Scale up of two-dimensional conductivity tensor for heterogenous fracture networks

An approach is developed to scale up the two-dimensional conductivity tensor for highly heterogenous fracture networks, based on a numerical modelling approach that was proposed previously by Zhang et al., J. Rock Mech. Min. Sci. 33, 17-37 (1996). In that approach, it was assumed that the fractured rock mass was statistically uniform and only a unit square of sample rock was needed to work out the conductivity tensor. Hence, its application was limited where the heterogenous characteristics of a fracture network was not negligible. In the present paper, the local conductivity tensors, both magnitude and direction, either calculated based on small fracture networks or samples measured on separate exposures are scaled up to estimate the overall nature of conductivity for a relatively large region. The approach developed is used to estimate the two-dimensional conductivity tensor of naturally fractured rock masses for two types of fracture networks, constant aperture and variable aperture under stress. The effects of sample number and sample size of local sub-areas were examined against the totally sampled area. Finally, field data were used to predict the overall conductivity tensor of a large region, based on four fracture networks sampled on separate exposures within the region. (C) 1999 Elsevier Science B.V. All rights reserved.