Development of a novel 3D roughness index with an explicit physical-mechanical meaning for quantifying the roughness of rock joints

A roughness index with an explicit physical-mechanical meaning will improve the shear strength estimation model of rock joints. Based on the macroscopic shear mechanical behaviours of rock joints， this study analysed the microscopic shear failure mechanisms of rock joints. Subsequently， through rigorous mechanical and mathematical derivation， a new three-dimensional （3D） roughness index， θ_3D， that quantitatively characterizes the average inclination angle of a rock joint surface was established. θ_3D is closely related to the shear strength of rock joints and has an explicit physical-mechanical meaning. Six rock joint specimens with different lithologies and roughness characteristics were selected for roughness analysis. Through comparative analysis with four other 3D roughness indices， the results demonstrated that θ_3D can well characterize the roughness of rock joints and reflect the anisotropic properties of joint roughness. Additionally， the effects of sampling interval and joint scale on joint roughness are discussed in this paper， and the results of this study can provide a reference for related research.