Fracture Energy and Breakdown Work During Earthquakes

Abstract

Large seismogenic faults consist of approximately meter-thick fault cores surrounded by hundreds of meter-thick damage zones. Earthquakes are generated by rupture propagation and slip within fault cores and dissipate the stored elastic strain energy in fracture and frictional processes in the fault zone and in radiated seismic waves. Understanding this energy partitioning is fundamental in earthquake mechanics to explain fault dynamic weakening and causative rupture processes operating over different spatial and temporal scales. The energy dissipated in the earthquake rupture propagation along a fault is called fracture energy or breakdown work. Here we review fracture energy estimates from seismological, modeling, geological, and experimental studies and show that fracture energy scales with fault slip. 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. ▪ Earthquake ruptures propagate on geological faults and dissipate energy in fracture and frictional processes from micro- (less than a millimeter) to macroscale (centimeters to kilometers). ▪ The energy dissipated in earthquake rupture propagation is called fracture energy ( G) or breakdown work ( Wb) and scales with coseismic slip. ▪ For earthquake ruptures in natural faults, the estimates of G and Wb are consistent with a macroscale description of causative processes. ▪ The energy budget of an earthquake remains controversial, and contributions from different disciplines are required to unravel this issue. Expected final online publication date for the Annual Review of Earth and Planetary Sciences, Volume 51 is May 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Influence of Grain‐Scale Properties on Localization Patterns and Slip Weakening Within Dense Granular Fault Gouges

“…Slip instabilities may occur if the loading stiffness of the fault K (i.e., stiffness of the loading system) is lower than $${K}_{c}$$ ($${K}_{c} > K)$$ (Scholz, 2002). The linear fitting of the weakening part of the effective friction curve may however induce errors because this weakening is sometimes governed by power laws (Abercrombie & Rice, 2005; Cocco et al., 2023). We, therefore, adopt a different approach to determine the weakening slope $${K}_{c}$$, which is related to the breakdown energy released during the slip.…”

“…This figure is modified from Cocco et al. (2023), and laboratory datasets can be downloaded at https://doi.org/10.5281/zenodo.6833943. Colors represent distinct datasets (change in the type of energy density and experimental configuration): estimates of the fracture energy G (red) by Aretusini et al.…”

“…Figure 14 shows the evolution of breakdown and fracture energy as a function of slip for laboratory experiments, from (Cocco et al., 2023), where we added our breakdown energy for numerical samples, Figure 14. Even if it is not straightforward to compare with laboratory data sets, our breakdown energy data highlighted in zone (a), perfectly fit within the range explored in laboratory experiments and are consistent with the scaling between energy and slip (Cocco et al., 2023). We can notice that the energy released by the numerical gouge samples is in between the shear fracture energy $${G}_{\mathrm{I}\mathrm{I}\mathrm{c}}$$ computed on intact rock experiments (purple) and the fracture energy G computed for stick‐slip experiments (orange).…”

“…Indeed, the breakdown energy observed in our model can be framed as mechanical energy in absence of thermal weakening, which is the contribution of: dilation energy (strain localization and fabric development during shearing) and frictional energy (contact interaction and friction between particles). Figure 14 shows the evolution of breakdown and fracture energy as a function of slip for laboratory experiments, from (Cocco et al., 2023), where we added our breakdown energy for numerical samples, Figure 14. Even if it is not straightforward to compare with laboratory data sets, our breakdown energy data highlighted in zone (a), perfectly fit within the range explored in laboratory experiments and are consistent with the scaling between energy and slip (Cocco et al., 2023).…”

A Struggled Rupture Initiation of the Mw 6.1 2009 L’Aquila Earthquake

“…We now combine the stress drop ( 𝐴𝐴 ∆𝜎𝜎 ) with the seismic efficiency ( 𝐴𝐴 𝐴𝐴 ) to estimate the total energy ( 𝐴𝐴 𝐴𝐴𝑇𝑇 ), fracture energy ( 𝐴𝐴 𝐴𝐴𝐺𝐺 ) and energy density ( 𝐴𝐴 𝐴𝐴 ′ ) using the expressions derived by Eshelby (1957) and for a circular shear crack model of constant stress drop. 𝐴𝐴 𝐴𝐴 ′ is especially useful because it allows us to compare our results with values of 𝐴𝐴 𝐴𝐴 ′ as a function of 𝐴𝐴 ∆𝑢𝑢 estimated from laboratory experiments, geological observations, modeling and seismological observations (for a review see Cocco et al, 2023):…”