Euler-bernoulli pile element for nonlinear buckling analysis of single piles in slope

Piles are sometimes unavoidably embedded in slopes for supporting buildings on hills. In contrast to a pile on a horizontal ground, a pile in slope is acted on by additional sliding force from the slope, impairing its load-bearing capacity and buckling resistance. Nevertheless, proper assessment for the buckling of piles in slopes is difficult because of the simulation of distributed sliding forces and nonlinear pile-soil interactions. This paper refines the newly developed Euler-Bernoulli pile element formulation for the nonlinear buckling analysis of single piles in slopes by including the sliding force in element formulation, enabling a rigorous consideration of soil-pile interactions. Detailed mathematical derivations are provided. The numerical implementation is illustrated with a flowchart. Four examples for verification are demonstrated to reveal the robustness of the proposed method and the importance of considering the sliding force.