Engineering Rock Mechanics

152 Permeability

A9.6 We can use the same solution procedure as in A9.5 to determine
the nodal head values and hence the flow directions. The aperture values
given in the question lead to the following matrix equation.

-27.3 3.3 0.0 0.0 0.0 0.0 8.5 0.0 0.0 0.0

3.3 -23.2 0.9 0.0 19.1 0.0 0.0 0.0 0.0 0.0

0.0 0.9 -142.4 1.4 0.0 118.8 0.0 0.0 0.0 0.0

0.0 0.0 1.4 -6.7 0.0 3.7 0.0 0.0 0.0 0.0

0.0 19.1 0.0 0.0 -54.0 2.1 0.0 32.8 0.0 0.0

0.0 0.0 118.8 3.7 2.1 -168.9 0.0 0.0 0.0 44.3

8.5 0.0 0.0 0.0 0.0 0.0 -10.3 1.4 0.0 0.0

0.0 0.0 0.0 0.0 32.8 0.0 1.4 -48.7 1.4 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.4 -8.9 0.9

0.0 0.0 0.0 0.0 0.0 44.3 0.0 0.0 0.9 -46.(

X

-46.6

0.0

-63.9

-3.7

0.0

0.0

-0.6

-13.0

-6.6

-0.8

And from this we find the following values for the unknown nodal
heads.

H4 H5 H6 HI H9 HlO H12 H13 H14 H15

2.704 1.864 2.730 2.631 1.680 2.689 2.489 1.509 1.240 2.632

These nodal head values are illustrated in the diagram below.

,\\ Hvdraulic head

',

Hydraulic head

3m

Node 6+ 5 local flow

direction contrary

to the overall trend

Note that there are isolated examples (e.g. node 6+5) of water flows

occurring in a direction contrary to the overall hydraulic head decrease

(which is from the left to the right of the diagram). This is in direct

contrast to the flow regime determined in A9.5, and illustrates the

hazards of assuming regional flow patterns from observations made on

a single fracture.