Rock Joint Roughness Quantification Using 2d And 3d Fractal Methods

In this study, two-dimensional (2D) fractal parameters (DRL and A as well as Dv and Kv) calculated through the roughness length, and variogram methods, and a three-dimensional (3D) fractal parameter, Ds calculated through the 3D modified divider method were used to investigate some important factors that could influence the accurate quantification of rock joint roughness. The results showed that nonstationarity resulting from a linear trend did not have any effect on Dv and Kv (variogram method). A significant effect of heterogeneity was found on all the computed 2D and 3D fractal roughness metrics; irrespective of the X value, the Y(0–500mm) section of the joint surface was found to be relatively homogeneous with a low level of roughness while the Y(750–1000mm) section of the joint surface had a higher level of roughness. For the relatively homogeneous section, the 2D fractal parameters indicated no joint size effect. For the whole rock joint, which is somewhat heterogeneous, the results showed negligible joint size effect on DRL and A for all investigated profiles while Dv and Kv values showed negligible joint size effect and small joint size effect for profiles in the X and Y directions, respectively. Also, the results showed a significant reduction in roughness variability with an increase in joint size. A negligible effect of joint size was found on Ds for the joint surface. These findings indicated that the roughness heterogeneity is most likely the reason for the conflicting observations in the literature regarding the effect of scale on joint roughness. The studied joint surface exhibited anisotropy resulting from a shear joint.