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建立了受全水压作用直墙半圆拱斜井井壁模型,首先利用混合罚函数方法计算出不规则井壁的映射函数方程;其次利用复变函数理论,推导出井壁弹性近似解析解,并分析了无量纲化水压、井壁设计参数等因素对井壁应力和位移分布的影响;最后结合全组合方案设计给出了井壁底板曲率半径与侧墙高度比值合理取值范围.分析表明:映射函数式中ξ~(-n)系数n=4时可获得精度较高的映射效果;水压、井壁厚度、侧墙高度和底板曲率半径均对井壁受力有显著影响;侧墙高度h_0>0.8时,拱顶开始向井外变形;底板曲率半径r_(d0)<1.4后,底板全部转为受压状态;在现有井壁形状条件下,当r_(d0)/h_0=2.3~2.5且h_0<0.8时,井壁侧墙高度和底板曲率半径设计最优.
The wall model of semi-circular arch inclined shaft under full hydraulic pressure was established. First, the mixed penalty function method was used to calculate the mapping function equation of irregular shaft wall. Secondly, by using the theory of complex variable function, The influence of non-dimensional water pressure and design parameters of shaft lining on the distribution of stress and displacement in wellbore is analyzed. Finally, a reasonable range of the ratio of curvature radius and sidewall height of wellbore floor is given according to the design of combined project. : Mapping function where the ξ ~ (-n) coefficient n = 4 can get a mapping effect with high accuracy; water pressure, wall thickness, sidewall height and the radius of the curvature of the bottom wall have a significant impact on the shaft wall stress; When the height of the wall h_0> 0.8, the dome began to deform to the outside of the well. When the curvature radius r_ (d0) of the bottom plate was less than 1.4, the bottom plate was all changed to the compression state. Under the condition of the existing wall shape, when r_ (d0) / h_0 = 2.3 ~ 2.5 and h_0 <0.8, the wall sidewall height and bottom radius of curvature design is optimal.