Relations between fracture tensor parameters and jointed rock hydraulics

The fracture tensor is a combined measure of joint geometry parameters. The possible relations between the properties of the fracture tensor and the hydraulic properties of jointed rock including the equivalent continuum behavior are investigated in this paper through numerical experiments performed at the two-dimensional level incorporating joint networks with two joint sets. The possibility of a nonzero average block permeability and the equivalent continuum behavior of a joint system can be expressed with the help of the first invariant of fracture tensor (F₀). A threshold value of F₀ (to achieve nonzero block permeability) between 3 and 6 and a cutoff value of F₀ (to achieve equivalent continuum behavior) between 10 and 30 were obtained for the joint geometry configurations studied in the investigation. Both the threshold value and the cutoff value of F₀ were found to depend on the relative orientation of joint sets. Joint systems with low relative orientation angles (for systems with only two joint sets) and low densities do not show hydraulically equivalent continuum behavior. A nonlinear relation seems to exist between the directional permeability and the fracture tensor component for the connected joint configuration when rock blocks contain only minor discontinuities. For rock blocks containing major discontinuities, this relation becomes linear.