为了获得非均匀荷载作用下非圆形斜井井壁的弹性解析解，获悉非圆形井壁的应力应变分布规律，建立了受围岩土骨架压力与孔隙水压共同作用的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，推导出井壁全应力和位移场弹性近似解析解，并通过数值模拟对解析解进行了验证，最后考虑了接触面孔隙率np、卸载率η、侧压力系数λ和井壁厚径比ξ等因素的影响。结果表明，映射函数可高度映射非圆形井壁断面，保证井壁形状对理论解的影响;针对直墙半圆拱型井壁，底板和侧墙与底板连接处应力梯度最大，井壁底板和拱顶内缘中心为防裂控制点，接触面孔隙率变大会缓解顶底板的拉应力，但同时会增加侧墙处拉应力，接触面孔隙率可改变拱顶和侧墙的受力状态，np≥0.8后，侧墙上端为防裂控制点，拱顶内缘转为受压状态;井壁厚径比ξ的变化可显著减小井壁的受力和变形值，但不改变井壁的受力和变形状态;因此在井壁设计时需综合考虑井径与侧墙高度比，合理优化井壁断面，围岩卸载率直接反映了井筒开挖后围岩作用在井壁上的荷载，在设计和施工时应充分利用围岩自承载能力，减小井壁所受荷载。

In order to obtain the elastic analytical solution of the non circular inclined shaft wall under non-uniform load,and to learn the stressstrain distribution of the non circular shaft wall,a straight wall semi circular arch affected by the surrounding rock and soil skeleton pressure and pore water pressure was established.Firstly,the mapping function equation of the irregular wall shape was calculated.Secondly,the complex analytical method was used to derive the approximate analytical solution of the total stress and displacement field of the shaft wall,and the analytical solution was verified by numerical simulation method.Finally the influence of factors such as interface porosity np,unloading rate η,side pressure coefficient λ,and well wall thickness diameter ratio ξ were considered.The results show that the mapping function can highly map the non-circular cross section of the wall and ensure the effect of the shape of the wall on the theoretical solution.By comparing the theoretical and numerical simulation,the theoretical solution has a higher accuracy.For a straight walled semi circular arch shaft wall,the largest stress gradient occurs at the floor and the joint between the floor and the side wall.The crack control point lies on the bottom edge of shaft wall and the vault.The change in the porosity of the contact surface will ease the tensile stress of the top and bottom,but will also increase the tension at the side wall.The stress and the porosity of the contact surface can change the stress state of the vault and the side wall.After np≥0.8,the crack control point turns to upper side wall,and the inner edge of the vault turns to a compressed state.It can reduce the stress and deformation value of the borehole wall,but does not change the stress and deformation state of the borehole wall with the increase of wall thickness.Therefore,in the design of the shaft wall,it is necessary to comprehensively consider the ratio of shaft radius to the side wall height,reasonably optimize the shaft section.The unloading rate directly reflects the stress of the surrounding rock applied on the shaft wall after the excavation of the shaft.In the design and construction,the self-bearing capacity of the surrounding rock should be fully used to reduce the load on the wall

1 问题描述

   1.1 力学模型

   1.2 应力和位移复势表达

   1.3 边界条件

   1.4 参数无量纲化

2 复应力函数的求解

3 结果分析

   3.1 映射函数求解

   3.2 理论与数值模拟对比

   3.3 孔隙率np的影响

   3.4 卸载率η的影响

   3.5 侧压系数λ的影响

   3.6 井壁厚径比ξ的影响

4 结论