A micromechanical model of rate and state friction: 1. Static and dynamic sliding

Rate and state friction has been extensively used to explain many features of the seismic cycle but the scaling of the experimentally derived parameters a, b and d(c) for real faults is problematic. The purpose of this paper is to present a micromechanical model for rate and state friction in which the contact between the two surfaces occur via plastic and elastic contacts. Shear deformation is accommodated in the bulk of cylindrical contacts rather than at the surface of the contact, as done classically. Assuming that the viscoplastic response is governed by the J(2) plastic flow theory, we retrieve the rate and state framework. Unlike previous works, we identify the state variable as representing the changes of plastic contact area. In our model, all macroscopic frictional parameters of the rate and state framework are related to the parameters of the elementary contacts. We provide a derivation of the aging evolution law for the state variable and propose a new evolution law that reconciles the aging, Linker-Dieterich and Nagata evolution laws. We discuss the scaling of the frictional parameters for active faults and landslides. The a and b parameters should have comparable value at fault scale since friction is mostly controlled by plastic contacts at large normal stress (typically hundreds of MPa). Our model predicts that the critical slip distance d(c) should be scale independent and controlled solely by the plastic contacts. Plain Language Summary The seismic cycle is controlled by the way friction evolves on active faults. We present here a micromechanical model, based on the idea that friction is accomodated by the plastic and elastic contacts on the fault interface. Our model allows the derivation of the rate and state friction laws, which have been widely used to model the seismic cycle. Our approach allows extrapolating laboratory results to the fault scale and suggests that laboratory experiments are suitable to describe fault dynamics. Our model presents an alternative to the reference Bowden and Tabor friction model, and allows, for the first time, the extrapolation of the frictional parameters derived in the laboratory to fault scale.