(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:tonyfeng@nchu.edu.tw (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

81

42(1)65-82 (2010) Journal of Soil and Water Conservation, 42(1)65-82 (2010)

82