Engineering Rock Mechanics

1 58 Permeability

volume increases, so the measured values become more representative.
This leads automatically to the concept of the representative elemental
volume, or REV.
In Fig. 9.9, we present the generalized figure foreshadowed in the
discussion referring to Fig. 4.12 presented in Section 4.5. This illustrates that
wide variations in permeability are expected when the measured sample
volume is small. Also, we have seen directly in Fig. 9.8 how the permeability
stabilizes with an increase in volume, despite the fact that earlier we
mentioned that permeability is a tensor, and hence the property at a point,
i.e. at 0 on the volume (horizontal) axis in Fig. 9.9. Clearly, like in situ rock
stress, this presents a problem because the tensorial permeability concept
can only apply to primary permeability: by definition, the secondary
permeability must involve a non-zero volume.
All this is summarized concisely in Fig. 9.9 and the REV introduced, infer
alia, by Bear (1972), is the position on the volume axis when the between-
test variability of the permeability measurements is acceptably low. It has
been tacitly assumed in this discussion that the discontinuity occurrence
is statistically homogeneous in the region being measured: discontinuity
inhomogeneity can also be a problem if the discontinuity geometry is
changing within the REV volume scale. This is indicated by showing that
it is possible for the mean permeability to be changing above the REV
volume when the rock mass is inhomogeneous. A question that naturally
arises is whether the mean of many measurements performed on sub-REV
samples is in fact equal to the REV value of permeability. The answer will
depend on the type of discontinuity inhomogeneity.
We have intimated here some of the difficulties that will arise in any
attempt to use the permeability concepts in a practical arena. However, the
key to good rock engineering is to understand the principles of rock
mechanics and then to make engineering decisions on the optimal course
of action. For example, we can predict that, when a tunnel is constructed
in rock, there will be local increases in the water flow rate into the

Permeability

Typical variation for one rock mass sample

/'Discontinuous media Porous media

I'

REV Volume

Figure 9.9 The representative elemental volume (REV) for permeability.