This paper presents a matrix-form complex variable method that can predict the stress and displacement field around multiple tunnels in layered media. The proposed matrix-form method avoids complicated coefficient determinations and iterative algorithm, which effectively improves the computation efficiency. Firstly, the expressions for the stress and displacement field are given under the generalized complex variable theory. The conformal mapping technique and fast Fourier transform algorithm are used to formulate the matrix-form expressions of boundary conditions. Considering the boundary conditions of the tunnels and soil interfaces, the global matrix solution for multiple tunnels in layered media are obtained by assembling the matrix solutions of all single layers. The present theory is verified by comparison with the existing literature, finite element analysis and field data in engineering practices, and several numerical examples are given to reveal the effects of elastic properties, tunnels' position, equivalent layer and the layer thickness surrounding tunnels.

中文翻译：

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层状介质中多个非圆形隧道的矩阵复变量法

本文提出了一种矩阵形式的复变量方法，可以预测层状介质中多个隧道周围的应力和位移场。所提出的矩阵形式方法避免了复杂的系数确定和迭代算法，有效提高了计算效率。首先，给出了广义复变量理论下的应力场和位移场的表达式。采用共形映射技术和快速傅里叶变换算法来制定边界条件的矩阵形式表达式。考虑隧道和土壤界面的边界条件，通过组装所有单层的矩阵解，获得层状介质中多个隧道的全局矩阵解。通过与现有文献比较、有限元分析和工程实践中的现场数据验证了该理论，并给出了几个数值算例，揭示了弹性特性、隧道位置、等效层和隧道周围层厚度的影响。