Research on the calculation method for equivalent elastic mechanical parameters of rock masses based on the fabric tensor

Fracture roughness and spatial distribution significantly influence the anisotropic behavior of rock masses. Traditional fabric tensor models often simplify fractures as planes, whereas natural fractures exhibit rough surfaces. This study aims to modified the existing fabric tensor and derive a detailed method for calculating the equivalent elastic mechanical parameters of rough discrete fracture networks(RDFN). By introducing fractal theory, a case model is constructed, and a comparative analysis between planar discrete fracture networks(DFN) and RDFN is conducted. To further enhance the reliability of the study, a simple model is generated using numerical software, and both analytical and numerical solutions of the model are computed. The results indicate that: (1) the modified method that considers roughness effectively mitigates the limitations of the fabric tensor. (2) The RDFN case model constructed based on the W-M fractal function exhibits significant rough characteristics, with the fractal dimension (<italic>D</italic>) and fractal roughness(<italic>G</italic>) greatly impacting the surface roughness of fractures. (3) Compared to the DFN model, the inherent roughness influences the equivalent elastic mechanical parameters of RDFN models by approximately 5% to 15%. (4) The numerical solutions of the simple numerical models closely match the analytical solutions, with minimal error, validating the accuracy of the constitutive relationship based on the modified fabric tensor. These findings provide valuable insights for analyzing the equivalent elastic behavior of rock masses with rough fractures.