Energy budget and propagation of faults via shearing and opening using work optimization

Abstract

We present numerical models of faults propagating by work optimization in a homogeneous medium. These simulations allow quantification and comparison of the energy budgets of fault growth by shear versus tensile failure. The energy consumed by growth of a fault, Wgrow, propagating by in-line shearing is 76% of the total energy associated with that growth, while 24% is spent on frictional work during propagation. Wgrow for a fault propagating into intact rock by tensile failure, at an angle to the parent fault, consumes 60% of the work budget, while only 6% is consumed by frictional work associated with propagation. Following the conservation of energy, this leaves 34% of the energy budget available for other activities and suggests that out-of-plane propagation of faults in Earth's crust may release energy for other processes, such as permanent damage zone formation or rupture acceleration. Comparison of these estimates of Wgrow with estimates of the critical energy release rate and earthquake fracture energy at several scales underscores their theoretical similarities and their dependence on stress drop.