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Abstract

We develop a simple fracture mechanics model for the stable growth of a penny-shaped shear crack under friction. We assume equilibrium between released strain energy and frictional energy and suggest a stability criterion that combines the tip stress intensity in fracture mechanics with the threshold criterion of frictional strength in a Coulomb failure approach. Fracture growth causes a slow but steady buildup of stress. On a larger fault, patches of increased shear stress may develop with the time to failure and the size of the patch depending on the background stress and the constitutive relations. The model predicts a self-regulating feedback loop that keeps stress intensity low until a strength threshold is exceeded at the point of high stress. At this point, instability occurs and a rupture nucleation phase may start culminating in a co-seismic rupture. The available fracture energy scales with the third power of the fracture length, while the slip on the fracture is a linear function of the fracture length. The new model may explain how a slow preparatory phase transitions into rupture nucleation. It suggests that large earthquakes tend to develop on faults with intermediate stress levels. Faults with very low stress may not produce stress asperities and remain stable, while faults with very high stress tend to produce smaller earthquakes after a short preparation period.