Civil Engineering Reference
In-Depth Information
(b) A log
10
(time) method
As an alternative, it is sometimes more convenient to fit the experimental and theoret-
ical consolidation curves at
U
t
=
0.5, i.e. when half of the consolidation is complete.
The value of
T
v
for
U
t
=
0.5 may be found from Eq. (15.33) and is
T
v
=
0.196.
To estimate a value for
t
50
, the time for
U
t
=
0.5 during a single stage of consolidation
in an oedometer test, it is convenient to plot
U
t
against log
t
as shown in Fig. 15.10(b).
The value for
t
50
may be read directly from the experimental consolidation curve.
Theoretical and experimental curves fit when
c
v
t
50
H
2
T
v
=
=
0.196
(15.37)
0.196
H
2
t
50
c
v
=
(15.38)
Note that
U
t
cannot be calculated until the final settlement
ρ
∞
has been found.
Ideally, settlement-time curves would approach horizontal asymptotes as illustrated
in Fig. 15.10 and it would not be difficult to estimate a value for
ρ
∞
. For most
experimental settlement-time curves, however, these horizontal asymptotes are not
clearly defined and, moreover, there is often an initial settlement which is observed
immediately after the loading increment has been applied. For most practical cases it is
necessary to estimate a value for
ρ
∞
bymeans of sp
e
cial constructions. A construction
ρ
t
against
√
t
was proposed by Taylor and a
for estimating
ρ
∞
from a plot of
construction for estimating
t
against log
10
t
was proposed by
Casagrande; both constructions are described by Taylor (1948).
ρ
∞
from a plot of
ρ
15.8 Continuous loading and consolidation
If the loading in a test which is supposed to be drained is applied too quickly excess
pore pressures will occur but there will also be some drainage, so the loading is neither
fully drained nor fully undrained. This is, of course, what happens in the ground, but
solutions of general problems of coupled loading and drainage are very difficult. There
are, however, relatively simple solutions for coupled one-dimensional loading and these
form the basis of continuous loading consolidation tests (Atkinson and Davison, 1990).
Figure 15.11(a) shows a continuous loading one-dimensional compression test with
a drain at the top and an impermeable boundary at the bottom. At a particular instant
in the test the total stress is
and the pore pressures at the top
an
d bottom of the sample are
u
0
and
u
b
, so the excess pore pressure at the base is
u
b
σ
, the settlement is
ρ
σ
is the mean vertical
effective stress and the isochrone is taken to be parabolic. Figure 15.11(c) shows the
variations of total stress
σ
H
, where
=
u
b
−
u
0
. The shaded are in Fig. 15.11(b) is
σ
, settlement
ρ
and pore pressures
u
0
and
u
b
, all of which
must be measured during the test.
From Eqs. (15.7) and (15.8) the basic equation for coupled loading and consolida-
tion is
2
u
=−
∂σ
∂
c
v
∂
=
∂
−
∂σ
∂
u
(15.39)
z
2
∂
∂
t
t
t
