A micromechanical model of rate and state friction: 2. Effect of shear and normal stress changes

Abstract

In this paper we analyze the influence of shear and normal stress changes on frictional properties. This problem is fundamental as, for instance, sudden stress changes are naturally induced on active faults by nearby earthquakes. As any stress changes can be seen as resulting from a succession of infinitesimal stress steps, the role of sudden stress changes is crucial to our understanding of fault dynamics. Laboratory experiments carried out by Linker and Dieterich (1992) and Nagata et al. (2012), considering steps in normal and shear stress, respectively, show an instantaneous response of the state variable (a proxy for the evolution of contact surface in our model) to a sudden stress change. We interpret this response as being due to an (instantaneous) elastic response of the plastic and elastic contacts. We assume that the anelastic response of the plastic contacts is frozen during sudden stress changes. The contacts, which were driven by plasticity before the stress change, are elastically accommodated during the sudden variation of the load. On the contrary, when the loading is slowly varying, elastic deformation of plastic contacts can be neglected. Our model is able to explain the evolution law for the state variable reported by Linker and Dieterich (1992).