An Empirically-based Steady-state Friction Law and its Implications for Fault Stability

Abstract:

Empirically-based rate-and-state friction laws (RSFL) have been proposed to model the dependence of friction forces with slip and time. The relevance of the RSFL for earthquakes mechanics is that few constitutive parameters (e.g. A-B= dτ/dlog(V) with τ and V the shear stress and slip rate respectively, allow us to define the stability conditions of a fault. According to RSFL if A-B> 0, τ increases with V (rate-hardening behavior) resulting in an unconditionally stable behavior; if A-B< 0, τ decreases with V (rate-weakening behavior) potentially resulting in an unstable behavior leading to dynamic runaway. Given that τ at steady state conditions allows us also to define a critical fault stiffness, the RSFL determine a condition of stability for faults as their stiffness approaches the critical conditions. However, the conditions of fault stability, determined by the critical stiffness under the assumption of either a rate-weakening or a rate-hardening behavior, might be restrictive given that frictional properties sensibly change as a function of slip or slip rate. Moreover, the RSFL were determined from experiments conducted at sub-seismic slip rates (< 1 cm/s) and their extrapolation to earthquake deformation conditions remains questionable on the basis of the experimental evidence of large dynamic weakening at seismic slip rates and the plethora of slip events which characterize the seismic cycle. Here, we propose a modified RSFL based on the review of a large published and unpublished dataset of rock-friction experiments performed with different testing machines (rotary shear, bi-axial, tri-axial). The modified RSFL is valid at steady-state conditions from sub-seismic to seismic slip rates (0.1 µm/s <V< 3 m/s). This law describes fault frictional stability and the diversity of slip events observed at the laboratory scale. This law leads to a new definition of critical stiffness with relevance to models of seismic rupture nucleation, propagation and arrest.