A new determination method for the permeability tensor of fractured rock masses

Abstract

Hydraulic characteristics are important fundamental properties of fractured rock masses and involve various geoscience and engineering disciplines. The determination of the permeability tensor is the basic input of the equivalent continuum (EC) model for hydraulic behavior analysis. An analytical method to determine the permeability tensor of fractured rock masses is developed based on the orientation and linear frequency of fractures along with a value of the permeability in any direction. The orientation and linear frequency of fractures can be easily sampled in practice, and the value of the permeability in some direction can be tested by a relatively cheap single-well pumping test. The key step of this method is to derive the theoretical relationship between the permeabilities in two different directions. In addition, an anisotropy index of permeability AIp is defined to quantitatively describe the permeability anisotropy. Some numerical experiments were conducted with the universal distinct element code (UDEC) to validate the developed method. The results show that: (a) the predicted values are very close to the real ones; (b) for all cases of rock masses with equal-aperture fracture sets, the mean error rate of the permeabilities in 23 different directions is approximately 10%; (c) for rock masses with different-aperture fracture sets, the mean error rate increases from 8.6% to 28.9% as the aperture ratio increases from 1 to 4; and (d) therefore, the estimation method for directional permeability proposed in this study is valid, especially for those rock masses in which the aperture ratios of the fracture sets are small (e.g., less than 3).