Civil Engineering Reference
In-Depth Information
In the oedometer test the vertical strains
δε
z
are given by Eq. (8.9) as
δσ
z
δε
=
m
v
(22.24)
z
δσ
z
=
=
δσ
where, for complete consolidation when
u
z
. Notice that,
as discussed in Sec. 8.5 the value on
m
v
is not a soil constant but it depends on the
current stress
0 we have
δσ
z
and is different for loading and unloading.
At the ground the surface settlements due to consolidation
σ
z0
on the change of stress
δρ
c
are given by
δρ
c
δσ
z
=
δε
=
m
v
(22.25)
z
z
δσ
z
where, for complete consolidation, we have
q
is the net bearing
pressure at the surface. Final consolidation settlements for wide foundations can be
calculated using Eq. (22.25). However, because the one-dimensional compression and
swelling behaviour of soil is non-linear,
m
v
is not a soil constant and it is necessary
to measure
m
v
in an oedometer test in which the initial stress and the change of stress
both correspond to those in the ground.
The rate at which consolidation settlements occur in one-dimensional oedometer
tests was considered in Chapter 15. General solutions for rates of consolidation emerge
as relationships between the degree of consolidation
U
t
and the time factor
T
v
. These
are defined as
=
δ
q
, where
δ
=
ρ
t
ρ
∞
U
t
(22.26)
c
v
t
H
2
T
v
=
(22.27)
where
ρ
t
, and
ρ
∞
are the settlements at times
t
and
t
=∞
,
c
v
is the coefficient of
consolidation and
H
is the drainage path length.
Relationships between
U
t
and
T
v
depend on the geometry of the consolidating layer
and its drainage conditions and on the distribution of initial excess pore pressure
but not on its absolute value. The most common drainage conditions are shown in
Fig. 22.14. For one-dimensional drainage the seepage may be one-way towards a
drainage layer at the surface, two-way towards drainage layers at the base and at the
surface or many-way towards silt or sand layers distributed through the deposit. For
radial drainage seepage is towards vertical drains placed on a regular grid. In each
case the drainage path length,
H
or
R
, is the maximum distance travelled by a drop of
water seeping towards a drain.
For one-dimensional consolidation the relationships between
U
t
and
T
v
for different
initial excess pore pressure conditions are given in Fig. 15.9 in terms of
T
v
. These could
also be given in terms of
T
v
plotted to a logarithmic scale, as shown in Fi
g.
22.15(a),
which corresponds to consolidation with the initial excess pore pressure
u
i
uniform
