Theory to Practice of Unsaturated Soil Mechanics - Unsaturated Soil Mechanics in Engineering Practice - page 4

can be defined as “a unique and important step that brings
theories and analytical solutions into engineering practice”
(Fredlund, 2000a). There are several stages in the devel-
opment of a science that must be brought together in an
efficient and appropriate manner in order for the implemen-
tation of a science to become reality. The primary stages
are as follows (Fredlund, 2000a): (1) state variable stage,
(2) constitutive stage, (3) formulation stage, (4) solution
stage, (5) design stage, (6) verification and monitoring stage,
and (7) implementation stage.
The “state variable” stage identifies each of the
non-material variables that are required to understand
material behavior on a scientific basis within the context of
continuum mechanics. The “constitutive” stage identifies
the basic equation of soil behavior for each physical
process of interest. Constitutive equations provide a linkage
between state variables and incorporate soil properties
(or soil property functions), which must be measured or
estimated. At the “formulation” stage a referential elemental
volume, REV, is selected to which the conservative laws
of physics must be satisfied. The “formulation” stage
generally results in the derivation of a (partial) differential
type equation which must then be solved. The “solution”
stage is identified as an independent stage because it is
sometimes possible to derive a partial differential equation
that describes material behavior; however, it might not be
possible to solve the derived equation. In other words, the
solution of the formulated equation(s) of behavior is worthy
of being referred to as an independent stage. The “design”
stage takes the formulated and solved equations of behavior
and determines how the equations can be used for design
purposes. If it is possible to determine and implement
cost-effective design procedures, then it is important to also
go through a “verification” stage where all previous stages
are tested for reliability in routine engineering practice.
The “implementation” stage suggests that conditions
related to all previous stages have been met and engineering
protocols can be clearly identified. Implementation suggests
that a reliable engineering science is available for describing
particular material behavior, and it is prudent and in the
best interest of the public to utilize the engineering science
in engineering practice. Research studies are necessary to
develop practical, efficient, cost-effective, and appropriate
technologies.

each “challenge” area is given to show that these major
problems have been essentially resolved or solved. Tech-
niques and engineering procedures have been forthcoming
from research in various parts of the world, thereby prepar-
ing the way for more widespread application of unsaturated
soil mechanics.
Challenge No. 1: The development of a theoretically sound
basis for describing the physical behavior of unsaturated
soils starting with appropriate state variables.
Solution No. 1: The adoption of independent stress state
variables based on multiphase continuum mechanics
has formed the basis for describing the stress state inde-
pendent of soil properties. The stress state variables can
then be used to develop suitable constitutive models.
Challenge No. 2: Constitutive relations commonly
accepted for saturated soil behavior needed to be
extended to also describe unsaturated soil behavior.
Solution No. 2: Gradually it became apparent that all
constitutive relations for saturated soil behavior could
be extended to embrace unsaturated soil behavior and
thereby form a smooth transition between saturated and
unsaturated soil conditions. In each case, research stud-
ies needed to be undertaken to verify the uniqueness of
the extended constitutive relations.
Challenge No. 3: Nonlinearity associated with the partial
differential equations formulated for unsaturated soil
behavior resulted in iterative procedures in order to
arrive at a solution. The convergence of highly non-
linear partial differential equations proved to be an
important challenge.
Solution No. 3: Computer solutions for numerical models
have embraced automatic mesh generation, automatic
mesh optimization, and automatic mesh refinement tech-
niques (i.e., known as adaptive grid refinement, AGR).
These techniques have proved to be of great assistance
in obtaining convergence when solving nonlinear par-
tial differential equations. The solution procedures were
largely forthcoming from cooperative research in the
mathematics and computer science disciplines.
Challenge No. 4: Greatly increased costs and time were
required for the testing of unsaturated soils. As well,
laboratory equipment for measuring unsaturated soil
properties has proved to be technically demanding and
quite complex to operate.
Solution No. 4: Indirect estimation procedures for the
characterization of unsaturated soil property functions
were developed. These procedures were related to the
SWCC and saturated soil properties. Several estima-
tion procedures have emerged for each of the unsatu-
rated soil property functions. The computer has proven
to be useful in calculating unsaturated soil property
functions.
Challenge No. 5: Highly negative pore-water pressures
(i.e., matric suctions greater than 100 kPa) have proven
to be difficult to measure, particularly in the field.

1.1.4 Challenges to Implementation
There are a number of major challenges that needed to be
addressed before unsaturated soil mechanics could become a
part of routine geotechnical engineering practice. Each chal-
lenge has an associated solution that has emerged through
ongoing research studies. In some cases it has been neces-
sary to adopt new approaches to solving problems involving
unsaturated soils. Some of the key problems that needed
to be solved for unsaturated soil mechanics to take on the
form of a science are listed below. A brief explanation of