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

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.