基桩屈曲问题的大挠度摄动解

Large-Deflection Solution of the Buckling of Pile by Perturbation Approach

基于温克尔地基模型,采用能量法建立了两端铰支完全入土桩的大挠度微分方程.假设其挠曲函数及桩头荷载为摄动参数的幂级数展开式,采用二次摄动方法将非线性大挠度微分方程化为一系列线性摄动方程求解.在求得大挠度渐近解的基础上,通过摄动参数转换,得到以桩身挠度为摄动参数的后屈曲平衡路径高阶渐近解.最后,利用本文解答分析了桩长、地基土弹簧刚度、桩身抗弯刚度等因素对基桩临界荷载值及其后屈曲平衡路径的影响.结果表明,基桩屈曲临界荷载随桩土刚度比增大而提高,且较小的桩土刚度比对后屈曲平衡路径的稳定较为有利.

To investigate the buckling load and post - buckling equilibrium path of an axially loaded pile entirely embedded in a soil, the non-linear large deflection differential equation for pinned pile, based on the Winkler-model, was first established in the energy method. Then, by supposing that the deflection function accord- ing with the boundary condition and load on the pile were power series of some perturbation parameter, the nonlinear large deflection differential equation was transformed to a series of linear differential equations with perturbation approach to be solved. By taking the place of the perturbation parameter by middle deflection, the higherorder asymptotic solution of load-deflection was founded. Lastly, the effect of pile length, the stiffness ratio of the pile and the soil on the buckling load and the behavior of the pile after flexural buckling was analyzed, which showed that the buckling load increased with larger stiffness ratio of the pile and the soil, and the pile became more stable as the depth ratio and the stiffness ratio of the soil and the pile decreased.