Civil Engineering Reference
In-Depth Information
⇒
u
=
r u
(
+
u
−
2
u
)
+
u
0
,
k
+
1
2
,
k
4
,
k
0
,
k
0
,
k
where
c
∆
∆
2
t
v
r
=
z
The schematic form of this expression is shown in Fig.
12.12d
. Hence if a series of points in a consoli-
dating layer are established,
Δ
z apart, it is possible by numerical iteration to work out the values of u at
any time interval after consolidation has commenced if the initial excess values, ui,
i
, are known.
Impermeable boundary conditions
Figure
12.13a
illustrates this case in which conditions at the boundary are represented by
∂
∂
u
z
0
=
Hence between the points 2
k
and 4
k
:
∂
∂
u
z
u
−
u
z
2
,
k
4
,
k
=
=
0
2
∆
i.e.
u
u
=
2
,
k
4
,
k
The equation therefore becomes:
u
2
r u
(
u
)
u
+
=
−
+
0
,
k
1
2
,
k
0
,
k
0
,
k
and is shown in schematic form in Fig.
12.13
b.
The boundary equation can also be used at the centre of a double drained layer with a symmetrical
initial pore pressure distribution, values for only half the layer needing to be evaluated.
Fig. 12.13
Explicit recurrence formula: treatment for an impermeable boundary.
