Geotechnical and Geological Engineering

, Volume 32, Issue 6, pp 1477–1483 | Cite as

Slope Stability Analysis Based on Autocorrelated Shear Strength Parameters

Original paper


The stability of a slope is governed by the spatial average of the shear strength over the extent of the failure surface. In Eurocode 7 the average soil properties are taken into account by defining the characteristic soil parameter as being “a cautious estimate of the value affecting the occurrence of the limit state” and further stating that this value should be based on, among other factors, “the extent of the zone of ground governing the behavior of the geotechnical structure at the limit state being considered”. To completely quantify the characteristic shear strength along a failure surface, three statistical values are required: the arithmetic mean, the variance and the spatial correlation. The mean soil properties and to a lesser degree the variance (or equivalently the standard deviation or the coefficient of variation) are known and used by most geotechnical engineers for the selection of characteristic soil properties. The scale of fluctuation, however, is not generally used. The scale of fluctuation is a measure of the soil spatial variability and can be understood as the range within which soil properties are correlated and beyond which they are statistically uncorrelated. This paper investigates the influence of the variability of shear strength on the reliability of slopes based on simulated autocorrelated random fields created by the turning bands method. In particular, the influence of the length of the failure surface on the characteristic value is investigated. Numerical Monte Carlo analyses verify the validity of a simplified practical approach presented to determine the characteristic soil properties according to Eurocode 7.


Slope stability Characteristic value Eurocode 7 Spatial variability Monte Carlo analysis Random fields 

La stabilité d’un versant basé sur l’autocorrélation de la résistance de cisaillement


La stabilité d’un versant est régnée par la moyenne spatiale de la résistance de cisaillement sur l’extension de la surface coulissante. Dans l’Eurocode 7 une moyenne des propriétés du sol est tenue compte, par définir le paramètre caractéristique du sol comme “une estimation prudent de la valeur, qui concerne l’apparition de l’état limité” et puis, que cette valeur devrait, entre autres facteurs, être basée sur “l’implication de l’extension de la zone du sol régné du comportement de la structure géotechnique dans l’état limité”. Pour pouvoir quantifier complètement les caractéristiques de la résistance de cisaillement le long de la surface coulissante, il y en a besoin de trois valeurs: la valeur moyenne arithmétique, la variance et la corrélation spatiale. La valeur moyenne des propriétés du sol, et dans une moindre mesure la variance (ou bien aussi l’écart normal ou le coefficient de variation) sont connus et utilisés d’une majorité des ingénieurs en géotechnique pour sélectionner des propriétés caractéristiques du sol. La corrélation spatiale n’est pas beaucoup utilisée en général. C’est une mesure pour l’échelle de fluctuation, par exemple la marge entre les propriété du sol qui sont en corrélation et au-delà quelles ne sont statistiquement pas en corrélation. Cette mémoire recherche l’influence de la variabilité de la résistance de cisaillement sur la fiabilité d’un versant, basé sur des prélèvements simulés en autocorrélation avec la turning bands method. L’influence de la longueur de la surface coulissant sur la valeur caractéristique est en particulier recherchée. L’analyse numérique de Monte Carlo vérifie la validité d’une approche plus simple et plus pratique, présenté pour déterminer les caractéristiques des propriétés du sol selon l’Eurocode 7.



We gratefully acknowledge the support of HSR (University of Applied Sciences, Rapperswil, Switzerland) and the contributions of Santiago Quinteros (HSR).


  1. Anagnostopoulos A et al (eds) (2011) Proceedings of the 15th European conference on soil mechanics and geotechnical engineering. IOS Press, AmsterdamGoogle Scholar
  2. Bond A, Harris A (2008) Decoding Eurocode 7. Taylor & Francis, LondonGoogle Scholar
  3. Christian JT, Ladd CC, Baecher GB (1994) Reliability applied to slope stability analysis. J Geotech Eng Asce 120:2180–2207CrossRefGoogle Scholar
  4. EN 1997-1, Eurocode 7: Gotechnical design: part 1: General rulesGoogle Scholar
  5. Fellenius W (1936) Calculation of the stability of earth dams. Transactions of the 2nd Congress on Large Dams, Washington, DC, pp 445–462Google Scholar
  6. Mantoglou A (1987) Digital simulation of multivariate two- and three-dimensional stochastic processes with a spectral turning bands method. Math Geol 19:129–149Google Scholar
  7. Matheron G (1973) The intrinsic random functions and thir applications. Adv Appl Probab 5:439–468CrossRefGoogle Scholar
  8. NRC (1995) Probabilistic methods in geotechnical engineering. National Academy Press, Washington, DCGoogle Scholar
  9. Orr TLL, Breysse D (2008) Eurocode 7 and reliability-based design. In: Phoon K-K (ed) Reliability-based design in geotechnical engineering: computations and applications. Taylor & Francis, London, pp 298–343Google Scholar
  10. Phoon KK, Kulhawy FH (1999) Characterization of geotechnical variability. Can Geotech J 36:612–624CrossRefGoogle Scholar
  11. Schneider HR (1997) Definition and determination of characteristic soil properties. 12th Int Conf. Soil Mech. & Fdn Engng, Balkema, HamburgGoogle Scholar
  12. Schneider HR (2010) Characteristic soil properties for EC7: influence of quality of test results and soil volume involved. In: Proceedings of 14th Danube-European conference on geotechnical engineering, Bratislava, SlovakiaGoogle Scholar
  13. Schneider HR, Fitze P (2011) Characteristic shear strength values for EC7: guidelines based on a statistical framework. XV European Conference on SMGE, AthensGoogle Scholar
  14. Tietje O, Richter O (1992) Stochastic modeling of the unsaturated water flow using auto-correlated spatially variable hydraulic parameters. Model Geo Biosphere Process 1:163–183Google Scholar
  15. Vanmarcke E (1977) Probabilistic modeling of soil profiles. J Geotech Eng Asce 103:1227–1246Google Scholar
  16. Vanmarcke E (1983) Random fields, analysis and synthesis. MIT Press, Cambridge, MassGoogle Scholar

Copyright information

© The authors and IOS Press, All rights reserved.* 2011

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of Applied Sciences Rapperswil HSRRapperswilSwitzerland

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