Abstract
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.
Similar content being viewed by others
References
Ayyub BM, Chao RJ, Patev RC, Leggett MA (1998) Reliability and stability assessment of concrete gravity structures. Theoretical manual, US Army corps of engineers
Barakat S, Alzubaidi R, Omar M (2015) Probabilistic-based assessment of the bearing capacity of shallow foundations. Arab J Geosci 8:6441–6457
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, Allemagne
Cherubini C (2000) Reliability evaluation of shallow foundation bearing capacity on c´, φ´ soils. Can Geotech J 37:264–269
Christian JT, Baecher GB (1999) Point estimate method as numerical quadrature. J Geotech Geoenviron 125:779–786
Chu X, Li L, Wang Y (2015, 2015) Slope reliability analysis using length-based representative slip surfaces. Arab J Geosci. https://doi.org/10.1007/s12517-015-1905-5
El-ramly H, Morgenstern NR, Cruden DM (2005) Probabilistic assessment of stability of a cut slope in residual soil. Géotechnique 55:77–84
Eurocode 7 (2011) Geotechnical design. Part 1 «general rules»
Evans M, Hastings N, Peacock B (1993) Statistical distributions. Wiley, New York
Fieβler B, Hawranek H, Rackwitz R (1976) Numerische Methoden für probabilistische Bemessungsverfahren und Sicherheitsnachweise, Heft 14. TU München, Germany
Freudenthal AM, Garrelts JM, Shinozuka M (1966) The analysis of structural safety. J Struct Div ASCE 92(ST1):267–325
Gäβler G (1987) Vernagelte Gel\( \ddot{\mathrm{a}} \)ndespr\( \ddot{\mathrm{u}} \)nge-Tragverhalten und Standsicherheit. Thèse de doctorat, Heft 108, université de Karlsruhe, Allemagne
Genske D D, Walz B (1987) Anwendung der probabilistischen Sicherheitstheorie auf Grundbruchberechnungen nach DIN 4017. Geotechnik n°10, p. 53–66
Harr MT (1989) Probabilistic estimates for multivariate analyses. Appl Math Model 13(5):313–318
Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. Journal of the engineering mechanics division. ASCE 100(EM):111–121
Hong HP (1998) An efficient point estimate method for probabilistic analysis. Reliab Eng Syst Saf 59(3):261–267
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):04014096
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. 255–282
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. 49–75
Lemaire M (2005) Fiabilité des structures-Couplage mécano-fiabiliste statique. Hermès
Li KS (1992) Point-estimate method for calculating statistical moments. J Eng Mech ASCE 118(7):1506–1511
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):866–880
Lind NC (1983) Modelling uncertainty in discrete dynamical systems. Appl Math Model 7(3):146–152
Lumb P (1969) Safety factors and the probability distribution of soil strength. Can Geotech J 7(3):225–242
Nottrodt H P (1990) Beitrag zur Einf\( \ddot{\mathrm{u}} \)hrung semiprobabilistischer Methoden in der Geotechnik. Thèse de doctorat, université de Weimar, Allemagne
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, Paris
Orr TLL (2000) Selection of characteristic values and partial factors in geotechnical designs to Eurocode 7. Comput Geotech 26:263–279
Prandtl L (1921) Eindringungsfestigkeit und Festigkeit von Schneiden. Z Angew Math Mech 1:15–20
Rosenblatt M (1952) Remarks on a multivariate transformation. Ann Math Stat 23(3):470–472
Rosenblueth E (1975) Point estimates for probability moments. Proc Natl Acad Sci USA 72(10):3812–3814
Rosenblueth E (1981) Two-point estimates in probabilities. Appl Math Model 5(2):329–335
Russelli C (2008) Probabilistic methods applied to the bearing capacity problem. These de doctorat, Université de Stuttgart, Almagne
Lizarraga HS, Lai CG (2014) Effects of spatial variability of soil properties on the seismic response of an embankment dan. Soil Dyn Earthq Eng 64:113–128
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 2271–4
Seung-Kyum C, Ramana VG, Robert AC (2007) Reliability-based structural design. Springer-Verlag, London Limited 2007
Srivastava A, Babu GLS (2009) Effect of soil variability on the bearing capacity of clay and in slope stability problems. Eng Geol 108:142–152
Terzaghi K (1943) Theoretical soil mechanics. Whiley, New York
Wolf TH (1985) Analysis and design of embankment dam slopes a probabilistic approach. Phd Thesis, purdue University, Lafayette, Indiana.
Zhou J, Nowak AS (1988) Integration formulas to evaluate functions of random variables. Struct Saf 5:267–284
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sekfali, N., Belabed, L. Reliability of geotechnical structures: case of bearing capacity failure of strip footing. Arab J Geosci 11, 296 (2018). https://doi.org/10.1007/s12517-018-3649-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12517-018-3649-5