Earthquake Source Processes inferred from a 6-meter-long laboratory fault (2): Fracture Energy Estimation from Dynamic Stress Fields

Fracture energy is a key scaling parameter governing the transition from quasi-static nucleation to dynamic rupture propagation, and it also controls the dynamic stress field around the rupture front. In principle, when fracture energy is uniform along a fault, a single intrinsic fracture energy should describe both quasi-static nucleation and the stress field during rupture propagation. However, this unifying role has not been fully validated experimentally, primarily because conventional laboratory faults are too small to capture the entire rupture process from nucleation to propagation toward limiting speed. Here, we compare the fracture energy evaluated from the shear stress changes associated with the dynamic rupture propagation (Γ) with that inferred from the independently observed critical nucleation length (G^Lc) on a 6-meter-long laboratory fault.

We conduct faulting experiments on a 6-meter-long laboratory fault and evaluate fracture energy by fitting a steady-state rupture model with a linear cohesive zone to local shear stress changes recorded 15 mm away from the fault. In the biaxial rock-friction apparatus, vertically stacked rock specimens form a simulated fault with dimensions of 6 m × 0.5 m. Six independently controlled jacks applying normal loading enable rupture nucleation at prescribed timing and location by unloading a selected jack while maintaining the shear stress near the peak frictional strength. Rupture velocity is constrained by cross-correlating shear stress histories between neighboring strain gauges spaced at 130 mm. Using the locally estimated rupture velocity, fracture energy Γ and cohesive zone size are determined by minimizing the residual between observed and modeled shear stress time histories.

Fracture energy inferred from critical nucleation length, G^Lc, is computed following the formulation of Palmer and Rice (1973) and Andrews (1976), using the critical nucleation length examined by Matsumoto et al. (2026, EGU) togather with the measured stress drops.

We analyze three nucleation-controlled events conducted under a macroscopic normal stress of 3 MPa. From local shear stress time histories associated with rupture velocities lower than 0.95 of the Rayleigh wave speed, we obtained an average fracture energy Γ of 0.04 ± 0.01 J/m². This value is consistent with G^Lc of 0.05 J/m², inferred from events with an average stress drop of 0.05 MPa. These results contribute to the quantitative interpretation of laboratory observations and to improved understanding of earthquake source processes on natural faults.