A new mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface to eliminate displacement singularity at infinity, and the originally unbalanced tunnel excavation problem in existing solutions is turned to an equilibrium one of mixed boundaries. By applying analytic continuation, the mixed boundaries are transformed to a homogenerous Riemann-Hilbert problem, which is subsequently solved via an efficient and accurate iterative method with boundary conditions of static equilibrium, displacement single-valuedness, and traction along tunnel periphery. The Lanczos filtering technique is used in the final stress and displacement solution to reduce the Gibbs phenomena caused by the constrained far-field ground surface for more accurte results. Several numerical cases are conducted to intensively verify the proposed solution by examining boundary conditions and comparing with existing solutions, and all the results are in good agreements. Then more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery, and several engineering advices are given. Further discussions on the defects of the proposed solution are also conducted for objectivity.

翻译：本文提出一种考虑初始应力场的非圆形浅埋隧道新力学模型，通过约束远场地表位移消除无穷远处的位移奇异性，将现有解中原本不平衡的隧道开挖问题转化为混合边界的平衡问题。通过解析延拓方法，混合边界被转化为齐次黎曼-希尔伯特问题，随后采用兼具静力平衡、位移单值性及隧道周边牵引力边界条件的高效精确迭代方法进行求解。在最终应力与位移解中引入Lanczos滤波技术，以降低因约束远场地表引起的吉布斯现象，从而提高计算精度。通过检验边界条件并与现有解进行对比，开展了多组数值算例对本文解进行严格验证，所有结果均吻合良好。进一步通过多组数值算例研究地表及隧道周边的应力与变形分布规律，并提出了若干工程建议。为保持客观性，本文还针对该解存在的不足进行了深入讨论。