Geoscience Reference
In-Depth Information
application 6.2
Consider a normally consolidated saturated clay layer of 10 m thick. On top a
sand layer must be placed of 3 m thick (
d
=
15 kN/m
3
) for a road construction,
which invokes consolidation in the clay. The works have to wait for the
consolidation to be finished. The question is whether it is economic to install a
vertical-drain system in the clay (drain distance
1.5
m), given that cost for
installation is 250 €/m
2
and delay of works by consolidation costs 25 €/m
2
per year
(note, m
2
refers to ground surface).
A soil sample is taken at a depth of 3 m. Characteristic properties are porosity
n =
0.40 and saturated unit weight
=
18 kN/m
3
. It is tested in an oedometer (
h
=
0.02 m). The initial condition, reflecting the field condition, is
0
'=
3x(18-10) = 24
kPa, which is met by preloading the sample. Next, the loading is applied
corresponding the sand layer weight
=
3x15 = 45 kPa. The observed
settlements in the oedometer are as follows (time
t
in seconds, settlement
S
in mm).
TABLE 6.3a
t
10
20
30
40
60
120
240
600
1200
1800
3600
7200
S
0.70
0.82
0.89
0.94
1.05
1.27
1.57
2.01
2.30
2.40
2.58
2.75
Asaoka's method is applied. By interpolation two sets of three successive
measurements are selected (first one at
t
0
), the first set more in the beginning and
the second set more at the end of the process. The corresponding graphs, according
to Fig 6.3, yield for
= 45 kPa the following values.
TABLE 6.3b
t
t
0
A
B
C
S
&
m
c
v
k
o
m
2
/s
m
2
/kN
s
s
mm
mm
mm
mm
mm
m/s
1
st
trial
1.4
6
2.0
1
2.2
4
2.4
0
1.4
2
2
0
2.6x10
-7
2.5x10
-3
6.5x10
-9
400
200
2
nd
trial
2.0
1
2.3
1
2.4
0
2.4
2
1.7
2
1
5
2.0x10
-7
2.6x10
-3
5.2x10
-9
600
600
These 2
nd
trial results show that 0.2
h
2
/c
v
=
400
s. Since
t
0
is smaller, the 1
st
trial
is less appropriate (Asaoka's method is not applicable for
t
< 400 s). The
hydrodynamic period (99.4% completion of consolidation) is
t = T
hd
= 2
h
2
/
c
v
=
4000 s. Therefore, the last two measured settlements are mainly due to creep. At
50% consolidation (
t =
400) the actual effective stress reaches
'
50%
=
24 + 0.5x45
= 46.5 kPa. An approximate value for the (virginal) compression index becomes
b
=
'
50%
=
0.12. The last two measurements provide a value for the creep
index (difference in strain divided by logarithm of time interval):
c =
(0.00275/0.02
=
0.00258/0.02) / ln(3600/7200) = 0.012.
In the field, practical completion of consolidation will take
t > T
hd
= 2
h
2
/
c
v
=
2
10
2
/(2.0 10
7
) = 10
9
s = 31.7 year! Application of vertical drains - taking for
h
the
mutual drain distance as seepage path - will reduce the hydrodynamic period to
about
T
hd
= 2
h
2
/c
v
=
2 1.5
2
/(2.0x10
-7
) = 0.71 year. Delay of 30 years will cost 750
€/m
2
, and vertical drains 250 €/m
2
. A vertical-drain system is therefore preferred.
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