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 引用本文: 高子坤 施建勇. 沉桩挤土位移应力变分解和积分泛函收敛性分析[J]. 力学学报, 2009, 41(4): 555-562.
Zikun Gao, Jianyong Shi. Convergence of integral functional and variational solutions of displacement and stress of soil due to pile-driving[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(4): 555-562.
 Citation: Zikun Gao, Jianyong Shi. Convergence of integral functional and variational solutions of displacement and stress of soil due to pile-driving[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(4): 555-562.

## Convergence of integral functional and variational solutions of displacement and stress of soil due to pile-driving

• 摘要: 静压桩是一种挤土桩，沉桩挤土作用将引发很多工程问题. 实际的贯桩过程发生在半无限成层土体中，且单桩具有空间轴对称性，桩的形状和长度也各不相同，因此需要研究半无限土体中一般桩孔扩张的特性和解. 通过对沉桩挤土的研究现状和实际存在问题的分析，建立沉桩挤土三维模型、设定符合变分约束条件的位移函数. 根据研究区域的积分泛函得到问题的位移和应力解. 由于能量泛函涉及三维广义积分问题，所以重点对积分和解的收敛性进行了分析，并应用经典土压力理论、小孔扩张理论和Ansys计算结果对计算和分析结果进行验证.

Abstract: Driving-in piles are widely used in the constructionengineering. There are many theoretical and practical problems with thecompaction effects of pile driving on the soil. Generally, the process ofpile penetration occurs in the semi-infinite and stratified soil. Singlepile has spatial axial symmetry, and the shape and length of piles aredifferent. Therefore, squeezing model due to pile-driving is developed inthis paper to study the effect of the final shape and displacement boundaryof pile wall, stress-free ground surface, the finite length of pile andnon-linearity of soil material. Displacement, strain and stress solutionsare then obtained based on variation principal and their convergence ofimproper integral is also verified. The theoretical scheme is validatedusing passive soil pressure theory, classical CEM results and the numericalsimulation results with Ansys code. The theoretical results illustrate theconvergent three-dimensional improper integral of energy functional and thevalidity of variational solutions.

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