This paper proposes a method for solving the stress field of a deep circular tunnel affected by an unsteady temperature field. The tunnel is idealized as an infinite domain problem, and the solution of the unsteady temperature field can be regarded as solving the temperature field in the infinite domain under the first type of boundary conditions. The temperature field distribution inside the tunnel surrounding rock is obtained by the Laplace transform method. On this basis, through the stress condition at the boundary of the tunnel and the zero displacement boundary condition at infinity, the solution equations expressed by the analytic functions are listed, and then the power series method of the complex variable function method is used to obtain the desired analytic functions. From this, the temperature stress field caused by the temperature change can be calculated (the displacement field caused by the temperature change is also derived). By superimposing this stress field upon the surrounding rock stress caused by in situ stress, the total stress field inside the surrounding rock can be obtained. The example shows that when the time t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t$$\end{document} is small and the range of the numerical model is suitably large, the results of the analytical method and the numerical method agree well. This paper also discusses two cases in which the tunnel boundary temperature is greater than and less than the initial temperature of the surrounding rock.

中文翻译：

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非定常温度场下深埋圆形隧道应力解析解

本文提出了一种求解受非定常温度场影响的深圆形隧道应力场的方法。隧道被理想化为无限域问题，非定常温度场的求解可视为求解第一类边界条件下无限域的温度场。隧道围岩内的温度场分布是通过拉普拉斯变换方法得到的。在此基础上，通过隧道边界应力条件和无穷远零位移边界条件，列出解析函数表示的解方程，然后利用复变函数法的幂级数法得到所需的解析函数。由此，可以计算出温度变化引起的温度应力场（也导出了温度变化引起的位移场）。将该应力场叠加在地应力引起的围岩应力上，就可以得到围岩内部的总应力场。该示例显示，当时间 t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek } \setlength{\oddsidemargin}{-69pt} \begin{document}$$t$$\end{document} 小，数值模型范围适当大，解析法和数值法的结果一致出色地。