Nature and Phase Properties of Unsaturated Soil - Unsaturated Soil Mechanics in Engineering Practice - page 31

common to continuum mechanics and thermodynamics are
expressed in a succinct form:

constitutive relationships of a system and are not to be part
of the description of stress state.

State variables: Non-material variables required for the
characterization of a material system.
Stress state variables: Non-material variables required for
the characterization of stress equilibrium conditions.
Deformation state variables: Non-material variables
required for the characterization of deformation
conditions or deviations from an initial state.
Constitutive relations: Single-valued equations expressing
a mathematical relationship between state variables.

2.1.5 Designation of Stress State Variables
State variables should be defined within the context of con-
tinuum mechanics as variables that are independent of soil
properties. These variables are required for the characteriza-
tion of a system or a mixture of phases (Fung, 1965). The
theoretical basis for state variables lies within the funda-
mental conservative laws of physics. More specifically, the
stress state variables arise from the conservation of energy.
The stress state variables associated with an unsaturated
soil are related to equilibrium considerations (i.e., Newto-
nian summation of forces or conservation of momentum)
of a multiphase system (Fredlund and Morgenstern, 1977).
The stress state variables in the equilibrium equations can be
extracted to form one or more tensors (i.e., 3

The International Dictionary of Physics and Electronics
(Michels, 1961) defines state variables as “a limited set of
dynamical variables of the system, such as pressure, tem-
perature, volume, etc., which are sufficient to describe or
specify the state of the system completely for the consider-
ations at hand.”
Fung (1965) describes the state of a system as that “infor-
mation required for a complete characterization of the sys-
tem for the purpose at hand.” Typical state variables for
an elastic body are given as those variables describing the
strain field, the stress field, and its geometry. The state vari-
ables must be independent of the physical properties of the
material system. Temperature is also a state variable. Tem-
perature is of particular importance for the consideration of
the behavior of unsaturated soils found near ground surface.
Constitutive relations, on the other hand, are single-valued
expressions or equations that relate one state variable to
one or more other state variables (Fung, 1977). As an
example, a stress-versus-strain relationship is a constitutive
relationship which describes the mechanical behavior of a
material. The material properties involved may be Young's
elastic modulus and Poisson's ratio. There are also many
complex constitutive models that have been proposed for
describing the behavior of both saturated and unsaturated
soils. Common to all constitutive equations is the fact that
selected state variables are linked to form a mathematical
equation.
The ideal gas law equation relates gas pressure and tem-
perature to density and is called a constitutive equation.
The density term defines the relationship between volume
and mass. The gas constant is the material property. Sim-
ple, idealized constitutive equations are well established for
nonviscous fluids, Newtonian viscous fluids, and perfectly
elastic solids (Fung, 1965).
Examples of constitutive relations for unsaturated soils
are equations relating stress state variables to deformation
state variables. Other examples of constitutive relations are
equations for shear strength (e.g., Mohr-Coulomb equation)
and pore pressure generation (i.e., pore-air and pore-water
pressure parameter equations). Soil-water characteristic
curve, SWCC , equations are also constitutive relationships.
Basic definitions from continuum mechanics clearly indi-
cate that the physical properties of a system belong to the

×

3 matrices).
The stress state variables take on the form of tensors because
of the three-dimensional Cartesian coordinate system gener-
ally used for the formulation of engineering problems (i.e.,
our three-dimensional world).
The description of the state variables for an unsaturated
soil becomes the fundamental building block for developing
an applied engineering science. It is the ability to describe
soil behavior in terms of stress state variables that allows us
to refer to unsaturated soil mechanics as a science. The uni-
versal acceptance of unsaturated soil mechanics as a science
depends largely upon how well the stress state variables can
be defined, justified, and measured. The universal accep-
tance of the description of the stress state for an unsaturated
soil has unfortunately been slow. The end result has been
a slow emergence of a consistent theoretical framework for
unsaturated soil behavior.

2.1.6 Designation of Deformation State Variables
Deformation state variables must satisfy conditions pre-
scribed by the conservation of mass. Deformation state
variables allow the movement of various phases of a
multiphase system to be described. Stated another way,
deformation state variables describe the mapping of relative
movements for each phase of a multiphase system.
Deformation state variables associated with the fluid
phases describe relative changes in volume or amount of
fluid in a soil element. It is necessary to independently
define both shear and normal types of strain or deformation
in the case of a solid particulate system constituting the soil
structure. The term “deformation state variables” is used
in this topic to embrace both strain- and deformation-type
variables.
A referential type of soil element has been most com-
monly used in saturated soil mechanics and is suitable for
developing theories in unsaturated soil mechanics. A refer-
ential element is linked to a fixed number of soil particles.
Deformation state variables should ensure that conservation