Effect of dilatancy on the transition from aseismic to seismic slip due to fluid injection in a fault

Aseismic crack growth upon activation of fault slip due to fluid injection may or may not lead to the nucleation of a dynamic rupture depending on in-situ conditions, frictional properties of the fault and the value of overpressure. In particular, a fault is coined as unstable if its residual frictional strength $\tau_r$ is lower than the in-situ background shear stress $\tau_o$. We study here how fault dilatancy associated with slip affect shear crack propagation due to fluid injection. We use a planar bi-dimensional model with frictional weakening and assume that fluid flow only takes place along the fault (impermeable rock {/ immature fault}). Dilatancy induces an undrained pore-pressure drop locally strengthening the fault. We introduce an undrained residual fault shear strength $\tau_r^u$ (function of dilatancy) and show theoretically that under the assumption of small scale yielding, an otherwise unstable fault ($\tau_r