Experimental and modeling insights into fault stick-slip behavior under dynamic normal stress condition

As the key mechanism of shallow earthquakes, the fault stick-slip behavior is usually explored under the assumption of constant normal stress. However, dynamic natural processes (tides, far-field earthquakes, etc.) and human activities (blasting, water injection, mining, etc.) generate periodic stress disturbances in the fault zone. So far the coupled results of fault seismic slips under variable normal stress are poorly understood.

We performed laboratory direct shear tests on saw-cut granite joints under constant and cyclic normal stress (σ_n), considering the role of load point velocity (V_lp), normal stress oscillation amplitude (ε) and normal stress oscillation frequency (f). Under constant normal stress, the joint exhibits a spontaneous stick-slip phenomenon for different V_lp. The shear stress drops and recurrence timespans of stick-slip events are reduced with faster V_lp. Under equivalent σ_n level, the cyclic σ_n weakens the frictional strength when V_lp is small and enhances the strength when V_lp is large. As ε grows, the joint slip style switches from regular stick-slip to chaotic slip, and eventually to compound stick-slip. The frictional strength is first increased and later weakened. In respect to effect of f: when f is small, one σ_n cycle can produce several stick-slip events. When f is medium, the period of the stick-slip event is equal to the cyclic σ_n period. For further increase of f , the recurrence period of stick-slip events becomes double the cyclic σ_n period. The frictional strength is decreasing or increasing at the critical point for frictional resonance.

The improved spring-block model equipped with rate-and-state friction framework matches the lab observations satisfactorily. Especially, the introduction of a stiffness response coefficient (Ψ) allows the model to reflect realistic fault frictional behavior, where shear stiffness varies with σ_n. A new parameter Θ is defined whose symbol (+ or -) directly determines the compression/relaxation status of the spring, and satisfactorily explains transitions in shear stress trends. Comparative analysis with the conventional Linker-Dieterich model highlights the improved physical consistency of our new approach, particularly in preserving the physical interpretation of the state variable, θ. The model also demonstrates that under large σ_n disturbances, a frictional system can effectively exhibit stick-slip behavior even in the velocity-strengthening scope. More importantly, the modeling implies that fast slip events greatly reduce the contact density of the fault interface. The contact state of the stick-slip joint/fault cannot be judged solely by σ_n. The contact area during the shear process is determined by both, the real-time σ_n level and the state variable θ.