Duran, A 2019, 'Probabilistic stability analyses for sedimentary deposits', in J Wesseloo (ed.), Proceedings of the First International Conference on Mining Geomechanical Risk
, Australian Centre for Geomechanics, Perth, pp. 429-442.
This paper presents several approaches utilised by the author in assessing slope designs, inclusive of Probabilities of Failure, in sedimentary strata. A common issue seen by the author in probabilistic analyses is the use of population statistics, which honour variability in point sampling, but do not reflect variability at the larger scale. This then results in overestimates of the Probability of Failure. Issues in assessing the variability in inputs for analyses are discussed. Two case studies are presented with focus and discussion on use of the appropriate variability in the respective analyses. The cases have considered the scale at which the data is collected, and, critically, the analysis methodology which influences the approach in selection of variability. The case studies have utilised a Monte Carlo approach and use of limit equilibrium stability analysis software. Recent trends in analysis methodology (surface response methodology) and emergence of improvements in software (which allow generation of random fields) suggest the field of probabilistic analysis has matured. However, without careful consideration to the key design parameters, probabilistic analysis may simply serve to provide what appears as more sophisticated results, but which offer no additional value in managing risk for a project.
Keywords: probabilistic analyses, Monte Carlo, sedimentary strata
Bewick, RP, Kaiser, PK & Valley, B 2011, ‘Interpretation of triaxial testing data for estimation of the Hoek-Brown strength parameter mi’, Proceedings of the 45th U.S. Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association, Alexandria.
Cammack, R & Duran, A 2015, ‘A review of methods for assessing the Hoek-Brown miconstant from triaxial testing’, Proceedings of the 13th ISRM International Congress of Rock Mechanics, International Society for Rock Mechanics and Rock Engineering, Lisbon.
Cargill, JS & Shakoor, A 1990, ‘Evaluation of empirical methods for measuring unconfined compressive strength of rock’, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol. 27, issue 6, pp. 495–503.
Chiwaye, HT & Stacey, TR 2010, ‘A comparison of limit equilibrium and numerical modelling approaches to risk analysis for open pit mining’, Journal of the Southern African Institute of Mining and Metallurgy, vol. 110, no. 10, pp. 571–580.
Cylwik, SD, Beck, JA & Ryan, TM 2018, ‘The uncertainty of rock mass shear strength estimates: how to incorporate the reduction in variance due to spatial averaging for use in probabilistic analysis’, Proceedings of Slope Stability 2018, Asociacion Nacional de Ingenieros de Minas and Colegio Oficial de Ingenieros de Minas del Sur, Seville.
Deere, DU & Miller, RP 1966, Engineering Classification and Index Properties for Intact Rock, University of Illinois, Urbana.
Fillion, MH & Hadjigeorgiou, J 2013, ‘Reliability of strength estimates based on limited laboratory testing’, 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.
Gill, DE, Corthésy, R & Leite, MH 2005a, ‘Determining the minimal number of specimens for laboratory testing of rock properties’, Journal of Engineering Geology, vol. 78, issue 1, pp. 29–51.
Gill, DE, Corthésy, R & Leite, MH 2005b, ‘A statistical approach for determining practical rock strength and deformability values from laboratory tests’, Journal of Engineering Geology, vol. 78, issue 1, pp. 53–67.
Hess, PE, Bruchman, D, Assakkaf, IA & Ayyub, BM 2002, ‘Uncertainties in material and geometric strength and load variables’, Naval Engineers Journal, vol. 114, no. 2, pp. 139–166.
Hoek, E 1983, ‘Strength of jointed rock masses’, Géotechnique, vol. 23, no. 3, pp. 187–223.
Hoek, E & Brown, ET 1997, ‘Practical estimates of rock mass strength’, International Journal of Rock Mechanics and Mining Sciences, vol. 34, no. 8, pp. 1165–1186.
Hoek, E, Carranza‐Torres, CT & Corkum, B 2002, ‘Hoek‐Brown failure criterion – 2002 edition’, in R Hammah, W Barden, J Curran & M Telesnicki (eds), Proceedings of the Fifth North American Rock Mechanics Symposium, University of Toronto Press, Toronto, pp. 267–273.
Kirsten, HAD 1983, ‘Significance of probability of failure in slope engineering’, The Civil Engineer in South Africa, vol. 25, no. 1, January, pp. 17–27.
McMahon, BK 1971, ‘Statistical methods for the design of rock slopes’, Proceedings First Australia New Zealand Conference Geomechanics, vol. 1, pp. 314–321.
McMahon, BK 1985, Geotechnical Design in the Face of Uncertainty: EH Davis Memorial Lecture, Australian Geomechanics Society, Barton, p. 38.
Read, J 2009, ‘Data uncertainty’, in J Read & P Stacey (eds), Guidelines for Open Pit Slope Design, CRC Press, Boca Raton,
Renani, HR, Martin, CD, Varona, P & Lorig, L 2018, ‘Probabilistic stability analysis of slopes in highly heterogeneous rock masses’, Proceedings of Slope Stability 2018, Asociacion Nacional de Ingenieros de Minas and Colegio Oficial de Ingenieros de Minas del Sur, Seville.
Rocscience Inc. 2004, RocLab, computer software, Rocscience Inc., Toronto
Rocscience Inc. 2010, SLIDE, version 6, computer software, Rocscience Inc., Toronto
Rocscience Inc. 2018a, ‘Tutorial 33: spatial variability’, Slide 2018 Tutorial Manual, Rocscience Inc., Toronto.
Rocscience Inc. 2018b, ‘Tutorial 34: spatial variability multi material’, Slide 2018 Tutorial Manual, Rocscience Inc., Toronto.
Rocscience Inc. 2018c, Slide2, computer software, Rocscience Inc., Toronto
Rosenblueth, E 1975, ‘Point estimates for probability moments’, Proceedings of the National Academy of Sciences, vol. 72, no. 10, pp. 3812–3814.
Wesseloo, J & Read, J 2009, ‘Acceptance criteria’, in J Read & P Stacey (eds), Guidelines for Open Pit Slope Design, CRC Press, Boca Raton, pp. 221–236