A semi-analytical solution for laterally loaded non-circular piles in elastic soil

The traditional method for analysis and design of laterally loaded piles with non-circular cross-sections such as rectangular, H-shaped, and X-shaped piles involves the simplification of converting the non-circular pile to a circular pile with equivalent second moment of inertia. A rigorous semi-analytical method is developed for calculating the response for laterally loaded piles with arbitrary non-circular cross-sections in multi-layered elastic soil without using any simplification regarding the shape of the pile cross-section. The governing differential equations for the pile–soil system are obtained using the principle of virtual work. The soil displacements around the pile are described as products of separable functions that are compatible with horizontal pile movement. As a result, the three-dimensional (3 D) boundary value problem (BVP) is described by a fourth-order linear ordinary differential equation (ODE) governing horizontal pile displacement and second-order partial differential equations (PDEs) governing soil displacements. New solution techniques for the ODE and PDEs are proposed, and the accuracy of the present method is verified by comparing the predicted pile and soil responses with the corresponding results of equivalent 3 D finite element method. The effects of pile cross-section shape and lateral loading direction on the pile and soil responses are highlighted through a series of parametric analyses.