An analytical solution for a non-circular tunnel excavated in an elastic homogeneous half-plane is obtained, which considers gravity and different lateral pressure coefficients. The solution is deduced using the complex variable method, mapping the region containing a non-circular tunnel onto a circular ring. The basic equations for the analytic functions are established using the stress boundary conditions at the ground surface and the edges of the tunnel and the analytical functions are solved by the power series method. In the process of solving, the Fourier series was used. To elaborate the solution process clearly and verify the correctness of the solution, a shallow quasi-ellipse tunnel was analyzed as a computational example, and the results obtained using the presented analytical method are compared with that obtained by the numerical software ANSYS.

中文翻译：

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弹性半平面非圆形隧道的复变解

得到了考虑重力和不同侧压力系数的弹性均匀半平面开挖非圆形隧道的解析解。使用复变量方法推导出解决方案，将包含非圆形隧道的区域映射到圆环上。利用地表和隧道边缘应力边界条件建立解析函数的基本方程，并用幂级数法求解解析函数。在求解过程中，用到了傅立叶级数。为清楚阐述求解过程并验证求解的正确性，以浅层准椭圆隧道为例进行分析，