Civil Engineering Reference
In-Depth Information
Fig. 4.29
Mohr circle diagram for triaxial compression and tension tests.
i.e.
′
1
1
+
sin
sin
φ
φ
σ
′
f
(max)
= ′
σ
1
3
f
−
′
′
′
where
σ
3f
are the respective stresses at failure.
It is possible to fail the sample in axial tension by first subjecting it to equal pressures
σ
1f
and
′
′
σ
1
and
σ
3
and
′
′
then gradually reducing
σ
3
until failure occurs. This test is known as an extension
test and the Mohr-Coulomb expression becomes:
σ
1
below the value of
1
1
sin
sin
′
−
φ
φ
′
=
′
′
<
′
=
′
σ
(min)
σ
where
σ
σ
σ
1
f
3
f
1
2
3
′
+
The Mohr circle diagram showing the maximum and minimum values of
σ
1
for a fixed value of
′
σ
3
is
′
′
>
′
=
′
shown in Fig.
4.29.
In the triaxial compression test the stress state is
σ
σ
σ
3
, and in the triaxial exten-
1
2
sion test the stress state is
1 2 3
.
The symbols used in Fig.
4.29
might be confusing to a casual observer. Strictly speaking, for the exten-
sion test,
σ
′ < ′ = ′
σ
σ
σ
1f
. In
order to avoid this sort of confusion between major and minor principal stresses it has become standard
practice to designate the axial effective stress as
σ
1f
(min)
should really be given the symbol
′
σ
3f
and its accompanying
′
σ
3f
given the symbol
′
′
σ
r
.
A comprehensive survey of techniques used in the triaxial test was prepared by Bishop and Henkel
(
1962)
. For the standard triaxial tests discussed in this chapter, fuller descriptions can be found in BS 1377,
and are given by Head (
1992)
.
σ
a
and the radial effective stress as
′
′
4.12 Behaviour of soils under shear
We saw in Section
4.8.2
that the behaviour of granular soil under shear depends on the initial density of
the soil. Before continuing the subject, it is useful to introduce the following definitions.
●
Overburden
:
The overburden pressure at a point in a soil mass is simply the weight of the material
above it. The effective overburden is the pressure from this material less the pore water pressure due
to the height of water extending from the point up to the water table.
●
Normally consolidated clay
:
Clay which, at no time in its history, has been subjected to pressures greater
than its existing overburden pressure.
