1315
Technical Committee 202 /
Comité technique 202
Figure 1: Longitudinal bending moment and settlement map of example
engine foundation.
4 RESULTS OF ANALYSES
The investigations and models performed for this study agree
with the observation that subgrade reaction modulus is not a
fundamental soil property and, for a single soil, varies not only
with the foundation dimensions, but also beneath a given
foundation. Significant variability in calculated subgrade
modulus was observed beneath a single foundation.
A close match was found between computed foundation slab
settlements and bending moments within the foundation slab
using the Plaxis model and the model using Winkler’s Spring
Model. The subgrade modulus is observed to be lowest in the
middle and highest at the ends of the foundation slab. Between
these two points the subgrade modulus variation correlates well
with a second-degree parabolic distribution.
In the example engine foundation case presented in this
article, from which the settlement and bending moment
distributions are presented in Figure 1, the best correlation
between the modeled foundation settlements and bending
moments were found with subgrade modulus being 1190kN/m
3
at the center and 3160kN/m
3
at the ends of the foundation and
being parabolically distributed between these peak values.
Due to good correlation between results from parabolic
subgrade modulus distribution used in Winkler’s soil model and
3D soil-structure model, parabolic distribution of subgrade
modulus was considered to provide sufficiently accurate results.
Therefore, more detailed analysis on which the peak subgrade
modulus would be located somewhere near the edge of the
foundation, due to yielding of soil, were not considered to be
required.
5 DISCUSSION OF COMPUTATION METHODS
The method which was used to determine distribution of
modulus of subgrade reaction below a foundation was time
consuming, but the results were considered positive and logical.
The method allowed definition of subgrade modulus in such
a way that reinforcement quantity in the engine blocks could be
reduced significantly; resulting in large cost savings for the
customer. The designs have since been employed in the field
and the engine foundations exhibit acceptable performance in
operation.
In common structural design programs Winkler’s soil spring
method is often used to model the behavior of soil below a
foundation, even though this method is widely found to be
inaccurate and not reflective of reality. The usage of soil spring
method of Winkler was justified in the past, when only
structural computation methods based on differential equations
have been available. However the structural design programs
based on finite element methods commonly use Winkler’s soil
model for analysis as well in modern engineering practice, even
though modern computation methods (e.g. FE modeling) is
capable of modeling the soil in much greater detail and more
accurately. Use of more sophisticated soil models can be
expected to increase the accuracy of design significantly.
As improvements to the current situation, the authors
propose the following:
Clause 1: Three dimensional finite element soil space shall
be modeled below and around footings.
Clause 2: Soil shall be modeled as elasto-plastic.
Clause 1 would lead to more correct stress distribution
within soil. Using this method a foundation slab would bend
even when being loaded with uniformly distributed loading.
Clause 1 would also take into consideration settlements due to
closely spaced foundations, as was the case with the modeled 6
engine foundations, presented in this article.
The plasticization requirement set in Cause 2 would result in
more realistic pressure distribution below foundation and
problems of extremely high peak pressures occurring at the
corners of foundation would not be observed. This will result in
more realistic bending moments and shear stresses within
foundation slabs.
When the yielding stress of soil is being determined, it
should be noted that if the yielding pressure is set to be too low,
the region of yielded soil will become too large and the
analyzed foundation may not bend as much as it should. This
will result into too small bending moments within the analyzed
foundation slab, resulting into under reinforcement.
Conversely, if the yield strength of soil is set too high, the total
displacements may become too small.
In the conducted analysis, it is found to be very time
consuming for structural engineer to determine distribution of
subgrade reaction below foundation manually. This is due to the
reason that distribution of spring stiffness varies significantly
below footing and different spring variation shall be determined
separately for each load condition. As such it is recommended
that in structural design programs using finite element methods,
the soil would be modeled using more sophisticated soil models
than Winkler’s soil model.
6 REFERENCES
Abdullah W. S. 2008. New elastoplastic method for calculating the
contact pressure distribution under rigid foundations.
Jordan
journal of civil engineering, Volume 2, No. 1, 2008
.
Bergdahl U., E. Ottosson and B. S. Malmborg. 1993. Platt
grundläggning. SIG Statens geotekniska institut. ISBN 91-7332-
662-3
Brinkgreve R. B. J. and Swolfs W. M. 2007. Plaxis 3D foundation.
Version 2. ISBN-13: 978-90-76016-04-7
Coduto D. P. 1994. Foundation design Principles and practices. ISBN 0-
13-335381-8
Das B. M. 2006. Principles of foundation engineering 6
th
edition.
Cengage learning. ISBN 978-81-315-0202-0
Horvath J. S. and Colasanti R. J. January 2011. Soil-structure
interaction research project – a practical subgrade model for
improvement soil-structure interaction analysis: parameter
assessment. <
Lambe T. W. and Whitman R. V. 1969. Soil mechanics. Wiley. ISBN
978-81-265-1779-4
Robobat ROBOT Millenium version 20.0 – User’s manual
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