ON DEFINITIONS OF SAFETY FACTOR OF SLOPE STABILITY ANALYSIS WITH FINITE ELEMENT METHOD

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1 4 Vol.4 No Chinee Journal of Rock Mechanic and Engineering July 005 ( ) O 4. A (005) 5 06 ON DEFINITIONS OF SAFETY FACTOR OF SLOPE STABILITY ANALYSIS WITH FINITE ELEMENT METHOD ZHENG Hong TIAN Bin LIU De-fu FENG Qiang (. Intitute of Rock and Soil Mechanic Chinee Academy of Science Wuhan 4007 China). College of Civil and Hydroelectric Engineering China Three Gorge Univerity Yichang 4400 China) Abtract There exit three definition of afety factor in lope tability analye by limit equilibrium method (LEM). Definition define the afety factor a the ratio of the hear trength of oil to the hear tre required for equilibrium. Definition define the margin of afety factor a the factor of the trength reduction by which the hear trength of the oil would have to be divided to bring the lope into a tate of critical equilibrium. Definition define the afety factor a the ratio of the reitant hear force to the driving hear force along a certain lip urface. Thi tudy dicue the relation between Definition and. A unified algorithm i given which i ued to locate the critical lip line correponding to Definition and Definition repectively. It i alo proved while the finite element method i ued to analyze lope tability both the afety factor and the potential lip urface baed on Definition are different from thoe on Definition. Some irrational reult might be obtained if Definition i ued in finite element lope tability analyi. Key word numerical analyi lope tability analyi afety factor finite element method(fem) [ 6] [] (964 ) 985 hzheng@whrm.ac.cn

2 a [] [ τ ]d F = () τ d Fellieniu F [7] 7 [ 7] F = [τ ] () [] τ τ [τ ] [] Mohr-Coulomb [ τ ] = c σ tanϕ () F F F F = F c ϕ σ () () [ τ ] = F τ (4) [] (5) F [ τ ]d = F τ d (5) F τ [4] ξ [8] F τ d = Fξ τ d (6) Fξ F ξ () (6) ( cl + N tanϕ) l F F = F ξ (7) N F F F (7) [9 ] F F F [] F F

3 4. 7 F [τ ] F( x l) = (8) τ F Mohr-Coulomb π ϕ l x σ ± [5 5 6] F 4 F( x l) (7) ) F( x l x F F F ( F ) ( F ) dx = co β i dl (9) dy = in β i dl dl βi dl [6] π ϕ β i = α ± (0) F 4 α σ x (8) F [ 6] N N [6] (8) N F F [6] F (9) ϕ ϕ tanϕ ϕ = tan F 5 4 [7] F x x l []

4 m 4 m 0 m 4 m 0 m m 5.00 m 5 m 8.8 m F =.48 F =.58.4 m Fig. Section for computation Table Parameter of rock γ /(kn m ) c/kpa ϕ /( ) E/MPa µ Fig. Safety factor and potential lip urface baed on Definition and repectively uing FEM Fig.4 Contour line of equivalent platic train in the critical tate Fig. Meh and boundary condition Table Safety factor of two lip urface F LEM ν [6] ( = FEM F F.48) F ( F =.58) 6.% F ( ) F ( ) ( ) Felleniu.9.44 Bihop ( ) [7] Fellieniu ( Felleniu ) 5% 0% 4 Fellieniu Bihop ( ) (.580) Bihop (.56).8% 6.%

5 4. 9 [J]. 00 4() 57 6.(Zheng Yingren Zhao 6 Shangyi Zhang Luyu. Slope tability analyi by trength reduction FEM[J]. Engineering Science 00 4() 57 6.(in Chinee)) ( ) F F trength reduction[j]. Géotechnique (6) F Bihop Spencer Geo-Denver 000[C]. [. l. ] [. n. ] (Reference) [9] Matui T San K C. Finite element lope tability analyi by hear trength reduction technique[j]. Soil and Foundation 99 () [0] Dawon E M Roth W H Drecher A. Slope tability analyi by [] Dawon E Motamed F Nearajah S et al. Geotechnical tability analyi by trength reduction[a]. In Griffith D V ed. Geotechnical Special Publication Slope Stability 000 Proceeding of Seion of [] Lechman J B Griffith D V. Analyi of the progreion of failure of earth lope by finite element[a]. In Griffith D V ed. Geotechnical Special Publication Slope Stability 000 Proceeding of Seion of [] Duncan J M. State of the art limit equilibrium and finite-element Geo-Denver 000[C]. [. l. ] [. n. ] analyi of lope[j]. Journal of Geotechnical and Geoenvironmental [] Dawon E You K Park Y. Strength-reduction tability analyi of Engineering ASCE 996 (7) rock lope uing the Hoek-Brown failure criterion[a]. In Labuz J F []. [J]. ed. Geotechnical Special Publication Trend in Rock Mechanic[C]. 00 (4) (Lian Zhenying Han [. l. ] [. n. ] Guocheng Kong Xianjing. Stability analyi of excavation by trength [4] Jeremić B. Finite element method for D lope tability reduction FEM[J]. Chinee Journal of Geotechnical Engineering analyi[a].in Griffith D V ed. Slope Stability 000 Proceeding of 00 (4) (in Chinee)) Seion of Geo-Denver 000[C]. [. l. ] [. n. ] []. [J]. [5]. # 997 9() 7.(Song Erxiang. Finite element analyi of afety [J]. 00 5(4) (Ge factor for oil tructure[j]. Chinee Journal of Geotechnical Xiurun Ren Jianxi Li Chunguang et al. D FEM analyi of deep Engineering 997 9() 7.(in Chinee)) liding tability of # dam foundation of left power houe of the Three [4] Griffith D V Lane P A. Slope tability analyi by finite element[j]. Géotechnique () Gorge project[j]. Chinee Journal of Geotechnical Engineering 00 5(4) (in Chinee)) [5] Zou J Z William D J. Search for critical lip urface baed on finite element method[j]. Canadian Geotechnical Journal 995 () 46. [6]. [J]. 00 () 8.(Luan Maotian Wu Yajun Nian Tingkai. A criterion for evaluating lope [6]. [J]. tability baed on development of platic zone by hear trength 00 4(5) (Zheng Hong Li Chunguang Lee Chaofeng et al. Finite element method for olving the factor of afety[j]. Chinee Journal of Geotechnical Engineering 00 4(5) reduction FEM[J]. Journal of Diater Prevention and Mitigation Engineering 00 () 8.(in Chinee)) [7] Craig R F. Soil Mechanic[M]. London [. n. ] (in Chinee)) [8] Bihop A W. The ue of the lip circle in the tability analyi of [7]. [J]. lope[j]. Géotechnique 955 5() () 5 55.(Shi Hengtong Wang Chenghua. Some problem in finite element analyi of lope tability[j]. Rock and Soil Mechanic 000 () 5 55.(in Chinee)) [9] Wright S G Kulhawy F G Duncan J M. Accuracy of equilibrium lope tability analyi[j]. J. Soil Mech. and Found. Div. ASCE 97 99(0) [8]. [0] Tavena F Trak B Leroueil S. Remark on the validty of tability

6 0 005 analye[j]. Canadian Geotechnical Journal 980 7() 6 7. [] Chugh A K. Variable factor of afety in lope tability analyi[j]. Géotechnique () Pre 979.(in Chinee)) [5]. [J]. 00 (5) 8 89.(Wang []. [J]. Chenghua Xia Xuyong Li Guangxin. An algorithm in earch of the 00 (5) (Shao Guojian Zhuo Jiahou Zhang Qing. Reearch on analyi method and criterion of rock ma tability[j]. Chinee Journal of Rock Mechanic and Engineering 00 (5) (in Chinee)) critical lip urface in oil lope baed on tre field[j]. Chinee Journal of Rock Mechanic and Engineering 00 (5) 8 89.(in Chinee)) [6]. [J]. []. [M]. 004 (6) (Zheng Hong Liu 00.(Chen Zuyu. Stability Analyi of Soil Slope[M]. Bejing China Water Power Pre 00.(in Chinee)) Defu Luo Xianqi. Determination of potential lide line of lope baed on deformation analyi[j]. Chinee Journal of Rock Mechanic and [4]. ( )[M]. Engineering 004 (6) (in Chinee)) 979.(Chen Chuanzhang Chen Chuanlin Zhu Xueyan et al. Mathematical Analyi(Vol. )[M]. Beijing People Education [7] Zienkiewicz O C Taylor R L. The Finite Element Method[M]. [. l. ] [. n. ]

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