The analysis of an axially loaded pile with account for its varying length

Abstract

First variations of a vertical displacement and an axial force at a specified cross-section of axially loaded pile due to changes of location of its end-points are derived. A simple one-dimensional idealization of the pile in conjunction with the soil model consisting of a continuously distributed system of springs and a spring located at the pile toe is assumed. The considerations based on calculus of variations enable us to define the adjoint structure and finally to express the first variations of quantities under consideration by means of the variations of location of the pile end-points. A detailed discussion of calculation of the variations for the pile embedded in a multi-layered soil is also included. Comparison between the exact results of analysis of the pile with changed location of its end-points and the approximate ones obtained by means of the first variations derived is given as well.