Keywords: genetic algorithm, slope stability, interslice force slip surface, limit equilibrium.

The conventional limit equilibrium method of slope stability analysis consists of two steps; calculation of the safety factor of a particular trial slip surface, and the other, searching for a critical slip surface with the lowest value of safety factor. During the past thirty years considerable attention has been given to the first step. The use of optimization techniques in locating the critical slip surface is becoming increasingly popular among the researchers. The traditional mathematical optimization methods that have been used include conjugate-gradient [1], random search and simplex optimization [2]. More recently, Pham and Fredlund [3] applied dynamic programming to the stability analysis of slopes. In their approach, stresses acting along the critical slip surfaces were computed using a finite element analysis and thus eliminating the need to describe the relationship between interslice forces.

The genetic algorithm (GA) differs from other search methods in that it searches among a population of points and works with a coding of the parameter set rather than the parameters themselves. It also uses probabilistic rather than deterministic transition rules. This paper presents a method for determining the critical "non-circular" slip surfaces using a GA, satisfying both force and moment equations of equilibrium. Fundamental formulations of the generalized (rigorous) Janbu approach were adopted as the limit equilibrium method. The proposed method is capable of determining the interslice forces and their location without any apriori assumption, as well as the safety factor. The robustness of the proposed approach is illustrated using some example problems and the results are compared with conventional methods. The GA adopted here minimizes an objective function that has three terms, namely, the error in equilibrium equations, the safety factor and a penalty term. By minimizing this objective function, the 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 and its position is determined through the GA process.

The penalty term guarantees kinematic admissibility of slip surfaces. The proposed algorithm is applied to a number of problems and the results are compared with previous work. From the examples considered it may be concluded that a population size of 50, a crossover rate of 0.95, crossover mode of single point and two points together with a ranking method and a variable mutation technique can locate the critical non-circular surface and yield the generalized interslice forces. The safety factors obtained are in some cases greater than those calculated by other investigators. The reasons are discussed in the paper.

1

Malkawi, H., Hassan W.F. and Sarma, S.K. (2001) "Global search method for locating general slip surface using Monte Carlo technique", J. Geotechnical and Geoenvironmental Engrg., 127(8), 688-698. doi:10.1061/(ASCE)1090-0241(2001)127:8(688)

2

De Natale, J.S. (1991) "Rapid identification of critical slip surface", J. Geotech. Engrg., ASCE, 122(7), 577-596.

3

Pham, H.T.V. and Fredlund, D.G. (2003) "The application of dynamic programming to slope stability analysis", Can. Geotech. J. 40: 830-847. doi:10.1139/t03-033

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