Determination of Slope Safety Factor with Analytical Solution and Searching Critical Slip Surface with Genetic-Traversal Random Method

Wen-Jie Niu

doi:10.1155/2014/950531

Abstract

In the current practice, to determine the safety factor of a slope with two-dimensional circular potential failure surface, one of the searching methods for the critical slip surface is Genetic Algorithm (GA), while the method to calculate the slope safety factor is Fellenius' slices method. However GA needs to be validated with more numeric tests, while Fellenius' slices method is just an approximate method like finite element method. This paper proposed a new method to determine the minimum slope safety factor which is the determination of slope safety factor with analytical solution and searching critical slip surface with Genetic-Traversal Random Method. The analytical solution is more accurate than Fellenius' slices method. The Genetic-Traversal Random Method uses random pick to utilize mutation. A computer automatic search program is developed for the Genetic-Traversal Random Method. After comparison with other methods like slope/w software, results indicate that the Genetic-Traversal Random Search Method can give very low safety factor which is about half of the other methods. However the obtained minimum safety factor with Genetic-Traversal Random Search Method is very close to the lower bound solutions of slope safety factor given by the Ansys software.

Highlights

IntroductionThe geotechnical engineer frequently uses limit equilibrium methods of analysis when studying slope stability problems, for example, Ordinary or Fellenius’ method (sometimes referred to as the Swedish circle method or the conventional method), Simplified Bishop method, Spencer’s method, Janbu’s simplified method, Janbu’s rigorous method, Morgenstern-Price method, or unified solution scheme [1,2,3]
The geotechnical engineer frequently uses limit equilibrium methods of analysis when studying slope stability problems, for example, Ordinary or Fellenius’ method, Simplified Bishop method, Spencer’s method, Janbu’s simplified method, Janbu’s rigorous method, Morgenstern-Price method, or unified solution scheme [1,2,3]
This paper first intends to determine a cohesive soil slope safety factor with Fellenius’ slices method, while the 2D critical failure surface is searched with genetic algorithm (GA)

Summary

Introduction

The geotechnical engineer frequently uses limit equilibrium methods of analysis when studying slope stability problems, for example, Ordinary or Fellenius’ method (sometimes referred to as the Swedish circle method or the conventional method), Simplified Bishop method, Spencer’s method, Janbu’s simplified method, Janbu’s rigorous method, Morgenstern-Price method, or unified solution scheme [1,2,3]. Previous research employed the Variational Calculus, the dynamic programming, alternating variable methods, the Monte Carlo technique, or the genetic algorithm (GA) into slope stability analysis for critical surface identification [7,8,9,10,11,12,13]. This paper first intends to determine a cohesive soil slope safety factor with Fellenius’ slices method, while the 2D critical failure surface is searched with GA. The fitness of each chromosome is determined using the objective function that the resulting safety factors should be lower enough, and the fitness of all solutions is compared, while the chromosome of large safety factors shall be deleted [18] This part is realized with hand calculation. Genetic-Traversal Random Search Method is compared with other solutions such as slope/w software

A Slope Stability Problem Example

Compared with Other Solutions

C2 C3 C4

Conclusions