Locating the critical slip surface with the minimum factor of safety of a rock slope is a difficult problem. In recent years, some modern global optimization methods have been developed with success in treating various types of problems, but very few of these methods have been applied to rock mechanical problems. In this paper, we use Bishop's simplified method and particle swarm optimization to locate the critical slip surface. The results show that this method is an effective and efficient optimization method with a high level of confidence.


The rock slope stability analysis has been extensively studied in the last two decades. Many methods for analysis slopes have been developed. The common analytical method in use include Bishop's simplified method [1], Morgenstern and Price's method [2], Spencer's method [3], the General Limit Equilibrium method [4] and the generalized Wedge method [5].Many new approaches base on intelligence and machine learning have been developed to automate search for critical slip surface such as fuzzy logic [6] artificial neural network [7] genetic algorithm [8] and particle swarm optimization [9–11]. In this paper, Bishop's simplified method using PSO is applied to locate the critical slip surface with the minimum factor of safety of jointed rock mass slope stability. The paper is divided as follows. The second section presents the Particle Swarm optimization. Rock slope stability method is introduced in the third section. Experimental results are reported in Section 4 and the paper closes with conclusions in Section 5.

Particle Swarm Optimization

Particle Swarm Optimization (PSO) was introduced in 1995 by Eberhart and Kennedy as a numerical optimization algorithm [12,13]. The main ideas behind the development of PSO stem from the fields of social psychology and evolutionary computation. PSO's dynamic is governed by fundamental laws encountered in swarms in nature and it follows the five principles of swarm intelligence [14], namely proximity (i.e., ability to perform simple space and time computations), quality (i.e., ability to respond to quality factors in the environment), diverse response (i.e., the method should not commit its activities along excessively narrow channels), stability (i.e., the behavior of the method must not change with small changes in the environment) and adaptability (i.e., the method must be able to alter its behavior when the computational cost is not prohibitive); hence it was categorized as a swarm intelligence algorithm [15]. Similarly to other population-based algorithms, PSO exploits a population of search points to probe the search space. In the context of PSO, the population is called a swarm, while the search points are called particles, following 598 the notation in early precursors of the algorithm that were used for the simulation of swarms [15]. Each particle moves in the search space with an adaptable velocity, recording the best position it has ever visited in the search space, i.e., (in minimization problems) the position with the lowest function value.

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