Authors: González, F; Calderón, A; Castellón, R; Vargas, M; Mena, C; Orellana, L; Wiche, S; Calderón, C

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González, F, Calderón, A, Castellón, R, Vargas, M, Mena, C, Orellana, L, Wiche, S & Calderón, C 2020, 'Automated geolocalised identification of polyhedral blocks and their safety factor calculation in open pit mining', in PM Dight (ed.), Proceedings of the 2020 International Symposium on Slope Stability in Open Pit Mining and Civil Engineering, Australian Centre for Geomechanics, Perth, pp. 1003-1016,

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Traditionally in open pit mining, predicting and sizing potential structurally controlled instabilities has been carried out by statistically processing field mapped structures and slope design parameters, mainly bench orientation and face angle. This methodology usually identifies plane faults (one structure) and wedges (two structures), whose estimated size and probability of existence are based on the assumption of the most unfavourable case. The above is a result of not having simple and fast tools that can provide a georeferenced prediction of instabilities, analysing real surfaces and not only simple benches, and identify polyhedral blocks (three or more structures) with their associated safety factor (SF) and assessing the stability of the blocks on a case-by-case basis. This paper introduces the results of the implementation of algorithms that help to (1) make geolocalised prediction of structurally controlled instabilities using real and mine design surfaces, and to (2) calculate the SF for unstable blocks classified as either planar, wedge, or polyhedral failures, considering rotation. For this, examples from Chile’s large-scale mining sites were used as study cases. Doing a back-analysis exercise that was later proven in the constructed slope, plane failures, wedges and polyhedral blocks were detected in old design surfaces. In addition, potential instabilities were identified by extending the structures mapped at the current operation level to lower benches in the design surface, which were confirmed once those benches were built. The safety factors calculated with this new methodology are consistent with the plane faults, wedges and blocks that were stable or unstable in the slopes evaluated. In the case of wedges, a sample of 207 wedges was evaluated obtaining that the 74% of cases with SF associated to this new methodology had less than 0.2 points of variation comparing to the SF calculated with other software of the industry. In the rest of the cases there is a relation between the bigger variation of SFs and the geometry of the wedges, where the biggest differences among the classic SF and this methodology is associated to the wedges that are more likely to rotate. In the case of polyhedral blocks, whose SF calculation had not been easily obtained with current methodologies, the SF obtained is consistent with those from representative wedges for these blocks. By implementing these algorithms, identification and stability assessment of georeferenced blocks in a bench, wall, structural domain, and even an entire pit, based on actual onsite mapped structures, is streamlined. This enables operational and planning teams to predict geotechnical events and to promptly evaluate measures to improve operational continuity and safety of benches under construction.

Keywords: polyhedral blocks, instabilities, safety factor, structure, slope, rotation, real surface, prediction

Chan, H & Einstein, H 1981, ‘Approach to complete limit equilibrium analysis for rock wedges – the method of ‘artificial supports’’, Rock Mechanics, vol. 14, no. 2, pp. 59–86.
Chen, Z 2004, ‘A generalized solution for tetrahedral rock wedge stability analysis’, International Journal of Rock Mechanics and Mining Sciences, vol. 41, pp. 613–628.
Goodman, R & Shi, G 1985, Block Theory and its Application to Rock Engineering, Prentice-Hall, London.
Hoek, E & Bray, J 1981, Rock Slope Engineering, 3rd edn, Institute of Minerals and Metallurgy, London.
Jiang, Q, Liu, X, Wei, W & Zhou, C 2013, ‘A new method for analyzing the stability of rock wedges’, International Journal of Rock Mechanics and Mining Sciences, vol. 60, pp. 413–422.
Jiang, Q & Zhou, C 2017, ‘A rigorous solution for the stability of polyhedral rock blocks’, Computers and Geotechnics, vol. 90,
pp. 190–201.
Jimenez-Rodriguez, R & Sitar, N 2007, ‘Rock wedge stability analysis using system reliability methods’, Rock Mechanics and Rock Engineering, vol. 40, no. 4, pp. 419–427.
John, K 1968, ‘Graphical stability analysis of slopes in jointed rock’, Journal of the Soil Mechanics and Foundations Division, vol. 94, no. 2, pp. 497–256.
Kumsar, H, Aydan, I & Ulusay, R 2000, ‘Dynamic and static stability assessment of rock slopes against wedge failures’, Rock Mechanics and Rock Engineering, vol. 33, no. 1, pp. 31–51.
Londe, P, Vigier, G & Vormeringer, R 1969, ‘Stability of rock slopes, a three-dimensional study’, Journal of the Soil Mechanics and Foundations Division, vol. 95, no. 1, pp. 235–262.
Priest, S 1985, Hemispherical projection methods in rock mechanics, London.
Rocscience Ltd. 2001, Swedge – Probabilistic Analysis of the Geometry and Stability of Surface Wedges, computer software, Toronto, Canada,
TIMining 2019, TIMining Tangram – Software for Detection of Instabilities with Structural Control, computer software, Santiago,
Wang, Y & Yin, J 2002, ‘Wedge stability analysis considering dilatancy of discontinuities’, Rock Mechanics and Rock Engineering, vol. 35, no. 2, pp. 127–137.
Wittke, W 1965, ‘Method to analyse the stability of rock slopes with and without additional loading’ (in German), Felsmechanik und Ingenieurgeologie, vol. 30, no. 2, pp. 52–79.
Yeung, R, Jiang, Q & Sun, N 2003, ‘Validation of block theory and three dimensional discontinuous deformation analysis as wedge stability analysis methods’, International Journal of Rock Mechanics and Mining Sciences, vol. 40, pp. 265–275.

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