Civil Engineering Reference
In-Depth Information
Figure 10.7
Normalized peak and critical states for triaxial tests.
sustain tensile (negative) effective stresses, this represents a limit to possible states; the
line OT is known as the tension cut-off and it is equivalent to the
τ
axis for shear tests
in Fig. 10.4. The parameter
G
pv
is simply a parameter that defines the position of the
peak state line and is not necessarily the peak strength at low effective stress.
After normalization with respect to
p
c
the results of triaxial tests appear as shown
in Fig. 10.7, which is similar to Fig. 10.5 for shear tests. The critical state and normal
compression lines reduce to single points and the peak states fall on a single line given by
H
p
p
p
p
c
q
p
p
c
=
+
G
p
(10.8)
where the gradient is
H
p
and the intercept is
G
p
.
From the geometry of Fig. 10.7
G
p
=
M
−
H
p
(10.9)
and Eq. (10.8) becomes
p
p
p
c
H
p
q
p
p
c
=
−
−
(
M
H
p
)
(10.10)
Equation (10.10) for triaxial tests is equivalent to Eq. (10.6) for shear tests. In both
there are two independent parameters
φ
p
and
φ
c
or M and
H
p
. The voids ratio, or
σ
c
through Eq. (9.8) or in the critical
water content, is contained in the critical stress
pressure
p
c
through Eq. (9.13).
10.4 A power law equation for peak strength
Uncemented soil can have no strength when the normal effective stress is zero. This is
why you can pour dry sand from a jug. This means that the peak strength envelope
must pass through the origin where
τ
p
=
σ
p
=
0 and it must meet the critical state line
