预应力锚杆边坡稳定性评价 原文 另附译文 请自行下载

Zhuetal.

[23d]cb

b

1=Fx+∫aωudx,

c2=Fy+∫a

s′ωudx,

c3=Mc+∫b

a

rcωudx

Thesolutiontoeq.[22]followstheCramerrule,with[24a]λp= 3 [24b]η1= 1 [24c]η2= 2 3

inwhich

a11

a12a13[25a] =a21

a22a23a31a32a33c1

a12a13[25b] 1=c2

a22a23c3a32a33a11

c1a13[25c] 2=a21

c2a23a31c3a33a11

a12c1[25d] 3=a21

a22c2a31

a32

c3

Illustrativeexamples

Example1

Aslopewithaheightof15mandaninclinationof45°isshowninFig.3a.Theslopemassconsistsoftwotypesofsoils,whoseparametersarepresentedinFig.3a.Theanchoristobeappliedatthehalfheightoftheslopewithanincli-nationof30°tothehorizontal.

Beforetheanchorisapplied,thefactorofsafetyforthisslopeis0.998,calculatedwiththeSpencermethod.Whenananchorloadof300kNperunitlengthisappliedtotheslopeandadrainedconditionisassumed(i.e.,=0),thefactorofsafetyoftheslopeisincreasedto1.286inthepresentap-proach.ThenormalstressdistributionovertheslipsurfaceaftertheapplicationoftheanchorloadisshowninFig.3b.Itcanbeseenthatundertheactionoftheanchorload,thenormalstressontheslipsurfaceiscontinuousandfairlysmoothinshape,withamaximumvalueof103kPaoccur-ringincloseproximitytothepointofactionoftheanchorload.Ifaminimumfactorofsafetyisrequiredfortheslope,thentheminimumanchorloadcanbedirectlycomputedbyusingeq.[24a]withavalueof485kN/m.

Forcomparisonpurposes,theSpencermethod,withcon-ventionaltreatmentofanchorloads,isalsousedinthisex-ample,andthecorrespondingresultsareshowninFig.3a.Inthiscase,thefactorofsafetyfortheslopewiththeanchor

1347

Fig.3.Slopeprofileandnormalstressesontheslipsurfaceforexample1.(a)Slopeprofileandsoilparameters.(b)Normalstressesonslipsurfacecomputedbyconventionalandpresentmethods.GWL,groundwaterlevel.

loadof300kN/mis1.357,whichis6%largerthanthatpro-videdintheabovesolution.Fromthepracticalpointofview,suchadifferenceisrathersmall.Theassociatednor-malstressdistributionontheslipsurfaceisalsoshowninFig.3b.Itcanbeseenthatthenormalstressontheslipsur-faceincreasesabruptlyatthepointimmediatelyunderthepointofactionoftheanchorload.Thisisquiteunreasonablefromthestaticpointofview,andthusonecannotensurethattheconventionalprocedureisvalidforanchorloadsinallcases(Krahn2003).

Example2

Theslopeprofileofanotherexampleandthesoilparame-tersareshowninFig.4.Threeanchorsaretobeappliedtostabilizethisslope.Foraslopewithoutapredefinedfailuresurface,thestabilizationmeasureshouldensurethatallpo-tentialslipsurfaceshavefactorsofsafetygreaterthanaspecifiedvalue,say1.2forthisexample.Alllocalcriticalslipsurfaceswithfactorsofsafetyof<1.2arelocatedbyus-ingthecriticalslipfieldmethod(Zhu2001).Atotalof11criticalslipsurfacesareplottedinFig.4.Thevaluesoffac-torsofsafety(Floadss0)correspondingtotheseslipsurfaceswith-outanchorarepresentedinthesecondcolumnofTable1.Toevaluatetheeffectonslopestabilityofpossibleexcesspore-waterpressureinducedbyabruptapplicationoftheanchorload,weassumethattheporepressureparameter()variesbetween0and1.0.

Thefactorsofsafetywithanchorloads(P1000kN/m)andtheloadfactorsrequiredby1=Pthe2=Pspecified3=factorofsafetyof1.2arepresentedinTable1for=0.00,0.25,0.50,0.75,and1.00.ItcanbeseenfromTable1that