Applicability of Timoshenko, Euler–Bernoulli and rigid beam theories in analysis of laterally loaded monopiles and piles

Abstract

In various analytical, semi-analytical and numerical studies on laterally loaded piles, the pile is conventionally modelled as an Euler–Bernoulli beam. Modelling large-diameter monopiles and piles using the Euler–Bernoulli beam theory may not be appropriate, because the Euler–Bernoulli beam theory is strictly valid for long, slender piles and does not account for shear deformations, which may have a significant effect on the lateral pile response of large-diameter piles. In order to investigate the effect of shear deformation in the modelling of monopiles and piles, a framework for static analysis of laterally loaded piles is developed, in which the monopile/pile is modelled using the Timoshenko beam theory and the soil as an elastic continuum. A rational soil displacement field is assumed and the differential equations of pile and soil displacements are obtained using calculus of variations. Solutions are obtained analytically and numerically following an iterative scheme. The analysis framework also incorporates the Euler–Bernoulli and rigid beam theories as progressive simplifications of the Timoshenko beam theory. Pile responses obtained using the three beam theories are compared with three-dimensional finite-element analysis to establish the relative accuracies of each beam theory in predicting lateral pile response. Systematic parametric studies are performed to establish which beam theory is most appropriate to model laterally loaded monopiles and piles, particularly the large-diameter piles, and to find out the range of applicability of the different beam theories in predicting lateral pile response. The Timoshenko beam theory can be used for all cases of laterally loaded piles to produce the most accurate results, particularly for piles with hollow cross-sections. The Euler–Bernoulli beam theory produces accurate results for most piles with solid cross-sections. The rigid beam theory can be used for a quick initial estimate of pile head displacement, particularly for piles with high values of relative pile–soil stiffness ratio.