Winkler model for axially loaded piles in inhomogeneous soil

Analytical closed-form solutions are developed for the elastic and elasto-plastic settlement of axially loaded piles in inhomogeneous soil. The soil is modelled by way of a bed of Winkler ('t-z') springs with stiffness varying as a power function of depth, described by two dimensionless inhomogeneity parameters. The associated governing differential equation is solved in an exact manner using Bessel functions, which reproduce the solution for homogeneous soil. Additional limiting cases are explored including: (a) infinitely long piles, (b) short piles, (c) perfectly floating piles and (d) perfectly end-bearing piles. The solution is extended to the non-linear range by employing elastic-perfectly plastic Winkler springs. A systematic approach for predicting the full load-settlement curve is presented and applied to tests from a site in London. Dimensionless charts are provided for routine design.