Estimation and prediction of the representative elementary volume of three-dimensional fracture networks using an innovative computational framework and a harmony dimension method

The representative elementary volume (REV) of a fractured rock mass is crucial for evaluating the equivalent continuum approach. An innovative computational framework and a harmony dimension method were proposed to estimate and predict the REV, respectively. These methods were applied to a slope along a road. Initially, a high-fidelity 3D discrete fracture network (DFN) was generated using data from unmanned aerial vehicle photogrammetry. Then, the Möller–Trumbore algorithm and Stokes' theorem were extended for fracture intersection analysis and intensity (P₃₂) calculation. Subsequently, an equivalent porous medium model was developed. These components were integrated into a framework to calculate the P₃₂ and equivalent permeability of DFNs of varying sizes, thus determining the optimal REV. Additionally, the harmony dimension method, based on the Levenberg–Marquardt algorithm, was used to predict the relationship between two-dimensional (2D) and 3D DFN properties. This method underwent validation with 10 Poisson processes and 570 percolation simulations. The results show that REV sizes vary with different hydraulic gradients, highlighting the anisotropic nature of 3D fractured media. REV predictions can be made using the variability of 2D parameters. The proposed framework accurately captures geometric and hydraulic behaviors of fractured rock masses with reduced computational cost, while the harmony dimension method simplifies and accelerates prediction. The novel finding of the 2D3D parameter relationship can streamline DFN modeling and analysis.