Civil Engineering Reference
In-Depth Information
Figure 10.16
Normalized peak states.
For triaxial tests the equation which is analogous to Eq. (10.19) is
q
p
=
d
ε
v
M
−
(10.20)
d
ε
s
(The negative sign is required because d
v
is negative for dilation.) Again the stress
ratio
q
/
p
is the sum of a friction component
M
and a component due to dilation.
The relationship between the peak strength and the specific volume for triaxial tests
is qualitatively similar to that for shear tests. Figure 10.16(b) shows peak strengths
measured in two tests plotted with axes
q
/
p
ε
and
v
λ
. The critical state line is at
q
/
p
and the normal compression line is at
q
/
p
=
M
and
v
λ
=
=
0 and
v
λ
=
N
.
Figure 10.16(b) is similar to Fig. 9.10(b).
10.6 Comparison between the Mohr-Coulomb and the
stress-dilatancy theories
Remember that the Mohr-Coulomb and stress-dialatancy theories are two different
ways of describing the same soil behviour. The relationships between the two are
illustrated in Fig. 10.17.
This shows four peak state points. The points B
1
and C
1
have the same voids ratio
e
1
and they lie on the same Mohr-Coulomb line given by
c
p1
and
φ
p
.B
2
and C
2
are similar points at the same voids ratio
e
2
and they lie on the Mohr-Coulomb line
given by
c
p2
and
σ
b
, but B
2
is more
heavily overconsolidated than B
1
and has a lower voids ratio. Since B
2
and B
1
will
reach the same critical states at B
c
, sample B
2
must dilate more (i.e. have a larger
value of
φ
p
. Points B
1
and B
2
have the same normal stress
p
) than sample B
1
.
C
1
and
C
2
are similar points. Points B
1
and C
2
have the
same overconsolidation ratio but different voids ratios and normal stresses; their peak
states are given by Eq. (10.19) with the same value of
ψ
ψ
p
.
These simple analyses demonstrate the importance of considering voids ratio, or
water content and dilation, as well as shear and normal effective stresses when
analysing test results and soil behaviour.
