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Probabilistic stability analysis of tunnel roof in two-layer soil mass combining upper bound theorem and response surface method

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Abstract

In this work, with reference to the nonlinear Mohr–Coulomb failure criterion and upper bound theorem of limit analysis, two-dimensional (2D) collapse mechanism of deep buried rectangular tunnel in layered soil mass is established with consideration of varying water tables and excess pore water pressure. The present results are compared with existing research primarily, and the agreement shows that the method is valid. Numerical analyses are conducted to investigate the influences of corresponding parameters on the potential collapse surfaces. Subsequently, a probabilistic model is performed by consolidating collapse mechanism into responses surface method (RSM). The initial cohesion and tensile strength are regarded as random variables while the remaining parameters are considered as nonrandom variables due to their lower variations or specifics for special projects. The impacts of individual nonrandom variables and cross correlations of random variables on the failure chances are studied. Then, reliability analysis is displayed to evaluate the influences of different distribution types of random variables on the tunnel stability, various cases are also designed to discuss the most unfavorable layer combination, eventually, a reliability-based design is provided to evaluate target support pressure to the tunnel roof according to the different coefficients of variation of random variables. In short, the global behaviors can be caught by means of deterministic and probabilistic analysis and which certainly facilitates to assess the stability of tunnel roof.

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Data availability

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank the editor and the reviewers for their valuable comments that improved this manuscript.

Funding

This work is financially supported by the National Nature Science Foundation of China (NSFC through grant no. 41672260).

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Authors and Affiliations

  1. Faculty of Engineering, China University of Geosciences, Wuhan, 430000, China

    Dexin Lei, Lingli Xie, Jing Wang & Li Wu

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  1. Dexin Lei
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  2. Lingli Xie
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  3. Jing Wang
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  4. Li Wu
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Correspondence to Li Wu.

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The authors declare no competing interests.

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Responsible Editor: Zeynal Abiddin Erguler

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Lei, D., Xie, L., Wang, J. et al. Probabilistic stability analysis of tunnel roof in two-layer soil mass combining upper bound theorem and response surface method. Arab J Geosci 15, 1201 (2022). https://doi.org/10.1007/s12517-022-10346-5

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  • DOI: https://doi.org/10.1007/s12517-022-10346-5

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