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Determination of distribution of modulus of subgrade reaction
Détermination de la distribution du module de réaction d’un sol de fondation
Larkela A., Mengelt M., Stapelfeldt T.
Ramboll Finland Oy
ABSTRACT: In this investigation, three dimensional finite element soil modeling was used to model the behavior of a rectangular
foundation block for on-grade cases in which the foundation experiences uniform loading. Modeling was completed using the
commercially available three-dimensional finite element software Plaxis 3D Foundation, Version 2.2. Based on analyzing results,
distribution of modulus of subgrade reaction was determined.
RÉSUMÉ : Lors de cette étude à éléments finis tridimensionnels, on a analysé le comportement d'une fondation rectangulaire de taille
variable qui a été soumise à différentes sollicitations uniformes. La modélisation a été effectuée à l'aide du logiciel commercial aux
éléments finis Plaxis 3D Foundation, version 2.2. A l'aide des résultats obtenus, le module de réaction a été terminé.
KEYWORDS: Modulus of subgrade reaction, soil structure interaction, foundation design, three dimensional finite element modeling.
1 GENERAL
The modulus of subgrade reaction is a parameter expressing
the pseudo-elastic behavior of subgrade soil beneath the
foundation, and is used for structural analysis of soil-structure
interaction. The subgrade modulus concept models the
behavior of soil as a series of single springs, and is commonly
called Winkler’s spring model. The method allows estimation
of settlement beneath a loaded shallow foundation member, and
thereby facilitates calculation of shear stresses and bending
moment magnitudes within the foundation. These calculated
values are used for example to dimension the reinforcements for
a concrete footing.
The basis of the extensive usage of Winkler’s soil model is
in its simplicity to the differential equations which have been
used to develop the method. However, it is commonly
acknowledged that the assumption of soil units acting as
separate, elastic springs of uniform stiffness below a footing
does not model realistic foundation behavior. Results are
unconservative for example in cases when the foundation is
loaded with uniform loading.
In this investigation, three dimensional finite element soil
modeling was used to model the behavior of a foundation block
on grade cases in which the foundation experiences uniform
loading. Modeling was completed using the commercially
available three-dimensional finite element software Plaxis
Foundation 3D, Version 2.2.
The modeling program was completed for Wärtsilä Finland,
a major northern European supplier of integrated power
generation solutions. The foundations considered in this
program were foundation blocks for large diesel engines. A
variety of engine foundations were considered for the study,
representing the foundation blocks of a variety of diesel engine
sizes and weights.
2 NATURE OF MODULUS OF SUBGRADE REACTION
Modulus of subgrade reaction is a spring constant describing
the relationship between applied pressure and resulting
deflection (settlement) below a structural element founded on
grade. In the structural analysis the soil is modeled as an elastic
half space, and local supporting pressure is assumed to be
directly proportional to settlements. The subgrade modulus is
not a fundamental soil property and its magnitude depends on
many factors, among them shape of the foundation, stiffness of
foundation slab, shape of loading on the foundation, depth of
the loaded area below the ground surface, and time. As such, it
is not constant for a given type of soil, which makes the
estimation of a single general value for design a challenging
task.
Modeling work performed in this study demonstrates that the
theoretical springs of the subgrade reaction modulus also vary
below a foundation. The variation of the subgrade reaction
modulus arises especially when a foundation slab is loaded with
uniform loading, because vertical pressure near the edges and
corners of the foundation are significantly higher while the
settlements at the same locations are smallest due to bending of
the foundation slab, producing high spring constant.
Conversely, at the center of the foundation the pressure is
smaller and the settlement higher; thus, the spring constant is
smaller at that location. The variation in the calculated
subgrade reaction modulus causes the foundation to bend even
under uniformly distributed loading.
Further, plastification of soil plays an important role in the
determination of modulus of subgrade reaction. If the soil is
modeled as purely elastic, pressure concentrations are observed
at foundation edges and corners, leading to over conservative
reinforcement design of the concrete foundation.
3 METHOD OF CALCULATION
3.1
General
The Finite Element Program PLAXIS 3D Foundation 2.2
was used for the analyses. PLAXIS 3D is programmed and
built specifically for analysis of interaction between soil and
structures.
3.2
Foundation Model
The foundation type used to support the engines is a
rectangular block of reinforced concrete. The analyses
