A closed-form solution for kinematic bending of end-bearing piles

Kinematic soil-pile interaction is indispensable for seismic design of pile foundations and superstructures. The current understanding of kinematic pile bending mostly relies on either continuum approaches, requiring complex numerical calculation or iterative decoupling, or Winkler beam approaches, overlooking the continuity and shear stiffness of soils. In this study, a closed-form solution was proposed for the kinematic bending of end-bearing piles. In this solution, the conventional Beam-on-Dynamic-Winkler-Foundation (BDWF) was extended to incorporate the shear resistance of soils via Pasternak model. The proposed solution can provide an explicit analytical formulation for kinematic bending of end-bearing piles which is convenient for engineering practice. In addition, the proposed solution was compared with the conventional BDWF solution and the numerical solution, indicating that the proposed solution can maintain both accuracy and simplicity. At last, a series of parametric study was carried out and showed that the shear resistance of soils may considerably contribute to lowering the kinematic responses but increasing the maximum bending moment at the pile tip.