On the scale dependence in the dynamics of frictional rupture: constant fracture energy versus size-dependent breakdown work

Potential energy stored during the inter-seismic period by tectonic loading around faults is released during earthquakes as radiated energy, heat and fracture energy. The latter is of first importance since it controls the nucleation, propagation and arrest of the seismic rupture. On one side, fracture energy estimated for natural earthquakes (breakdown work) shows a clear slip-dependence. On the other side, recent experimental studies highlighted that, fracture energy is a material property limited by an upper bound value corresponding to the fracture energy of the intact material independently of the size of the event. To reconcile these contradictory observations, we performed stick-slip experiments in a bi-axial shear configuration. We analyzed the fault weakening during frictional rupture by accessing to the near-fault stress-slip curve through strain gauge array. We first estimated fracture energy by comparing the measured strain with the theoretical predictions from Linear Elastic Fracture Mechanics and a Cohesive Zone Model. By comparing these values to the breakdown work obtained from the integration of the stress-slip curve, we show that, at the scale of our experiments, fault weakening is divided into two stages; the first one consistent with the estimated fracture energy, and a long-tailed weakening corresponding to a larger energy not localized at the rupture tip, increasing with slip. Through numerical simulations, we demonstrate that only the first weakening stage controls the rupture initiation and that the breakdown work induced by the long-tailed weakening can enhance slip during rupture propagation and allow the rupture to overcome stress heterogeneity along the fault. We conclude that the origin of the seismological estimates of breakdown work could be related to the energy dissipated in the long-tailed weakening rather than to the one dissipated near the tip.