A rate-, state-, and temperature-dependent friction law with competing healing mechanisms

The constitutive behavior of faults is central to many interconnected aspects of earthquake science, from fault dynamics to induced seismicity, to seismic hazards characterization. Yet, a friction law applicable to the range of temperatures found in the brittle crust and upper mantle is still missing. In particular, rocks often exhibit a transition from steady-state velocity-strengthening at room temperature to velocity-weakening in warmer conditions that is poorly understood. Here, we investigate the effect of competing healing mechanisms on the evolution of frictional resistance in a physical model of rate-, state-, and temperature-dependent friction. The yield strength for fault slip depends on the real area of contact, which is modulated by the competition between the growth and erosion of interfacial micro-asperities. Incorporating multiple healing mechanisms and rock-forming minerals with different thermodynamic properties allows a transition of the velocity- and temperature-dependence of friction at steady-state with varying temperatures. We explain the mechanical data for granite, pyroxene, amphibole, shale, and natural fault gouges with activation energies and stress power exponent for weakening of 10-50 kJ/mol and 55-150, respectively, compatible with subcritical crack growth and inter-granular flow in the active slip zone. Activation energies for the time-dependent healing process in the range 90-130 kJ/mol in dry conditions and 20-65 kJ/mol in wet conditions indicate the prominence of viscoelastic collapse of micro-asperities in the absence of water and of pressure-solution creep, crack healing, and cementation when assisted by pore fluids.