Civil Engineering Reference
In-Depth Information
9.8 Relationships between strength measured in shear
and triaxial tests
The relationships between stress ratios in shear and triaxial tests using the Mohr circle
constructions were introduced in Chapter 2 and these can be used to relate the results
of triaxial and shear tests. From Fig. 9.12 the radius of the Mohr circle is
t
=
1
2
(
σ
a
−
σ
r
)
1
2
(
and the position of its centre is
s
=
σ
a
+
σ
r
) and
t
s
=
σ
a
−
σ
r
)
(
φ
=
sin
(9.15)
σ
a
+
σ
r
)
(
σ
a
σ
r
=
φ
)
(1
+
sin
tan
2
(45
1
2
φ
)
φ
)
=
+
(9.16)
(1
−
sin
φ
=
φ
c
. Relationships between
φ
c
and
M
can be obtained
and, at the critical state
from Eqs. (9.10) and (9.16) with
q
=
σ
a
−
σ
r
and
p
1
3
(
σ
a
+
σ
r
), noting that
=
2
σ
a
>σ
r
while for extension
σ
a
<σ
r
, so that in Eq. (9.16)
σ
a
/
σ
r
for
for compression
σ
a
for extension. Readers are invited to work
through the algebra and demonstrate that
σ
r
/
compression must be replaced with
φ
c
6 sin
=
M
c
(9.17)
3
−
sin
φ
c
φ
c
6 sin
M
e
=
(9.18)
φ
c
3
+
sin
where
M
c
is for triaxial compression and
M
e
is for triaxial extension. The critical
friction angle
φ
c
is approximately the same for triaxial compression and extension, so
Eqs. (9.17) and (9.18) demonstrate that
M
c
and
M
e
are not equal and
M
c
>
M
e
.
9.9 State and state parameters
In Chapter 8 I introduced the concept of the state of a soil as the combination of
its current voids ratio or water content, normal effective stress and overconsolida-
tion ratio. It is important to understand that it is the state which controls many aspects
Figure 9.12
Stress ratios in triaxial tests.
