Velarde, G & Macciotta, R 2023, 'Probabilistic pit slope stability analysis targeting a reliability-based design acceptance criteria: a parametric study', in PM Dight (ed.), SSIM 2023: Third International Slope Stability in Mining Conference
, Australian Centre for Geomechanics, Perth, pp. 161-184, https://doi.org/10.36487/ACG_repo/2335_08
Design of open pit slopes is a decision-making process which aims to maximise the ore recovery while minimising the excavation volumes. The current practice of designing open pit slopes adopts the widely accepted Guidelines for Open Pit Slope Design by Read & Stacey (2009). An optimum design should satisfy a design acceptance criteria (DAC). However, designing open pit slopes is a complex process that involves inherent risks and uncertainties. As a result, reliability analyses are becoming increasingly important for performance-based slope designs. In a reliability approach, the amount of information on the slope materials and behaviour would reflect the reliability of a slope design. This paper presents a parametric study defined by the uncertainties of the rock mass strength properties and the slope geometric configurations at three different design reliability levels targeting a reliability-based DAC (RBDAC). The reliability assessment is performed using probabilistic analysis adopting the two-dimensional limit equilibrium method and Monte Carlo simulations. The input variables for the rock mass strength are defined through probability density functions (PDF) that capture the natural variability, while the input variables of geological structures are defined through kinematic assessments.
The PDFs of the rock mass strength properties were modelled based on the generalised Hoek–Brown criterion using the mean, coefficient of variation (COV) and dependence between quantitative properties of the criterion. Results show that most of the resultant pairs of Factor of Safety (FoS) and probability of failure and associated COV of the resulting FoS (COVFoS) are consistent with the RBDAC. Based on this, a redesign is proposed showing the applicability of the RBDAC and comparing it to the current DAC. This approach has significant implications for slope optimisation or mitigation plans for future pushbacks in case of instabilities.
Keywords: reliability-based design acceptance criteria, coefficient of variation, probability density functions
Baecher, GB & Christian, JT 2003, Reliability and Statistics in Geotechnical Engineering, John Wiley & Sons, New York, pp. 19–33.
Bedi, A & Harrison, JP 2013, ‘Characterisation and propagation of epistemic uncertainty in rock engineering: a slope stability example’, Proceedings of the ISRM International Symposium - EUROCK 2013, International Society for Rock Mechanics, Lisbon.
Bewick, RP, Amann, F, Kaiser, PK & Martin, CD 2015, ‘Interpretation of UCS test results for engineering design’, Proceedings of the 13th ISRM International Congress of Rock Mechanics, International Society for Rock Mechanics, Lisbon.
Creighton, A, Bixley, M, Elmouttie, M, Hassall, M, Macciotta, R & Juldz, A 2022, ‘A reliability-based design acceptance criteria approach for inter-ramp and overall open pit slopes’, Proceedings of the International Slope Stability 2022 Symposium, Tucson.
Darling, P 2011, ‘Introduction to openpit mining’, SME Mining Engineering Handbook, 3rd edn, Society for Mining, Metallurgy & Exploration, Engelwood.
Ferson, S & Ginzburg, LR 1996, ‘Different methods are needed to propagate ignorance and variability’, Reliability Engineering & System Safety, vol. 54, no. 2-3, pp. 133–144,
Gaida, M, Cambio, D, Robotham, ME & Pere, V 2021, ‘Development and application of a reliability-based approach to slope design acceptance criteria at Bingham Canyon Mine’, in PM Dight (ed.), SSIM 2021: Second International Slope Stability in Mining, Australian Centre for Geomechanics, Perth, pp. 83–94,
Hadjigeorgiou, J & Harrison, JP 2011, ‘Uncertainty and sources of error in rock engineering’, Proceedings of the 12th ISRM Congress, International Society for Rock Mechanics, Lisbon.
Hoek, E 1998, ‘Reliability of Hoek-Brown estimates of rock mass properties and their impact on design’, International Journal of Rock Mechanics and Mining Sciences, vol. 53, no. 1, pp. 63–68,
Hoek, E & Bray, J 1981, Rock Slope Engineering, 3rd edn, Institution of Mining and Metallurgy, London.
Hoek, E, Carranza-Torres, C & Corkum, B 2002, ‘Hoek-Brown criterion – 2002 edition’, in R Hammah, W Bawden, J Curran & M Telesnicki (eds), Proceedings of the 5th North American Rock Mechanics Symposium and 17th Tunnelling Association of Canada Conference, University of Toronto, Toronto., pp. 267–273.
Hoek, E & Brown, ET 2018, ‘The Hoek–Brown failure criterion and GSI – 2018 edition’, Journal of Rock Mechanics and Geotechnical Engineering, vol. 11, no. 3, pp. 445–463,
Hudson, JA & Feng, X 2015, ‘Uncertainty and risk’, Rock Engineering Risk, CRC Press/Balkema, Leiden, pp. 9–27.
Hustrulid, WA, McCarter, MK & Van Zyl, DJA 2001, ‘Slope stability at Escondida mine’, in Slope Stability in Surface Mining, Society for Mining, Metallurgy & Exploration, Engelwood, pp. 153–162.
Kiureghian, AD & Ditlevsen, O 2008, ‘Aleatory or epistemic? Does it matter?’, Structural Safety, vol. 31, no. 2, pp. 105–112,
Ma, T, Cami, B, Javankhoshdel, S, Yacoub, T, Corkum, B & Curran, J 2022, ‘Effect of disturbance factor distribution function on stability of an open pit mine’, Proceedings of the 56th U.S. Rock Mechanics/Geomechanics Symposium, American Rock Mechanics Association, Alexandria,
Martin, D & Stacey, P 2018, Guidelines for Open Pit Slope Design in Weak Rocks, CSIRO Publishing, Clayton South.
Macciotta, R, Creighton, A & Martin, CD 2020, ‘Design acceptance criteria for operating open pit slopes: an update’, CIM Journal, vol. 11, no. 4, pp. 248–265,
Macciotta, R, Creighton, A & Martin, CD 2021, ‘Design acceptance criteria and risk tolerance for inter-ramp and overall open pit slopes’, Canadian Geotechnique, vol. 2, no. 3, pp. 48–51.
Macciotta, R, Creighton, A & Martin, CD 2022, ‘Reliability based design acceptance criteria for inter-ramp and overall pit slopes – fundamental considerations and mathematical background’, Proceedings of the International Slope Stability 2022 Symposium, Tucson.
Padilla, RA, Titley, SR & Pimentel, F 2001, ‘Geology of the Escondida porphyry copper deposit, Antofagasta Region, Chile’, Economic Geology, vol. 96, no. 2, pp. 307–324,
Phoon, KK & Ching, J 2015, Risk and Reliability in Geotechnical Engineering, CRC Press, Boca Raton, pp. 3–72.
Phoon, KK & Retief, JV 2016, Reliability in Geotechnical Structures in ISO2394, CRC Press/Balkema, Leiden, pp. 49–82.
Rapiman, MM & Sepulveda, MR 2006, ‘Slope optimization at Escondida Norte Open Pit’, in Proceedings of Stability of Rock Slopes, The South African Institute of Mining and Metallurgy Symposium Series, Johannesburg, pp. 265–278.
Rafiei Renani, H & Martin, CD 2020, ‘Slope stability analysis using equivalent Mohr–Coulomb and Hoek–Brown criteria’, Rock Mechanics and Rock Engineering, vol. 53, no. 1, pp. 13–21,
Rafiei Renani, H, Martin, CD, Varona, P 2019, ‘Stability analysis of slopes with spatially variable strength properties.’, Rock Mechanics and Rock Engineering, vol. 52, no. 10, pp. 3791–3808,
Read, J & Stacey, P 2009, Guidelines for Open Pit Slope Design, CSIRO Publishing, Collingwood.
Rocscience Inc 2022, DIPS-Graphical and statistical analysis of orientation data, computer software, Toronto, Canada.