Approach to characterize rock fracture surface: Insight from roughness and fractal dimension

The characterization of rock fracture is essential for revealing and understanding the fracture mechanism. In this research, the fracture of sandstone is characterized from the perspective of the 3D morphology of fracture surface. The 3D morphology is quantified by two fractal dimension (D) calculation methods: cubic covering method (CCM) and surface area method (SAM). The applicability of both methods is verified by two special cases of which one is a 2D plane and another one is a novel surface model with a dimension of 3. However, in actual application, one shortcoming of the CCM rooted in the algorithm is exposed, which introduces a distorted D for the surface with a small degree of undulation. On the contrary, relying on a new algorithm proposed to calculate the fracture surface area, the SAM can completely avoid the distortion problem. Based on the SAM, the 3D morphologies of a series of fracture surfaces of sandstone in the conventional triaxial test are quantified. It is observed that D has a strong correlation with the fracture mechanism. With the transition of failure mechanism from tension fracture to shear fracture, D presents a decreasing trend. The reason underlying this correlation is analyzed. In Discussion, several improved CCMs are introduced, and whether the improvements have solved the distortion problem is assessed. The accuracy of the SAM is also evaluated using the Takagi fractal surfaces.