Civil Engineering Reference
In-Depth Information
Because the pore pressures remain constant at
u
0
, the changes of effective stress follow
the change of total stress, as shown in Fig. 6.10(d). When the stresses remain constant at
σ
0
+
σ
, the volume remains constant at
V
0
V
. This kind of relatively slow loading
is called drained because all the drainage of water takes place during the loading. The
most important feature of drained loading is that the pore pressures remain constant
at
u
0
, which is known as the steady state pore pressure.
Figure 6.11(a) illustrates the same increment of total stress
−
as in Fig. 6.10 but
now applied so quickly that there was no time for any drainage at all and so the volume
remains constant, as shown in Fig. 6.11(b). If the loading was isotropic with no shear
distortion and undrained with no volume change then nothing has happened to the soil.
From the principle of effective stress this means that the effective stress must remain
constant, as shown in Fig. 6.11(d), and, from Eq. (6.16), the change in pore pressure
is given by
σ
σ
=
σ
−
u
=
0
(6.17)
u
=
σ
(6.18)
This increase in pore pressure gives rises to an initial excess pore pressure
u
i
, as shown
in Fig. 6.11(c). Notice that the pore pressure
u
c
onsists of the sum of the steady state
pore pressure
u
0
a
n
d the excess pore pressure
u
; if the pore pressures are in equilib-
rium
u
0. Relatively quick loading is known as 'undrained loading'
because there is no drainage of water during the loading. The most important feature
of undrained loading is that there is no change of volume.
At the end of the undrained loading the pore pressure i
s
u
=
u
0
and
u
=
=
+
u
i
, where
u
0
is
the initial steady state, or equilibrium, pore pressure and
u
i
is an initial excess pore
pressure. This excess pore pressure will cause seepage to occur and, as time passes,
there will be volume changes as shown in Fig. 6.11(b). The volume changes must be
associated with changes of effective stress, as shown in Fig. 6.11(d), and these occur
as a result of decreasing pore pressures, as shown in Fig. 6.11(c). The pore pressures
decay towards the long term steady state pore pressure
u
∞
. Fig. 6.11(c) shows
u
∞
=
u
0
u
0
but there are cases in which construction, especially of excavations changes the steady
state groundwater and
u
∞
can be greater or s
m
aller than
u
0
.
At some time
t
the excess pore pressure is
u
t
and this is what drives the drainage
and so, as the excess pore pressure decreases, the rate of volume change, given by the
gradient d
V
/d
t
, also decreases, as shown in Fig. 6.11(b). Notice that while there are
excess pore pressures in the soil, water pressures outside the surface of the soil will not
be the same as the pore pressures; this means that the pore pressure in soil behind a
new quay wall need not be the same as the pressure in the water in the dock.
This dissipation of excess pore pressure accompanied by drainage and volume
changes is known as cons
ol
idation. The essential feature of consolidation is that there
are excess pore pressures
u
that change with time. Usually, but not always, the total
stresses remain constant. Consolidation is simply compression (i.e. change of volume
due t
o
change of effective stress) coupled with seepage. At the end of consolidation,
when
u
∞
=
0, the total and effective stresses and the volume are all the same as those at
the end of the drained loading shown in Fig. 6.10. Thus, the changes of effective stress
for undrained loading plus consolidation are the same as those for drained loading.
