Simplified method for evaluating shield tunnel deformation due to adjacent excavation

- Pasternak foundation model and a modified subgrade modulus are both applied to consider the shield-ground interaction.
- Two-stage analysis method and finite difference method are used to analyze to responses of existing tunnel due to above-excavation.
- The effectiveness of proposed method is verified by a three-dimensional finite element analysis and two published case histories.

Due to the repaid development of underground space in big cities, increasing excavation pits is being constructed or planned in a close proximity to existing metro tunnels in dense urban areas. Adjacent excavation inevitably changes ground stress state and leads to soil movements around nearby tunnels, which may cause a series of adverse impacts on the underlying existing tunnels. Thus, to evaluate the responses of existing shield tunnels associated with adjacent excavation tunnel is crucial and essential for geotechnical engineers. Current semi-analytical methods generally utilize the Winkler foundation with the Vesic′s subgrade modulus to consider tunnel-excavation interactions. However, the Winkler model cannot further consider the interaction between adjacent springs and the Vesic′s subgrade modulus expression is incapable of considering the effect of tunnel embedment depth on the tunnel-ground relative stiffness. In this paper, a simplified analytical method is thus proposed to predict the shield tunnel behaviors associated with adjacent excavation by introducing the Pasternak foundation model with a modified subgrade modulus. The shield tunnel is treated as a continuous Euler-Bernoulli beam resting on the Pasternak foundation model and a modified subgrade modulus expression is presented to consider the effect tunnel embedment depth on subgrade modulus. Two-stage analysis method is applied to analyze the tunnel responses. First, the excavation induced vertical unloading stress acting on the underlying tunnel is calculated via widely-used Mindlin′s solution, ignoring the presence of the existing shield tunnel. Second, the responses of the shield tunnel due to the imposing vertical unloading stress are analyzed using the finite difference method. The feasibility of the proposed method is verified by comparison with the results from a three-dimensional finite element analysis and two published filed measurements. The predicted results are also compared with the results from the Winkler-based method. Finally, parametric studies are performed to investigate the effects of different factors on the responses of existing shield tunnel, including the ground elastic modulus, excavation depth and excavation geometry.