长江科学院院报 ›› 2018, Vol. 35 ›› Issue (5): 85-92.DOI: 10.11988/ckyyb.20171106

• 岩土工程 • 上一篇    下一篇

光滑接触条件下非圆形有压隧洞应力及位移解析解

尹崇林, 吕爱钟, 陶钧烨   

  1. 华北电力大学 水电与岩土工程研究所,北京 102206
  • 收稿日期:2017-09-25 出版日期:2018-05-01 发布日期:2018-06-16
  • 作者简介:尹崇林(1992-),男,四川绵阳人,博士研究生,主要从事岩石力学的研究。E-mail:yinchonglin@ncepu.edu.cn
  • 基金资助:
    国家自然科学基金项目(11572126)

Analytic Solutions of Stress and Displacement for a Non-circular Pressure Tunnel under Full-slip Contact Condition

YIN Chong-lin , LÜ Ai-zhong, TAO Jun-ye   

  1. Institute of Hydroelectric and Geotechnical Engineering,North China Electric Power University,Beijing 102206,China
  • Received:2017-09-25 Online:2018-05-01 Published:2018-06-16

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。

关键词: 非圆形隧洞, 光滑接触, 保角变换, 幂级数解法, 内水压力, 应力解析解, 位移解析解

Abstract: In consideration of the mechanical process of support delay, the analytic solutions of stress and displacement for a non-circular tunnel subjected to in-situ stress and internal water pressure are derived by using the complex 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 continuity along the rock-lining interface. The basic equations can be solved by the power series method, and the stresses and displacements in the surrounding rock and lining can be calculated. The analytic solutions are verified by finite 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 along the rock-lining interface in the presence of different displacement release coefficient, lateral pressure coefficient and internal water pressure.

Key words: non-circular tunnel, full-slip contact, conformal transformation, power series method, internal water pressure, analytical solution of stress, analytical solution of displacement

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