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.
