中文摘要：

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h0〉0.8时,拱顶开始向井外变形;底板曲率半径rd0〈1.4后,底板全部转为受压状态;在现有井壁形状条件下,当rd0/h0=2.3-2.5且h0〈0.8时,井壁侧墙高度和底板曲率半径设计最优.

英文摘要：

The inclined shaft lining model with semi-circular arch and straight wall was estab- lished subjected to water pressure in this paper. The mapping function equation of irregular shaft wall was first calculated using mixed penalty function. Then, the elastic approximate an- alytical solution of the lining was derived using the complex function theory, and the influence of dimensionless water pressure and lining parameters on the stress and displacement distribu- tion of lining were analyzed. Finally, the reasonable ratio of radius of inverted arch to the height of side wall was given by entire combination experiment method. The analysis results show that the mapping effect can be obtained with the ξ-n coefficient n equal to 4. All the di- mensionless water pressure, wall thickness, side wall height and radius of inverted arch have significant influence on the wall force. When the side wall height h0 beyond to 0.8, the vault begins to deform out of the lining; when the radius of inverted arch rd0 less than 1.4, the bottom plate is fully pressed; under the existing shape of the lining, the optimal design for the side wall height and radius of floor is achieved when rf0/h0 ranges between 2.3 and 2.5 and h0 less than 0.8.