针对圆形地下连续墙基坑开挖受力过程复杂且采用有限元通用程序计算效率低的问题，分析了墙体承受的内衬环向支撑力、坑外水平土压力荷载、坑内水平地基反力计算方法，基于轴对称荷载作用下柱壳的三维弹性力学基本方程，建立了圆形地下连续墙墙体的形变势能、内衬弹性势能、水平土压力势能、水平地基反力弹性势能等的计算公式，从而得到了求解墙体位移问题的泛函；引入单傅里叶级数作为求解位移的试探函数，根据变分原理对试探函数的待定参数进行全微分，得到了待定参数的求解方程组；同时，给出了各种边界条件下的待定参数方程组，从而得到了圆形地下连续墙的里兹解法；最后采用里兹法和有限元法对外径73 m的黄埔大桥北锚碇圆形地下连续墙进行了分析对比。结果表明：里兹法与三维弹性地基板法有限元计算的施工阶段最大位移仅相差0.49%，最大弯矩仅相差1.2%，计算结果几乎一致，尤其是位移曲线几乎完全重合，说明了里兹法方法的正确性，且其有很高的计算精度；算例中里兹法计算的未知数为17个，而有限元计算节点数为40 075个，未知数为240 450个，可见里兹法计算效率非常高，非常适合编制小型程序求解；研究结果为圆形地下连续墙受力研究提供了一种新方法，可广泛应用于工程设计。
Abstract
Aimed at the complicated loading process in excavating circular underground diaphragm wall and the low computational efficiency of finite element general program, the computing method of lining ring support force of the wall, horizontal earth pressure outside of the pit foundation and horizontal counterforce in the pit foundation were analyzed. The calculation formulas of deformation potential energy, lining elastic potential energy, horizontal soil pressure potential energy and elastic potential energy of foundation horizontal counterforce of the circular underground diaphragm wall were established based on the basic three-dimensional elasticity equation of cylindrical shells under axisymmetric load, and then the function to solve wall displacement was obtained. At the same time, the single Fourier series was introduced as the trial function for displacement and then the solving equations of undetermined parameters were established after the total differential of the undetermined parameters of trial function according to the variational principle. Finally, the equations of undetermined parameters under different boundary conditions were established, and force analysis of circular underground diaphragm wall based on Ritz method was proposed. Ritz method and finite element method based on the three-dimensional elastic foundation plate method were separately used to analyze the circular diaphragm wall of the north anchor of Huangpu Bridge with outside diameter of 73 meters. The results show that the difference of maximum displacement between the Ritz method and the three-dimensional elastic foundation plate method is only 0.49% in the construction stage, and that of maximum bending moment is 1.2%. Besides, the calculation results of these two methods are almost the same, especially displacement curves, which are almost completely coincide, indicating validity of correctness and high precision of Ritz method. Further, the unknown numbers in Ritz method are 17, while the numbers of finite element calculation node are 40 075 and those of unknown are 240 450 in three-dimensional elastic foundation plate method, which indicates that Ritz method is of great efficiency and very suitable for solving results with a small program. The research results can provide a new method for force analysis of circular underground diaphragm wall, which can be widely used in engineering design.
关键词
桥梁工程 /
圆形地下连续墙 /
里兹法 /
受力分析 /
傅里叶级数
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Key words
bridge engineering /
circular underground diaphragm wall /
Ritz method /
force analysis /
Fourier series
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中图分类号：
U441.5
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脚注
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基金
交通运输部建设科技项目（2013318798320）；湖南省交通科技项目（201219）
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