Equivalent mechanical parameters and representative elementary volume of rock masses material using a modified fabric tensor

The roughness and spatial distribution of fractures are fundamental to the study of the equivalent strength and deformation characteristics of complex fractured rock masses. Traditional fabric tensor models often approximate fractures as planar surfaces, which introduces certain limitations, while natural fractures typically exhibit rough and undulating surfaces. Thus, this study improves upon the existing fabric tensor model and develops a method for calculating the mechanical parameters of rough discrete fracture networks (RDFN). Besides, example models are constructed to accurately quantify fracture roughness, and a comparative analysis is conducted between planar discrete fracture networks (DFN) and RDFN. According to the research results, the RDFN model generating by the W-M fractal function, exhibits significant roughness characteristics. Compared to the DFN model, the inherent roughness of RDFN significantly affects the equivalent elastic mechanical parameters, with an influence ranging from 5% to 15%. Further, the numerical solutions of the simple model closely match the analytical solutions, with minimal error. While the increase in fracture roughness significantly influences the mechanical properties, it has a relatively small impact on the representative elementary volume (REV) of the rock mass. The findings provide valuable insights into the analysis of the equivalent behavior of fractured rock masses with rough fractures.