Rock joint surface roughness is characterized by using statistical parameters and fractal parameters estimated by various methods. It was found that at least two parameters are required to quantify joint surface roughness. By limiting only to statistical parameters, an average I angle is suggested to capture the large-scale undulations (non-stationary part of roughness) and Z₂' is suggested to capture the small-scale roughness (stationary part of roughness). Fractal parameters estimated by different method were used to describe the stationary part of surface roughness. Relation between fractal dimension estimated by the divider method and roughness was investigated by introducing a new term called specific length. With the help of the specific length it was proved that even though fractal dimension is a useful parameter, it alone is not sufficient to describe roughness. Two fractal roughness parameters, K(d) and D are suggested to quantify the stationary roughness. Available box methods were found not suitable for quantification of roughness of non-self-similar profiles. Using the initial portion of the variogram function a relation between the fractal dimension and a variogram parameter is presented. It is clear that at least two variogram/fractal related parameters are needed to describe at least two variogram/fractal related parameters are needed to describe stationary roughness. The fractal dimension D and Kᵥ are suggested to quantify stationary roughness. The power spectral density function is used to obtain spectral parameters to quantify stationary roughness. The relation between the fractal dimension and a spectral parameter is given. It is shown that the fractal dimension alone is insufficient to characterize stationary roughness of non-self-similar profiles. The fractal dimension and the spectral intercept K(s) are suggested to quantify stationary roughness. Four new equations are suggested to predict peak shear strength of joints incorporating one or two aforementioned parameters to capture stationary roughness and I angle to capture non-stationary roughness. Roughness parameters should be calculated in different directions to capture the anisotropic roughness that exist in most of rock joint surfaces. The validation exercise performed showed clearly that the new equations have a good capability of predicting anisotropic peak shear strength of joints.
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