G: Fracture energy, friction and dissipation in earthquakes

Abstract

Recent estimates of fracture energy G ′ in earthquakes show a power-law dependence with slip u which can be summarized as G ′ ∝ u a where a is a positive real slightly larger than one. For cracks with sliding friction, fracture energy can be equated to G f : the post-failure integral of the dynamic weakening curve. If the dominant dissipative process in earthquakes is friction, G ′ and G f 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 G f is similar to the seismological estimates, with G f and G ′ being comparable over most of the slip range. However, G f appears to saturate after several meters of slip, while in most of the reported earthquake sequences, G ′ appears to increase further and surpasses G f at large magnitudes. We analyze several possible causes of such discrepancy, in particular, additional off-fault damage in large natural earthquakes.