Fluid-driven slow slip and earthquake nucleation on a slip-weakening circular fault

Abstract

We investigate the propagation of fluid-driven fault slip on a slip-weakening frictional interface separating two identical half-spaces of a three-dimensional elastic solid. Our focus is on axisymmetric circular shear ruptures as they capture the most essential aspects of the dynamics of unbounded ruptures in three dimensions. In our model, fluid-driven aseismic slip occurs in two modes: as an interfacial rupture that is unconditionally stable, or as the quasi-static nucleation phase of an otherwise dynamic rupture. Unconditionally stable ruptures progress through four stages. Initially, ruptures are diffusively self-similar and the interface behaves as if it were governed by a constant friction coefficient equal to the static friction value. Slip then accelerates due to frictional weakening while the cohesive zone develops. Once the latter gets properly localized, a finite amount of fracture energy emerges along the interface. The rupture dynamics is then governed by an energy balance of the Griffith’s type. In this stage, fault slip transitions from a large-toughness to a small-toughness regime due to the diminishing effect of the fracture energy in the near-front energy balance. Ultimately, self-similarity is recovered and the fault behaves again as having a constant friction coefficient, but this time equal to the dynamic friction value. This condition is equivalent to a fault interface operating to leading order with zero fracture energy. When slow slip is the result of a frustrated dynamic instability, slip also initiates self-similarly at a constant peak friction coefficient. The maximum size that aseismic ruptures can reach before becoming unstable can be as small as a critical nucleation radius (shear modulus divided by the slip-weakening rate) and as large as infinity when faults are close to a well-defined limit that separates the two modes of aseismic sliding. In the former case, earthquake nucleation occurs unaffected by the dynamic friction coefficient. In contrast, the latter case exhibits fracture-mechanics behavior, characterized by a finite influx of elastic strain energy being supplied to and dissipated at the rupture front. We provide analytical and numerical solutions for the problem solved over its full dimensionless parameter space, including expressions for relevant length and time scales characterizing the transition between different stages and regimes. Due to its three-dimensional nature, the model enables quantitative comparisons with field observations as well as preliminary engineering design of hydraulic stimulation operations. Existing laboratory and in-situ experiments of fluid injection into simulated and natural faults are briefly discussed in light of our results.