Fracture energy and breakdown work scaling with coseismic slip

Geological observations reveal that earthquakes nucleate, propagate, and arrest in complex fault zones whose structural heterogeneity depends on the tectonic loading, geometry, lithology, rheology, presence of fluids, and strain localization processes. These fault zones can host a wide range of fault slip behaviors (e.g., creep, aseismic- and slow-slip events, afterslip, and earthquakes). This implies that the environment in which earthquakes occur is diverse, and that different physical and chemical processes can be involved during the coseismic dynamic rupture.

Earthquakes are generated by rupture propagation and slip within fault cores and dissipate the stored elastic and gravitational strain energy in fracture and frictional processes in the fault zone (from microscale - less than a millimeter - to macroscale - centimeters to kilometers) and in radiated seismic waves. Understanding this energy partitioning is fundamental in earthquake mechanics to describe dynamic fault weakening and causative rupture processes operating over different spatial and temporal scales.

The energy dissipated in earthquake rupture propagation is commonly called fracture energy (G) or breakdown work (W_b). Here we discuss these two parameters, and we review fracture energy estimates from seismological, modeling, geological, and experimental studies and show that fracture energy scales with fault slip and earthquake size. Our analysis confirms that seismological estimates of fracture energy and breakdown work are comparable and scale with seismic slip. The inferred scaling laws show modest deviations explained in terms of epistemic uncertainties. The original collection of fracture energy estimates from laboratory experiments confirms the scaling with slip over a slip range of more than 10 decades. Fracture energy associated with breaking of intact rocks is larger than for precut specimens and might suggest differences between the role of fracture and friction, or a different size of the rupture front zone. It is important to recall that fault products after deformation in the laboratory correspond to fault products observed in nature, and acoustic emissions recorded in the laboratory can be processed as seismic waves on a natural fault. We conclude that although material-dependent constant fracture energies are important at the microscale for fracturing grains of the fault zone, they are negligible with respect to the macroscale processes governing rupture propagation on natural faults.

In this study we discuss the scaling of fracture energy and breakdown work with slip, and we propose different interpretations relying on different processes characterizing complex fault zones. Our results suggest that, for earthquake ruptures in natural faults, the estimates of G and Wb are consistent with a macroscale description of the causative processes.

Reconciling observations and results from laboratory experiments and numerical modeling with geological observations can be done, provided that we accept the evidence that earthquakes can occur in a variety of geological settings and fault zone structures governed by different physical and chemical processes.