Non-stationarity, heterogeneity, scale effects, and anisotropy investigations on natural rock joint roughness using the variogram method

The variogram method is used to investigate the effect of non-stationarity, heterogeneity, scale-related parameters and anisotropy on roughness quantification of a natural rock joint of size 1 m × 1 m. The methodology quantifies two parameters to capture the stationary roughness. The effect of the non-stationarity of the used profiles was found to be negligible on the computed fractal parameters. Calculated fractal parameter values reflected significant heterogeneity on one part of the roughness surface compared to the rest of the surface studied in the paper. Effect of joint size was found to be negligible on the calculated fractal parameter values. The authors believe that the controversial findings appear in the literature on scale effects have resulted from roughness heterogeneity, which has not been investigated in detail in the literature in quantifying roughness. Rock discontinuity surface showed major anisotropy with respect to roughness. Roughness in the direction along the axis of ridges and troughs (X-direction) of the joint surface was found to be significantly less compared to that in the direction perpendicular to the direction of axis of ridges and troughs. Thus, it agreed with the intuition that the discontinuity resulted from a shear fracture with the main shearing direction approximately parallel to the X direction.