Advertisement

Comparative analyses of finite element and limit-equilibrium methods for heavily fractured rock slopes

Abstract

Limit-equilibrium method (LEM) and finite element method (FEM) with shear strength reduction (SSR) technique are the most widely used analysis tools in slope stability assessment. Recently, researchers have reported that both factor of safety (FOS) values and failure surfaces obtained from LEM and FEM are generally in good agreement except in some particular cases. On the other hand, the consistency between two methods has not been adequately discussed for heavily fractured rock mass models by employing Generalized Hoek–Brown Criterion (GHBC). In this study, the FOS values and failure surfaces derived from LEM and FE-SSR based on GHBC were compared concerning static and pseudo-static conditions, various overall slope angles, geological strength index (GSI) values, and various water table levels. In this context, three homogeneous, highly fractured rock slope models with irregular geometry and different slope heights were generated by two-dimensional Slide and Phase2 software. Limit-equilibrium (LE) analyses were performed by Bishop, Fellenius, Morgenstern–Price, and Spencer techniques. The comparisons of global minimum FOS values for 431 cases and the effects of variables on two methods were investigated by statistical analyses. Consequently, it was determined that the difference between the FOS values are statistically significant. However, if the seismic coefficient is higher than 0.1 g, slope angle is higher than 34°, and the slope is assumed to be fully saturated, Morgenstern–Price is the most well-matched technique with FE-SSR than the others. For the same cases, the failure surfaces detected by Fellenius is more similar to the ones detected by FE-SSR.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7

References

  1. Ahmad I S B 2012 Limit equilibrium method and finite element method in slope stability analysis; Dissertation, Universiti Teknologi Malaysia.

  2. Akbas B and Huvaj N 2015 Probabilistic slope stability analyses using limit equilibrium and finite element methods; In: Geotechnical Safety and Risk (eds) Schweckendiek T, Van Tol A F and Pereboom D, https://doi.org/10.3233/978-1-61499-580-7-716.

  3. Alemdağ S, Kaya A, Karadağ M, Gürocak Z and Bulut F 2015 Utilization of the limit equilibrium and finite element methods for the stability analysis of the slope debris: An example of the Kalebaşı District (NE Turkey); J. Afr. Earth Sci. 106 134–146.

  4. Alkasawneh W, Malkawi A I H, Nusairat J H and Albataineh N 2008 A comparative study of various commercially available programs in slope stability analysis; Comput. Geotech. 35 428–435.

  5. Aryal K P 2006 Slope stability evaluations by limit equilibrium and finite element methods; Dissertation, Norwegian University of Science and Technology.

  6. Aswathi C K, Jana A, Dey A and Sreedeep S 2017 Stability assessment of a heavily jointed rock slope using limit equilibrium and finite element methods; Proceedings of Indian Geotechnical Conference (GeoNEst), Guwahati, India.

  7. Azami A, Yacoub T, Curran J and Wai D 2013 A constitutive model for jointed rock mass; Proceedings of International Society for Rock Mechanics and Rock Engineering (ISRM) Symposium (EUROCK), Wroclaw, Poland.

  8. Baba K, Bahi L, Ouadif L and Akhhsas A 2012 Slope stability evaluations by limit equilibrium and finite element methods applied to a railway in the Moroccan Rif; Open J. Civil Eng. 2 27–32.

  9. Berisavljević Z, Berisavljević D, Čebašek V and Rakić D 2015 Slope stability analyses using limit equilibrium and strength reduction methods; Građevinar 67(10) 975–983, https://doi.org/10.14256/JCE.1030.2014.

  10. Bishop A W 1955 The use of slip circles in stability analysis of slopes; Geotechnique 5(1) 7–17.

  11. Burman A, Acharya S P, Sahay R R and Maity D 2015 A comparative study of slope stability analysis using traditional limit equilibrium method and finite element method; Asian J. Civil Eng. (BHRC) 16(4) 467–492.

  12. Cai M, Kaiser P K, Uno H, Tasaka Y and Minami M 2004 Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI System; Int. J. Rock Mech. Min. Sci. 41(1) 3–19.

  13. Chen Y and Lin H 2018 Consistency analysis of Hoek–Brown and equivalent Mohr–Coulomb parameters in calculating slope safety factor; Bull. Eng. Geol. Environ., https://doi.org/10.1007/s10064-018-1418-z.

  14. Cheng Y M, Lansivaara T and Wei W B 2007 Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods; Comput. Geotech. 34 137–150.

  15. Craig R F 2004 Craig’s Soil Mechanics; 7th edn, Spon Press, London.

  16. Deng D, Liang L, Wang J and Zhao L 2016 Limit equilibrium method for rock slope stability analysis by using the Generalized Hoek–Brown criterion; Int. J. Rock Mech. Min. Sci. 89 176–184.

  17. Duncan J M 1996 State of the art: Limit equilibrium and finite-element analysis of slopes; J. Geotech. Eng. ASCE 122(7) 577–597.

  18. Duncan J M and Wright S G 1980 The accuracy of equilibrium of slope stability analysis; Eng. Geol. 16(2) 5–17.

  19. Fellenius W 1936 Calculations of the Stability of Earth Dams. In Proceedings of Second Congress of Large Dams, Washington DC, pp. 445–463.

  20. Fredlund D G and Krahn J 1977 Comparison of slope stability methods of analysis; Can. Geotech. J. 14 429–436.

  21. Fredlund D G, Krahn J and Pufahl D E 1981 The relationship between limit equilibrium slope stability methods; Proceedings of 10th International Conference on Soil Mechanics and Foundation Engineering, Stockholm, pp. 409–416.

  22. Ghazaly Z, Rahim M A, Jee K A C, Isa N F and Sofri L A 2016 Landslide simulation using limit equilibrium and finite element method; Mater. Sci. Forum 857 555–559.

  23. Gover S and Hammah R 2013 A comparison of finite elements (SSR) and limit-equilibrium slope stability analysis by case study; Civil Eng. 21(3) 31–34.

  24. Griffiths D V and Lane P A 1999 Slope stability analysis by finite elements; Geotechnique 49(3) 387–403.

  25. Hammah R E, Curran J H, Yacoub T E and Corkum B 2004 Stability analysis of rock slopes using the finite element method; Proceedings of ISRM Regional Symposium (EUROCK 2004) and the 53rd Geomechanics Colloquium, Salzburg, Austria.

  26. Hammah R E, Yacoub T E, Corkum B and Curran J H 2005a The shear strength reduction method for the Generalized Hoek–Brown Criterion; Proceedings of 40th U.S. Symposium on Rock Mechanics, Anchorage, Alaska.

  27. Hammah R E, Yacoub T E, Corkum B and Curran J H 2005b A comparison of finite element slope stability analysis with conventional limit-equilibrium investigation; Proceedings of 58th Canadian Geotechnical and 6th Joint IAH-CNC and CGS Groundwater Specialty Conferences, Saskatoon Saskatchewan, Canada.

  28. Hammouri N A, Malkawi A I H and Yamin M M A 2008 Stability analysis of slopes using the finite element method and limiting equilibrium approach; Bull. Eng. Geol. Environ. 67 471–478.

  29. Hoek E, Carter T and Diederichs M 2013 Quantification of the Geological Strength Index Chart; Proceedings of 47th U.S. Rock Mechanics/Geomechanics Symposium, San Francisco, CA, USA.

  30. Hoek E, Carranza-Torres C and Corkum B 2002 Hoek–Brown criterion – 2002 edition; Proceedings of North American Rock Mechanics Symposium, Toronto, Canada, pp. 267–273.

  31. Jing L 2003 A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering; Int. J. Rock Mech. Min. Sci. 40 283–353.

  32. Kadakci Koca T and Koca M Y 2014 Slope stability assessment of rock slopes in an open pit albite mine using finite element method (FEM); J. Geol. Eng. 38(1) 1–18 (in Turkish).

  33. Kadakci T 2011 Slope stability assessment of the open pit albite mine in the Çine-Karpuzlu (Aydın) Area; Dissertation, Dokuz Eylül University.

  34. Kruskal W H and Wallis W A 1952 Use of ranks in one-criterion variance analysis; J. Am. Stat. Assoc. 47(260) 583–621.

  35. 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. 45 689–700.

  36. Liu S Y, Shao L T and Li H J 2015 Slope stability analysis using the limit equilibrium method and two finite element methods; Comput. Geotech. 63 291–298.

  37. Mansour Z S and Kalantari B 2011 Traditional methods vs. finite difference method for computing safety factors of slope stability; Electron J. Geotech. Eng. 16 1119–1130.

  38. Marinos P and Hoek E 2000 A geologically friendly tool for rock mass strength estimation; Proceedings of International conference on geotechnical and geological engineering (GeoEng2000), Melbourne, pp. 1422–1440.

  39. Matthews C, Farook Z and Helm P R 2014 Slope stability analysis – limit equilibrium or the finite element method? Ground Eng. 48(5) 22–28.

  40. Moni M and Sazzad M 2015 Stability analysis of slopes with surcharge by LEM and FEM; IJASE 4(3) 216–225.

  41. Morgenstern N R and Price V E 1965 The analysis of the stability of general slip surfaces; Geotechnique 15(1) 79–93.

  42. Moudabel O A M 1997 Slope stability case study by limit equilibrium and numerical methods; Dissertation, Oklahoma State University.

  43. Neves M, Cavaleiro V and Pinto A 2016 Slope stability assessment and evaluation of remedial measures using limit equilibrium and finite element approaches; Procedia Eng. 143 717–725.

  44. Ozbay A and Cabalar A F 2015 FEM and LEM stability analyses of the fatal landslides at Çöllolar open-cast lignite mine in Elbistan, Turkey; Landslides 12 155–163.

  45. Putu Tantri K S and Lastiasih Y 2015 Slope stability evaluation using limit equilibrium method (LEM) and finite element method (FEM) for Indonesia soft soil; Proceedings of the 3rd Bali International Seminar on Science and Technology (BISSTECH), Bali, Indonesia.

  46. Rabie M 2014 Comparison study between traditional and finite element methods for slopes under heavy rainfall; HBRC J. 10(2) 160–168.

  47. Rocscience Inc. 2002 RocLab Version 1.0 Rock mass strength analysis using the generalized Hoek–Brown failure criterion; www.rocscience.com, Toronto, Ontario, Canada.

  48. Rocscience Inc. 2003 Slide Version 5.0 2D limit equilibrium slope stability analysis; www.rocscience.com, Toronto, Ontario, Canada.

  49. Rocscience Inc. 2008 Phase2 Version 7.0 Finite Element Analysis for Excavations and Slopes; www.rocscience.com, Toronto, Ontario, Canada.

  50. Russo G 2009 A new rational method for calculating the GSI; Tunn. Undergr. Sp. Tech. 24 103–111.

  51. Sazzad M, Rahman F I and Mamun A A 2016 Effects of water-level variation on the stability of slope by LEM and FEM; Proceedings of the 3rd International Conference on Civil Engineering for Sustainable Development (ICCESD), Khulna, Bangladesh.

  52. Shapiro S S and Wilk M B 1965 An analysis of variance test for normality (complete samples); Biometrika 52(3–4) 591–611.

  53. Singh R, Umrao R K and Singh T N 2014 Stability evaluation of road-cut slopes in the Lesser Himalaya of Uttarakhand, India: Conventional and numerical approaches; Bull. Eng. Geol. Environ. 73(3) 845–857.

  54. Sönmez 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.

  55. Spencer E 1967 A method of analysis of the stability of embankments, assuming parallel interslice forces; Geotechnique 17 11–26.

  56. SPSS Inc. 2007 SPSS Version 16.0. Statistical Package for Social Sciences; Chicago.

  57. Tschuchnigg F, Schweiger H F and Sloan S W 2015 Slope stability analysis by means of finite element limit analysis and finite element strength reduction techniques. Part I: Numerical studies considering non-associated plasticity; Comput. Geotech. 70 169–177.

  58. Turner M J, Clough R W, Martin H C and Topp L J 1956 Stiffness and deflection analysis of complex structures; IJASS 23(9) 805–823.

  59. Vinod B R, Shivananda P, Swathivarma R and Bhaskar M B 2017 Some of limit equilibrium method and finite element method based software are used in slope stability analysis; IJAIEM 6(9) 6–10.

  60. Wei L, Koutnik T and Woodward M 2010 A slope stability case study by limit equilibrium and finite element methods; Proceedings of GeoFlorida: Advances in Analysis, Modeling & Design, Florida, pp. 3090–3099.

  61. Whitman R V and Bailey W A 1967 Use of computers for slope stability analysis; J. Soil Mech. Found Div. ASCE 93(SM4) 475–498.

  62. Wilcoxon F 1945 Individual Comparisons by Ranking Methods; Biometr. Bull. 1(6) 80–83.

  63. Wright S G, Kulhawy F H and Duncan J M 1973 Accuracy of equilibrium slope stability analyses; J. Soil Mech. Found. Div. 99(10) 783–791.

  64. Zienkiewicz O C, Humpheson C and Lewis R W 1975 Associated and non-associated visco-plasticity and plasticity in soil mechanics; Geotechnique 25(4) 671–689.

Download references

Acknowledgement

We sincerely thank the editor and reviewers for critical reading and helpful comments.

Author information

Correspondence to Tümay Kadakci Koca.

Additional information

Communicated by Arkoprovo Biswas

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kadakci Koca, T., Koca, M.Y. Comparative analyses of finite element and limit-equilibrium methods for heavily fractured rock slopes. J Earth Syst Sci 129, 49 (2020). https://doi.org/10.1007/s12040-019-1314-3

Download citation

Keywords

  • Fractured rock mass
  • finite element method
  • limit-equilibrium methods
  • rock slope stability
  • statistical analysis