Reliability of geotechnical structures: case of bearing capacity failure of strip footing

  • Nasser SekfaliEmail author
  • Lazhar Belabed
Original Paper


Traditionally, the design of geotechnical structures is based on a deterministic approach in which all parameters take a fixed value, which leads to an oversized and unjustified underestimation of the bearing capacity of soil, as well as the overestimation of stress. However, the effects on structure safety of uncertainties associated with the design parameters are not quantifiable. An alternative method with which to study the reliability of geotechnical structures is based on the theory of probability and involves the application of partial safety factors for all design parameters (random variables). These factors are derived using probabilistic methods and take into account the dispersion of soil parameters (stochastic model). In this paper, a benchmark for a strip footing with axial load was used, with security expressed via a probability of failure or reliability index and evaluated by means of a universal computer code based on probabilistic methods. Analysis is carried out by considering the various types of parameter distributions, thereby enabling a better assessment of the effects of uncertainty and the identification of a set of parameters with high incidence.


Geotechnical Probability of failure Reliability index Probabilistic methods Calculation algorithm 


  1. Ayyub BM, Chao RJ, Patev RC, Leggett MA (1998) Reliability and stability assessment of concrete gravity structures. Theoretical manual, US Army corps of engineersGoogle Scholar
  2. Barakat S, Alzubaidi R, Omar M (2015) Probabilistic-based assessment of the bearing capacity of shallow foundations. Arab J Geosci 8:6441–6457CrossRefGoogle Scholar
  3. Belabed L (1996) Zuverl\( \ddot{\mathrm{a}} \)ssigkeitsuntersuchung des Tragsystems. Mehrfach verankerte St\( \ddot{\mathrm{u}} \)tzw\( \ddot{\mathrm{a}} \)nde, mit probabilistischen methoden. Thèse de doctorat, université de Weimar, AllemagneGoogle Scholar
  4. Cherubini C (2000) Reliability evaluation of shallow foundation bearing capacity on c´, φ´ soils. Can Geotech J 37:264–269Google Scholar
  5. Christian JT, Baecher GB (1999) Point estimate method as numerical quadrature. J Geotech Geoenviron 125:779–786CrossRefGoogle Scholar
  6. Chu X, Li L, Wang Y (2015, 2015) Slope reliability analysis using length-based representative slip surfaces. Arab J Geosci.
  7. El-ramly H, Morgenstern NR, Cruden DM (2005) Probabilistic assessment of stability of a cut slope in residual soil. Géotechnique 55:77–84CrossRefGoogle Scholar
  8. Eurocode 7 (2011) Geotechnical design. Part 1 «general rules»Google Scholar
  9. Evans M, Hastings N, Peacock B (1993) Statistical distributions. Wiley, New YorkGoogle Scholar
  10. Fieβler B, Hawranek H, Rackwitz R (1976) Numerische Methoden für probabilistische Bemessungsverfahren und Sicherheitsnachweise, Heft 14. TU München, GermanyGoogle Scholar
  11. Freudenthal AM, Garrelts JM, Shinozuka M (1966) The analysis of structural safety. J Struct Div ASCE 92(ST1):267–325Google Scholar
  12. Gäβler G (1987) Vernagelte Gel\( \ddot{\mathrm{a}} \)ndespr\( \ddot{\mathrm{u}} \)nge-Tragverhalten und Standsicherheit. Thèse de doctorat, Heft 108, université de Karlsruhe, AllemagneGoogle Scholar
  13. Genske D D, Walz B (1987) Anwendung der probabilistischen Sicherheitstheorie auf Grundbruchberechnungen nach DIN 4017. Geotechnik n°10, p. 53–66Google Scholar
  14. Harr MT (1989) Probabilistic estimates for multivariate analyses. Appl Math Model 13(5):313–318CrossRefGoogle Scholar
  15. Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. Journal of the engineering mechanics division. ASCE 100(EM):111–121Google Scholar
  16. Hong HP (1998) An efficient point estimate method for probabilistic analysis. Reliab Eng Syst Saf 59(3):261–267CrossRefGoogle Scholar
  17. Jiang SH, Li DQ, Cao ZJ, Zhou CB, Phoon KK (2015) Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation. J Geotech Geoenviron Eng 141(2):04014096CrossRefGoogle Scholar
  18. Katzenbach R, Moormann C (2003) Überlegungen zu stochastischen Methoden in der Bodenmechanik am Beispiel des Frankfurter Tons. Beiträge anlässlich des 60. Geburtstages von Herrn Prof. Dr. S. Semprich, Heft 16 der Gruppe Geotechnik, Technische Universität Graz: pp. 255–282Google Scholar
  19. Lacasse S, Nadim F (1996) Uncertainties in characterizing soil properties. In: Uncertainty in the geologic environment: from theory to practice. Shackelford CD, Nelson PP, Roth MJS (eds) Proceedings of Uncertainty 96, ASCE Geotechnical Special publication No. 58, pp. 49–75Google Scholar
  20. Lemaire M (2005) Fiabilité des structures-Couplage mécano-fiabiliste statique. HermèsGoogle Scholar
  21. Li KS (1992) Point-estimate method for calculating statistical moments. J Eng Mech ASCE 118(7):1506–1511CrossRefGoogle Scholar
  22. Li DQ, Qi XH, Cao ZJ, Tang XS, Zhou W, Phoon KK, Zhou CB (2015) Reliability analysis of strip footing considering spatially variable undrained shear strength that linearly increases with depth. Soils Found 55(4):866–880CrossRefGoogle Scholar
  23. Lind NC (1983) Modelling uncertainty in discrete dynamical systems. Appl Math Model 7(3):146–152CrossRefGoogle Scholar
  24. Lumb P (1969) Safety factors and the probability distribution of soil strength. Can Geotech J 7(3):225–242CrossRefGoogle Scholar
  25. Nottrodt H P (1990) Beitrag zur Einf\( \ddot{\mathrm{u}} \)hrung semiprobabilistischer Methoden in der Geotechnik. Thèse de doctorat, université de Weimar, AllemagneGoogle Scholar
  26. Ogunsanwo O (1985) Variability in the shear strength characteristics of an amphibolite Drived laterite soil. Bulletin of the international Association of Engineering Geology, N°32, ParisGoogle Scholar
  27. Orr TLL (2000) Selection of characteristic values and partial factors in geotechnical designs to Eurocode 7. Comput Geotech 26:263–279CrossRefGoogle Scholar
  28. Prandtl L (1921) Eindringungsfestigkeit und Festigkeit von Schneiden. Z Angew Math Mech 1:15–20CrossRefGoogle Scholar
  29. Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23(3):470–472CrossRefGoogle Scholar
  30. Rosenblueth E (1975) Point estimates for probability moments. Proc Natl Acad Sci USA 72(10):3812–3814CrossRefGoogle Scholar
  31. Rosenblueth E (1981) Two-point estimates in probabilities. Appl Math Model 5(2):329–335CrossRefGoogle Scholar
  32. Russelli C (2008) Probabilistic methods applied to the bearing capacity problem. These de doctorat, Université de Stuttgart, AlmagneGoogle Scholar
  33. Lizarraga HS, Lai CG (2014) Effects of spatial variability of soil properties on the seismic response of an embankment dan. Soil Dyn Earthq Eng 64:113–128CrossRefGoogle Scholar
  34. Schneider H R (1999) Definition and determination of characteristic soil properties. In: Proceeding XII international conference on soil mechanics and geotechnical engineering, Vol 4, Hamburg, 1999, p 2271–4Google Scholar
  35. Seung-Kyum C, Ramana VG, Robert AC (2007) Reliability-based structural design. Springer-Verlag, London Limited 2007Google Scholar
  36. Srivastava A, Babu GLS (2009) Effect of soil variability on the bearing capacity of clay and in slope stability problems. Eng Geol 108:142–152CrossRefGoogle Scholar
  37. Terzaghi K (1943) Theoretical soil mechanics. Whiley, New YorkCrossRefGoogle Scholar
  38. Wolf TH (1985) Analysis and design of embankment dam slopes a probabilistic approach. Phd Thesis, purdue University, Lafayette, Indiana.Google Scholar
  39. Zhou J, Nowak AS (1988) Integration formulas to evaluate functions of random variables. Struct Saf 5:267–284CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2018

Authors and Affiliations

  1. 1.Laboratory of Civil Engineering and HydraulicsUniversity of GuelmaGuelmaAlgeria

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