光滑接触条件下非圆形有压隧洞应力及位移解析解

摘要

考虑支护滞后的力学过程,并在衬砌与围岩为光滑接触的条件下,利用平面弹性复变函数法推导出非圆形隧洞在原始地应力和内水压力作用下的应力及位移解析解.根据衬砌内边界的应力边界条件及围岩与衬砌接触面上的应力和法向位移连续条件,获得了求解围岩和衬砌解析函数的基本方程.利用幂级数方法求解基本方程,再由此计算围岩和衬砌中的应力和位移,并且利用数值方法验证了所得结果.以直墙半圆拱形隧洞为例,分析了不同位移释放系数、侧压力系数和内水压力条件下的围岩开挖边界和衬砌内外边界的切向应力及围岩与衬砌接触面上的法向应力分布规律.研究成果可为求解深埋隧洞围岩与衬砌的应力及位移解析解提供参考.%In consideration of the mechanical process of support delay,the analytic solutions of stress and displace-ment for a non-circular tunnel subjected to in-situ stress and internal water pressure are derived by using the com-plex variables function under the assumption that the interface between lining and surrounding rock is fully slip.The basic equations for solving the analytic functions of surrounding rock and lining are obtained according to the stress boundary condition along the inner boundary of the lining and the condition of stress and normal displacement conti-nuity along the rock-lining interface. The basic equations can be solved by the power series method,and the stres-ses and displacements in the surrounding rock and lining can be calculated.The analytic solutions are verified by fi-nite element method. An inverted U-shaped tunnel is taken as an example to analyze the distributions of tangential stresses along the excavation boundary, the inner and outer boundary of the lining as well as the normal stresses alongthe rock-lining interface in the presence of different displacement release coefficient, lateral pressure coefficientand internal water pressure.