Dilatant strengthening as a mechanism for slow slip events

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 φ evolves toward steady state φ_ss over distance d_c and φ_ss = φ₀ + ε ln(v/v₀); v is slip speed. We consider two diffusion models. Membrane diffusion (MD) is approximated by -(p - p^∞)/t_f where p and p^∞ 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 ε = 1 - a/b between slow and fast slip, where ε ≡ f ₀ε/βb(σ - p^∞), f₀, a, and b are friction parameters and β is compressibility. When ε < 1 - a/b slip accelerates to instability for sufficiently large faults, whereas for ε > 1 - a/b slip speeds remain quasi-static. For HD, E_p εh/( β(σ - p^∞)√v^∞/c _hydd_c) defines dilatancy efficiency, where h is shear zone thickness and v^∞ is plate velocity. SSE are favored by large εh and low effective stress. The ratio E_p to thermal pressurization efficiency scales with 1/(σ - p^∞), so high p^∞ favors SSE, consistent with seismic observations. For E_p ∼ 10^-3 transient slip rates, repeat times, average slip, and stress drops are comparable to field 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 accommodate only a fraction of plate motion; the remaining deficit must be accommodated during coseismic or postseismic slip.