Keywords: slope stability analysis, optimisation.

The analysis of the stability of non-uniform earth slopes requires the consideration of the limiting equilibrium of a potentially sliding mass of soil defined by a non-circular failure surface. Methods of slices are most commonly used, such as that of Morgenstern and Price, but kinematically based multiple wedge methods are most appropriate. In either case, much more information is needed to define the geometry of the failure surface than the simple centre co-ordinates and radius for circular surfaces, and finding the surface with the lowest factor of safety becomes a serious optimisation problem.

The Simple Genetic Algorithm (SGA) has been used for the determination of the critical circular failure surface [1], and for non-circular failure surfaces [2] with the Morgenstern and Price method. The latter work used fifty slices of equal width, and defined the geometry in terms of the angle of the base of each slice, in a similar way to that used by Bardet and Kapuskar [3] in their investigation of the capabilities of a simplex optimisation routine. This allowed the simple genetic algorithm to work in a conventional way.

For the present work, the application of SGA to multiple wedge analysis has been investigated, using a departure from the conventional application of SGA. Each failure surface is described by a sequence of numbers that place the actual x co-ordinates of the wedge junctions and the angles of the bases of the wedges within the range of realistic possibilities. This ensures that the vast majority of surfaces generated are realistic and can be analysed. Rather than encoding all the data in a single sequence in one binary string, the data for x co-ordinates and for wedge angles have been assembled into two separate strings which are handled in parallel. The crossover operation which is used to produce each new generation is carried out at the same points in each of the strings, so that the information describing a section of the failure surface is always kept together. This allows the genetic process to operate on data which represent the actual surface as closely as possible, allowing efficient optimisation.

The analysis of a relatively simple cross-section is presented in the paper, and a number of stages in the optimisation process are shown. It can be seen that the optimisation is successful in both driving the majority of the population towards optimised values, whilst still introducing sufficient variation to allow alternative forms of failure surface to be explored. This ensures that the problems of simple optimisation routines, which tend to find the closest minimum to the starting point rather than a global minimum, are avoided. The results are compared with a random generation process, and show the clear benefits of the systematic approach.

An analysis is also presented which includes the additional complexity of some soil reinforcement. The randomised process is unsuccessful, producing a factor of safety which is unacceptably high compared with that discovered by SGA. In practice this would mean that a design considered safe would not have an adequate margin of safety.

Each run of forty generations presented in the paper, with populations of forty surfaces, took less than ten seconds on an ordinary desktop computer. This demonstrates the practicality of the Simple Genetic Algorithm for the rapid location of the critical surface in non-circular analysis of slope stability.

1

P. McCombie and P. Wilkinson, "The use of the simple genetic algorithm in finding the critical factor of safety in slope stability analysis", Computers and Geotechnics 29, 699-714. 2002. doi:10.1016/S0266-352X(02)00027-7

2

A.R. Zolfaghari, A.C. Heath, P.F. McCombie, "Simple Genetic Algorithm search for Critical Non-circular failure surface in slope stability analysis", Computers and Geotechnics, in press, 2005. doi:10.1016/j.compgeo.2005.02.001

3

J.P. Bardet M.M. Kapuskar, "A simple analysis of slope stability", Computers and Geotechnics, 8, 329-348, 1989. doi:10.1016/0266-352X(89)90039-6

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