A genetic approach for determining the generalized interslice forces and the critical non-circular slip surface

 In this paper, a genetic algorithm (GA) method is employed to determine the location of the critical non-circular slip surface giving the minimum factor of safety in conjunction with the magnitude of interslice forces and their points of application. A generalized method of slices satisfying both force and moment equations of equilibrium is adopted for stability calculations. The GA adopted here minimizes an objective function that has three terms, namely, error in equilibrium equations, safety factor and a penalty term. By minimizing this objective function, a critical slip surface (with minimum safety factor) is obtained that satisfies both force and moment equations of equilibrium and is kinematically admissible as well. No assumption is made regarding the location of the thrust line where its position is determined through the GA process. Furthermore, all slip surfaces are kinematically admissible and physically acceptable by considering a suitable penalty term.  The proposed algorithm is applied to a number of problems and the results are compared with previous work and discussed in detail.