A Method for Estimating the Surface Roughness of Rock Discontinuities

The primary objective of this study is to develop a parameter with a clear physical meaning to estimate the surface roughness of rock discontinuities. This parameter must be closely related to the shear strength of rock discontinuities. The first part of this study focuses on defining and computing this parameter. The estimation formula for the shear strength of a triangle within a discontinuity surface is derived based on Patton’s model. The parameter, namely, the index of roughness ( ), is then proposed to quantitatively estimate discontinuity roughness. Based on laser scanning techniques, digital models of discontinuities and discontinuity profiles are constructed, and then their corresponding values are computed. In the second part of this study, the computational processes and estimated effects of the two-dimensional (2D) and three-dimensional (3D) values of the discontinuities are illustrated through several applications. Results show that the 2D and 3D values of these discontinuities indicate anisotropy and sampling interval effects. In addition, a strong linear correlation is detected between and the joint roughness coefficient (JRC) for seventy-four profiles and eleven discontinuity specimens, respectively. Finally, the proposed method, back analysis method, root mean square ( ) method, and Grasselli’s method are compared to study the use of the parameter .