预应力锚杆边坡稳定性评价 原文 另附译文 请自行下载

Zhuetal.Asisshownineqs.[1a]–[1c],ifonlyoneanchorloadacts,thechangesinmajorandminorprincipalstresseswouldbe[7a] σ1=λpσr[7b] σ3=0

Thus[8]

u=λpσrwhere=BA.

However,iftwoormoreanchorloadsact,thesoilintheslopewillnolongerbeunderuniaxialstress.Becauseweareattemptingtoonlyapproximatelyevaluatetheeffectofthedegreeofdrainageonslopestability, σthesimplealgebraicsumofσ1ishereinassumedtobercausedbyindividualan-chorloads.

Beforetheapplicationofanchorloads,wecancalculatethefactorofsafetyfortheslopewithexistingmethodsofslicesandobtainthenormalstressontheslipsurfaceσ0.Af-tertheanchorloadsareapplied,thefactorofsafetyfortheslopewouldchangeandwouldneedtoberecalculated.Ratherthanusingtheconventionalmethodsofslices,whichmakeassumptionsabouttheintersliceforces,weapplytheprincipleofthenewlyproposedprocedure(Zhuetal.2003)bymodifyingthenormalstressontheslipsurfaceandusingittocomputethestabilityoftheanchor-reinforcedslopes.Becausetherearethreeequilibriumconditionsforthewholeslidingbody,andoneunknown(i.e.,thefactorofsafety,Fs)istobedetermined,wecanassumenormalstress(σ)ontheslipsurface,withtwoauxiliaryunknowns.Natu-rally,theσnormalstress(σ)iscontributedbytwoparts:σandλweassume0thatpp.Torendertheproblemdeterminate,[9]

σ=η1σ0+η2λpσp

whereη1andη2aretheauxiliaryunknowns.

Aconstantfactorofsafety(Fs)isassignedtothewholeslipsurface.TheshearresistancealongtheslipsurfaceisdeterminedbytheMohr–Coulombfailurecriterionandtheprincipleofeffectivestress:[10]

τ=

1

F[(σ u u)tanφ′+c′]s

whereφ′andc′aretheeffectiveinternalfrictionangleand

cohesion,respectively.

Forsimplicity,supposethat[11]

ψ=tanφ′;c=c′

Fromeqs.[10]and[11],itfollowsthat[12]

τ=

1F[(σ u)ψ+c] 1λp σ1ψsFs

Fromthehorizontalandverticalforceequilibriumandthemomentequilibriumwithrespecttoanarbitrarilyspecifiedpoint(xc,yc),oneobtains[13a]

∫b

a( σs′+τ kcw)dx= λp∑Px

1345

[13b]∫b

a(σ+τs′ w)dx=

λp∑Py

[13c]

∫b

a( σs′+τ)(yc s)+(σ+τs′ w)(x xc)

kcw(yc 0.5∑s 0.5g)]dx

=λpPx(yp yc)+λp∑Py(xp xc)

wherePx(positivetotheright)andPverticalcomponentsy(positivedownwards)arehorizontalandofanchorloadP(thesuffixidentificationisomittedforsimplicity);s(x)andg(x)denotethecurvesoftheslipsurfaceandtheground,re-spectively;w(x)denotestheself-weightofasliceofunitwidth;ands′(x)istheinclinationoftheslipsurface(i.e.,s′=tanα).

Assumingthat[14a]Fb

x=∫akcwdx

[14b]

Fb

y=∫awdx

[14c]Mbc=∫a

[kcw(yc 0.5s 0.5g)+w(x xc)]dx[14d]

∑Mp=∑Px(yp yc)+∑Py(xp xc)

[14e]rσ(x)= s′(yc s)+x xc[14f]

rτ(x)=yc s+s′(x xc)

andconsideringeqs.[9]and[12],eqs.[13a]–[13c]arere-writtenas[15a]

∫b

a(η1σ0+η 2λpσp) s′+ψ1

F dxs

=Fx λp∑Px+

1b

F(uψ c)dxs∫a

+λp

b

F σ1ψdxs

∫a[15b]

∫b

a(η1σ0+η2λpσp) 1

1+s′ψF

dxs=Fy+λp∑Py+

1b

Fs′(uψ c)dxs∫a

+λpb

Fs

∫as′ σ1ψdx

[15c]

∫b

a(η1σ0+η2λ pσp) 1

rσ+rτψF

dxs

=Mc+λp∑Mp+

1b

Frτ(uψ c)dxs∫a

+λpb

Frτ σ1ψdx

s

∫aSolvingeqs.[15a]–[15c]simultaneouslywillyieldsolutionstothefactorofsafety(Fs)—ortheloadfactor(λp)ifFauxiliaryunknowns(λandλsisprescribed—andthe12)aswell.