Integrated Soil–Pile Elements for Inelastic Design of Steel Piles Considering Lateral Soil–Pile Interactions

Steel piles are widely used in deep foundation systems to transfer significant structural loads to strong soil layers. A steel pile may buckle or fail by forming multiple plastic hinges at different locations. The pile’s plastic hinge distributions and failure mode are considerably affected by soil–pile interactions (SPIs). A proper consideration of SPIs is essential for the successful design of a steel pile foundation. In practice, empirical calculation or numerical modeling analysis methods are commonly utilized. Nevertheless, the conventional design methods are cumbersome in the modeling process and may be inaccurate in considering SPIs. This paper develops a new integrated soil–pile element to explicitly reflect SPIs and capture steel piles’ inelastic behaviors based on the plastic hinge method and the Euler–Bernoulli beam theory. Two virtual nonlinear springs, the concentrated rotational and distributed lateral springs, are used to simulate the plastic hinge deformations and the soil responses, respectively. The rotational and lateral springs are assigned at both ends and the Gauss integration points of an element, respectively. The Gaussian quadrature method is utilized to consider the soil reactions and generate the soil stiffness matrix. Based on the numerical integration and condensation methods, the virtual springs are directly integrated into the element formulation, simplifying the programming and practical modeling process. The updated Lagrangian approach is adopted for describing the element kinematic motions. The element tangent and secant relations between nodal forces and displacements are derived based on the potential energy principle. Several verification examples are presented to demonstrate the capability of the proposed element.