Computational tools for the estimation of Factor of Safety and location of the critical failure surface for slopes in rock masses that satisfy the Hoek–Brown failure criterion

Authors: Carranza-Torres, C; Hormazábal, E

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DOI https://doi.org/10.36487/ACG_repo/2025_73

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Carranza-Torres, C & Hormazábal, E 2020, 'Computational tools for the estimation of Factor of Safety and location of the critical failure surface for slopes in rock masses that satisfy the Hoek–Brown failure criterion', 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. 1099-1122, https://doi.org/10.36487/ACG_repo/2025_73

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Abstract:
This paper presents dimensionless graphical representations, computer spreadsheets and regression analysis equations for the quick estimation of Factor of Safety (FS) and location of the critical failure surface for slopes excavated in rock masses that satisfy the Hoek–Brown failure criterion. The problem considered in this paper involves slopes with planar faces and arbitrary values of height and inclination angle, excavated in homogeneous, isotropic and dry rock masses with shear strength characterised by the Hoek–Brown failure criterion. To reduce the number of variables in the problem and to be able to present stability results in the most compact way possible, a transformation law for the Hoek–Brown failure criterion that considers the parameter ‘a’ to be equal to 0.5 is applied in the analysis. Development of the proposed tools involved computation of more than 60,000 selected cases of slopes using the Bishop method of slices in a commercial limit equilibrium software. Results obtained from the analysis are summarised in dimensionless graphical representations and an Excel workbook made freely available on the internet. Based on the results obtained from the limit equilibrium models, equations for the quick estimation of conservative measures of FS of slopes are provided. The various tools presented in this paper allow casting light into the problem of establishing mechanical similarity of slopes excavated in rock masses that satisfy the Hoek–Brown failure criterion, in regard to FS and position of the critical circular failure surface. To illustrate the application of the proposed computational tools, a practical example involving the analysis of the stability of a slope in an actual open pit mine is provided.

Keywords: slope stability, Factor of Safety, Hoek–Brown, rock mass, limit equilibrium, Bishop, method of slices, shear strength reduction technique

References:
Abramson, LW, Lee, TS, Sharma, S & Boyce, GM 2002, Slope stability and stabilisation methods, 2nd edn, John Wiley & Sons, New York.
Balmer, G 1952, ‘A general analytical solution for Mohr’s envelope’, American Society for Testing Materials, vol. 52, pp. 1260–1271.
Bishop, AW 1955, ‘The use of the slip circle in the stability analysis of slopes’, Geotechnique, vol. 5, issue 1, pp. 7–17.
Carranza-Torres, C 2004, ‘Some comments on the application of the Hoek-Brown failure criterion for intact rock and rock masses to the solution of tunnel and slope problems’, in G Barla & M Barla (eds), Proceedings of the X Conference on Rock and Engineering Mechanics, Politecnico di Torino, Turin, pp. 285–326.
Carranza-Torres, C & Fairhurst, C 1999, ‘The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion’, International Journal of Rock Mechanics and Mining Sciences, vol. 36, issue 8, pp. 777–809.
Carranza-Torres, C & Fairhurst, C 2000, ‘Application of the convergence-confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criterion’, Tunneling and Underground Space Technology, vol. 15, issue 2, pp. 187–213.
Carranza-Torres, C & Hormazabal, E 2018, ‘Computational tools for the determination of factor of safety and location of the critical failure surface for slopes in Mohr-Coulomb dry ground’, Proceedings of the 2018 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, Asociacion Nacional de Ingenieros de Minas, Sevilla,
Carter, T & Carranza-Torres, C 2019, ‘Global characterization of high rock slopes using the Hoek–Brown mb parameter as controlling index’, Proceedings of the 14th International Congress on Rock Mechanics and Rock Engineering, Foz do Iguassu.
Chapra, SC & Canale, RP 2015, Numerical methods for engineers, 7th edn, Mc Graw Hill, New York.
Cheng, YM, Lansivaara, T & Wei, WB 2007, ‘Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods’, Computers and Geotechnics, vol. 34, issue 3, pp. 137–150.
Cleveland, WS & Loader, C 1996, ‘Smoothing by local regression: Principles and methods’, in W Hardle & M Schimek (eds), Statistical theory and computational aspects of smoothing, Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg, Berlin, pp. 10–49.
Contreras, LF & Brown, ET 2018, ‘Bayesian inference of geotechnical parameters for slope reliability analysis’, Proceedings of the 2018 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, Asociacion Nacional de Ingenieros de Minas, Sevilla.
Contreras, LF & Brown, ET 2019, ‘Slope reliability and back analysis of failure with geotechnical parameters estimated using Bayesian inference’, Journal of Rock Mechanics and Geotechnical Engineering, vol. 11, issue 3, pp. 628–643.
Dawnson, EM, Roth, WH & Drescher, A 1999, ‘Slope stability analysis by strength reduction’, Geotechnique, vol. 49, issue 6,
pp. 835–840.
Dawson, E, You, K & Park, Y 2000, ‘Strength-reduction stability analysis of rock slopes using the Hoek-Brown failure criterion’, Proceedings of Geo-Denver 2000. Volume: Trends in Rock Mechanics, American Society of Civil Engineers, Reston, pp. 65–77.
de Bruyn, I, Coulthard, M, Baczynski, N & Mylvaganam, J 2013, ‘Two-dimensional and three-dimensional distinct element numerical stability analyses for assessment of the west wall cutback design at Ok Tedi Mine, Papua New Guinea’, 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. 653–668, https://doi.org/10.36487/ACG_rep/1308_43_deBruyn
Hammah, RE, Yacoub, TE, Corkum, BC & Curran, JH 2005, ‘The shear strength reduction method for the generalized Hoek-Brown criterion’, Proceedings of the 40th US Rock Mechanics Symposium: Rock Mechanics for Energy, Mineral and Infrastructure Development in the Northern Regions, American Rock Mechanics Association, Alexandria.
Hoek, E & Bray, J 1974, Rock slope engineering, 1st edn, Institution of Mining and Metallurgy, London.
Hoek, E & Bray, J 1977, Rock slope engineering, 2nd edn, Institution of Mining and Metallurgy, London.
Hoek, E & Bray, J 1981, Rock slope engineering, 3rd edn, Institution of Mining and Metallurgy, London.
Hoek, E & Brown, ET 1980, ‘Empirical strength criterion for rock masses’, Journal of the Geotechnical Engineering Division, vol. 106, issue GT9, pp. 1013–1035.
Hoek, E & Brown, ET 1997, ‘Practical estimates of rock mass strength’, International Journal of Rock Mechanics and Mining Sciences, vol. 34, issue 8, pp. 1165–1186.
Hoek, E & Brown, ET 2019, ‘The Hoek–Brown failure criterion and GSI – 2018 edition’, Journal of Rock Mechanics and Geotechnical Engineering, vol. 11, issue 3, pp. 445–463.
Hoek, E, Carranza-Torres, C & Corkum, B 2002, ‘Hoek–Brown failure criterion – 2002 edition’, Proceedings of the 5th North American Rock Mechanics Symposium and the 17th Tunnelling Association of Canada Conference, Toronto, pp. 267–273.
Hoek, E & Karzulovic, A 2000, ‘Rock-mass properties for surface mines’, in WA Hustrulid, MK McCarter & DJA van Zyl (eds), Proceedings of the Slope Stability in Surface Mining, Society for Mining, Metallurgical and Exploration, Littleton, pp. 59–67.
Hormazabal, E, Rovira, F, Walker, M & Carranza-Torres, C 2009, Analysis and design of slopes for Rajo Sur, an open pit mine next to the subsidence crater of El Teniente mine in Chile, Proceedings of the 2009 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, University de los Andes, Santiago,
Jiang, X, Cui, P & Liu, C 2016, ‘A chart-based seismic stability analysis method for rock slopes using Hoek–Brown failure criterion’, Engineering Geology, vol. 209, pp. 196–208.
Juang, CH, Jhi, YY & Lee, DH 1998, ‘Stability analysis of existing slopes considering uncertainty’, Engineering Geology, vol. 49, issue 2, pp. 111–122.
Kotze, G & Bosman, J 2015, ‘Towards expediting large-scale slope design using a re-worked design chart as derived from limit equilibrium methods’, in TR Stacey (ed.), Proceedings of the 2015 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, The Southern African Institute of Mining and Metallurgy, Johannesburg, pp. 341–362.
Lacasse, S, Nadim, F, Liu, ZQ, Eidsvig, UK, Le, TMH & Lin, CG 2019, ‘Risk assessment and dams. Recent developments and applications’, Proceedings of the XVII European Conference on Soil Mechanics and Geotechnical Engineering, Icelandic Geotechnical Society, Reykjavik,
Leshchinsky, B 2013, ‘Comparison of limit equilibrium and limit analysis for complex slopes’, in C Meehan, D Pradel, MA Pando & JF Labuz (eds), Geo-Congress 2013: Stability and Performance of Slopes and Embankments III, American Society of Civil Engineers, Reston, pp. 1280–1289.
Li, AJ, Merifield, RS & Lyamin, AV 2008, ‘Stability charts for rock slopes based on the Hoek–Brown failure criterion’, International Journal of Rock Mechanics and Mining Sciences, vol. 45, issue 5, pp. 689–700.
Londe, P 1988, ‘Discussion on the paper ‘Determination of the shear stress failure in rock masses’ by R Ucar’, Journal of the Geotechnical Engineering Division, vol. 112, no.3, pp. 374–376.
Michalowski, RL 2002, ‘Stability charts for uniform slopes’, Journal of Geotechnical and Geoenvironmental Engineering,
vol. 128-4, issue GT9, pp. 351–355.
Michalowski, RL 2013,’ Stability assessment of slopes with cracks using limit analysis’, Canadian Geotechnical Journal, vol. 50,
pp. 1011–1021.
Nekouei, AM & Ahangari, K 2013, ‘Validation of Hoek–Brown failure criterion charts for rock slopes’, International Journal of Mining Science and Technology, vol. 23, issue 6, pp. 805–808.
Read, J & Stacey, P 2009, Guidelines for open pit slope design, CSIRO Publishing, Melbourne.
Rocscience Inc. 2018, SLIDE, computer software, Rocscience, Toronto.
Rocscience Inc. 2019, RS2, Rocscience, Toronto.
Rose, N, Scholz, M, Burden, J, King, M, Maggs, C & Havaej, M 2018, ‘Quantifying transitional rock mass disturbance in open pit slopes related to mining excavation’, Proceedings of the 2018 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, Asociacion Nacional de Ingenieros de Minas, Sevilla.
Shen, J, Karakus, M & Xu, C 2013, ‘Chart-based slope stability assessment using the generalized Hoek–Brown criterion’, International Journal of Rock Mechanics and Mining Sciences, vol. 64, pp. 210–219.
Sun, C, Chai, J, Xu, Z, Qin, Y & Chen, X 2016, ‘Stability charts for rock mass slopes based on the Hoek–Brown strength reduction technique’, Engineering Geology, vol. 214, pp. 94–106.
Utili, S 2013, ‘Investigation by limit analysis on the stability of slopes with cracks’, Geotechnique, vol. 6, issue 2, pp. 140–154.
Utili, S & Abd, AH 2016, ‘On the stability of fissured slopes subject to seismic action’, International Journal for Numerical and Analytical Methods in Geomechanics, vol. 40, pp. 785–806.
Wang, L, Hwang, J, Juang, H & Atamturktur, S 2013, ‘Reliability-based design of rock slopes a new perspective on design robustness’, Engineering Geology, vol. 154, pp. 56–63.
Wyllie, DC 2018, Rock slope engineering. Civil Applications, CRC Press, Boca Raton.
Xu, J, Pan, Q, Yang, X L & Li, W 2017, ‘Stability charts for rock slopes subjected to water drawdown based on the modified nonlinear Hoek–Brown failure criterion’, International Journal of Geomechanics, vol. 18, issue 1, pp. 805–808.
Yu, HS, Salgado, R, Sloan, SW & Kim, JM 1998, ‘Limit analysis versus limit equilibrium for slope stability’, Journal of Geotechnical and Geoenvironmental Engineering, vol. 124, issue 1, pp. 1–11.




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