Effective hydraulic conductivity of discrete fracture network with aperture-length correlation

Abstract

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.