Civil Engineering Reference
In-Depth Information
Fig. 12.7
The square root of time 'fitting' method.
It is seen that the point of 90% consolidation rather than the point for 100% consolidation is used to
establish c
v
. This is simply a matter of suitability. A consolidation test sample is always drained on both
surfaces and in the formula H is taken as half the mean thickness of the sample for the pressure range
considered. At first glance it would seem that c
v
could not possibly be constant, even for a fairly small
pressure range, because as the effective stress is increased the void ratio decreases and both k and m
v
decrease rapidly. However, the ratio of k/m
v
remains sensibly constant over a large range of pressure so
it is justifiable to assume that c
v
is in fact constant.
One drawback of the consolidation theory is the assumption that both Poisson's ratio and the elastic
modulus of the soil remain constant whereas in reality they both vary as consolidation proceeds. Owing
to this continuous variation there is a continuous change in the stress distribution within the soil which, in
turn, causes a continuous change in the values of excess pore water pressures. Theories that allow for this
effect of the change in applied stress with time have been prepared by Biot (
1941
) and extended by
others, but the approximations involved (together with the sophistication of the mathematics) usually force
the user back to the original Terzaghi equation.
12.7 Determination of the permeability coefficient from the
consolidation test
Having established c
v
, k can be obtained from the formula k
=
c
v
m
v
γ
w
. It should b
e
noted
th
at since the
mean thickness of the sample is used to determine c
v
, m
v
should be taken as
a
/(
1
+
where
e
is the mean
e
)
void ratio over the appropriate pressure range.
12.8 Determination of the consolidation coefficient from the triaxial test
It is possible to determine the c
v
value of a soil from the consolidation part of the consolidated undrained
triaxial test. In this case the consolidation is three-dimensional and the value of c
v
obtained is greater than
would be the case if the soil were tested in the oedometer. Filter paper drains are usually placed around
the sample to create radial drainage so that the time for consolidation is reduced. The effect of three-
dimensional drainage is allowed for in the calculation for c
v
, but the value obtained is not usually depend-
able as it is related to the relative permeabilities of the soil and the filter paper (Rowe, 1959).
