A revised rate- and state-dependent friction law obtained by constraining constitutive and evolution laws separately with laboratory data

We propose two major revisions on the rate- and state-dependent friction (RSF) law on the basis of rigorous analysis of friction experiments. First, we find that the direct effect coefficient a, a parameter playing a central role in the RSF constitutive law, is much larger than the traditional, consensual estimate of less than about 0.01. We derive a lower bound of 0.035 for a directly from stress-velocity relations measured during carefully designed step tests, without relying on any evolution laws as traditional methods do. After correcting for state changes during the steps, inferred indirectly from observed changes in acoustic transmissivities across the interface, we obtain an estimate of a as large as 0.05. Second, we calculate values of the RSF state variable Phi by feeding the measured shear stress and slip velocity values into the constitutive law. The results showed systematic deviations from predictions of the RSF evolution law of the aging type. This leads us to propose a revised evolution law, which incorporates a previously unknown weakening effect related to the shear stress. We also present additional experiment results to corroborate the presence of this new effect. Forward simulations based on our revised evolution law, combined with the larger, revised value of a, very well explain observed variations in both the shear stress and Phi throughout different phases of experiments, including quasi-static hold, reloading after a hold, and steady state sliding at different velocities, as well as their mutual transitions, all with an identical set of parameter values.