19 - NPTEL

Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

19


Module 5:

Lecture -1 on Stability of Slopes


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


Contents of this lecture

Types of slopes

Failure types

Causes of slope failures

Analysis of slopes by using LE methods

Comparison

Concluding remarks


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.


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


R

R

Types of slope failure

Circular

Non-circular


Translational slip




Compound slip

Rigid stratum


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 =


Causes of slope failure

Gravity

Seepage

Earthquake

Erosion

Geological features

Construction activities


Typical slope failures


Courtesy: Geological natural hazardsSeptember 15, 2004



Landslide damage adjacent to a residential structure

Courtesy: North Carolina Geological Survey


Highway slope failure at Krishnabhir, Tribhuwan highway Nepal (Aryal, 2003)


(After Loher et al. 2002)

Typical sacrificial slope failure in highway embankment


Uttarakand (2013)


Landslide in Chongqing and Hong Kong

After Kwong et al. 2004


Effect of raising GWT


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)


Aerial view of landfill on Feb. 6, 1996

Stark et al. (2000)


Slope FailureSlope failures depend on

• Soil type• Soil stratification• Ground water• Seepage• Slope geometry


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


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


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


Toe slide

• The failure surfacepasses through thetoe of the slope.

Rotational slide


Slope slide

• The failure surface passes through the slope

Rotational slide


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.


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.


FallsSimple detachment of rock mass from its parent body The process is only gravity governed.

Rock falls


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


• Erosion:

Rivers and streamscontinuously scour theirbanks undermining theirnatural or man-madeslopes.

Scour by rivers and streams



• Rainfall:

Long periods of rainfallsaturate, soften, anderode soils.

Water enters intoexisting cracks and mayweaken underlying soillayers, leading to failure,(for example, mud slides)



• Earthquakes: Earthquakes induce dynamic forces especiallydynamic shear forces that reduce the shear strengthand stiffness of the soil.

Causes Of Slope Failure


• 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.


• Geological features:

Many failures commonly result from unidentifiedgeological features.

Soil stratification



•External Loading:

Loads placed on thecrest of a slope add togravitational load andmay cause slopefailure.

Overloading at the crest of the slope



• 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


• 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.


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.


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)


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)


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.


Infinite Slope Stability Analysis


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


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


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 −=


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 +−′+′

=


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


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′′+′

=


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


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

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