Simulation of Frictional Strength and Steady Relaxation Using the Rate and State Dependent Friction Model

Abstract

In this paper, frictional strength of hard solids, such as rock–rock sliding surfaces, is studied as a function of waiting time and shearing velocity. A one dimensional spring–mass sliding system is numerically simulated under the quasistatic condition using the rate and state dependent friction model. It is established that frictional strength varies linearly with the logarithm of waiting time (also known as time of stationary contact or relaxation time, etc.) as well as logarithm of shearing velocity. Analytical expression developed for frictional strength is found to be valid only in the case of high stiffness of the connecting spring. In the steady relaxation simulation, a steadily sliding mass is suddenly brought to zero velocity and relaxation of the interfacial stress and corresponding velocity at the sliding interface is studied as a function of relaxation time in the velocity strengthening regime of friction. A mathematical relation is derived between state variable and waiting time using the concept of steady relaxation. The relaxation model is also compared with the experimental data from the literature. Finally, the present study enables one to unify the slide–hold–slide friction experiments.