A numerical discrete fracture flow approach was used to evaluate the effect of block size on the permeability of jointed rock.. The following conclusions were made: (a) Chances to reach REV size associated with the equivalent continuum behaviour for a jointed rock block increases with the block size. (b) REV size decreases with increasing joint density and joint size. (c) REV size does not exist for joint systems with low relative orientation angles and low densities. (d) The first invariant of fracture tensor (F0) can be used to estimate the joint geometry requirements for the REV size associated with the equivalent continuum behaviour. (e) Average block permeability seems to be related to the first invariant of fracture tensor and the joint geometry requirements for non zero block permeability can be determined from the threshold value of F0. (f) A strong correlation exists between the directional coefficient of permeability and the fracture tensor component for the connected joint configuration.
The fluid flow through jointed rock is a very important topic of research in rock mechanics and hydrogeology disciplines. At present some researchers try to use an equivalent continuum medium approach to simulate fluid flow through jointed rock media. Definitely, it is not a suitable assumption for all different scales of a rock mass. The equivalent continuum behavior may exist for a given rock mass with minor discontinuities only at a size greater than or equal to REV (representative elementary volume) size. REV may be defined for a given rock mass as the size beyond which very little variation is found for mass hydraulic properties. There is no guarantee that REV size exists for all jointed rock masses. For some rock masses, it may not be possible to find the equivalent continuum behavior at any scale. At present, very little information is available in the rock mechanics or hydrogeology literature about the relation between REV size and joint geometry parameters. To estimate the REV associated with the equivalent continuum behavior, it is necessary to study the effect of block size on hydraulic properties of jointed rock. Numerical discrete fracture flow models are used in the past by several researchers (Long and Witherspoon 1985, Dershowitz and Schrauff 1987) to find the effect of block size on the flow behaviour of jointed rock masses. This study was based on an isotropic system of fractures with deterministic distributions for aperture and length. The effect of orientation of joint sets on the equivalent porous medium behaviour was not addressed by them. Dershowitz and schrauf (1987) presented a discrete fracture flow model, based on measured fracture parameters from five crystalline rock sites in order to determine the equivalent conductivity of fractured media. They found that the hydrological behaviour of a fractured rock mass is significantly influenced by the scale of the flow region relative to the average fracture length. The change in equivalent conductivity with the region size was found to be strongly dependent on fracture density. Their study too has not addressed the effect of joint orientation on equivalent conductivity of the jointed rock.