Analytical solution of stress and displacement of double-arch tunnel without middle drift based on functions of complex variables

BI Tai-jun; DENG Qin; TANG Hua; JIANG Cheng-ye; QIN Yu-qiao

doi:10.16285/j.rsm.2023.0380

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Analytical solution of stress and displacement of double-arch tunnel without middle drift based on functions of complex variables

更新时间：2026-06-25

- Analytical solution of stress and displacement of double-arch tunnel without middle drift based on functions of complex variables
- Vol. 45, Issue 3, Pages: 777-787(2024)
- 作者机构：
  
  1. 中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,湖北,武汉,430071
  2. 中国科学院大学,北京,100049
- 作者简介：
- 基金信息：
- DOI：10.16285/j.rsm.2023.0380
  CLC： U451.4
- Online First：20 March 2024，
  
  Published：2024
- 稿件说明：
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BI Tai-jun, DENG Qin, TANG Hua, et al. Analytical solution of stress and displacement of double-arch tunnel without middle drift based on functions of complex variables[J]. 2024, 45(3): 777-787.
DOI：

BI Tai-jun, DENG Qin, TANG Hua, et al. Analytical solution of stress and displacement of double-arch tunnel without middle drift based on functions of complex variables[J]. 2024, 45(3): 777-787. DOI： 10.16285/j.rsm.2023.0380.

摘要

无中导连拱隧道由于后行洞衬砌搭接于先行洞衬砌拱腰之上，围岩与衬砌受力情况复杂，开展相应的围岩与衬砌应力和位移分析具有重要的工程意义。基于复变函数理论和Schwarz交替法，提出了深埋条件下考虑衬砌的无中导连拱隧道围岩与衬砌应力和变形的计算方法。针对无中导连拱隧道两洞具有共用边界的特点，在利用柯西积分法进行求解时，将单洞衬砌与围岩接触的边界积分条件转化为仅存在单洞时的完整边界积分与共用边界积分之差，对于Schwarz交替法中求解“附加面力”的过程亦进行类似处理。给出共用边界应力与位移的计算方法。通过算例，将上述解析结果和数值仿真结果进行对比，证明了方法的可行性和准确性。

Abstract

Due to the fact that the lining of the secondary tunnel overlaps on the arch waist of the lining of the front tunnel

the stress situation of the surrounding rock and lining is complex. Therefore

it is of important engineering significance to carry out stress and displacement analysis of the surrounding rock and lining. This study proposes a calculation method for stress and deformation analysis of the surrounding rock and lining in a double-arch tunnel without a middle drift

considering the deep burial conditions and the presence of the lining. The method utilizes the complex variable function theory and Schwarz alternating method. In the case of a double-arch tunnel without a middle drift

where the two tunnels intersect

the Cauchy integral method is employed to solve the problem. The boundary integral condition for the contact between the lining of a single tunnel and the surrounding rock is transformed into the subtraction between the complete boundary integral and the intersectional boundary integral when only a single tunnel exists. A similar treatment is applied to the calculation of the “additional surface force” in the Schwarz alternating method. Finally

the calculation method of intersectional boundary stress and displacement is given. A numerical example is provided to demonstrate the feasibility and accuracy of the method by comparing the analytical results with numerical simulation results.

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