Civil Engineering Reference
In-Depth Information
p
y
with an irrecover-
the soil yielded and hardened as the yield stress increased by
δ
v
p
. Along AB and CD the state was inside the boundary
surfaces and the behaviour is taken to be elastic.
The stress-strain behaviour of an isotropic elastic material is decoupled (i.e. the
shearing and volumetric effects are separated) and from Eq. (3.27),
able plastic volume change
δ
1
3
G
δ
q
δε
=
(11.1)
s
1
K
δ
p
δε
=
(11.2)
v
Another expression for the elastic volumetric strains can be obtained from the equation
for the swelling and recompression lines (see Sec. 8.2) as
δε
v
=
vp
δ
q
(11.3)
κ
where
is the slope of the lines AB and CD in Fig. 11.8. A similar expression for
shearing can be written as
g
3
vp
δ
q
δε
=
(11.4)
s
where
g
is a soil parameter which describes shear stiffness in the same way that
κ
describes volumetric stiffness. (The basic assumption made here is that
G
/
K
=
κ
=
/
g
constant, which implies that Poisson's ratio is a constant.)
With the simple idealization that soil is isotropic and elastic, shear and volumetric
effects are decoupled and volume changes are related only to changes of
p
and are
independent of any change of
q
. This means that, inside the state boundary surface,
the state must remain on a vertical plane above a particular swelling and recompression
line. This vertical plane is sometimes known as an elastic wall (see Fig. 11.9). Notice
that an elastic wall is different from a constant volume section (except for the case of
a soil with
0). Since the soil yields when the state reaches the boundary surface
a yield curve is the intersection of an elastic wall with the state boundary surface, as
shown in Fig. 11.9. Remember that there will be an infinite number of elastic walls,
each above a particular swelling and recompression line, and an infinite number of
yield curves.
κ
=
11.5 Soil behaviour during undrained loading
Figure 11.10 shows the behaviour during undrained loading of sample W initially on
the wet side of the critical state and sample D initially on the dry side, both with the
same initial specific volume. The broken line in Fig. 11.10(a) is the yield curve which is
the intersection of the elastic wall with the state boundary surface so the samples yield
at Y
W
and Y
D
where the stress paths meet the yield curve. Thereafter the stress paths
follow the yield curve and reach the critical state line at the same point at F
u
because
their specific volumes remain constant, as shown in Fig. 11.10(d). Figure 11.10(a)
