G: Fracture energy, friction and dissipation in earthquakes

Recent estimates of fracture energy G′ in earthquakes show a power-law dependence with slip u which can be summarized as G′ ∝ ua where a is a positive real slightly larger than one. For cracks with sliding friction, fracture energy can be equated to Gf: the post-failure integral of the dynamic weakening curve. If the dominant dissipative process in earthquakes is friction, G′ and Gf should be comparable and show a similar scaling with slip. We test this hypothesis by analyzing experiments performed on various cohesive and non-cohesive rock types, under wet and dry conditions, with imposed deformation typical of seismic slip (normal stress of tens of MPa, target slip velocity > 1 m/s and fast accelerations ≈ 6.5 m/s2). The resulting fracture energy Gf is similar to the seismological estimates, with Gf and G′ being comparable over most of the slip range. However, Gf appears to saturate after several meters of slip, while in most of the reported earthquake sequences, G′ appears to increase further and surpasses Gf at large magnitudes. We analyze several possible causes of such discrepancy, in particular, additional off-fault damage in large natural earthquakes.