Civil Engineering Reference
In-Depth Information
conductivity matrices
kc
“analytically” (see Section 3.2.2). The assembly is made into a
global conductivity matrix
kv
stored as a skyline in the usual way. Solution of the mod-
ified problem leads to another set of nodal total head values and further updating of the
mesh nodal coordinates. This process is repeated until the change in computed total head
values from one iteration to the next is less than a tolerance value
tol
. The convergence
check is performed by library subroutine
checon
, which outputs the logical variable
con-
verged
. The subroutine sets
converged
to
.TRUE.
if the solution has converged and
to
.FALSE.
if another iteration is required.
The first example shown in Figure 7.12 is of a vertical-sided dam. The free surface
described by nodes 1 through 9 at the top of the mesh is initially assumed to be horizontal.
The initial data relates to the number of elements in the
x
-(
nxe
)and
y
-(
nxe
) directions,
and this is followed by the tolerance
tol
, set to 0.01 and the iteration ceiling
limit
,set
to 20. The dam is homogeneous in this example, so
np types
is set to 1. The perme-
abilities in the
x
-and
y
-directions are read followed by the
x
-coordinates of the bottom
bottom width
and top nodes
top width
of the starting mesh. The next line of data
reads the initial height of the horizontal free surface
initial height
whichinthis
example is set to 7.0. The value of the upstream total head value of
hup=7.0
is then
read, followed by the number of nodes to be fixed on the upstream side
fixed up
and
their node numbers
node up
. Similarly on the downstream side, the total head is set to
hdown=2.0
followed by
fixed down
and
node down
. The final data
nci
relates to
the number of contour intervals to be plotted.
The output for this example is shown in Figure 7.13 and the Postscript output file
fe95.msh
shown in Figure 7.14 gives the deformed mesh at convergence. The graphics
file
fe95.con
produces the contour map of total head values given in Figure 7.15.
Free surface nodes fixed to elevation
1 23456789
7.0
10
18
Seepage face
nodes fixed
to elevation
19
27
Upstream
nodes
potential
fixed at
7.0
28
36
37
45
46
54
55
Downstream
nodes
potential
fixed at
2.0
63
64
72
No flow
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Figure 7.12 Mesh and data for first Program 7.3 example (
Continued on page 336
)
