156 Permeability9.5 Scale effect
There are no length dimensions in Fig. 9.7: the discontinuity array could
represent small fractures over lengths of a few centimetres or master joints
over lengths of many tens of metres. Imagine that a borehole had been
drilled into this array to estimate the flow rate through the rock. In the case
of short fractures, it may well be that the borehole would be approximately
the same size as the diagram and hence the result be fairly reliable. In the
case of joints, the borehole could well intersect no discontinuities, or
perhaps one or two, at a number of discrete locations. Moreover, the hydraulic
heads and flow directions at these points might in no way reflect the overall
pattern of flow. This is an important practical consideration, and is
generally termed the scale effect.
The scale effect for fluid flow has been studied via computer simulation
by Long (1983). In Fig. 9.8, we present one of her most illuminating
diagrams illustrating the connectivity within a fracture network and the
associated scale effect. The column of diagrams on the left-hand side of the
figure shows different sized samples of the same simulated discontinuity
network. The column of diagrams on the right-hand side shows the
connected network within the samples to the left, i.e. those discontinuities
through which water can flow throughout the network. The diagrams
dramatically illustrate the effect of scale. In the top right-hand diagram,
water can only flow from top to bottom through the sample. In the fourth
diagram down, water can only flow laterally. Progressing through the suite
of diagrams, one can see the permeability stabilizing as the number of
discontinuities in the sample increases. So, estimation of the permeability
from small samples can give almost any result but, as the sampled
3.03.03.01.4
Figure 9.7 Nodal head values for flow through a simulated discontinuity array
(from Samaniego and Priest, 1985).