非静水应力场中圆形隧道衬砌与围岩间两种接触的黏弹性解析

Analytical viscoelastic solutions for lined circular tunnels under two contact conditions in a non-hydrostatic stress field

基于非静水应力场中圆形衬砌隧道围岩与衬砌的弹性复变函数表达,利用黏弹性对应原理推导了隧道衬砌与围岩在光滑接触和完全接触情况下的黏弹性通解。推导中围岩符合黏弹性,衬砌为线弹性,且考虑了衬砌支护滞后效应,得到的理论解适用于所有线弹性元件模型。推导的理论解与以往理论解及数值解较一致。根据解答,假定围岩符合广义开尔文(H-K)黏弹性体时,分析表明,衬砌所受的径向、切向应力、衬砌的环向位移以及轴力弯矩均随时间增长而逐渐增大,并收敛于定值;两种接触条件下,围岩的位移、衬砌的应力、位移和内力沿环向分布规律均有较大不同,且随时间增大,二者相差越大。相比已有解析,文中所推导的非静水应力场中衬砌与围岩两种接触下黏弹性解更具普适性,且完全接触下的黏弹性解与深埋圆形衬砌隧道实际情况更为接近。对比两种解析可为实际中衬砌的合理选择和施工提供参考。

In this study, analytical viscoelastic solutions were derived for the lined circular tunnels by the correspondence principle and complex variable method under full contact and smooth contact conditions between liner and ground in non-hydrostatic stress field. In the solutions, all kinds of viscoelastic tunnels with an elastic liner was considered and the delayed installation of the liner was also taken into account. Therefore, the obtained analytical solutions can be applied to all linear viscoelastic models. The analytical solutions were verified by the solutions of references and numerical results. According to the solution, the surrounding rock was assumed to conform to the generalized Kelvin（H-K） viscoelastic body. The results showed that the radial, tangential stress, the circumferential displacement of the lining and the bending moment of the lining increased with time until converged to the fixed value. Under two kinds of contact conditions, there were quite differences on the displacement of the surrounding rock, the stress distribution of the lining, the distribution of the displacement and the internal force. Furthermore, the above differences between these two conditions increased with the time. Compared with the existing solutions, the solutions derived in this paper are more suitable and reasonable for practical deep buried tunnels especially for the full contact condition. The comparison between the two solutions can provide a useful reference for selecting liner and construction reasonably.