When considering initial stress field in geomaterial, nonzero resultant of shallow tunnel excavation exists, which produces logarithmic items in complex potentials, and would further lead to a unique displacement singularity at infinity to violate geo-engineering fact in real world. The mechanical and mathematical reasons of such a unique displacement singularity in the existing mechanical models are elaborated, and a new mechanical model is subsequently proposed to eliminate this singularity by constraining far-field ground surface displacement, and the original unbalanced resultant problem is converted into an equilibrium one with mixed boundary conditions. To solve stress and displacement in the new model, the analytic continuation is applied to transform the mixed boundary conditions into a homogenerous Riemann-Hilbert problem with extra constraints, which is then solved using an approximate and iterative method with good numerical stability. The Lanczos filtering is applied to the stress and displacement solution to reduce the Gibbs phenomena caused by abrupt change of the boundary conditions along ground surface. Several numerical cases are conducted to verify the proposed mechanical model and the results strongly validate that the proposed mechanical model successfully eliminates the displacement singularity caused by unbalanced resultant with good convergence and accuracy to obtain stress and displacement for shallow tunnel excavation. A parametric investigation is subsequently conducted to study the influence of tunnel depth, lateral coefficient, and free surface range on stress and displacement distribution in geomaterial.

翻译：在地质材料中考虑初始应力场时，浅埋隧道开挖存在非零合力，导致复势函数中出现对数项，进而产生独特的无穷远位移奇异性，这与现实世界的地质工程事实相悖。本文阐述了现有力学模型中此类独特位移奇异性的力学与数学原因，并提出了一种新型力学模型，通过约束远场地表位移来消除该奇异性，将原始的不平衡合力问题转化为具有混合边界条件的平衡问题。为求解新模型中的应力与位移，应用解析延拓法将混合边界条件转化为带有额外约束的齐次黎曼-希尔伯特问题，随后采用数值稳定性良好的近似迭代法进行求解。对应力与位移解应用兰佐斯滤波技术，以减小地表边界条件突变引起的吉布斯现象。通过多个数值算例验证了所提力学模型，结果有力证明该模型成功消除了不平衡合力引起的位移奇异性，且能良好收敛且精确地获取浅埋隧道开挖的应力与位移。后续进行了参数研究，分析了隧道埋深、侧压力系数及自由地表范围对地质材料中应力与位移分布的影响。