Grey wolf optimization approach for searching critical failure surface in soil slopes

Abstract

Detection of critical failure surface and associated minimum factor of safety (F) constitutes a constrained global optimization problem during the task of slope analysis. Morgenstern–Price method is an established limit equilibrium-based technique satisfying both moment and force equilibrium of all slices in the failure mass has been used to evaluate F against slope failure. The main objective of current study is to investigate the applicability and efficiency of grey wolf optimization (GWO) in solving slope stability problem. GWO is a nature inspired metaheuristic optimization method which mimics the social interaction between a pack of grey wolves in their endeavour to search, hunt and prey. The effectiveness of the recently developed GWO is examined by analyzing four different slope problems. Each soil slope model has been analysed for wolf pack size (NP) range 10–50 and maximum iteration count $$ (k_{\hbox{max} } ) $$ range 50–250. In effect, the number of evaluated functions (NFE) is found to lie in the range of 500–12,500. The results demonstrate that the GWO technique can detect the critical failure surface with very good accuracy. Furthermore, the statistical analysis is presented in terms of best $$ F_{\text{b}} $$, worst $$ F_{\text{w}} $$, mean $$ \overline{F} $$, standard deviation (SD) and % error (%E) of the optimum solutions i.e. factor of safety (F) from 10 independent runs. The effect of GWO parameters such as NP and $$ k_{\hbox{max} } $$ to obtain optimum solution are also presented. The $$ F_{\text{b}} , \, F_{\text{w}} , \, \overline{F} \;{\text{and}}\;{\text{SD}} $$ for 1st slope model are (1.7295, 1.7296, 1.7295, 0.000038) and they have been obtained for maximum NFE equal to 12,500. Similarly, for 2nd and 3rd slope model, the respective values are (1.4032, 1.4038, 1.4034, 0.000209) and (1.2530, 1.2546, 1.2537, 0.000741). The discrepancy or percentage error (%E) in best $$ F_{\text{b}} $$ from optimum (F) for NFE up to 500 are found to be equal to (0.0615, 0.2531, 0.8419) for studied slope models respectively. The evaluation of safety factor F for the fourth slope model has been studied for four different combinations of earthquake loadings and pore water pressures. The values of SD for all four cases are reported for maximum NFE equal to 12,500. It is found that uncertainty in reported F reduces if higher numbers of objective function evaluations are performed. This proves the excellent performance of GWO in evaluating minimum F of the slope.