4 Vol.4 No. 005 7 Chinee Journal of Rock Mechanic and Engineering July 005 (. 4007. 4400) O 4. A 000 695(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] [] 996 004 0 004 06 05 (964 ) 985 E-mail hzheng@whrm.ac.cn
6 005 5 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
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 []
8 005. 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 4.0 4.0 6 0 4 0.5 5.0 9.0 5 5 0 4 0.0 9.07 0.07 4 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.54.56.480.580 ( ) [7] Fellieniu ( Felleniu ) 5% 0% 4 Fellieniu Bihop ( ) (.580) Bihop (.56).8% 6.%
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