Analytical Solution for Axially Loaded Piles in Two-Layer Soil

George Anoyatis*, George Mylonakis

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

13 Citations (Scopus)
198 Downloads (Pure)


An analytical elastic continuum model is developed for the settlement of end-bearing piles in a two-layer soil over a rigid stratum. The model has its roots in the point-load solution of Westergaard, which was later extended by Tajimi to deep foundations and lies on the assumption of a vanishing soil stress or displacement component. For piles in homogeneous soils, such solutions were elaborated on by Nogami and Novak. Contrary to these solutions, the proposed generalized formulation can handle layered soils using, for the first time, two sets of eigenfunctions (static "modes") that are different for the soil and the pile. Stresses and displacements are determined in the form of Fourier series with coupled coefficients obtained by solving a system of algebraic equations of rank equal to the number of modes considered. This is in contrast with existing models, where the Fourier coefficients are obtained individually. Pile-head stiffnesses obtained from this model are verified against results from rigorous finite-element analyses and other solutions. Results for pile settlement, pile stresses, side friction, and Winkler moduli are presented.

Original languageEnglish
Number of pages15
JournalJournal of Engineering Mechanics
Issue number3
Publication statusPublished - 10 Jan 2020


  • Analytical model
  • Elasticity
  • End-bearing piles
  • Layered soil
  • Soil-pile interaction


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