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An analytical method of continuous upper bound limit analysis for the stability of shallow shield tunnels in cohesive-frictional soils

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Abstract

For stability analysis of shallow shield tunnels in cohesive-frictional (clayey–sandy) soils, an analytical method of continuous upper bound limit analysis is developed to determine the most critical slip line position and the minimum required tunnel support pressure. The ground displacement field due to composite volume loss is calculated using a complex variable solution, and the optimization problem is solved by employing the particle swarm optimization technique. Energy dissipation at the potential slip boundary, which is determined through a system of tracking schemes, and in the corresponding potential plastic zone is taken into account. Example calculations are carried out to verify the proposed method via finite element simulations and comparisons with solutions from existing methods, and to study the effects of soil strength properties and tunnel size and depth. The results show that both the internal friction and the cohesion of the surrounding soil may help reduce the range of the potential collapse zone and the magnitude of the necessary support pressure. This study represents the first attempt to deal with cohesive-frictional soils via an analytical and continuous approach, and the developed method can be extended for various tunnel and other geotechnical stability problems involving cohesive-frictional soils.

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References

  1. Davis EH, Gunn MJ, Mair RJ et al (1980) The stability of shallow tunnels and underground openings in cohesive material. Géotechnique 30(30):397–416

    Article  Google Scholar 

  2. Leca E, Dormieux L (1990) Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material. Géotechnique 40(4):581–606

    Article  Google Scholar 

  3. Mollon G, Dias D, Soubra AH (2011) Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield. Int J Numer Anal Met. 35(12):1363–1388

    Article  Google Scholar 

  4. Yamamoto K, Lyamin AV, Wilson DW, Sloan SW, Abbo AJ (2011) Stability of a circular tunnel in cohesive-frictional soil subjected to surcharge loading. Comput Geotech 38(4):504–514

    Article  Google Scholar 

  5. Sloan SW, Assadi A (1993) Stability of shallow tunnels in soft ground. Predictive soil mechanics. In: Houlsby GT, Schofield AN (eds) Proceedings of the Wroth Memorial Symposium. Thomas Telford, London pp 644–663

  6. Sahoo JP, Kumar J (2013) Stability of long unsupported twin circular tunnels in soils. Tunn Undergr Sp Tech 38:326–335

    Article  Google Scholar 

  7. Sahoo JP, Kumar J (2014) Stability of a circular tunnel in presence of pseudostatic seismic body forces. Tunn Undergr Sp Tech 42:264–276

    Article  Google Scholar 

  8. Sahoo JP, Kumar J (2018) Required lining pressure for the stability of twin circular tunnels in soils. Int J Geomech 18(7):04018069.1-15

    Google Scholar 

  9. Jang G (1998) Limit analysis of the stability of shallow tunnels in soft ground. China Civil Eng J 31(5):65–72 (in Chinese)

    Google Scholar 

  10. Yang F, Yang J, Zhao L, Zhang J (2015) Finite element upper bound limit analysis and application for the stability of the surrounding rocks of tunnels. Academic Press, Beijing (in Chinese)

    Google Scholar 

  11. Smith C, Gilbert M (2007) Application of discontinuity layout optimization to plane plasticity problems. Proc R Soc A 463:2461–2484

    Article  MathSciNet  Google Scholar 

  12. Zhang Y, Zhuang X, Lackner R (2018) Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization. Int J Number Anal Met 42(11):1199–1216

    Article  Google Scholar 

  13. Osman AS, Mair RJ, Bolton MD (2006) On the kinematics of 2D tunnel collapse in undrained clay. Géotechnique 56(9):585–595

    Article  Google Scholar 

  14. Osman AS, Bolton MD, Mair RJ (2006) Predicting 2D ground movements around tunnels in undrained clay. Géotechnique 56(9):597–604

    Article  Google Scholar 

  15. Klar A, Osman AS, Bolton M (2007) 2D and 3D upper bound solutions for tunnel excavation using ‘elastic’ flow field. Int J Numer Anal Met 31(12):1367–1374

    Article  Google Scholar 

  16. Mollon G, Dias D, Soubra AH (2013) Continuous velocity fields for collapse and blowout of a pressurized tunnel face in purely cohesive soil. Int J Numer Anal Met 37(13):2061–2083

    Article  Google Scholar 

  17. Klar A, Klein B (2014) Energy-based volume loss prediction for tunnel face advancement in clays. Géotechnique 64(10):776–786

    Article  Google Scholar 

  18. Xiang Y, Song W (2017) Upper bound limit analysis of shield tunnel stability in undrained clays using complex variable solutions for different ground loss scenarios. Int J Geomech 17(9):04017057.1-8

    Article  Google Scholar 

  19. Song W (2020) A continuous upper bound limit analysis for the transverse stability of shallow shield tunneling in undrained clays. Eur J Environ Civil Eng 24(3):401–422

    Article  Google Scholar 

  20. Chen WF (1975) Limit analysis and soil plasticity. Elsevier, Amsterdam

    MATH  Google Scholar 

  21. Sagaseta C (1998) On the role of analytical solutions for the evaluation of soil deformation around tunnels. In: Cividini A (ed) Application of numerical methods to geotechnical problems. Springer, Vienna, pp 3–24

    MATH  Google Scholar 

  22. Sloan SW (1989) Upper bound limit analysis using finite elements and linear programing. Int J Numer Anal Met 13(3):263–282

    Article  Google Scholar 

  23. Eberhart RC, Kennedy J (1995) A new optimizer using particles swarm theory. Proceedings of the 6th International Symposium on Micro Machine and Human Science pp 39–43

  24. Kennedy J, Eberhart R (1995) Particle swarm optimization. Proceedings of IEEE International Conference on Neural Networks. 1942–1948

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Acknowledgements

This study was sponsored by the China National Key Basic Research and Development Project (973 Project) under Grant No. 2015CB057800.

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  1. School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Wenjie Song & Yanyong Xiang

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  1. Wenjie Song
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  2. Yanyong Xiang
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Correspondence to Wenjie Song.

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Song, W., Xiang, Y. An analytical method of continuous upper bound limit analysis for the stability of shallow shield tunnels in cohesive-frictional soils. J Eng Math 122, 101–116 (2020). https://doi.org/10.1007/s10665-020-10050-x

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  • DOI: https://doi.org/10.1007/s10665-020-10050-x

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