Rate- and State-dependent Friction and its Underlying Physics

Abstract

Despite its impact on fault mechanics, rate- and state- dependent friction (RSF) is a minor correction to traditional Amonton-Coulomb friction. A classical physical theory of friction called ‘adhesive friction’ can be modified to explain RSF, by simply incorporating thermally activated rheology expected for the high stress conditions of microscopic frictional contacts. We emphasize that the sense of opaqueness long hanging about RSF is rather due to the lack of awareness of its logical structure. Unlike traditional friction laws, which are strength laws to give frictional strength at various conditions, RSF’s framework is a constitutive law giving the relation between applied stress and incurred slip velocity. By consciously distinguishing stress and strength, we highlight such logical structure. Then, quite a straightforward physical interpretation emerges. The RSF constitutive law derives from thermally activated shearing of atom-scale bonding at the contacts. The amount of bonding, i.e., strength, is given by the RSF evolution law, a sophisticated strength law occupying the same logical position as traditional friction laws but incorporating detailed mechanisms affecting the real contact area of adhesive friction theory. The reviewed physical models for constitutive law and evolution law are both quantitatively consistent with laboratory data.