Safety Assessment of Shallow Foundations Resting on Sandy Soils with Correlated Parameters

  • S. Lakehal
  • B. TiliouineEmail author
Research Article -- Civil Engineering


A probabilistic study of the analysis and design of rigid shallow foundations resting on sandy soils is presented for a range of expected variations of soil properties. Simplified expressions of bearing capacity factors derived from Terzaghi’s ultimate bearing capacity model are used in conjunction with reliability analysis in order to facilitate the calculation of Hasofer–Lind reliability index and foundation failure probability. First, the influence of cross-correlation between random variables values of effective angle of internal friction φ′ and soil unit weight γ on the probability distribution of ultimate bearing capacity and on foundation failure probability is investigated using Monte Carlo simulation. Both cases of normal and lognormal distributions are considered. Further, a comparison of the reliability results with those of FORM and SORM methods for correlated input soil variables is performed and it is demonstrated that the application of these methods significantly reduces the CPU time and memory requirements. Next, the effects of increasing applied load on foundation safety along with a sensitivity analysis of the correlated soil properties are examined. Contrary to c′–φ′ soils, results for increasing positive cross-correlation between the input soil variables are shown to increase foundation failure probability. For design purposes, values of the foundation breadth calculated using the conventional and reliability-based design approaches are compared and conclusions of practical interest are given.


Probabilistic analysis Correlation Reliability-based design Bearing capacity failure Shallow foundations Sandy soils 



The authors would like to acknowledge the effective assistance of Malek Hammoutene, Professor of Civil Engineering at ENP, through the many hours of fruitful discussions during the preparation of the present research article.


  1. 1.
    Kayser, M.; Gajan, S.: Application of probabilistic methods to characterize soil variability and their effects on bearing capacity and settlement of shallow foundations: state of the art. Int. J. Geotech. Eng. 8(4), 352–364 (2014)CrossRefGoogle Scholar
  2. 2.
    Tani, N.K.; Nedjar, D.; Tamine, T.; Hamane, M.: A probabilistic assessment for failure prediction of buried cracked spread foundations. Arab. J. Sci. Eng. 42(3), 1161–1170 (2017)CrossRefGoogle Scholar
  3. 3.
    Low, B.K.: Reliability-based design applied to retaining walls. Geotechnique 55(1), 63–75 (2005)CrossRefGoogle Scholar
  4. 4.
    Viviescas, J.; Osorio, J.; Cañón, J.: Reliability-based designs procedure of earth retaining walls in geotechnical engineering. Obras y Proyectos 2, 50–60 (2007)Google Scholar
  5. 5.
    Chowdhury, R.N.; Xu, D.W.: Reliability index for slope stability assessment: two methods compared. Reliab. Eng. Syst. Saf. 37, 99–108 (1992)CrossRefGoogle Scholar
  6. 6.
    Hamrouni, A.; Dias, D.; Sbartai, B.: Reliability analysis of shallow tunnels using the response surface methodology. Undergr. Sp. 2(4), 246–258 (2017)CrossRefGoogle Scholar
  7. 7.
    Uzielli, M.; Nadim, F.; Lacasse, S.; Kaynia, A.M.: A conceptual framework for quantitative estimation of physical vulnerability to landslides. Eng. Geol. 102(3), 251–256 (2008)CrossRefGoogle Scholar
  8. 8.
    Cherubini, C.: A closed form probabilistic solution for evaluating the bearing capacity of shallow foundations. Can. Geotech. J. 27, 526–529 (1990)CrossRefGoogle Scholar
  9. 9.
    Easa, S.M.: Exact probabilistic solution of two-parameter bearing capacity for shallow foundations. Can. Geotech. J. 29, 867–870 (1992)CrossRefGoogle Scholar
  10. 10.
    Griffiths, D.V.; Fenton, G.A.; Manoharan, N.: Bearing capacity of rough rigid strip footing on cohesive soil: probabilistic study. J. Geotech. Geoenviron. Eng. 128(9), 743–755 (2002)CrossRefGoogle Scholar
  11. 11.
    Lingwanda, M.I.: Uncertainty, reliability and factor of safety for bearing capacity of shallow foundations in cohesive soils. Int. J. Comput. Eng. Res. (IJCER) 8(4), 22–29 (2018)Google Scholar
  12. 12.
    Cherubini, C.: Reliability evaluation of shallow foundation bearing capacity on C′, φ′ soils. Can. Geotech. J. 37(1), 264–269 (2000)Google Scholar
  13. 13.
    Youssef, D.S.; Soubra, A.H.; Low, B.K.: Reliability-based analysis and design of strip foundations against bearing capacity failure. J. Geotech. Geoenviron. Eng. 134(7), 917–928 (2008)CrossRefGoogle Scholar
  14. 14.
    Mao, N.; Al-Bittar, T.; Soubra, A.H.: Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek–Brown failure criterion. Int. J. Rock Mech. Min. Sci. 49, 45–58 (2012)CrossRefGoogle Scholar
  15. 15.
    Madsen, H.O.; Krenk, S.; Lind, N.C.: Methods of Structural Safety. Dover Publications, Inc, New York (2006)Google Scholar
  16. 16.
    Rosenblueth, E.: Two-point estimates for probability. Appl. Math. Model. 5, 329–335 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Hasofer, A.M.; Lind, N.C.: Exact and invariant second moment code format. J. Energy Mech. Div. 100(1), 111–121 (1974)Google Scholar
  18. 18.
    Ching, J.: Practical Monte Carlo based reliability analysis and design methods for geotechnical problems. In: Mordechai, S. (ed.) Applications of Monte Carlo Method in Science and Engineering, Chapter 31, Rijeka. In Tech Europe and Shanghai, China, Croatia (2011)Google Scholar
  19. 19.
    Pula, W.; Zaskórski, L.: Estimation of the probability distribution of the random bearing capacity of cohesionless soil using the random finite element method. Struct. Infrastruct. Eng. Maint. Manag. Life Cycle Des. Perform. 11(5), 707–720 (2015)CrossRefGoogle Scholar
  20. 20.
    Johari, A.; Hosseini, S.M.; Keshavarz, A.: Reliability analysis of seismic bearing capacity of strip footing by stochastic slip lines method. Comput. Geotech. 91, 203–217 (2017)CrossRefGoogle Scholar
  21. 21.
    Hamrouni, A.; Sbartai, B.; Dias, D.: Probabilistic study of the ultimate seismic bearing capacity of strip foundations. J. Rock Mech. Geotech. Eng. 10(4), 717–724 (2018)CrossRefGoogle Scholar
  22. 22.
    Kumbhojkar, A.S.: Numerical evaluation of Terzaghi’s Nγ. J. Geotech. Eng. ASCE 119(3), 598–607 (1993)CrossRefGoogle Scholar
  23. 23.
    Sivakumar Babu, G.L.; Srivastava, A.: Reliability analysis of allowable pressure on shallow foundation using response surface method. Comput. Geotech. 34(3), 187–194 (2007)CrossRefGoogle Scholar
  24. 24.
    Eurocode 1: bases of calculation and actions on structures. National application documents, Appendix A (2003)Google Scholar
  25. 25.
    Benjamin, J.R.; Cornell, C.A.: Probability, Statistics, and Decision for Civil Engineers. Dover Books in Engineering, Paperback (2014)Google Scholar
  26. 26.
    Duncan, J.M.: Factors of safety and reliability in geotechnical engineering. J. Geotech. Geoenviron. Eng. 126(4), 307–316 (2000)CrossRefGoogle Scholar
  27. 27.
    Phoon, K.K.; Kulhawy, F.H.: Characterization of geotechnical variability. Can. Geotech. J. 36(4), 612–624 (1999)CrossRefGoogle Scholar
  28. 28.
    Phoon, K.K.; Kulhawy, F.H.: Evaluation of geotechnical property variability. Can. Geotech. J. 36(4), 625–639 (1999)CrossRefGoogle Scholar
  29. 29.
    Forrest, W.S.; Orr, T.L.L.: Reliability of shallow foundations designed to Eurocode. Georisk Assess. Manag. Risk Eng. Syst. Geohazards 4(4), 186–207 (2010)CrossRefGoogle Scholar
  30. 30.
    Becker, D.E.: Limit states design for foundations. Part II. Development for National Building Code of Canada. Can. Geotech. J. 33(6), 984–1007 (1996)CrossRefGoogle Scholar
  31. 31.
    Parker, C.; Simon, A.; Thorne, C.R.: The effects of variability in bank material properties on river bank stability: Goodwin Creek, Mississippi. Geomorphology 101, 533–543 (2008)CrossRefGoogle Scholar
  32. 32.
    Matsuo, M.; Kuroda, K.: Probabilistic approach to design of embankments. Soils and foundations. Jpn. Soc. Soil Mech. Found. Eng. 14(2), 1–17 (1974)CrossRefGoogle Scholar
  33. 33.
    Ameratunga, J.; Sivakugan, N.; Das, B.: Correlations of Soil and Rock Properties in Geotechnical Engineering, Developments in Geotechnical Engineering. Springer, New York (2016)CrossRefGoogle Scholar
  34. 34.
    Terzaghi, K.: Theoretical Soil Mechanics. Wiley, Hoboken (1943)CrossRefGoogle Scholar
  35. 35.
    Krizek, R.J.: Approximation for Terzaghi’s bearing capacity factors. ASCE J. Soil Mech. Found. Div. 91(SM2), 1–3 (1965)Google Scholar
  36. 36.
    Tiliouine, B.; Chemali, B.: On the sensitivity of dynamic response of structures with random damping. 21st French Congress of Mechanics. Bordeaux, pp. 26–30 (2013)Google Scholar
  37. 37.
    Lemaire, M.: Fiabilité des Structures. Hermès-Lavoisier, Paris (2005)Google Scholar
  38. 38.
    Rackwitz, R.; Fiessler, B.: Structural reliability under combined random load sequences. Comput. Struct. 9(5), 484–494 (1978)zbMATHCrossRefGoogle Scholar
  39. 39.
    Madsen, H.O.: Omission sensitivity factors. Struct. Saf. 5, 35–45 (1988)CrossRefGoogle Scholar
  40. 40.
    Meyerhof, G.G.: Limit state designs in geotechnical engineering. Struct. Saf. 1(7), 67–71 (1982)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.Civil Engineering DepartmentEcole Nationale Polytechnique (ENP)AlgiersAlgeria

Personalised recommendations