Geomechanics and Engineering

  • 제22권1호
  • /
  • Pages.11-23
  • /
  • 2020
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A new analytical-numerical solution to analyze a circular tunnel using 3D Hoek-Brown failure criterion

  • Ranjbarnia, Masoud (Department of Geotechnical Engineering, Faculty of Civil Engineering, University of Tabriz) ;
  • Rahimpour, Nima (Department of Geotechnical Engineering, Faculty of Civil Engineering, University of Tabriz) ;
  • Oreste, Pierpaolo (Department of Environmental, land and infrastructure Engineering, Politecnico di Torino)
  • 투고 : 2019.06.08
  • 심사 : 2020.05.19
  • 발행 : 2020.07.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, a new analytical-numerical procedure is developed to give the stresses and strains around a circular tunnel in rock masses exhibiting different stress-strain behavior. The calculation starts from the tunnel wall and continues toward the unknown elastic-plastic boundary by a finite difference method in the annular discretized plastic zone. From the known stresses in the tunnel boundary, the strains are calculated using the elastic-plastic stiffness matrix in which three dimensional Hoek-Brown failure criterion (Jiang and Zhao 2015) and Mohr-Coulomb potential function with proper dilation angle (i.e., non-associated flow rule) are employed in terms of stress invariants. The illustrative examples give ground response curve and show correctness of the proposed approach. Finally, from the results of a great number of analyses, a simple relationship is presented to find out the closure of circular tunnel in terms of rock mass strength and tunnel depth. It can be valuable for the preliminary decision of tunnel support and for prediction of tunnel problems.

키워드

참고문헌

  1. Alejano, L.R. and Alonso, E. (2005), ''Considerations of the dilatancy angle in rocks and rock masses", Int. J. Rock Mech. Min. Sci., 42(4), 481-507. https://doi.org/10.1016/j.ijrmms.2005.01.003.
  2. Alejano, L.R., Alonso, E., Rodriguez-Dono, A. and Fernandez-Manin, G. (2010), ''Application of the convergenceconfinement method to tunnels in rock masses exhibiting Hoek- Brown strain-softening behavior", Int. J. Rock Mech. Min. Sci., 1(47), 150-160. https://doi.org/ 10.1016/j.ijrmms.2009.07.008.
  3. Alejano, L.R., Rodriguez-Dono, A., Alonso, E. and Manin, G.F. (2009), ''Ground reaction curves for tunnels excavated in different quality rock masses showing several types of post-failure behavior", Tunn. Undergr. Sp. Technol., 24(6), 689-705. https://doi.org/10.1016/j.tust.2009.07.004.
  4. Alonso, E., Alejano, L.R., Varas, F., Fdez-Manin, G. and Carranza-Torres, C. (2003), ''Ground response curves for rock masses exhibiting strain-softening behavior", Int. J. Numer. Anal. Meth. Geomech., 27(13), 1153-1185. https://doi.org/10.1002/nag.315.
  5. Brown, E.T., Bray, J.W., Ladanyi, B. and Hoek, E. (1983), ''Ground response curves for rock tunnels", J. Geotech. Eng., 109(1), 15-39. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(15).
  6. Carranza-Torres, C. (1998), ''Self-similarity analysis of the elastoplastic response of underground openings in rock and effects of practical variables", University of Minnesota, Minnesota, U.S.A.
  7. Carranza-Torres, C. (2004), ''Elasto-plastic solution of tunnel problems using the generalized form of the Hoek-Brown failure criterion", Int. J. Rock Mech. Min. Sci., 41(S1), 1-11. https://doi.org/10.1016/j.ijrmms.2004.03.111.
  8. Carranza-Torres, C. and Fairhurst, C. (1999), "The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion", Int. J. Rock Mech. Min. Sci., 36(6), 777-809. https://doi.org/10.1016/S0148-9062(99)00047-9.
  9. Fahimifar, A. Ghadami, H. and Ahmadvand, M., (2015), "The ground response curve of underwater tunnels, excavated in a strain-softening rock mass", Geomech. Eng., 8(3), 323-359. https://doi.org/10.12989/gae.2015.8.3.323.
  10. FAMA, M.E.D. (1993), Numerical Modeling of Yield Zones in Weak Rock, in Analysis and Design Methods, 49-75.
  11. Gonzalez-Cao, J., Varas, F., Bastante, F.G. and Alejano, L.R. (2013), ''Ground reaction curves for circular excavations in non-homogeneous, axisymmetric strain-softening rock masses", J. Rock Mech. Geotech. Eng., 5(6), 431-442. https://doi.org/10.1016/j.jrmge.2013.08.001.
  12. Griffiths, D.V. and Willson, S.M. (1986), ''An explicit form of the plastic matrix for a Mohr-Coulomb material", Commun. Appl. Numer. Meth., 2(5), 523-529. https://doi.org/10.1002/cnm.1630020511.
  13. Hoek, E. (1999), "Putting numbers to geology-an engineer's viewpoint", Quart. J. Eng. Geol. Hydrogeol., 32(1), 1-19. https://doi.org/10.1144/GSL.QJEG.1999.032.P1.01.
  14. Hoek, E. and Brown, E.T. (1997), "Practical estimates of rock mass strength", Int. J. Rock Mech. Min. Sci., 34(8), 1165-1186. https://doi.org/10.1016/S1365-1609(97)80069-X.
  15. Hoek, E. and Diederichs, M.S. (2006), "Empirical estimation of rock mass modulus", Int. J. Rock Mech. Min. Sci., 43(2), 203-215. https://doi.org/10.1016/j.ijrmms.2005.06.005.
  16. Hoek, E. and Marinos, P. (2000), ''Predicting tunnel squeezing problems in weak heterogeneous rock masses", Tunn. Tunn. Int., 32(11), 45-51.
  17. Hoek, E., Carranza-Torres, C. and Corkum, B. (2002), ''Hoek-Brown failure criterion-2002 edition", Proc. NARMS-Tac, 1(1), pp.267-273. https://doi.org/10.1016/j.tust.2017.11.004.
  18. Jiang, H. and Xie, Y.L. (2012), ''A new three-dimensional Hoek-Brown strength criterion", Acta Mechanica Sinica, 28(2), 393-406. https://doi.org/10.1007/s10409-012-0054-2.
  19. Jiang, H. and Zhao, J. (2015), ''A simple three-dimensional failure criterion for rocks based on the Hoek Brown criterion", Rock Mech. Rock Eng., 48(5), 807-1819. https://doi.org/10.1007/s00603-014-0691-9.
  20. Lai, W.M., Rubin, D.H., Krempl, E. and Rubin, D. (2009), Introduction to Continuum Mechanics, Butterworth-Heinemann.
  21. Lee, Y.K. and Pietruszczak, S. (2008), ''A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass", Tunn. Undergr. Sp. Technol., 23(5), 588-599. https://doi.org/10.1016/j.tust.2007.11.002.
  22. Nikadat, N. and Fatehi Marji, M., (2016), "Analysis of stress distribution around tunnels by hybridized FSM and DDM considering the influences of joints parameters", Geomech. Eng., 11(2), 269-288. https://doi.org/10.12989/gae.2016.11.2.269.
  23. Oreste, P. (2009), "The convergence-confinement method: roles and limits in modern geomechanical tunnel design", Amer. J. Appl. Sci., 6(4), 757. https://doi.org/10.3844/ajassp.2009.757.771.
  24. Osguii, R. and Oreste, P. (2007), ''Convergence-control approach for rock tunnels reinforced by grouted bolts, using the homogenization concept", Geotech. Geol. Eng., 25(4), 431-440. https://doi.org/10.1007/s10706-007-9120-0.
  25. Panet, M. (1993), Understanding Deformations in Tunnels, in Comprehensive Rock Engineering, Pergamon Press, 1, 663-690.
  26. Paraskevopoulou, C. and Diederichs, M. (2018), "Analysis of time-dependent deformation in tunnels using the convergenceconfinement method", Tunn. Undergr. Sp. Technol., 71, 62-80. http://doi.org/10.1016/j.tust.2017.07.001.
  27. Park, K. (2017), "Simple solutions of an opening in elastic-brittle plastic rock mass by total strain and incremental approaches", Geomech. Eng., 13(4), 585-600. https://doi.org/10.12989/gae.2017.13.4.585.
  28. Park, K.H. and Kim, Y.J. (2006), ''Analytical solution for a circular opening in an elastic-brittle-plastic rock", Int. J. Rock Mech. Min. Sci., 43(4), 616-622. https://doi.org/10.1016/j.ijrmms.2005.11.004.
  29. Park, K.H., Tontavanich, B. and Lee, J.G. (2008), ''A simple procedure for ground response curve of circular tunnel in elastic-strain softening rock masses", Tunn. Undergr. Sp. Technol., 23(2), 151-159. https://doi.org/10.1016/j.tust.2007.03.002.
  30. Potts, D.M., Zdravkovic, L. and Zdravkovic, L. (2001), Finite Element Analysis in Geotechnical Engineering: Application (Vol. 2), Thomas Telford.
  31. Quevedo, F. and Bernaud, D. (2018), "Parametric study of the convergence of deep tunnels with long term effects: Abacuses", Geomech. Eng., 15(4), 973-986. https://doi.org/10.12989/gae.2018.15.4.973.
  32. Ranjbarnia, M., Fahimifar, A. and Oreste, P. (2015), ''Analysis of non-linear strain-softening behaviour around tunnels", Proc. Inst. Civ. Eng. Geotech. Eng., 168(1), 16-30. https://doi.org/10.1680/geng.13.00144.
  33. Sadd, M.H. (2009), Elasticity: Theory, Applications, and Numeric, Academic Press.
  34. Sharan, S.K., (2003), ''Elastic-brittle-plastic analysis of circular openings in Hoek-Brown media", Int. J. Rock Mech. Min. Sci., 40(6), 817-824. https://doi.org/10.1016/S1365-1609(03)00040-6.
  35. Tu, H., Qiao, C. and Han, Z. (2018), ''Elastic-brittle-plastic analysis of the radial subgrade modulus for a circular cavity based on the generalized nonlinear unified strength criterion", Tunn. Undergr. Sp. Technol., 71, 623-636. https://doi.org/10.1016/j.tust.2017.11.004.
  36. Wang, F. and Zou, J.F. (2018), "A simple prediction procedure of strain-softening surrounding rock for a circular opening", Geomech. Eng., 16(6), 619-626. https://doi.org/10.12989/gae.2018.16.6.619.
  37. Wang, Sh., Yin, X., Tang, H. and Ge, X. (2010), ''A new approach for analyzing circular tunnel in strain-softening rock mass", Int. J. Rock Mech. Min. Sci., 47(1), 170-178. https://doi.org/10.1016/j.ijrmms.2009.02.011.
  38. Yoo, C. (2016), "Effect of spatial characteristics of a weak zone on tunnel deformation behavior", Geomech. Eng., 11(1), 41-58. https://doi.org/10.12989/gae.2016.11.1.041.
  39. Zareifard, M.R. (2019), "Ground response curve of deep circular tunnel in rock mass exhibiting Hoek-Brown strain-softening behaviour considering the dead weight loading", Eur. J. Environ. Civ. Eng. https://doi.org/10.1080/19648189.2019.1632745.
  40. Zhuang, P.Z. and Yu, H.S. (2018), "A unified analytical solution for elastic-plastic stress analysis of a cylindrical cavity in Mohr-Coulomb materials under biaxial in situ stresses", Geotechnique, 69(4), 369-376. https://doi.org/10.1680/jgeot.17.P.281.
  41. Zou, J.F. and Wei, X.X. (2018), "An improved radius-incrementalapproach of stress and displacement for strain-softening surrounding rock considering hydraulic-mechanical coupling", Geomech. Eng., 16(1), 59-69. https://doi.org/10.12989/gae.2018.16.1.059.
  42. Zou, J.F. and Zheng, H. (2016), ''Numerical approach for strainsoftening rock with axial stress", Proc. Inst. Civ. Eng. Geotech. Eng., 169(3), 276-290. https://doi.org/10.1680/jgeen.15.00097.
  43. Zou, J.F., Li, C. and Wang, F. (2017), "A new procedure for ground response curve (GRC) in strain-softening surrounding rock", Comput. Geotech., 89, 81-91. https://doi.org/10.1016/j.compgeo.2017.04.009.
  44. Zou, J.F., Yang, T., Ling, W., Guo, W. and Huang, F. (2019), "A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass", Geomech. Eng., 18(3), 225-234. https://doi.org/10.12989/gae.2019.18.3.225.

피인용 문헌

  1. Deformation behavior analysis of tunnels opened in various rock mass grades conditions in China vol.26, pp.2, 2020, https://doi.org/10.12989/gae.2021.26.2.191