Winkler modulus for axially loaded piles

The problem of elastic soil-pile interaction and its modelling using the concept of a Winkler support are revisited. It is shown that dividing the vertical soil shear tractions and the corresponding settlements along the pile generates depth-dependent Winkler springs that accurately describe the pile-soil interaction, contrary to the widespread belief that the Winkler representation is always approximate. A simplified theoretical model is then derived for analysing the response of an end-bearing cylindrical pile in a homogeneous soil stratum. Explicit solutions are obtained for: (a) pile settlement; (b) depth-dependent Winkler modulus; (c) average (depth-independent) Winkler modulus to match pile head settlement. Both infinitely long piles and piles of finite length are examined. The approximate analytical solution compares favourably with finite-element and boundary-element solutions. A simple regression formula for the average Winkler modulus is developed.