Abstract The mechanical analysis of multiple tunnels at great depth is an extremely common problem in practical engineering. Previous studies usually used the Schwarz alternating method to solve the multiple-tunnel problem with an iterative scheme, which resulted in low efficiency and precision. To this end, this paper presents a non-iterative analytical method to calculate the mechanical field of multiple lined tunnels. In this method, the analytic function is expanded by Laurent series on each tunnel boundary so that the stress and displacement fields in the whole multiply-connected domain can be expressed accurately. The conformal mappings of different tunnels are independent of each other, which makes it convenient to deal with multiple arbitrary-shaped boundaries. The basic equations for solving the mechanical fields are obtained according to the contact conditions and stress boundary conditions. In the solving process, the Fourier transform method is used to transform the boundary conditions into the frequency equations. Compared with the Schwarz alternating method, our method can directly obtain the high-quality result without any iteration. Finally, several examples are given to verify the accuracy and effectiveness of the proposed method.

中文翻译：

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考虑衬砌与围岩相互作用的大深度多隧道广义复变量法

摘要 深埋多条隧道的力学分析是实际工程中极为普遍的问题。以往的研究通常采用 Schwarz 交替法以迭代方案解决多隧道问题，导致效率和精度较低。为此，本文提出了一种计算多衬砌隧道力学场的非迭代解析方法。该方法在每个隧道边界上通过洛朗级数展开解析函数，从而可以准确表达整个多重连通域中的应力和位移场。不同隧道的保形映射相互独立，便于处理多个任意形状的边界。根据接触条件和应力边界条件，得到求解力学场的基本方程。在求解过程中，采用傅里叶变换方法将边界条件转化为频率方程。与 Schwarz 交替法相比，我们的方法无需任何迭代即可直接获得高质量的结果。最后，给出了几个例子来验证所提出方法的准确性和有效性。