Civil Engineering Reference
In-Depth Information
Fig. 12.17
Schematic form of the finite difference equation (three dimensional).
and the equation becomes:
u
+
=
ru
+
4
ru
+
ru
+
u
,
(
1 6
−
r
)
0
,
k
1
2
,
k
3
,
k
4
,
k
0
k
Using the convention R
=
mh, the schematic form for the explicit equation is shown in Fig.
12.17a
(for a
point at the origin) and Fig.
12.17b
(for other interior points).
For drainage in the vertical direction the procedure is the same, but for radial drainage the expression
for u
0,k
+
1
at a boundary point, where
δ
u/
δ
R
=
0, is given by:
u
+
=
r u
(
+
u
)
+
2
ru
+
u
(
1 4
−
r
)
0
,
k
1
2
,
k
4
,
k
1
,
k
0
,
k
Value of r
In three-dimensional work the explicit recurrence formula is stable if r is either equal to or less than 1/6.
This is not so severe a restriction as it would at first appear, since with three-dimensional drainage the
time required to reach a high degree of consolidation is much less than for one-dimensional drainage.
For two-dimensional work r should not exceed 0.5.
12.14.3 Determination of initial excess pore water pressure values
For one-dimensional consolidation problems, ui
i
can at any point be taken as equal to the increment of
the total major principal stress at that point. For two- and three-dimensional problems ui
i
must be obtained
from the formula:
u
i
=
B
[
∆
σ
+
A
(
∆
σ
−
∆
σ
)]
3
1
3
As the clay is assumed saturated, B
=
1.0.
12.15 Sand drains
Sometimes the natural rate of consolidation of a particular soil is too slow, particularly when the layer
overlies an impermeable material and, in order that the structure may carry out its intended purpose, the
rate of consolidation must be increased. An example of where this type of problem can occur is an
