Development of empirical correlations for limit equilibrium methods of slope stability analysis

Abstract

Determining the safety factor by limit equilibrium methods is based on different assumed slip surfaces and equilibrium equations for forces and moments to be satisfied. The safety factor can be predicted using empirical correlations instead of going through lengthy calculations. In this paper, empirical equations between the factor of safety (FS), unit weight (γ), cohesion (c), internal friction angle (φ), slope angle (α), and height of the slope (H) have been proposed for Spencer’s, Morgenstern-Price, Janbu’s simplified, Bishop’s simplified, and Lowe-Karafiath methods. Data of 50 slopes having homogeneous soil strata with non-identical shearing strength parameters, containing different geometries and the water table below the base of the slope, have been selected to determine FS using Slope-W and for the development of correlations using SPSS software. Unit weight, cohesion, friction angle, slope angle, and height of the slope vary from 11.5 to 21 (kN/m³), 0 to 137 (kPa), 0 to 39 (°), 11 to 78 (°), and 3.5 to 22 (m), respectively. Multiple regression analyses were performed on Slope-W outcomes, and equations for the prediction of FS were formulated. Validation of the proposed FS equations was done both internally and externally as well. The validation graphs are drawn between Slope-W FS versus developed equations for FS of each method. The correlations are helpful for the calculation of FS to have a quick prediction of failure of a slope, and ultimately preventive measures can be taken. The regression constant (R²) values for Spencer’s, Morgenstern-Price, Janbu’s simplified, Bishop’s simplified, and Lowe-Karafiath methods are 0.940, 0.940, 0.922, 0.932, and 0.935, respectively.