Arabian Journal of Geosciences

, Volume 6, Issue 6, pp 2147–2163 | Cite as

3D modeling of stratified and irregularly jointed rock slope and its progressive failure

  • K. Ma
  • C. A. TangEmail author
  • L. C. Li
  • P. G. Ranjith
  • M. Cai
  • N. W. Xu
Original Paper


Little has been published on the three-dimensional (3D) simulation of the progressive failure of rock slopes, possibly because the process of failure involves a complex, nonlinear evolution from initiation, through propagation and crack. In addition, rock is typically anisotropic, which makes it difficult to identify and describe the slope constituents and failure processes accurately. Despite such difficulties, further study of the fracture process is just as important as analyzing stress fields in 3D rock slope failures. In this paper, the 3D realistic failure process analysis code using finite element programming, and an extended version of numerical centrifugal method, is used to simulate slopes failure with different dip angles. The numerical centrifugal analysis results in this paper are found that the critical failure surface develops along the weak structural surface when the slope dip angle β is below 30°; conversely, the failure surface is formed along the toe of circular sliding when β is above 30°. In addition, it is also found that whether or not including the irregularity of joint into modeling to analyze the 3D slope stability problem will lead to a significant difference in factors of safety, it can reach 8.41 % at the same slope angle. Furthermore, the acoustic emission analyzing reveals deformed location characters of rock slope during the failure processes. With such capabilities, the approach contributes significantly to the in-depth study of the mechanisms of rock slope instability process.


Three-dimensional Failure processes Numerical centrifugal method Critical failure surface Acoustic emission 



Financial support from the National Natural Science Foundation of China (grant nos. 51121005, 51004020, 51174039, 51079017, and 41172265), National Basic Research Program of China (973Program, grant no. 2011CB013503), the Fundamental Research Funds for the Central Universities and the Foundation for the Author of National Excellent Doctoral Dissertation of China (no. 200960), and the Program for New Century Excellent Talents in University (NECT-09-0258) are greatly appreciated. In particular, the author is grateful to Professor Hong Li for his helpful guide and opinions during the revise processes. Thanks are also extended to the authors of the references cited in this review for their original contributions. We also thank the reviewers for discerning comments on this paper.


  1. Adhikary D, Dyskin A (2007) Modelling of progressive and instantaneous failures of foliated rock slopes. Rock Mech Rock Eng 40(4):349–362CrossRefGoogle Scholar
  2. Bishop AW (1955) The use of the slip circle in the stability analysis of slopes. Geotechnique 5(1):7–17CrossRefGoogle Scholar
  3. Cai M, Kaiser P, Martin C (2001) Quantification of rock mass damage in underground excavations from microseismic event monitoring. Int J Rock Mech Min Sci 38(8):1135–1145CrossRefGoogle Scholar
  4. Cao J, Deng A (2006) Centrifugal loading finite element method for slope stability analysis[J]. Chin J Geotech Eng 28(Supp):1336–1339Google Scholar
  5. Cavounidis S (1987) On the ratio of factor safety in slope stability analyses. Geotechnique 37(2):207–210CrossRefGoogle Scholar
  6. Chen R, Chameau JL (1983) Three-dimensional limit equilibrium analysis of slopes. Geotechnique 33(1):31–40CrossRefGoogle Scholar
  7. Cheng Y, Lansivaara T, Wei W (2007) Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods. Comput Geotech 34(3):137–150CrossRefGoogle Scholar
  8. Dawson E, Roth W, Drescher A (1999) Slope stability analysis by strength reduction. Geotechnique 49(6):835–840CrossRefGoogle Scholar
  9. Donald I (1988) Application of the nodal displacement method to slope stability analysis. In: Proceedings of the 5th Australia–New Zealand Conference on Geomechanics. Sydney, Australia. vol. 22, p. 23Google Scholar
  10. Fredlund D, Krahn J (1977) Comparison of slope stability methods of analysis. Can Geotech J 14(3):429–439CrossRefGoogle Scholar
  11. Ge M (2005) Efficient mine microseismic monitoring. Int J Coal Geol 64(1–2):44–56CrossRefGoogle Scholar
  12. Gemperline MC, Hon YK (1988) Centrifugal model tests for ultimate bearing capacity of footings on step slopes in cohesion less soils (Chen and Chameau). Centrifuge 88:203–221Google Scholar
  13. Gens A, Hutchinson JN, Cavounidis S (1988) Three-dimensional analysis of slides in cohesive soils. Geotechnique 38(1):1–23CrossRefGoogle Scholar
  14. Griffiths D, Lane P (1999) Slope stability analysis by finite elements. Geotechnique 49(3):387–403CrossRefGoogle Scholar
  15. Hovland HJ (1977) Three-dimensional slope stability analysis method. J Geotech Eng Div 103(9):971–986Google Scholar
  16. Hungr O (1987) An extension of Bishop's simplified method of slope stability analysis to three dimensions. Geotechnique 37(1):113–117CrossRefGoogle Scholar
  17. Janbu N (1973) Slope stability computations. In: Hirschfeld RC, Poulos SJ (eds) Embankment dam engineering—Casagrande volume. Wiley, New York, pp 47–86Google Scholar
  18. Kidger DJ (1990) Visualization of finite clement eigenvalues and three dimensional plasticity. Ph.D. thesis. Department of Engineering, University of Manchester.Google Scholar
  19. Lam L, Fredlund D (1993) A general limit equilibrium model for three-dimensional slope stability analysis. Can Geotech J 30(6):905–919CrossRefGoogle Scholar
  20. Lei SY (1998) Centrifugal modeling and its application in China. J Xi'an Highway Univ 18(4):222–225Google Scholar
  21. Leshchinsky D, Baker R (1986) Three-dimensional slope stability: end effects. Soils Foundation 26(4):98–110CrossRefGoogle Scholar
  22. Lesniak A, Isakow Z (2009) Space-time clustering of seismic events and hazard assessment in the Zabrze–Bielszowice coal mine, Poland. Int J Rock Mech Min Sci 46(5):918–928CrossRefGoogle Scholar
  23. Li AJ, Merifield RS (2009) Limit analysis solutions for three dimensional undrained slopes. Comput Geotech 36(8):1330–1351CrossRefGoogle Scholar
  24. Li L, Tang C, Li C, Zhu W (2006) Slope stability analysis by SRM-based rock failure process analysis (RFPA). Geomech Geoengineer 1(1):51–62CrossRefGoogle Scholar
  25. Li L, Tang C, Zhu W, Liang Z (2009) Numerical analysis of slope stability based on the gravity increase method. Comput Geotech 36(7):1246–1258CrossRefGoogle Scholar
  26. Liang Z, Tang C, Li H, Xu T, Zhang Y (2004) Numerical simulation of 3-D failure process in heterogeneous rocks. Int J Rock Mech Min Sci 41:323–328CrossRefGoogle Scholar
  27. Liu H, Kou S, Lindqvist PA, Tang C (2004) Numerical simulation of shear fracture (mode II) in heterogeneous brittle rock. Int J Rock Mech Min Sci 41(3):355–355Google Scholar
  28. Matsui T, San KC (1992) Finite element slope stability analysis by shear strength reduction technique. Soils Foundation 32(1):59–70CrossRefGoogle Scholar
  29. Morgenstern N, Price VE (1965) The analysis of the stability of general slip surfaces. Geotechnique 15(1):79–93CrossRefGoogle Scholar
  30. Naylor D (1982) Finite elements and slope stability. Numerical methods in geomechanics: proceedings of the NATO Advanced Study Institute, University of Minho, Braga, Portugal, held at Vimeiro, August 24–Sept. 4, 1981, 92: 229Google Scholar
  31. Peng RD, Xie HP, Ju Y (2005) Effect of elastic accumulation energy of testing machine on the mechanical measurement of rocks(Chen and Chameau). Mechanics Eng 27(3):51–55Google Scholar
  32. Rowe P (1972) Embankments on soft alluvial ground. Q J Eng Geol Hydrogeol 5(1–2):127CrossRefGoogle Scholar
  33. Spencer E (1967) A method of analysis of the stability of embankments assuming parallel inter-slice forces. Geotechnique 17(1):11–26CrossRefGoogle Scholar
  34. Stead D, Eberhardt E, Coggan J, Benko B (2001) Advanced numerical techniques in rock slope stability analysis—applications and limitations. Davos, Switzerland. In: Kühne M, Einstein HH, Krauter E, Klapperich H, Pöttler R (eds) UEF International Conference on Landslides—causes, impacts and countermeasures. Glückauf GmbH, Essen, pp 615–624Google Scholar
  35. Tang C, Kaiser P, Yang G (1997) Numerical simulation of seismicity in rock failureGoogle Scholar
  36. Tang C, Liu H, Lee P, Tsui Y, Tham L (2000) Numerical studies of the influence of microstructure on rock failure in uniaxial compression—part I: effect of heterogeneity. Int J Rock Mech Min Sci 37(4):555–569CrossRefGoogle Scholar
  37. Tang C, Tham L, Lee P, Yang T, Li L (2002) Coupled analysis of flow, stress and damage (FSD) in rock failure. Int J Rock Mech Min Sci 39(4):477–489CrossRefGoogle Scholar
  38. Ugai K, Leshchinsky D (1995) Three-dimensional limit equilibrium and finite element analyses: a comparison of results. Soils and Foundations 35(4):1–7CrossRefGoogle Scholar
  39. Wei W, Cheng Y, Li L (2009) Three-dimensional slope failure analysis by the strength reduction and limit equilibrium methods. Comput Geotech 36(1–2):70–80CrossRefGoogle Scholar
  40. Xie M, Esaki T, Qiu C, Wang C (2006) Geographical information system-based computational implementation and application of spatial three-dimensional slope stability analysis. Comput Geotech 33(4–5):260–274CrossRefGoogle Scholar
  41. Xing Z (1988) Three-dimensional stability analysis of concave slopes in plan view. ASCE J Geotech Eng 114:658–671CrossRefGoogle Scholar
  42. Zhu W, Tang C (2002) Numerical simulation on shear fracture process of concrete using mesoscopic mechanical model. Constr Build Mater 16(8):453–463CrossRefGoogle Scholar
  43. Zienkiewicz O, Humpheson C, Lewis R (1975) Associated and non-associated visco-plasticity and plasticity in soil mechanics. Geotechnique 25(4):671–689CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2012

Authors and Affiliations

  • K. Ma
    • 1
    • 2
  • C. A. Tang
    • 1
    • 2
    Email author
  • L. C. Li
    • 1
    • 2
  • P. G. Ranjith
    • 3
  • M. Cai
    • 4
  • N. W. Xu
    • 1
    • 2
  1. 1.Institute of Rock Instability and Seismicity Research, School of Civil EngineeringDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.The State Key Laboratory of Coastal and Offshore EngineeringDalian University of TechnologyDalianPeople’s Republic of China
  3. 3.Department of Civil EngineeringMonash UniversityMelbourneAustralia
  4. 4.Bharti School of EngineeringLaurentian UniversitySudburyCanada

Personalised recommendations