State Variables for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 105

σ h ) .
The selected stress point represents the state of stress on a
plane with an orientation of 45 ◦ from the principal planes,
as shown in Fig. 3.24.
The vertical net normal stress for the condition shown in
Fig. 3.24 is greater than the horizontal net normal stress (i.e.,
σ v −

The q -coordinate is one half the deviator stress (σ v − 3.6 ROLE OF OSMOTIC SUCTION

Total suction ψ is made up of two primary components,
namely, matric suction u a − u w and osmotic suction π , and

can be mathematically represented by

ψ = (u a − u w ) + π (3.63)

u a ). This results in a positive
q -coordinate. A negative q -coordinate would indicate the
condition where σ h −

u a is greater than σ h −

Matric suction is known to vary with time mainly as a
result of conditions imposed by environmental changes. Any
change in suction affects the overall equilibrium of the soil
mass. Changes in soil suction may be caused by a change
in either one or both components of soil suction.
The role of osmotic suction has been associated more
with unsaturated soils than with saturated soils. However,
osmotic suction is related to the salt content in the pore-
water. It should be remembered that salts are present in the
pore-water of both saturated and unsaturated soils. The role
of osmotic suction is therefore equally applicable to both
unsaturated and saturated soils. Osmotic suction changes can
have an effect on the mechanical behavior of a soil. There
can be a change in the overall volume and shear strength of
the soil if the salt content changes.
Most engineering problems involving unsaturated soils
are commonly the result of environmental changes. The
accumulation of water below a house may result in a reduc-
tion in matric suction and subsequent heaving of the struc-
ture. Similarly, the stability of an unsaturated soil slope
may be endangered by excessive rainfall that reduces the
suction in the soil. These weather-imposed conditions pri-
marily affect the matric suction component. Osmotic suc-
tion changes are generally less significant and consequently
receive less attention. However, there are situations where
the salt content of a soil is changed and, as a result, there
can be a change in the physical properties of the soil.
Figure 3.25 shows the relative importance of changes
in osmotic suction as compared to changes in matric suc-
tion when water content is varied. The total and matric
suction curves are almost congruent one to another, par-
ticularly in the higher water content range. In other words,
a change in total suction is essentially equivalent to a change
in the matric suction [i.e., ψ

u a is greater than σ v − u a . For the

hydrostatic or isotropic stress state (i.e., σ h − u a ),

the q -coordinate is equal to zero. A zero q -coordinate means
the absence of shear stresses.
There are three independent stress points and as a result it
is somewhat difficult to graphically present the stress paths
being followed in practical engineering problems.

u a = σ v −

3.5.2.2 Stress Points (Elastoplastic system; Wheeler
and Sivakumar, 1995)
The laboratory testing of saturated and unsaturated soils is
most commonly performed in a triaxial test. The mean net
total stress can be defined for the triaxial test specimen as
the vertical total stress plus two times the horizontal stresses.
In other words, the stress state is defined for the special
three-dimensional coordinate system defined by the triax-
ial test.
The triaxial test representation of the stress state can then
be used as the reference condition for describing the physi-
cal properties of the soil. Wheeler (1996) suggested the use
of the net mean total stress, the maximum principal stress
difference, and the matric suction to describe the stress path
followed when testing and analyzing an unsaturated soil
problem:

σ v +

u a

σ 1 +

u a
(3.60)

2 σ h

σ 2 + σ 3

p = − p = −

or

3 3

q = σ v − σ h or q = σ 1 − σ 3 (3.61)

r = u a − u w (3.62)

u w ) ]. Matric suc-
tion changes are almost the same as total suction changes,
and vice versa, for many geotechnical problems involving
unsaturated soils as long as additional salts are not added to
the soil.
There is another reason why it is generally not neces-
sary to take osmotic suction into account. The reason is
related to the laboratory test procedures adopted when solv-
ing geotechnical engineering problems. Changes in osmotic
suction that occur in the field are essentially simulated dur-
ing the laboratory testing for pertinent soil properties. For
example, let us consider the swelling process of a soil as
a result of rainfall infiltration into the soil. The rainfall,
which is essentially distilled water, dilutes the pore-water
and changes the osmotic suction. In the laboratory, the soil

≈ (u a −

where:

σ 2 = intermediate principal stress.

The shear stress is defined in terms of the difference
between the maximum and minimum principal stresses,
σ 1 − σ 3 .

Wheeler (1996) selected specific volume as the deforma-
tion state variable for overall volume change or soil struc-
ture deformations. The state variables proposed were used
to advance an elastoplastic framework for unsaturated soil
behavior. Once again, it is a challenge to graphically illus-
trate multidimensional stress and deformation changes due
to the number of variables involved.