Engineering Rock Mechanics

150 Permeability

matrix below is incomplete, although we have included illustrative rows
and columns based on the equations given above).

X

where A = +1,4 + C2.4 + c5,4 + C12.4)

B = +7,6 + c10,7), and

c = -(c10,15 + c14,15)

Substituting all the numerical values given above gives the following

for the complete matrix equation (note that we have divided by a

constant value of 1 x

-31.3 16.6 0.0 0.0 0.0 0.0 3.6 0.0 0.0 0.0

16.6 -26.6 4.3 0.0 5.6 0.0 0.0 0.0 0.0 0.0

0.0 4.3 -29.1 7.2 0.0 14.9 0.0 0.0 0.0 0.0

0.0 0.0 7.2 -23.9 0.0 8.8 0.0 0.0 0.0 0.0

0.0 5.6 0.0 0.0 -20.3 5.0 0.0 9.7 0.0 0.0

0.0 0.0 14.9 8.8 5.0 -34.2 0.0 0.0 0.0 5.5

3.6 0.0 0.0 0.0 0.0 0.0 -18.1 11.3 0.0 0.0

0.0 0.0 0.0 0.0 9.7 0.0 11.3 -35.7 10.9 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 10.9 -23.1 7.1

0.0 0.0 0.0 0.0 0.0 5.5 0.0 0.0 7.1 -19.(

X

-33.3

0.0

-8.0

-18.8

0.0

0.0

-4.5

-3.9

-5.2

-6.4

With a modern spreadsheet program, the left-hand matrix can be

inverted and hence solved for the unknown nodal heads. Doing this

leads to the following values (where the units are in m).

H4 H5 H6 H7 H9 Hio Hi2 Hi3 Hi4 HIS

2.507 2.339 2.229 2.223 1.930 2.062 1.759 1.626 1.438 1.472