Transcription
Lecture 12: Slope StabilityKey Questions1. How do “friction” and “cohesion” work together to stabilize slopes?2. What is trying to “pull” slope material down?Kelso, WA Landslide3. How does the slope angle play a role in slope stability?4. What is the “factor of safety” index.html
Decemeber 2007 storm event near Chehalis
Naches Landslide in October 2009A massive landslide that closed a section of State Route 410, destroyed at leasttwo homes, blocked and changed the flow of the Naches River (10/11/2009)
Slope stability is controlled by relief material strength soil water content vegetationTons of earth and vegetation washed away from clear-cut hillsides into StillmanCreek, a tributary of the south fork of the Chehalis River.
Slope mechanics and material strength.
Arboretumunconsolidated sediment.dipping Chuckanut sandstone
ArboretumWhat holds the sediment in place?.
ArboretumWhat holds the sediment in place?.What’s pulls it down?
Conceptual Model.Wθ
Conceptual Model.Wθ
w weight is concentrated at the center of the block(center of mass).Wθ
.Wθθ slope angle
.Wθ
.Wweight always points straight downθ
.Wweight forceθ
Fp component of weight parallel to the slope.Wθ
trigonometry states that θ slope angle.Wθθ
.WFp W x sinθθθ
.WFp W x sinθθsinθ oppositehypotenuseθ
The force parallel to the inclined plane Fp is what “pulls’ it down the slopeDriving Force Fp W x sinθ.Wθ
.small angle small pulling force FpθFf.θclarge angle large pulling force Fpθ
Slope mechanics and material strength.
.FN W x cosθWθcosθ adjacenthypotenuseθ
FN component of weight “normal” or perpendicular to the slope.Wθ
FN component of weight “normal” or perpendicular to the slope.Wθ
The “normal” force FN is what contributes to a force the “resists”movement down the slope (i.e., it in part controls the material strength)FN W x cosθ.Wθθ
When the block is horizontal (θ 0) then FN w.WFN
push.FNfriction force
.pullFNfriction force
Ff friction force FN x coefficient of friction.pullFNfriction force
The coefficient of friction quantifies the degree ofroughness between the two surfaces (bottom of theblock and the horizontal surface).pullFNfriction force
low coefficient of frictionsmooth blocksmooth surface
high coefficient of frictionrough blockrough surface
The coefficient of friction changes with geologic materialClay 0.1 to 0.3Sand 0.4 to 0.8Broken rock 0.5 to 0.9Note: the Greek symbol μ (mu) is usually used for coefficient offriction
The coefficient of friction is also controlled by mineralogy (quarts is strong, olivine is not) grain shape (angular versus rounded) packing arrangement (loose versus tight packing)
The magnitude of FN increases the interlocking of the two surfacebecause the force “pushes” the imperfections together making itharder for the block to slide—this increase the friction forceFNFf friction force FN x μ
The magnitude of FN increases the interlocking of the two surfacebecause the force “pushes” the imperfections together making itharder for the block to slideFNFf friction force FN x μ
The magnitude of FN increases the interlocking of the two surfacebecause the force “pushes” the imperfections together making itharder for the block to slideFNFf friction force FN x μ
increases if these increaseFriction force FN x coefficient of friction.pullFNfriction force
Mechanical friction keeps the block from sliding.WFfFNθFpθ
FNslip plane.WFfFNθFpθ
FNslip plane.WFfFNθFpθ
Molecular cohesion between the grains also contributes to thematerial strength and keeps the block from sliding.WFNFfθFpcohesionθ
Moist sand has strength
The strength is created by “molecular” forces of attractionbetween the sand – water – air
Calcite and silica cements that bind mineralstogether is another form of molecular cohesion
The stability of slopes is analyzed by comparing themagnitude of the “driving” forces to the “resisting” forcesFNFf.WθFpcohesionθ
Driving Force Fp W x sinθ.Wθ
Resisting forces friction cohesion.WFfFNθFpcohesionθ
resisting forceFactor of Safety driving forceFNFf.WθFpcohesionθ
friction cohesionFactor of Safety FpFNFf.WθFpcohesionθ
resisting forceFactor safety driving forceFNFf.WθFpcohesionθ
Ff cFactor safety FpFNFf.WθFpcohesion cθ
W x cosθ x μ cFactor safety W x sinθ.WFfFNθFpcohesion cθ
At low slope angles “θ” Fp is small and FN and hence Ff are largerFf cFactor safety FS 1Fp.FfcθW x cosθ x μ cFactor safety FS 1W x sinθ
At high slope angles “θ” Fp is large and FN and hence Ff are smallerFf cFactor safety FS 1FpFf.θcθW x cosθ x μ cFactor safety FS 1W x sinθ
resisting forcesFactor safety FS 1driving forcesThe slope fails if FS is less than “1”Ff.θcθ
Thirteen homes had to be evacuated in Burien near Shorewood Drive SW and 131stStreet when a hillside gave way and sent a wall of mud on homes and the street below.December 03, 2007)
Crews work to clear Westlake Avenue North after heavy rains caused a mud slide.(December 03, 2007)
A car rests beneath a section of Golden Gardens Drive NW, which collapsed early thismorning during heavy rains. (December 03, 2007)
At low slope angles “θ” F. p. is small and F. N. and hence F. f. are larger. Factor safety W . x. cosθ. x. μ c. W . x . sinθ FS 1. Factor safety F. f c. F. p FS 1
