Application of a Rigorous Subgrade Model in the Analysis of Rectangular Plates on an Elastic Foundation Using Finite Difference Method
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Date
2019
Authors
Journal Title
Journal ISSN
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Publisher
Addis Ababa University
Abstract
Plate on elastic foundation establishes an adequate idealization in the analysis of shallow
foundations, which includes isolated footings, combined footings, mat foundations, and flexible
pavement.
The
important
issue
in
the
analysis
is
modeling
the
contact
between
the
plate
and
the
soil
medium
that
is
a
soil-structure
interaction
(SSI)
problem.
The
primary
difficulty
in
the
analysis
of
the
soil–structure
interaction
lies
in
the
determination
of
the
contact
pressure.
The
simplest
subgrade
model
is
the
single
parameter
Winkler
mechanical
model,
which
represents
the
foundation
soil
by
a
series
of
independent
springs.
Winkler
model
is
widely
used
and
practiced
in
spite
of
its
deficiency
in
representing
the
continuous
behavior
of
real
soils.
Later, many advanced mechanical subgrade models have been proposed in order to
improve on the inherent lack of shear interaction among the individual springs. However,
these models still have their drawbacks in that they do not represent the subgrade shear
interaction adequately. With the objective to improve on such drawbacks, a generalized continuum-based
model
has
been
recently
proposed
by
Worku.
This
generalized
subgrade
model
satisfies
the
fundamental
elastic
laws
and
all
the
boundary
conditions
since
it
is
derived
by
considering
all
stress,
strain
and
displacement
components.
The main objective of this work is to implement and calibrate the generalized continuum
based subgrade model for the analysis of rectangular plates on an elastic foundation. The
governing differential equation of a rectangular plate that incorporates Pasternak type subgrade
model
is
formulated.
Thus,
an
ordinary
finite
difference
method
is
developed
to
solve
the
partial
differential
equations.
Code
based
on
MATLAB
®
programming language is writ-
ten for determining deflections and internal actions of the plate. Finite Element based software
is
used
as
a
tool
to
determine
an
adjustment
factor
for
the
generalized
model.
Finally,
the
proposed
method
has
been
validated
by
comparing
the
results
with
other
numerical
models
for
selected
loading
conditions.
The
results
of
the
comparison
show
that
the
generalized
model
shows
an
excellent
agreement
with
the
FE
outputs
and
capable
of
predicting
the
behavior
of
the
rectangular
plates
on
elastic
foundations.
Description
Keywords
Elastic Foundation, Rigorous Subgrade Model, Rectangular Plates, Finite Difference Method