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(1) (2) (3)
Zolfaghari (2005) Morgenstern and Price Method
SLOPE/W
A Preliminary Application of Genetic Algorithm on Slope Stability Analysis
Mei-ling Wang1 Zheng-yi Feng2* Yu-hsan Chang3
University Student (1), Associate Professor (2), Doctoral Student, (3) Department of Soil and Water Conservation, National Chung-Hsing University,Taichung402, Taiwan , R.O.C.
Abstract
This study adopts genetic algorithm (GA) by Zolfaghari (2005) and analyzes the stability of soil slope with Morgenstern and Price method using method of slices to search the factor of safety and failure surface. The assignment of primarily parameters is according to the rule-of-thumb values from homogeneous slope for calculation. The paper compares the results carried out by GA for two test sites with those results of SLOPE/W to verify the reliability and accuracy of the analysis.
KeywordGenetic algorithm, slope stability, factor of safety, slip surface
(1) (2) e-mail:[email protected] (3)
65
(Simple genetic algorithm)
McCombie
and Wilkinson(2002)
(Simple genetic algorithm)
xy
(brute
force approach)
Zolfaghari, et al.(2005)
Morgenstern-Price
42(1)65-82 (2010) Journal of Soil and Water Conservation, 42(1)65-82 (2010)
66
1960 Holland
(1975) Adaptation in
Natural and Artificial Systems
Holland (1975)
()
(Chromosome)
(Population)
(Fitness value)
(Crossover)
1
(2005; Coley, 1999; Haupt and Haupt, 2004)
(Initial Population)
(Chromosome)
(Population)
(Local Optima)
(Encoding)
(Binary Encoding)(Real-valued
Encoding) (Signal Encoding)
67
1
Fig. 1 GA flow chart
42(1)65-82 (2010) Journal of Soil and Water Conservation, 42(1)65-82 (2010)
68
(Gray Encoding)
0 1
x
2x
(Chromosome)
(Genotype)(Phenotype)
()
()
(Fitness Function)
(Selection and Reproduction)
(Crossover)
:
(mating pool)()
(Single point crossover)(Two point
crossover)(Uniform crossover)
2 3
69
2
Figure2. Single point crossover
3
Figure3 Two point crossover
(Mutation)
()
4
4
Fig.4 Mutation process
Morgenstern and Price (1965)
Morgenstern-Price Method
Morgenstern-Price Method (Zolfaghari, et al., 2005; Abramson, et al., 2002)
Morgenstern-Price Method
(Zolfaghari, et al., 2005):
42(1)65-82 (2010) Journal of Soil and Water Conservation, 42(1)65-82 (2010)
70
f(x)
X E
( 5)
(Zolfaghari, et al., 2005)
5 (Zolfaghari, et al., 2005)
Figure. 5 Forces of a slice
( 4)( 5)
0( 6)(Zolfaghari, et al., 2005):
0
71
( 9)
9
=0
(Zolfaghari, et al., 2005) 6
Fig.6 Crossover of safety factor
(Zolfaghari,et al., 2005)
1 (F)()
2
()
Zolfaghari, et al. (2005)
:
(Zolfaghari, et al., 2005)
1
1 1( cos ) ( cos sin ) 0
n n
x i i i i Qi i i Qii i
QM F M Q Q Y Q X = =
= + = + + = ..... (9)
42(1)65-82 (2010) Journal of Soil and Water Conservation, 42(1)65-82 (2010)
72
100
2
(Initial Population)
F 70
70 X1
F
3
100 F 70
F
Morgenstern-Price Method
100
QM
(QM) 0
Morgenstern-Price Method QM
() 50%
100 F QM
50 50
Morgenstern-Price Method
50 50
QM 50%
50%
50% 35
Case1.
F
(Chromosome)
F
100
73
80% 40%
40%Case2.
(Chromosome) x
n
X 111
7
Fig7. Crossover of slip surface
8% 0~100
8
1
0
8%
Visual Basic Zolfaghari, et al.
(2005)
8
9
1
100~120
90~120cm
2
42(1)65-82 (2010) Journal of Soil and Water Conservation, 42(1)65-82 (2010)
74
8
Figure.8 Search procedure of F.S.
75
9
Figure.9 Search procedure of critical surface
42(1)65-82 (2010) Journal of Soil and Water Conservation, 42(1)65-82 (2010)
76
2007
1
1.1 (Generation)
(
)
10 100
1000
1 (GA analysis) Table 1 F.S. of different iteration number - GA analysis
10 ( GA analysis )
Figure. 10 Influence of iteration numbers of slip surface on F.S.
77
10
150
1.364 SLOPE/W
1.367
2
2.1
16
C 0 KPa
37 31.7
GA analysis 30cm
20
74
2m 2.214 SLOPE/W
1m
45
2.44( 11)
GA analysis
GA analysis
11 GA analysis SLOPE/W ()
Figure. 11 Comparison of slip surface searched by GA and SLOPE/W for Wan-ya test site
42(1)65-82 (2010) Journal of Soil and Water Conservation, 42(1)65-82 (2010)
78
12 GA analysis SLOPE/W ()
Figure. 11 Comparison of slip surface searched by GA and SLOPE/W for Don-Shi test site
SLOPE/W
2.2
19
C 0 KPa 30
GA analysis
30cm 20
27 1.567
SLOPE/W
Morgenstern-Price method
33 1.593
( 12)GA analysis
SLOPE/W
79
1.
2.
3.
4.
5.
NSC97-2815-C-005-017-E
Dr. Zolfaghari, A.R.
1. Holland, John H(1992) ,Adaptation in Natural and Artificial Systems: An Introductory Analysis With Applications to Biology, Control, and Artificial Intelligence,Cambridge, Mass. MIT Press
2. Coley, D.A.(1999),World Scientific: An Introduction to Genetic Algorithms for Scientists and Engineers.
3. Haupt, R.L., Haupt, S.E.(2004),Practical Genetic Algorithms,Second edition, John Wiley & Sons, Inc.
4. McCombie, P.F., Wilkinson, P.(2002),The use of the simple genetic algorithm in finding the critical factor of safety in slope stability analysis, Computer and Geotechnics, Vol.29, pp.699-714.
5. Zolfaghari, A.R., Heath, A.C., McCombie, P.F. (2005), Simple genetic algorithm search for critical non-circular failure surface in slope stability analysis, Computer and Geotechnics,
42(1)65-82 (2010) Journal of Soil and Water Conservation, 42(1)65-82 (2010)
80
Vol.32, pp.139-152.
6. Zolfaghari, A., Heath, A.C. (2008), A GIS application for assessing landslide hazard over a large area, Computer and Geotechnics, Vol.35, pp.278-285.
7. GEO-SLOPE International Ltd.(2008),Stability Modeling with SLOPE/W 2007, An Engineering Methodology, Third Edition, GEO-SLOPE International Ltd.
8. (2005)
http://apc.iim.nctu.edu.tw/2005intelligen
t/GP.pdf/
980524
980810
990125
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