基桩后屈曲的摄动分析方法

基桩自由长度较大或桩周土较软弱时,易发生屈曲破坏,故研究基桩发生屈曲时的力学性状具有重要意义。首先基于两端铰支桩,用能量法建立出大挠度微分方程,然后选取符合边界条件的基桩位移挠曲函数,采用二次摄动技术将非线性大挠度微分方程化为一系列摄动方程求解,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基桩埋置率、地基土弹簧刚度与桩身抗弯刚度等因素对基桩荷载达临界值后力学性状的影响,结果表明,随埋置率和土桩刚度比的增大,基桩后屈曲平衡路径趋于不稳定。

PERTURBATION ANALYSIS OF PILE'S POSTBUCKLING

It is of significant meanings to study the post-buckling equilibrium path of an axially loaded pile embedded partially in soil, for the long slender pile can fail in buckling mode, especially in soft soil. The non-linear large deflection differential equation of the pinned pile was established by energy method firstly. Then, the non-linear large deflection differential equation was solved by adopting the deflection function compatible to the boundary condition of the pile and by transforming the deflection function to a series of linear differential equations with perturbation approach. Through exchanging the perturbation parameter of the middle deflection, the higher-order asymptotic solution of load-deflection was founded. Finally, the behavior of the pile after flexural buckling was analyzed, which shows that the pile will be unstable as the.increase of the depth ratio and the stiffness ratio of the pile to soil.