Higher-order winkler solutions for laterally-loaded piles

Eva Agapaki, Xenia Karatzia, George Mylonakis

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

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Novel analytical solutions are derived for the response of a flexible elastic pile in homogeneous soil to dynamic inertial and kinematic loads. The solutions are based on the Winkler model of soil reaction and encompass three soil constants (three-parameter model) instead of one in the classical formulation (one-parameter model). This extension allows for a more rational calibration of the model against reference solutions such as finite or boundary elements, by matching all three stiffness constants – in swaying, rocking and cross-swaying rocking – at the pile head. This approach leads to a more realistic representation of pile-soil interaction and a better estimation of internal forces– notably peak pile bending moments – along the pile. Both inertial and kinematic interaction is examined, induced by pile head loads and vertically propagating shear waves, respectively. Closed-form solutions are obtained for: (1) the stiffness coefficients at the pile head, (2) the maximum bending moments, (3) the kinematic response coefficients. Remarkably, the method does not lead to a significant increase in complexity of the analysis, as the order of the governing differential equation and the boundary conditions at the pile head and tip are the same as in the classical model. A novel geometric interpretation of the three elastic constants is provided.
Original languageEnglish
Title of host publicationProceedings of the 16th European Conference on Earthquake Engineering
PublisherEuropean Association for Earthquake Engineering (EAEE)
Publication statusPublished - 22 Jun 2018


  • Three-parameter Winkler model
  • Flexible piles
  • Stiffness constants
  • Kinematic coefficients


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