Dilatant Strengthening as a Mechanism for Slow Slip Events

Abstract

The mechanics of slow slip events (SSE) in subduction zones remain unresolved. We suggest that SSE nucleate in areas of unstable friction under drained conditions, but as slip accelerates dilatancy reduces pore pressure \(p\) quenching instability. Competition between dilatant strengthening and thermal pressurization may control whether slip is slow or fast. We model SSE with 2‐D elasticity, rate-state friction, and a dilatancy law where porosity \(\phi\) evolves toward steady state \(\phi_{ss}\) over distance \(d_c\) and \(\phi_{ss}=\phi_0+\epsilon ln(v/v_0)\); \(v\) is slip speed. We consider two diffusion models. Membrane diffusion (MD) is approximated by \(-(p-p^{\infty})/t_f\) where \(p\) and \(p^{\infty}\) are shear zone and remote pore pressure and \(t_f\) is a characteristic diffusion time. Homogeneous diffusion (HD) accurately models fault-normal flow with diffusivity \(C_{hyd}\). For MD, linearized analysis defines a boundary \(\epsilon \equiv 1-a/b\) between slow and fast slip, where \(\epsilon \equiv f_0 \epsilon /\beta b(\sigma-p^{\infty})\), \(f_0\), \(a\), and \(b\) are friction parameters and \(\beta\) is compressibility. When \(\epsilon < 1-a/b\) slip accelerates to instability for sufficiently large faults, whereas for \(\epsilon > 1-a/b\) slip speeds remain quasi-static. For \(HD\), \(E_p\equiv \epsilon h/(\beta (\sigma-p^{\infty})\sqrt{v^\infty / C_{hyd}d_c} )\) defines dilatancy efficiency, where \(h\) is shear zone thickness and \(v^{\infty}\) is plate viscosity. SSE are favored by large \(\epsilon h\) and low effective stress. The ratio \(E_p\) to thermal pressurization efficiency scales with \(1/(\sigma - p^{\infty})\), so high \(p^{\infty}\) favors SSE, consistent with seismic observations. Model updip propagation speeds are comparable to those observed along-strike. Many simulations exhibit slow phases driven by steady downdip slip and faster phases that relax the accumulated stress. Model SSE accomodate only a fraction of pale motion; the remaining deficit must be accommodated during coseismic or postseismic slip.