This study presents a theoretical analysis of the deformation induced in an existing curved subway tunnel by a new shield tunnel crossing diagonally beneath it. A refined two-stage method is developed to address this engineering problem. In the first stage, the additional stress on the existing tunnel is calculated using Mindlin’s solution. In the second stage, the existing tunnel is modeled as an Euler–Bernoulli beam on a Pasternak foundation, explicitly incorporating the effects of tunnel curvature and a stress reduction factor for the grout-reinforced zone. The proposed method is validated against monitoring data from a case study of the Zhengzhou Metro, showing good agreement. A systematic parametric analysis investigates the influence of key factors: the clearance and intersection angle between tunnels, the curvature radius of the existing tunnel, the length of the grouted section, and Poisson’s ratio of the grouted soil. Results demonstrate that the crossing angle and grouting length are the most significant parameters affecting deformation, whereas the existing tunnel’s curvature and the grout’s Poisson’s ratio have a negligible impact.
Li et al. (Sat,) studied this question.