Since the directional permeability of fractured rock masses is significantly dependent on the geometric properties of fractures, in this work, a numerical study was performed to analyze the relationships between them, in which fracture length follows a fractal distribution. A method to estimate the representative elementary volume (REV) size and directional permeability ([Formula: see text] by extracting regular polygon sub-models with different orientation angles ([Formula: see text] and side lengths ([Formula: see text] from an original discrete fracture network (DFN) model was developed. The results show that the fracture number has a power law relationship with the fracture length and the evolution of the exponent agrees well with that reported in previous studies, which confirms the reliability of the proposed fractal length distribution and stochastically generated DFN models. The [Formula: see text] varies significantly due to the influence of random numbers utilized to generate fracture location, orientation and length when [Formula: see text] is small. When [Formula: see text] exceeds some certain values, [Formula: see text] holds a constant value despite of [Formula: see text], in which the model scale is regarded as the REV size and the corresponding area of DFN model is represented by [Formula: see text] (in 2D). The directional permeability contours for DFN models plotted in the polar coordinate system approximate to circles when the model size is greater than the REV size. The [Formula: see text] decreases with the increment of fractal dimension of fracture length distribution ([Formula: see text]. However, the decreasing rate of [Formula: see text] (79.5%) when [Formula: see text] increases from 1.4 to 1.5 changes more significantly than that (34.8%) when [Formula: see text] increases from 1.5 to 1.6 for regular hexagon sub-models. This indicates that the small non-persistent fractures dominate the preferential flow paths; thereafter, the flow rate distribution becomes more homogeneous when [Formula: see text] exceeds a certain value (i.e. 1.5). A larger [Formula: see text] results in a denser fracture network and a stronger conductivity.

中文翻译：

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基于多边形子模型的分形裂缝网络代表性初等体积和方向渗透率研究

由于裂隙岩体的定向渗透率显着依赖于裂隙的几何特性，本研究通过数值研究分析了它们之间的关系，其中裂隙长度服从分形分布。一种通过提取具有不同方位角（[公式：见文本]和边长（[公式：见文本]由原始离散裂缝网络（DFN）模型开发，结果表明，裂缝数量与裂缝长度呈幂律关系，指数的演变与以往研究报道的一致，这证实了所提出的分形长度分布和随机生成的 DFN 模型的可靠性。当[公式：见文本]较小时，由于用于生成裂缝位置、方向和长度的随机数的影响，[公式：见文本]变化很大。当[公式：见文]超过某些特定值时，[公式：见文]尽管有[公式：见文]仍保持恒定值，其中模型尺度被视为REV大小，DFN模型的对应面积为由[公式：见文本]（二维）表示。当模型尺寸大于 REV 尺寸时，在极坐标系中绘制的 DFN 模型的定向渗透率等值线近似于圆形。【公式：见正文】随着裂缝长度分布分形维数的增加而减小（【公式：见正文】。然而，[公式：见文]从1.4增加到1.5时[公式：见文]的下降率（79.5%）比[公式：见文]从1.5增加到1.6时（34.8%）变化更显着。正六边形子模型。这表明小的非持久性裂缝主导了优先流动路径；此后，当[公式：见正文]超过某个值（即1.5）时，流量分布变得更加均匀。较大的[公式：见正文]导致裂缝网络更密集，传导性更强。这表明小的非持久性裂缝主导了优先流动路径；此后，当[公式：见正文]超过某个值（即1.5）时，流量分布变得更加均匀。较大的[公式：见正文]导致裂缝网络更密集，传导性更强。这表明小的非持久性裂缝主导了优先流动路径；此后，当[公式：见正文]超过某个值（即1.5）时，流量分布变得更加均匀。较大的[公式：见正文]导致裂缝网络更密集，传导性更强。