A new theory for the static contact between rough, unmated surfaces in non-elastically deforming rock and its implications for rock friction

Abstract

The closure behavior of fractures in marble and alabaster is markedly different from that in quartzite. The aperture decreases considerably more under normal stress and remains permanently reduced, for the same ratio of normal stress to unconfined compressive strength. Also, a larger permanent relative contact area develops between the surfaces of marble and alabaster than it does between surfaces of quartzite. The permanent contact area increases at an increasing rate with normal stress in marble and alabaster, unlike the nearly linear increase in quartzite. The failure of surface asperities of calcite and gypsum during closure accounts for these differences. We modeled this process by considering the surfaces to consist of paraboloids lying on a flat plane and having a range of initial heights. Closure occurs by pressing a plane rigid surface against the ‘hills’, flattening their peaks, keeping the base area of the hills constant. To allow for a changing resistance to deformation, the contact stress is assumed to vary linearly with the shortening strain, to a first approximation. This model was tested against measurements of fracture closure and contact area of rough surfaces of calcite marble with a known initial height distribution of surface peaks. The fit to the data is quite good. In all cases, the model shows that closure is accompanied by a decrease in contact strength of deforming asperities, suggested also by the cataclastic deformation observed petrographically. The number of contact spots and the total length of contact seen in profile are also reasonably well modeled. These results have important implications for our understanding of frictional strength of fractures. The overall resistance to shear along rough surfaces depends upon the product of the shear strength and true area of the contacts, both of which are affected by normal stress. Application of this model approach shows that the initial frictional resistance of some fractures in ductile rocks can be directly related to the topographic characteristics of the surfaces and the rheological properties of the asperities.