Modified 2D roughness parameters for rock joints at two different scales and their correlation with JRC

To overcome the drawbacks of the existing two-dimensional (2D) roughness parameters, this paper proposes two parameters to characterise the roughness of rock joints. One is used to represent the local features of the joint profiles, and the other is used to characterise the overall features. The proposed local 2D parameter θ2d can provide an alternative approach and facilitate the characterisation of the roughness of the joint rock surface when a three-dimensional measuring apparatus is unavailable. This parameter is calculated using 10 standard joint roughness coefficient (JRC) profiles, and the value of θ2d does not increase monotonically with an increase in the JRC. The results suggest that θ2d can reflect the local waviness but fails to describe the overall features of the profiles. Another parameter, h1, is introduced to consider the overall features of the profiles. A new equation for the JRC is derived by combining the small- and large-scale roughness parameters. Predictions based on the new equation are compared with the experimental data, and the results indicate the applicability of the new equation.