ROCK JOINT ROUGHNESS QUANTIFICATION USING 2D AND 3D FRACTAL METHODS

In this study, two-dimensional (2D) fractal parameters ([Formula: see text] and [Formula: see text] as well as [Formula: see text] and [Formula: see text] calculated through the roughness length, and variogram methods, and a three-dimensional (3D) fractal parameter, [Formula: see text] 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 [Formula: see text] and [Formula: see text] (variogram method). A significant effect of heterogeneity was found on all the computed 2D and 3D fractal roughness metrics; irrespective of the [Formula: see text] value, the [Formula: see text](0–500[Formula: see text]mm) section of the joint surface was found to be relatively homogeneous with a low level of roughness while the [Formula: see text](750–1000[Formula: see text]mm) 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 [Formula: see text] and [Formula: see text] for all investigated profiles while [Formula: see text] and [Formula: see text] values showed negligible joint size effect and small joint size effect for profiles in the [Formula: see text] and [Formula: see text] 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 [Formula: see text] 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.