Discontinuous mechanical behaviors of existing shield tunnel with stiffness reduction at longitudinal joints

Abstract

An analytical model is proposed to estimate the discontinuous mechanical behavior of an existing shield tunnel above a new tunnel. The existing shield tunnel is regarded as a Timoshenko beam with longitudinal joints. The opening and relative dislocation of the longitudinal joints can be calculated using Dirac delta functions. Compared with other approaches, our method yields results that are consistent with centrifugation test data. The effects of the stiffness reduction at the longitudinal joints (α and β), the shearing stiffness of the Timoshenko beam GA, and different additional pressure profiles on the responses of the shield tunnel are investigated. The results indicate that our proposed method is suitable for simulating the discontinuous mechanical behaviors of existing shield tunnels with longitudinal joints. The deformation and internal forces decrease as α, β, and GA increase. The bending moment and shear force are discontinuous despite slight discontinuities in the deflection, opening, and dislocation. The deflection curve is consistent with the additional pressure profile. Extensive opening, dislocation, and internal forces are induced at the location of mutation pressures. In addition, the joints allow rigid structures to behave flexibly in general, as well as allow flexible structures to exhibit locally rigid characteristics. Owing to the discontinuous characteristics, the internal forces and their abrupt changes at vulnerable sections must be monitored to ensure the structural safety of existing shield tunnels.

Graphical abstract

Keywords

tunnel–soil interaction / discontinuous analysis / longitudinal joints / existing shield tunnel / Timoshenko beam / Dirac delta function

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant No. 52108363), Postdoctoral Science Foundation of China (No. 2021M700654), Fundamental Research Funds for the Central Universities (No. 3132022175), Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University (No. TUL2022-01), and Liaoning Revitalization Talents Program (No. XLYC1905015).

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11709-022-0920-3 and is accessible for authorized users.

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