Analytical solutions for piles' lateral deformations: The nonlinear stiffness case

Design of piles under lateral loads requires accurate estimation of the pile deflections. The Winkler beam model is the most popular mechanical model for piles, employed by both researchers and engineers. However, it assumes a constant soil stiffness, which is unrealistic since experimental data, referred to homogeneous soils, prove a nonlinear trend of the soil stiffness with depth. This paper discusses the limits of existing pile models and proposes an unprecedented analytical model for piles under lateral loads embedded in soils with stiffness that does not linearly depend on depth. The analytical solution of the governing Ordinary Differential Equation is derived and represented in explicit closed-form in terms of generalized hypergeometric functions. In addition, the paper delivers parametrized solutions for typical load conditions where a horizontal force and bending moment are applied at the pile's top. The paper examines a pile response in three cases assuming as soil stiffness the constant, linear and cubic fitting of experimental estimates of the subgrade stiffness of an actual clay deposit. No negligible difference in displacement, moment and shear were detected. Still, the proposed nonlinear model leads to the most conservative estimates of the displacement. Peculiar trends characterize the results in shear and bending moment responses compared to the constant and linear soil profiles.