Optimisation of strength reduction finite element method codes for slope stability analysis

  • Ashley P. Dyson
  • Ali TolooiyanEmail author
Technical papers


One of the modern methods for estimating the factor of safety for the stability of slopes is the strength reduction method. In recent times, computer codes have utilised the strength reduction method in conjunction with finite element analysis. This paper explores the implementation of a strength reduction finite element method with FORTRAN and Python codes in conjunction with the computer-aided engineering package Abaqus, incorporating a modified strength reduction definition, allowing for a refinement of the factor of safety search space. The computational efficiency of the modified method is compared with the traditional technique, for both 2D and 3D analysis. The algorithm results are compared for contrasting FEM element types and geometries and benchmarked against proprietary geotechnical finite element solvers.


Strength reduction method Finite element method Slope stability Factor of safety Abaqus FEM 



Financial support for this research has been provided by Earth Resources Regulation of the Victorian State Government Department of Economic Development, Jobs, Transport and Resources. The first author is funded by the Australian Government Research Training Program (RTP) and the GHERG scholarship programme.


  1. 1.
    Tschuchnigg F, Schweiger HF, Sloan SW (2015) Slope stability analysis by means of finite element limit analysis and finite element strength reduction techniques. Part II: back analyses of a case history. Comput Geotech 70(Supplement C):178–189CrossRefGoogle Scholar
  2. 2.
    Bishop AW (2008) The use of the slip circle in the stability analysis of slopes. The essence of geotechnical engineering: 60 years of géotechnique. Thomas Telford Publishing, London, pp 223–233Google Scholar
  3. 3.
    Duncan JM (1996) State of the art: limit equilibrium and finite-element analysis of slopes. J Geotech Eng 122:577CrossRefGoogle Scholar
  4. 4.
    Zienkiewicz OC, Humpheson C, Lewis RW (1975) Associated and non-associated visco-plasticity and plasticity in soil mechanics. Geotechnique 25:671–689CrossRefGoogle Scholar
  5. 5.
    Griffiths DV, Lane PA (1999) Slope stability analysis by finite elements. Géotechnique 49(3):387–403CrossRefGoogle Scholar
  6. 6.
    Li XW, Yuan X, Li XW (2012) Analysis of slope instability based on strength reduction method. Applied mechanics and materials. Trans Tech Publ, Princeton, pp 1238–1242Google Scholar
  7. 7.
    Su K, Li Y (2012) Discussion of SRFEM with Mohr–Coulomb plasticity model in slope stability analysis. 2012 Asia-Pacific Power and Energy Engineering Conference. pp 1–4Google Scholar
  8. 8.
    Ugai K, Leshchinsky D (1995) Three-dimensional limit equilibrium and finite element analyses: a comparison of results. Soils Found 35(4):1–7CrossRefGoogle Scholar
  9. 9.
    Zheng H, Tham LG, Liu D (2006) On two definitions of the factor of safety commonly used in the finite element slope stability analysis. Comput Geotech 33(3):188–195CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Zheng Y, Tang X, Zhao S, Deng C, Lei W (2009) Strength reduction and step-loading finite element approaches in geotechnical engineering. J Rock Mech Geotech Eng 1(1):21–30CrossRefGoogle Scholar
  12. 12.
    Wei WB, Cheng YM (2009) Strength reduction analysis for slope reinforced with one row of piles. Comput Geotech 36(7):1176–1185CrossRefGoogle Scholar
  13. 13.
    Krahn J (2003) The 2001 R.M. Hardy Lecture: the limits of limit equilibrium analyses. Can Geotech J 40(3):643–660CrossRefGoogle Scholar
  14. 14.
    Schneider-Muntau B, Medicus G, Fellin W (2017) Strength reduction method in Barodesy. Comput Geotech 95:57–67CrossRefGoogle Scholar
  15. 15.
    Hammouri NA, Malkawi AIH, Yamin MMA (2008) Stability analysis of slopes using the finite element method and limiting equilibrium approach. Bull Eng Geol Environ 67(4):471CrossRefGoogle Scholar
  16. 16.
    Dawson E, Roth W, Drescher A (1999) Slope stability analysis by strength reduction. Geotechnique 49(6):835–840CrossRefGoogle Scholar
  17. 17.
    Lane PA, Griffiths DV (2000) Assessment of stability of slopes under drawdown conditions. J Geotech Geoenviron Eng 126(5):443CrossRefGoogle Scholar
  18. 18.
    Xue H, Dang F, Yin X, Ding W, Yang C (2016) Nonproportional correlative reduction finite element method for slope strength parameters. Math Probl Eng. CrossRefGoogle Scholar
  19. 19.
    Zheng H, Sun G, Liu D (2009) A practical procedure for searching critical slip surfaces of slopes based on the strength reduction technique. Comput Geotech 36(1):1–5CrossRefGoogle Scholar
  20. 20.
    Waterman D (2016) Plaxis 2D: Plaxis B.V. Delft University, DelftGoogle Scholar
  21. 21.
    Matsui T, San K-C (1992) Finite element slope stability analysis by shear strength reduction technique. Soils Found 32(1):59–70CrossRefGoogle Scholar
  22. 22.
    Smith M. ABAQUS/Standard User’s Manual, Version 7.5: Simulia, 2017Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Geotechnical and Hydrogeological Engineering Research Group (GHERG)Federation University AustraliaChurchillAustralia

Personalised recommendations