Frictional response induced by time-dependent fluctuations of the normal loading

We study the effect of time-variable normal stress perturbations on a creeping fault which satisfies a velocity-weakening rate- and state-dependent friction law and is slipping at constant speed. We use the spring-block model and include the effect of inertia. To account for the variable normal stress, we use the description introduced by Linker and Dieterich [1992], which links normal stress fluctuations to changes of the state variable. We consider periodic perturbations of the normal stress in time las caused, for instance, by tides) and compare the behavior for two commonly used friction laws (the "slip" and the "ageing" laws). Their mechanical response is shown to be significantly different for normal stress fluctuations. It could be used to probe these two laws during laboratory friction experiments. We show that there is a resonance phenomenon, involving strong amplification of the shear and velocity response of the interface, when the spring stiffness is modestly above its critical value (or when, at a given stiffness, the normal stress is modestly below its critical value). We show that such an amplification is also observed when periodic fluctuations of the shear loading are considered, making the resonance phenomenon a general feature of the response of a near-critical creeping surface to periodic fluctuations of the external loading. Analytical solutions are based on a linear expansion for low amplitude of normal or shear stress variations and are in very good agreement with numerical solutions. A method to find the evolution of friction in the case of an arbitrary perturbation of the normal stress is also presented. The results show that a creeping fault may be destabilized and enter a stick-slip regime owing to small normal stress oscillations. This may also account for a mechanism for the generation of "creep bursts." However, these phenomena require very specific parameter ranges to excite the resonance, which may not be met very generally in nature. This study illustrates the importance of the normal stress fluctuations on stable sliding and suggests further friction laboratory experiments.