Hydraulic properties of rock fractures are important issues for many geoengineering practices. Previous studies have revealed that natural rock fractures have variable apertures that could significantly influence the permeability of single rock fractures, yet the effect of aperture variation on the hydraulic properties of fractured rock masses has received little attention. The present study implemented a series of flow calculations on two kinds of 3D fractal-like tree network models constituted by fractures with heterogeneous aperture distributions and parallel plates with uniform apertures to gain insight into the effect of aperture variation on the hydraulic properties of fractured rock masses. The fluid flows through the two kinds of models are simulated using a developed numerical code, whose validity is verified by comparisons with the analytical solutions and previous experimental results. The effects of heterogeneous aperture distributions on the permeability of the models are illustrated by changing the geometrical parameters including the aperture ratio and mean aperture of the initial fracture branch. The results show that a significant channeling flow is observed in the 3D fractal-like tree network models constituted by fractures with heterogeneous aperture distributions. These preferential flow paths are mainly located in the large aperture channels, bypassing the contacts and/or low aperture barriers. The equivalent permeability of the 3D fractal-like tree network models increases with increasing fracture aperture ratio and/or increasing mean aperture of the initial fracture branch. The permeability ratio of the model of fractures with heterogeneous aperture distributions to the model with uniform mean apertures is always smaller than 1.0, and the ratio increases following a logarithmic relationship as the mean aperture of the initial fracture branch increases. A regression function is proposed to estimate the equivalent permeability of the model of fractures with heterogeneous aperture distributions. The deviations between the predicted permeability and the simulated/experimental results are less than half of the order of magnitude, which verifies that the proposed equation is capable of predicting the equivalent permeability of 3D fractal-like tree networks as a first-order estimation.

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评价孔径变化对三维分形树网络模型水力性能的影响

岩石裂缝的水力特性是许多地球工程实践的重要问题。以往的研究表明，天然岩石裂缝具有可变孔径，可以显着影响单个岩石裂缝的渗透率，但孔径变化对裂隙岩体水力特性的影响却很少受到关注。本研究对由孔径分布不均匀的裂缝和孔径均匀的平行板构成的两种 3D 分形树网络模型进行了一系列流动计算，以深入了解孔径变化对裂隙岩体水力特性的影响。 . 使用开发的数字代码模拟流过两种模型的流体，通过与解析解和以前的实验结果的比较，验证了其有效性。通过改变初始裂缝分支的孔径比和平均孔径等几何参数来说明非均质孔径分布对模型渗透率的影响。结果表明，在由具有不均匀孔径分布的裂缝构成的3D分形树网络模型中观察到显着的窜流。这些优先流动路径主要位于大孔径通道中，绕过触点和/或低孔径屏障。3D 分形树网络模型的等效渗透率随着裂缝孔径比的增加和/或初始裂缝分支的平均孔径的增加而增加。非均质孔径分布模型与均匀平均孔径模型的渗透率比值始终小于1.0，随着初始裂缝分支平均孔径的增大，该比值呈对数关系增大。提出了一种回归函数来估计具有非均质孔径分布的裂缝模型的等效渗透率。预测渗透率与模拟/实验结果之间的偏差小于一半数量级，这验证了所提出的方程能够预测 3D 分形树网络的等效渗透率作为一阶估计。并且随着初始裂缝分支的平均孔径增加，该比率遵循对数关系增加。提出了一种回归函数来估计具有非均质孔径分布的裂缝模型的等效渗透率。预测渗透率与模拟/实验结果之间的偏差小于一半数量级，这验证了所提出的方程能够预测 3D 分形树网络的等效渗透率作为一阶估计。并且随着初始裂缝分支的平均孔径增加，该比率遵循对数关系增加。提出了一种回归函数来估计具有非均质孔径分布的裂缝模型的等效渗透率。预测渗透率与模拟/实验结果之间的偏差小于一半数量级，这验证了所提出的方程能够预测 3D 分形树网络的等效渗透率作为一阶估计。