Microscopic elasticity and rate and state friction evolution laws

Norman H. Sleep

Published December 2012, SCEC Contribution #1680

Rate and state friction formalism represents the dependence of macroscopic shear traction on sliding velocity and the history of the sliding surface. In macroscopic terms, , where is normal traction, is the coefficient of friction, are small dimensionless parameters, is a reference velocity, is the state variable that depends on history, and represents the effect of changes in normal traction. This representation does not consider microscopic elasticity and is inadequate at over very small times. The apparent value of just after a small decrease in shear traction is a factor of a few larger than its traditional value of ~0.01. Changes of microscopic elastic strain energy may cause this effect. Microscopic elasticity affects friction after changes in normal traction. Shear traction does not change instantly after a sudden change in normal traction because time is required for real contact area to change. A hybrid of the aging law (where increases linearly with time during holds) and the slip law behavior (where the state variable does not change in the limit of zero sliding velocity) is necessary. Slip-law behavior dominates near steady state and also applies to sudden initial sliding where the state variable and porosity are far from steady state. Porosity increases from its initial value toward the steady state value over slip scaling with the critical displacement . The ratio of dilatant to shear strain in low porosity material is a modest fraction of 1 and related to the construct of dilatancy angle in engineering.

Sleep, N. H. (2012). Microscopic elasticity and rate and state friction evolution laws. Geochemistry, Geophysics, Geosystems, 13(12).