Theory to Practice of Unsaturated Soil Mechanics - Unsaturated Soil Mechanics in Engineering Practice - page 17

The purpose of the cover system can be viewed as func-
tioning quite differently in differing situations. For example,
the cover may operate as a “store-and-release” system in one
case, but it might be desirable to have it function as a sat-
uration oxygen barrier in another situation. The location of
the water table in the underlying materials also has a strong
influence on the functionality of the cover system. Elements
of a soil cover system (i.e., atmosphere, cover, and under-
lying soils) are variable, highly nonlinear, hysteretic, and
random in nature (Fredlund, 2006). The challenges related
to solving such a problem are formidable but not impossible.
At present, it is fair to say that several geotechnical engi-
neers might produce somewhat different design solutions for
a particular cover system.

three aspects of unsaturated soil mechanics behavior when
dealing with a particular engineering problem. Typically,
a flux boundary condition produces an unsteady-state
saturated/unsaturated flow situation which results in volume
change and a change in the shear strength of the soil.
The change in shear strength can be translated into a
change in factor of safety. There may also be an interest in
quantifying the change of other volume-mass soil properties
(i.e., water content and degree of saturation).

1.6 PARTIAL DIFFERENTIAL EQUATIONS
IN SOIL MECHANICS

Various classes of soil mechanics problems can be visu-
alized as the solution of one or more partial differential
equations (PDEs). The PDE is derived by applying appro-
priate constitutive relationships to a REV while adhering
to the conservative laws of physics (i.e., conservation of
mass and conservation of energy). The resulting PDE sat-
isfies the physical conditions associated with the behavior
of the soil for a particular class of geotechnical engineering
problems.
The physics for a REV can then be applied to a finite-sized
element of a continuum which is called a “finite element.”
Combining many finite elements together allows an entire
continuum to be modeled. Boundaries or limits must be
placed on the region that is being considered. This gives
rise to what is called a “boundary value problem” such as
is shown in Fig. 1.19. At the heart of boundary value for-
mulation is a description of the physical soil behavior for
the REV.
The laws of physics that pertain to the REV are extended
throughout a region until the boundaries of the selected
geometry are reached. A numerical solving technique (e.g.,
the finite element method) is used to solve a series of
equations that embrace the physics for the entire region
under consideration.

1.5.9 Road and Railroad Structures
Some of the oldest infrastructural components of civiliza-
tion are roads and railroads. The preparation of the subgrade
and the placement of subbase and base materials have been
largely determined over decades of trial and error. Conse-
quently, the design of pavement and railroad structures is
quite empirical in nature.
There are many aspects related to the performance of
pavements and railroads which are not well understood
because the underlying materials are most often unsaturated.
Little research has been focused on understanding the
physical behavior of unsaturated subgrade materials as well
as subbase and base materials. Attempts to model pavement
structures have provided new insight into the movement of
water through the unsaturated granular materials (Barbour
et al., 1992). Normally, granular materials are perceived
of as being highly pervious; however, this is not true
when the materials are unsaturated. These materials have
the capability of forming capillary barriers and resisting
the movement of water. Much more could be learned
about the suitability of various granular materials from an
engineering standpoint if the water movement properties
were characterized and actual climate events were simulated
using numerical saturated-unsaturated seepage models.
Matric suction in the subgrade of highways and railroads
plays a major role in the performance of the structure
(Khogali et al., 1991; Marjerison et al., 2001; Zapata et al.,
2009). Measurements of matric suction in the subgrade
have been shown to decrease in the spring of the year or
during wet periods of the year. Sattler et al. (1989) proposed
bearing capacity approaches to the design of railroads and
highways based on the unsaturated shear strength of the
subgrades.

Finite element

REV

Element for which a
PDE must be derived

Must define initial conditions

1.5.10 Characteristics of Unsaturated Soil Examples
The above examples show that there are many situations
that require an in-depth understanding of seepage, volume
change, and shear strength characteristics of unsaturated
soils. There is often a need to simultaneously consider all

Boundary value must be specified

Figure 1.19 Use of REV to formulate PDE to solve a “boundary
value problem” (BVP).