Unconventional singularities and frictional rupture energy budget

A widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. In ordinary cracks, near rupture edge fields feature a conventional square root singularity, accompanied by an associated edge-localized energy balance. It has been recently demonstrated that this analogy holds to a very good approximation, yet that overall rupture (earthquake) energy budget includes also a significant non-edge-localized excess frictional dissipation, which is predicted to vanish in the crack analogy. We develop a macroscopic theory that address these puzzling observations and fully resolves the apparent contradiction. The theory identifies a "hidden" small parameter, which quantifies the deviation from a conventional singular behavior of near-edge fields, and predicts non-edge-localized excess frictional dissipation that is dominated by an accumulated spatially-extended contribution. The latter, which is also position dependent, is associated with the generic rate-dependent nature of friction and compensates the aforementioned smallness. The theoretical predictions are quantitatively supported by available numerical results, and their possible implications for earthquake physics are discussed.