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sanzhiyifu三支一扶

correspondingequilibriumbearingpressure.There-Anotherdefinitionthathasbeensuggestedforthefac-

torofsafetyisonebasedonmoments.Inthiscasethe

factorofsafetyisdefinedastheratiooftheavailable

resistingmomentdividedbytheactualdrivingmo-

ment:

availableresistingmoment

（6.100）

actualdrivingmoment

sultsaresummarizedinTable6.5.ReferringtoTable

6.5,itcanbeseenthatafactorofsafetyof1.25applied

totheshearstrengthproducesequilibriumofthefoot-

ingundertheappliedloadof10,000psf.Thisvalue

（1.25）forthefactorofsafetyappliedtoshearstrength

isconsiderablylessthanthecorrespondingvalueof

2.80appliedtoload,whichwascalculatedearlier[Eq.

（6.97）].Factorsofsafetythatareappliedtoloadfor

bearingcapacityarethusnotcomparabletothefactors

ofsafetyappliedtoshearstrength,asusedforslope

stabilityanalyses.

Thefactorofsafetywithrespecttoshearstrengthis

closerto1.0thanthefactorofsafetywithrespectto

load;however,themagnitudeofthedifferencevaries

significantlydependingonthevalueof?

.Consider,

forexample,theslopeshowninFigure6.32.Factors

ofsafetywerecalculatedforthethreedifferentsetsof

shearstrengthparametersshowninthisfigure.Theval-

uesoftheshearstrengthparameterswereselectedso

thatthefactorofsafetywithrespecttoshearstrength

[Eq.（6.1）]wasapproximately1.5.Foreachslopethe

factorsofsafetybothwithrespecttoshearstrengthand

withrespecttoloadwerecalculated.Thefactorof

safetywithrespecttoloadwascalculatedbymultiply-

ingtheunitweightofthesoilbyafactorofsafety

untiltheslopewasinjust-stableequilibriumwiththe

shearstrengthfullydeveloped.Thefactorsofsafety

forshearstrengthandloadaresummarizedforthe

threeslopesinTable6.6.Forthefirstsetofshear

strengths（?

0）thefactorsofsafetyforshear

strengthandloadareidentical.Thiswillalwaysbethe

casewhen?

0,forslopestabilityaswellasfor

bearingcapacityproblemssuchasthefootingshown

previously.Forthesecondsetofshearstrengthpa-

rameters,thefactorofsafetywithrespecttoloadwas

approximately11,whereasthefactorofsafetyfor

shearstrengthwasapproximately1.5.Thisrepresents

adifferenceofover700%.Finally,forthethirdsetof

shearstrengthparameters,?

36.9?

andc?

0,the

factorofsafetywithrespecttoshearstrengthwas1.5,

whereasthefactorofsafetywithrespecttoloadis

infinite（i.e.,nomatterhowlargetheweightofsoil,

theshearstrengthalwaysremainsgreaterthanthe

shearstress）.Insummary,thefactorsofsafetyfor

shearstrengthandforloadcanvaryfrombeingthe

sametobeingverydifferentforlargevaluesof?

and

thetwovaluesarenotcomparable.Becausethesoil

shearstrengthisoneofthelargestunknownsinaslope

stabilityanalysis—certainlyitpresentsgreateruncer-

taintythantheunitweightofsoilinalmostallin-

stances—itseemslogicaltoapplythefactorofsafety

toshearstrength.

FactorofSafetyforMoments

Anotherdefinitionthathasbeensuggestedforthefac-

torofsafetyisonebasedonmoments.Inthiscasethe

factorofsafetyisdefinedastheratiooftheavailable

resistingmomentdividedbytheactualdrivingmo-

ment:

availableresistingmoment

（6.100）

actualdrivingmoment

Thiscanberearrangedandwrittenas

CopyrightedMaterial

MECHANICSOFLIMITEQUILIBRIUMPROCEDURES

Md=Wa

Ms=rsl

Mt=TdT

Figure6.33

Simplereinforcedslopewithdrivingandre-

sistingmoments.

（6.101）

Equation（6.101）isanequilibriumequationthatex-

pressesabalancebetweenthedrivingmomentanda

developedresistingmomentthatisequaltothetotal

availableresistingmomentfactoredbythefactorof

safety.Iftheresistingmomentisdueentirelytothe

shearstrengthofthesoil,thefactorofsafetyapplied

totheresistingmomentisthesameasthefactorof

safetydefinedearlierwithrespecttoshearstrength.In

fact,itwasshownearlierfortheSwedishCircle

method[Eq.（6.28）]thatthefactorofsafetydefined

withrespecttoshearstrengthwasequaltotheratioof

momentsexpressedbyEq.（6.100）.Inthiscasethere

isnodifferencebetweenthefactorsofsafetydefined

withrespecttoshearstrength[Eq.（6.1）]andwithre-

specttomoments[Eq.（6.100）].

Ifinsteadofasimpleslope,whereallresistanceis

fromtheshearstrengthofthesoil,thereareadditional

forcesduetoreinforcement,thetwodefinitionsoffac-

torofsafety[Eqs.（6.1）and（6.100）]canbequitedif-

ferent.Also,thedefinitionofthefactorofsafetyasa

ratioofmomentscanbeambiguous.Toillustratethis,

considertheslopeandcircularslipsurfaceshownin

Figure6.33.Thisslopehasasinglelayerofreinforce-

ment.Letthemomenttakenaboutthecenterofthe

circleduetothereinforcementbedesignatedasMt.

Letthecorrespondingmomentsduetotheavailable

shearstrengthbedesignatedasMs,andthemoment

duetotheweightofsoilbedesignatedasMd.Wecan

nowdefineafactorofsafetywithrespecttoresisting

anddrivingmoments.Ifwechoosetoaddthemoment

duetothereinforcementtotheresistingmomentdue

totheshearstrengthofthesoil,wecanwrite

（6.102）

Alternatively,wecanchoosetosubtracttherestoring

momentduetothereinforcementfromthedrivingmo-

mentduetothesoilweightandwrite

（6.103）

Equations（6.102）and（6.103）bothrepresentlegiti-

matedefinitionsforthefactorofsafetydefinedasa

ratioofmoments;however,thetwodefinitionsgive

differentvaluesforthefactorofsafety.Equations

（6.102）and（6.103）aremoreeasilyinterpretedifwe

rewritethemasfollows:

ForEq.（6.102）wecanwrite

（6.104）

andforEq.（6.103）wecanwrite

（6.105）

Bothoftheseequationscanbeinterpretedasequilib-

riumequations.Thefirstequation,wherethecontri-

butionofthereinforcementwasaddedtotheresisting

moment,statesthatthedrivingmomentisbalancedby

momentsduetothedevelopedshearstrengthandthe

developedreinforcementforces,wheredevelopedval-

uesaretheavailablevaluesreducedbyafactorof

safety,F.Thus,thefactorofsafetyinEq.（6.104）is

appliedequallytothereinforcementforcesandthe

shearstrength.Thesecondofthetwoequilibrium

equations[Eq.（6.105）],wherethereinforcementcon-

tributionwasusedtoreducethedrivingmoments,

statesthatthedrivingmomentisinequilibriumwith

thefullreinforcementforce,plusthefactoredresis-

tanceduetotheshearstrengthofthesoil.Inthiscase

thefactorofsafetyisappliedonlytothesoilshear

strength.

Toillustratethedifferencesinvaluescomputedfor

thefactorsofsafetyofreinforcedslopesdependingon

howthefactorofsafetyisdefined,considertheslope

CopyrightedMaterial

POREWATERPRESSUREREPRESENTATION

0.5

Saturatedclay

c=350psf,φ=0,γ=98pcf

T=9000lb/ft.

Case

FactorofSafety

Factorofsafetyappliedtoshearstrength

only.

1.51

Factorofsafetyappliedtoreinforcement

forceonly.

4.82

Factorofsafetyappliedtobothshear

strengthandreinforcementforce.

1.32

10ft

20ft

Figure6.34

Reinforcedslopewithcomputedfactorsofsafetydefined（applied）inthree

differentways.

showninFigure6.34.Thisslopehasasinglelayerof

reinforcementand?

0.Thefactorofsafetyforthe

unreinforcedslopeis0.91,thusindicatingthatthere-

inforcementisnecessarytomaketheslopestable.Fac-

torsofsafetywerefirstcomputedbyapplyingthe

factorofsafetytoshearstrengthonly[Eq.（6.105）]and

tobothshearstrengthandreinforcementforceequally

[Eq.（6.104）].Athirdfactorofsafetywascomputed

byapplyingthefactorofsafetytoonlythereinforce-

mentforce（i.e.,theshearstrengthwasassumedtobe

fullymobilizedandthereinforcementforcewasre-

ducedbythefactorofsafety）.Thethreedifferentval-

uesforthefactorofsafetyshowninFigure6.34range

fromapproximately1.3to4.8,adifferenceofover

threefold.Clearly,themannerinwhichthefactorof

safetyisdefinedwillaffectthecomputedvalue.

Althoughanyoftheforegoingdefinitionsforfactor

ofsafetycouldbeusedtocomputeafactorofsafety,

onlyEq.（6.105）isconsistentwiththedefinitionof

factorofsafetygenerallyusedforslopestabilityanal-

ysesthroughoutthisbook.Insteadofdefiningand

computingafactorofsafetythatisappliedequallyto

thereinforcementforcesandsoilstrength[Eq.（6.104）]

ortoonlythereinforcementforce,itseemsmoreap-

propriatefirsttoapplyasuitablefactorofsafetytothe

reinforcementforcesbeforeanyslopestabilitycom-

putationsbeginandthencomputeaseparatefactorof

safetywithrespecttotheshearstrengthofthesoil.

Thisapproachisrecommendedandisdiscussedfurther

inChapter8.

POREWATERPRESSUREREPRESENTATION

Whenevertheshearstrengthofoneormorematerials

isexpressedintermsofeffectivestresses,theporewa-

terpressuresmustbedeterminedandrepresentedin

theslopestabilityanalysis.Severalmethodsexistfor

doingthis,dependingontheseepageandgroundwater

conditionsandthedegreeofrigorrequired.Thevari-

ousmethodsaredescribedanddiscussedinthissec-

tion.

FlowNetSolutions

Whensteady-stateseepageconditionsexistinaslope,

agraphical

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