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- 1. Slope Stability updated June 7, 2007Haryo Dwito Armono, M.Eng, Ph.D
- 2. Types of Slope Failures Falls Topless Slides Spreads FlowsFalls Topless Slope failures consisting p g Similar to a fall, of soil or rock fragments except that it begins with that droprapidly down a a mass of rock of stiff slope l clay rotating away from a l t ti f Most often occur in vertical joint steep rock slopes Usually triggered by water pressure or seismic activity
- 3. Slides Spreads Slope failures that p Similar to translational involve one ore more slides except that the blocks of earth that block separate and move ddownslope b l by move apart as they also t th l shearing along well move outward defined surfaces or thin Can be very destructive shear zonesFlows Types of Slides Downslope movement of p Rotational slides earth where earth Most often occur in resembles a viscous homogeneous materials fluid fl id such as fills or soft clays Mudflow can start with a Translational slides snow avalanche, or be in avalanche Move along planar shear surfaces conjuction with flooding Compound slides Complex and composite slides
- 4. The driving force (g g (gravity) overcomes the y) resistance derived from the shear strength of the soil along the rupture surface g pSlope stability analysis Calculation to check the safety of natural slopes, slopes of excavations and of compacted embankments. t d b k t The check involves determining and comparing the shear stress de eloped developed along the most likely rupture surface to the shear strength of soil.
- 5. Factor of Safety τfFs = τdFs = factor of safety with respect to strengthτ f = average shear strength of the soilτ d = average s ea st ess de e oped a o g t e potential failure su ace a e age shear stress developed along the pote t a a u e surfaceτ f = c + σ tan φc = cohesionφ = angle of frictionσ = average normal stress on the potential failure surfacesimilarlyτ d = cd + σ tan φdsubscript d refer to p p potential failure surface c + σ tan φFs = cd + σ tan φdwhen Fs = 1, the slope is in a state of impending of failure.In general Fs > 1.5 is acceptableStability of Slope Infinite slope without seepage Infinite slope with seepage Finite slope with Plane Failure Surface (Cullman s (Cullmans Method) Finite slope with Circular Failure Surface (Method of Slices)
- 6. Infinite slope L c tan φ β Fs = + γ H cos2 β tan β tan β d a F W Na B For granular soils, c=0 Fs is independent soils c 0, F Ta c of height H, and the slope is stable as H long as β < φ b Tr β N A r R L d Direction of γ tan φ a seepage W c Na F = Fs + γ sat H cos2 β tan β γ sat tan β B Ta c H T β b r β N A r R Finite slope with Plane Failure Surface B C W β + φd Na θcr = Ta 2 τ f = c + σ tan φH unit weight of soil = γ 4c ⎡ sin β cos φ ⎤ Tr Nr R Hcr = A β θ γ ⎢ 1 − cos( β − φ ) ⎥ ⎣ ( ⎦
- 7. Finite slope with Circular Failure Surface Slope Failure Shallow Slope Failure O Toe Circle Firm Base O Base Failure L L O Slope Circle Midpoint circle Firm Base Firm Base Slopes in Homogeneous Clay (φ=0)For equilibrium, resisting and driving moment about O: τ f = cu OMR = Md θ C Dc dr 2θ = W1l1 − W2 l 2 Radius = r W l −W lcd = 11 2 2 2 l2 l1 cd rθ H F W1 A B τf cuFs = = W2 cd cd cd Nr (normal reaction) E cdcritical when Fs is minimum, → trials to find critical planesolved analitically by Fellenius (1927) and Taylor (1937) cuHcr = γmpresented graphically by Terzaghi &Peck, 1967 in Fig 11.9 Brajam is stability number
- 8. Swedish Slip Circle MethodSlopes in Homogeneous Clay (φ>0) τ f = c + σ tan φ c d = γ H ⎡f (α , β ,θ ,φ ) ⎤ ⎣ ⎦ c = f (α , β ,θ ,φ ) = m γ Hcr where m is stability number
- 9. Method of SlicesFor equilibriumNr = Wn cos α n n=p ∑ ( c ΔL n + Wn cos α n tan φ )Fs = n =1 n=p ∑W n =1 n sin α n bnΔLn ≈ where b is the width of nth slice cos α n Bishop Method Bishop (1955) refine solution to the previous method of slices. In his method, the effect of forces on the sides of each slice are accounted for some degree . n=p 1 ∑ ( cb n =1 n + Wn tan φ ) mα ( n ) Fs = n=p ∑Wn =1 n sin α n where tan φ sin α n mα ( n ) = cos α n + Fs The ordinary method of slices is presented as learning tools. It is rarely used because is too tools conservative
- 10. Computer Programs STABL GEO-SLOPE etc BibliographyHoltz, R.D and Kovacs, W.D., “An Introduction to Geotechnical An Engineering”Das, B.M., “Soil Mechanics”Das, B.M., “Advanced Soil Mechanics”

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