Deformation of underlying shield tunnel caused by adjacent excavation considering the consolidation effect

Excavation above existing tunnels induces vertical deformation due to unloading effects, with the underlying tunnel deformation exhibiting time-dependent behavior caused by soil consolidation. However, prevailing theoretical frameworks often neglect the consolidation process and the influence of the complete excavation sequence, resulting in an inability to predict time-evolving deformation. This study establishes a consolidation model tailored for foundation pit excavation, deriving a theoretical solution for excess pore water pressure. Vertical soil deformation induced by excavation is determined using the effective stress principle coupled with generalized Hooke's law. A consolidation model for internally loaded foundations is then formulated to obtain a flexibility matrix incorporating consolidation effects. By simplifying the tunnel as an Euler-Bernoulli beam and applying soil-tunnel displacement coupling conditions, a time-dependent solution for vertical deformation is derived and validated against physical model tests. Meanwhile, the results of data comparison further indicate that the time-dependent characteristics of the tunnel's vertical deformation are closely related to the dissipation of excess pore water pressure (i.e., the soil's consolidation characteristics). Parametric analysis shows that: Lowering the soil permeability coefficient reduces the tunnel’s deformation rate but also extends the time required for the deformation to stabilize, resulting in a smaller vertical displacement at the completion of excavation. An increase in the resilient modulus not only enhances the soil's ability to resist deformation but also weakens the soil's consolidation effect, thereby inhibiting the development of vertical displacement of the tunnel. The tunnel stiffness only affects the deformation magnitude, but not the time required to reach stability. Introducing an intermittent excavation schedule tends to increase the deformation of the tunnel by the end of excavation while attenuating the subsequent time-dependent deformation. The theory in this paper is of guiding significance for engineering practice.