Sequential excavation is common in shallow tunnel engineering, especially for large-span tunnels. However, existing complex variable solutions can not handle sequential shallow tunnelling effectively. This paper proposes a new complex variable solution on sequential shallow tunnelling in gravitational geomaterial with reasonable far-field displacement in a non-iterative manner by incorporating a bidirectional stepwise conformal mapping combining Charge Simulation Method and Complex Dipole Simulation Method. The non-iterative manner ensures that the mechanical models of sequential excavation stages share similar mathematical formation with non-successive mixed boundary conditions, which are respectively transformed into corresponding homogenerous Riemann-Hilbert problems, which are solved to obtain stress and displacement fields of sequential shallow tunnelling. The proposed solution is subsequently validated by sufficient comparisons with equivalent finite element solution with good agreements. The comparisons also suggest that the proposed solution should be more accurate than the finite element one. A parametric investigation is finally conducted to illustrate possible practical applications of the proposed solution with several engineering recommendations. Additionally, the theoretical improvements and defects of the proposed solution are discussed for objectivity.

翻译：顺序开挖在浅埋隧道工程中较为常见，尤其适用于大跨度隧道。然而，现有复变解难以有效处理浅埋隧道顺序开挖问题。本文通过结合电荷模拟法与复偶极子模拟法的双向渐进保角映射，提出了一种非迭代形式的复变解，用于分析重力地质材料中考虑合理远场位移的浅埋隧道顺序开挖问题。该非迭代方法确保顺序开挖各阶段的力学模型具有相似的数学形式与非连续混合边界条件，这些条件被分别转化为相应的齐次Riemann-Hilbert问题，通过求解这些问题获得了浅埋隧道顺序开挖的应力场与位移场。随后，通过与等效有限元解的充分对比验证了所提解的正确性，两者吻合良好。对比结果同时表明，所提解应具有比有限元解更高的精度。最后通过参数分析阐明了该解在实际工程中可能的应用场景，并提出了若干工程建议。此外，为保持客观性，本文亦讨论了所提解的理论改进空间与不足之处。