Geotechnical and Geological Engineering

, Volume 30, Issue 6, pp 1323–1333 | Cite as

Factors Affecting Differential Settlements of Framed Structures

  • Angeliki E. Arapakou
  • Vasileios P. Papadopoulos
Original paper


The estimation of settlements, differential settlements and relative rotations on critical positions of the foundation is indispensable when carrying out analyses of both ultimate and serviceability limit states. The use of finite element method is recommended in cases where soil–structure interaction is expected to be significant. The scope of this paper is a contribution to the investigation of general trends in the effects of main parameters on the interaction. A typical five-span frame building with varying rigidity was examined by using finite element numerical method under 2-D conditions. Soil below the foundation was simulated as linearly elastic or elastoplastic medium. The effects of superstructure and foundation rigidity are closely related to the effect of soil deformability thereby analyses were performed in terms of relative rigidity factors. The effects of specific foundation types, namely isolated footings, flexible and rigid mat, were investigated in detail. The conclusions were focused on the development of normalized differential settlements, on the influence of the relative rigidity factor as well as on the determination of those cases where the interaction approach is necessary to be used for the analysis.


Differential settlements Rotation Relative rigidity Footings Mat foundations 

List of symbols


Equivalent thickness of the beam of the frame


Thickness of very flexible beam


Thickness of medium stiffness of the beam


Thickness of very rigid beam


Modulus of elasticity of the soil


Modulus of elasticity of the concrete


Moment of inertia


Length of the foundation


Span length


Flexural moments


Flexural moments when soil–structure interaction is ignored


Flexural moments of the extreme rigid foundation slab


Maximum settlement


Global safety factor

Rb = Eb × J/E × l3

Relative rigidity factor of the beam of the frame

Rf = Eb × J/E × L3

Relative rigidity factor of the foundation slab


Thickness of the foundation


Thickness of very flexible foundation


Thickness of very rigid foundation


Axial load of column


Axial load of column when soil–structure interaction is ignored


Relative rotation


Relative deflection


Differential settlement






Poisson’s ratio


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Angeliki E. Arapakou
    • 1
  • Vasileios P. Papadopoulos
    • 1
  1. 1.School of Civil EngineeringNational Technical University of AthensAthensGreece

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