Rock slope stability charts based on limit equilibrium method incorporating Generalized Hoek–Brown strength criterion for static and seismic conditions

Abstract

Stability charts present a graphical approach for the estimation of factor of safety (FOS) of a finite slope with uniform soil properties which are routinely used by geotechnical engineers. They provide a way for quick and efficient determination of stability of slopes sidestepping the need for carrying out actual analysis. In the present work, authors have developed stability charts of rock mass to determine global minimum FOS for rock slope stability problems. The rock mass is modelled by incorporating generalized Hoek–Brown strength criterion proposed by Hoek et al. (Hoek–Brown criterion—2002 edition, 2002). Limit equilibrium technique based Morgenstern and Price (Geotechnique 15:79–93, 1965) method is used to determine the value of factor of safety of the rock slope against failure. An evolutionary optimization method i.e. Particle swarm optimization (PSO) is used to search for the minimum FOS values and the associated critical failure surface out of all possible slip surfaces. A MATLAB code has been developed for this purpose. The charts have been developed for the entire range of Geological Strength Index (GSI) values ranging from 0 to 100 for intact rock mass characterized by the disturbance factor D = 0 for both static and seismic loading conditions. The seismic slope analysis is performed by an equivalent static method using a horizontal seismic coefficient (kh) with values ranging from 0.10 to 0.30. Stability charts contain stability numbers which are inversely proportional to FOS value of the slope. In the present work, stability numbers are plotted for different inclination angles ( $$\beta$$ ) equal to 15°, 30°,45°, 60° and 75+°, respectively, for both static and seismic conditions considering the variations of other material parameters such as $$m_{i}$$ and $${\text{GSI}}$$ . Stability numbers are observed to increase with an increase in angle of inclination ( $$\beta$$ ) of the slope and correspondingly FOS values follow a decreasing trend. However, stability numbers follow a decreasing pattern with increasing values of material parameters $$m_{i}$$ and $${\text{GSI}}$$ designating improved rock quality with corresponding increase in FOS values of the rock slope.