Environmental Engineering Reference
In-Depth Information
CHAPTER 15
Compressibility and Pore Pressure Parameters
15.1
INTRODUCTION
of an unsaturated soil is considered simply in terms
of changes in pore-water pressures and displacements
with respect to time and space. The theory of con-
solidation involves the solution of two PDEs with
respect to time (provided the problem geometry is one
dimensional). The consolidation problem could also
have a two- or three-dimensional geometry, in which
case the solution would involve the solution of three
or four PDEs, respectively (i.e., two or three stress-
deformation PDEs and one water flow PDE).
2. The theory of consolidation of an unsaturated soil can
also be considered as involving air flow in addition to
water flow and stress-deformation. In this case there
would be an additional air flow PDE that needs to be
solved in a time and space domain.
3. While the theory of consolidation is generally viewed
as a volume decrease problem in response to the
application of an external load, there are similar pro-
cesses associated with the swelling of an expansive or
unsaturated soil. As well, the collapse phenomena in
low-plasticity unsaturated soils can be viewed as
undergoing a consolidation-type process. The number
of PDEs that need to be solved depends on how rigor-
ous a solution is required and the number of geometric
dimensions.
4. Heat flow physical processes can also be combined
with water and/or air flow to form other combinations
of processes that might need to be solved.
5. Soil-atmospheric models involve the solution of PDEs
related to liquid water flow, water vapor flow, and heat
flow, in addition to satisfying other thermodynamic
considerations. Climatic factors are used to generate a
net moisture flux at the ground surface. These solu-
tions are common to the design of soil cover systems
[i.e., store-and-release covers or evapotranspirative
(ET) covers].
6. Thermal, mechanical, flow (TMF) models refer to
mechanical (i.e., stress-deformation), heat flow, and
moisture flow (i.e., liquid and vapor water flow) pro-
cesses. The TMF models involve three unsaturated soil
There are a variety of physical processes that are of inter-
est to geotechnical engineering. Several have been presented
in previous chapters as independent physical processes that
form the basis of a science for unsaturated soil mechanics.
Some of the processes are as follows: (i) flow of liquid water
through porous media, (ii) flow and compression of air and
water vapor in an unsaturated soil, (iii) heat flow in soils, and
(iv) stress-deformation analysis that allow the calculation of
normal and shear components of stress and strain. There
are also processes such as the contaminant transport phe-
nomena that could be presented as an independent process;
however, diffusive flow is usually presented in conjunction
with advective water flow.
Each of the above-mentioned physical processes has been
discussed and the theory of behavior has been presented. In
each case, a REV element was selected and a mathemati-
cal equation was derived to describe the particular physical
phenomena. It was shown that each physical process could
be described in the form of one or more PDEs to be solved.
Flow processes were described for either steady-state or
unsteady-state (or transient) conditions.
It is important to have a thorough understanding of each
independent physical process from a theoretical, soil prop-
erty, and solution standpoint. It is also important to realize
that many of the processes common to geotechnical engi-
neering involve multiple or combined processes. The real
world of soil mechanics quite often involves a combination
of two or more independent physical processes. It is neces-
sary to solve more than one set of PDEs when more than one
physical process is associated with a particular geotechnical
engineering problem.
Following are some examples of geotechnical engineering
problems that involve the solution of more than one physical
process:
1. The theory of consolidation involves a combination
of the physics associated with the flow of water and
air as well as the physics associated with a stress-
deformation analysis. Often the theory of consolidation
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