正交各向异性非圆形水工隧洞的应力解析解

doi:10.13722/j.cnki.jrme.2016.1615

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摘要

为了探讨深埋正交各向异性水工隧洞的力学响应问题，考虑洞边作用均布内水压力的情况，基于平面弹性复变函数方法，推导任意孔形水工隧洞的应力解析解。推导中建立3套极坐标系，将物理平面孔外域映射到了像平面的单位圆外域，并建立孔边应力边界条件，再利用幂级数解法，求解出隧洞的应力场。以直墙半圆拱形隧洞为例，通过ANSYS数值计算对解析解进行对比验证，在此基础上，又运用解析方法研究马蹄形和圆形隧洞的孔边应力分布规律。研究结果表明：不同于各向同性岩体，隧洞的正交各向异性围岩应力场表现明显的非对称性；增大侧压力系数会使孔边的切向应力增加，但马蹄形隧洞2个曲率较大位置的切向应力却几乎保持不变；内水压力的增加能减小洞口的应力集中，曲率越大的位置减小越明显，但内水压力过大，会使孔边出现明显的拉应力，不利于隧洞的安全。

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	张晓莉
	吕爱钟
	王少杰

关键词 ：隧道工程, 正交各向异性岩体, 非圆形隧洞, 内水压力, 应力解析解

Abstract：

In order to explore the mechanical response of a deep hydraulic tunnel in orthotropic rock mass，the analytical solutions of a non-circular tunnel under the action of the in-situ stresses and the internal water pressure，are derived. In the process，three polar coordinates are introduced and the conformal transformation method of complex function is adopted，mapping the outer region of the hole in the physical plane to the outer region of the unit circle in the image plane. Then，the stress boundary conditions on the excavation boundary are established. Finally，the stress field is obtained using the power-series method. Taking the inverted U-shaped tunnel as an example，the analytical solutions are verified by the numerical results obtained by ANSYS. The stress distributions along the boundary of a horse hoof-shaped tunnel and a circular tunnel are also analyzed. The results show that，unlike the isotropic rock mass，the stress field for an orthotropic rock mass shows obvious asymmetry. The tangential stresses along the hole boundary increase with the increase of the lateral pressure coefficients except the two corners of the horse hoof-shaped tunnel. Moreover，the internal water pressure can release the tangential stress concentration along the hole boundary，which is more obvious on the regions where the curvature is greater. But great internal pressure may also lead to tensile stress which will affect the stability of the tunnel.

Key words： tunnelling engineering orthotropic rock mass non-circular tunnel internal water pressure analytic stress solutions

引用本文:

张晓莉，吕爱钟，王少杰 . 正交各向异性非圆形水工隧洞的应力解析解[J]. 岩石力学与工程学报, 2017, 36(S2): 3808-3815.
ZHANG Xiaoli，LU Aizhong，WANG Shaojie. Analytic stress solutions for an orthotropic rock mass with a non-circular hydraulic tunnel. , 2017, 36(S2): 3808-3815.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2016.1615 或 https://rockmech.whrsm.ac.cn/CN/Y2017/V36/IS2/3808

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