Calculation Method of Permeability Tensor Based on the Size Effect and Anisotropy of Rock Fracture Surface Roughness

The roughness correction factor ( C ) mentioned in the cubic law correction formula is a parameter that reflects the roughness characteristics. In this study, high precision three‐dimensional (3D) scanning was used to scan natural rock samples, and both analytical and numerical simulation methods were employed to investigate the size effect and anisotropy of the C . The results show that C exhibits both size effects and anisotropy. Through ellipse fitting analysis, it was found that the C can be expressed in tensor form. Based on this, a new method for representing the permeability tensor is proposed by combining the roughness correction tensor and the average aperture. By comparing experimental results from 3D printed models, traditional cubic law, corrected cubic law, and Navier–Stokes (N–S) equation simulations, it is demonstrated that the roughness correction tensor, in conjunction with the average aperture, can effectively quantify the permeability characteristics of complex rough fractures. This provides a new quantitative approach for single‐fracture flow studies.