Geoscience Reference
In-Depth Information
A boundary condition is imposed at the aquifer: a unit-step load
B
at time
t
= 0
at
x
= 0 (
h
=
B
for
t
> 0 and
h
= 0 for
t
< 0) , and the aquifer is supposed to be long.
The corresponding solution of (6.21) becomes
B
x
h
exp(
)
(6.22)
s
s
The real solution can be found by Laplace Inverse Transform, but it is complex.
The so-called Simple Method is applied, which is easy an
d
quite accurate for this
consolidation problem (error less than 3%). It states that
s
h
h
for
s
= 1/2
t
, which
results in
sinh((
d
z
)
/
2
tc
)
x
v
h
B
exp(
)
and
h
with
(6.23)
sinh(
d
/
2
tc
)
t
v
0
5
/
,
Sd
d
d
coth(
)
-
.
*
+
t
2
tk
'
2
tc
2
tc
-
*
v
v
t
is the transient leakage factor. For large time
32
,
Here,
t
becomes equal to the
steady leakage factor
, see Fig 6.5b. Solution (6.23) shows that the storage in the
aquifer proceeds with
t
0.5
and that consolidation in the aquitard proceeds with
t
0.25
,
much slower. Since for shallow sand layers the storage effect is less than the
consolidation effect of adjacent clay layers, this has implications for the response
of sand-clay systems to time-dependent loading (see Chapter 8, Fig 8.4).
For varying boundary conditions (
B
is not a constant) convolution can be used
with solution (6.23)
t
B
x
h
0
exp(
)
d
(6.24)
t
This method has been validated by field tests and is implemented in the Dutch
guideline for dike design.
application 6.1
Consider a three-layer system: sand, clay and silty clay. Characteristic properties
are given (Table 6.2). The groundwater table is at the top of the clay layer. The
question is to determine the settlement due to a loading of 100 kPa and the creep
thereafter for a period of 27 years (~ 10
4
days). The preconsolidation load is 50
kPa.
32
x
coth(
x
) tends to 1 for
x
0
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