Environmental Engineering Reference
In-Depth Information
It is possible that the above conditions might be met
by more than one set of stress state variables. The final
selection of state variables may come back to personal pref-
erence and in the end constitute a philosophical preference.
In any case, it is not prudent to incorporate soil properties
into the selection of stress state variables. Developments
within continuum mechanics have, in general, adhered to
this condition and the framework of continuum mechanics
has proven to be an all-encompassing and unifying theory
embracing the behavior for many types of materials.
σ
1
u
a
σ
3
σ
3
u
w
σ
1
(a)
160
3.2.1 Experimental Evidence for Stress State Variables
Numerous laboratory experiments have been performed
which assist in understanding the stress state description
of unsaturated soils. The laboratory tests are not a test for
“uniqueness” but rather are a test based on deviations from
equilibrium conditions. Stress state variables can only be
“tested” for equilibrium considerations.
A key experiment on unsaturated soils was performed
by Bishop and Donald (1961) (Fig. 3.1). In this experi-
ment, a specimen of loose Braehead silt was subjected to
drained triaxial compression where there was independent
control of
σ
3
(i.e., the all-round confining pressure),
u
a
,
and
u
w
. The pressure components were changed during the
experiment with the restriction that changes in net confining
120
σ
3
σ
3
−
u
a
= 13.8 kPa
u
a
80
u
a
−
u
w
= 58.6 kPa
σ
3
u
a
40
u
w
σ
3
0
u
a
u
w
-40
u
w
-80
02
6
0
4
8
Strain,
ε
(%)
(b)
pressure [i.e.,
σ
3
−
u
a
] remained at zero and changes in
1
2
3
4
5
Portion
matric suction [i.e.,
u
a
−
u
w
] remained at zero while the
individual components of stress were changed. Deviatoric
stresses and volumetric strain were monitored and found to
vary monotonically with axial strain, as shown in Fig. 3.1.
The results can be interpreted as confirming that each of the
stress state variables (i.e.,
σ
3
−
160
120
80
Rate of strain
0.03% per hour
40
u
w
),
was not altered and therefore the unsaturated soil behav-
ior remained monotonic. It is interesting to note that the
experimental results can also be used to lend support to the
Bishop (1959) type of effective stress equation in this case
because the material soil property linking the state variables
remained constant.
The experimental results support the validity of using
independent stress state variables but do not allow exclu-
sive interpretation of the data in favor of a particular set
of stress state variables. It is also possible to suggest that
any one of three possible combinations of the stress state
variables is experimentally justifiable.
In 1956, Hilf proposed the axis translation testing tech-
nique along with test results on several soils. The axis trans-
lation technique made it possible to measure matric suc-
tions greater than 1 atm. Unsaturated soil specimens were
placed onto a high-air-entry disk and the negative pore-
water pressure was measured (i.e., provided the matric suc-
tion was less than 1 atm). Results in Fig. 3.2 show that
when the air pressure above the soil specimen was changed
by a particular amount, the measured pore-water pressure
reaction was always equal to the air pressure change. This
u
a
,
u
a
−
u
w
,
and
σ
3
−
Partial unloading
0
02
6
0
4
8
Strain,
ε
(%)
e
final
= 0.86
Liquid limit = 29%
Plastic limit = 23%
S
= 43%
(c)
Figure 3.1
(a) Drained triaxial test on unsaturated loose silt with
σ
3
,
u
a
,
and
u
w
, varied while keeping
σ
3
−
u
w
constant.
(b) Pressure changes versus strain. (c) Deviator stress versus strain.
(Data from Bishop and Donald, 1961.)
u
a
and
u
a
−
meant that the measured matric suction remained at a con-
stant value.
Examination of the axis translation procedure reveals that
the test constituted a special “null” type of test under which
the stress state remains constant. It should be noted that in
this test the total pressure is equal to the applied air pres-
sure [i.e.,
σ
u
a
=
−
0]. Therefore, the stress variables
σ
u
w
, remain constant throughout the axis
translation test. As a consequence, the axis translation type
−
u
a
and
u
a
−
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