Characterization of Anisotropy of Joint Surface Roughness and Aperture by Variogram Approach Based on Digital Image Processing Technique

The mechanical and hydraulic anisotropy of rock joints are strongly dependent on the surface roughness and aperture. To date, accurate quantification of the anisotropic characteristics of joint surfaces remains a key issue. For this purpose, the digital image processing (DIP) technique was used to retrieve the joint surface topography, and a variogram function was used to characterize the anisotropy of the joint surface roughness and estimate the joint aperture. A new index, SR (V) , related to both the sill and the range of the variogram is proposed to describe the anisotropy of the joint surface roughness, and a new aperture index, b, is derived to quantify the joint aperture. These newly proposed indexes, SR (V) and b, were validated by characterizing three artificial triangular joint surfaces, then the values of both SR (V) and b were calculated along 42 directions on an artificial joint surface. The range of SR (V) was between 0.058622 and 0.331283, while that of b was from 0.270433 to 0.397715 mm. The results show that the newly proposed indexes SR (V) and b are effective for quantifying the anisotropic roughness and aperture of joint surfaces, respectively. In addition, based on the hypothesis that there exists a smooth upper wall for the artificial joint, a relationship between the indexes SR (V) and b was obtained based on the data analysis. It indicates that the trends of the indexes SR (V) and b tend to coincide, although some of their individual values differ. In this respect, the hydraulic aperture of rock joints is related to not only surface roughness but also the distribution of asperities on the surface. In addition, this method can also be used to characterize the roughness of real rock joints when the joint surface is treated by dying with ink before taking digital photos. This study provides a new method for properly quantifying the directional variability of joint surface roughness and estimating the mechanical and hydraulic properties of rock joints based on the DIP technique.