A granular numerical model for the friction and wear of a lab-scale fault asperity

Seismic faults are often represented using two different and self-excluding conceptual models. In the first representation, seismic faults are seen as the interface between two surfaces of bare rock, with a roughness extending at all scales. These surfaces interact mechanically through a certain number of “asperities” which constitute the “real contact area”. When adopting this view, attention is paid on the statistics of the asperities population in the fault plane. Faults are thus considered as 2D objects, since their thickness is disregarded. In the second representation, seismic faults are seen as mathematical planes separated by a certain thickness of granular gouge created by abrasive wear of the surfaces during previous slips. This view is analogous to the tribological “third body” theory, and is supported by field observations and experimental evidences of gouge creation in rotary shear and triaxial experiments. It is convenient to adopt this perspective when weakening phenomena within the gouge are to be spatially resolved in the direction orthogonal to the fault plane. Variations along this plane are then ignored, as well as fault roughness, and faults are mostly seen as 1D objects. Unification of these two representations requires a better understanding of the interactions between geometrical asperities and a layer of gouge, and in particular of the phenomena that lead to the creation of the latter through the wear of the former. In this communication, we present a numerical model which aims at reproducing lab tests of millimetric single-asperity friction and wear. The model is essentially granular in order to represent the progressive degradation of the asperity along sliding, the separation of powdery matter, its successive ejection and reinjection by the contact (thanks to a periodicity in boundary conditions), and the build-up of a gouge layer. It also includes a coupling with continuum mechanics in order to maintain a meaningful stress field in the asperity beyond the region of degradable rock. Numerical results show that: (i) the rate of wear of the asperity and the counterface are directly linked to the normal load applied to the contact; (ii) an established layer of gouge develops in the interface and controls the friction coefficient; (iii) a constant level of surface roughness is established after a sufficient sliding distance, both for the asperity and the counterface; (iv) an accurate control of the asperity boundary conditions is necessary in order to obtain repeatable friction and wear. These results are a first step towards a better understanding of the wear kinetics as a function of asperity geometry, load, and roughness, before the introduction of thermal aspects (including melting) in a future version of the model.