基于里兹法的圆形地下连续墙受力分析

发布时间：2018-04-25 08:37

本文选题：桥梁工程 + 圆形地下连续墙　；参考：《中国公路学报》2017年01期

【摘要】：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73m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]:In order to solve the problem that the excavation process of circular diaphragm wall foundation pit is complicated and the calculation efficiency of finite element general program is low, the calculation method of inner lining circumferential supporting force, horizontal earth pressure load outside the pit and horizontal foundation reaction force in the pit is analyzed. Based on the basic equations of three-dimensional elastic mechanics of cylindrical shells under axisymmetric loads, the calculation formulas of deformation potential energy, lining elastic potential energy, horizontal earth pressure potential energy and horizontal foundation reaction elastic potential energy of circular underground continuous wall wall are established. The function of solving the wall displacement problem is obtained, the single Fourier series is introduced as the trial function to solve the displacement, the undetermined parameters of the trial function are fully differential according to the variational principle, and the equations of the undetermined parameters are obtained. The equations of undetermined parameters under various boundary conditions are given, and the Ritz solution of circular underground continuous wall is obtained. Finally, the circular underground diaphragm wall of Huangpu Bridge with outer diameter of 73 m is analyzed and compared by using the Ritz method and the finite element method. The results show that the maximum displacement and the maximum bending moment are only 0.49 and 1.2 respectively in the construction stage calculated by the Ritz method and the three-dimensional elastic foundation plate method, and the calculated results are almost consistent, especially the displacement curve is almost completely coincident. It is shown that the Ritz method is correct and has a high calculation accuracy. In the example, the Ritz method has 17 unknowns, while the finite element method has 40,075 nodes and 240,450 unknowns, so the efficiency of the Ritz method is very high. The research results provide a new method for the research of circular underground continuous wall, and can be widely used in engineering design.
【作者单位】：湖南大学土木工程学院;湖南省交通规划勘察设计院;
【基金】：交通运输部建设科技项目(2013 318 798 320) 湖南省交通科技项目(201219)
【分类号】：U443.1

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