Civil Engineering Reference
In-Depth Information
ln
p
c
, where
p
c
is the stress at the intersection of the constant volume section
and the critical state line and is
v
=
−
λ
ln
p
p
c
q
Mp
+
λ
λ
−
κ
=
1
(12.3)
ln
p
with the
state boundary surface. At the critical state line the specific volume is
v
c
and the mean
stress is
p
c
, as shown in Fig. 12.2(b) where
v
c
A yield curve is the intersection of an elastic wall given by
v
=
v
κ
−
κ
ln
p
c
=
−
λ
ln
p
c
. Eliminating
=
v
κ
−
κ
v
and
v
κ
, the equation for the yield curve shown in Fig. 12.2(a) is
ln
p
p
c
q
Mp
+
=
1
(12.4)
Note that the equations of the constant volume section, or undrained stress path, and
the yield curve are different except for the special case of a soil with
κ
=
0. From
Eq. (12.4), with
q
=
0, the yield stress
p
y
is related to the critical state stress
p
c
on the
same yield curve by
p
y
p
c
=
exp(1)
=
2.72
(12.5)
Figure 12.2
Yield curve for ordinary Cam clay.
