界面完全接触时正交各向异性围岩深埋非圆形隧道衬砌的应力和位移

doi:10.3901/JME.2021.23.149

摘要/Abstract

摘要： 利用复变函数的方法，研究了双向挤压应力作用下的正交各向异性围岩中的深埋非圆形衬砌隧道，得到了围岩和衬砌中级数形式的应力函数，从而得到应力和位移的解析解。以工程中常见的双线隧道作为算例，给出了沿衬砌内外边界的应力和位移的解析解。可以看出，解析解满足界面完全接触条件和边界条件，在对称轴上满足对称条件。并利用有限元软件ANSYS给出了应力和位移的数值解，与解析解吻合性很好。研究结果还表明：衬砌内外边界的切线方向正应力变化趋势不一致，内边界的最大值约为外边界的2倍，发生在拱脚。衬砌内外边界的位移变化趋势一致，且数值接近。最大沉降发生在拱顶，最大隆起发生在拱底，最大水平方向位移发生在拱腰处。在隧道的设计时，要注意使衬砌内边界上这些位置的应力和位移满足要求。

关键词: 衬砌隧道, 正交各向异性围岩, 复变函数, 应力, 位移

Abstract: The method of complex variable function is used to study the deeply buried non-circular lined tunnel in the orthotropic surrounding rock under far-field biaxial compression. The stress functions in series form of surrounding rock and lining are obtained, thus the analytical solutions of stress and displacement can be derived. Considering a two-lane tunnel common in engineering as an example, the analytical solutions of stress and displacement along the inner and outer boundaries of the lining are given. The complete contact interface condition, boundary condition, and the symmetry condition are all satisfied. At the same time, the numerical solutions of stress and displacement are given by using the finite element software ANSYS, which are in good agreement with the analytical solutions. The results also show that the tangent stress variations of the inner and outer boundaries of the lining are not consistent, and the maximum value of the inner boundary is about 2 times than that of the outer boundary, which occurs at the arch springing. While the displacement variations of the inner and outer boundaries of the lining are consistent, and the values are close. The maximum settlement, uplift and horizontal displacement occur at the roof, floor, and waist of the tunnel, respectively. In the design of the tunnel, the stress and displacement at those positions on the inner boundary of the lining should be paid more attention to meet the requirements.

Key words: lined tunnel, orthotropic surrounding rock, complex variable function, stress, displacement

中图分类号:

U451

刘淑红, 张鹏, 陈时玉, 朱永全. 界面完全接触时正交各向异性围岩深埋非圆形隧道衬砌的应力和位移[J]. 机械工程学报, 2021, 57(23): 149-159.

LIU Shuhong, ZHANG Peng, CHEN Shiyu, ZHU Yongquan. Stress and Displacement of Orthotropic Surrounding Rock with a Deeply Buried Non-Circular Lined Tunnel under the Complete Contact Interface Condition[J]. Journal of Mechanical Engineering, 2021, 57(23): 149-159.

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