Study on Effect of Scaling and Anisotropy on Roughness of Natural Fractured Rock Surfaces

In the modified formula for the cubic law, the roughness correction coefficient C serves as a parameter that indicates the characteristics of the roughness of a rock’s surface. In this study, surface data for natural rock samples were acquired through high-precision 3D scanning and combined with publicly accessible CT scan data on rough rock fractures to generate spatial coordinates. The roughness correction coefficient C was calculated and analyzed using both formulaic and numerical methods. The analysis revealed significant effects of scale on the roughness correction coefficient for rock fractures within a size range of 5 to 10 cm (determined based on the actual sample size), with tensile fractures demonstrating greater variations compared to shear fractures. When calculating the roughness correction coefficient on the same fracture surface in different directions, significant directional effects were observed. Furthermore, elliptical fitting demonstrated favorable results. The conclusion drawn was that the roughness correction coefficient for fracture surfaces can be represented effectively using a tensor form, thereby simplifying the expression of directionality. Calculating and analyzing the fractal dimension of a rough surface further confirmed the existence of effects of size on roughness.