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 () calculation. Subsequently, an equivalent porous medium model was developed. These components were integrated into a framework to calculate the 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.

中文翻译：

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使用创新的计算框架和和谐维数方法估计和预测三维裂缝网络的代表性单元体积


裂隙岩体的代表性单元体积（REV）对于评估等效连续体方法至关重要。提出了一种创新的计算框架和和谐维数方法来分别估计和预测 REV。这些方法被应用于道路沿线的斜坡。最初，使用无人机摄影测量数据生成高保真 3D 离散断裂网络 (DFN)。然后，将Möller-Trumbore算法和Stokes定理扩展到裂缝相交分析和强度()计算。随后，开发了等效多孔介质模型。这些组件被集成到一个框架中，以计算不同尺寸的 DFN 的等效磁导率和等效磁导率，从而确定最佳 REV。此外，基于 Levenberg-Marquardt 算法的和谐维数方法用于预测二维 (2D) 和 3D DFN 属性之间的关系。该方法经过 10 次泊松过程和 570 次渗滤模拟的验证。结果表明，REV 尺寸随水力梯度的不同而变化，凸显了 3D 裂缝介质的各向异性本质。 REV 预测可以利用 2D 参数的变化进行。所提出的框架能够准确地捕获裂隙岩体的几何和水力行为，同时降低计算成本，而和谐维数方法则简化并加速了预测。 2D3D 参数关系的新发现可以简化 DFN 建模和分析。