Physics of friction and strain rate localization in synthetic fault gouge

Data on synthetic fault gouge previously collected by Richardson and Marone [1999] were compared with the predictions of a unified theory for rate- and state-dependent Friction compiled by Sleep [1997]. The theory treats the gouge as a continuum one-dimensional fluid sheared between parallel plates. It is predicted that the strain rate localized into a shear band of width called W-ss during steady state sliding from the nominal width of the gouge zone W-nom. The critical displacement during velocity stepping tests is predicted to be W(ss)epsilon (int), where epsilon (int) is the critical strain, an intrinsic material property. It is predicted that the strain rate for renewed sliding after holds delocalizes to a width W-new which is greater than W-ss and for long holds approaches the full gouge zone width W-nom. The displacement for recovery of the shear traction to its steady state value is predicted to be W(new)epsilon (int), which for long holds is much greater than the critical displacement obtained by velocity stepping. Only the macroscopic effects of this process could be studied using the laboratory data in hand. Compaction during the hold and the difference between peak shear traction upon restart and the steady state shear traction during sliding (healing) were measured. To simulate more complex normal traction variations on real faults, the normal traction was varied sinusoidally about its previous value during some holds. The theory reasonably predicts the observed relationship between healing and compaction and healing versus hold time. It predicts the slip needed for recovery of shear traction following holds but poorly predicts the shear traction versus time during recovery. We attribute this failure to the fact that the laboratory gouge is a heterogeneous three-dimensional substance. Qualitatively, the delocalized width W-new varies with position within the gouge plane, and slip is required for localized shear to organize in three dimensions. As strain rate was not observed as a function or time and position within the gouge, other explanations for the observed long recovery times following holds remain viable, including consolidation strengthening.