Determination of Critical Slip Surface in Slope Stability Analysis Using Particle Swarm Optimization Algorithm

Slope stability analysis is routinely performed by engineers to evaluate the stability of embankment dams, road embankments, river training works, excavations and retaining walls. Slope stability analysis can be carried out by the limit equilib-rium method (LEM), the limit analysis method, the finite element method (FEM) or the finite difference method. By far, most engineers still use the limit equilibrium method with which they are familiar. Although the limit equilibrium method of slices does not consider the stress-strain relation of soil, it is widely used by engineers and researchers for slope stability analysis due to its simplicity and the related accumulated experiences. One of the main tasks in using the limit equilibrium method is the determination of the critical slip surface having the minimum factor of safety. Non-linear functions associated with the optimization of critical failure slip surface, a considerable number of local minimums during the process of optimization as well as, the need for a fast and efficient algorithm for generating the circular or non-circular trial slip surfaces, are the notable aspects of this complexity. In recent years, numerous modern global optimization methods have been proposed with success to solve the various types of problems, but very few of these methods have been applied to geotechnical problems. In this study, a Particle Swarm Optimization method (PSO) is developed to solve the factor-of-safety minimization problem. In this study by applying particle swarm optimization algorithm, circular and non-circular critical slip surfaces were determined in both homogeneous and non-homogeneous slopes under various static and seismic loadings. To locate the critical circular or non-circular failure surface, a trial slip surface generation algorithm is required. In this paper, the first section defines the generation of trial circular and non-circular slip surfaces and the safety factors of the general slip surfaces are calculated using a Bishop and Janbu methods. The second section briefly reviews the principle of the particle swarm optimization method as well as its specific initialization and convergence criterion. PSO is based on the simulation of simplified social models, such as bird flocking, fish schooling, and the swarming theory. This method is developed on a very simple theoretical framework and can be implemented easily with only primitive mathe-matical operators. This optimum position is usually characterized by the optimum value of a fitness function (e.g., factor of safety for the present problem). The third section applies the present method to four different types of slope analysis and compares the numerical results to previously published solutions and other famous software results. The proposed heuristic algorithm and generation of trial slip surfaces algorithm represents slip surfaces as circular and noncircular curves and solves for the optimal curve yielding the minimum factor of safety. To demonstrate its applicability and to investigate the validity and effectiveness of the algorithm, the obtained results are compared with the available softwares and the proposed algorithm is demonstrated to be effective and efficient in solving complicated problems with a high level of confidence. The calculation results show that the PSO has stronger adaptive ability, faster calculation rate and better global optimal character. The presented PSO algorithm method can be applied to find the non-circular failure surface with the lowest factor of safety very quickly compared to software’s or other methods and approaches.