Theoretical t-z Curves for Axially Loaded Piles

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


Estimation of non-linear pile settlement can be simplified using one-dimensional “t-z” curves which conveniently divide the soil into multiple horizontal “slices”. This reduces the continuum analysis to a two-point boundary-value problem of the Winkler type, which can be tackled by standard numerical procedures. Theoretical “t-z” curves can be established using the “shearing-of-concentric-cylinders” theory of Cooke and Randolph-Wroth, which involves two main elements: (a) a constitutive model cast in flexibility form, γ =γ(τ); (b) an attenuation function of shear stress with radial distance from the pile, τ =τ(r). Soil settlement can then be determined by integrating shear strains over the radial coordinate, which often leads to closed-form solutions. Despite the simplicity and physical appeal of the method, only a few theoretical “t-z” curves are available in the literature. This paper introduces three novel attenuation functions for shear stresses, inspired by continuum solutions, which are employed in conjunction with eight soil constitutive models leading to a set of 32 “t-z” curves. Illustrative examples of pile settlement calculation in two soil types are presented to demonstrate application of the method.
Original languageEnglish
JournalJournal of Geotechnical and Geoenvironmental Engineering
Publication statusAccepted/In press - 5 Nov 2021


  • piles
  • settlement
  • non-linear analysis
  • "t-z" curves
  • soil/structure interaction


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