Theoretical “t-z” Curves for Piles in Radially Inhomogeneous Soil

Abigail Bateman, Jamie Crispin

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


Accurate estimates of pile settlement are key for efficient design of axially loaded piles. Calculations of pile settlement can be simplified using one-dimensional “t-z” curves describing pile settlement at a certain depth as a function of side friction. In the realm of this simplified framework, theoretical “t-z” curves can be derived by substituting an attenuation function describing the variation of shear stress with distance from the pile, into a soil constitutive model relating shear strain to shear stress, then integrating with respect to distance to get the settlement at the pile circumference due to an applied shear stress. A handful of analytical “t-z” curves are available in the literature using the concentric cylinder model to define an attenuation function; these include solutions for linear-elastic, power-law and hyperbolic constitutive models. However, radially homogeneous soil has often been assumed, ignoring the effect of the pile installation resulting in unconservative calculations of pile settlement. This paper considers the installation of the pile, resulting in a radially variable shear modulus distribution in the surrounding soil. A radial inhomogeneity correction factor has been developed for selected constitutive models based on two simplified functions for the soil inhomogeneity, which can be applied to the previously derived “t-z” curves produced assuming radially homogeneous soil. The performance of this simplified method is investigated.
Original languageEnglish
JournalDFI Journal: Journal of the Deep Foundation Institute
Publication statusAccepted/In press - 7 Apr 2020


  • piles
  • settlement
  • "t-z" curves
  • radial inhomogeneity
  • soil/structure interaction

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