Engineering Rock Mechanics

9.4 Flow through discontinuity networks

Often, in discontinuity arrays, one discontinuity will terminate against

another and it is therefore of interest, not only to be able to compute the

permeability of a set of parallel discontinuities, but also to analyse condi-

tions where two discontinuities meet, and indeed, to study the complex

discontinuity networks that are contained within rock masses.

To start, we can consider the flow at a node in a simple network, as

illustrated in Fig. 9.5. This figure indicates the notation for node, channel

and flow numbering, such that application of the continuity equation (i.e.

‘what goes in must come out’) gives

The equation given earlier for flow through a single discontinuity, i.e. Q =

cHL, can be generalized as Qij = cii(Hi - Hi) = c& - cqHj so that the

hydraulic head at the jth node can be expressed as

CcijH,

H. =-.

CCq

Assuming the flow in the network is laminar, Bernoulli’s equation

P V2

total head = - + z +-

Y 2g

may be applied. Generally, the velocity of the flow will be sufficiently low

to permit the velocity head term, 2/2g, to be ignored, giving

P

Y

total head = - + z.

Thus, for a more complex discontinuity array, and applying this type of

analysis, we can establish the hydraulic heads at nodal points by solving

Hi = Head at node i

Q, =Flow from i to j

C,, = Conductance of channel ij

Figure 9.5 Flow at a network node.