Quantitative three-dimensional description of a rough surface and parameter evolution with shearing

Abstract

The choice of a general criterion to determine the shear strength of rough rock joints is a topic that has been investigated for many years. The major problem is how to measure and then to express the roughness with a number (e.g., joint roughness coefficient) or a mathematical expression in order to introduce the morphology of the joint into a shear strength criterion. In the present research a large number of surfaces have been digitised and reconstructed using a triangulation algorithm. This approach results in a discretisation of the joint surface into a finite number of triangles, whose geometric orientations have been calculated. Furthermore, during shear tests it was observed that the common characteristic among all the contact areas is that they are located in the steepest zones facing the shear direction. Based on this observations and using the triangulated surface data , it is possible to describe the variation of the potential contact area versus the apparent dip angle with the expression A θ * = A 0 [( θ max * − θ * )/ θ max * ] C , where A 0 is the maximum possible contact area, θ max * is the maximum apparent dip angle in the shear direction, and C is a “roughness” parameter, calculated using a best-fit regression function , which characterises the distribution of the apparent dip angles over the surface. The close agreement between analytical curves and measured data therefore suggests the possibility of defining the influence of roughness on shear strength by the simple knowledge of A 0 , C and θ max * . Based on the samples studied here, the values of these parameters capture the evolution of the surface during shearing. Moreover, they tend to be characteristic for specific rock types, indicating that it might be possible to determine ranges for each rock type based on laboratory measurements on representative samples.