A semi-theoretical method for determining the permeability tensor of fractured rock masses in three-dimensional space.

This article focuses on a novel semi-theoretical method for determining the three-dimensional (3D) permeability tensor of fractured rock masses, a key parameter for analyzing anisotropic hydraulic behavior. The method introduces the concepts of anisotropic ellipses and ellipsoids to describe permeability anisotropy based on geometric fracture information, enabling calculation of the 3D permeability tensor from only one known permeability value along any flow direction. By constructing anisotropic ellipses on three orthogonal cutting planes and combining them into an anisotropic ellipsoid, the approach circumvents the high costs and complexities of traditional field tests and numerical simulations. Numerical experiments using discrete fracture network models validated the method, showing predicted permeabilities closely match computed values with average errors below 18% on inclined planes. The method requires the rock mass size to exceed the representative elementary volume and has so far been verified only through numerical modeling, with further real-world testing needed.