4_chapter 4 classic methods of slope stability analysis

40
CHAPTER FOUR Classic methods of slope stability analysis Overview Historically, the stability of slopes has been assessed by methods of calculation `by hand' ± before the advent of computers, spreadsheets and bespoke software packages. The most widely accepted of these classic methods are described below. Principally, these are by Bishop (1955) and Janbu (1957). The chore of calculation `by hand' was speeded up by the introduction of stability coef®cients and design charts by Bishop and Morgenstern (1960) and Hoek and Bray (1977). Computer programs have automated the methods of Bishop and Janbu and others, but not replaced them. On the contrary, these classic methods continue, except now they are in computer-automated form so that numerous trial slip and slope geometries can be rapidly evaluated. Wider accessibility to (`main frame') computing in the late 1950s to the early 1960s gave rise to methods of analysis that could only be solved by computer-automated numerical methods, principally by Little and Price (1958) ± at that time, this was thought to be the most complicated program ever written for a computer of British origin (Bromhead, 1985) ± and Morgenstern and Price (1965, 1967). Now commercial computer programs for slope stability analysis are widely available and some can link with other programs for stress distribution and for seepage (e.g. see SLOPE/ W Student Edition CD supplied with this book). While classic methods have been automated by computer and new computer methods have been devised, it is still the responsibility of the design engineer to ensure that ground properties (inputs) and design predictions (outputs) pass the sanity test! Indeed, it is the explicit duty of the engineer to check the outputs of computer programs by `hand' calculation, i.e. in an immediately obvious and transparent way without the aid of a `black box' (or mysterious) computer program ± although perhaps a computer spreadsheet may be permitted! These checks `by hand' will use the same classic methods described below, many of which are still used to this day by commercial software packages. 77

Upload: saxlamag

Post on 07-Nov-2014

91 views

Category:

Documents


7 download

DESCRIPTION

geotechnical

TRANSCRIPT

Page 1: 4_Chapter 4 Classic Methods of Slope Stability Analysis

!"#$%&' ()*'

!"#$$%& '()*+,$ +- $"+.( $)#/%"%)0 #1#"0$%$

!"#$"%#&!"#$%&"'())*+ $,- #$(.")"$* %/ #)%0-# ,(# .--1 (##-##-2 .* 3-$,%2# %/

'()'4)($"%1 5.* ,(126 7 .-/%&- $,- (28-1$ %/ '%304$-&#+ #0&-(2#,--$#

(12 .-#0%9- #%/$:(&- 0('9(;-#< =,- 3%#$ :"2-)* (''-0$-2 %/ $,-#-

')(##"' 3-$,%2# (&- 2-#'&".-2 .-)%:< >&"1'"0())*+ $,-#- (&- .* ?"#,%0

@ABCCD (12 E(1.4 @ABCFD< =,- ',%&- %/ '()'4)($"%1 5.* ,(126 :(# #0--2-2

40 .* $,- "1$&%24'$"%1 %/ #$(.")"$* '%-/G'"-1$# (12 2-#";1 ',(&$# .* ?"#,%0

(12 H%&;-1#$-&1 @ABIJD (12 !%-9 (12 ?&(* @ABFFD< K%304$-& 0&%;&(3#

,(8- (4$%3($-2 $,- 3-$,%2# %/ ?"#,%0 (12 E(1.4 (12 %$,-&#+ !"# $%#

&'()*+', #-'.< L1 $,- '%1$&(&*+ $,-#- ')(##"' 3-$,%2# '%1$"14-+ -M'-0$

1%: $,-* (&- "1 '%304$-&N(4$%3($-2 /%&3 #% $,($ 143-&%4# $&"() #)"0

(12 #)%0- ;-%3-$&"-# '(1 .- &(0"2)* -8()4($-2<

O"2-& (''-##".")"$* $% @53("1 /&(3-6D '%304$"1; "1 $,- )($- ABCJ# $% $,-

-(&)* ABIJ# ;(8- &"#- $% 3-$,%2# %/ (1()*#"# $,($ '%4)2 %1)* .- #%)8-2 .*

'%304$-&N(4$%3($-2 143-&"'() 3-$,%2#+ 0&"1'"0())* .* P"$$)- (12 >&"'-

@ABCQD 7 ($ $,($ $"3-+ $,"# :(# $,%4;,$ $% .- $,- 3%#$ '%30)"'($-2 0&%;&(3

-8-& :&"$$-1 /%& ( '%304$-& %/ ?&"$"#, %&";"1 @?&%3,-(2+ ABQCD 7 (12

H%&;-1#$-&1 (12 >&"'- @ABIC+ ABIFD< R%: '%33-&'"() '%304$-& 0&%;&(3#

/%& #)%0- #$(.")"$* (1()*#"# (&- :"2-)* (8(")(.)- (12 #%3- '(1 )"19 :"$,

%$,-& 0&%;&(3# /%& #$&-## 2"#$&".4$"%1 (12 /%& #--0(;- @-<;< #-- SPL>TU

O S$42-1$ T2"$"%1 KV #400)"-2 :"$, $,"# .%%9D<

O,")- ')(##"' 3-$,%2# ,(8- .--1 (4$%3($-2 .* '%304$-& (12

1-: '%304$-& 3-$,%2# ,(8- .--1 2-8"#-2+ "$ "# #$")) $,- &-#0%1#".")"$* %/

$,- 2-#";1 -1;"1--& $% -1#4&- $,($ ;&%412 0&%0-&$"-# @"104$#D (12

2-#";1 0&-2"'$"%1# @%4$04$#D 0(## $,- #(1"$* $-#$W X12--2+ "$ "# $,-

-M0)"'"$ 24$* %/ $,- -1;"1--& $% ',-'9 $,- %4$04$# %/ '%304$-& 0&%;&(3#

.* 5,(126 '()'4)($"%1+ "<-< "1 (1 "33-2"($-)* %.8"%4# (12 $&(1#0(&-1$

:(* :"$,%4$ $,- ("2 %/ ( 5.)('9 .%M6 @%& 3*#$-&"%4#D '%304$-& 0&%;&(3 7

()$,%4;, 0-&,(0# ( '%304$-& #0&-(2#,--$ 3(* .- 0-&3"$$-2W =,-#-

',-'9# 5.* ,(126 :")) 4#- $,- #(3- ')(##"' 3-$,%2# 2-#'&".-2

.-)%:+ 3(1* %/ :,"', (&- #$")) 4#-2 $% $,"# 2(* .* '%33-&'"() #%/$:(&-

0('9(;-#<

22

Anar
Anar
Anar
Anar
Anar
Anar
Anar
Anar
Anar
Anar
Anar
Anar
Anar
Page 2: 4_Chapter 4 Classic Methods of Slope Stability Analysis

'($)*)+),-/0%))%12$3 #-' 4"++'44 %5 624-%(74 #-'%&8 9%5 4)%(' 4#*!2)2#8 *$*)8424:;

*$, 12#- 3%%, &'4")#4 %!#*2$*!)' 5&%. #-' &%"#2$' .'#-%, 9624-%(<

42.()2=',:; '55%&#4 1'&' .*,' #% ,'>')%( * 42.2)*& #-'%&8 *(()2+*!)'

#% 4)2,'4 12#- *$8 4-*(' %5 4)2( 4"&5*+'? @-' +-&%$%)%38 %5 #-' '*&)8

,'>')%(.'$#4 24 +%$5"4',; !"# *(('*&4 #% -*>' !''$ *4 5%))%14?

624-%(74 (*('& 1*4 (&'4'$#', *# * +%$5'&'$+' * 8'*& !'5%&' 2#

*(('*&', 2$ (&2$#? A'(*&*#' &'4'*&+-'4 )', B*$!" *$, C'$$'8 #%

#-' 4*.' &'4")# DC'$$'8 1%&E2$3 "$,'& 624-%( *# F.('&2*) G%))'3'H?

B*$!" ("!)24-', =&4#; 2$ IJKK; !"# 2$ *$ 2$+%&&'+# 5%&.; *$, C'$$'874

#-'424 *(('*&', #-' 5%))%12$3 8'*&? A"!4'L"'$#)8; B*$!" &'("!<

)24-', * +%&&'+#', 5%&. %5 #-' 'L"*#2%$4; !"# 2$ * 5%&. &')*#2>')8

2$*++'442!)' #% M$3)24- &'*,'&4? F$ #-' .'*$#2.'; 624-%( -*,

('&4"*,', N&2+'; 1-% -*, !''$ %$' %5 #-' *"#-%&4 %5 #-' =&4# 4#*!2)2#8

*$*)8424 +%.("#'& (&%3&*. D4'' O2##)' *$, N&2+'; IJKPH; #% #&8 #% (&%<

3&*. C'$$'874 'L"*#2%$4 5%& $%$<+2&+")*& 4)2(4? F# 1*4 #-'$ 5%"$,

#-*# #-' !*42+ 'L"*#2%$4 +%"), 32>' &24' #% $".'&2+*) (&%!)'.4

1-'$ '>*)"*#', #% -23- (&'+242%$ #-*# 1%"), $%# *(('*& *# 4)2,'<

&")' *++"&*+8 92?'? #% 12#-2$ *!%"# KQ *# !'4#:R -' *$, S%&3'$4#'&$

DS%&3'$4#'&$ *$, N&2+'; IJTK; IJTUH #-'$ ,'>')%(', * .%&' 4%(-24<

#2+*#', .'#-%, D*3*2$ *# F.('&2*) G%))'3'H? @-24 #2.'; #-'8 1'&'

4'+"&' 2$ #-' E$%1)',3' #-*# +%.()'V2#8 2$ +%.("#*#2%$ 1*4 $%

)%$3'& * !*& #% 12,'4(&'*, "4' %5 * .'#-%, !'+*"4' %5 #-' 3&%12$3

*>*2)*!2)2#8 %5 +%.("#'&4? B*$!" ,'>')%(', -24 .'#-%, 5"&#-'&; *$,

("!)24-', -24 3'$'&*)2W', (&%+',"&' %5 4)2+'4 2$ IJUX; *$, * $".!'&

%5 %#-'& .'#-%,4 *)4% *(('*&', 2$ (&2$# #-&%"3-%"# #-' )*#' IJTY4

*$, IJUY4?7

!"#$%&'( )*+,-.

=,-&- /%))%:# ( #433(&* "1 )-'$4&-N1%$- /%&3 %/ $,- 3-$,%2# %/ #)%0-

#$(.")"$* (1()*#"# '%33%1 $,&%4;,%4$ $,- ;-%$-',1"'() )"$-&($4&-<

.%/0+# 123#34$- 3+)0# %* 32*5Y-/-&&"1; $% Z";< [<A+ (##43- $,($ $,- #$&-##-# %1 $,- 8-&$"'() #"2-# %/ $,-

#)"'- (&- -\4() (12 %00%#"$-< Y-#%)8"1; /%&'-# 0(&())-) $% $,- #)%0- ;"8-

$,- 2"#$4&."1; /%&'- Z #"1 !< Y-#%)8"1; /%&'-# 1%&3() $% $,- #)%0- ;"8-

$,- &-#4)$(1$ 1%&3() /%&'- Z '%#!<

=,- /('$%& %/ #(/-$* (;("1#$ #)"2"1; "# $,-1

0 ! Y-#"#$"1; /%&'-

V"#$4&."1; /%&'-!Z '%#! $(1" "

Z #"1 !! $(1" "

$(1!

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

2<

Page 3: 4_Chapter 4 Classic Methods of Slope Stability Analysis

:,-1'-+ /%& )"3"$"1; -\4")".&"43+

!3(M ! " "

?@++- 3@A/#$,#5 3+)0# %* 32*5Y-/-&&"1; $% Z";< [<]+ '%1#"2-& ( #)"'- %/ :"2$, * (12 2-0$, ,< =,- .4%*(1$

:-";,$ %/ $,- #)"'- "#^

Z " ! *,# " ## " ! # $ #:%

=,- -//-'$"8- #$&-## 1%&3() $% $,- .(#- %/ $,- #)"'- "#^

$"1 ! *,# " '%#!

'%#!

*

=,- #,-(& #$&-## ()%1; $,- #)%0"1; .(#- %/ $,- #)"'- "#^

% ! *,# " #"1 !'%#!

*

=,- /('$%& %/ #(/-$* (;("1#$ #)"2"1; 3(* .- 2-&"8-2 (#

0 ! ,#" '%#] ! $(1" "

,# #"1 ! '%# !& :,-1'-

0 ! $(1" "

$(1!

R%$- $,($ $,- -M0&-##"%1 /%& /('$%& %/ #(/-$* /%& $,- /4))* #4.3-&;-2 #)%0-

"# "2-1$"'() $% $,($ /%& ( 2&* #)%0-<

W

!

023? [?I \'=$2#2%$ 4E'#+- 5%& * ,&8 4)%(' 2$ 4*$,

W "

a

d

!

#

023? [?] \'=$2#2%$ 4E'#+- 5%& * 5"))8 4"!.'&3', 4)%(' 2$ 4*$,

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

2@

Page 4: 4_Chapter 4 Classic Methods of Slope Stability Analysis

.#/%G%*H*%I# 3+)0#J ! K L 2*2+-3%3Y-/-&&"1; $% Z";< [<_+ '%1#"2-& ( #)"'- %/ :"2$, ! (12 2-0$, W< =,- 2"#$4&.N

"1; /%&'- "# #W! #"1 !< =,- &-#$%&"1; /%&'- "#

44*

'%#!

=,- /('$%& %/ #(/-$* (;("1#$ #)"2"1; "# $,-&-/%&-

0 ! 44#W '%#! #"1 !

a

z !

# = bulk unit weight

023? [?X \'=$2#2%$ 4E'#+- 5%& * 4'.2<2$=$2#' 4)%('; " ! Y *$*)8424

M!:;=4 =N8B<7=K%1#"2-& ( 1($4&() #)%0- "1 %8-&N'%1#%)"2($-2 P%12%1 ')(* 1-(& )"3"$"1;

-\4")".&"43<

=(9- W ! F 3+ 44 ! AJJ9>(+ # ! ]J9RU3_+ ! ! AJ! :,"', (&- $*0"'()

8()4-#< =,-1

0 ! 44#W '%#! #"1 !

! AJJ

]J & F & '%# AJ! #"1 AJ!

! [']

=,"# "# ( 1%1#-1#- /%& P%12%1 ')(* #)%0-# :,"', '(1 /(") ($ $,"# "1')"1(N

$"%1W =,"# '()'4)($"%1 #-&8-# $% "))4#$&($- ,%: "1(00&%0&"($- ( " ! J

(1()*#"# "# :,-1 (00)"-2 $% 1($4&() #)%0-#<

R%: '%1#"2-& ( 1($4&() #)%0- "1 #%/$ 1%&3())* '%1#%)"2($-2 R%&:-;"(1

')(*<

=(9- W ! _ 3+ 4" ! AJ9>(+ # ! AQ9RU3_+ ! ! AC!+ (# $*0"'() 8()4-#

/%& ( #)%0- (.%4$ $% /(")< R%: 0 ! J'F[<

@-24 +*)+")*#2%$ *3*2$ +%$=&.4 #-*# * " ^Y *$*)8424 4-%"), $%# !'

*(()2', #% *44'44 #-' 4#*!2)2#8 %5 * $*#"&*) 4)%(' 1-'#-'& 2$ *$ %>'&<

+%$4%)2,*#', =44"&', +)*8 %& * $%&.*))8<+%$4%)2,*#', 2$#*+# +)*8?

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

<A

Page 5: 4_Chapter 4 Classic Methods of Slope Stability Analysis

! K L 2*2+-3%3 O)$ "#$I%12+ 1@IJ *) I#*3%)* 1$21PX1 Z";< [<[+ $,- 2"#$4&."1; /%&'- "# A(]#_] #"1)( $(1)< =,- &-#$%&"1; /%&'- "#

44_(#"1)<

=(9"1; $,- '&"$"'() (1;)- %/ #)"2"1; (# )'&"$ ! [C!+ $,-1 _' ! [44(#<

`)$-&1($"8-)*+ (##43"1; ( #)"0 '"&')-+ $,- '%&&-#0%12"1; &-#4)$ :%4)2 .-

_' ! _'QC44(#< =,-#- 0&-2"'$"%1# :%4)2 .- 41#(/- "1 0&('$"'- .-'(4#-

&-() ')(* #%")# (&- :-(9 "1 $-1#"%1<

! K L 2*2+-3%3 O)$ "#$I%12+ 1@IJ &%I( I#*3%)* 1$21PY-/-& $% Z";< [<C< `##43- $,- 2-0$, %/ $-1#"%1 '&('9 \ ! _#(]+ /%))%:"1;

=-&a(;," @AB[_D<

=,- 2"#$4&."1; /%&'- "#

#_

[_' &

_'

]& #"1 [C!

=,- &-#$%&"1; /%&'- "#

44_'

]& A

#"1 [C!

`$ /(")4&- :,-1 0 ! A+ $,- '&"$"'() ,-";,$ "# _' ! ]'IF44(#< =,"# ;"8-# (

3%&- &-()"#$"' 0&-2"'$"%1 /%& $,- ,-";,$ %/ ( $-30%&(&* 8-&$"'() '4$ "1 ')(*<

H

H

tan $

$

023? [?[ \'=$2#2%$ 4E'#+- 5%& * >'&#2+*) !*$E; " ! Y *$*)8424; $% #'$42%$+&*+E

Hc

45˚

D = Hc/2

# = bulk unit weightsu = undrained shear strength

023? [?K \'=$2#2%$ 4E'#+- 5%& * >'&#2+*) !*$E; " ! Y *$*)8424; 12#- #'$42%$+&*+E

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

<B

Page 6: 4_Chapter 4 Classic Methods of Slope Stability Analysis

M!:;=4 =N8B<7=K%1#"2-& $,- 2"//-&-1$ (00&%(',-# $% (1()*#"1; $,- #,%&$ $-&3 #$(.")"$*

%/ ( 8-&$"'() .(19 "))4#$&($-2 "1 Z";< [<I<

K(#- @(D 3(* .- #433(&"a-2 (# /%))%:#<

IJ!^ V"#$4&."1; ! A] & AJ & C'FF[ & ]J & #"1 IJ!! CJJ9R

Y-#$%&"1; ! IJ & AA'CC ! IB_9R

0 ! IB_(CJJ ! A<_J

[C!^ V"#$4&."1; ! A] & AJ & AJ & ]J & #"1 [C! ! FJF9R

Y-#$%&"1; ! A['A[ & IJ ! Q[Q9R

0 ! Q[QUFJF ! A<]

_J!^ V"#$4&."1; ! A] & AJ & AF'_ & ]J & #"1 _J! ! QIC9R

Y-#$%&"1; ! IJ & ]J b A]JJ9R

0 ! A]JJ(QIC ! A<_B

Z%& '(#- @.D :- ,(8-^

Z%& ( 2&* #)%0-^

V"#$4&."1; ! C & F'C & ]J & #"1 [C! ! C_J9R

Y-#$%&"1; ! F'JF & IJ ! [<][9R

02&* ! [][UC_J ! J<QJ

45˚

45˚ 30˚60˚

10 m

10 m

10 m

10 m

5 m

5 m

Qw

4·24 m

(a)

(b)

(c)

# = 20 kN/m3

su = 60 kN/m2

023? [?T \'=$2#2%$ 4E'#+-'4 5%& 1%&E', 'V*.()' D*H *44".2$3 ,255'&'$#

*$3)'4 %5 4)2( ()*$'4; D!H #*E2$3 * [K! 4)2( ()*$' *$, * 1*#'&<=))',#'$42%$ +&*+E; D+H *44".2$3 4)2( ()*$' 24 #-' L"*,&*$# %5 * +2&+)'

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

<C

Page 7: 4_Chapter 4 Classic Methods of Slope Stability Analysis

.#/%G%*H*%I# 3+)0#J #Q#1I%"# 3I$#33 2*2+-3%3Y-/-& $% Z";< [<F< Z%& c%: 0(&())-) $% #)%0-+ (1 -//-'$"8- #$&-## (1()*#"#

;"8-# $,- /%))%:"1;<

S%") #$&-1;$, "# 4 ! + " ' $" $(1" "<

S,-(& #$&-## ! % ! #W #"1 !#A('%#!%

! #W #"1 ! '%# !

R%&3() #$&-## ! $ ! #W '%#!#A('%# !%

! #W '%#] !

>%&- :($-& 0&-##4&- ! " ! .W#: '%# ! '%#!

! .W#: '%#] !

=,- 1%&3() -//-'$"8- #$&-## %1 $,- .(#- %/ $,- #)"'- "#^

$" ! ## $.#1%W '%#] !

O,-1'- $,- /('$%& %/ #(/-$* (;("1#$ #)"2"1; "#

0 ! +" ' ## $.#1%W '%#] ! $(1" "

#W #"1 ! '%#!

Z%& ( :-$ #)%0- @$-1#"%1 '&('9 G))-2 :"$, :($-&D

O($-& /%&'- ! A] & C & C & AJ ! A]C9R

TM$&( 2"#$4&."1; ! A]C & #"1 [C! ! QQ<[ 9R

0:-$ ! [][(C_J ' QQ'[ ! J<IB

X$ '(1 .- #--1 $,($ $,- G))"1; %/ $,- $-1#"%1 '&('9 :"$, :($-& ,(# (

#";1"G'(1$ -//-'$ %1 #$(.")"$*<

Z%& '(#- @'D :- ,(8- @1%$"1; $,- '-1$&%"2 %/ ( \4(2&(1$ %/ ( '"&')-

&(2"4# ` "# )%'($-2 [`(_* /&%3 $,- '-1$&- %/ $,- '"&')-D^

`&-( ! *& AJ]([ ! FQ<C3]

>-&"3-$-& ! *& AJ(] ! AC<FA 3

=(9"1; 3%3-1$# ;"8-#^

V"#$4&."1; ! FQ'C & ]J & ['][ ! IICI<Q 9RU3

Y-#$%&"1; ! AC'FA & IJ & AJ ! B[][ 9RU3

0 ! B[][UIICI<Q ! A<[]

X1 #433(&* :- ,(8-^

'(#- @(D 0 ! A<_B @IJ!D+ A<]J @[C!D+ A<_B @_J!D<'(#- @.D 0 ! J'QJ @2&*D+ J<IB @:-$D

'(#- @'D 0 ! A'[]

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

<D

Page 8: 4_Chapter 4 Classic Methods of Slope Stability Analysis

X/ +" ! J+ $,- '&"$"'() #)%0- "# ;"8-1 .*

$(1!' !## $.#1% $(1" "

#

X/ "1 (22"$"%1 . ! A+ "<-< $,- :($-& $(.)- "# ($ $,- ;&%412 #4&/('-+ $,-1

$(1!' !#"

#$(1" "

X/ c%: "# ,%&"a%1$()+ ,%:-8-&+ $,-1

" ! #:W (12

0 ! A $ #:

# '%#] !

! "

$(1" "

$(1!

'%30(&-2 :"$,

0 ! A $ #:

#

! "

$(1" "

$(1!

/%& 0(&())-) c%: (12 +" ! J<

1 !

Seepage parallel to slope

Z

mZU#w

#z #z cos !

cos !

#z sin !

1

023? [?U \'=$2#2%$ 4E'#+- 5%& * 4'.2<2$=$2#' 4)%(' 12#- 4''(*3' (*&*))') #%

#-' 4)%('; '55'+#2>' 4#&'44 *$*)8424

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

<?

Page 9: 4_Chapter 4 Classic Methods of Slope Stability Analysis

8*%3)I$)0- )O 0#$/#2A%+%I-=,- -//-'$ %/ (1"#%$&%0* :"$, &-#0-'$ $% 0-&3-(.")"$* %1 $,- #$(.")"$* %/ (

)%1; #)%0- "1 ( /&"'$"%1() #%") @"<-< +" ! JD+ /%& ( '%12"$"%1 %/ #--0(;- 0(&())-)

$% $,- #)%0- #4&/('- (12 $,- :($-& $(.)- ($ $,- ;&%412 #4&/('- 3(* .-

(##-##-2 4#"1; $,- -\4($"%1 %/ =-))"1; @ABQQD^

0 ! (A $ ##:(#%! #-'] 2) $(1" "( $(1 2

M!:;=4 =N8B<7=Y-/-&&"1; $% Z";< [<Q+ $(9- # ! AB9RU3_+ +" ! ] 9>(< `##43- $,- #)%0-

"# %1 $,- 0%"1$ %/ #)"2"1;+ "<-< 0 ! A< O,($ "# $,- 8()4- %/ $,- (1;)- %/

#,-(&"1; &-#"#$(1'- :"$, &-#0-'$ $% -//-'$"8- #$&-##+ " "d

R%: $,- /('$%& %/ #(/-$* (;("1#$ #)"2"1; "#^

0 ! +" ' ## $.#1%W '%#] ! $(1" "

#W #"1 ! '%#!& :,-1'-

$(1" " ! ]F'J[C $ ]

IB'Q_Q

! J'_CQI

" " ! AB'F!

X/ +" ! J+ " " ! ]A']! (12 "/ W "# "1G1"$-+ " " ! ][']!<

1 m

6 m

12˚

u = #w ! 6 ! cos2 12˚

023? [?P \'=$2#2%$ 4E'#+- 5%& * 4'.2<2$=$2#' 4)%(' 12#- 4''(*3' (*&*))')

#% #-' 4)%('; 1%&E', 'V*.()'

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

<E

Page 10: 4_Chapter 4 Classic Methods of Slope Stability Analysis

:,-&-"1 ! ! A(#A ' E] $(1] 2%e E !##############

E!(Ef

$

+ :,-&- E! "# $,- ,%&"a%1$()

0-&3-(.")"$*+ (12 Ef "# $,- 8-&$"'() 0-&3-(.")"$*e 2 "# $,- #)%0- (1;)- (12

#:+ # (12 " " (&- (# 4#4())* 2-G1-2<

?* :(* %/ "))4#$&($"%1+ $,- 8(&"($"%1 %/ 0 :"$, E "# (# /%))%:# /%& 2 ! A[!(12 " " ! ]F!^

E ! A 0 ! A'J]

E ! AJ 0 ! A'CI

E ! ]J 0 ! A'F_

.+%0 1%$1+# 2*2+-3%3J ! ! L /#I()5R%$- $,($ $,- " ! J (1()*#"# "# (00&%0&"($- %1)* $% $-30%&(&* #,%&$ $-&3

-M'(8($"%1# :,-&- $,- 412&("1-2 %& #,%&$ $-&3 #$&-1;$, "# (##43-2 $%

.- '%1$&%))"1; #$(.")"$*< =,- #)"0 '"&')- " ! J 3-$,%2 "# %4$)"1-2 "1 Z";<

[<B :,-&- $,- #)%0- "# 2"8"2-2 "1$% '%18-1"-1$ #)"'-# (12 $,- /('$%& %/

#(/-$* "# $,- &($"% %/ $,- #43 %/ $,- &-#$%&"1; 3%3-1$# $% $,- #43 %/ $,-

2"#$4&."1; 3%3-1$#< S%+ &-/-&&"1; $% Z";< [<B+

0 ! `%

44)%

ZV

a

i

x

HDH

l

$

W = A# su

F

023? [?JC'8 4E'#+- 5%& #%#*) 4#&'44 *$*)8424 %5 * 4)%(' *44".2$3 * +2&+")*&

4)2( 4"&5*+'; .'#-%, %5 4)2+'4

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

<F

Page 11: 4_Chapter 4 Classic Methods of Slope Stability Analysis

R%$"1; $,($ V ! ` #"1)+ ) ! * #-') (12 Z ! (* ;"8-#

0 !%

44 #-')%

( #"1)

/%& -\4() #)"'- :"2$,#+ :,"', "# ( '%18-1"-1$ /%&3 /%& ,(12 '()'4)($"%1<

S%)4$"%1# (&- (8(")(.)- /%& #"30)- ;-%3-$&* (12 /%&^

" '%1#$(1$ 412&("1-2 #,-(& #$&-1;$, @=(*)%&+ AB_FD

0·19

0·18

0·17

0·16

0·15

0·14

0·13

0·12

0·11

0·10

0·091 2 3 4

i = 53˚

45˚

30˚

15̊

7·5̊

22·5 ˚ n = 3

2

1

0

nHH

DHi

Depth factor D

Sta

bilit

y nu

mbe

r N

= s

u/F#

H

023? [?IY @*8)%&74 +"&>'4 5%& 4#*!2)2#8 $".!'&4

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

<2

Page 12: 4_Chapter 4 Classic Methods of Slope Stability Analysis

" #,-(& #$&-1;$, "1'&-(#"1; )"1-(&)* :"$, 2-0$, /&%3 a-&% ($ ;&%412

#4&/('- @g".#%1 (12 H%&;-1#$-&1+ ABI]D<

C2-+)$R3 3)+@I%)*=,"# "# /%& #"30)- #)%0-# :"$, 1% #--0(;- (12 1% $-1#"%1 '&('9#< X$ "#

2-&"8-2 /&%3 #)"0 '"&')- (1()*#"# :"$, 44 '%1#$(1$ :"$, 2-0$,< Y-/-&&"1;

$% Z";< [<AJ+ #%)4$"%1# (&- -M0&-##-2 "1 $-&3# %/ ( 5#$(.")"$* 143.-&6 a

:,-&-^

a ! 44#_

/%& 0 ! A :,-1'- "1 0&('$"'-

0 ! 44a#_

/%& #)%0- (1;)-# )-## $,(1 C[!

X$ "# (28"#(.)- $% 4#- $,"# 3-$,%2 (# ( G&#$ (00&%M"3($"%1 /%& $%$() #$&-##

@" ! JD '(#-< S$(.")"$* 143.-&# /%& #)%0- (1;)-# ;&-($-& $,(1 C[! (&-

;"8-1 "1 =(.)- [<]<

;+)($ +1 7#0"+GH$ &*#G)$ -+G " ! A &#$(@AD /%& ! + C[!+ '&"$"'() '"&')-# (&- $%- '"&')-# (12 _+ ! 5#!%@]D /%& ! , C[!+ '&"$"'() '"&')-# (&- %/ ;&-($ 2-0$, (12_' "# "12-0-12-1$ %/ !

@_D /%& ! , C[! (12 \ *! ++ _' ! 5#!%<

M!:;=4 =N8B<7=.@AD =(9- - ! AJ 3+ 44 ! CJ9>(+ , ! ++ # ! ]J9RU3_<

Z%& ! , C[!+ 44(#_ ! J'AQ

0 ! CJ

J'AQ & ]J & AJ! A'_Q

Z%& ! ! BJ!+ 44(#_ ! J']I

0 ! CJ

J']I & ]J & AJ! A'BI

@]D =(9- 44 ! _J9>(+ # ! AQ9RU3_+ 0 ! A'_<

V-$-&3"1- _3(M /%& ! ! [C! (12 BJ! (12 /%& \ ! A (12 +< =,-

#%)4$"%1 "# #-$ %4$ "1 =(.)- [<A<

_3(M ! 44#a0

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

<<

Page 13: 4_Chapter 4 Classic Methods of Slope Stability Analysis

>%A3)* 2*5 B)$,#*3I#$* STUVWX=,- (##430$"%1# "1 Z";< [<AA (&-^

" $%$() #$&-## (1()*#"#

" #)"0 '"&')-

" 1% $-1#"%1 '&('9

R%$-^ 4#"1; ( 0)(1- /(")4&- #4&/('- /%& ! ! BJ! ;"8-#

_3(M ! [44#

! 44J']C#

"<-< _3(M ! _J

J']C & AQ & A'_! C'A]3

S$(.")"$* 143.-&# /%& ( " ! J (1()*#"# (&- 0&-#-1$-2 "1 =(.)- [<]<

R%$-^ a ! 44(#_

! ! #)%0- (1;)-

`##430$"%1# (&-^

" '%1#$(1$ 44" 1% $-1#"%1 '&('9#

" #)"0 '"&')- (1()*#"#<

@*!)' [?I b*)"'4 %5 #"(#! ! R

\ ! A \ ! +

! ! [C! J<AIC J<AQA_3(M F<FF3 F<JQ3! ! BJ! J<]I J<]I_3(M [<B_3 [<B_3

@*!)' [?] A#*!2)2#8 $".!'&4 5%& " ! J *$*)8424

! >)(1- K"&')-

BJ! J<]CJ J<]IA&

$%- '"&')-# (&- '&"$"'() '"&')-#FC! J<AB] J<]ABIJ! J<A[[ J<ABA[C! J<AJ[ J<AQA @J<AFJD, @J<AIID,,

_J! J<JIF J<AQA @J<ACID, @J<A_[D,,

AC! J<J__ J<AQA @J<A[CD, @J<JQQD,,

, $%- '"&')-#+ ,, $%- '"&')-# (12 \ ! A

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

<@

Page 14: 4_Chapter 4 Classic Methods of Slope Stability Analysis

! !! "#$%&'("#) *"#&'%*+ ,"-. /&0-. 1%23 4&%2 '- )%2!#/ (!%1'$& '00%256

"3'-"#) -2 ' #2%3'**+ $2#(2*"/'-&/ $*'+

! " /&0&#/( #$% 2# &7 8!- 2# (*20& '#)*&7 !!!'!7 '#/ 2# "7 -.& !#"-

,&").-9 " "( )":&# 8+

" " (!!")

" (!!'! ;# ",

"

! "

"*+, -,.. /*0!$# 1#2 3$4+5#!%54#6! 78495! :$4 !%10*;*%< #8=054!

!"#$%& %'()*+%<1 !!!'

! " =#>7 " " ;?@AB3>7 ,.'- (*20& ,2!*/ 8& %&C!"%&/ -2 )":&

" " ;#> 12% '# &5$':'-&/ $!--"#)D

E!8(-"-!-"#) "# -.& &C!'-"2# '82:& )":&( ( " ?#;FGH '#/ .&#$& -.&

%&C!"%&/ (*20& "( ;I"9

!"#$% &#'$!( )* ,"-+ (.& #"/$ ,+"*% %.0-.%%#-.0

+,

Page 15: 4_Chapter 4 Classic Methods of Slope Stability Analysis

=Q#1I%"# 3I$#33 3+%0 1%$1+# 2*2+-3%3J E%3()0 STUYYX=,- #)"0 '"&')- /(")4&- 3-',(1"#3 "# #,%:1 "1 Z";< [<A]@(D (12 $,- /%&'-#

('$"1; %1 (1 "12"8"24() #)"'- (&- #,%:1 "1 Z";< [<A]@.D< =,- 0%)*;%1 %/

/%&'-# "# ;"8-1 "1 Z";< [<A]@'D< h-* 0%"1$# $% 1%$- (&- (# /%))%:#<

" =,- /('$%& %/ #(/-$*

0 ! (8(")(.)- #$&-1;$,

#$&-1;$, &-\4"&-2 /%& -\4")".&"43

(12 $,4# $,- 3%.")"a-2 #$&-1;$, "# ;"8-1 .*

4 ! +"

0' #$1 $ "% $(1" "

0'

$ negative

$ positive

R

x

b

W

P

n

n

n + 1

n + 1

Xn + 1

En + 1

O

D C B

A

En

Xn

C

B

$

u#w

(a)

(b)

T = sf

W

P "

Xn –ul

Xn +1

En – En +1

%

P " tan &"

F

c" l

F

tan % = tan &"F

P = P " + ul

(c)

023? [?I] \'=$2#2%$ 4E'#+-'4 5%& '55'+#2>' 4#&'44 *$*)8424 %5 * 4)%('; .'#-%, %5 4)2+'4; D*H

4)2( +2&+)' 5*2)"&' .'+-*$24.; D!H 5%&+'4 *+#2$3 %$ *$ 2$,2>2,"*) 4)2+'; D+H 5%&+' (%)83%$

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

@B

Page 16: 4_Chapter 4 Classic Methods of Slope Stability Analysis

" ` ;-1-&()"a-2 (1()*$"'() #%)4$"%1 "# 1%$ 0%##".)- (12 ( 143-&"'() #%)4N

$"%1 "# &-\4"&-2 @?"#,%0 (12 H%&;-1#$-&1+ ABIJD<

" =% -#$"3($- 8()4-# %/ $1 ($ -(', 0%"1$ %1 /(")4&- #4&/('- :- 4#- $,-

#)"'-# 3-$,%2 %/ Z-))-1"4# @AB_ID+ G&#$ 04.)"#,-2 ($ $,- P(&;- V(3#

K%1;&-##<

Y-/-&&"1; $% Z";< [<A]+ $,- (1()*#"# $,-1 0&%'--2# (# /%))%:#< =,- 3%.")"a-2

#$&-1;$, "#

4 ! +"

0' #$1 $ "% $(1" "

0#['A%

=,- $%$() 1%&3() #$&-## ($ $,- .(#- %/ ( #)"'- "#

$1 ! N() #[']%

:,-1'- 4 ! +"

0' (#N()% $ ") $(1""

0#['_%

=,- #,-(& /%&'-+ 4+ ('$"1; %1 .(#- %/ #)"'- "# 4)< =(9"1; 3%3-1$# (.%4$ L

;"8-#+ /%& )"3"$"1; -\4")".&"43'

ZV !'

A` !'

4)` #['[%

/&%3 -\4($"%1 @[<_D

'

ZV ! `' +")

0' #N$ ")% $(1" "

0

"<-< 0 ! `%

ZV

'

+")' #N$ ")% $(1" "( )

#['C%

$% %.$("1 N &-#%)8- 1%&3() $% #)"0 #4&/('-

N ! #Z ' c$ $ c$'A% '%#)$ #M$ $ M$'A% #"1) #['I%

X1#-&$"1; -\4($"%1 @[<ID "1$% -\4($"%1 @[<CD ;"8-#

0 ! `%

ZV

'

-+")' $(1" "#Z '%#)$ ")%

' $(1" "(#c$ ! c$'A% '%#)$ #M$ $ M$'A% #"1)). #['F%

S"1'- $,-&- (&- 1% -M$-&1() /%&'-# %1 $,- #)%0-+ "$ /%))%:# $,($ $,- #43 %/

$,- "1$-&1() /%&'-# 34#$ .- a-&%+ "<-<'

#c$ $ c$'A% ! J #['Q(%'

#M$ $ M$'A% ! J #['Q.%

.4$ $,- $-&3# "1 c$ ! ! ! (12 M$ ! ! ! 2% 1%$ 2"#(00-(&e $,-* %1)* 2% #% "/

" " ! '%1#$(1$ (12 ) ! '%1#$(1$+ "<-< :- ,(8- #)"2"1; %1 ( 0)(1-<

L1- 0&%0%#()+ $,- i1"$-2 S$($-# ?4&-(4 %/ Y-')(3($"%1 @iS?YD #%)4$"%1+

"# $% (##43- $,($'

$(1" "(#c$ $ c$'A% '%#)$ #M$ $ M$'A% #"1)) ! J

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

@C

Page 17: 4_Chapter 4 Classic Methods of Slope Stability Analysis

=,-1+ 04$$"1; V ! ` #"1) ;"8-#

0 ! A%

Z #"1)

'

(+")' $(1" "#Z '%#)$ ")%) #['B%

=,"# /%&3 %/ #%)4$"%1 ;"8-# &-#4)$# %1 $,- '%1#-&8($"8- #"2-+ 0(&$"'4)(&)* /%&

2--0 '"&')-#<

X1 #"30)- $-&3#+ :- ,(8- &-#%)8-2 $,- $%$() :-";,$Z 1%&3() $% $,- #)"'-

(12 $,-1 #4.$&('$-2 $,- /%&'- 24- $% 0%&- :($-& 0&-##4&- ")+ #-- -\4($"%1

@[<BD<

Z%))%:"1; =(*)%&+ :- '%4)2 '%1#"2-& $,- .4%*(1$ :-";,$ %/ $,- #)"'- $%

.- Z $ "! (12 &-#%)8- $,"#+ "<-<

#Z $ "!% '%#) !Z '%#)$ " '%#))

#-')

!Z '%#)$ ") '%#] )

(12 %.$("1

0 ! A%

Z #"1)

'

(+")' $(1" "#Z '%#)$ ") '%#] )%) #['AJ%

=% (8%"2 $,-#- -&&%&#+ :- &-$4&1 $% -\4($"%1 @[<CD (.%8-< >4$

#N$ ")% ! N"+ (12 &-#%)8- 8-&$"'())* $% -)"3"1($- $,- M$ $-&3# (# /%))%:#^

Z ' c$ $ c$'A ! ") '%#)' N" '%#)' N" $(1" "

0#"1)' +

"

0) #"1)

$,-1

N" !Z ' c$ $ c$'A $ )(" '%#)' #+" #"1)(0%)('%#)' #$(1" " #"1)%(0 ) #['AA%

S4.#$"$4$"1; $,"# "1 -\4($"%1 @[<CD (12 04$$"1; ) ! ! #-')+ V ! ` #"1)

*"-)2#^

0 ! A%

Z #"1)

'

-+ "!' $(1" "(Z $ "!' c$ $ c$'A# %).

& #-')

A ' (#$(1" " $(1)%(0) #['A]%

=,"# '%18-&;-# &(0"2)*<

O"$, #4/G'"-1$ (''4&('* /%& 3%#$ 0&('$"'() 04&0%#-#+ :- '(1 $(9-

c$ $ c$'A ! J (12 %.$("1 $,- ?"#,%0N#"30)"G-2 #%)4$"%1 @?"#,%0 ABCCD<

Z%& $,- #0-'"() '(#- %/ -\4() #)"'- :"2$,#+ -\4($"%1 @[<A]D '(1 .- :&"$$-1

0 ! (%

+" ' #($ "% $(1" ")(.)%

( #"1)#['A_%

:,-&-

.) ! '%#) A ' $(1) $(1" "

0

! "

#['A[%

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

@D

Page 18: 4_Chapter 4 Classic Methods of Slope Stability Analysis

(12 ( "# $,- $%$() 8-&$"'() #$&-## ($ .(#- %/ #)"'-< f()4-# %/ .) (&- ;"8-1 "1

Z";< [<A_< =,"# /%&3 %/ #%)4$"%1 "# :-)) #4"$-2 $% ,(12 '()'4)($"%1#<

=,-&- (&- $,-&-/%&- $,&-- /%&3# %/ #%)4$"%1 :,"', ,(8- .--1 "1 '%33%1

4#-< =,-#- (&-^

" 0 ! A%

Z #"1)

'

(+")' $(1" "#Z '%#)$ ")%) 7 $,- iS?Y #%)4$"%1

" 0 ! A%

Z #"1)

'

(+")' $(1" "#Z '%#)$ ") '%#] )%) 7 $,"# "# 91%:1 (#

=(*)%&6# #%)4$"%1 @&-#%)8"1; .4%*(1$ :-";,$D (12 ;"8-# 8()4-# %/ 0

;&-($-& $,(1 $,%#- ;"8-1 .* -\4($"%1 @[<BD

" 0 ! (%

+" ' #($ "% $(1" ")(.)%

( #"1)7 $,"# "# $,- ?"#,%0N#"30)"G-2 /%&3

;"8-1 .* E(1.4+ ?j-&&43 (12 hj(-&1#)" @ABFAD<

` :%&9-2 -M(30)- 4#"1; $,- ?"#,%0N#"30)"G-2 /%&3 "# ;"8-1 "1

Z";< [<A[< =:% '(#-# \4%$-2 .* ?"#,%0 @ABCCD ;(8- 8()4-# %/ 0 (# #,%:1

"1 =(.)- [<_<

`''%&2"1; $% ?"#,%0 @ABCCD $,- 2"//-&-1'-# "1 0 .-$:--1 ?"#,%0N

&";%&%4# (12 ?"#,%0N#"30)"G-2 3-$,%2# (&- ;-1-&())* )-## $,(1 Ak<

'%$1@+2$ 2*2+-3#3 1)/02$#5O,"$3(1 (12 ?(")-* @ABIFD '%1#"2-&-2 /%4& '(#-#< =,- &-#4)$# (&- ;"8-1 "1

=(.)- [<[<

1·5

1·4

1·3

1·2

1·1

1·0

1·0

0·9

0·8

0·7

0·6

0·5

0·0 0·2 0·4 0·6 0·0

0·2

0·4

0·6

1·0

0·8

0·8

–50 –40 –30 –20 –10 10 20 30 40 50 60 700

$: degree

tan &"F

tan &"F

m$

023? [?IX B*$!"74 +"&>'4 %5 3) ! +%4)(I' ##*$) #*$" "(Z%)

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

@?

Page 19: 4_Chapter 4 Classic Methods of Slope Stability Analysis

!"#$%& %'()*+%

!"#$ %$&%'()*+, +-./01+ (2 +22+34"5+ 64)+66 .7.186"6 (2 . 61(0+ .669/"7# . 3")391.)

6:+.) 69)2.3+

!"#$%&' ( ,+(--., )%/0"&- "1 -+"*% -/(2.+./3 (4(+3-.-

)*

Page 20: 4_Chapter 4 Classic Methods of Slope Stability Analysis

.+%0 1%$1+# 2*2+-3%3J B)$,#*3I#$* 2*5 <$%1# STUVYX` 3%&- &";%&%4# /%&3 %/ #)"0 '"&')- (1()*#"# "# ;"8-1 .* H%&;-1#$-&1 (12

>&"'- @ABICD< =,"# "# 1%$ ( 5,(12 '()'4)($"%16 3-$,%2 .4$ "# '(&&"-2 %4$ .*

143-&"'() 3-(1# "1 ( '%304$-& 0&%;&(3< =,- 3-$,%2 "18%)8-# $,-

#%)4$"%1 %/ ( 0("& %/ #"34)$(1-%4# 0(&$"() 2"//-&-1$"() -\4($"%1# 7 %1- /%&

/%&'- -\4")".&"43 (12 %1- /%& 3%3-1$ -\4")".&"43 7 4#"1; ( $:%N8(&"(.)-

R-:$%1 (00&%M"3($"%1 3-$,%2< X$ "# :"2-)* &-;(&2-2 (# $,- 5.-1',3(&96

(;("1#$ :,"', %$,-& 3-$,%2# (&- 3-(#4&-2+ 0(&$"'4)(&)* '()'4)($"%1# 5.*

,(126< =,"# "# .-'(4#- $,-"& 3-$,%2 #($"#G-# .%$, /%&'- (12 3%3-1$

-\4")".&"43 ($ $,- #(3- $"3- :,-&-(# %$,-& 3-$,%2# 2% 1%$< O,"$3(1

(12 ?(")-* @ABIFD 4#-2 $,- H%&;-1#$-&1 (12 >&"'- 3-$,%2 (# ( 2($43 %/

3-(#4&-3-1$ "1 $,-"& &-8"-: (12 '%30(&"#%1 %/ 8(&"%4# '%304$-&

3-$,%2#<

=,- 9-* -)-3-1$# %/ $,- 3-$,%2 (&-^

" /(")4&- #4&/('- %/ ;-1-&() #,(0-

" $:%N2"3-1#"%1()"$*

" /%&'- (12 3%3-1$ -\4")".&"43

" '%304$-& (1()*#"#

" .(#-2 %1 (##430$"%1# "1$-&&-)($"1; $,- #)"'- #"2- /%&'-# c (12 M<

X$ '(1 .- #--1 $,($ )(&;- -&&%&# '(1 (&"#- :"$, $,- iS?Y 3-$,%2 (12 :-

&-'%33-12 $,-&-/%&- $,($ 4#- %/ $,- iS?Y 3-$,%2 #,%4)2 .- (.(12%1-2<

` 2"/G'4)$* :"$, $,- ?"#,%0N#"30)"G-2 3-$,%2 '(1 (&"#- "/!

A ' $(1)$(1" "

0

"

@*!)' [?X 0*+#%&4 %5 4*5'#8 5%"$, !8 #-' dA6`; 42.()2=', *$, &23%&%"4.'#-%,4 5%& #1% +*4'4; *5#'& 624-%( DIJKKH

TM(30)- iS?Y ?"#,%0N#"30)"G-2 ?"#,%0N&";%&%4#

A A<_Q A<C_ A<IJ7A<IA] A<C A<Q[ A<B]

@*!)' [?[ 0*+#%&4 %5 4*5'#8 5%"$, !8 #-' dA6`; 42.()2=', *$, &23%&%"4.'#-%,4 5%& 5%"& +*4'4; *5#'& Z-2#.*$ *$, 6*2)'8 DIJTUH

TM(30)- iS?Y ?"#,%0N#"30)"G-2 ?"#,%0N&";%&%4#

A A<[B A<IA A<CQ7A<I]] A<AJ A<__ A<][7A<]I_ J<II J<FJ7J<Q] J<F_7J<FQ[ A<A[ ]<JJ ]<JA7]<J_

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

@F

Page 21: 4_Chapter 4 Classic Methods of Slope Stability Analysis

.-'%3-# 1-;($"8- %& J< =,"# '(1 %''4& "/ ) "# 1-;($"8- (12 $(1" "(0 "# )(&;-<

X/!

A ' $(1)$(1" "

0

"

"# )-## $,(1 J<] $,- 4#- %/ %$,-& 3-$,%2# "# &-'%33-12-2<

.I2A%+%I- 1)#Z1%#*I3 O)$ #2$I( 3+)0#3?"#,%0 (12 H%&;-1#$-&1 @ABIJD+ 4#"1; $,- ?"#,%0N#"30)"G-2 3-$,%2+ ,(8-

0&%24'-2 ',(&$# %/ #$(.")"$* '%-/G'"-1$# /&%3 :,"', ( /('$%& %/ #(/-$* /%& (1

-//-'$"8- #$&-## (1()*#"# '(1 .- &(0"2)* %.$("1-2< =,-#- ',(&$# (&- ;"8-1 "1

`00-12"M A< =,- ;-1-&() #%)4$"%1# (&- .(#-2 %1 $,- (##430$"%1 $,($ $,-

0%&- 0&-##4&- " ($ (1* 0%"1$ "# ( #"30)- 0&%0%&$"%1 &4 %/ $,- %8-&.4&2-1

0&-##4&- #-< =,"# 0&%0%&$"%1 "# $,- 0%&- 0&-##4&- &($"% &4 ! "(#- (12 "#

&-;(&2-2 (# .-"1; '%1#$(1$ $,&%4;,%4$ $,- '&%##N#-'$"%1< =,"# "# '())-2 (

,%3%;-1-%4# 0%&- 0&-##4&- 2"#$&".4$"%1<

Z%& ( #"30)- #%") 0&%G)- (12 #0-'"G-2 #,-(& #$&-1;$, 0(&(3-$-&#+ $,-

/('$%& #(/-$*+ 0+ 8(&"-# )"1-(&)* :"$, $,- 3(;1"$42- %/ $,- 0%&- 0&-##4&-

-M0&-##-2 .* $,- &($"% &4 #4', $,($

0 ! .$ $&4

@#-- Z";< [<ACD :,-&- . (12 $ (&- $-&3-2 5#$(.")"$* '%-/G'"-1$#6 /%& $,-

0(&$"'4)(& #)%0- (12 #%") 0&%0-&$"-#< =,- 4#- %/ 0%&- 0&-##4&- &($"%+ &4+

3·00

2·00

1·00

0·00·0 0·2 0·4 0·6 0·8 1·0

ru

F

&" = 30˚c "

#IH

cot! = 3

D = 1·0

= 0·05

023? [?IK O2$'*& &')*#2%$4-2( !'#1''$ 5*+#%& %5 4*5'#8 Z *$, (%&' (&'44"&'

&*#2% &"; *5#'& 624-%( *$, S%&3'$4#'&$ DIJTYH

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

@2

Page 22: 4_Chapter 4 Classic Methods of Slope Stability Analysis

0-&3"$# $,- &-#4)$# %/ #$(.")"$* (1()*#"# $% .- 0&-#-1$-2 "1 2"3-1#"%1)-##

/%&3<

=,-&- (&- #-8-1 8(&"(.)-# @#-- Z";< [<AID^

" $,- ,-";,$ %/ $,- #)%0- _

" $,- 2-0$, $% ( ,(&2 #$&($43 \_

" $,- 0%&- 0&-##4&- &($"% &4 ! "(#-" $,- #)%0- (1;)- !

" $,- '%,-#"%1 "1$-&'-0$ :"$, &-#0-'$ $% -//-'$"8- #$&-## +"

" $,- (1;)- %/ #,-(&"1; &-#"#$(1'- :"$, &-#0-'$ $% -//-'$"8- #$&-## " "

" $,- .4)9 41"$ :-";,$ #<

" /%& ( ;"8-1 8()4- %/ +"(#_+ 0 2-0-12# %1 '%$!+ \+ &4 (12 " "< =,&--

8()4-# %/ +"(#_ ,(8- .--1 4#-2^ J+ J<J]C+ J<JC

" #)%0- "1')"1($"%1 8(&"-# /&%3 ]^A $% C^A

" " " &(1;-# /&%3 AJ! $% [J!" \ ! A'JJ+ A<]C+ A<CJ

" X/ &4 + &4-+ :,-&- &4- "# "12"'($-2 .* $,- 2%$$-2 )"1- %1 $,- ',(&$#+ $,-

'&"$"'() '"&')- "# ($ ;&-($-& 2-0$,

" 4#- )"1-(& -M$&(0%)($"%1 "1 &(1;- +"(#_ J<JC $% J<AJ @Z";< [<AFD<

=,- 8()4-# %/ $,- #$(.")"$* '%-/G'"-1$# ,(8- .--1 0)%$$-2 (;("1#$ $,-

'%$(1;-1$ %/ $,- #)%0- (1;)- @#-- `00-12"M A+ Z";#< `A<A $% `A<QD /%& " "

8(&*"1; .-$:--1 AJ! (12 [J! :"$, 8()4-# %/ $,- 2"3-1#"%1)-## 0(&(3-$-&#

+"(#_ (12\ #0-'"G-2 /%& -(', G;4&-< =,- .%)2 )"1-# #,%: 8()4-# %/. (12

$ ($ "1$-&8()# %/ ]<C!< =,- .&%9-1 )"1-# (&- $,%#- %/ -\4() &4 @2-1%$-2 .*

&4-D< =% '()'4)($- $,- /('$%& %/ #(/-$* %/ ( #-'$"%1 :,%#- +"(#_ )"-# :"$,"1

$,- &(1;- '%8-&-2 .* $,-#- G;4&-#+ "$ "# 1-'-##(&* %1)* $% (00)* $,- -\4(N

$"%1 0 ! .$ $&4+ $% 2-$-&3"1- $,- /('$%& %/ #(/-$* %/ $,- $:% 1-(&-#$ 8()4-#

%/ +"(#_ (12 $,-1 0-&/%&3 ( )"1-(& "1$-&0%)($"%1 .-$:--1 $,-#- 8()4-#+ /%&

$,- #0-'"G-2 8()4- %/ +"(#_<

Z%& ( ;"8-1 #-$ %/ 0(&(3-$-&# @!+ " "+ +"(#_D+ $,-&- "# ( 8()4- %/ $,- 0%&-

0&-##4&- &($"% /%& :,"', $,- /('$%& %/ #(/-$*+ :,-1 \ -\4()# A<JJ+ "# $,-

DHh

H

!#w

u

023? [?IT A('+2=+*#2%$ %5 (*&*.'#'&4; *5#'& 624-%( *$,S%&3'$4#'&$ DIJTYH

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

@<

Page 23: 4_Chapter 4 Classic Methods of Slope Stability Analysis

#(3- (# $,- /('$%& %/ #(/-$* :,-1 \ -\4()# A<]C< X/ $,- 2-#";1 8()4- %/ $,-

0%&- 0&-##4&- &($"% "# ,";,-& $,(1 &4- /%& $,- ;"8-1 #-'$"%1 (12 #$&-1;$,

0(&(3-$-&#+ $,-1 $,- /('$%& %/ #(/-$* :"$, ( 2-0$, /('$%& \ ! A']C ,(# (

)%:-& 8()4- $,(1 :"$, \ -\4() $% A<JJ< =,"# (&;43-1$ '(1 .- -M$-12-2

$% 2"#'-&1 :,-$,-& $,- /('$%& %/ #(/-$* :"$, \ -\4() $% A<CJ "# 3%&- '&"$"'()

$,(1 :"$, \ -\4() $% A<]C<

M!:;=4 =N8B<7=.@AD i#- #$(.")"$* '%-/G'"-1$# $% "18-#$";($- $,- #)%0- #,%:1 "1 Z";< [<A[<

=,- 2($( (&- '%$! ! ]'C^A+ +" ! AQ9>(+ " " ! ]_!+ _ ! A]3+ # ! AB'C7

]J<J 9RU3_+ #(* AB<Q 9RU3_< !-1'-+ &-/-&&"1; $% Z";< [<A[^

&4 ! J&_F

A]F&

I]

A_Q&

II

A]Q&[B

BI&][

[F

! J& J']B& J'[C& J'C]& J'CA& J'CA

/%& -(', #)"'-+ &-#0-'$"8-)*+ :,-1'- $,- (8-&(;- &4 @)"1-(& "1$-&N

0%)($"%1D!J<_Q+ %& ()$-&1($"8-)*+ $,- (8-&(;- &4 @4#"1; (&-(#D! J<_B<

+"

#_! A'Q

AB'Q & A]! J'JFI

=,-&-/%&- 2% '()'4)($"%1# /%& +"(#_ ! J'J]C (12 J<JCJ (12 4#- )"1-(&

-M$&(0%)($"%1 @#-- Z";< [<AFD<

4·0

3·0

2·0

1·0

0·00·0 0·02 0·04 0·06 0·08 0·10

F

c " / #H

Actual

Linear extrapolation

023? [?IU 0*+#%& %5 4*5'#8 e 4#*!2)2#8 $".!'& &')*#2%$4-2( 4-%12$3

'V#&*(%)*#2%$ 2$ #-' &*$3' %5 '"(#! Y?YK #% Y?IY

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

@@

Page 24: 4_Chapter 4 Classic Methods of Slope Stability Analysis

Z%& , ! A'JJ+ +"(#_ ! J'JC

. ! A'FB& $ ! A'[]& &4- ! J'[C

=,-&-/%&- 2--0-& '"&')-# (&- 1%$ '&"$"'() #"1'- &4 ! J'_B , J'[C

0 ! A'FB $ J'_B & A'[] ! A'][

Z%& \ ! A'JJ+ +"(#_ ! J'J]C

. ! A'C]& $ ! A'_C& &4- ! J'Q

=,-&-/%&- 2--0-& '"&')-# (&- 1%$ '&"$"'()

0 ! A'C] $ J'_B & A'_C ! J'BB

/%& +"(#_ ! J'JFI

0 ! A'][ ' J'JFI $ J'JCJ

J'JCJ $ J'J]C& A'][ $ J'BB# %

! A'][ ' J']I

! A'CJ

=,"# '(1 .- '%30(&-2 :"$, 0 ! A'[_ .* #)"0 '"&')- (1()*#"# @#--

Z";< [<A[D<

@]D K%1#"2-& $,- #$(.")"$* %/ (1 -(&$, 2(3 :,-&- # ! ]J9RU3_+

+ " ! ]_9>(+ " " ! ]C!+ _ ! _C3+ &4 ! J'C+ #"2- #)%0-# [ ,%&"a%1$() $%

A 8-&$"'() %1 ( &%'9 /%412($"%1<

R%:

+"(#_ ! ]_(]J & _C ! J'J__

+"(#_ . $

J<J]C ]<[J ]<AC

J<JCJ ]<FC ]<]J

Z%& " " ! ]C!+ #)%0- [^A

/%& +"(#_ ! J'J]C+ 0 ! ]'[J $ J'C & ]'AC ! A'_]C

/%& +"(#_ ! J'JCJ+ 0 ! ]'FC $ J'C & ]']J ! A'IC

/%& +"(#_ ! J'J__+ 0 ! A'_]C ' #A'IC $ A'_]C% & Q(]C ! A'[_ 4#"1; )"1-(&

"1$-&0%)($"%1<

@_D K,-'9 P%2()-1 @#-- Z";< C<AJD 4#"1; ?"#,%0 (12 H%&;-1#$-&16#

#$(.")"$* '%-/G'"-1$#<

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

BAA

Page 25: 4_Chapter 4 Classic Methods of Slope Stability Analysis

9)*G()/),#*#)@3 0)$# 0$#33@$# $2I%) 5%3I$%A@I%)*X/ $,- &4 8()4- 8(&"-# /&%3 0%"1$ $% 0%"1$ "1 ( #)%0-+ "$ "# 1-'-##(&* $% 4#-

#%3- (8-&(;- 8()4- %/ &4 :,-1 4#"1; #$(.")"$* '%-/G'"-1$#< L1- :(* %/

2%"1; $,"# "# "))4#$&($-2 "1 Z";< [<AQ<

Z%& #-'$"%1 (&-( A^

(8-&(;-^ &4 ! -A&4A ' -]&4] ' -]&4]

-A ' -] ' -_

%8-&()) (8-&(;-^ &4 !%$

A f$&4$%$

A f$

:,-&- f$ "# $,- (&-( %/ (1* #)"'-<

_ ! AQ3+ #(*<

+"(#_ ! B'Q(AQ'F & AQ ! J'J]B

&4 ! J'[

/%& +"(#_ ! J'J]C&\ ! A'J

. ! A'[C&$ ! A'[J

0 ! A'[C $ J'[ & A'[J ! J'QB

/%& +"(#_ ! J'JC&\ ! A'J

. ! A'FC&$ ! A'CJ

0 ! A'FC $ J'[ & A'CJ ! A'AC

/%& +"(#_ ! J'J]B

0 ! A'QB ' [(]C#A'AC $ J'QB%! J'B_

S-8()2#%1 @ABCID /%412 0 ! A'JC<

ru1 h1

h2

h3 A2 A4A3

ru2

ru3

023? [?IP \'=$2#2%$ 4E'#+- 5%& *>'&*32$3 $%$<-%.%3'$'%"4 (%&' (&'44"&'

&*#2% ,24#&2!"#2%$; *5#'& 624-%( *$, S%&3'$4#'&$ DIJTYH

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

BAB

Page 26: 4_Chapter 4 Classic Methods of Slope Stability Analysis

D)#P 2*5 E$2- 5#3%,* 1(2$I3!%-9 (12 ?&(* @ABQ]D 0&-#-1$-2 ( #-&"-# %/ 2-#";1 ',(&$#< =,-* '%1#"2-&-2

G8- 2"//-&-1$ ;&%412 :($-& c%: '%12"$"%1# (# #,%:1 "1 `00-12"M ]+ Z";<

`]<A< =,- &-#4)$# %/ #$(.")"$* '()'4)($"%1# .(#-2 %1 ?"#,%06# #-3"N&";%&%4#

#)"0 '"&')- 3-$,%2 (&- 0&-#-1$-2 "1 G8- 2-#";1 ',(&$# '%&&-#0%12"1; $% $,-

G8- ;&%412 :($-& c%: '%12"$"%1#< =,-#- ',(&$# (&- ;"8-1 "1 `00-12"M ]+

Z";< `]<] $% Z";< `]<I<

[3# )O D)#P 2*5 E$2- 1(2$I3=,- 3-$,%2 4#-# $,- /%))%:"1; #$-0#^

" 2-'"2- %1 ;&%412:($-& '%12"$"%1#

" '()'4)($- +"(#_ $(1" "

" G12 $,"# 8()4- %1 %4$-& '"&'4)(& #'()- (12 /%))%: &(2"() )"1- $% "1$-&N

#-'$"%1 :"$, '4&8- '%&&-#0%12"1; $% #)%0- (1;)-

" &-(2 %// $(1" "(0 %& +"(#_0 (12 '()'4)($- 0 @#-- ()#% Z";# AJ<]] (12

AJ<]_D<

M!:;=4 =N8B<7=@AD K,-'9 $,- -M(30)- ;"8-1 "1 Z";< [<A[ 4#"1; !%-9 (12 ?&(*<

i#"1; ',(&$ 143.-& _+

+"

#_ $(1" " !AQ

AB'Q & A] & $(1 ]_!! J'AFQC

R%: #)%0- (1;)- ! (&' $(1 A(]'C ! ]A'Q! :,-1'- $(1" "(0 ! J'_ @/&%3

',(&$ 143.-& _D :,-1'- 0 ! $(1 ]_!(J'_ ! A'[A<

K%30(&- $,"# :"$, 0 ! A'[_ .* ?"#,%0N#"30)"G-2 #)"0 '"&')- (1()*#"#+

(12 0 ! A'CJ .* ?"#,%0 (12 H%&;-1#$-&16# #$(.")"$* '%-/G'"-1$#<

@]D K,-'9 P%2()-1 @#-- Z";< C<AJD 4#"1; !%-9 (12 ?&(* 2($(<

i#"1; ',(&$ 143.-& _+

+"(#_ $(1" " ! B'Q(AQ'F & AQ & $(1 ]F'A

! J'JCIB

#)%0- (1;)- ! ]I'I!

$(1" "

0! J'C # 0 ! A'J]

+"

#_0! J'J]Q # 0 ! A'J[

#(* 0 ! A'J_+ :,"', '(1 '%30(&-2 :"$, 0 ! A'JC (# %.$("1-2 /%&

P%2()-1 .* S-8()2#%1 @ABCID<

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

BAC

Page 27: 4_Chapter 4 Classic Methods of Slope Stability Analysis

<2$I%2++- 3@A/#$,#5 3+)0#3Y-/-& $% Z";< [<AB< =,- 1-$ 2"#$4&."1; 3%3-1$ "# $,($ 24- $% $,- #%") )-## $,-

3%3-1$ (.%4$ L %/ $,- 3(## %/ :($-& ('$"1; %1 ?`Z< X3(;"1- ( #-'$"%1 %/

:($-& .%412-2 .* ( /&-- #4&/('- ($ T?g (12 %4$)"1-2 .* TZg? (# #,%:1

"1 Z";< [<]J< R%: $,- 3%3-1$ %/ $,- 3(## %/ :($-& Z`?T 34#$ -\4() $,-

3%3-1$ %/ $,- 3(## %/ :($-& ?`Zg< ?4$ $,- :-";,$ %/ ( 3(## %/ #($4&($-2

#%") )-## $,- :-";,$ %/ ( 3(## %/ :($-& %''40*"1; $,- #(3- 8%)43- "# $,-

#4.3-&;-2 41"$ :-";,$< =,-&-/%&- $,- &-#4)$(1$ 2"#$4&."1; 3%3-1$ 24-

$% $,- 3(## %/ #%") )-## $,- 3%3-1$ 24- $% $,- :($-& ('$"1; %1 ?`Z "#

;"8-1 .* 4#"1; .4)9 41"$ :-";,$ (.%8- $,- )-8-) %/ /&-- :($-& #4&/('-

(12 #4.3-&;-2 41"$ :-";,$ .-)%: (# 2-0"'$-2 "1 Z";< [<]A<

i#"1; $,- .%412(&* T?g "1 $,"# :(* "30)"-# 1%$,"1; (.%4$ 3(;1"$42-#

%/ 0%&- :($-& 0&-##4&-# "1#"2- #)%0- 7 "$ "# %1)* 4#-2 $% ;"8- $,- #$($"'())*

-\4"8()-1$ 2"#$4&."1; 3%3-1$+ "<-< $,- #$($"'# %/ Z";< [<]A@(D %/ %4& 0(&$"())*

#4.3-&;-2 #)%0- (&- -\4"8()-1$ $% $,- &-0&-#-1$($"%1 "1 Z";< [<][email protected]<

X/ :- (&- 2%"1; (1 -//-'$"8- #$&-## (1()*#"#+ ,%:-8-&+ 1%$ %1)* 34#$ $,-

3%3-1$# .- '%&&-'$+ .4$ ()#% $,- -//-'$"8- #$&-##-# (12 ,-1'- $,- #,-(&

#$&-1;$, 34#$ .- '%&&-'$< =% (',"-8- $,"#+ :- 34#$ %0-&($- :"$, :($-&

0&-##4&-# &-/-&&-2 $% $,- -M$-&1() :($-& )-8-) (# #433(&"a-2 "1 Z";< [<]]+

O

D C

G

FA

BE ##

#w

023? [?IJ \'=$2#2%$ 4E'#+- 5%& * (*&#2*))8 4"!.'&3', 4)%('? @-' $'#

,24#"&!2$3 .%.'$# 24 #-' .%.'$# ,"' #% #-' .*44 %5 4%2) D"42$3 4*#"&*#',

"$2# 1'23-# #H )'44 #-' &'4#%&2$3 .%.'$# ,"' #% #-' 1*#'& D"$2# 1'23-# #1H

#w

#w

E B

A F

G

023? [?]Y \'=$2#2%$ 4E'#+- 4-%12$3 * +8)2$,&2+*) 4"&5*+' !'$'*#- * 5&''

1*#'& )'>') +%&&'4(%$,2$3 #% #-' 3'%.'#&8 %5 #-' (*&#2*))8 4"!.'&3',

4)%(' 4-%1$ 2$ 023? [?IJ

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

BAD

Page 28: 4_Chapter 4 Classic Methods of Slope Stability Analysis

"<-< $,- 0%&- 0&-##4&- "# 3-(#4&-2 /&%3 $,- -M$-&1() )-8-) :($-& #4&/('- (#

2($43< =,- .4)9 41"$ :-";,$ "# 4#-2 (.%8- $,- -M$-&1() :($-& )-8-) (12 $,-

#4.3-&;-2 41"$ :-";,$ "# 4#-2 .-)%: $,- -M$-&1() :($-& )-8-)< g('&*#2$3

2$ #-24 1*8; 1' *"#%.*#2+*))8 *$, +%&&'+#)8 #*E' 2$#% *++%"$# #-' '55'+# %$

4#*!2)2#8 %5 #-' 'V#'&$*) 1*#'& (&'44"&'<

(a)

(b)

#w

##

## "

No water pressureacting here

023? [?]I @-' (*&#2*))8 4"!.'&3', 4)%(' 4-%1$ 2$ D*H 24 4#*#2+*))8

'L"2>*)'$# #% #-' 4)%(' 4-%1$ 2$ D!H "42$3 4"!.'&3', "$2# 1'23-#; #";

!')%1 #-' )'>') )2$' %5 4"!.'&3'$+'; *$, *)4% .'*4"&2$3 (%&' 1*#'&

(&'44"&'4 5&%. #-24 )'>') )2$' %5 4"!.'&3'$+' *4 ,*#".

P

Hw

Z2

Z1

Hw

Hw

Z Z

'W

'W

'W 'W

'x

q

(#)

(#)

(# ")

(# ")

(a)

P

'x

q

(b)

'x

(c)

= (#z + q) 'x + Pp = #z + q + p / 'x u = #w Hw

p = # "z1 + # "z2 +q + p / 'x u = #w Hw# " = # – #w

'W = (# "z1+ # "z2 + q )b + Pp = # "zu = #w Hw# " = # – #w

'W = # "z 'x

023? [?]] A"..*&8 4E'#+- 4-%12$3 -%1 >'&#2+*) #%#*) 4#&'44 0 *$, (%&'

1*#'& (&'44"&' 4 24 +*)+")*#', 5%& '*+- 4)2+' %5 * 4)%(' #-*# 24 D*H ,&8;

D!H (*&#2*))8 4"!.'&3', *$, D+H +%.()'#')8 4"!.'&3',

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

BA?

Page 29: 4_Chapter 4 Classic Methods of Slope Stability Analysis

!"#$%& %'()*+%,!"# $% &'' (%) *(+& )%,-& %.* +/ 0,12*+2'3 2%/&+4', *(' &5%0' 6+7'/ +/

8+69 :9;<9 8%, *(' &5+2' &(%)/3 *(' 7',*+215 *%*15 &*,'&& 1* *(' =1&' %>

*(' &5+2' +&?

! ! @" ;A ! "BA-C1

$(' 0%,' )1*', 0,'&&.,' 1* *(' =1&' %> *(' &5+2' +&?

" ! D" "A ! DA-C1

*1-+/6 !) ! "A-EFG< !+* +& 12*.155H @9B"-EFG< >%, >,'&( )1*',#9

$(' 7',*+215 '>>'2*+7' &*,'&& 1* *(' =1&' %> *(' &5+2' +&?

!# " ! "<A-C1

I'>',,'4 *% *(' >,'' )1*', 5'7'53 122%,4+/6 *% %., ,.5'&3 )' (17' *('

'J.+715'/* &*,'&&'&3 !' 1/4 "' )(',' *(' &.=&2,+0* K'L &*1/4& >%,

K'J.+715'/*L3 1&?

!' ! :" ;A$ D" "A ! "<A-C1

"' ! A-C1

!' # "' ! "<A-C1

M> /%) )' (17' 1 ,10+4 4,1)N4%)/ %> ;G3 *('/ *(',' +& /% 2(1/6' +/

'>>'2*+7' &*,'&& =.* *(',' +& 1/ +/2,'1&' +/ 4+&*.,=+/6 G%G'/*9

!' ! O" ;A$ <" "A ! "DA-C1

"' ! ;" "A ! ;A-C1

!' # "' ! "<A-C1

M* 21/ =' &''/ *(1*3 ='>%,' ,10+4 4,1)N4%)/3 *(' 715.' %> !' *% =' .&'4

+/ 1 &*1=+5+*H 1/15H&+& +& "<A-C13 1/4 1>*', ,10+4 4,1)N4%)/ !' (1&

+/2,'1&'4 *% "DA-C13 ,'&.5*+/6 +/ 1 51,6', 4+&*.,=+/6 G%G'/* 1/4 1

2%,,'&0%/4+/6 ,'4.2*+%/ +/ *(' >12*%, %> &1>'*H9

#$%& '&() *+,-$.$/- 01+.23 4/5 6/51+7 +89:!;+

!"#$%&' ( -+(,,.- )%/0"&, "1 ,+"*% ,/(2.+./3 (4(+3,.,

)*+

Page 30: 4_Chapter 4 Classic Methods of Slope Stability Analysis

@]D X1 Z";< [<][ :- '%1#"2-& $,- #$&-##-# .-/%&- (12 (/$-& &(0"2 2&(:N

2%:1 ($ $,- $,&-- 0%"1$# `+ ? (12 K #,%:1< `$ 0%"1$ ` $,-&- "# 1%

',(1;- "1 $,- :($-& )%(2 2"&-'$)* (.%8- $,- 0%"1$ 24- $% &(0"2 2&(:N

2%:1< `$ 0%"1$ ?+ $,- ',(1;- "1 :($-& )%(2 "# A 3 %/ :($-&< `$ 0%"1$ K

$,- ',(1;- "1 :($-& )%(2 "# ] 3 %/ :($-&<

f# (%2$# f^

.-/%&- &(0"2 2&(:N2%:1

(- ! _ & AB ' ] & B ! FC9>(

"- ! AC9>(

(- $ "- ! IJ9>(

(/$-& &(0"2 2&(:N2%:1

(- ! C & AB ! BC9>(

"- ! _C9>(

(- $ "- ! IJ9>(

"<-< 1% ',(1;- "1 -//-'$"8- #$&-##<

f# (%2$# 6^

.-/%&- &(0"2 2&(:N2%:1

(- ! ] & AB ! AQ9>(

"- ! J 9>(

(- $ "- ! AQ9>(

(/$-& &(0"2 2&(:N2%:1

(- ! A & AB ' A & B ! ]Q9>(

"- ! ]J $ AJ ! AJ9>( @&-3%8() %/ A 3 %/ :($-&D

(- $ "- ! AQ9>(

2 m

1 m1 m

1 m

1 m

3 m

2 m

1·5 m

# = 19 kN/m3

CB

A

30 kPau = 35 kPa

u = 30 kPa

u = 0

023? [?][ \'=$2#2%$ 4E'#+- 5%& 1%&E', 'V*.()' 12#- &*(2, ,&*1<,%1$

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

BAF

Page 31: 4_Chapter 4 Classic Methods of Slope Stability Analysis

f# (%2$# G^

.-/%&- &(0"2 2&(:N2%:1

(- ! A & B ! B 9>(

"- ! J 9>(

(- $ "- ! B 9>(

(/$-& &(0"2 2&(:N2%:1

(- ! A & B ! B 9>(

"- ! AJ $ AJ ! J 9>( @&-3%8() %/ ] 3 %/ :($-&D

(- $ "- ! B 9>(

@_D K%1#"2-& $,- -M(30)- ;"8-1 "1 Z";< [<]C< h-* 0(&(3-$-&# (&- (# /%)N

)%:#^ + " ! J (12 C 9>(+ " " ! ]J!+ # ! AB'C 9RU3_< =,- $&"() #)"0 '"&')- "#

2"8"2-2 "1$% #"M #)"'-# %/ -\4() :"2$,#< ?* #'()"1; ,-";,$# /&%3 $,-

2&(:"1;+ :- ,(8- 3(;1"$42-# %/ #$&-##-# ;"8-1 .-)%:<

?-/%&- &(0"2 2&(:N2%:1 $,- #$&-##-# (&- (# #,%:1 "1 =(.)- [<C<

`/$-& &(0"2 2&(:N2%:1 $,- #$&-##-# (&- (# #,%:1 "1 =(.)- [<I<

?-/%&- &(0"2 2&(:N2%:1 $,- #$(.")"$* (1()*#"# 0&%'--2# (# #,%:1 "1

=(.)- [<F<

`/$-& &(0"2 2&(:N2%:1 $,- #$(.")"$* (1()*#"# 0&%'--2# (# #,%:1 "1

=(.)- [<Q<

Z%& $,"# $&"() '"&')-+ $,- /('$%&# %/ #(/-$* (&- #,%:1 "1 =(.)- [<B<

X$ '(1 .- #--1 $,($^

" &(0"2 2&(:N2%:1 #";1"G'(1$)* &-24'-# $,- /('$%& %/ #(/-$*+ (12

0 10 m

Scale

12

3

4

5

6

60

50

40

30

20

10

u = 0h1

h2

hw

kPa

023? [?]K \'=$2#2%$ 4E'#+- 5%& 1%&E', 'V*.()'

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

BA2

Page 32: 4_Chapter 4 Classic Methods of Slope Stability Analysis

" $,- /('$%& %/ #(/-$* "# #-1#"$"8- $% $,- 8()4- %/ + " 4#-2 "1 $,- (1()*#"#

7 2# 24 #-'&'5%&' 'V#&'.')8 2.(%&#*$# 2$ (&*+#2+' #% +-%%4' #-' >*)"'

%5 + " #% !' "4', 2$ #-' 4)%(' 4#*!2)2#8 *$*)8424 12#- 3&'*# +*&'<

Y-3-3.-& $,- %)2 #(*"1; 51% '-- $%% )%:+ 1% 0," $%% ,";,6W

@*!)' [?K? ML"2>*)'$# 4#&'44'4 5%& #-' 4"!.'&3', +*4'

S)"'- (-^ 9>( "-^ 9>( (- $ "-^ 9>(

A ] & AB'C ' A & B'C ! [Q'C AJ _Q<C] A'C & AB'C ' [ & B'C ! IF'_ I IA<__ J'C & AB'C ' C'[ & B'C ! IA'A ] CB<A[ C'_ & B'C ! CJ'[ A [B<[C _'B & B'C ! _F'A ] _C<AI A'I & B'C ! AC'] _ A]<]

@*!)' [?T ML"2>*)'$# 4#&'44'4 5%& &*(2, ,&*1<,%1$

S)"'- (-^ 9>( "-^ 9>( (- $ "-^ 9>(

A _ & AB'C ! CQ'C ]J _Q<C] _'C & AB'C ' ] & B'C ! QF'_ ]I IA<__ ]'C & AB'C ' _'[ & B'C ! QA'A ]] CB<A[ A'C & AB'C ' _'Q & B'C ! IC'[ AI [B<[C J'C & AB'C ' _'[ & B'C ! []'A F _C<AI A'I & B'C ! AC'] _ A]<]

R%$- $,-&- "# 1% ',(1;- "1 $,- 8-&$"'() -//-'$"8- #$&-##+ ($ "+ /%& -(', #)"'-W

@*!)' [?U A#*!2)2#8 *$*)84'4 5%& 4"!.'&3', +*4'

+" ! C9>( +" ! J

S)"'- )^2-;&--

( #"1)^9>(

f+" ' (" $(1""

6.)

0 ! A'CB

f(6 f(" $(1"

6.)

0 ! A']J

f(6

A CF [J<IQ AB<J J<F[ ]C<IQ A[<J J<QJ AF<CJ] _[ _F<I_ ]F<_ J<BF ]Q<A[ ]]<_ A<JJ ]]<_J_ AI AI<Q[ ]I<C A<J_ ]C<F_ ]A<C A<J[ ]J<IF[ J J ]_<J A<JJ ]_<JJ AQ<J A<JJ AQ<JJC $AC $B<IJ AF<Q J<BJ AB<FQ A]<Q J<QB A[<_QI $_] $Q<JC B<[ J<FA A_<][ [<[ J<FJ I<]B

%

FF<CJ%

A]_<J%

! A_C'CF%

B_<J%

! BB'A[0A ! A]_(FF'C

!A<CB0] ! A'FC 0A ! B_(FF'C

!A<]J0] ! A']Q

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

BA<

Page 33: 4_Chapter 4 Classic Methods of Slope Stability Analysis

@[D K%1#"2-& $,- #)%0- ;"8-1 "1 Z";< [<]I &-0&-#-1$"1; ( '4$ /%&3-2

(# 0(&$ %/ ( &"8-& '%1$&%) :%&9#< =,- #$-(2* #$($- :($-& )-8-) "#

;"8-1 (# $,- )"1- `?K< V4- $% ( #422-1 %0-1"1; %/ ( #)4"'- ;($-+ $,-

:($-& )-8-) "1 $,- :($-&:(* "# #4.j-'$-2 $% ( &(0"2 2&(:N2%:1 ($ $,-

-12 %/ :,"', $,- :($-& #4&/('- "# &-0&-#-1$-2 .* `?V+ "<-< ($ &(0"2

@*!)' [?P A#*!2)2#8 *$*)8424 5%& &*(2, ,&*1<,%1$

+" ! C9>( +" ! J

S)"'- )^2-;&--

( #"1)^9>(

f+" ' (" $(1""

6.)

0 ! A']A

f(6 f(" $(1"

6.)

0 ! J'B]

f(6

A CF [B<JI AB<J J<QJ ]_<FC A[<J J<QB AC<F_] _[ [Q<Q] ]F<_ A<JJ ]F<_J ]]<_ A<JC ]A<][_ AI ]]<_C ]I<C A<J[ ]C<[Q ]A<C A<JF ]J<JB[ J J ]_<J A<JJ ]_<JJ AQ<J A<JJ AQ<JJC $AC $AJ<BJ AF<Q J<QB ]J<JJ A]<Q J<QI A[<QQI $_] $Q<JC B<[ J<FJ A_<[_ [<[ J<IC I<FF

%

AJA<]Q%

A]_<J%

! A_]'BI%

B_<J%

! BI'FA0A ! A]_(AJA']Q

!A<]A0] ! A'_A 0A ! B_(AJA']Q

!J<B]0] ! J'BC

@*!)' [?J A"..*&8 %5 &'4")#4 5%& 1%&E', 'V*.()' ,'(2+#', 2$ 023? [?]K

+"^ 9>( ?-/%&- &(0"2 2&(:N2%:1 `/$-& &(0"2 2&(:N2%:1

C A<FC A<_AJ A<]Q J<BC

0 5 10 m

Scale

1

2

3

4

5

6

3·4

3·1

3·16·2

6·54·6

1·0

1·7

C

D

# = 19 kN/m3

# = 20 kN/m3

c " =

A B

18 kPa, &" = 23˚

023? [?]T \'=$2#2%$ 4E'#+- 5%& 1%&E', 'V*.()'

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

BA@

Page 34: 4_Chapter 4 Classic Methods of Slope Stability Analysis

2&(:N2%:1+ :($-& "# 5#$&(12-26 "1 $,- #)%0- .-'(4#- $,-&- ,(# 1%$ .--1

#4/G'"-1$ $"3- /%& 2&("1(;- $% $(9- 0)('-< Z%& $,- 0&%0%#-2 #)"0 '"&')-+

$,- #$(.")"$* %/ $,- #)%0- "# $% .- 2-$-&3"1-2 /%& .%$, $,- 0&"%& #$-(2*

#$($- (12 /%& $,- '%12"$"%1 %/ 5&(0"2 2&(:N2%:16<

=,- $-',1"\4- "# $% #4.N2"8"2- $,- 0&%0%#-2 #)"00"1; 3(## "1$% #"M

#)"'-# %/ -\4() :"2$,< Z%& $,"# #"30)- -M(30)-+ 4#"1; G8- #)"'-# "# $%%

;&-($ (1 (00&%M"3($"%1+ :,")- 4#"1; #-8-1 #)"'-# ;"8-# 8-&* )"$$)-

"30&%8-3-1$ %8-& $,- (''4&('* %.$("1-2 /&%3 #"M #)"'-#< =,- 3-2"(1#

%/ -(', #)"'- (&- 2%$$-2 "1 (12 3-(#4&-2 .%$, (.%8- (12 .-)%: $,-

:($-& )-8-) (# #,%:1< =,- #)%0- %/ $,- $(1;-1$ $% $,- '"&')- ($ $,-

.(#- %/ -(', 3-2"(1 ;"8-# $,- 8()4-# %/ )< X$ 3(* .- 1%$-2 $,($ -(',

&(2"() )"1- /&%3 $,- '-1$&- %/ $,- #)"0 '"&')- $% $,- .(#- %/ -(',

3-2"(1 ()#% 3(9-# (1 (1;)- ) :"$, $,- 8-&$"'()<

=,- 2($( (12 '%304$($"%1 3(* .- 0&-#-1$-2 '%18-1"-1$)* "1 ( $(.4)(&

/%&3 (# #,%:1 "1 =(.)- [<AJ< =,- #$-(2* #$($- '%12"$"%1 "# (1()*#-2 "1

=(.)- [<AJ< X$ '(1 .- #--1 $,($ $,- 8-&$"'() $%$() #$&-## /%& -(', #)"'- "#

'%304$-2 4#"1; #4.3-&;-2 41"$ :-";,$ .-)%: $,- :($-& )-8-) `?K<

=,- '%1#-\4-1'- %/ $,"# (1()*$"'() 2-8"'- "# $,($ $,- 0%&- :($-&

0&-##4&-# 34#$ .- '()'4)($-2 /&%3 $,- #(3- )"1- `?K< K%1#-\4-1$)*+

'%)431 _ "1 =(.)- [<AJ '%1$("1# %1)* a-&%#< =,- '%304$($"%1# 3(* .-

-(#")* '(&&"-2 %4$ 4#"1; ( #'"-1$"G' '()'4)($%& %& ( #0&-(2#,--$< T\4($"%1

AJ<AI '%1$("1# $,- 4191%:1 /('$%& %/ #(/-$* 0 %1 .%$, #"2-# %/ $,- -\4(N

$"%1< =,- "$-&($"8- #%)4$"%1 %/ $,"# -\4($"%1 "# '(&&"-2 %4$ .* G&#$ %.$("1"1;

( &%4;, (00&%M"3($"%1 %/ 0 .* 2"8"2"1; $,- #43 %/ '%)431 C @"<-< -//-'N

$"8-)* (##43"1; .) ! A $,&%4;,%4$D .* $,- #43 %/ '%)431 [+ :,-1'-

0A ! ]I_'Q(A_I'I ! A'B_

=,- 0(&(3-$-& $(1" "(0 ! $(1 ]_!(A'B_ ! J']] "# $,-1 4#-2 $% -1$-&

$,- '4&8-# %/ Z";< [<A_ @#%3-$"3-# '())-2 5E(1.46# '4&8-#6D $% %.$("1

@*!)' [?IY A#*!2)2#8 *$*)8424 5%& 4"!.'&3', +*4'

K%)431 R%< A ] _ [ C I F

S)"'- R%< )^2-;&--

(-^ 9>( "-^ 9>( ( #"1) +" ' #($ "% $(1" " .)

@0A ! A'BDCUI

A [I II<_ J [F<F [I<A J<QC C[<_] _[ BA<[ J CA<A CI<Q J<BI CB<]_ ]] QA<C J _J<C C]<I A<JJ C]<I[ ]J IC<J J AA<_ [C<I A<J_ [[<_C $A [I<J J $J<Q _F<C A<JJ _F<CI $AA AF<J J $_<] ]C<] J<B[ ]I<QSiH A_I<I ]I_<Q ]F[<F

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

BBA

Page 35: 4_Chapter 4 Classic Methods of Slope Stability Analysis

.@//2$- )O I(# 3I#03 $#\@%$#5 I) 2*2+-3# I(# 3I2A%+%I- )O 2 3+)0# A-(2*5@(D A#'( IR A+*)' ,&*12$3< >&-0(&- ( #'()- 2&(:"1; %/ ( '&%##N#-'$"%1

$,&%4;, $,- #)%0-< V&(: "1 ( &-()"#$"' 0&%0%#-2 /(")4&- #4&/('-<

@.D A#'( ]R A)2+' (*&*.'#'&4< V"8"2- $,- #)"2"1; 3(## "1$% #)"'-#+ 0&-/-&N

(.)* %/ -\4() :"2$,< =,- #)"'- :"2$, #,%4)2 .- #-)-'$-2 $% $(9-

(''%41$ %/ ',(1;-# "1 #%") 0&%0-&$"-#+ #)%0- ;-%3-$&* (12 0%&-

0&-##4&- 2"#$&".4$"%1< L.$("1 $,- "1')"1($"%1 :"$, &-#0-'$ $% $,-

,%&"a%1$()+ )+ %/ $,- $(1;-1$ $% $,- '-1$&- %/ $,- .(#- %/ -(', #)"'-

@1%$- $,($ ) "# ()#% $,- "1')"1($"%1 $% $,- 8-&$"'() %/ $,- &(2"() )"1-

j%"1"1; $,- '-1$&- %/ $,- #)"0 '"&')- $% $,- '-1$&- %/ $,- .(#- %/ -(',

#)"'-D<

@'D A#'( XR Z'23-# (*&*.'#'&4< Z"12 $,- $%$() 8-&$"'() #$&-## ('$"1; ($

$,- '-1$&- %/ $,- .(#- %/ -(', #)"'-< =,"# :")) .- $,- #)"'- ,-";,$

$"3-# $,- 41"$ :-";,$ /%& ( 41"/%&3 #%")< Z%& $,- 0(&$)* #4.3-&;-2

'(#-+ #4.3-&;-2 41"$ :-";,$ :")) .- 4#-2 .-)%: $,- :($-& )-8-) $%

'%30-1#($- /%& $,- &-#$&("1"1; -//-'$ %/ :($-& 0&-##4&- %1 $,- #4.N

3-&;-2 /('- %/ $,- #)%0-<

$,- 8()4- %/ .) '%&&-#0%12"1; $% -(', 8()4- %/ )< T(', 8()4- %/

+" ' #($ "% $(1" " "1 '%)431 C "# $,-1 2"8"2-2 .* $,- '%&&-#0%12"1;

.) 8()4- (12 $,- &-#4)$ 04$ "1 '%)431 F< ` 3%&- (''4&($- 8()4- %/

$,- /('$%& %/ #(/-$* "# $,-1 %.$("1-2 (# 0] ! ]F['F(A_I'I ! ]'JA< Z4&$,-&

"$-&($"%1# 3(9- )"$$)- "30&%8-3-1$<

=,- 2($( (12 '%304$($"%1# /%& $,- &(0"2 2&(:N2%:1 '(#- (&- ;"8-1 "1

=(.)- [<AA< !-&- 0A ! ]I_'Q(AQ['[ ! A'[_+ (12 $,- 0(&(3-$-& $(1" "(0 !$(1 ]_!(A'[_ ! J'_+ :,-1'- 0] ! ]IF'F(AQ['[ ! A'[C<

X1 #433(&*+ 0 ! ]'JA /%& $,- #4.3-&;-2 '(#- (12 0 ! A'[C (/$-& &(0"2

2&(:N2%:1<

@*!)' [?II A#*!2)2#8 *$*)8424 5%& &*(2, ,&*1<,%1$

K%)431 R%< A ] _ [ C I F

S)"'- R%< )^2-;&--

(-^ 9>( "-^ 9>( ( #"1) +" ' #($ "% $(1" " .)

@0A ! A'[DCUI

A [I II<_ J [F<F [I<A J<BA CJ<F] _[ A]]<[ _A IQ<C CI<Q A<JJ CI<Q_ ]] A[_<C I] C_<F C]<I A<J[ CJ<I[ ]J A_J<J IC ]]<I [C<I A<J_ [[<_C $A B]<J [I $A<I _F<C J<BB _F<BI $AA _[<J AF $I<C ]C<] J<B] ]F<[SiH AQ[<[ ]I_<Q ]IF<F

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

BBB

Page 36: 4_Chapter 4 Classic Methods of Slope Stability Analysis

@2D A#'( [R N%&' 1*#'& (&'44"&'< X1 ( $%$() #$&-## (1()*#"#+ $,- 0%&-

0&-##4&-# (&- 1%$ 91%:1 (12 1%$ 4#-2< X1 (1 -//-'$"8- #$&-## (1()*#"#+

$,- 0%&- 0&-##4&-# :")) .- /%412 /&%3 #'()"1; %// $,- 2&(:"1;< Z%& $,-

'(#- %/ #$-(2* #--0(;-+ ( c%: 1-$ :")) .- 4#-2< Z%& $,- '(#- %/ (

#4.3-&;-2 #)%0-+ 0%&- 0&-##4&-# :")) .- 3-(#4&-2 /&%3 $,- )-8-)

)"1- %/ #4.3-&;-1'- (# 2($43< Z%& &(0"2 2&(:N2%:1+ "$ "# (##43-2

$,($ 2&("1(;- @#--0(;-D 24&"1; &(0"2 2&(:N2%:1 ,(# 1%$ %''4&&-2

(12 $,($ ( c%: 1-$ ,(# 1%$ .--1 -#$(.)"#,-2 (12 ,-1'- 0%&-

0&-##4&-# (&- 2-G1-2 .* $,- ;-%3-$&* %/ $,- #)%0-<

@-D A#'( KR \'#*2)', +*)+")*#2%$4< K()'4)($- ( #"1) /%& -(', #)"'- (12 #43

$,-3 "1 ( $(.)-<

Z%& $%$() #$&-## (1()*#"#+ '%304$- /('$%& %/ #(/-$* 0 !#%

44( '%#)%(%

( #"1)< Z%& -//-'$"8- #$&-## (1()*#"#+ -8()4($- 0%&-

0&-##4&-# " %& "-+ (12 -8()4($- $,- #$&-1;$, $-&3 /%& -(', #)"'-+

+ " ' #($ "% $(1" "+ (12 #43 "1 ( $(.)-< Z"12 $,- G&#$ $&"()

0A !%

+" ' #($ "% $(1" "%

( #"1)

R%: 4#- $,"# G&#$ $&"() 0A $% -8()4($- $,- 0(&(3-$-& $(1" "(0A "1 %&2-&

$% -1$-& E(1.46# '4&8-# @Z";< [<A_D $% G12 8()4-# %/.) $% 3%2"/* $,-

+" ' #($ "% $(1" " $-&3# (12 -8()4($- ( &-8"#-2 8()4- %/ /('$%& %/

#(/-$*+ 0]+ :,-1'- $,- 0&%'-## '(1 .- "$-&($-2 $% ;"8- 0_<

9)*G1%$1@+2$ 3+%0 2*2+-3%3!"#$"%#&R%1N'"&'4)(& #)"0# %''4& .* #)"2"1; %1 ( #%/$ )(*-& %&+ /%& -M(30)-+ .*

#)"2"1; $,&%4;, $,- #)%0"1; ')(* '%&- %/ (1 -(&$, 2(3< O,")- '"&'4)(&

#)"0# '(1 3%8- :"$,%4$ "1$-&1() 2"#$%&$"%1+ :"$, 1%1N'"&'4)(& #)"0# "1$-&1()

#,-(& 34#$ $(9- 0)('-< X/ "1$-&1() #,-(& /%&'-# (&- 1-;)-'$-2 $,-1 (1

(&$"G'"())* )%: /('$%& %/ #(/-$* :")) &-#4)$< =,- ')(##"' 3-$,%2 /%& (1()*#"1;

1%1N'"&'4)(& #)%0- #$(.")"$* "# $,($ %/ E(1.4 '# *)< @ABCID<

I#1/J '()*+,Z%& ( $%$() #$&-## (1()*#"#+ &-/-& $% Z";< [<]F< Y-#%)8"1; 0(&())-) $% $,- #)%0-

@:,-&- ) "# $,- "1')"1($"%1 %/ $,- #)%0-D ;"8-#^

'

Z #"1) !%

4)

0

0 !%

4)%

Z #"1)

%& 0 !%

4)( '%#)%

Z $(1)

1-;)-'$"1; "1$-&#)"'- /%&'-#<

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

BBC

Page 37: 4_Chapter 4 Classic Methods of Slope Stability Analysis

=% $(9- (''%41$ %/ "1$-&#)"'- /%&'-# 4#- $,- E(1.46# \4(#"N-30"&"'() '%&N

&-'$"%1 /('$%& 5J :,-1'-

0 ! 5J%

4)( '%#)%

Z $(1)

:,-&- 5J "# +A (12 8(&"-# .-$:--1 A (12 A<A_ 2-0-12"1; %1 ;-%3-$&*<

Z%& (1 -//-'$"8- #$&-## (1()*#"# /%& ( 1%1N'"&'4)(& /(")4&- #4&/('-+ 4#- $,-

E(1.4 #%)4$"%1< Y-/-&&"1; $% Z";< [<]Q

0 ! 5J%

-(+ " ' #($ "% $(1" ")*.($)%

Z $(1)#['AC%

:,"',+ /%& -\4() #)"'- :"2$,#+ &-24'-# $%

0 ! 5J%

(+" ' #($ "% $(1" ")($)%

( $(1)#['AI%

:,-&- $) ! '%#] )#A ' $(1) $(1" "(0%<

')/0@I#$ 0$),$2/3C(# >#)I#1(*%12+ 2*5 >#)G#*"%$)*/#*I2+ .)OI&2$# 4%$#1I)$- S>>.4X=,"# :-. #"$- @:::<;;#2<'%3D '($()%;4-# 0&%;&(3# "1 $,- G-)2# %/

;-%$-',1"'() -1;"1--&"1;+ #%") 3-',(1"'#+ &%'9 3-',(1"'#+ -1;"1--&"1;

;-%)%;*+ /%412($"%1 -1;"1--&"1;+ ,*2&%;-%)%;*+ ;-%N-18"&%13-1$()

-1;"1--&"1;+ -18"&%13-1$() -1;"1--&"1;+ 2($( (1()*#"# (12 2($( 8"#4()"N

a($"%1 (12 )"#$# :%&)2:"2- #400)"-&# (12 04.)"#,-&# %/ $,-#- 0&%;&(3#<

>&%;&(3# (&- "12-M-2 .* 0&%;&(3 1(3-+ 0&%;&(3 '($-;%&*+ %0-&($"1;

#*#$-3 (12 0&%;&(3 #$($4#+ (12 $,- V"&-'$%&* -1$&"-# (&- )"#$-2 .*

'($-;%&*< >&%;&(3 04.)"#,-&# (12 #400)"-&# (&- "12-M-2 .* %&;(1"a($"%1

1(3- (12 .* '%41$&*+ (12 $,- V"&-'$%&* -1$&"-# (&- )"#$-2 "1 ()0,(.-$"'()

%&2-&< =,- V"&-'$%&"-# %/ 0&%;&(3#+ 04.)"#,-&# (12 #400)"-&# (&- '&%##N

&-/-&-1'-2< =,- V"&-'$%&* ()#% ;"8-# )"19# $% %$,-& :-. #"$-# /-($4&"1;

;-%$-',1"'()+ ;-%N-18"&%13-1$() %& &-)($-2 #%/$:(&-< =,-&- "# ( /&--

ggSV R-:#)-$$-&< =,- ggSV :-. #"$- /%& #)%0- #$(.")"$* 0&%;&(3# )"#$#

$,- /%))%:"1; 2-#'&"0$"%1# %/ 0&%;&(3#+ ')(##"G-2 .* 0&%;&(3 1(3-+

$*0- @'%33-&'"()+ /&--:(&- %& #,(&-:(&-D+ (12 %0-&($"1; #*#$-3 @VLS+

a

s

l

W

023? [?]U \'=$2#2%$ 4E'#+- 5%& $%$<+2&+")*& #%#*) 4#&'44 *$*)8424 !8 .'#-%,

%5 4)2+'4; $'3)'+#2$3 42,' 5%&+'4

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

BBD

Page 38: 4_Chapter 4 Classic Methods of Slope Stability Analysis

1·20

1·10

1·000·1 0·2 0·3 0·40

(c)

(b)

(a)

0·6

0·8

1·0

–1·0 –0·5 0·5 1·0 2·0 3·00

1·2

1·4

40 40 50 60 7030 3020 2010 100

0·2

0

00·6

0·4

1·0

0·2 0·4

0·6 0·8

1·0

tan $

n $

tan &"F

tan &"F

$: degree

L d

'n

'l

'W

pq

Q

sF

$ positive

&" = 0

c " > 0, & > 0

c " = 0

f 0

d /L

023? [?]P D*H B*$!"74 +"&>'4 5%& 1) ! +%4] )#I' #*$) #*$" "(Z%;D!H ,'=$2#2%$ 4E'#+- 5%& $%$<+2&+")*& '55'+#2>' 4#&'44 *$*)8424; D+H B*$!"74

4'.2<'.(2&2+*) +%&&'+#2%$ 5*+#%& 5%& 2$h"'$+' %5 42,' 5%&+'4?

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

BB?

Page 39: 4_Chapter 4 Classic Methods of Slope Stability Analysis

O"12%:#+ H('D< V-$(")-2 40N$%N2($- 2-#'&"0$"%1# %/ -(', 0&%;&(3 (12

:%&)2:"2- #400)"-&# (&- ;"8-1 "1 $,- g-%$-',1"'() (12 g-%-18"&%13-1$()

S%/$:(&- V"&-'$%&* ($ :::<;;#2<'%3< ?* 3"2N]JJJ+ $,"# :-. #"$- ,(2

&-'-"8-2 %8-& %1- 3"))"%1 ,"$# (12 :(# ($ $,($ $"3- ;-$$"1; A[J JJJ ,"$#

0-& 3%1$,<

3"+.( $)#/%"%)0 K$+%"L $+-)M#G( %1,(N" K!`SH 7 K%33-&'"() 7 O"1_M+ O"1BCUBQ+ O"1R=+ iRXl

" VPXS` 7 Z&--:(&- 7 VLS

" TS`i 7 K%33-&'"() 7 VLS+ iRXl+ !>

" TS=`fTP 7 K%33-&'"() 7 VLS

" g()-1( 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" g?SPL>T 7 K%33-&'"() 7 O"1_M+ O"1BCUBQ+ O"1R=

" g-%N=-' ? 7 K%33-&'"() 7 H('+ >%:-&H('

" gTLSPL>T 7 K%33-&'"() 7 VLS

" g-%S$(& 7 K%33-&'"() 7 VLS

" gZ`]V 7 Z&--:(&- 7 VLS+ O"1_M+ O"1BCUBQ

" ggiNSPXKT 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=+ O"1]JJJ

" ggiNSPL>T 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=+ O"1]JJJ

" g>SN>K 7 K%33-&'"() 7 VLS

" gS)%0- 7 K%33-&'"() 7 VLS

" gS=`?PF 8< A<A[ 7 K%33-&'"() 7 O"1_M+ O"1BCUBQ+ O"1R=

" X<P<`< 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" PXS` 7 Z&--:(&- 7 VLS

" H>YLS=`? 7 K%33-&'"() 7 VLS

" HS=`? 7 K%33-&'"() 7 VLS

" >KS=`?P C H 7 >4.)"' 2%3("1 7 VLS

" >-1$( 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" YT`HT 7 K%33-&'"() 7 VLS

" S(&3( 7 S,(&-:(&- 7 VLS

" S?NSPL>T 7 K%33-&'"() 7 VLS

" S)"2- 7 K%33-&'"() 7 VLS+ O"1_M+ O"1BCUBQ+ O"1R=

" SPX> 7 K%33-&'"() 7 VLS

" SPL>?g 7 K%33-&'"() 7 VLS

" S)%0- @g-%#%)8-D 7 K%33-&'"() 7 VLS

" S)%0- @L(#*#D 7 K%33-&'"() 7 VLS+ O"1BCUBQ+ O"1R=

" SPL>T QY 7 K%33-&'"() 7 VLS

" S)%0-NO 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" SPL>RK 7 K%33-&'"() 7 VLS

" S$(.) /%& O"12%:# 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=+ O"1]JJJ

" S=`?PT 7 K%33-&'"() 7 VLS+ O"1_M+ O"1BCUBQ+ O"1R=

" S=`?PT>YL /%& O"12%:# 7 K%33-&'"() 7 O"1_M+ O"1BCUBQ

" S=TV:"1 ]<] 7 K%33-&'"() 7 O"1_M+ O"1BCUBQ+ O"1R=

!4=>796 ? '78..6' B=CD!4. !? .7!<= .C8E676CF 8987F.6.

BBE

Page 40: 4_Chapter 4 Classic Methods of Slope Stability Analysis

" SO`ST 7 K%33-&'"() 7 VLS

" =SPL>T 7 K%33-&'"() 7 O-.UE(8(+ E(8( ')"-1$+ #-&8-& '()'4)($"%1<

" =SPL>T_ 7 K%33-&'"() 7 VLS+ iRXl

" =S=`? 7 K%33-&'"() 7 VLS+ iRXl

" i=Tl`S_ 7 K%33-&'"() 7 VLS

" O"1S$(.) 7 S,(&-:(&- 7 O"1_M+ O"1BCUBQ+ O"1R=

" lS=`?P 7 K%33-&'"() 7 VLS

3"+.( $)#/%"%)0 KG+&OL $+-)M#G( %1,(N" `KKTK`PK 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" KPimS=`Y 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" TaS)"2- 7 Z&--:(&- 7 O"1BCUBQ+ O"1R=

" >)(1- Z(")4&- `1()*#"# 7 Z&--:(&- 7 O"1BCUBQ+ O"1R=

" Y%'Z()) 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" YLKh_V 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" YLKh>Z 7 K%33-&'"() 7 VLS

" YLZTl 7 K%33-&'"() 7 O"1_M+ O"1BCUBQ

" YL=LH`> 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" S)%0- h-*.)%'9 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" SPL>T>`Kh 7 K%33-&'"() 7 VLS

" SO`YS 7 K%33-&'"() 7 VLS

" S:-2;- 7 K%33-&'"() 7 O"1BCUBQ+ O"1R=

" OTVgT 7 K%33-&'"() 7 VLS

" O-2;- Z(")4&- `1()*#"# 7 Z&--:(&- 7 O"1BCUBQ+ O"1R=

.7!<=]M .I@5#*I =5%I%)* '4=,- SPL>TUO S$42-1$ T2"$"%1 KV "# 0&%24'-2 .* gTLNSPL>T X1$-&N

1($"%1() P$2 (12 "# 0&%8"2-2 :"$, $,"# .%%9< =,- .-#$ :(* $% ;-$ ;%"1;

"# $% "1#$()) $,- #%/$:(&- (12 $,-1 /%))%: $,- $4$%&"() "1 K,(0$-& _ "1 $,-

i#-&6# g4"2-< L1'- *%4 ,(8- ;%1- $,&%4;, $,"# #"30)- $4$%&"() *%4 :"))

,(8- ( 0&-$$* ;%%2 "2-( %/ ,%: $% %0-&($- $,- #%/$:(&-< n%4 #,%4)2 $,-1

.- (.)- $% ;% $,&%4;, $,- S$42-1$ T2"$"%1 )-##%1#< =,- '%30)-$- i#-&6#

g4"2- "# ()#% "1 $,- %1N)"1- ,-)0< n%4 '(1 ;-$ ($ $,- %1N)"1- ,-)0 .* 0&-##N

"1; $,- ZA 9-* :,-1 ( '%33(12 "# ,";,)";,$-2+ .* )%%9"1; ($ $,- $(.)- %/

'%1$-1$# %& .* #-(&',"1; "12-M-2 :%&2# @"$ :%&9# 34', )"9- (1* O"12%:#

(00)"'($"%1 %1N)"1- ,-)0 #*#$-3D< `1%$,-& :(* %/ ;-$$"1; (1 "1$&%24'$"%1

$% $,- #%/$:(&- "# $% %0-1 $,- G)-# "1')42-2 :"$, $,- S$42-1$ T2"$"%1< ?*

%0-1"1; $,-#- G)-# "1 VTZXRT (12 KLR=LiY *%4 '(1 \4"'9)* #-- $,-

2-G1"$"%1 -18"&%13-1$ (12 ,%: *%4 '(1 8"-: $,- &-#4)$#<

=,- $-',1"'() %8-&8"-: %/ SPL>TUO '(1 .- 2%:1)%(2-2 /&%3 $,- gTLN

SPL>T X1$-&1($"%1() P$2 :-. #"$- "1 '%)%4& @:::<;-%N#)%0-<'%3D< =,-

SPL>TUO 0('9(;- "1$-&/('-# :"$, $,- %$,-& gTLNSPL>T X1$-&1($"%1()

P$2 3%24)-# /%& #--0(;- @STT>UOD (12 /%& #$&-## 2"#$&".4$"%1 @SXgH`UOD<

34567 !58639 :; .!67 894 :!'; .7!<= =9>69==:69>

BBF