Civil Engineering Reference
In-Depth Information
Figure 8.3
Isotropic compression and swelling.
The behaviour shown in Fig. 8.2 is repeated in Fig. 8.3(a) but plotted as specific
volume instead of volumetric strain and with
p
plotted horizontally; this is the con-
ventional representation of soil compression and swelling. Figure 8.3(b) shows the
same behaviour but now with the stress on a logarithmic scale. In Fig. 8.3(b) the com-
pression curve from Fig. 8.3(a) is now linear, which is a very good approximation
for the behaviour of many soils over a wide range of loadings. This idealization is
good for most clays and for sands. For coarse-grained soils volume changes during
the first loading are often accompanied by breakage of the soil grains and it is usually
necessary to apply large stresses (greater than 1000 kPa) to identify the full range
of behaviour. The unloading-reloading loop A
C in Fig. 8.3(a) is approx-
imated by the straight line AB in Fig. 8.3(b). This approximation is less good than
the one for the line OACD. In many soils, especially fine-grained ones, the differences
between unloading and reloading are substantial and both unloading and reloading
lines are non-linear even when
p
is plotted to a logarithmic scale. Stiffness of soil will
be discussed further in Chapter 13. The idealization for isotropic compression and
swelling shown in Fig. 8.3(b) is, however, widely used in basic soil mechanics theories
and in practice.
The line OACD corresponding to first loading is known as the normal compression
line (NCL) and is given by
→
B
→
ln
p
v
=
N
−
λ
(8.2)
is the gradient and
N
is the value of
v
at
p
=
1.0 kPa where ln
p
=
λ
where
0. The
line ABC is known as a swelling line and is given by
ln
p
v
=
v
κ
−
κ
(8.3)
is the gradient and
v
κ
is the value of
v
at
p
=
where
1.0 kPa. The swelling line ABC
meets the normal compression line at C which is a yield point and the yield stress is
p
y
.
κ
