A study of the relationship between two-dimensional and three-dimensional roughness parameters

The roughness of rock discontinuities is a crucial parameter that influences mechanical properties. Many scholars have proposed different roughness parameters from both 2D and 3D perspectives. 3D roughness parameters capture more detailed discontinuity surface undulations, while 2D parameters remain popular due to their easier measurement and simpler calculations. However, systematic investigations into the correlations between 2D and 3D roughness parameters using the same evaluation method are notably lacking. In this study, three natural discontinuities were selected, and their point cloud data were obtained. The roughness of each discontinuity was evaluated based on three sets of parameters (\({Z^{\prime}_2}\) and \({Z^{\prime}_{23{\text{D}}}}\), \(\theta _{{max}}^{*}/{(C+1)_{2{\text{D}}}}\) and \(\theta _{{max}}^{*}/{(C+1)_{3{\text{D}}}}\), PAP_2D and PAP_3D), respectively, and the correlations of each set of parameters were analyzed. Additionally, the roughness evaluation effects of them were further studied and compared with the JRC values via direct shear tests of artificial discontinuities. The results show that: (1) Certain deviations exist between the evaluation results of 2D parameters based on local profiles and those of their corresponding 3D counterparts. (2) There is a linear correlation between the 2D parameter evaluation results using uniform profiles and the corresponding 3D parameter evaluation results, and the correlation increases with reduced profile. (3) When both the profile spacing and the point cloud point spacing reach 0.3 mm, uniform profile-based 2D roughness evaluations match 3D counterpart analyses.