A Non Linear and Plastic-Hardening Modelling of Vertically Loaded Piles-Paper

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The paper presents a nonlinear analytical model for vertically loaded piles based on the work–energy principle. It treats pile settlement as the sum of tip settlement and elastic shortening of the shaft, using tip settlement as the model’s independent variable. At each depth, the elastic strain energy associated with axial load is balanced against the tip-reaction energy and the plastic-hardening work of shaft friction.<br /><br />The soil’s nonlinear response is represented through load-transfer relationships between displacement and shaft shear stress or tip pressure. The model identifies dimensionless interaction parameters describing the relative stiffness of the pile and soil, including a characteristic interaction length and pile slenderness. It provides upper- and lower-bound load–settlement responses and estimates settlement components, axial load distribution, and load sharing between shaft friction and end bearing. For layered soils, the pile is divided into segments, each treated as a homogeneous layer; the segments act as superimposed piles connected by compatibility and equilibrium.<br /><br />Two case studies compare model predictions with pile load tests: one in broadly homogeneous soil and another in layered clay and dense sand. The results show good agreement with measurements and illustrate how the model can support back-analysis and evaluation of pile behavior. In the layered-soil example, tip movement in the dense sand mobilizes end bearing and contributes to further capacity development. The approach offers a relatively simple analytical tool for interpreting pile response and checking more complex models.

Keywords

pile settlement

work-energy principle

load-settlement response

shaft friction

end bearing

nonlinear analytical model

vertical piles

layered soil

axial load distribution

soil-pile interaction