EVALUATING THE EFFECT OF APERTURE VARIATION ON THE HYDRAULIC PROPERTIES OF THE THREE-DIMENSIONAL FRACTAL-LIKE TREE NETWORK MODEL

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.