Civil Engineering Reference
In-Depth Information
The one-dimensional compression modulus
M
is given by
σ
z
d
1
m
v
M
=
z
=
(8.9)
d
ε
and, as before,
C
is a yield point. A parameter often quoted in practice is the one-
dimensional coefficient of compressibility
m
v
.
Note that the compression and swelling lines in Fig. 8.9 are non-linear and so
M
and
m
v
(like
K
in Eq. 8.5) are not constants but depend on the current stress and are
different for loading and unloading.
Figure 8.10(a) shows the same behaviour as that in Fig. 8.9 and is equivalent to
Fig. 8.3(a) for isotropic compression. Figure 8.10(b) shows the same behaviour with
σ
z
plotted to a log
10
scale and specific volume replaced by voids ratio. (The axes
e
and
log
σ
z
are commonly used in practice for plotting the results of one-dimensional tests.)
All the essential features for isotropic compression and swelling described in Sec. 8.2
are repeated for one-dimensional compression and swelling. The principal differences
are that the parameter
N
for isotropic compression is replaced by
e
0
and the parameters
λ
and
κ
are replaced by
C
c
and
C
s
. The normal compression line OACD is given by
σ
z
e
=
e
0
−
C
c
log
(8.10)
and the swelling and recompression line ABC is given by
σ
z
e
=
e
κ
−
C
s
log
(8.11)
Since
.
For overconsolidated soil at a point such as B in Fig. 8.10(a) the yield stress ratio
Y
0
is given by
δ
v
=
δ
e
and log
10
x
=
0.43 ln
x
we have
C
c
=
2.3
λ
and
C
s
=
2.3
κ
Y
0
=
σ
y
σ
0
(8.12)
Figure 8.10
One-dimensional compression and swelling.
