Coupling stress and transmissivity to define equivalent directional hydraulic conductivity of fractured rocks

A DFN (Discrete Fracture Network) modelling approach is developed to couple stresses with fracture transmissivities and to evaluate large scale rock mass hydraulic conductivity. The transmissivity-stress coupling relies on a negative exponential correlation between normal stress acting on a fracture and fracture transmissivity, bounded by residual and maximal apertures. The remote stresses and the local stress fluctuations induced by the fractures themselves are combined in a semi-analytical approach to compute the normal stress acting on each fracture of a DFN. Directional equivalent hydraulic conductivities are numerically computed in all directions from a spherical permeameter setup. The resulting properties are first a cloud of points, where each point defines a direction and an equivalent hydraulic conductivity. The distribution of equivalent hydraulic conductivities is analyzed to define mean values, preferential directions and anisotropy ratio. The entire workflow is developed in the numerical platform DFN.lab. The capacity of the method to investigate the impact of the in-situ stresses on the rock mass hydraulic conductivity is illustrated for fracturing and in-situ stress conditions similar to the conditions at the Forsmark site in Sweden. We find that the stress fluctuations induced by the fractures have a significant impact on the resulting hydraulic conductivity field. They limit the anisotropy ratio to values close to a factor of 3 while the transmissivity distribution is correlated to orientations and spans several orders of magnitude. Sensitivity analyses, performed by changing the parameters of the transmissivity-stress law, show quantitatively how the directional hydraulic conductivities are rather controlled by the orientations of the in-situ stresses or by the underlying connectivity structure of the DFN.