Studies on the P-delta effects of piles embedded in cohesionless soil

C. W. Law, Yung Ming Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review


In this paper, an approach is formulated for analysing a pile embedded in soil in terms of the combined action of axial load and lateral shear with the inclusion of the "P-δ effect" by solving the fundamental differential equation governing the behaviour of an elastic strut supported by elastic springs by the finite difference method. As noted during the formulation of the approach, the lateral deflection and subsequently the internal force in the pile (the elastic strut) are controlled by the applied lateral shear at the pile head only under constant axial load. This phenomenon enables parametric studies to be conducted for piles so as to arrive at charts for quick determination of the lateral deflections and moments for pile heads and tips under different restraints. The approach is then used to analyse piled foundations against horizontal shears with the inclusion of the P-δ effect for piles being hinged and rigidly jointed on the underside of the pile caps with demonstration through the use of worked examples. As an alternative, another approach formulated by the finite element method is outlined and compared. Finally, the applications of the approaches for non-linear soil response, together with the tracing of load-displacement relation, are discussed.
Original languageEnglish
Pages (from-to)134-152
Number of pages19
JournalHKIE Transactions Hong Kong Institution of Engineers
Issue number3
Publication statusPublished - 1 Jan 2015


  • Finite difference method
  • Horizontal subgrade reaction theory
  • Lateral shear stiffness
  • P-δ effect
  • Soil-structure interaction
  • Winkler's spring

ASJC Scopus subject areas

  • General Engineering


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