Geotechnical and Geological Engineering

, Volume 37, Issue 5, pp 4603–4612 | Cite as

Stability of Twin Shallow Tunnels in Unsaturated Soils Considering Vertical Steady State Flow

  • Zi-han YangEmail author
  • Shui-sheng Li
  • Dong Yang
  • Shuai Zhou
  • Quan Zhou
Technical Note


This paper presents an analytical investigation on the stability of twin shallow tunnels excavated in unsaturated soils. The vertical steady state flow is considered to simulate the infiltration or evaporation condition during tunnel construction. The unified effective stress approach is employed to depict shear strength of unsaturated soils and the closed-form solution for the profile of apparent cohesion is established. A multi-block failure mechanism for twin shallow tunnels is then constructed, and on this basis, the analytical expression of required supporting pressure is deduced in accordance of the kinematical approach of limit analysis. The upper bound solution of supporting pressure is then searched through numerical optimization, and parametric analysis is performed to discuss the influence of unsaturated soil strength and vertical discharge on tunnel stability.


Twin shallow tunnel Unsaturated soils Limit analysis Steady state flow Supporting pressure 



The preparation of the paper has received financial supports from National Natural Science Foundation of China (51804113), China State Construction Engineering Corporation Limited Funded Project (CSCEC-2018-Z-1), and Hunan Provincial Natural Science Foundation of China (2018JJ3578). The financial supports are greatly appreciated.


  1. Akl SA, Metwally KG (2017) Optimizing arching creation for Abou Muharik Tunnel in Egypt using numerical analysis. KSCE J Civ Eng 21(1):160–167CrossRefGoogle Scholar
  2. Chen WF, Liu XL (1990) Limit analysis in soil mechanics. Elsevier Scientific Publishing Company, New YorkGoogle Scholar
  3. Davis EH, Gunn MJ, Mair RJ et al (1980) The stability of shallow tunnels and underground openings in cohesive material. Geotechnique 30(4):397–416CrossRefGoogle Scholar
  4. Do NA, Dias D, Oreste P (2016) 3D numerical investigation of mechanized twin tunnels in soft ground—influence of lagging distance between two tunnel faces. Eng Struct 109:117–125CrossRefGoogle Scholar
  5. Fraldi M, Guarracino F (2009) Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion. Int J Rock Mech Min Sci 46(4):665–673CrossRefGoogle Scholar
  6. Fraldi M, Guarracino F (2010) Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections. Int J Solids Struct 47(2):216–223CrossRefGoogle Scholar
  7. Fredlund DG, Rahardjo H, Fredlund MD (2012) Unsaturated soil mechanics in engineering practice. Wiley, HobokenCrossRefGoogle Scholar
  8. Guan K, Zhu WC, Niu LL et al (2017) Three-dimensional upper bound limit analysis of supported cavity roof with arbitrary profile in Hoek-Brown rock mass. Tunn Undergr Space Technol 69(10):147–154CrossRefGoogle Scholar
  9. Kiani M, Akhlaghi T, Ghalandarzadeh A (2016) Experimental modeling of segmental shallow tunnels in alluvial affected by normal faults. Tunn Undergr Space Technol 51(1):108–119CrossRefGoogle Scholar
  10. Klar A, Osman AS, Bolton M (2007) 2D and 3D upper bound solutions for tunnel excavations using elastic flow fields. Int J Numer Anal Meth Geomech 31(12):1367–1374CrossRefGoogle Scholar
  11. Lanzano G, Bilotta E, Russo G et al (2015) Experimental and numerical study on circular tunnels under seismic loading. Eur J Environ Civ Eng 19(5):539–563CrossRefGoogle Scholar
  12. Lu N, Likos WJ (2004) Unsaturated soil mechanics. Wiley, New YorkGoogle Scholar
  13. Lu N, Kim TH, Sture S et al (2009) Tensile strength of unsaturated sand. J Eng Mech 135(12):1410–1419CrossRefGoogle Scholar
  14. Lu N, Godt JW, Wu DT (2010) A closed-form equation for effective stress in unsaturated soil. Water Resour Res 46(5):W05515CrossRefGoogle Scholar
  15. Ng CWW, Fong KY, Liu HL (2018) The effects of existing horseshoe-shaped tunnel sizes on circular crossing tunnel interactions: Three-dimensional numerical analyses. Tunn Undergr Space Technol 77:68–79CrossRefGoogle Scholar
  16. Osman AS (2010) Stability of unlined twin tunnels in undrained clay. Tunn Undergr Space Technol 25(3):290–296CrossRefGoogle Scholar
  17. Osman AS, Mair RJ, Bolton M (2006) On the kinematics of 2D tunnel collapse in undrained clay. Geotechnique 56(9):585–595CrossRefGoogle Scholar
  18. Pang Z, Gu D (2019) Seismic stability of a fissured slope based on nonlinear failure criterion. Geotech Geol Eng. CrossRefGoogle Scholar
  19. Perazzelli P, Anagnostou G (2013) Stress analysis of reinforced tunnel faces and comparison with the limit equilibrium method. Tunn Undergr Space Technol 38(9):87–98CrossRefGoogle Scholar
  20. Sahoo JP, Kumar J (2013) Stability of long unsupported twin circular tunnels in soils. Tunn Undergr Space Technol 38(9):326–335CrossRefGoogle Scholar
  21. Sahoo JP, Kumar J (2018) Required lining pressure for the stability of twin circular tunnels in soils. Int J Geomech 18(7):04018069CrossRefGoogle Scholar
  22. Vahedifard F, Leshchinsky BA, Mortezaei K et al (2015) Active earth pressures for unsaturated retaining structures. J Geotech Geoenviron Eng 141(11):1–11CrossRefGoogle Scholar
  23. Vahedifard F, Leshchinsky D, Mortezaei K et al (2016) Effective stress-based limit equilibrium analysis for homogeneous unsaturated slopes. Int J Geomech 16(6):D4016003CrossRefGoogle Scholar
  24. Wang HN, Utili S, Jiang MJ (2014) An analytical approach for the sequential excavation of axisymmetric lined tunnels in viscoelastic rock. Int J Rock Mech Min Sci 68(6):85–106CrossRefGoogle Scholar
  25. 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):04017057CrossRefGoogle Scholar
  26. Xie J, Liu CG, Yu HY (2006) Upper bound solutions of plastic limit analysis for the stability of two parallel circular tunnels. Chin J Rock Mech Eng 25(9):1835–1841 (in Chinese) Google Scholar
  27. Yang XL, Yao C (2017) Axisymmetric failure mechanism of a deep cavity in layered soils subjected to pore pressure. Int J Geomech 17(8):04017031CrossRefGoogle Scholar
  28. Yang XL, Yao C (2018) Stability of tunnel roof in nonhomogeneous soils. Int J Geomech 18(3):06018002CrossRefGoogle Scholar
  29. Yang W, Li L, Shang Y et al (2018) An experimental study of the dynamic response of shield tunnels under long-term train loads. Tunn Undergr Space Technol 79(9):67–75CrossRefGoogle Scholar
  30. Yao C, Yang XL (2017) Limit analysis of unsaturated soil slope stability considering intermediate principal stress and strength nonlinearity. Geotech Geol Eng 35(5):2053–2063CrossRefGoogle Scholar
  31. Zhang JH, Xu JS, Zhang B (2014) Energy analysis of stability of twin shallow tunnels based on nonlinear failure criterion. J Cent South Univ 21(12):4669–4676CrossRefGoogle Scholar
  32. Zhang B, Wang X, Zhang JS et al (2018) Safe range analysis of clear distance of twin shallow tunnels based on limit analysis and reliability theory. J Cent South Univ 25(1):196–207CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Zi-han Yang
    • 1
    Email author
  • Shui-sheng Li
    • 1
  • Dong Yang
    • 1
  • Shuai Zhou
    • 1
  • Quan Zhou
    • 1
  1. 1.Research and Development CenterChina Construction Fifth Engineering Division Corp., LtdChangshaChina

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