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One Dimensional Shallow Foundation Macro-element

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Developments in Earthquake Geotechnics

Part of the book series: Geotechnical, Geological and Earthquake Engineering ((GGEE,volume 43))

Abstract

Recently a number of macro-element models have been formulated for assessing the performance of shallow foundations during earthquake loading. These provide a computational tool that represents the nonlinear dynamic behavior of the foundation in a manner much simpler than finite element modelling; consequently, they are useful for preliminary design. The basis of this chapter is the shallow foundation moment-rotation pushover curve, which is bracketed by the rotational stiffness at small deformations, determined by the small strain stiffness of the soil, and the moment capacity, which is a function of the soil shear strength and the vertical load carried by the foundation. Between these two limits there is a curved transition. The paper argues that when the vertical load carried by an embedded foundation is a small fraction of the vertical bearing strength, the moment-rotation behavior dominates the response. This means that the structure-foundation system can be reduced to a single degree of freedom (SDOF) model.

The form of the shallow foundation moment-rotation curve obtained from experimental and computational modelling is approximately hyperbolic; the nonlinear shape is due in part to the nonlinear deformation of the soil beneath the foundation but also to gradual loss of contact between the underside of the foundation and the soil below. The paper proposes a generalization of the pushover curve to give a shallow foundation cyclic moment-rotation relationship. The hysteretic damping properties of the model, as a function of the foundation rotation amplitude, are demonstrated as is the relation between secant stiffness and foundation rotation.

This chapter shows how the model can be applied in numerical simulation of structure-foundation systems subject to earthquake time histories. The significance of the maximum displacement (foundation rotation) in relation to the damping and residual rotation at the end of the earthquake record are discussed.

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Authors and Affiliations

  1. Department of Civil & Environmental Engineering, University of Auckland, Auckland, 1142, New Zealand

    M. J. Pender

  2. Partners in Progress Ltd., Sydney, Australia

    T. B. Algie

  3. Tonkin and Taylor Ltd., Auckland, New Zealand

    R. Salimath & L. B. Storie

Authors
  1. M. J. Pender
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  2. T. B. Algie
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  3. R. Salimath
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  4. L. B. Storie
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Corresponding author

Correspondence to M. J. Pender .

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Editors and Affiliations

  1. Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan

    Susumu Iai

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Pender, M.J., Algie, T.B., Salimath, R., Storie, L.B. (2018). One Dimensional Shallow Foundation Macro-element. In: Iai, S. (eds) Developments in Earthquake Geotechnics. Geotechnical, Geological and Earthquake Engineering, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-62069-5_9

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