Theory to Practice of Unsaturated Soil Mechanics - Unsaturated Soil Mechanics in Engineering Practice - page 18

1.6.1 Components of Boundary Value Problem
The primary components of a BVP can be listed as follows:

further approximations to represent the effect of “leaf
area index,” growing season, and other variables.
3. The soil properties for an unsaturated soil take on
the character of unsaturated soil property functions
(USPFs). Estimation procedures are widely accepted
for the assessment of unsaturated soil property
functions (Fredlund, 1996a; Fredlund et al., 1997a).
However, not all estimation procedures are equally
reliable and the geotechnical engineer needs to
understand the limitations and assumptions associated
with each USPF (M.D. Fredlund et al., 2003). Some
of the factors that need to be taken into consideration
when determining unsaturated soil property functions
are discussed later in the topic.
The assessment of the SWCC forms the basis for
the estimation of all other unsaturated soil property
functions. Later discussions in the topic deal with the
factors that need to be taken into consideration in order
to obtain reliable soil property estimations. There is a
linkage between the SWCCs and the unsaturated soil
property functions, and this linkage must always be
maintained in order to obtain acceptable results from
a numerical analysis.
4. The above information forms the basis for perform-
ing a numerical modeling simulation of a boundary
value problem in geotechnical engineering (Fredlund,
1998a). The partial differential equation that describes
the physics of the problem is nonlinear when unsatu-
rated soils are involved, and consequently there can
be challenges in achieving convergence to the cor-
rect solution. It is important to meet two criteria when
solving nonlinear numerical problems: (i) the computer
software must converge when solving the problem and
(ii) the software must ensure convergence to the cor-
rect solution. In other words, convergence alone is
not a sufficient criterion since there must be assurance
that the solution has converged to the correct solution.
Fortunately, there have been significant advances in
solving highly nonlinear PDEs.
Unsaturated soil problems are distinctive in that the
soil properties always take on a nonlinear soil property
form. The unsaturated soil properties are a function of
the primary state variables for which a solution is being
sought. Consequently, the PDE must be solved through
use of an iterative technique. The PDEs being solved
generally fall into the category of a nonlinear solution
with complex boundary conditions.
Not all computer software packages are equally
capable of solving unsaturated soil problems.
Researchers in the mathematics and computing sci-
ence disciplines have made significant progress with
respect to solving highly nonlinear PDEs. Software
dedicated to solving unsaturated soil problems needs to
take advantage of the latest findings in complimentary
mathematics and computing disciplines.

1. Characterization of the ground surface geometry and
stratigraphy that define the ground surface and the
separation of soil strata (or other materials). The
geometry and stratigraphy can take on a one-, two- or
three-dimensional representation of the engineering
problem. In some situations a one-dimensional
representation is satisfactory; however, with advanced
computing capabilities, two-, and three-dimensional
representations become relatively easy, more realistic,
and more representative of in situ conditions. The
description of the geometry and stratigraphy for
problems involving unsaturated soils is essentially the
same as required for a saturated soil problem.
2. Assessment of the boundary and initial conditions for
analyzing the problem at hand. For flow-type prob-
lems, specifying the head for water flow, pressure for
air flow, or temperature for heat flow results in what
is called a Dirichlet boundary condition. The specifi-
cation of a flow rate across a boundary of the problem
results in a Neumann type boundary condition. Other
intermediate type boundary conditions are also possi-
ble. Similar type boundary conditions can be specified
for stress-deformation types of analyses.
The boundary condition that often needs to be
assessed for many unsaturated soils problems is the
ground surface moisture flux. This means the downward
flux (e.g., rainfall), as well as “actual evaporation” and
evapotranspiration needs to be quantified for one or
more years. For soil cover design the length of weather
records that may be used in simulations may exceed
10 years in length. Initial conditions also need to be
determined because the problem being analyzed is
nonlinear in character.
The assessment of moisture flux conditions at the
ground surface plays a primary role in performing reli-
able simulations of an unsaturated soil problem. It can
be said that most unsaturated soil problems are moisture
flux problems due to the proximity of unsaturated soil
to the ground surface. Precipitation conditions need to
be assessed based on measured weather station data. It
might be necessary to determine precipitation records
that capture (i) typical average year conditions, (ii) typ-
ical dry year conditions, and (iii) typical wet year con-
ditions. As an example, the design of soil cover systems
relies heavily upon actual measured weather conditions
over numerous past years.
A coupled moisture and thermal flow model can be
used to compute actual evaporation at the ground sur-
face (Wilson et al., 1994, 1997b). The solution takes
the form of a “soil-atmosphere model.” Evapotrans-
portation involves the effect of vegetation and requires