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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 (IR), 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 IR 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) IR values of the discontinuities are illustrated through several applications. Results show that the 2D and 3D IR values of these discontinuities indicate anisotropy and sampling interval effects. In addition, a strong linear correlation is detected between IR 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 (Z2) method, and Grasselli’s method are compared to study the use of the parameter IR.

Scanline observation is known to introduce an angular bias into the probability distribution of orientation in three-dimensional space. In this paper, numerical solutions expressing the functional relationship between the scanline-observational distribution (in one-dimensional space) and the inherent distribution (in three-dimensional space) are derived using probability theory and calculus under the independence hypothesis of dip direction and dip angle. Based on these solutions, a novel method for obtaining the inherent distribution (also for correcting the bias) is proposed, an approach which includes two procedures: 1) Correcting the cumulative probabilities of orientation according to the solutions, and 2) Determining the distribution of the corrected orientations using approximation methods such as the one-sample Kolmogorov-Smirnov test. The inherent distribution corrected by the proposed method can be used for discrete fracture network (DFN) modelling, which is applied to such areas as rockmass stability evaluation, rockmass permeability analysis, rockmass quality calculation and other related fields. To maximize the correction capacity of the proposed method, the observed sample size is suggested through effectiveness tests for different distribution types, dispersions and sample sizes. The performance of the proposed method and the comparison of its correction capacity with existing methods are illustrated with two case studies.Rockmass is a discrete medium composed of rock material and discontinuities including faults, fractures, joints, veins, bedding planes, cleavage planes, and schistosity planes, among others. Such discontinuities dominate the kinematical and mechanical behaviour of engineering rockmass [1][2][3][4][5] , with the analysis of this behaviour extending to various applications in such areas as rockmass stability evaluation, rockmass permeability analysis, rockmass quality calculation and other related fields, using three-dimensional rockmass models frequently generated via discrete fracture network (DFN) modelling with input geometrical variables including orientation [6][7][8][9][10][11][12][13][14][15] . These orientations are primarily measured on fresh rock exposures, with previous studies reporting various representative techniques [16][17][18][19]