Chapter 5 - Slope Stability

7/24/2019 Chapter 5 - Slope Stability

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CHAPTER 5

SLOPE STABILITY

Canals

Dam

Highway


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Introduction

Slopes in soils and rocks are exist innature and in manmade structures!

"anmade structure# Hi$%&a's( dams(canals

Natural slope


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Question related to slopestability)! *%at t'pes o+ slope +ailure are

common in soils,

-! *%at +actors pro.oke slope +ailures,

/! *%at met%ods o+ anal'sis are usedto estimate t%e +actor o+ sa+et' o+ aslope

0! *%at are t%e assumptions o+ t%e.arious met%ods o+ anal'sis

Natural slope


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Some types of slopefailure

Natural slope


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Factor of safety

Natural slope

Factor of safety with respect to strength, FSs=d

f

f= average shear strength of the soild= average shear stress develop along the potential failure surface

The usual range of factor of safety is!" to !"

Factor of safety with respect to cohesion, FSc#= '

'

dc

c

Factor of safety with respect to friction, FSc#= 'tan

'tan

d

'' tan'

'tan''

dd

sc

cFS

++

=

Common slope,

FS !$

Dam, FS !%


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Stability of Innite slopewithout seepage

Factor of safety, FS =

tan

'tan

tancos

'2

+H

c

bili f i l


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Stability of Innite slopewith seepage

Factor of safety, FS =

tan

'tan'

tancos

'2

satH

c+

i h l f il


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with plane failuresurface- Culmanns

method

&ssumption' (lane failure surface

i h l f il


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with plane failuresurface- Culmanns

method ( )

=

'

''

cossin

cos1

4 d

dd

Hc

Factor of safety with respect to cohesion, FSc#=dc

c

'

'

To calculate the ma)imum height of the slope, c#d=c# and #d= #

( )

=

'cos1'cossin'4

cHcr


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na ys s o n e s ope wcircularly cylindrical failuresurface- General


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na ys s o n e s ope wcircularly cylindrical failuresurface- General

*ethod of analysis can +e divided into two maor classes'

! *ass procedure - consider the mass a+ove the surface of sliding

. suita+le for homogenous soil

/! *ethod of slices - the soil a+ove the surface of sliding is divided intoa num+er of vertical parallel slices!

. can +e used for nonhomogenous soil

. pore water pressure can +e ta0e into consideration


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ass !rocedure of StabilityAnalysis

Slopes in Homogeneous clay soil with = 1 2undrained condition3

. 4alid for saturated clay and undrained condition only


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*oment of driving force a+out 5, *d= 6l . 6/l/

*oment of resisting force a+out 5, *7= c

dr/

For e8uili+rium, *7= *d, so

cdr/= 6l . 6/l/

2

2211

r

lWlWcd

=

d

u

d

f

s

c

c

c

FS ==


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& num+er of trials should +e made to find the minimum value of F!5!S!

Fellenius 29/:3 and Taylor 29$:3 introduce the e8uation to calculate

the critical circles corresponding to lowest value of F!5!S!'

Hmcd = or mH

cd =

6here, cdis developed cohesion

is soil unit weight H is height of the slope

m is the sta+ility num+er


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Hmcd = or mH

cd =

HDHD /=

d

us

c

cFS =


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How to determine of the location of the critical toe circle

a3 Slope angle, ; "$


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How to determine of the location of the critical toe circle

a3 Slope angle, < "$


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How to determine of the location of the critical midpoint circle

a3 Slope angle, < "$


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"#ample

& cut slope in saturated clay ma0es an angle of 1owith the hori>ontal'

a3 Determine the ma)imum depth up to which the cut could +e made!

&ssume that the critical surface for sliding is circularly cylindrical!6hat will +e the nature of the critical circle?

+3 7efering to part a, determine the distance of the point of intersection

of the critical failure circle from the top of the edge of the slope!

c3 How deep should the cut +e made if a factor of safety of / against

sliding is re8uired?


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ethod of slices

- &C is an arc of a circle of trial failure surface!- The soil a+ove is divided into several vertical slices

nnr wN cos=

( ) [ ] nndr LcFS

LT +== 'tan''1


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ethod of slices

( )

+=nn

nnn

W

WLcFS

sin

'tancos'

( )' ( cos ) tan '

sin

n n n n n

n n

c L W u LFS

W

+ =

1r' slope

Considerin$*ater le.el

For e8uili+rium, the moment of the driving force a+out 5 e8uals to moment of

the resisting force a+out 5!

rLL

Wc

FSrW n

n

nnnn

+= 'tancos'1sin

$ishops Simplied ethod of


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$ishops Simplied ethod ofslices

- *ore accurate solution than ordinary method of slices!- @n this method the effect of forces on the sides of each slice is considered!

E2uili3rium +orce

1+= nn TTT

1+= nn PPP

FS

Lc

FSNT nrr

+

=

''tan



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( )

++=

nn

n

nn

W

mTWbcFS

sin

1'tan'tan'

)(

FS

m nnn

sin'tan

cos)( +=where

@f T =1

( )

+=

nn

n

nn

W

m

Wbc

FS

sin

1'tan'

)(



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( )

+

=nn

n

nn

W

m

Wbc

FS

sin

'tan'

)(

Slope with ground water

level

Dry slope

( )

+

=nn

n

nnnn

W

m

buWbc

FS

sin

'tan)('

)(



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$ishop s Simplied ethod ofslices

Simplified figure in determination of m2n3


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Spencers solution

#amp


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#ampe %

#amp


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#ampe %

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Chapter 5 - Slope Stability