ABSTRACT
With the development of computer technology, optimum techniques have shed lights on addressing such problems (Baker 1980, Arai & Tagyo 1985 & Bardet & Kapuskar 1989). Boutrop and Lovell (Boutrop & Lovell 1980) used the random slip surface generators to generate kinematically admissible slip surface. The surface with the smallest safety factor was selected from those generated. Greco (Greco 1996) used Monte Carlo based techniques of the random walk type to locate the critical slip surface, in which only safety factor computations, without derivatives, are required. Nuyen (Nuyen 1985) developed a method where the safety factor is formulated as a multivariate function F(x) with independent variables x describing the geometry of the slip surface, which can be circular or non-circular. He employed the simplex method as the optimization technique. Chen and Shao (Chen & Shao 1983) used simplex, steepest descent and Davidson-Fletcher-Powell methods. Celestina and Duncan (Celestina & Duncan 1981) used the alternating-variable optimization technique for non-circular slip surfaces. Li and White (Li & White 1986) proposed a more efficient onedimensional optimization technical to replace the quadratic interpolation method which Celestina and Duncan have used in the alternating-variable technique. Baker (Baker & Garber 1978) defined the slip surface by a number of nodal points connected by
straight lines. The vertical coordinates of the nodal points are the variables in Baker’s method and the dynamic programming technique is employed as the optimization method. Recently, some researchers have addressed the problem by using artificial intelligent method (including genetic algorithm (Ali et al. 2005), simulated annealing algorithm (Cheng 2003), particle swarm optimization (Li et al. 2005) etc) to determine the critical slip surface and corresponding minimum safety factor.
