Scale effects and spatial distribution characteristics of 3D roughness of natural rock fracture surfaces: statistical analysis

The roughness feature of a natural rock fracture surface is an important factor affecting the shear and poromechanical behavior of rock. The scale effect and spatial distribution characteristics of the fracture surface roughness are notable challenges at rock engineering sites. In this article, morphological data of a large-scale field rock fracture surface were collected using a 3D scanner. Then, the original surface was divided into several small fracture surfaces. With the use of a 2D roughness statistical index, the 2D roughness (JRC^2D) of the fracture profile was evaluated. The 3D roughness (JRC^3D) of the fracture surface along different directions was obtained via the weighted averaging method. Based on four oblique analysis schemes, the elevation statistical trend and roughness scale effect of fracture surfaces with different widths were examined. With increasing fracture size, the average elevation ( \(\mu\) $\mu$ ) and the standard deviation of elevation ( \(\sigma\) $\sigma$ ) showed different typical change patterns. The impact of size variation on the fracture surface roughness includes four types and exhibits significant anisotropy. Based on small fissure surfaces without mutual coverage, the spatial distribution characteristics of the fracture roughness were analyzed and were proven to exhibit high dispersion and anisotropy. With increasing width of the analyzed small fracture, the roughest position on the fracture surface basically remained the same, but there was a significant change in roughness anisotropy.