Frictional response of a thick gouge sample: 2. Friction law and implications for faults

On the basis of experimental results, we propose a new friction law aiming at describing the mechanical behavior of thick gouge layers. As shown in the companion paper, the dominant effect to take into account is a significant slip-weakening process active over decimetric slip distances. This slip weakening is strongly nonlinear and, formerly, does not involve any characteristic length scale. The decrease of the gouge friction coefficient m with imposed slip d is well modeled by a power law: m = m0 + adb, with b = 0.4. On this major trend are superimposed second-order velocity-weakening and time-strengthening effects. These effects can be described using classical rate- and state-dependent friction (RSF) laws and are associated with a small length scale dc 100 mm. Consistent with the general RSF framework, we combine slip-weakening and second-order effects in a slip, rate, and state (SRS) friction law with two state variables. We then compute the fracture (or breakdown) energy Gc and the apparent weakening distance Dc app associated with the slip-weakening process. Once extrapolated to realistic geophysical' confining pressures, the obtained values are in excellent agreement with those inferred from real earthquakes: Gc 5 106 J m2 and Dc app 20 cm. We also find that fracture energy scales with imposed slip in our experiments: Gc d0.6.