Axial Force Analysis and Geometric Nonlinear Beam-Spring Finite Element Calculation of Micro Anti-Slide Piles

This study investigates the development of axial force in micro anti-slide piles under soil movement during slope stabilization. Axial force arises from two primary mechanisms: axial soil displacement (zs) and pile kinematics. The former plays a dominant role, producing either tensile or compressive axial force depending on the direction of zs, while the kinematically induced component remains consistently tensile. A sliding angle of α=5° represents an approximate transition point where these two effects balance each other. Furthermore, the two mechanisms exhibit distinct mobilization behaviors: zs-induced axial force mobilizes earlier than both bending moment and shear force, whereas kinematically induced axial force mobilizes significantly later. The study reveals two distinct pile–soil interaction mechanisms depending on proximity to the slip surface: away from the slip surface, axial soil resistance is governed by rigid cross-section translation, whereas near the slip surface, rotation-dominated displacement accompanied by soil–pile separation introduces significant complexity in predicting both the magnitude and direction of axial friction. A hyperbolic formulation was adopted to model both the lateral soil resistance relative to lateral pile–soil displacement (p-y behavior) and the axial frictional resistance relative to axial pile–soil displacement (t-z behavior). Soil resistance equations were derived to explicitly incorporate the effects of cross-sectional rotation and pile–soil separation. A novel beam-spring finite element method (BSFEM) that incorporates both geometric and material nonlinearities of the pile behavior was developed, using a soil displacement-driven solution algorithm. Validation against both numerical simulations and field monitoring data from an engineering application demonstrates the model’s effectiveness in capturing the distribution and evolution of axial deformation and axial force in micropiles under varying soil movement conditions.