Civil Engineering Reference
In-Depth Information
Figure 9.8
Critical state line for triaxial tests.
for shear tests. The critical state line in Fig. 9.8 is given by
q
f
=
Mp
f
(9.10)
ln
p
f
v
f
=
−
λ
(9.11)
where, as before, the subscripts f denote failure at the critical states. Comparing
Eq. (9.10) with Eq. (9.2), the critical stress ratio
M
is equivalent to the critical friction
angle
φ
c
. In Fig. 9.8(b) the gradients of the critical state line and the isotropic normal
compression line are both
λ
and the lines are parallel.
The parameters
M
,
λ
and
which describe the critical states in triaxial tests are
φ
c
,
C
c
and
e
which describe the critical states in shear
tests. Both sets of parameters are material parameters. They depend only on the nature
of the grains of the soil. (However, values of
M
and
equivalent to the parameters
measured in triaxial compression
σ
a
<σ
r
).
Results of triaxial tests may be normalized like the results of shear tests. The nor-
malizing parameters, shown in Fig. 9.9, are the critical pressure
p
c
and the equivalent
specific volume
v
λ
; these are comparable to
σ
a
>σ
r
) are a little different to the values measured in triaxial extension tests (
(
σ
c
and
e
λ
in Fig. 9.6. (The equivalent pres-
sure on the isotropic normal compression line
p
e
is often used as a normalizing parame-
ter for triaxial tests but, again, I want to use
p
c
because the critical state line is unique.)
