Skip to main content
SpringerLink
Log in

Minimum safe thickness of rock plug in karst tunnel according to upper bound theorem

  • Geological, Civil, Energy and Traffic Engineering
  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

High pressure and water-bearing caverns ahead of a karst tunnel face tend to cause geological disasters, such as water and mud bursts. So, the determination of safe thickness of the reserved rock plug is a key technical problem to be solved for karst tunnel construction. Based on the Hoek-Brown nonlinear failure criterion, the minimum safe thickness of rock plug was investigated in the light of the limit analysis theory. On the basis of the proposed failure mode, the expression of the minimum thickness for rock plug was obtained by means of upper bound theorem in combination with variational principle. The calculation results show the influence of each parameter on safe thickness and reveal the damage range of rock plug. The proposed method is verified by comparing the results with those of the drain cavern of Maluqing Tunnel. The research shows that with the increase of compressive strength and tensile strength as well as constant A of Hoek-Brown criterion, the safe thickness decreases, whereas with the increase of cavern pressure, tunnel diameter, and constant B from Hoek-Brown criterion, the safe thickness increases. Besides, the tensile strength, or constants A and B affect the shear failure angle of rock plug structure, but other parameters do not. In conclusion, the proposed method can predict the minimum safe thickness of rock plug, and is useful for water burst study and prevention measures of tunnels constructed in high-risk karst regions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. SENENT S, MOLLON G, JIMENEZ R. Tunnel face stability in heavily fractured rock masses that follow the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 60(1): 440–451.

    Article  Google Scholar 

  2. YANG X L, ZOU J F. Stability factors for rock slopes subjected to pore water pressure based on the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(7): 1146–1152.

    Article  Google Scholar 

  3. YANG X L, WANG J M. Ground movement prediction for tunnels using simplified procedure [J]. Tunnelling and Underground Space Technology, 2011, 26(3): 462–471.

    Article  Google Scholar 

  4. YANG X L. Seismic bearing capacity of a strip footing on rock slopes [J]. Canadian Geotechnical Journal, 2009, 46(8): 943–954.

    Article  Google Scholar 

  5. MEGUID M A, DAND H K. The effect of erosion voids on existing tunnel linings [J]. Tunneling and Underground Space Technology, 2008, 4(2): 1–9.

    Google Scholar 

  6. GEREMEW A M. Pore-water pressure development caused by wave-induced cyclic loading in deep porous formation [J]. International Journal of Geomechanics, 2011, 13(1): 65–68.

    Article  Google Scholar 

  7. PESENDORFER M, LOEW S. Subsurface exploration and transient pressure testing from a deep tunnel in fractured and karstifiedlimestones (Lötschberg Base Tunnel, Switzerland) [J]. International Journal of Rock Mechanics and Mining Science, 2010, 47(1): 121–137.

    Article  Google Scholar 

  8. LI Li-ping, LI Shu-cai, ZHANG Qing-song. Study of mechanism of water inrush induced by hydraulic fracturing in karst tunnels [J]. Rock and Soil Mechanics, 2010, 31(2): 523–528. (in Chinese)

    Google Scholar 

  9. YANG X L, YIN J H, LI L. Influence of a nonlinear failure criterion on the bearing capacity of a strip footing resting on rock mass using a lower bound approach [J]. Canadian Geotechnical Journal, 2003, 40(3): 702–707.

    Article  Google Scholar 

  10. GUO Jia-qi. Study on against-inrush thickness and water-burst mechanism of karst tunnel [D]. Beijing: Beijing Jiaotong University, 2011. (in Chinese)

    Google Scholar 

  11. YANG X L. Seismic passive pressures of earth structures by nonlinear optimization [J]. Archive of Applied Mechanics, 2011, 81(9): 1195–1202.

    Article  MATH  Google Scholar 

  12. YANG X L, YIN J H. Estimation of seismic passive earth pressures with nonlinear failure criterion [J]. Engineering Structures, 2006, 28(3): 342–348.

    Article  Google Scholar 

  13. YANG X L, YIN J H. Slope stability analysis with nonlinear failure criterion [J]. Journal of Engineering Mechanics, 2004, 130(3): 267–273.

    Article  Google Scholar 

  14. YANG X L, ZOU J F. Cavity expansion analysis with non-linear failure criterion [J]. Proceedings of the Institution of Civil Engineers- Geotechnical Engineering, 2011, 164(1): 41–49.

    Article  MathSciNet  Google Scholar 

  15. YANG X L, LI L, YIN J H. Seismic and static stability analysis for rock slopes by a kinematical approach [J]. Geotechnique, 2004, 54(8): 543–549.

    Article  Google Scholar 

  16. CHEN W F. Limit analysis and soil plasticity [M]. The Netherland: Elsevier, 2013: 37–39.

    Google Scholar 

  17. LI A J, MERIFIELD R S, LYAMIN A V. Stability charts for rock slopes based on the Hoek-Brown failure criterion [J]. Rock Mechanics and Mining Sciences, 2008, 45(5): 689–700.

    Article  Google Scholar 

  18. FRALDI M, GUARRACINO F. Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(4): 665–673.

    Article  Google Scholar 

  19. YANG X L, HUANG F. Three-dimensional failure mechanism of a rectangular cavity in a Hoek-Brown rock medium [J]. International Journal of Rock Mechanics and Mining Sciences, 2013, 61: 189–195.

    Article  Google Scholar 

  20. YANG X L, HUANG F. Collapse mechanism of shallow tunnel based on nonlinear Hoek-Brown failure criterion [J]. Tunnelling and Underground Space Technology, 2011, 26(6): 686–691.

    Article  Google Scholar 

  21. YANG X L, YIN J H. Slope equivalent Mohr-Coulomb strength parameters for rock masses satisfying the Hoek-Brown criterion [J]. Rock Mechanics and Rock Engineering, 2010, 43(4): 505–511.

    Article  MathSciNet  Google Scholar 

  22. HOEK E, CARRANZA C, CORKUM B. Hoek-Brown failure criterion-2002 edition [C]// HAMMAH R, BAWDEN W F, CURRAN J. Proceedings of the North American Rock Mechanics Society NARMS-TAC 2002. Toronto: University of Toronto Press, 2002: 267–273.

    Google Scholar 

  23. HOEK E, BROWN E T. Practical estimates of rock mass strength [J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(8): 1165–1186.

    Article  Google Scholar 

  24. PAUL M, HOEK E. Estimating the geotechnical properties of heterogeneous rock masses such as flash [J]. Bulletin of Engineering Geology and the Environment, 2001, 60(2): 85–92.

    Article  Google Scholar 

  25. YANG X L, YIN J H. Upper bound solution for ultimate bearing capacity with a modified Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2005, 42(4): 550–560.

    Article  MathSciNet  Google Scholar 

  26. YANG X L, LI L, YIN J H. Stability analysis of rock slopes with a modified Hoek-Brown failure criterion [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2004, 28(2): 181–190.

    Article  MATH  Google Scholar 

  27. YANG X L. Seismic displacement of rock slopes with nonlinear Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(6): 948–953.

    Article  Google Scholar 

  28. FRALDI M, GUARRACINO F. Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections [J]. International Journal of Solids and Structures, 2010, 47(2): 216–223.

    Article  MATH  Google Scholar 

  29. SUN Zhi-bin, ZHANG Dao-bing. Back analysis for soil slope based on measuring inclination data [J]. Journal of Central South University, 2012, 19(11): 3291–3297.

    Article  Google Scholar 

  30. SUN Zhi-bin, LIANG Qiao. Back analysis of general slope under earthquake forces using upper bound theorem [J]. Journal of Central South University, 2013, 20(11): 3274–3281.

    Article  Google Scholar 

  31. YANG X L, Long Z X. Seismic and static 3D stability of two-stage rock slope based on Hoek-Brown failure criterion [J]. Canadian Geotechnical Journal, 2016, 53(3): 551–558.

    Article  MathSciNet  Google Scholar 

  32. YANG X L, XU J S, LI Y X, YAN R M. Collapse mechanism of tunnel roof considering joined influences of nonlinearity and non-associated flow rule [J]. Geomechanics and Engineering, 2016, 10(1): 21–35.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, Central South University, Changsha, 410075, China

    Zi-han Yang  (杨子汉) & Jia-hua Zhang  (张佳华)

Authors
  1. Zi-han Yang  (杨子汉)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jia-hua Zhang  (张佳华)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zi-han Yang  (杨子汉).

Additional information

Foundation item: Project(2013CB036004) supported by the National Basic Research Program of China; Project (51378510) supported by the National Natural Science Foundation of China; Project (CX2014B069) supported by Hunan Provincial Innovation Foundation for Postgraduate, China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Zh., Zhang, Jh. Minimum safe thickness of rock plug in karst tunnel according to upper bound theorem. J. Cent. South Univ. 23, 2346–2353 (2016). https://doi.org/10.1007/s11771-016-3293-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-016-3293-8

Key words

Search

Navigation