Civil Engineering Reference
In-Depth Information
Figure 7.8
Stresses on a triaxial sample.
frame and a motor drive applies a constant rate of strain loading. There is a drain at
the base of the sample connected to flushing and drainage apparatus like that shown in
Fig. 7.3; if the drainage valve is open the sample is drained and if it is closed the sample
is undrained. Radial strains are generally not measured directly but are calculated from
measurements of the axial and volumetric strains.
The axial and radial total stresses on the sample,
σ
a
and
σ
r
, are shown in Fig. 7.8(a).
The radial stress is
σ
=
σ
(7.10)
r
c
where
σ
c
is the cell pressure as shown in Fig. 7.8(b) but
σ
c
acts also on the top of the
sample. From Fig. 7.8 the axial stress
σ
a
is given by
F
a
A
σ
a
=
σ
r
+
(7.11)
or
F
a
A
=
σ
=
σ
a
−
σ
r
−
σ
(7.12)
a
r
If you go back to Sec. 3.2 you will see that
F
a
/
A
is the same as the deviator stress
q
.
A simple way to think of the stresses in a triaxial sample is to decompose
σ
a
and
σ
r
into an isotropic state
F
a
/
A
as
in Fig. 7.8(c); thus the force in the ram
F
a
(divided by the area of the sample) applies
a stress that deviates from an isotropic state. Note that
A
is the current area of the
sample allowing for changes of axial and volumetric strain. If the loading ram is raised
away from the top platen so that
F
a
σ
a
=
σ
r
=
σ
c
as in Fig. 7.8(b) plus a deviatoric state
q
=
r
.
In a conventional triaxial test the sample would be isotropically compressed, either
drained or undrained to the required initial state. The loading ram would then be
lowered to touch the top platen, the axial strain set to zero and the sample sheared
by increasing the deviator stress
q
, either drained or undrained, at a constant rate of
strain. If the cell pressure
=
0 the state of stress is isotropic, with
σ
=
σ
a
σ
c
is zero (in this case you need not fill the cell with water)
the test is known as unconfined compression. There are a number of other special tests
that can be carried out in the triaxial apparatus. These require special modifications
to be made to the conventional apparatus, which are discussed in Sec. 7.9.
