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马蹄形隧道衬砌的曲墙,为一弹性地基上的变截面梁,目前大都采用分块求和的近似方法进行计算,当其截面厚度有一定的变化规律可循时,仍可用解析法进行分析。本文对截面厚度随其埋深按双曲线规律变化的曲墙进行了静力分析。从墙轴受力挠曲时的基本微分方程出发,导出了各种常见荷载作用下任一截面的弯矩、剪力、水平位移及转角的初值解,列出了初值解中各影响函数的计算公式。文中对墙底的支承条件进行了探讨,提出了按固定端考虑时的无量纲解以及各无量纲系数的计算公式,根据这些公式推导了墙顶在单位水平力、单位弯矩以及墙体在侧向均布荷载和侧向三角形分布荷载分别作用下墙顶水平位移和转角的计算公式,它们正是隧道拱圈内力计算时所必须求得者。文中还列出了各影响函数和无量纲系数表的编制方法,利用电算可事先算出这些系数以供设计计算时查用,这样就可使马蹄形曲墙隧道衬砌的计算与直墙式衬砌一样简便。目前在桩基设计计算中所采用的某些影响函数及无量纲系数可在曲墙的静力计算中应用。
The curved wall of the horseshoe tunnel lining is a variable cross-section beam on an elastic foundation. Currently, the approximate method of block summation is mostly used for calculation. When the section thickness has certain variation rules, the analytical method can still be used for analysis. In this paper, static analysis is performed on the curved wall whose section thickness changes with the hyperbolic law. Starting from the basic differential equations when the wall shaft was flexed by force, the initial value solutions of bending moment, shear force, horizontal displacement and rotation angle under any common load were derived, and the influences of the initial value solutions were listed. The formula for calculating the function. In this paper, the support conditions of the wall are discussed. The dimensionless solution considering the fixed end and the calculation formula of each dimensionless coefficient are proposed. Based on these formulae, the wall top is expressed in the unit horizontal force, unit bending moment, and the wall. The calculation formulas for the horizontal displacement and rotation angle of the wall top under the effect of the lateral uniform distribution load and the lateral triangular distributed load, respectively, are exactly those that must be obtained when calculating the internal force of the tunnel arch. The paper also lists the method of compiling various impact functions and non-dimensional coefficient tables. The coefficients can be calculated in advance for calculation and calculation in the design calculation. This can make the calculation of the horseshoe-shaped curved wall tunnel lining the same as the vertical wall lining. Simple. At present, some influence functions and dimensionless coefficients used in pile foundation design calculations can be applied in the static calculation of curved walls.