Civil Engineering Reference
In-Depth Information
Consolidation
15.1 Basic mechanism of consolidation
In Sec. 6.9 we saw th
a
t, in general, any undrained loading or unloading will create
excess pore pressures
u
in the region of the loading. These excess pore pressures may
be positive or negative with respect to the long term steady state pore pressures
u
∞
and
they give rise to hydraulic gradients that cause seepage flow. These seepage flows lead
to volume changes that, in turn, are associated with the changes of effective stress as
the excess pore pressures dissipate. As the excess pore pressure diminish the hydraulic
gradients and rates of flow also diminish, so that the volume changes continue at a
reducing rate. After a long time the seepage and volume changes will stop when the
excess pore pressures and hydraulic gradients become zero and the pore pressures reach
their steady state values.
The coupling of seepage due to hydraulic gradients with compression or swelling
due to the resulting seepage flow and changes of effective stress is known as consol-
idation. This process accounts for settlement of foundations with time, progressive
softening of soil in excavations and other similar effects. In order to calculate the rate
at which excess pore pressures reduce it is necessary to develop a simple theory for
consolidation.
A general theory for three-dimensional consolidation is quite complicated and here
I will consider a simpler theory for one-dimensional consolidation in which all seepage
flow and soil strains are vertical and there is no radial seepage or strain. This is relevant
to conditions in an oedometer test (see Sec. 7.6), as shown in Fig. 15.1(a), and in
the ground below a wide foundation on a relatively thin layer of soil, as shown in
Fig. 15.1(b). In both cases the seepage of water from within the body of the soil is
vertical and upwards towards a surface drainage layer where the steady state pore
pressure is always
u
0
=
u
∞
and the excess pore pressure is always zero.
15.2 Theory for one-dimensional consolidation
Figure 15.2 shows an element in a consolidating soil. (Here all dimensions increase
positively downwards to avoid difficulties with signs.) In a time interval
δ
t
the thickness
changes by
h
. The flow of water through the element is one-dimensional and the rates
of flow in through the top and out through the bottom are
q
and
q
δ
+
δ
q
respectively.
