Analysis of Structure Supported By Elastic Foundation – Foundation Models

Analysis of Structure Supported By Elastic Foundation

Soil Structure Interaction

  • Soil is a very complex material for the modeling.
  • It is very difficult to model the soil-structure interaction problem.
  • In RCC buildings slab on grade is a very common construction system e.g. mat footing
  • Very heavy slab loads occur in these structures.
  • For safe and economical design, compute plate displacement and stresses accurately.
  • Difficult to obtain samples for testing producing results in accordance with ground behavior.
  • Necessary to make simplifying assumptions.

Scope Of Study

  • To develop a workable approach for analysis of plates on elastic foundations.
  • Structural Engineers go for simplified assumptions of rigid foundation
  • STAAD Pro is used to incorporate the elasticity of soil that will provide approximate solutions as close to the exact solutions.

Types of Foundation Models

  • The plate-foundation system is idealized as a thin elastic plate resting on a linearly elastic foundation.
  • Various foundation models were given by the investigators which are discussed ahead.


Deformation Of A Uniformly Loaded Plate On Typical Winkler Model
Deformation Of A Uniformly Loaded Plate On Typical Winkler Model
  • Winkler first studied beam on elastic springs
  • Model based on the pure bending beam theory.

p = Kw

Here, w = vertical translations of the soil, p = contact pressure, K = modulus of subgrade reaction

  • Plates based on Winkler  model involve fourth order differential equation:

D ▼4 w+ Kw = q

Here D is the plate flexural rigidity, q is the pressure on the plate and▼ is the Laplace operator.

  • The deformations outside the loaded area were neglected and taken as zero.
  • Winkler foundation model has two major limitations:
    • No interaction between springs is considered.
    • The spring constant may depend on a number of parameters, such as stiffness of beam, geometry of beam, soil profile, and behavior.


Filonenko Borodich Model

  • Top ends of springs connected to a elastic membrane stretched to constant tension T.
  • It was done to achieve some degree of interaction between the spring elements,
  • Modulus of subgrade reaction is given by


p = Kw – T ▼2 w


  • Embedded a plate in the three-dimensional case in the material of the Winkler foundation to accomplish interaction among springs.
  •  Assumed that the plate deforms in bending only.

p = Kw + D▼2 ▼2 w

Here, p = load, w = vertical translation, D = flexural rigidity of plate.


  • Pasternak assumed shear interactions between spring elements.
  • Connecting the ends of springs to a beam or plate consisting of incompressible vertical elements, which can deform only by transverse shear.

p = Kw – G ▼2 w


  • This model is based on Timoshenko beam theory
  • Plane sections still remain plane after bending but are no longer normal to the longitudinal axis.
  • This model considers both the bending and shear deformations.

Modulus Of Subgrade Reaction

  • Pressure sustained per unit deformation of subgrade at specified deformation or pressure level.
  • Calculated from plate load test from the plot of q versus δ

K  = q/δ

Here , q = mean bearing pressure,    K = modulus of subgrade reaction,    δ = mean settlement

For Analytical Study refer PPT

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