Civil Engineering Reference
In-Depth Information
Figure 12.5
Vectors of plastic strain for Cam clay.
in Cam clay, the change of the yield stress is related to the plastic volume change.
Figure 12.6 shows an increment of loading A
B on the wet side of critical, and the
state moves from one yield curve to a larger one with an increase in yield stress and a
reduction in volume. The increment of loading C
→
D on the dry side is associated
with a decrease in yield stress and an increase in volume. Equation (12.1) can be
rewritten as
→
)
q
Mp
(
λ
−
κ
ln
p
−
=
+
λ
−
κ
−
λ
v
(12.12)
Differentiating, dividing by
v
and noting that
δε
v
=−
δ
v
/
v
, we have
λ
−
κ
vp
M
vp
−
η
(
λ
−
κ
)
q
+
p
δε
=
δ
δ
(12.13)
v
vp
M
If we now subtract the elastic volumetric strains given by Eq. (11.3), the plastic
volumetric strains are
λ
−
κ
vp
M
δ
p
v
q
+
−
η
)
δε
=
δ
(
M
(12.14)
and, from Eq. (12.11), the plastic shear strains are
λ
−
κ
vp
M
δ
p
q
p
s
δε
=
−
η
+
δ
(12.15)
M
