Slope Stability Analysis using Equivalent Mohr–Coulomb and Hoek–Brown criteria

  • Hossein Rafiei RenaniEmail author
  • C. Derek Martin
Technical Note


Slope stability is a major design objective in civil and mining projects such as dams and open pit mines. Stability of slopes is evaluated primarily based on the factor of safety, defined as the factor by which the shear strength of the slope material must be divided to bring the slope to the point of failure. It is evident from the definition that factor of safety is controlled by shear strength of the material. Failure criteria describing material strength under various loading conditions are used in stability analysis to determine the slope factor of safety.

The linear Mohr–Coulomb and nonlinear Hoek–Brown criteria (Hoek and Brown 1980, 2018; Hoek et al. 2002) are by far the most commonly used failure criteria in slope stability analysis. As a result, there are many instances in which it is desirable to convert one criterion to another without significantly affecting the results of analysis. It is crucial at this point to make a distinction between conversion methods...


Factor of safety Elastic analysis Confining stress range Limit equilibrium analysis Area of failure In situ stress ratio 



This work was financially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC: RES0014117).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Antony J (2003) Design of experiments for engineers and scientists. Butterworth Heinemann, OxfordGoogle Scholar
  2. Bishop AW (1955) The use of the slip circle in the stability analysis of slopes. Geotech 5:7–17CrossRefGoogle Scholar
  3. Brown ET (2008) Estimating the mechanical properties of rock masses. In: Potvin Y et al (eds) Proceedings of the 1st Southern hemisphere international rock mechanics symposium. Australian Centre for Geomechanics, Perth, pp 3–21Google Scholar
  4. Carranza-Torres C, 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 36:777–809CrossRefGoogle Scholar
  5. Cheng YM, Lansivaara T, Wei WB (2007) Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods. Comput Geotech 34:137–150CrossRefGoogle Scholar
  6. Cundall P, Carranza-Torres C, Hart R (2003) A new constitutive model based on the Hoek–Brown criterion. In: Brummer R et al (eds) Proceedings of the 3rd international FLAC symposium, Balkema, Lisse, pp 17–25Google Scholar
  7. Dawson EM, Roth WH, Drescher A (1999) Slope stability analysis by strength reduction. Geotech 49:835–840CrossRefGoogle Scholar
  8. Doghozlou HM, Goodarzi M, Rafiei Renani H, Salmi EF (2016) Analysis of spalling failure in marble rock slope: a case study of Neyriz marble mine, Iran. Environ Earth Sci 75:1478CrossRefGoogle Scholar
  9. Fredlund DG, Krahn J (1977) Comparison of slope stability methods of analysis. Can Geotech J 14:429–439CrossRefGoogle Scholar
  10. Fu W, Liao Y (2010) Non-linear shear strength reduction technique in slope stability calculation. Comput Geotech 37:288–298CrossRefGoogle Scholar
  11. Grenon M, Caudal P, Amoushahi S, Turmel D, Locat J (2017) Analysis of a large rock slope failure on the east wall of the LAB Chrysotile mine in Canada: back analysis, impact of water infilling and mining activity. Rock Mech Rock Eng 50:403–418CrossRefGoogle Scholar
  12. Griffith AA (1924) Theory of rupture. In: Proceedings of the 1st international congress on applied mechanics. Delft, pp 55–63Google Scholar
  13. Griffiths DV, Lane PA (1999) Slope stability analysis by finite elements. Geotech 49:387–403CrossRefGoogle Scholar
  14. Hammah RE, Yacoub TE, Curran JH (2009) Numerical modelling of slope uncertainty due to rock mass jointing. In: Proceedings of the international conference on rock joints and jointed rock masses, Tucson. Accessed 13 June 2019
  15. Hoek E (1983) Strength of jointed rock masses. Geotech 23:187–223CrossRefGoogle Scholar
  16. Hoek E (1990) Estimating Mohr–Coulomb friction and cohesion values from the Hoek–Brown failure criterion. Int J Rock Mech Min Sci 27:227–229CrossRefGoogle Scholar
  17. Hoek E, Brown ET (1980) Underground excavations in rock. The Institution of Mining and Metallurgy, LondonGoogle Scholar
  18. Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34:1165–1186CrossRefGoogle Scholar
  19. Hoek E, Brown ET (2018) The Hoek–Brown failure criterion and GSI-2018 edition. J Rock Mech Geotech Eng. Google Scholar
  20. Hoek E, Diederichs MS (2006) Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci 43:203–215CrossRefGoogle Scholar
  21. Hoek E, Carranza-Torres C, Corkum B (2002) Hoek–Brown failure criterion- 2002 edition. In: Hammah R et al (eds) Proceedings of the 5th North American rock mechanics symposium. University of Toronto, Toronto, pp 267–273Google Scholar
  22. Hoek E, Carranza-Torres C, Diederichs M, Corkum B (2008) The 2008 Kersten lecture: integration of geotechnical and structural design in tunnelling. In: Proceedings of the 56th annual geotechnical engineering conference. University of Minnesota, Minneapolis, pp 1–53Google Scholar
  23. Kumar P (1998) Shear failure envelope of Hoek–Brown criterion for rockmass. Tunn Undergr Space Technol 13:453–458CrossRefGoogle Scholar
  24. Langford JC, Diederichs MS (2015) Reliable support design for excavations in brittle rock using a global response surface method. Rock Mech Rock Eng 48:669–689CrossRefGoogle Scholar
  25. Li AJ, Merifield RS, Lyamin AV (2008) Stability charts for rock slopes based on the Hoek–Brown failure criterion. Int J Rock Mech Min Sci 45:689–700CrossRefGoogle Scholar
  26. Morgenstern NR, Price VE (1965) The analysis of the stability of general slip surfaces. Geotech 15:79–93CrossRefGoogle Scholar
  27. Priest SD (2005) Determination of shear strength and three-dimensional yield strength for the Hoek–Brown criterion. Rock Mech Rock Eng 38:299–327CrossRefGoogle Scholar
  28. Rafiei H, Moosavi M (2012) An approximate ANN-based solution for convergence of lined circular tunnels in elasto-plastic rock masses with anisotropic stresses. Tunn Undergr Space Technol 27:52–59CrossRefGoogle Scholar
  29. Rafiei Renani H, Martin CD (2019) Stability analysis of slopes with spatially variable strength properties. Rock Mech Rock Eng. Google Scholar
  30. Rafiei Renani H, Martin CD, Hudson R (2016) Back analysis of rock mass displacements around a deep shaft using two- and three-dimensional continuum modeling. Rock Mech Rock Eng 49:1313–1327CrossRefGoogle Scholar
  31. Rocscience Inc. (2018a) SLIDE- 2D limit equilibrium analysis of slope stability, version 8.0. TorontoGoogle Scholar
  32. Rocscience Inc. (2018b) RS2- 2D finite element analysis of geotechnical structures, version 9.0. TorontoGoogle Scholar
  33. Shah S (1992) A study of the behaviour of jointed rock masses. Ph.D. thesis, University of TorontoGoogle Scholar
  34. Yang XL, Yin JH (2010) Slope equivalent Mohr–Coulomb strength parameters for rock masses satisfying the Hoek–Brown criterion. Rock Mech Rock Eng 43:505–511CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada

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