Numerical method for the determination of contact areas of a rock joint under normal and shear loads

Abstract

A numerical method to determine the contact areas of a rock joint under normal and shear loads is proposed. The method requires only three-dimensional surface coordinates at the initial stage before shearing, while some disparate materials are inserted between the joint surfaces or particular equipments are adopted for measurement of the contact areas during the test in other conventional methods. The joint surface is modeled as a group of triangular planes, and the contact condition of each plane is examined by calculating the relative displacements of both surfaces from their initial locations. To verify the method, a direct shear test on a rock joint was simulated using a bonded particle model in a discrete element code. The locations of the contact areas observed in the simulation showed good agreement with those determined using the proposed method. To characterize the roughness of the joint surface including the contact area, the concept of active and inactive micro-slope angle was defined based on the apparent inclination of the triangular element to the shear direction. To apply these techniques, the experimental results of shear tests on replicas of rock joints were analyzed for the location, size and micro-slope angle of contact areas according to the following shearing stages: prepeak, peak, post-peak and residual. The locations of the contact areas were closely correlated with the distribution of the micro-slope angle, which indicates that the joint roughness should be qualified with respect to the shear direction and the corresponding contact area. Additionally, the proposed method was applied to estimation of the distribution of aperture size within a rock joint.