Simplified analytical method for evaluating the effects of overcrossing tunnelling on existing shield tunnels using the nonlinear Pasternak foundation model

The excavation of a new tunnel above an existing shield tunnel at close proximity may cause a series of adverse impacts on the underlying tunnel. Thus, a reasonable assessment of the existing shield tunnel’s responses to overcrossing tunnelling is crucial to ensuring the safety and serviceability of the existing shield tunnel. In this study, a simplified nonlinear analytical method is proposed to rapidly assess existing shield tunnel responses to overcrossing tunnelling. A nonlinear Pasternak foundation model (NPFM), considering the nonlinear deformation of the ground as well as the interaction between adjacent springs and upward tunnel displacement, is proposed for modelling the tunnel-soil interaction associated with unloading stress. An effective Newton’s iterative computational program, combined with the finite difference method, is developed for the nonlinear responses of the existing shield tunnel. The reliability and applicability of the proposed method are subsequently validated by a comparison with the results of three-dimensional finite element analyses and two well-documented and published field measurements. The predictions are also compared with the results of six elastic simplified analytical methods based on different subgrade reaction moduli.