Civil Engineering Reference
In-Depth Information
Equations (12.16) and (12.17) are constitutive equations like Eq.
(3.26) and
components of the compliance matrix are
λ
−
κ
M
(
M
1
vp
g
3
C
11
=
−
η
)
+
(12.18)
λ
−
M
(
M
1
vp
−
η
)
C
22
=
+
κ
(12.19)
λ
−
κ
M
1
vp
C
12
=
C
21
=
(12.20)
These demonstrate that in Cam clay the basic compliances contain the intrinsic soil
parameters
M
,
q
/
p
. Thus, in
Cam clay, the behaviour is non-linear since, in general,
v
,
p
and
q
change during a
loading path. Notice that towards failure at the critical state when
and
g
and the current state given by
v
,
p
and
η
=
λ
,
κ
η
→
M
we have
C
11
→∞
0. Thus, near ultimate failure, shear strains become very large
while volumetric strains become very small.
and
C
22
→
12.7 Applications of Cam clay in design
Although Eqs. (12.16) and (12.17) are a complete set of constitutive equations for
soil there is still quite a lot of further analysis required before they can be used for
detailed design. For example, they are written in terms of shearing and volumetric
effects, but for calculations they need to be rewritten in terms of the normal and shear
stresses and strains on horizontal and vertical planes in the ground and possibly in
three dimensions.
Ordinary Cam clay has the advantage that with yield curves as logarithmic spirals the
algebra is relatively simple. Although it describes the main features of soil behaviour
qualitatively there are a number of detailed aspects where it is not so good. Another
model, modified Cam clay, is based on yield curves that are ellipses; this is described
in detail by Muir Wood (1991).
The Cam clay equations can be implemented in finite element and similar numerical
analyses as described by Britto and Gunn (1987). Be warned though: these analyses
are quite complex and difficult to do properly. If you are interested in making use of
these advanced techniques you are advised to start by working with people who have
previous experience.
12.8 Summary
1. Cam clay is a theoretical model for soil behaviour: it includes strength and stress-
strain behaviour within a single, relatively simple set of equations.
2. Cam clay combines the theories of critical state soil mechanics and the idea of a
state boundary surface with the theories of plasticity, including yielding, hardening
and plastic flow.
3. There are different versions of Cam clay, depending on the precise equation for
the state boundary surface.
