Seismic cycles in a DEM simulated granular gouge layer: influence of the loading stiffness

The contemporary model for tectonic earthquakes is based on the interplay between the frictional rheology of a potentially seismic fault and the electrodynamics of the surrounding medium. More specifically, it has been shown in many experimental and theoretical studies that a necessary condition for unstable sliding events on a fault is a weakening rate larger than the unloading stiffness of the surrounding rocks. By weakening rate, we refer here to the decrease of the resisting shear stress (i.e. of the instantaneous friction coefficient) with sliding. Conversely, by loading stiffness, we refer to the decrease of the loading shear stress with sliding.

 

We investigate the role and effect of the loading stiffness on the seismic cycles of a simulated granular fault. For this purpose, we build a numerical model based on the Discrete Element Method (DEM), inspired by laboratory experiments on fault gouge. In contrast to a typical DEM fault models, we employ an elastic loading system with user-controlled shear stiffness. We show that the coupling between fault granular rheology and country rock elasticity leads to seismic cycles with properties that are strongly influenced by their ratio. Stiff faults produce frequent contractional events with limited sliding distances and low to moderate stress drops, while soft faults produce rare dilatational events with large sliding distances and stress drops. Statistical distributions of events are extracted, and empirical scaling laws for the role of fault stiffness on these distributions are proposed.

 

We show that, on average, simulated events are well-described by a simple linear slip-weakening friction law, but that the weakening rate that best describes the events is tightly coupled with the loading stiffness. This contradicts the idea of an intrinsic friction law for the granular gouge layer and demonstrates the need to consider a fault as a tribosystem coupling the scale of the contact junction within the granular gouge and of the elastic surrounding medium. We conclude that, even in a highly-simplified model where the gouge layer is represented by a limited number of circular grains, there is no such thing as a “friction law” describing the behaviour of the interface. Rather, friction is a multiscale emerging property of the whole tribosystem defined by the interface and the elastic properties of the surrounding medium, as well as the past sliding history of the fault patch.