1314
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
considered the behavior of a variety of different engine
types/sizes, and the various engine foundation blocks associated
with each engine. Depending on the engine type and size, the
thickness of an individual engine foundation varies between
0.6m and 1.2m. The length of a foundation block varies
between 10.4m and 20.9m and width between 3.3m and 4.8m.
The analysis also considered groups of engines, ranging from
one to six engines in a row placed along their short axes.
During the usage period, the engine is founded on a spring
packet on top of the foundation slab. The purpose of the
packets is to damp vibration induced by the engine to the
foundation. Each engine is founded on a packet of 20 springs;
modeling work by others indicates that the load transmitted
through the foundation slab and into the subgrade is evenly
distributed. Pressure below each engine type varies between
24kPa and 50kPa. Due to relatively thick foundation slab and
heavy reinforcement within the slab, the engine foundations
were modeled as linearly elastic; this design assumption was
discussed and agreed with the structural engineer to be a valid
assumption.
Plaxis 3D Foundation 2.2 allows modeling of structural plate
units as two dimensional floor elements. This simplification
from three dimensional elements was employed, because using
this method the program provides bending moments, shear
stresses and settlements of plate units in an easily-usable format.
For the purposes of brevity a single engine type is discussed
in this report. The results of this engine analysis are reflective
of the results obtained for other engine foundation types.
Foundation dimensions of this example engine model are 11.9m
by 4.1m by 0.6m, with uniformly distributed pressure on a
foundation slab of 28.5kPa. Group affects of engines placed
closely in rows was found to influence the results obtained; as
such, the results provided in this article are representative for
the two middle engines in 6 engine foundation group. This
arrangement produces the largest estimated foundation
settlements, bending of foundations and therefore the largest
bending moments within the foundation blocks. Free distance
between each engine foundation was 1.1m, reflecting the
distance between the engines after installation in a typical
facility.
The analysis results reveal that with these rectangular
foundation dimensions, the variation of the subgrade modulus is
more significant over the length of the foundation as compared
with the width of the foundation. Thus the distribution of
modulus of subgrade reaction was determined only in
longitudinal direction of foundation. This assumption was
confirmed by investigating the bending moments and
settlements in the diagonal direction across the foundation.
3.3
Soil Model
Plaxis 3D Foundation offers various soil models for different
purposes and applications. In this particular case, application of
the hardening soil model was considered to be the most suitable
model because it is formulated in an elasto-plastic framework.
The soil model considers hardening of the soil by shear
hardening and isotropic compression hardening. The isotropic
compression hardening can be simplified as hardening of soil,
when the soil is placed under isotropic pressure and the pore
pressure within the soil is allowed to dissipate. The shear
hardening of soil is the increased shear strength of soil, as the
pore pressure between the soil particles decreases.
Yielding of the soil occurs if the shear strength of the soil is
exceeded in any element node point, because the soil is modeled
as elasto-plastic. Yielding of soil below the edges and corners
of foundation slab is considered to be very important in
determination of naturalistic bending of the foundation and
especially in determination of bending moments and shear
stresses within the foundation slab. If the yielding of soil would
be neglected from the analyses, unrealistically high bending
moments and shear stresses would occur at the edges and
corners of foundation slab.
The three dimensional model of the soil space below and
around the foundation slab allowed more realistic distributions
of stresses. Modeling of the soil space as three dimensional
around and below the foundation slab, was the key element in
resolving the bending of the foundation slab even with evenly
distributed loading in top of the foundation slab. As the
pressure is distributed on a wider area around the corners of the
foundation slab, the corners and edges of the foundation settle
less than the center portion of the foundation even when the
loading on the foundation slab is evenly distributed.
These considerations allowed more realistic analyses of the
soil especially when compared to conventional Winkler’s spring
model, even though simplifications were made.
The dimensions of the model were chosen to be 200m x
200m; depth was chosen to be 50m. Given these dimensions,
no boundary effects were observed due to induced stresses
during calculation stages.
3.4
Procedure and Order of Analysis
Due to the reason that modulus of subgrade reaction is
specifically used for structural analyses the modeling work with
PLAXIS was performed in close co-operation with structural
engineers. Therefore the following work flow net of work was
used in order to determine distribution of modulus of subgrade
reaction:
1. Dimensions and elastic modulus of foundation were
determined by the structural engineer.
2. Load acting on the foundation was determined by structural
engineer.
3. Soil parameters were defined by geotechnical engineer.
4. Soil – structure interaction was determined by geotechnical
engineer using PLAXIS 3D finite element modeling program.
5. Results from soil-structure interaction modeling, including
bending of slab, settlement of slab, and bending moments with
in the slab were provided for the structural engineer. Example
settlement and bending moment distribution maps are presented
in Figure 1 of this article.
6. Structural engineer evaluated whether assumption of elastic
behavior of foundation was valid.
7. The structural engineer used the modeled values and a finite
element model of a beam on Winkler’s springs to determine
subgrade reaction modulus (spring constant) distribution below
the foundation, to obtain a match between results from the
Plaxis model and the model of the beam on springs. Match
between both foundation settlements and bending moments
within the foundation slab were required to approve the spring
model.
8. The varying spring constants calculated in Step 7 were used
for design of the foundation reinforcements. Using this method,
no unique value of subgrade modulus was found, and the actual
soil-structural interaction was reflected by the non-uniform
values calculated from the modeling and analysis program.
