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Computational tools for the determination of factor of safety and location of the critical circular failure surface for slopes in Mohr-Coulomb dry ground

Carlos Carranza-Torres and Esteban Hormazabal
Tuesday, April 10, 2018
First presented: 
Slope Stability 2018
Published paper

Download the Excel Macro: Stability Calculator.xlsm

This paper presents computational tools for the quick estimation of factor of safety and location of the critical circular failure surface for simple slope problems. The analysis presented here applies to slopes of arbitrary height and inclination angle excavated in homogeneous/isotropic dry ground, assumed to obey the Mohr-Coulomb shear failure criterion, and characterized by arbitrary values of unit weight, cohesion and internal friction angle. The proposed procedure is based on ideas originally laid out in the classical book Rock Slope Engineering by Hoek and Bray (1981) and more recently in the books by Read and Stacey (Guidelines for Open Pit Slope Design) and by Wyllie (Rock Slope Engineering, Civil Applications) from 2009 and 2018, respectively. Development of the proposed procedure involved computation of approximately 3,400 selected cases of slopes using the Bishop Method in the limit equilibrium software SLIDE by Rocscience. Results obtained from the analysis are summarized in dimensionless graphical representations that not only allow factors of safety and location of the critical circular failure surface to be estimated, but also important, to put light into the fundamental problem of establishing the concept of mechanical similarity of slopes excavated in Mohr-Coulomb ground with regard to factors of safety and position of the critical circular failure surface. In addition to the graphical representation of factor of safety, the paper also provides an equation to compute the factor of safety of slopes based on these representations. Considering that in the current practice of geotechnical engineering design the use of computer spreadsheets may be preferred over the use of dimensionless charts, the proposed procedure is implemented in a simple to use EXCEL workbook that is freely available to readers, and that allows determination of factor of safety and location of the failure surface, as it would be obtained with the Bishop Method in the limit equilibrium method software SLIDE. Finally, to illustrate the application of the proposed tools, a practical example involving the analysis of stability of a slope in an actual open pit mine is provided.


Feature Author

Esteban Hormazabal
Esteban is a Civil Mining Engineer and holds a Master of Science (Geophysics) specialized in applied hydrogeology. He has 24 years of specific experience in geotechnical engineering, rock mechanics and geotechnical instrumentation, having worked in different mining and civil engineering projects. 
Additionally, he is an expert in analysis and geomechanical design of underground mining and surface excavations using 2D and 3D numerical modelling, stability analysis and slope design in open pits and waste dumps. 
He has led different and important open pit and underground mining projects in Argentina, Brazil, Chile, Colombia, Kazakhstan, Mexico, Peru, Russia, Uruguay and USA. 
Esteban has authored several publications and has been speaker at different national and international conferences. He is a Competent Person of AusIMM and the Commission for the Qualification of Competencies in Mineral Resources & Reserves of Chile (QP). He has been professor of  the Rock Mechanics Chair at the Universidad Católica de Chile from 2013-2018.


Head of Rock Mechanics Services
Min Eng, MSc (Geophysics), MAusIMM, SAIMM, CRIRSCO
SRK Santiago
SRK China