Civil Engineering Reference
In-Depth Information
Figure 9.2
Compression and dilation during shearing.
defined by
d
ε
v
tan
ψ
=−
(9.1)
d
γ
This is the gradient of the volume change curve as shown in Fig. 9.1(c) and it also
gives the direction of movement of the top of the sample as shown in Fig. 9.1(a). The
negative sign is introduced into Eq. (9.1) so that dilation (negative volumetric straining)
is associated with positive angles of dilation.
Figure 9.1(d) shows the change of voids ratio
e
rather than the volumetric strains
shown in Fig. 9.1(c), although, of course, they are related. Both samples have the same
effective normal stresses but the initial voids ratio of the sample on the wet side is
higher than that of the sample on the dry side. Notice, however, that both samples
reach their critical states at the same voids ratio
e
f
.
As volume changes in soils are principally due to rearrangement of particles it is easy
to see why soils on the wet side compress while soils on the dry side dilate. In Fig. 9.2
the grains of the loose or normally consolidated soil at W are spaced well apart and,
on shearing, they can move into the neighbouring void spaces, while the grains of the
dense or overconsolidated soil at D must move apart during shear. This is an example
of the coupling between shear and volumetric effects in soils.
9.2 Peak, critical state and residual strengths
As shown in Fig. 9.1, soils initially on the dry side of the critical line reach peak states
before the critical state. The peak state will normally be reached at strains of the order
of 1% while the critical state will be reached after strains greater than 10% (in some
soils the critical states are not reached until the strains have exceeded 50% or so).
Notice that the peak state coincides with the point of maximum rate of dilation (i.e. at
maximum
). Soils on the wet side compress throughout, shearing up to the ultimate
state, and there is no peak.
ψ
