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
(https://papers.acg.uwa.edu.au/p/2025_73_Carranza_Torres/)
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