Skip to main content
SpringerLink
Log in

Influence of pore water pressure on upper bound analysis of collapse shape for square tunnel in Hoek-Brown media

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

To investigate the effective shape of collapsing block in square tunnel subjected to pore water pressure, the analytical solution of detaching curve was derived using upper bound theorem of limit analysis with Hoek-Brown failure criterion. The work rate of pore water pressure, which was regarded as an external rate of work, was taken into account in the framework of limit analysis. Taking advantages of variational calculation, the objective function with respect to detaching curve was optimized to obtain the effective shape of collapsing block for square tunnel. According to the numerical results, it is found that the varying pore water pressure coefficient only affects the height and width of the collapsing block, whereas the shape of collapsing block remains unchanged.

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. MERIFIELD R S, LYAMIN A V, SLOAN S W. Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek-Brown criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(6): 920–937.

    Article  Google Scholar 

  2. YANG Xiao-li, YIN Jian-hua. Estimation of seismic passive earth pressures with nonlinear failure criterion [J]. Engineering Structures, 2006, 28(3): 342–348.

    Article  Google Scholar 

  3. YANG Xiao-li, ZOU Jin-feng. 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 

  4. DAVIS E H, DUNN M J, MAIR R J, SENEVIRATNE H N. The stability of shallow tunnels and underground openings in cohesive material [J]. Geotechnique, 1980, 30(4): 397–416.

    Article  Google Scholar 

  5. LECA E, DORMIEUX L. Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material [J]. Geotechnique, 1990, 40(4): 581–606.

    Article  Google Scholar 

  6. ASSADI A, SLOAN S W. Undrained stability of shallow square tunnel [J]. Journal of Geotechnical Engineering ASCE, 1991, 117(8): 1152–1173.

    Article  Google Scholar 

  7. SLOAN S W, ASSADI A. Undrained stability of a square tunnel in a soil whose strength increases linearly with depth [J]. Computers and Geothehnics, 1991, 12(4): 321–346.

    Article  Google Scholar 

  8. DAWSON E M, ROTH W H, DRESCHER A. Slope stability analysis by strength reduction [J]. Geotechnique, 1999, 49(6): 835–840.

    Article  Google Scholar 

  9. MICHALOWSKI R L. Slope stability analysis: A kinematical approach [J]. Geotechnique, 1995, 45(2): 283–293.

    Article  MathSciNet  Google Scholar 

  10. 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 

  11. MERIFIELD R S, LYAMIN A V, SLOAN S W. Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek-Brown criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(6): 920–937.

    Article  Google Scholar 

  12. CARRANZA-TORRES C, FAIRHURST C. The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 1999, 36(6): 777–809.

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. JIMENEZ R, SERRANO A, OLALLA C. Linearization of the Hoek and Brown rock failure criterion for tunnelling in elasto-plastic rock masses [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(7): 1153–1163.

    Article  Google Scholar 

  15. YANG Xiao-li. 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 

  16. 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  Google Scholar 

  17. 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 

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

    Article  Google Scholar 

  19. 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 

  20. 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  Google Scholar 

  21. YANG X L, YIN J H. Linear Mohr-Coulomb strength parameters from the nonlinear Hoek-Brown rock masses [J]. International Journal of Non-linear Mechanics, 2006, 41(8): 1000–1005.

    Article  Google Scholar 

  22. RAFAEL J, ALCIBIADES S, CLAUDIO O. Linearization of the Hoek and Brown rock failure criterion for tunneling in elasto-plastic rock masses [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(7): 1153–1163.

    Article  Google Scholar 

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

    Article  Google Scholar 

  24. VIRATJANDR C, MICHALOWSKI R L. Limit analysis of submerged slopes subjected to water drawdown [J]. Canadian Geotechnical Journal, 2006, 43(8): 802–814.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Fu Huang  (黄阜), Dao-bing Zhang  (张道兵), Zhi-bin Sun  (孙志彬) & Ben Wu  (吴贲)

Authors
  1. Fu Huang  (黄阜)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dao-bing Zhang  (张道兵)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhi-bin Sun  (孙志彬)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ben Wu  (吴贲)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fu Huang  (黄阜).

Additional information

Foundation item: Project(09JJ1008) supported by Hunan Provincial Science Foundation, China; Project(CX2009B043) supported by Hunan Provincial Postgraduate Innovation Program, China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, F., Zhang, Db., Sun, Zb. et al. Influence of pore water pressure on upper bound analysis of collapse shape for square tunnel in Hoek-Brown media. J. Cent. South Univ. Technol. 18, 530–535 (2011). https://doi.org/10.1007/s11771-011-0727-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-011-0727-1

Key words

Search

Navigation