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[1] 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 dc ≈ 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 Gc and the apparent weakening distance Dcapp 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 m−2 and Dcapp ≈ 20 cm. We also find that fracture energy scales with imposed slip in our experiments: Gc ∼ δ0.6.

[1] A 10-cm-thick layer of synthetic fault gouge (angular quartz sand with millimetric grains) is sheared over several meters at low confining pressures (0.1–0.5 MPa) using a ring shear apparatus (inner radius of 10 cm). The shear strength of the gouge exhibits a significant slip-weakening behavior active over decimetric slip distances. Tests on the influence of particle size, particle geometry, and boundary conditions are reported. A long-term compaction of the gouge samples is also observed but appears to be decoupled from the frictional slip weakening. At microscale, series of photographs taken during the runs enable us to follow the formation of a shear band in which most of displacements and strains localize. From image analysis we estimate the strain field in the material surrounding the shear band and show that this outer region accounts for most of the global volumetric strain. We argue that the mechanical coupling between this outer region and the shear band is responsible for the frictional slip weakening. Accordingly, the complex structure of the fault zone is shown to be crucial for its frictional behavior. Implications of our results for fault mechanics are discussed in the companion paper.