Geoscience Reference
In-Depth Information
Drainage can also occur downwards to a draining layer of sand. This is quite
possible in the Netherlands where the Pleistocene sands underlying the soft
Holocene deposits usually have potential heads equal to or even lower than the
surface ditch levels. However, the pore water in the Pleistocene often
communicates with seawater and can be silty. If potential head in the Pleistocene
can equal or exceed the polder levels, the drains are usually terminated 1 to 1.5 m
above the Pleistocene, to prevent upward seepage of silty water (Fig 13.5).
The flow of water escaping from the soft soil is predominantly horizontal when
vertical drains are present. The length of flow in the soft soil is drastically reduced
by the vertical drains, to at most one-half of the centre-to-centre distance of the
drains. A simple but rather approximate rule is that the duration of consolidation is
proportional to the square of the maximum drainage distance. If drains are centered
at 1.5 m in soft layers 10 m thick, the period of drainage is 10
2
/1.5
2
= 45 times
shorter. Vertical drainage is designed to obtain the necessary consolidation in a
period of less than 6 to 12 months. Sustainability of the soil and groundwater is of
special concern when vertical drains have been used. The drains remain in the soil
and they may provide an easy way for pollutants from the surface (industry plant)
to reach sandy layers and cause groundwater contamination.
The effect of the vertical drainage can be incorporated into the consolidation
equations. This was first achieved by Barron (1947). The (average) pore pressure
u
dissipating around a vertical drain (Fig 13.6a) during a consolidation process,
triggered by a sudden loading
0
, is, according to Barron, when assuming uniform
(vertical) strain
u =
0
exp(
8
T
h
/F
(
?
))
(13.1)
Here
51
,
T
h
= c
v
t/
4
R
2
, 2
R
is drain spacing and
F
(
?
)
ln(
?
)
¾, for
?
= R/r
0
>8,
with
r
0
the (equivalent) drain radius. Approximation of ln(
?
) yields (see Fig 13.6b)
ln(
?
)
0.16
?
+ ¾
for 5 <
?
< 20
(13.2)
Hence, Barron's formula can be rewritten into
B
= R
3
/(12.5
r
0
c
v
)
u =
0
exp(
8
T
h
/F
(
?
))
=
0
exp(
t/
B
) and
(13.3)
The condition of uniform strain, which Barron imposed, is fundamental to this
solution.
52
In reality, induced horizontal stress gradients may cause a redistribution
51
In fact, Barron wrote
T
h
= c
v
(1
+e
)
t/
4
R
2
, voids ratio
e = n/
(1
-n
). The introduction of the
voids ratio was in Barron's time generally in use after Terzaghi's suggestion to define
strains with reference to the solid part of the height. The parameter
c
v
is found accordingly.
Presently, one refers to the bulk height, and the corresponding parameter
c
v
is found.
Hence, the factor (1+
e
) can be disregarded.
52
For shallow layers the deformation is stress-conditioned, allowing for differential
settlements. For deep layers the overburden works like a stiff beam and the deformation is
strain-controlled (uniform), inducing stress redistribution. This causes additional horizontal
pressure gradients. In the oil/gas industry this phenomenon is called compaction drive.
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