Abstract The sequential excavation of a tunnel cross-section is usually employed in large scale tunnel construction to reduce the excavation impact on surrounding rock. Time-dependent sequential excavation combined with rock rheology makes the mechanical response of the surrounding rock a complex function of time, and it is possibly closely related to the excavation path. This study presents new analytical solutions that account for an arbitrary sequential excavation of the tunnel's cross-sections, the ground's viscoelastic properties, arbitrary tunnel shapes and pressures exerted at the internal tunnel boundaries due to liners or water pressures. The time-dependent analytical solutions for the stresses and displacements in each excavation step are derived by complex variable theory, conformal mapping and the Laplace transform technique. The solutions agree very well with the FEM numerical results for models that are completely consistent, and they are qualitatively consistent with the field data. In addition, the mechanical mechanism of the time-dependency of the displacement is analyzed in detail for two types of viscoelastic models. Then parametric analyses are conducted for the sequential excavation of a rectangular tunnel, a semi-arched tunnel with a vertical wall and a horseshoe tunnel to investigate the influence of the excavation sequences, excavation time and the supporting pressures on the ground displacements and stresses. The proposed analytical solutions can help reveal the particular mechanical mechanism of the time-dependent ground responses due to sequential excavations combined with rock rheology, as well as provide an alternative method in the preliminary designs of future tunnels.

中文翻译：

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粘弹性岩中非圆形隧道连续开挖引起的位移和应力解析解

摘要 在大型隧道施工中，为了减少开挖对围岩的影响，通常采用隧道断面的顺序开挖。时效序贯开挖结合岩石流变学，使围岩的力学响应成为复杂的时间函数，可能与开挖路径密切相关。这项研究提出了新的分析解决方案，这些解决方案解释了隧道横截面的任意顺序开挖、地面的粘弹性特性、任意隧道形状以及由于衬砌或水压在隧道内部边界施加的压力。每个开挖步骤中应力和位移的瞬态解析解是通过复变量理论、保角映射和拉普拉斯变换技术推导出来的。该解与完全一致的模型的 FEM 数值结果非常吻合，并且它们与现场数据定性一致。此外，还详细分析了两种粘弹性模型的位移随时间变化的力学机制。然后对矩形隧道、竖墙半拱隧道和马蹄形隧道的顺序开挖进行参数分析，研究开挖顺序、开挖时间和支护压力对地面位移和应力的影响。所提出的解析解有助于揭示由于连续开挖与岩石流变学相结合而引起的随时间变化的地面响应的特定力学机制，