非圆形压力隧洞考虑支护滞后过程的应力与位移解析解

Analytic Solutions of Stress and Displacement for a Non-circular Pressurized Tunnel in Consideration of Support Delay

基于平面弹性复变函数中的保角变换方法,考虑衬砌的支护滞后效应,并认为衬砌与围岩完全接触,提出了带有衬砌的非圆形水工隧洞在原始地应力和内水压力共同作用下的应力与位移解析解,且求解过程中采用幂级数法简化计算。以马蹄形隧洞为例,用ANSYS进行数值计算,并与解析解进行对比验证;计算隧洞围岩开挖边界和衬砌内外边界的切向正应力以及围岩与衬砌之间的接触应力;讨论在不同侧压力系数、位移释放系数和内水压力下围岩与衬砌的应力分布规律。结果显示:解析解与数值解吻合较好;位移释放系数和内水压力对衬砌及围岩的应力分布影响显著,当位移释放系数和内水压力较大时,在衬砌内边界将出现拉应力区。研究结果为非圆形水工隧洞的围岩与衬砌的应力与位移分析提供了可行方法。

In association with the conformal transformation method of plane elastic complex function,the analyticalsolutions of stress and displacement for a non-circular lined tunnel subjected to in-situ stress and internal water pressure are derived. The support delay and the full contact between surrounding rock-mass and lining are taken into consideration. The power series method is used to simplify the calculation process. With a horseshoe tunnel as an example,the analytical solutions are verified by numerical results. Furthermore,the tangential stresses along the excavation boundary and the inner and outer boundaries of the lining,as well as the contact stresses along the interface of the lining-surrounding rock mass are calculated. Besides,the stress distributions of the surrounding rock mass and the lining under different lateral pressure coefficients,displacement release coefficients and internal water pressures are discussed. The results show that the analytical solution is in good agreement with the numerical solution,and the displacement release coefficient and internal water pressure have significant influence on the stress distributions of the lining and surrounding rock mass. Great values of displacement release coefficient and internal water pressure will give rise to tensile stress along the inner boundary of the lining.