Epistemic uncertainty propagation in slope stability analysis and implications in safety margins

Authors: Valderrama, CE; Cofré, M; Hormazábal, E; Álvarez, R

Open access courtesy of:

DOI https://doi.org/10.36487/ACG_repo/2025_51

Cite As:
Valderrama, CE, Cofré, M, Hormazábal, E & Álvarez, R 2020, 'Epistemic uncertainty propagation in slope stability analysis and implications in safety margins', in PM Dight (ed.), Slope Stability 2020: Proceedings of the 2020 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, Australian Centre for Geomechanics, Perth, pp. 791-804, https://doi.org/10.36487/ACG_repo/2025_51

Download citation as:   ris   bibtex   endnote   text   Zotero


Abstract:
Stability analysis of slopes commonly deals with limited data relating to the characterisation of the material strength properties. This generates an uncertainty level that depends on the number of measurements used to determine them, and that is not related to the intrinsic variability of the material known as epistemic uncertainty. Considering a Mohr–Coulomb material characterised by its cohesion and friction angle, we describe a method to use interval estimation methods (confidence intervals) to estimate the level of epistemic uncertainty as a function of the number of available measurements (sample size), obtaining ranges of plausible values for the mean of the strength parameters. The calculated uncertainty in strength parameters is later propagated through a deterministic slope stability analysis, obtaining a relation between test sample size and the uncertainty in Factor of Safety (FoS) calculation, which can be compared with the typical safety margins used in slope designs.

Keywords: uncertainty quantification, uncertainty propagation, design safety margins

References:
Ang, A & Tang, W 2007, Probability Concepts in Engineering – Emphasis on Applications in Civil & Environmental Engineering, 2nd edn, John Wiley & Sons, Hoboken.
Baecher, G & Christian, J 2003, Reliability and statistics in Geotechnical Engineering, Chichester, Wiley.
Baudrit, C & Dubois, D 2006, ‘Practical representations of incomplete probabilistic knowledge’, Computational Statistics & Data Analysis, vol. 51, no. 1, pp. 86–108.
Bedi, A 2013, A proposed framework for characterizing uncertainty and variability in rock mechanics and rock engineering, PhD thesis, Imperial College London, London.
Cao, Z, Wang, Y & Li, D 2017, Probabilistic approaches for geotechnical site characterization and slope stability analysis,
Springer-Verlag, Berlin.
Carranza-Torres, C & Hormazabal, E 2018, ‘Computational tools for the determination of factor of safety and location of the critical circular failure surface for slopes in Mohr-Coulomb dry ground’, Proceedings of the 2018 International Symposium of Slope Stability in Open Pit Mining and Civil Engineering, Seville.
D’Agostino, R & Stephens, M 1986, Goodness of fit techniques, 1st edn, Marcel Dekker Inc, New York.
Dempster, AP 1968, ‘A generalization of Bayesian inference’, Journal of the Royal Statistical Society, vol. 30, pp. 205–247.
Diciccio, TJ & Romano, JP 1988, ‘A review of bootstrap confidence intervals’, Journal of the Royal Statistical Society, vol. 50, no. 3,
pp. 338–354.
Di Matteo, L, Valigi, D & Ricco, R 2013, ‘Laboratory shear strength parameters of cohesive soils: variability and potential effects on slope stability’, Bulletin of Engineering Geology and the Environment, vol. 72, no. 1, pp. 101–106.
Dong, W & Shah, HC 1987, ‘Vertex method for computing functions of fuzzy variables’, Fuzzy Sets and Systems, vol. 24, no. 1,
pp. 65–78.
Drosg, M 2007, Dealing with uncertainties - A guide to error analysis, Springer-Verlag, New York.
Dubois, D & Guyonnet, D 2011, ‘Risk-informed decision-making in the presence of epistemic uncertainty’, International Journal of General Systems, vol. 40, no. 2, pp. 145–167.
Dubois, D & Prade, HM 2009, ‘Formal representations of uncertainty’, Decision-making process, ISTE & Wiley, London, pp. 85–156.
Efron, B 1987, ‘Better bootstrap confidence interval’, Journal of the American Statistical Association, vol. 82, pp. 171–185.
Fillion, MH & Hadjigeorgiou, J 2013, ‘Reliability of strength estimates based on limited laboratory data’, in PM Dight (ed.), Proceedings of the 2013 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, Australian Centre for Geomechanics, Perth, pp. 163–176, https://doi.org/10.36487/ACG_rep/1308_05_Hadjigeorgiou
Gill, DE, Corthesy, R & Leite, MH 2005, ’Determining the minimal number of specimens for laboratory testing of rock properties’, Engineering Geology, vol. 78, pp. 53–67.
Guan, JW & Bell, DA 1991, Evidence theory and its applications, North-Holland, New York.
Helton, JC & Oberkampf, WL 2004, ‘Alternative representations of epistemic uncertainty’, Reliability Engineering & System Safety, vol. 85, no. 1–3, pp. 1–10.
Helton, JC 2011, ‘Quantification of margins and uncertainties: conceptual and computational basis’, Reliability Engineering & System Safety, vol. 96, pp. 1034–1052.
Jaulin, L, Kieffer, M, Didrit, O & Walter, E 2001, Applied interval analysis, Springer-Verlag, New York.
Kearfott, RB & Kreinovich, V 1996, Application of interval computations, Kluwer Academic Publishers, Boston.
Loy, A, Follet, L & Hofmann, H 2015, ‘Variations of Q-Q plots: The power of your eyes!’, The American Statistician, vol. 70,
pp. 202–214.
Moore, RE, Kearfott, RB & Cloud, MJ 2009, Introduction to interval analysis, Society for Industrial and Applied Mathematics, Philadelphia.
Neyman, J 1937, ‘Outline of a theory of statistical estimation based on the classical theory of probability’, Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences, vol. 236, no. 767, pp. 333–380.
Read, J & Stacey, P 2009, Guidelines for Open Pit Slope Design, CRC Press, Boca Raton.
Ruffolo, RM & Shakoor, A 2009, ‘Variability of unconfined compressive strength in relation to number of test samples’, Engineering Geology, vol. 108, pp. 16–23.
Scholz, F 2005, ‘Non-parametric tail extrapolation’, Boeing Information & Support Services ISSTECH 95-014, Seattle,
Walley, P 1991, Statistical reasoning with imprecise probabilities, Chapman and Hall, London.
Wyllie, D 2018, Rock Slope Engineering: Civil Applications, 5th edn, CRC Press, Boca Raton.
Zadeh, LA 1978, ‘Fuzzy sets as a basis for a theory of possibility’, Fuzzy Sets and Systems, vol. 1, pp. 3–28.




© Copyright 2024, Australian Centre for Geomechanics (ACG), The University of Western Australia. All rights reserved.
View copyright/legal information
Please direct any queries or error reports to repository-acg@uwa.edu.au