A Numerical Investigation of the Effect of Isotropic Spatially Variable Tensile Strength on Slope Stability

  • Khaoula BoudiafEmail author
  • Djamel Benmeddour
  • Messaoud Baazouzi
  • Abdelhak Mabrouki
  • Mekki Mellas
Technical Paper


The impact of uncertainty on the reliability of slope design is often significant. Spatial variability of soil properties has been recognized as an important factor influencing the reliability of the slope. This paper aims to investigate the influence of isotropic spatially variable tensile strength on the reliability of reinforced slope. For slope safety assessment, random finite element method represents a rigorous tool to combine spatially variable tensile strength into reliability analysis of slope stability. Numerical results showed that the spatial autocorrelation distance and the coefficient of variation of tensile strength for isotropic random field have a large influence on the probability of failure and on the normal forces when the isotropic autocorrelation distance is small in combination with a higher value of coefficient of variation of tensile strength.


Probability of failure Tensile strength Spatial variability Isotropic random field Normal forces 



  1. Ali, A., Lyamin, A., Huang, J., Li, J., Cassidy, M., Sloan, S.: Probabilistic stability assessment using adaptive limit analysis and random fields. Acta Geotech. 12(4), 937–948 (2017)CrossRefGoogle Scholar
  2. Bathurst, R., Jones, C.: Earth retaining structures and reinforced slopes. In: Rowe, R.K. (ed.) Geotechnical and Geoenvironmental Engineering Handbook, p. 1088. Kluwer Academic Publishing, Norwell (2001)Google Scholar
  3. Berg, R.R., Christopher, B.R., Samtani, N.C.: Design of mechanically stabilized earth walls and reinforced soil slopes–Volume I U.S. Federal Highway Administration. Report No. FHWA-NHI-10-025 FHWA GEC 011-Vol. II (2009)Google Scholar
  4. Cai, J.-S., Yan, E.-C., Yeh, T.-C.J., Zha, Y.-Y., Liang, Y., Huang, S.-Y., Wang, W.-K., Wen, J.-C.: Effect of spatial variability of shear strength on reliability of infinite slopes using analytical approach. Comput. Geotech. 81, 77–86 (2017)CrossRefGoogle Scholar
  5. Cho, S.E.: Effects of spatial variability of soil properties on slope stability. Eng. Geol. 92(3–4), 97–109 (2007)CrossRefGoogle Scholar
  6. Cho, S.E.: Probabilistic assessment of slope stability that considers the spatial variability of soil properties. J. Geotech. Geoenviron. 136(7), 975–984 (2010)CrossRefGoogle Scholar
  7. Der Kiureghian, A., Ke, J.-B.: The stochastic finite element method in structural reliability. Probab. Eng. Mech. 3(2), 83–91 (1988)CrossRefGoogle Scholar
  8. El-Ramly, H., Morgenstern, N., Cruden, D.: Probabilistic slope stability analysis for practice. Can. Geotech. J. 39(3), 665–683 (2002)CrossRefGoogle Scholar
  9. EN, B.: 1 (2004). Eurocode 7: Geotechnical design-Part 1: General rules. european committee for standardization, Brussels, Belgium. (1997)Google Scholar
  10. Fenton, G.A., Griffiths, D.: Bearing-capacity prediction of spatially random c φ soils. Can. Geotech. J. 40(1), 54–65 (2003)CrossRefGoogle Scholar
  11. Ferreira, F., Topa Gomes, A., Vieira, C.S., Lopes, M.: Reliability analysis of geosynthetic-reinforced steep slopes. Geosynth. Int. 23(4), 301–315 (2016)CrossRefGoogle Scholar
  12. Ghiocel, D.M., Ghanem, R.G.: Stochastic finite-element analysis of seismic soil–structure interaction. J. Eng. Mech. 128(1), 66–77 (2002)CrossRefGoogle Scholar
  13. Griffiths, D., Fenton, G.A.: Probabilistic slope stability analysis by finite elements. J. Geotech. Geoenviron. 130(5), 507–518 (2004)CrossRefGoogle Scholar
  14. Griffiths, D., Huang, J., Fenton, G.A.: Influence of spatial variability on slope reliability using 2-D random fields. J. Geotech. Geoenviron. 135(10), 1367–1378 (2009)CrossRefGoogle Scholar
  15. Javankhoshdel, S., Bathurst, R.: Deterministic and probabilistic failure analysis of simple geosynthetic reinforced soil slopes. Geosynth. Int. 24(1), 14–29 (2016)CrossRefGoogle Scholar
  16. Javankhoshdel, S., Luo, N., Bathurst, R.J.: Probabilistic analysis of simple slopes with cohesive soil strength using RLEM and RFEM. Georisk. 11(3), 231–246 (2016)Google Scholar
  17. Kitch, W.A.: Deterministic and probabilistic based analyses of reinforced soil slopes. Ph.D. Dissertation, University of Texas at Austin (1994)Google Scholar
  18. Kitch, W., Gilbert, R., Wright, S.: Probabilistic assessment of commercial design guides for steep reinforced slopes: implications for design. In: ASCE Proceedings of Georisk 2011, Atlanta, Georgia, d 20110000Geo-Risk 2011, pp. 1055–1062. American Society of Civil Engineers, Reston (2011)Google Scholar
  19. Krabbenhoft, K., Lyamin, A., Krabbenhoft, J.: Optum Computational Engineering (Optum G2). Computer software. Retrieved from: (2015)
  20. Liu, W.K., Belytschko, T., Mani, A.: Random field finite elements. Int. J. Numer. Methods Eng. 23(10), 1831–1845 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  21. Luo, N., Bathurst, R.J.: Probabilistic analysis of reinforced slopes using RFEM and considering spatial variability of frictional soil properties due to compaction. Georisk. 12(2), 87–108 (2018)Google Scholar
  22. Luo, N., Bathurst, R.J., Javankhoshdel, S.: Probabilistic stability analysis of simple reinforced slopes by finite element method. Comput. Geotech. 77, 45–55 (2016)CrossRefGoogle Scholar
  23. Metya, S., Bhattacharya, G.: Reliability analysis of earth slopes considering spatial variability. Geotech. Geol. Eng. 34(1), 103–123 (2015)CrossRefGoogle Scholar
  24. Phoon, K., Huang, S., Quek, S.: Implementation of Karhunen–Loeve expansion for simulation using a wavelet-Galerkin scheme. Probab. Eng. Mech. 17(3), 293–303 (2002)CrossRefGoogle Scholar
  25. Sivakumar Babu, G., Mukesh, M.: Effect of soil variability on reliability of soil slopes. Geotechnique. 54(5), 335–337 (2004)CrossRefGoogle Scholar
  26. Vanmarcke, E.: Random fields: analysis and synthesis (revised and expanded, newth edn). World Scientific Publishing Co. Pte. Ltd., Singapore (2010)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Khaoula Boudiaf
    • 1
    Email author
  • Djamel Benmeddour
    • 1
  • Messaoud Baazouzi
    • 2
  • Abdelhak Mabrouki
    • 1
  • Mekki Mellas
    • 1
  1. 1.Civil Engineering Research LaboratoryUniversity of BiskraBiskraAlgeria
  2. 2.University of Saad DahlabBlidaAlgeria

Personalised recommendations