A time-dependent solution for excavation-induced vertical deformation of underlying existing tunnels in two-layered saturated ground based on Biot consolidation theory

Current single-layer homogeneous ground models neglect the impact of soil stratification on consolidation when predicting excavation-induced deformation of underlying existing tunnels. Consequently, these models fail to accurately capture the time-dependent evolution of vertical deformation, hindering the precise assessment of potential engineering risks. Based on Biot consolidation theory, this study establishes three-dimensional governing equations for two-layered ground subjected to excavation. A semi-analytical solution for soil displacement and excess pore water pressure is then derived for two-layered saturated ground, and its engineering extension to simplified multilayered profiles is examined through field monitoring validation. By combining Euler-Bernoulli beam theory with a ground flexibility matrix that incorporates consolidation effects, a new calculation method is proposed to determine the vertical deformation of the existing tunnel. Centrifuge test and field monitoring results demonstrate that this solution accurately captures the spatial and time-dependent characteristics of vertical deformation in layered ground. It significantly enhances prediction accuracy compared to existing methods, making it highly suitable for multi-layered soil profiles. Parametric analysis indicates that key soil parameters—including the permeability coefficient, resilient modulus, and Poisson’s ratio—significantly influence the vertical deformation of the existing tunnel. Specifically, the permeability coefficient primarily dictates the time required for deformation stabilization, whereas the resilient modulus dictates the final deformation magnitude. Poisson’s ratio affects both the stabilization time and the final deformation. Overall, the parameters of the tunnel burial layer exert a stronger influence than those of the overlying layer. Sensitivity analysis further reveals that the initial physical properties of the soil and the layer thickness ratio alter the effectiveness of tunnel deformation control. The proposed solution provides a mechanistic basis for assessing long-term heave risks of existing tunnels beneath excavations in layered saturated ground.