Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Stability analysis of rock slopes using strength reduction adaptive finite element limit analysis

  • Chen, Guang-hui (School of Civil Engineering, Central South University) ;
  • Zou, Jin-feng (School of Civil Engineering, Central South University) ;
  • Zhang, Rui (School of Civil Engineering, Changsha University)
  • Received : 2019.08.17
  • Accepted : 2021.06.30
  • Published : 2021.08.25
⟨ Previous Next ⟩

Abstract

The main aim of this study is to propose an effective approach to conduct the stability analysis of rock slopes. Based on the strength reduction technology, the recent developed adaptive finite element limit analysis is adopted to investigate the stability of rock slopes for the first time. The rock mass strength is described by the latest generalized Hoek-Brown failure criterion. To better estimate the rock slope stability, the rock mass disturbance D and slope angle β are also incorporated into the determination of factor of safety by implementing the disturbance weighting factor ζ and the slope angle weighting factor fβ, respectively. The factors of safety obtained from this study are validated by those from existing works based on two real slope cases. For practical use, the factors of safety for the cases of β=45° in undisturbed rock masses are provided in the form of design charts. Finally, a set of design charts for ζ and a fitting formula for fβ are presented and discussed.

Keywords

Acknowledgement

The authors would like to acknowledgement the financial support of the Research Foundation of Education Bureau of Hunan Province, China (No. 19C0167) and Postgraduate Scientific Research Innovation Project of Hunan Province.

References

  1. Abbo, A.J., Wilson, D.W., Sloan, S.W. and Lyamin, A.V. (2013), "Undrained stability of wide rectangular tunnels", Comput. Geotech., 53, 46-59. https://doi.org/10.1016/j.compgeo.2013.04.005.
  2. Aksoy, C.O., Uyar, G.G. and Ozcelik, Y. (2016), "Comparison of Hoek-Brown and Mohr-Coulomb failure criterion for deep open coal mine slope stability", Struct. Eng. Mech., 60(5), 809-828. https://doi.org/10.12989/sem.2016.60.5.809.
  3. Basudhar, P.K. and Lakshminarayana, M.R. (2017), "Three-dimensional limit-equilibrium stability analyses of slopes and effect of inclusion of soil nails", Int. J. Geomech., 17(9), 04017067. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000932.
  4. Brown, E.T. (1980), Underground Excavations in Rock, CRC Press.
  5. Chen, G.H., Zou, J.F. and Qian, Z.H. (2019), "An improved collapse analysis mechanism for the face stability of shield tunnel in layered soils", Geomech. Eng., 17(1), 97-107. https://doi.org/10.12989/gae.2019.17.1.097.
  6. Chen, G.H., Zou, J.F., Pan, Q.J., Qian, Z.H. and Shi, H.Y. (2020), "Earthquake-induced slope displacements in heterogeneous soils with tensile strength cut-off", Comput. Geotech., 124(6), 103637. https://doi.org/10.1016/j.compgeo.2020.103637.
  7. Cheng, Y.M., Lansivaara, T. and Wei, W.B. (2007), "Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods", Comput. Geotech., 34(3), 137-150. https://doi.org/10.1016/j.compgeo.2006.10.011.
  8. Herskovits, J., Mappa, P., Goulart, E. and Soares, C.M.M. (2005), "Mathematical programming models and algorithms for engineering design optimization", Comput. Meth. Appl. Mech. Eng., 194(30-33), 3244-3268. https://doi.org/10.1016/j.cma.2004.12.017.
  9. Hoek, E., Carranza-Torres, C. and Corkum, B. (2002), "Hoek-Brown failure criterion-2002 edition", Proceedings of NARMS-TAC, Toronto.
  10. Hoek, E., Kaiser, P.K. and Bawden, W.F. (1995), Support of Underground Excavations in Hard Rock, Rotterdam.
  11. Kalatehjari, R., Arefnia, A., A Rashid, A.S., Ali, N. and Hajihassani, M. (2015), "Determination of three-dimensional shape of failure in soil slopes", Can. Geotech. J., 52(9), 1283-1301. https://doi.org/10.1139/cgj-2014-0326.
  12. Krabbenhoft, K. and Lyamin, A.V. (2015), "Strength reduction finite-element limit analysis", Geotechnique Lett., 5(4), 250-253. https://doi.org/10.1680/jgele.15.00110.
  13. Krabbenhoft, K., Lyamin, A.V. and Sloan, S.W. (2007), "Formulation and solution of some plasticity problems as conic programs", Int. J. Solid. Struct., 44(5), 1533-1549. https://doi.org/10.1016/j.ijsolstr.2006.06.036.
  14. Krabbenhoft, K., Lyamin, A.V., Hjiaj, M. and Sloan, S.W. (2005), "A new discontinuous upper bound limit analysis formulation", Int. J. Numer. Meth. Eng., 63(7), 1069-1088. https://doi.org/1069-1088. https://doi.org/10.1002/nme.1314.
  15. Li, A.J, Merifield, R.S. and Lyamin, A.V. (2008), "Stability charts for rock slopes based on the Hoek-Brown failure criterion", Int. J. Rock Mech. Min. Sci., 45(5), 689-700. https://doi.org/10.1016/j.ijrmms.2007.08.010.
  16. Lyamin, A.V. and Sloan, S.W. (2002a), "Lower bound limit analysis using nonlinear programming", Int. J. Numer. Meth. Eng., 55(5), 573-611. https://doi.org/10.1002/nme.511.
  17. Lyamin, A.V. and Sloan, S.W. (2002b), "Upper bound limit analysis using linear finite elements and nonlinear programming", Int. J. Numer. Anal. Meth. Geomech., 26(2), 181-216. https://doi.org/10.1016/0148-9062(89)91767-1.
  18. Mendjel, D. and Messast, S. (2012), "Development of limit equilibrium method as optimization in slope stability analysis", Struct. Eng. Mech., 41(3), 339-348. https://doi.org/10.12989/sem.2012.41.3.339.
  19. Michalowski, R.L. (2010), "Limit analysis and stability charts for 3D slope failures", J. Geotech. Geoenviron. Eng., 136, 583-593. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000251.
  20. Munoz, J.J., Bonet, J., Huerta, A. and Peraire, J. (2009), "Upper and lower bounds in limit analysis: adaptive meshing strategies and discontinuous loading", Int. J. Numer. Meth. Eng., 77(4), 471-501. https://doi.org/10.1002/nme.2421.
  21. Nian, T.K., Huang, R.Q., Wan, S.S. and Chen, G.Q. (2012), "Three-dimensional strength-reduction finite element analysis of slopes: geometric effects", Can. Geotech. J., 49(5), 574-588. https://doi.org/10.1139/t2012-014.
  22. Priest, S.D. (2005), "Determination of shear strength and three-dimensional yield strength for the Hoek-Brown criterion", Rock Mech. Rock Eng., 38(4), 299-327. https://doi.org/10.1007/s00603-005-0056-5.
  23. Roth, W.H., Dawson, E.M. and Drescher, A. (1999), "Slope stability analysis by strength reduction", Geotechnique, 49(6), 835-840. https://doi.org/10.1680/geot.1999.49.6.835.
  24. Shen, H. and Abbas, S.M. (2013), "Rock slope reliability analysis based on distinct element method and random set theory", Int. J. Rock Mech. Min. Sci., 61, 15-22. https://doi.org/10.1016/j.ijrmms.2013.02.003.
  25. Shen, J., Karakus, M. and Xu, C. (2013), "Chart-based slope stability assessment using the Generalized Hoek-Brown criterion", Int. J. Rock Mech. Min. Sci., 64, 210-219. https://doi.org/10.1016/j.ijrmms.2013.09.002.
  26. Sloan, S.W. (2013), "Geotechnical stability analysis", Geotechnique, 63(7), 531-572. https://doi.org/10.1680/geot.12.RL.001.
  27. Sonmez, H. and Ulusay, R. (1999), "Modifications to the geological strength index (GSI) and their applicability to stability of slopes", Int. J. Rock Mech. Min. Sci., 36, 743-760. https://doi.org/10.1016/S0148-9062(99)00043-1.
  28. Sun, C., Chai, J., Xu, Z., Qin, Y. and Chen, X. (2016), "Stability charts for rock mass slopes based on the Hoek-Brown strength reduction technique", Eng. Geol., 214, 94-106. https://doi.org/10.1016/j.enggeo.2016.09.017.
  29. Wilson, D.W., Abbo, A.J., Sloan, S.W. and Lyamin, A.V. (2011), "Undrained stability of a circular tunnel where the shear strength increases linearly with depth", Can. Geotech. J., 48(9), 1328-1342. https://doi.org/10.1139/cgj-2016-0072.
  30. Yang, X.L. and Li, Z.W. (2018), "Comparison of factors of safety using a 3D failure mechanism with kinematic approach", Int. J. Geomech., 18(9), 04018107. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001235.
  31. Zhang, R., Chen, G., Zou, J., Zhao, L. and Jiang, C. (2019), "Study on roof collapse of deep circular cavities in jointed rock masses using adaptive finite element limit analysis", Comput. Geotech., 111, 42-55. https://doi.org/10.1016/j.compgeo.2019.03.003.
  32. Zienkiewicz, O.C., Humpheson, C. and Lewis, R.W. (1975), "Associated and nonassociated visco-plasticity and plasticity in soil mechanics", Geotechnique, 25(4), 671-689. https://doi.org/10.1680/geot.1975.25.4.671.
  33. Zou, J.F., Chen, G.H. and Qian, Z.H. (2019), "Tunnel face stability in cohesion-frictional soils considering the soil arching effect by improved failure models", Comput. Geotech., 106, 1-17. https://doi.org/10.1016/j.compgeo.2018.10.014.
  34. Zouain, N., Herskovits, J., Borges, L.A. and Feijoo, R.A. (1993), "An iterative algorithm for limit analysis with nonlinear yield functions", Int. J. Solid. Struct., 30(10), 1397-1417. https://doi.org/10.1016/0020-7683(93)90220-2.