Civil Engineering Reference
In-Depth Information
Duncan and Chang (1970) and by Jardine
et al.
(1991). This method requires com-
plex laboratory tests in which the stress paths mimic the
in situ
paths and numerical
analyses that should stop and restart at each change in the direction of a stress path.
An alternative approach is to regard soil behaviour in the small strain region as inelas-
tic, with yielding and hardening with moving yield surfaces inside the state boundary
surface. One approach is to adapt the Cam clay models by including additional yield
surfaces (e.g. Mroz, Norris and Zienkiewics, 1979; Atkinson and Stallebrass, 1991).
In these models the parameters remain the fundamental parameters required by Cam
clay together with additional parameters that describe the relative sizes of the additional
yield surfaces.
At small strains in the region 0.001 to 1% the general relationships between shear
modulus, strain and stress shown in Fig. 13.10 are similar for normally consolidated
and overconsolidated soils. Furthermore, unloading and reloading loops, like those
illustrated in Fig. 13.2, result in substantial irrecoverable strains. These observa-
tions indicate that the basic rules governing stiffness of overconsolidated soils at small
strains are similar to those for normally consolidated soil which, as we have seen, are
essentially elasto-plastic and not purely elastic as assumed in the Cam clay theories.
All this is really quite advanced and any further discussion of developments in
theories for soil stiffness at small strain is clearly beyond the scope of this topic.
13.9 Summary
1. The stress-strain behaviour of soil is highly non-linear over the whole range of
loading except at very small strains less than about 0.001%. These are three ranges
of behaviour:
(a)
very small strain (usually less than 0.001%),
(b)
small strain,
(c)
large strains (for states on the state boundary surface).
2. For states on the state boundary surface the strains are relatively large and can be
modelled reasonably using Cam clay or a similar elasto-plastic model.
3. For very small strains the stress-strain behaviour is approximately linear and the
shear modulus is given by
A
p
p
r
n
G
0
p
r
=
Y
p
(13.8)
where
A
,
m
and
n
depend on the nature of the soil.
4. For small strains the soil is highly non-linear: at a particular strain the shear
modulus is given by
G
p
=
AY
p
(13.10)
where
A
and
m
depend both on the nature of the soil and on the strain.
