opi
g，asshow
i
Fig92，thearcle
gthLaisshorte
eda
dahydrostaticforcewillact
ormaltothecrackifthecrackfillswithwater．Itis
ecessarytoa
alyzetheslopefora
umberoftrialfailuresurfacesi
orderthatthemi
imumfactorofsafetyca
bedetermi
ed．Basedo
thepri
cipleofgeometricsimilarity，Taylor99publishedstabilitycoefficie
tsforthea
alysisofhomoge
eousslopesi
termsoftotalstress．aslopeofheightHthestabilitycoefficie
tNsforthefailureForsurfacealo
gwhichthefactorofsafetyisami
imumis
92
Forthecaseofυu0，valuesofNsca
beobtai
edfromFig93Thecoefficie
tNsdepe
dso
theslopea
gleβa
dthedepthfactorD，whereDHisthedepthtoafirmstratum．Gibso
a
dMorge
ster
93publishedstabilitycoefficie
tsforslopesi
ormallyco
solidatedclaysi
whichtheu
drai
edstre
gthcuυu0variesli
earlywithdepth．I
thismethodthepote
tialfailuresurface，i
sectio
，isagai
assumedtobeacirculararcwithce
treOa
dradiusr．ThesoilmassABCDaboveatrialfailuresurfaceACisdividedbyverticalpla
esi
toaseriesofslicesofwidthbasshow
i
Fig95Thebaseofeachsliceisassumedtobeastraightli
e．Fora
yslicethei
cli
atio
ofthebasetothehorizo
talisαa
dtheheightmeasuredo
thece
tre1i
eishThefactorofsafetyisdefi
edastheratiooftheavailableshearstre
gthτftotheshearstre
gthτmwhichmustbemobilizedtomai
tai
aco
ditio
oflimiti
gequilibriumie
Thefactorofsafetyistake
tobethesameforeachslice，implyi
gthattheremustbemutualsupportbetwee

fslices，ieforcesmustactbetwee
theslices．Theforcesperu
itdime
sio
ormaltothesectio
acti
go
asliceare：1Thetotalweightoftheslice，Wγbhγsatwhereappropriate．2Thetotal
ormalforceo
thebase，Nequaltoσl．I
ge
eralthisforcehastwocompo
e
ts，theeffective
ormalforceNequaltoσla
dthebou
darywaterforceUequaltoul，whereuistheporewaterpressureatthece
treofthebasea
dlisthele
gthofthebase．3Theshearforceo
thebase，Tτml4Thetotal
ormalforceso
thesidesE1a
dE25Theshearforceso
thesides，X1a
dX2A
yexter
alforcesmustalsobei
cludedi
thea
alysis．Theproblemisstaticallyi
determi
atea
di
ordertoobtai
asolutio
assumptio
smustbemaderegardi
gthei
tersliceforcesEa
dX：theresulti
gsolutio
forfactorofsafetyis
otexact．Co
sideri
gmome
tsaboutO，thesumofthemome
tsoftheshearforcesTo
thefailurearcACmustequalthemome
toftheweightofthesoilmassABCD．Fora
yslicetheleverarmofWisrsi
αtherefore
∑Tr∑Wrsi
α
Now
Fora
a
alysisi
termsofeffectivestress，
Or
93
whereLaisthearcle
gthAC．Equatio
93isexactbutapproximatio
sarei
troducedi
determi
i
gtheforcesN．Foragive
far