Civil Engineering Reference
In-Depth Information
into the whole range of states, both on the dry side and on the wet side of the critical
state.
12.4 Calculation of plastic strains
The yield curve is taken to be a plastic potential so that the vector of plastic strain
increment
p
is normal to the curve, as shown in Fig. 12.4. If two lines are orthogonal
the product of their gradients is
δε
−
1, so
s
d
q
d
p
·
ε
d
v
=−
1
(12.10)
d
ε
and, from Eq. (12.6), the plastic strain increments are given by
v
q
p
δε
s
=
M
−
(12.11)
p
δε
v
At the critical state when
q
/
p
0. On the wet side
q
/
p
<
=
M
we have
δε
=
M
v
is positive (i.e. compressive), while on the dry side
q
/
p
>
v
is
and so
δε
M
and so
δε
negative (i.e. dilative), as shown in Fig. 12.5.
Notice that Eq. (12.11) is almost the same as Eq. (10.20); the only difference is
that Eq. (10.20) gives total strains while Eq. (12.11) gives the plastic strains. Equation
(10.20) was obtained by analogy with the work done by friction and dilation and the
derivation was for peak states on the dry side. The similarity between Eqs. (10.20)
and (12.11) demonstrates that the basis of ordinary Cam clay is an equivalent work
equation, but now extended to the wet side as well as the dry side. A more rigorous
derivation of ordinary Cam clay from work principles was given by Schofield and
Wroth (1968).
12.5 Yielding and hardening
As the state moves on the state boundary surface from one yield curve to another
there will be yielding and hardening (or softening if the state is on the dry side) and,
Figure 12.4
Plastic potential and plastic strains for Cam clay.
