001 Elsevier Science Ltd. All rights r eserved.