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

摘要

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 μ with imposed slip δ is well modeled by a power law: μ = μ0 + αδ?β, with β = 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 d c ≈ 100 μm. 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 G c and the apparent weakening distance D c 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: G c ≈ 5 × 106 J m?2 and D c app ≈ 20 cm. We also find that fracture energy scales with imposed slip in our experiments: G c ～ δ0.6.