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SLOPE ANALYSIS IN FLAT PLANE

a. INFINITE SLOPE

Condition without seepage

Figure 2.1. Infinite sope without seepage

Infinite sope !eans that sope ength is "er# arge $o!pare to the depth %&'. Let(

the width L( hen$e for$es on the two "erti$a# pane are si!iar. Steps deri"ing the

fa$tor of safet# as foows )

*eight of soi a+$d

'1%LHW =

*here

W , weight of soi ee!ent a+$d %tones( -N'

, unit weight of soi %T!/'

L , soi width %!'

H , soi depth %!'

W$an +e di"ided into

LHCosWCosNa == %1.0'

LHSinWSinTa == %1.'

Slip plane

Width perpendicular the paper in 1 unit

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'%2 tgtgCos

cHc

= %1.13'

For granuar soi( $ohesion , 7

tg

tgFs= %1.1;'

Fro! e5uation 1.1;( it $an +e stated that infinite sope on the granuar

soi( as ong as < ,the sope in safe %sta+e'( +e$auseFs< 1.

For soi with , 7( at $riti$a $onditionFs, 1(

tgCosH

c 2= %1.27'

*here

H

c

, sta+iit# nu!+er( that is para!eter whi$h $o!paring the

$ohesion $o!ponent fro! shear resistan$e with Hre5uired to

-eep the sta+iit#Fs, 1

Fs , safet# fa$tor

c , $ohesion %T!2'

, fri$tion ange %o'

, ange of sope %o'

Problem:

Sope has soi data as foows )

c , 13 -N!2

, 21o

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, 13. -N!/

Condition without pore water pressure

a) LetH, 6! and , 20o( $a$uate safet# fa$tor fro! sip faiure

b) Let , 23o

( $a$uateH!a8i!u! forFs, 1

Solution)

a'

tg

tg

tgHCos

cFs +=

2

17/.120

21

20206.13

132

=+=tg

tg

xtgxCosxFs

b)H

!a8 atFs

, 1

H

at $riti$a $ondition ,Hc

mtgtgxxCostgtgCos

cHc ;.6

'2123%23.13

13

'% 22

=

=

=

E8er$ise)

=se the pre"ious soi data( et c, 7(

a) >is$uss how the sope $ondition if , 20o

b) If , 7( deter!ine safet# fa$tor fro! sip faiure

Condition with seepage

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Figure 2.2. Infinite sope with seepage

The water wi affe$t shear strength of soi as foows )

tguc '% += %1.21'

Or

tgc ?+= %1.22'

*here

, nor!a effe$ti"e stress %-N!2'

u , pore water pressure %-N!2' 2wHCosu=

w , unit weight of water %-N!/'

Steps in deter!ining the safet# fa$tor )

*eight of soi a+$d

'1%satLHW = %1.2/'

*here

W$an +e di"ided into

satLHCosWCosNa ==

%1.2:'

Slip plane

Flow line

Equipotential line

Width perpendicular the paper in 1 unit

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satLHSinWSinTa == %1.20'

4ea$tion due to WisRthat e5ua to Win opposite dire$tion.R$an +e

di"ided into )

satLHCosWCosRCosNr === %1.2'

satLHSinWSinRSinTr === %1.23'

Tota nor!a stress and shear for$e at the A pane in e5uii+riu! is

2

'1'%%satHCos

CosL

Nr== %1.2;'

SinsatHCosCosL

Trd ==

'1'%%%1.26'

And $an +e e8pressed with

dtgcddtgucdd ?'% +=+= %1./7'

or

dtgwHCossatHCoscdd '% 22 +=

dtgHCoscdd '?% 2+=

Safet# fa$tor $an +e deter!ined +# the e5uation of

sattg

tg

tgsatHCos

cFs

?2

+= %1./1'

For granuar soi( $ohesion , 7

sattg

tgFs

?=

%1./2'

For soi with , 7

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tgsatHCos

cFs

2=

%1.//'

Problem:

Sope has soi data as foows )

c , 1; -N!2

, 27o

=21o

sat , 22 -N!/

H , 17 !

$a$uate safet# fa$tor fro! sip faiure

Solution)

3.721@2227@12

21@21@17@221;?

22 =+=+=

tgtg

tgCossattgtg

tgsatHCoscFs

+. FINITE SLOPE

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