Determining effective hydraulic conductivity is critical to understand groundwater flow behavior in fractured rock masses and is required for large-scale numerical simulations. A new approach is developed to estimate the effective hydraulic conductivity of a discrete fracture network with aperture and trace length being stochastic and correlated. The aperture and length are assumed to follow a joint lognormal distribution. The average flowrate through the network is determined by integrating flowrate in the fracture ensemble with the laminar flow and non-linear flow being separately considered based on the Reynolds number. The effective hydraulic conductivity of the discrete fracture network is then determined from the idea that Darcy’s law still applies to the overall flow behavior through the network. For comparison, the simple average hydraulic conductivity is also developed based on the assumption that flow in all fractures is laminar and aperture and trace length are uncorrelated. Based on the developed approach, the effects of aperture and trace length uncertainty, their correlation degree, and non-linear flow characteristics on the ratio of effective hydraulic conductivity over simple average hydraulic conductivity are examined. The results demonstrate that the effective hydraulic conductivity can be either larger than or smaller than the simple average hydraulic conductivity depending on correlation level between aperture and trace length and the degree of non-linear effect in the network. Non-linear flow reduces the effective hydraulic conductivity of the fracture network. Correlation between aperture and trace length increases the effective hydraulic conductivity. Aperture uncertainty tends to reduce the effective hydraulic conductivity.

中文翻译：

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具有孔长相关性的离散裂缝网络有效水力传导率

确定有效的水力传导率对于理解裂隙岩体中的地下水流动行为至关重要，这是大规模数值模拟所必需的。开发了一种新方法来估计孔径和走线长度是随机且相关的离散裂缝网络的有效水力传导率。假定孔径和长度遵循联合对数正态分布。通过对网络的平均流量是通过将裂缝集合中的流量与基于雷诺数分别考虑的层流和非线性流进行积分确定的。然后，根据达西定律仍然适用于通过该网络的总体流动特性的想法确定离散裂缝网络的有效水力传导率。为了比较，基于所有裂缝中的流动都是层流且孔径与走线长度不相关的假设，还可以得出简单的平均水力传导率。基于开发的方法，研究了孔径和迹线长度不确定性，它们的相关程度以及非线性流动特性对有效水力传导率与简单平均水力传导率之比的影响。结果表明，有效的水力传导率可以大于或小于简单的平均水力传导率，这取决于孔径和走线长度之间的相关程度以及网络中的非线性影响程度。非线性流动会降低裂缝网络的有效水力传导率。孔径和走线长度之间的相关性增加了有效的水力传导率。孔径不确定性倾向于降低有效的水力传导率。