压桩挤土位移变分模型及理论解答研究

针对三维压桩挤土位移应力求解问题,综合考虑桩身段的径向扩张与桩端的似球形扩张,应用多项式连续函数曲线模拟桩孔直立段、过渡段和桩尖段,并通过引入曲线族参数构造带参数位移函数和积分泛函,实现较符合实际工程和变分法要求的桩土作用孔壁边界的数学模拟,并结合Duncan-Chang本构关系模型和变分理论,推导桩土作用问题的理论解答。应用本文解答进行的工程实例计算表明,变分理论解答极限平衡理论计算及现场测试结果均吻合较好。且随待定系数个数增加收敛于精确解答的速度也较快,研究过程对较复杂的工程问题的理论解答推导有借鉴意义。

Displacement Variation Model and Theoretical Solution Study for Pile-soil Interaction

In order to solv the displacement and stress due to pile jacked, theoretical solutions for pile-soil interaction are derived, considering the radial expansion of pile hole and spherical expansion at pile head, using cubic polynomial continuous function to simulate the vertical section, transition section and pile tip of a pile. By introducing set of curves, displacement and integral functional are established, and solutions is achieved according the actual effect of pile-soil interaction and hole boundary of the pile, with the Duncan-Chang constitutive model and variational theory. The calculation of engineering examples shows the variational results on the vertical section of the pile-hole border are in good agreement with the limit equilibrium theory results. Research findings show with the increase of the number of undetermined coefficients, calculation results converge to the actual solutions fast. The research content and method also have a certain significance to solve other complex engineering problem.