. In the pile-soil model, the lateral load is located at the pile head including both lateral force and bending moment. The single pile is considered as a beam on elastic foundation while shear beams model the soil column below the pile toe. The differential equations governing pile deflections are derived based on the energy principles and variational approaches. The differential equations are solved iteratively by using the finite element method that provides results of pile deflection, rotation angle, shear force, and bending moment along the pile and equivalent stiffness of the pile-soil system. The modulus reduction equation is also developed to match the proposed results well to the three-dimensional finite element analyses. Several examples are conducted to validate the proposed method by comparing the analysis results with those of existing analytical solutions, the three-dimensional finite element solutions. |
