Modified Harmony Methods for Slope Stability Problems - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 138

Modified Harmony Methods for Slope Stability Problems
Yung-Ming Cheng
Department of Civil and Structural Engineering, Hong Kong Polytechnic University,
Hong Kong
[e-mail]
Abstract. In many practical slope stability problems, a thin layer of soft material with very low
shear strength parameters may exist. Such soft and thin soil layer has caused many large scale
slope failures in Hong Kong and many other places. Determining the critical failure surface
with the smallest factor of safety for such a problem is extremely difficult. This chapter pro-
poses a domain transformation technique, which is coupled with two new versions of improved
harmony search algorithms to ensure both the efficiency and effectiveness of optimization
analysis for large scale difficulty problems. The improved harmony search algorithms differ
from the original harmony search algorithm in that: (1) the harmonies are rearranged into sev-
eral pairs and the better pairs are used to develop several new harmonies; (2) different prob-
abilities are assigned to different harmonies. The robustness of the newly proposed methods is
demonstrated by using some difficult slope stability problems, and the improvement in the effi-
ciency of the new algorithms is examined with respect to some large scale slope stability prob-
lems in China.
Keywords: Slope Stability, Factor of Safety, Modified Harmony Search, Objective Function,
Global Minimum.
1 Introduction
For the stability analysis of slope by the limit equilibrium method, the minimum factor
of safety is the basis for the design of slope stabilization measures. It is crucial that a
good result should be determined because failures of slopes have caused significant
loss of lives and properties in Hong Kong and many other cities. The evaluation of the
minimum factor of safety of a slope involves the generation of trial slip surfaces,
evaluation of the factors of safety for the trial slip surfaces and determination of the
critical slip surface with the lowest factor of safety. By nature, the slope stability prob-
lem is a difficult non-convex non-polynomial type global optimization problem whose
solution is difficult, and the objective function may also be discontinuous at different
locations within the solution domain. Many engineers are facing this problem in their
routine design works, and many of them are using the simple trial and error approach
with the support of experience. Cheng et al. [1] has demonstrated that the use of the
modern optimization method can greatly improve the results of analysis as compared
with the trial and error approaches used in some practical problems in Hong Kong. At
present, most of the engineers are still using the classical simplex method or Monte
Carlo simulation method in the optimization analysis (adopted in some commercial
software) which appears to function well for simple problems, but some engineers are
experiencing limitations in use of these methods in some difficult problems.