Post on 17-Oct-2021
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
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Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Module 5:
Lecture -1 on Stability of Slopes
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Stability analysis of a slope and finding critical slipsurface;
Sudden Draw down condition, effective stress andtotal stress analysis;
Seismic displacements in marginally stable slopes;
Reliability based design of slopes,
Methods for enhancing stability of unstable slopes.
Contents
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Contents of this lecture
Types of slopes
Failure types
Causes of slope failures
Analysis of slopes by using LE methods
Comparison
Concluding remarks
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Application of shear strength theory
Earth pressure theories
Stability analysis of slopes
Infinite slopes
Slope that extends over along distance and theconditions remain identicalalong some surface orsurfaces for quite somedistance.
Finite slopes
Slope that connect land at oneelevation to land that is not faraway but is at differentelevation.
Can also exist in nature and man-made.
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Slopes
Natural♦Hill side and valleys
♦Coastal and river cliffs
Man-made♦ Cuttings and embankments for
highways and rail roads
♦ Earth and ash pond dams
♦ Temporary excavations
♦ Waste heaps (landfill slopes)
♦ Landscaping for site development
Type of slopes
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
R
R
Types of slope failure
Circular
Non-circular
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Translational slip
Types of slope failure
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Types of slope failure
Compound slip
Rigid stratum
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
F
N
W
µsN
N
WF1
µkN
Block movement
As long as µsN > F --- block is said to be stationary
Resisting force FR : µsN
Disturbing force FD : F F1
D
R
FFFS =
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Causes of slope failure
Gravity
Seepage
Earthquake
Erosion
Geological features
Construction activities
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Typical slope failures
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Courtesy: Geological natural hazardsSeptember 15, 2004
Typical slope failures
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Landslide damage adjacent to a residential structure
Courtesy: North Carolina Geological Survey
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Typical slope failures
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Highway slope failure at Krishnabhir, Tribhuwan highway Nepal (Aryal, 2003)
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
(After Loher et al. 2002)
Typical sacrificial slope failure in highway embankment
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Uttarakand (2013)
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Landslide in Chongqing and Hong Kong
After Kwong et al. 2004
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Effect of raising GWT
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Aerial view of Waste slide on March 16, 1996 [USA]
Lateral displacements upto 275 m and vertical displacements upto 61 m
1.2 million m3 of waste
After Eid et al. (2000)
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Aerial view of landfill on Feb. 6, 1996
Stark et al. (2000)
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Slope FailureSlope failures depend on
• Soil type• Soil stratification• Ground water• Seepage• Slope geometry
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Types of Slope Failure
Translational Slide• Failure of a slope along
a weak zone of a soil
• Sliding mass travelslong distances beforecoming to rest.
• Common in coarse-grained soils.
Thin layer of weak soil
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Rotational slide• Common in homogenous fine-grained soil
• It has its point of rotation on an imaginary axis parallel to the slope
• There are three types of rotational failure:– Base slide– Toe slide– Slope slide
Types of Slope Failure
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Base slide
• Occurs by an arc engulfing the whole slope.
• A soft soil layer resting on a stiff layer of soil is prone to base slide
Rotational slide
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Toe slide
• The failure surfacepasses through thetoe of the slope.
Rotational slide
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Slope slide
• The failure surface passes through the slope
Rotational slide
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Flow slide• Occurs when internal and
external conditions force asoil to behave as a viscousfluid and flow down,spreading in all directions.
• Multiple failure surfaces occurand change continuously asflow proceeds.
• Occurs in dry and wet soils.
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Block and wedge slide• Occurs when a soil mass is shattered along joints, seams,
fissures and weak zones by forces emanating from adjacentsoils.
• The shattered mass moves as blocks and wedges down theslopes.
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
FallsSimple detachment of rock mass from its parent body The process is only gravity governed.
Rock falls
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Causes of Slope Failure
• Erosion
Water and windcontinuously erodeslopes.
Erosion changes thegeometry of the slopes,resulting in a slopefailure or a landslide. Steepening of slope by erosion
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
• Erosion:
Rivers and streamscontinuously scour theirbanks undermining theirnatural or man-madeslopes.
Scour by rivers and streams
Causes of Slope Failure
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
• Rainfall:
Long periods of rainfallsaturate, soften, anderode soils.
Water enters intoexisting cracks and mayweaken underlying soillayers, leading to failure,(for example, mud slides)
Causes of Slope Failure
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
• Earthquakes: Earthquakes induce dynamic forces especiallydynamic shear forces that reduce the shear strengthand stiffness of the soil.
Causes Of Slope Failure
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
• Earthquakes:Pore water pressures in saturated coarse-grainedsoils could rise to a value equal to the total meanstress and cause these soils to behave like viscousfluids. This phenomenon is known as dynamicliquefaction. Structures founded on these soils wouldcollapse.
The quickness in which the dynamic forces areinduced prevents even coarse–grained soils fromdraining the excess pore water pressures. Thus, failurein a seismic event often occurs under undrainedconditions.
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
• Geological features:
Many failures commonly result from unidentifiedgeological features.
Soil stratification
Causes of Slope Failure
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
•External Loading:
Loads placed on thecrest of a slope add togravitational load andmay cause slopefailure.
Overloading at the crest of the slope
Causes of Slope Failure
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
• Construction activities:Construction activities nearthe toe of an existing slopecan cause failure becauselateral resistance is removed.
Slope failures due toconstruction activities isdivided into two cases:
• Excavated slopes.• Fill slopes.
Excavation at toe of the slope
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
• Excavated slopes:
When excavation occurs, the total stresses arereduced and negative pore pressures aregenerated. With time the negative pore pressuresdissipate, causing a decrease in effective stressesand consequently lowering the shear strength of thesoil. If slope failures occur, they take place afterconstruction is completed.
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Fill slopes:Fill slopes are common in embankmentconstruction. If the foundation soil is saturated, thenpositive pore water pressures are generated from theweight of the fill and the compaction process.
The effective stress decrease and consequentlyshear strength decreases. Slope failures in slope arelikely to occur during or immediately afterconstruction.
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Factors that contribute to high shear stress:Factors contributing to instability of soil slopes
i) Removal of lateral supporta) Erosion – bank cutting by streams and riversb) Human agencies – cuts, canals, pits, etc.,
ii) Surchargea) Natural agencies – Weight of snow, ice and rain waterb) Human agencies – Fills, buildings, etc.,
iii) Transitory earth stresses – Earthquakesiv) Removal of underlying support
a) Sub aerial weathering – solutioning by ground waterb) Subterranean erosion – pipingc) Human agencies – mining
v) Lateral pressures – water in vertical cracks; freezing water in cracks; root wedging After Gray and Leiser (1982)
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Factors contributing to instability of soil slopesFactors that contribute to low shear strengthi) Initial state
a) Composition – inherently weak materialsb) Texture – loose soils, metastable grain structuresc) Gross structure – faults, joining, bedding, planes, varying, etc.,
ii) Changes due to weathering and other physicochemical reactions
- Frost action and thermal expansion, Hydration of clay minerals,Drying and cracking, Leaching
iii) Changes in inter-granular forces due to pore water
- Seepage pressure of percolating ground water, loss in capillarytension upon saturation, buoyancy in saturated state.
ii) Changes in structure – Fissuring of pre-consolidated clays due torelease of lateral restraint; Grain structure collapse upon disturbance.
After Gray and Leiser (1982)
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Slope Stability AnalysisGeneral Assumptions: The failure can be represented as a two dimensional
problem.
The sliding mass moves as a rigid body and thedeformations of the sliding mass has no significanteffects on the analysis.
The properties of soil mass are isotropic and shearresistance along failure surface remains sameindependent of the orientation of the failure surface.
The analysis is based on limit equilibrium method.
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Infinite Slope Stability Analysis
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Examples of slopes which can be infinite slopes
Ore or sand stock piling by dropping from a chute
Embankment formed by end dumping from a truck
Natural slopes formed in granular materials where thecritical failure mechanism is shallow sliding or surfaceravelling
Natural slopes formed in cohesive soils with great extent orweak cohesive material on ledge
Slopes in residual soils where a relatively thin layer ofweathered soil overlies a firmed soil or rock
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Analysis of infinite slopesAssumptions:
Soil is homogenous.
The stress and soilproperties on every verticalplane are identical; On anyplane parallel to the slopestresses and soil properties areidentical.
⇔ Failure in such slope takes place due to sliding of the soilmass along a plane parallel to the slope at a certain depth.
Failure surface
b β
zhw
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Analysis of infinite slopes
Weight of segment ABCD W = γzb(1)z
Db
W
B
C
A
N
T
Tangential stress τ down the slope
ββγββγτ cossin
cos/sin z
bzb
==
Normal stress σ within the segment
βγββγσ 2cos
cos/cos z
bzb
==
Pore water pressure u on the slip surface
( ) βγ 2coswwhzu −=
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Analysis of infinite slopesNormal effective stress σ ′ =
Shearing strength τf at the base of segment
φστ ′′+′= tancf
For the general case:
ττ fFS =
( )( ) βγγγ
βγβγ2
22
cos
coscos
www
ww
hzzhzz
+−=
−−=
Factor of safety can bedefined as:
( )ββγ
γγγβφcossin
costan 2
zhzzcFS www +−′+′
=
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Analysis of infinite slopesSpecial cases
For the critical case FS = 1 ⇔ β = φ′
zhc w ==′ ;0
⇔ FS of an infinite slope with a cohesion-lesssoil is independent of the depth of failureplane.β
φtantan ′
=FS
Case - A Dry Cohesion-less soil
Mohr failure envelope
β
φ′
σ
τ
(σ, τ)
(σf, τf)
For β < φ′ ⇒ τ < τf⇔ Slope is stable
(independent of depth of slope)
For β > φ′ ⇒ τ > τf Slope wouldhave already failed at all depths.
⇒ Slope is just stable
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Analysis of infinite slopesCase – B
βγφγ
tantan ′′
=FS
0;0 ==′ whcSaturated cohesion-less slope
Factor of safety of a saturated cohesion-less slope is about ½ for a slope without saturation.
Case - C For a c - φ soil 0=wh
( )ββγγβφ
cossincostan 2
zzcFS′′+′
=
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Analysis of infinite slopesCase - C For a c - φ soil 0=wh
( )ββγγβφ
cossincostan 2
zzcFS′′+′
=
Assuming FS = 1 z = hc
′′
−
′=
φγγβγ
β
tantan
sec2chc
β
φγγβ
γ 2sec
tantan
′′
−=
′
chc
Stability number
⇔ For c-φ soils there is a limiting depth for stability
Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay
Analysis of infinite slopes
For β1 < φ′ ⇒ τ < τf
For β2 > φ′ ⇒ τ = τf
The depth at which τ = τf is called the critical depth hc
Mohr failure envelope
β1
φ′
σ
τ
(σ, τ)
(σf, τf)
For this depth slope is just stable
β2
τ = τf
Case - C For a c - φ soil