Environmental Engineering Reference
In-Depth Information
The stress state variable for the normal stress in Eq. 3.67
can be subdivided into two components. The first component
is the conventional effective stress for a saturated soil (
σ
Chattopadhyay (1972) experimentally demonstrated that cal-
culated values of
R
A
produced equal changes in effective
stress when constant-volume conditions were maintained.
The second requirement for the use of a combined stress
state variable is that all components of the proposed stress
state variable be measurable. When using the true effective
stress
σ
∗
, it is not possible to directly measure
R
−
−
u
f
). The second component is the net interparticle repul-
sive stress minus attractive stress (
R
A
). The two stress
components can also be visualized as a single stress state
variable (
(σ
−
−
u
f
)
−
(R
−
A)
) provided there is a means of
−
A
.The
measuring the
R
A
stress variable. This expression is sim-
ilar to that proposed equation for “true” effective stress by
Balasubramonian (1972) and Chattopadhyay (1972):
−
computation of
R
A
is possible only under ideal condi-
tions. This results in a severe restriction to the use of
R
−
A
as a component of stress state. However, it is still possible
to use an independent approximation of
R
−
A
as a state
variable provided it is used in a manner independent of the
other components shown in Eq. 3.68.
The osmotic suction
π
concept relates the change in
repulsive stress between clay particles to the change in
the osmotic suction between the interparticle fluid and the
bulk pore fluid. Mitchell (1962) suggested that the double
layer interactions and the subsequent repulsions between
particles are a reflection of osmotic pressure.
Osmotic pressure can be visualized as having two compo-
nents: one component associated with the free salt in the bulk
solution and the other component caused by the additional
ions required to satisfy the double diffuse layer. The osmotic
suction
π
of the bulk solution can be evaluated using sam-
ples of the pore fluid; however, the net interparticle repulsive
stress minus attractive stress (
R
−
σ
∗
=
σ
−
u
f
−
(R
−
A)
(3.68)
where:
σ
∗
=
true effective stress.
Two requirements need to be met to justify the usage of
a combination of stresses as a single stress state variable.
The first requirement is that a particular change in one com-
ponent of the stress state variable be equally as effective
in changing physical soil properties as changing the other
component of the stress state variable. Fredlund and Morgen-
stern (1977) demonstrated that a null-type test could be used
to confirm the correct components for the stress state vari-
ables for unsaturated soils using this technique. Balasubramo-
nian (1972), Morgenstern and Balasubramonian (1980), and
−
A
) is difficult to measure.
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