Civil Engineering Reference
In-Depth Information
Figure 3.3
Common soil tests.
a uniaxial compression test. For soils, volume changes that occur during compression
and shearing are very important and to describe soil behaviour we must examine sep-
arately shearing and volumetric strains and responses to shearing and normal loading
and unloading.
The two tests commonly used in soil mechanics are the triaxial test and the shear
test illustrated in Fig. 3.3. These will be considered in more detail in Chapter 7.
The relationships between the stresses in the two tests can be obtained from the Mohr
circle construction, as shown in Fig. 3.4. This illustrates that, within the triaxial speci-
men with stresses (
σ
a
,
σ
r
) there are elements with stresses (
τ
n
,
σ
n
) like those in a shear
specimen and vice versa.
In a shear test the sample could be loaded or unloaded by increasing or decreasing
the effective normal stress
σ
n
with zero shear stress and it would compress or swell
with normal strains
n
. Alternatively it could be sheared to the left or to the right and
there would be shear strains
ε
γ
. The triaxial sample could be tested by increasing or
σ
a
or
σ
r
and there would be axial and radial strains
decreasing either
r
.
It is convenient to define special stress and strain parameters for triaxial test samples.
These describe shearing and normal or volumetric effects and they are defined as:
ε
a
and
ε
q
=
σ
a
−
σ
r
(3.3)
1/3
σ
a
+
σ
r
p
=
2
(3.4)
ε
=
2/3
(ε
−
ε
)
(3.5)
s
a
r
ε
=
ε
+
2
ε
(3.6)
v
a
r
The parameter
q
is the diameter of the Mohr circle and it is a measure of the maximum
shear stress. The parameter
p
is the average stress and it is approximately equal to the
distance of the centre of the circle from the origin as shown in Fig. 3.4. The parameter
ε
s
is equivalent to the shear strain and
v
is simply the volumetric strain.
The exact relationships between the pairs of parameters
ε
τ
and
q
for shear stress;
σ
n
and
p
for effective normal stress;
γ
and
ε
s
for shear strains;
ε
n
and
ε
v
for volumetric
