Civil Engineering Reference
In-Depth Information
12.9 The model law of consolidation
If two layers of the same clay with different drainage path lengths H
1
and H
2
are acted upon by the same
pressure increase and reach the same degree of consolidation in times t
1
and t
2
respectively, then theo-
retically their coefficients of consolidation must be equal as must their time factors, T
1
and T
2
:
c t
H
c t
H
v
1 1
v
2 2
T
=
;
T
=
1
2
2
2
1
2
Equating:
t
H
t
H
1
2
=
2
2
1
2
This gives a simple method for determining the degree of consolidation in a layer if the simplifying
assumption is made that the compression recorded in the consolidation test is solely due to primary
compression.
Example 12.2:
Consolidation in the field
During a pressure increment, a consolidation test sample attained 25% primary consoli-
dation in 5 minutes with a mean thickness of 18 mm. How long would it take a 20 m
thick layer of the same soil to reach the same degree of consolidation if (i) the layer was
drained on both surfaces and (ii) it was drained on the top surface only?
Solution:
In the consolidation test the sample is drained top and bottom
18
2
⇒
H
=
=
9 0
.
mm
1
(i) With layer drained on both surfaces H
2
=
10 m
=
10 000 mm.
t
H
H
5 10 000
9
×
2
1
60
1
24
1
365
1
t
=
2
=
× × ×
=
.
11 7
years
2
2
2
2
1
(ii) With layer drained on top surface only H
2
=
20 m.
⇒
t
= ×
4 11 7
.
=
47
years
2
Example 12.3:
Degree of consolidation
A 19.1 mm thick clay sample, drained top and bottom, reached 30% consolidation in 10
minutes. How long would it take the same sample to reach 50% consolidation?
Solution:
As U is known (30%) we can obtain T, either from Fig.
12.4
or by using the relationship
that
U
=
1 13
.
T
(up to U
=
60%).
