ilurearcthevalueofFwilldepe
do
thewayi
whichtheforcesNareestimated．I
thissolutio
itisassumedthatforeachslicetheresulta
tofthei
tersliceforcesiszero．Thesolutio
i
volvesresolvi
gtheforceso
eachslice
ormaltothebase，ie
NWCOSαul
He
cethefactorofsafetyi
termsofeffectivestressEquatio
93isgive
by
94
Thecompo
e
tsWCOSαa
dWsi
αca
bedetermi
edgraphicallyforeachslice．Alter
atively，valuetheofαca
bemeasuredorcalculated．Agai
，seriesoftrialfailuresurfacesmustbechose
i
ordertoobtai
theami
imumfactorofsafety．Thissolutio
u
derestimatesthefactorofsafety：theerror，comparedwithmoreaccuratemethodsofa
alysis，isusuallywithi
thera
ge52Fora
a
alysisi
termsoftotalstresstheparametersCua
dυuareuseda
dthevalueofui
Equatio
94
fiszero．Ifυu0thefactorofsafetyisgive
by
95
AsN’does
otappeari
Equatio
95a
exactvalueofFisobtai
ed．I
thissolutio
itisassumedthattheresulta
tforceso
thesidesoftheslicesarehorizo
tal，ie
XlX20
Forequilibriumtheshearforceo
thebaseofa
ysliceis
Resolvi
gforcesi
theverticaldirectio

96
Itisco
ve
ie
ttosubstitute
lbsecα
FromEquatio
93，aftersomerearra
geme
t，
97
Theporewaterpressureca
berelatedtothetotal‘fillpressure’ata
ypoi
tbymea
softhedime
sio
lessporepressureratio，defi
edas
98
γsatwhereappropriate．Fora
yslice
He
ceEquatio
97ca
bewritte

99
Asthefactorofsafetyoccurso
bothsidesofEquatio
99aprocessofsuccessiveapproximatio
mustbeusedtoobtai
asolutio
butco
verge
ceisrapid．Duetotherepetitive
atureofthecalculatio
sa
dthe
eedtoselecta
adequate
umberoftrialfailuresurfaces，themethodofslicesisparticularlysuitableforsolutio
bycomputer．Morecomplexslopegeometrya
ddiffere
tsoilstrataca
bei
troduced．
fI
mostproblemsthevalueoftheporepressureratioruis
otco
sta
toverthewholefailuresurfacebut，u
lessthereareisolatedregio
sofhighporepressure，averagevalueweightedo
a
areabasisis
ormallya
usedi
desig
．Agai
，thefactorofsafetydetermi
edbythismethodisa
u
derestimatebuttheerrorisu
likelytoexceed7％a
di
mostcasesislesstha
2％．Spe
cer98proposedamethodofa
alysisi
whichtheresulta
tI
tersliceforcesareparallela
di
whichbothforcea
dmome
tequilibriumaresatisfied．Spe
cershowedthattheaccuracyoftheBishopsimplifiedmethod，i
whicho
lymome
tequilibriumissatisfiedisduetothei
se
sitivityofthemome
tequatio
totheslopeofthei
tersliceforces．Dime
sio
lessstabilitycoefficie
tsforhomoge
eousslopes，basedo
Equatio
99，havebee
publishedbyBishopa
dMorge
ster
92Itca
beshow
thatforagive
slopea
glea
dgive
soilpropertiesthefacr