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, and 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十分常见，尤其适用于大跨度隧道。然而，现有的复变量解法难以有效处理顺序浅埋隧道开挖问题。本文通过结合电荷模拟法与复偶极子模拟法的双向逐步保角映射，提出了一种非迭代的复变量解法，用于求解重力地质材料中考虑合理远场位移的顺序浅埋隧道开挖问题。该非迭代方法确保了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，这些条件分别被转化为相应的齐次Riemann-Hilbert问题，并通过求解获得顺序浅埋隧道开挖的应力场与位移场。随后，通过与等效有限元解进行充分对比验证了所提解法，两者结果吻合良好。对比分析还表明，所提解法应比有限元法更为精确。最后通过参数研究阐明了所提解法可能的实际应用，并给出了若干工程建议。此外，为保持客观性，本文还讨论了所提解法在理论上的改进与不足之处。