retaining wall
DESCRIPTION
LFD Retaining WallTRANSCRIPT
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6/1/2015 751.24LFDRetainingWallsEngineeringPolicyGuide
http://epg.modot.org/index.php?title=751.24_LFD_Retaining_Walls 1/81
PrintableVersionofSeptember2011LFDRetainingWallsInfo
EPG751.24LFDRetainingWallspresentstheverylatestinformation,butthispdffilemaybehelpfulforthosewantingtoeasilyprinttheLFDseismicinformationasitwasinSeptember2011.
AdditionalInformationAASHTO5.1
AdditionalInformation
AASHTO5.2.1
AdditionalInformation
AASHTO5.2.1.4&5.8
751.24LFDRetainingWallsFromEngineeringPolicyGuide
Contents1751.24.1General
1.1751.24.1.1WallTypeSelection1.2751.24.1.2Loads
2751.24.2MechanicallyStabilizedEarth(MSE)Walls2.1751.24.2.1Design2.2751.24.2.2Details
3751.24.3CastInPlaceConcreteRetainingWalls3.1751.24.3.1UnitStresses3.2751.24.3.2Design
3.2.1751.24.3.2.1SpreadFootings3.2.2751.24.3.2.2PileFootings3.2.3751.24.3.2.3CounterfortWalls
3.3751.24.3.3Example1:SpreadFootingCantileverWall3.4751.24.3.4Example2:LShapedCantileverWall3.5751.24.3.5Example3:PileFootingCantileverWall3.6751.24.3.6Dimensions3.7751.24.3.7Reinforcement3.8751.24.3.8Details
751.24.1General
Retainingwallshallbedesignedtowithstandlateralearthandwaterpressures,includinganyliveanddeadloadsurcharge,theselfweightofthewall,temperatureandshrinkageeffect,liveloadandcollisionforces,andearthquakeloadsinaccordancewiththegeneralprinciplesofAASHTOSection5andthegeneralprinciplesspecifiedinthisarticle.
751.24.1.1WallTypeSelection
Selectionofwalltypeshallbebasedonanassessmentofthemagnitudeanddirectionofloading,depthtosuitablefoundationsupport,potentialforearthquakeloading,presenceofdeleteriousenvironmentalfactors,wallsitecrosssectionalgeometry,proximityofphysicalconstraints,tolerableanddifferentialsettlement,facingappearanceandeaseandcostofconstruction.
ThefollowingwalltypesarethemostcommonlyusedinMoDOTprojects
MechanicallyStabilizedEarthRetainingWallsCastInPlaceConcreteCantileverRetainingWalls
CantileverWallsonSpreadFootingsCantileverWallonPileFootingsLShapedWallsonSpreadFootings
MechanicallyStabilizedEarth(MSE)RetainingWalls
MSEretainingwallsuseprecastblockorpanellikefacingelementscombinedwitheithermetallicorgeosynthetictensilereinforcementsinthesoilmass.MSEwallsarepreferredovercastinplacewallsbecausetheyareusuallymoreeconomical.Otheradvantagesincludeawidevarietyofdesignstyles,easeandspeedofinstallation,andtheirabilitytoaccommodatetotalanddifferentialsettlements.Walldesignheightsupwardsof80ft.aretechnicallyfeasible(FHFWSA96071).MSEwallsmaybeusedtoretainfillforendbentsofbridgestructures.
SituationsexistwheretheuseofMSEwallsiseitherlimitedornotrecommended.Someobstaclessuchasdropinlets,signtrusspedestalsorfootings,andfencepostsmaybeplacedwithinthereinforcingstriparea,however,theseobstaclesincreasethedifficultyandexpenseofprovidingsufficientreinforcingstripsforstability.BoxculvertsandhighwaydrainagepipesmayrunthroughMSEwalls,butitispreferablenottorunthepipesclosetoorparalleltothewalls.Utilitiesotherthanhighwaydrainageshouldnotbeconstructedwithinthereinforcingstriparea.
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AdditionalInformation
AASHTO3.20.1
BecautiouswhenusingMSEwallsinafloodplain.Afloodcouldcausescouringaroundthereinforcementandseepageofthebackfillmaterial.SoilreinforcementsshouldnotbeusedwhereexposuretogroundwatercontaminatedbyacidminedrainageorotherindustrialpollutantsasindicatedbyalowpHandhighchloridesandsulfatesexist.Galvanizedmetallicreinforcementsshallnotbeusedwherestrayelectricalgroundcurrentscouldoccuraswouldbepresentnearanelectricalsubstation.
Sufficientrightofwayisrequiredtoinstallthereinforcingstripswhichextendintothebackfillareaatleast8ft.,70%ofthewallheightorasperdesignrequirements,whicheverisgreater.Finally,barriercurbsconstructedoverorinlinewiththefrontfaceofthewallshallhaveadequateroomprovidedlaterallybetweenthebackofthewallfacingandthecurborslabsothatloadisnotdirectlytransmittedtothetopwallfacingunits.
ConcreteCantileverWallonSpreadFooting
Concretecantileverwallsderivetheircapacitythroughcombinationsofdeadweightandstructuralresistance.Thesewallsareconstructedofreinforcedconcrete.
ConcretecantileverwallsareusedwhenMSEwallsarenotaviableoption.Cantileverwallscanreducetherockcutrequiredandcanalsoprovidesolutionswhentherearerightofwayrestrictions.Concretewallsalsoprovidebetterstructuralcapacitywhenbarriercurbsontopofthewallsarerequired.
Counterfortsareusedonrareoccasions.Signboardtyperetainingwallsareaspecialcaseofcounterfortretainingwalls.Theyareusedwherethesoilconditionsaresuchthatthefootingsmustbeplacedwellbelowthefinishedgroundline.Forthesesituationsthewallisdiscontinued12in.belowthegroundlineorbelowthefrostline.Counterfortsmayalsobeacostsavingsoptionwhenthewallheightapproaches20ft.(FoundationAnalysisandDesignbyJosephE.Bowles,4thed.,1988).However,otherfactorssuchaspoorsoilconditions,slopeoftheretainedsoil,walllengthanduniformityinwallheightshouldalsobeconsideredbeforeusingcounterforts.
ConcreteCantileverWallonPileFooting
Concretecantileverwallsonpilefootingsareusedwhenthesoilconditionsdonotpermittheuseofspreadfootings.Thesewallsarealsousedwhenanendbentrequireswingslongerthan22feet.Inthesecasesastubwingisleftattachedtotheendbentandtherestofthewingisdetachedtobecomearetainingwall.
ConcreteLShapedRetainingWallonSpreadFootings
ConcreteLShapedwallsarecantileverwallswithoutheels.Thesewallsareusedwhentherearespacelimitationsforcantileverwalls.Sincethereisnoheeltheheightofthesewallsislimitedtoabout7ft.dependingonthesoilconditionsandtheslopeoftheretainedsoil.
LShapedWallsareoftenusednexttoroadwayswherethefootingsarefrequentlyusedasshouldersandwherethewallwillrequirestructuralcapacityforcollisionforces.
751.24.1.2Loads
DeadLoads
DeadloadsshallbedeterminedfromtheWeightofMaterialsTableoftheLoadsSectionintheBridgeManual.
EquivalentFluidPressure(EarthPressures)
FordeterminingequivalentearthpressuresforGroupLoadingsIthroughVItheRankineFormulaforActiveEarthPressureshallbeused.
RankineFormula: where:
Ca= =coefficientofactiveearthpressure
Pa=equivalentactiveearthpressure
H=heightofthesoilfaceattheverticalplaneofinterest
=unitweightofsoil
=slopeoffillindegrees
=angleofinternalfrictionofsoilindegrees
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Example
Given:
=3:1(H:V)slope
=25
s=0.120kcf
H=10ft
=arctan =18.4
Ca= =0.515
Pa=(1/2)(0.515)(0.120kips/ft3)(10ft)2=3.090kipsperfootofwalllength
TheangleshallbedeterminedbytheMaterialsDivisionfromsoiltests.IftheanglecannotbeprovidedbytheConstructionandMaterialsDivision(http://wwwi/intranet/cm/default.htm)aangleof27degreesshallbeused.
Drainageshallbeprovidedtorelievewaterpressurefrombehindallcastinplaceconcreteretainingwalls.Ifadequatedrainagecannotbeprovidedthenwallsshallbedesignedtoresistthemaximumanticipatedwaterpressure.
SurchargeDuetoPoint,LineandStripLoads
Surchargeduetopointandlineloadsonthesoilbeingretainedshallbeincludedasdeadloadsurcharge.TheeffectoftheseloadsonthewallmaybecalculatedusingFigure5.5.2BfromAASHTO.
Surchargeduetostriploadsonthesoilbeingretainedshallbeincludedasadeadloadsurchargeload.ThefollowingprocedureasdescribedinPrinciplesofFoundationEngineeringbyBrajaM.Das(1995)shallbeappliedtocalculatetheseloadswhenstriploadsareapplicable.Anexampleofthisapplicationiswhenaretainingwallisusedinfrontofanabutmentsothatthewallisretainingthesoilfrombehindtheabutmentasastriploadonthesoilbeingretainedbythewall.
RetainingWallinfrontofanAbutment
Theportionofsoilthatisintheactivewedgemustbedeterminedbecausethesurchargepressureonlyaffectsthewallifitactsontheactive
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wedge.TheactualfailuresurfaceinthebackfillfortheactivestatecanberepresentedbyABCshowninthefigurebelow.AnapproximationtothefailuresurfacebasedonRankine'sactivestateisshownbydashedlineAD.Thisapproximationisslightlyunconservativebecauseitneglectsfrictionatthepseudowalltosoilinterface.
Thefollowingvariablesareshowninthefigurebelow:
=slopeoftheactivefailureplaneindegrees=slopeoffillindegreesH=heightofthepseudowall(fomthebottomofthefooting).L1=distancefrombackofstemtobackoffootingheelL2=distancefromfootingheeltointersectionoffailureplanewithgroundsurface
DeterminationofActiveWedges
Inordertodetermine,thefollowingequationwhichhasbeenderivedfromRankine'sactiveearthpressuretheorymustbesolvedbyiteration:
=angleofinternalfrictionofsoilindegrees
Agoodestimateforthefirstiterationistolet=45+(/2).Inlieuofiteratingtheaboveequationaconservativeestimateforis45.Oncehasbeenestablished,anestimateofL1isneededtodetermineL2.Fromthegeometryofthevariablesshownintheabovefigure:
Theresultantpressureduetothestriploadsurchargeanditslocationarethendetermined.Thefollowingvariablesareshowninthefigurebelow:
q=loadperunitareaPs=resultantpressureonwalldueonlytosurchargeearthpressure=locationofPsmeasuredfromthebottomofthefooting
L3=distancefrombackofstemtowheresurchargepressurebegins
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AdditionalInformation
AASHTO3.20.3&5.5.2
SurchargePressureonRetainingWall
Fromthefigure:
Ps= where
where
Whenapplicable,Psisappliedtothewallinadditiontootherearthpressures.Thewallisthendesignedasusual.
LiveLoadSurcharge
Liveloadsurchargepressureofnotlessthantwofeetofearthshallbeappliedtothestructurewhenhighwaytrafficcancomewithinahorizontaldistanceequaltoonehalfofthewallheight,measuredfromtheplanewhereearthpressureisapplied.
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AdditionalInformation
AASHTO3.24.5.1.1&5.5.6.1
AdditionalInformation
AASHTO3.24.2&3.30
AdditionalInformation
AASHTOFigure2.7.4B
LiveLoadSurcharge
PLLS=(2ft.)sCaH=pressureduetoliveloadsurchargeonly
s=unitweightofsoil(Note:AASHTO5.5.2specifiesaminimumof125pcfforliveloadsurcharge,MoDOTpolicyallows120pcfasgivenfromtheWeightofMaterialsTableoftheLoadsSectionintheBridgeManual.)Ca=coefficientofactiveearthpressure
H=heightofthesoilfaceattheverticalplaneofinterest
Theverticalliveloadsurchargepressureshouldonlybeconsideredwhencheckingfootingbearingpressures,whendesigningfootingreinforcement,andwhencollisionloadsarepresent.
LiveLoadWheelLines
Liveloadwheellinesshallbeappliedtothefootingwhenthefootingisusedasaridingorparkingsurface.
DistributeaLLWLequalto16kipsasastriploadonthefootinginthefollowingmanner.
P=LLWL/E
whereE=0.8X+3.75
X=distanceinft.fromtheloadtothefrontfaceofthewall
Thewheellinesshallmove1ft.fromthebarriercurborwallto1ft.fromthetoeofthefooting.
CollisionForces
Collisionforcesshallbeappliedtoawallthatcanbehitbytraffic.Applyapointloadof10kipstothewallatapoint3ft.abovethefinishedgroundline.
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AdditionalInformation
1992AASHTODiv.IAEqns.C63and
C64
Section
Distributetheforcetothewallinthefollowingmanner:
Forceperftofwall=(10kips)/2L
Profile
Whenconsideringcollisionloads,a25%overstressisallowedforbearingpressuresandafactorofsafetyof1.2shallbeusedforslidingandoverturning.
WindandTemperatureForces
Theseforcesshallbedisregardedexceptforspecialcases,consulttheStructuralProjectManager.
Whenwallsarelongerthan84ft.,anexpansionjointshallbeprovided.
Contractionjointspacingshallnotexceed28feet.
SeismicLoads
RetainingwallsinSeismicPerformanceCategoryA(SPCA)andSPCBthatarelocatedadjacenttoroadwaysmaybedesignedinaccordancewithAASHTOspecificationsforSPCA.RetainingwallsinSPCBwhicharelocatedunderabridgeabutmentorinalocationwherefailureofthewallmayaffectthestructuralintegrityofabridgeshallbedesignedtoAASHTOspecificationsforSPCB.AllretainingwallslocatedinSPCCandSPCDshallbedesignedinaccordancetoAASHTOspecificationsforthecorrespondingSPC.
InseismiccategoryB,CandDdetermineequivalentfluidpressurefromMononobeOkabestaticmethod.
PAE=equivalentactiveearthpressureduringanearthquake
PAE=0.5sH2(1kv)KAEwhere
KAE=seismicactivepressurecoefficient
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AdditionalInformation
AASHTO5.2.2.3&Div.IA6.4.3
AdditionalInformation
AASHTOTable3.22.1A
AdditionalInformation
AASHTO5.14.2
s=unitweightofsoil
kv=verticalaccelerationcoefficient
kh=horizontalaccelerationcoefficientwhichisequalto0.5Aforallwalls,
but1.5AforwallswithbatteredpileswhereA=seismicaccelerationcoefficient
Thefollowingvariablesareshowninthefigurebelow:
=angleofinternalfrictionofsoil
=
=slopeofsoilface
=angleoffrictionbetweensoilandwallindegrees
i=backfillslopeangleindegrees
H=distancefromthebottomofthepartofthewalltowhichthepressureisappliedtothetopofthefillatthelocationwheretheearthpressureistobefound.
ActiveSoilWedge
GroupLoads
ForSPCAandB(ifwalldoesnotsupportanabutment),applyAASHTOGroupILoadsonly.Bearingcapacity,stabilityandslidingshallbecalculatedusingworkingstressloads.Reinforcedconcretedesignshallbecalculatedusingloadfactordesignloads.
AASHTOGroupILoadFactorsforLoadFactorDesignofconcrete:=1.3
D=1.0forconcreteweight
D=1.0forflexuralmember
E=1.3forlateralearthpressureforretainingwalls
E=1.0forverticalearthpressure
LL=1.67forliveloadwheellines
LL=1.67forcollisionforces
E=1.67forverticalearthpressureresultingfromliveloadsurcharge
E=1.3forhorizontalearthpressureresultingfromliveloadsurcharge
ForSPCB(ifwallsupportsanabutment),C,andDapplyAASHTOGroupILoadsandseismicloadsinaccordancewithAASHTODivisionIASeismicDesignSpecifications.
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AdditionalInformation
AASHTODiv.IA4.7.3
Whenseismicloadsareconsidered,loadfactorforallloads=1.0.
751.24.2MechanicallyStabilizedEarth(MSE)Walls
751.24.2.1Design
DesignsofMechanicallyStabilizedEarth(MSE)wallsarecompletedbyconsultantsorcontractorsinaccordancewithSection5oftheAASHTOSpecifications.MoDOTInternetsitecontainsalistingoffacingunitmanufacturers,soilreinforcementsuppliers,andwallsystemsupplierswhichhavebeenapprovedforuse.SeeSec720(http://www.modot.mo.gov/business/standards_and_specs/Sec0720.pdf)andSec1010(http://www.modot.mo.gov/business/standards_and_specs/Sec1010.pdf)foradditionalinformation.TheGeotechnicalSection(http://wwwi/intranet/cm/materials/Geotechnical.htm)isresponsibleforcheckingglobalstability,whichshouldbereportedontheFoundationInvestigationGeotechnicalReport.ForMSEwallpreliminaryinformation,seeEPG751.1.4.3MSEWalls(http://epg.modot.mo.gov/index.php?title=751.1_Preliminary_Design#751.1.4.3_MSE_Walls).
Generalpolicy
Smallblockwallsarelimitedtoa10ft.heightinonelift.
Forsmallblockwalls,topcapunitsshallbeusedandshallbepermanentlyattachedbymeansofaresinanchorsystem.
Forlargeblockwalls,capstonemaybesubstitutedforcopingandeithershallbepermanentlyattachedtowallbypaneldowels.
MSEwallsshallnotbeusedwhereexposuretoacidwatermayoccursuchasinareasofcoalmining.
MSEwallsshallnotbeusedwherescourisaproblem.
MSEwallswithmetallicsoilreinforcementshallnotbeusedwherestrayelectricalgroundcurrentsmayoccuraswouldbepresentnearelectricalsubstations.
Noutilitiesshallbeallowedinthereinforcedearthiffutureaccesstotheutilitieswouldrequirethatthereinforcementlayersbecut,orifthereisapotentialformaterial,whichcancausedegradationofthesoilreinforcement,toleakoutoftheutilitiesintothewallbackfill,withtheexceptionofstormwaterdrainage.
Theinterioranglebetweentwowallsmustbegreaterthan70.
Smallblockwallsmaybebatteredupto1.5in.perfoot.
Thefrictionangleusedforthecomputationofhorizontalforceswithinthereinforcedsoilshallbegreaterthanorequalto34.
Allreinforcementshallbeepoxycoatedintheconcretefaceforwallssubjecttosprayingfromadjacentroadways(approximately10ft.orlessfromthecurb.)
AllconcreteexceptfacingpanelsorunitsshallbeCLASSBorB1.
Thefrictionangleofthesoiltoberetainedbythereinforcedearthshallbelistedontheplansaswellasthefrictionangleforthefoundationmaterialthewallistoreston.
Seismicperformancecategoryandaccelerationcoefficientshallbelistedontheplans.
FactorsofSafetyforMSEwallsshallbe2.0foroverturning,1.5forsliding,2.0forultimatebearingcapacityand1.5forpulloutresistance.
FactorsofSafetyforseismicdesignshallbe1.5foroverturningand1.1forsliding.
Guttertypeshouldbeselectedatthecoreteammeeting.
Whengutterisrequiredwithoutfencing,useTypeAorTypeBgutter(fordetail,seeStd.Plan609.00(http://www.modot.mo.gov/business/standards_and_specs/documents/60900.pdf)).
Whengutterisrequiredwithfencing,useModifiedTypeAorModifiedTypeBgutter(fordetail,seeStd.Plan607.11(http://www.modot.mo.gov/business/standards_and_specs/documents/60711.pdf)).
Whenfencingisrequiredwithoutgutter,placeintubeandgroutbehindtheMSEwall(fordetail,seeFig.751.24.2.1.7,FencePostConnectionBehindMSEWall(withoutgutter).
Donotusesmallblockwallsinthefollowinglocations:
Withinthesplashzonefromsnowremovaloperations(assumedtobe15ft.fromtheedgeoftheshoulder).
Wheretheblockswillbecontinuouslywetted,suchasaroundsourcesofwater.
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Whereblockswillbelocatedbehindbarriercurbsorotherobstaclesthatwilltrapsaltladensnowfromremovaloperations.
Forstructurallycriticalapplications,suchascontainingnecessaryfillaroundstructures.
Intieredwallsystems.
Forlocationswheresmallblockwallsarenotdesirable,considercoloringagentsand/orarchitecturalformsusinglargeblockwallsforaestheticinstallations.
Drainagepipesforalllargeandsmallblockwallsshallbeaminimumofa6in.diameterperforatedPVCorPEpipe(SeeSec1013(http://www.modot.mo.gov/business/standards_and_specs/Sec1013.pdf))unlesslargersizesarerequiredbydesignbythewallmanufacturer.Showdrainagepipesizeonplans.Screensshouldbeinstalledandmaintainedondrainpipeoutlets.Outletscreensandcleanoutsshouldbedetailed(shownonconstructiondrawing).
ForslabdrainlocationnearMSEWall,seeEPG751.10.3.1DrainType,AlignmentandSpacing.
RoadwayrunoffshouldbedirectedawayfromrunningalongfaceofMSEwallsusedaswingwallsonbridgestructures.
MSEWallConstruction:
CorrugatedMetalPipePileSpacersGuidance:
Corrugatedmetalpipepilespacers(CMPPS)shallbeusedatpilelocationsbehindmechanicallystabilizedearthwallstoprotectthewallreinforcementwhendrivingpileforthebridgesubstructureatendbents(s).CMPPSshallhaveaninsidediametergreaterthanthatofthepileandlargeenoughtoavoiddamagetothepipewhendrivingthepile.ThebottomoftheCMPPSshallbeplaced5ft.min.belowthebottomoftheMSEwalllevelingpad.Thepipeshallbefilledwithsandorotherapprovedmaterialafterthepileisplacedandbeforedriving.CMPPSshallbeaccuratelylocatedandcappedforfuturepileconstruction.
Alternatively,thecontractorshallbegiventheoptionofdrivingthepilesbeforeconstructionoftheretainingwallandplacingthewallreinforcingandbackfillmaterialaroundthepiling.Thecontractorshalladequatelysupportthepilingtoinsurethatproperpilealignmentismaintainedduringthewallconstruction.Thecontractorsplanforbracingthepileshallbesubmittedtotheengineerforreview.
Pilingshallbedesignedfordowndrag(DD)loadsduetoeithermethod.OversizedCMPPSwithsandplacedafterdrivingmaybeconsideredtomitigatesomeoftheeffectsofdowndrag(DD)loads.OversizedCMPPSshallaccountforpilesize,thermalmovementsofthebridge,pileplacementplan,andverticalandhorizontalplacementtolerances.
TheminimumclearancefromthebackfaceofMSEwallstothefrontfaceoftheendbentbeamshallbe3ft.9in.(typ.).The3ft.9in.dimensionisbasedontheuseof18in.CMPPS&FHWANHI1024,Figure517C,whichwillhelpensurethatsoilreinforcementisnotskewedmorethan15fornutandboltreinforcementconnections.Othertypesofconnectionsmayrequiredifferentmethodsforsplaying.Intheeventthatthe3ft.9in.dimensionorsetbackcannotbeused,thefollowingguidanceforCMPPSclearanceshallbeused:CMPPSshallbeplaced18in.clearmin.fromthebackfaceofMSEwallpanels12in.minimumclearanceisrequiredbetweenCMPPSandlevelingpadand18in.minimumclearanceisrequiredbetweenlevelingpadandpile.
MSEWallPlanandGeometrics
Aplanviewshallbedrawnshowingabaselineorcenterline,roadwaystationsandwalloffsets.Theplanshallcontainenoughinformationtoproperlylocatethewall.Theultimaterightofwayshallalsobeshown,unlessitisofasignificantdistancefromthewallandwillhavenobearingonthewalldesignorconstruction.
Stationsandoffsetsareestablishedbetweenoneconstructionbaselineorroadwaycenterlineandawallcontrolline(baseline).Somewalldesignscontainaslightbatter,whileothersarevertical.Awallcontrollineissetatthefrontfaceofthewall,eitheralongthetoporatthebaseofthewall,whicheveriscriticaltotheproposedimprovements.Forbatteredwalls,toallowforbatteradjustmentsofthesteppedlevelpadorvariationofthetopofthewall,thewallcontrolline(baseline)istobeshownatafixedelevation.Forbatteredwalls,theoffsetlocationandelevationofcontrollineshallbeindicated.Allhorizontalbreaksinthewallaregivenstationoffsetpoints,andwallswithcurvatureindicatestationoffsetstothePCandPTofthewall,andtheradius.
Anyobstacleswhichmaypossiblyinterferewithwallreinforcingstripsareshown.Drainagestructures,lighting,ortrusspedestalsandfootings,etc.aretobeshown,withstationoffsettocenterlineoftheobstacle,withobstaclesize.Skewanglesareshowntoindicatetheanglebetweenawallandapipeorboxwhichrunsthroughthewall.
Elevationsatthetopandbottomofthewallshallbeshownat25ft.intervalsandatanybreakpointsinthewall.
Curvedataand/oroffsetsshallbeshownatallchangesinhorizontalalignment.Ifbatteredwallsystemsareusedoncurvedstructures,showoffsetsat10ft.(max.)intervalsfromthebaseline.
Detailsofanyarchitecturalfinishes(formliners,concretecoloring,etc.).
Detailsofthreadedrodconnectingthetopcapblock.
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Estimatedquantities,totalsq.ft.ofmechanicallystabilizedearthsystems.
Proposedgradeandtheoreticaltopoflevelingpadelevationshallbeshowninconstantslope.Slopelineshallbeadjustedperproject.Topofwallorcopingelevationandstationingshallbeshowninthedevelopedelevationperproject.Iflevelingpadisanticipatedtoencounterrock,thencontacttheGeotechnicalSectionforlevelingpadminimumembedmentrequirements.
MSEWallCrossSections
Atypicalwallsectionforgeneralinformationisshown.
Additionalsectionsaredrawnforanyspecialcriteria.Thefrontfaceofthewallisdrawnvertical,regardlessofthewalltype.
Anyfencingandbarriercurbareshown.
Barriersifneededareshownonthecrosssection.Concretebarriersareattachedtotheroadwayorshoulderpavement,nottotheMSEwall.StandardTypeBbarriercurbsareplacedalongwallfaceswhentraffichasaccesstothefrontfaceofthewallovershouldersofpavedareas.
751.24.2.2Details
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Fig.751.24.2.2MSEWallDevelopedElevationandPlan
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Fig.751.24.2.2TypicalSectionThroughGenericLargeBlockWall
Fig.751.24.2.2TypicalSectionThroughGenericSmallBlockWall
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Fig.751.24.2.2CapstoneAnchorDetails
Notes: Holesare5/8"round,extend4"intothethirdlayerofblocks,recessed2"deepby11/2"round.RodsorreinforcingbarsaresecuredbyanapprovedresinanchorsysteminaccordancewithSec1039
(http://www.modot.mo.gov/business/standards_and_specs/Sec1039.pdf).Recessholetobebackfilledwithnonshrinkcementgrout.
BatteredSmallBlockWalls
Batteredmechanicallystabilizedearthwallsystemsmaybeusedunlessthedesignlayoutspecificallycallsforaverticalwall(largeblockwallsshallnotbebatteredandsmallblockwallsmaybebuiltvertical).IfabatteredMSEwallsystemisallowed,thenthefollowingnoteshallbeplacedonthedesignplans:
"Thetopandbottomofwallelevationsaregivenforaverticalwall.Ifabatteredsmallblockwallsystemisused,theheightofthewallshallbeadjustedasnecessarytofitthegroundslope.Iffenceisbuiltonanextendedgutter,thentheheightofthewallshallbeadjustedfurther."
Forbatteredwalls,noteontheplanswhetherthehorizontaloffsetfromthebaselineisfixedatthetoporbottomofthewall.Horizontaloffsetandcorrespondingverticalelevationshallbenotedonplans.
Fig.751.24.2.2TypicalSectionThroughGenericSmallBlockWall
Fencing
FencingmaybeinstalledontheModifiedTypeAorModifiedTypeBGutterorbehindtheMSEWall.
ForModifiedTypeAandModifiedTypeBGutterandFencePostConnectiondetails,seeStandardPlan607.11
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(http://www.modot.mo.gov/business/standards_and_specs/documents/60711.pdf).
ForFencePostConnectionBehindMSEWall,seedetailbelow.
Fig.751.24.2.2FencePostConnectionBehindMSEWall(WithoutGutter)
751.24.3CastInPlaceConcreteRetainingWalls
751.24.3.1UnitStresses
ConcreteConcreteforretainingwallsshallbeClassBConcrete(f'c=3000psi)unlessthefootingisusedasaridingsurfaceinwhichcaseClassB1Concrete(f'c=4000psi)shallbeused.
ReinforcingSteel
ReinforcingSteelshallbeGrade60(fy=60,000psi).
PileFooting
Forpilingcapacities,seetheUnitStressesandPilingSectionsoftheBridgeManual.
SpreadFooting
Forfoundationmaterialcapacity,seetheUnitStressesSectionoftheBridgeManualandtheDesignLayoutSheet.
751.24.3.2Design
Iftheheightofthewallorfillisavariabledimension,thenbasethestructuraldesignofthewall,toe,andheelonthehighquarterpointbetweenexpansionjoints.
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AdditionalInformation
AASHTO5.5.5
AdditionalInformation
AASHTO5.5.5
AdditionalInformation
AASHTO5.5.5
Fig.751.24.3.2
751.24.3.2.1SpreadFootings
LocationofResultant
Theresultantofthefootingpressuremustbewithinthesectionofthefootingspecifiedinthefollowingtable.
WhenRetainingWallisBuilton: AASHTOGroupLoadsIVI ForSeismicLoads
Soila Middle1/3 Middle1/2b
Rockc Middle1/2 Middle2/3aSoilisdefinedasclay,clayandboulders,cementedgravel,softshale,etc.withallowablebearingvalueslessthan6tons/sq.ft.bMoDOTismoreconservativethanAASHTOinthisrequirement.cRockisdefinedasrockorhardshalewithallowablebearingvaluesof6tons/sq.ft.ormore.
Note:Thelocationoftheresultantisnotcriticalwhenconsideringcollisionloads.
FactorofSafetyAgainstOverturning
AASHTOGroupLoadsIVI:
F.S.foroverturning2.0forfootingsonsoil.F.S.foroverturning1.5forfootingsonrock.
Forseismicloading,F.S.foroverturningmaybereducedto75%ofthevalueforAASHTOGroupLoadsIVI.Forseismicloading:
F.S.foroverturning(0.75)(2.0)=1.5forfootingsonsoil.F.S.foroverturning(0.75)(1.5)=1.125forfootingsonrock.
Forcollisionforces:
F.S.foroverturning1.2.
FactorofSafetyAgainstSliding
Onlyspreadfootingsonsoilneedbecheckedforslidingbecausespreadfootingsonrockorshaleareembeddedintotherock.
F.S.forsliding1.5forAASHTOGroupLoadsIVI.F.S.forsliding(0.75)(1.5)=1.125forseismicloads.F.S.forsliding1.2forcollisionforces.
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AdditionalInformation
AASHTO5.5.5A
AdditionalInformation
AASHTO5.5.2
AdditionalInformationMoDOTMaterials
Division(http://wwwi/intranet/cm/)
Theresistancetoslidingmaybeincreasedby:
addingashearkeythatprojectsintothesoilbelowthefooting.wideningthefootingtoincreasetheweightandthereforeincreasethefrictionalresistancetosliding.
PassiveResistanceofSoiltoLateralLoad
TheRankineformulaforpassivepressurecanbeusedtodeterminethepassiveresistanceofsoiltothelateralforceonthewall.Thispassivepressureisdevelopedatshearkeysinretainingwallsandatendabutments.
Thepassivepressureagainstthefrontfaceofthewallandthefootingofaretainingwallislooselycompactedandshouldbeneglectedwhenconsideringsliding.
RankineFormula: wherethefollowingvariablesaredefinedinthefigurebelow
Cp=
y1=
Pp=passiveforceatshearkeyinpoundsperfootofwalllength
Cp=coefficientofpassiveearthpressure
=unitweightofsoil
H=heightofthefrontfacefilllessthan1ft.min.forerosion
H1=Hminusdepthofshearkey
y1=locationofPpfrombottomoffooting
=angleofinternalfrictionofsoil
Theresistanceduetopassivepressureinfrontoftheshearkeyshallbeneglectedunlessthekeyextendsbelowthedepthoffrostpenetration.
Frostlineissetat36in.atthenorthborderofMissouriandat18in.atthesouthborder.
PassivePressureDuringSeismicLoading
Duringanearthquake,thepassiveresistanceofsoiltolateralloadsisslightlydecreased.TheMononobeOkabestaticmethodisusedtodeterminetheequivalentfluidpressure.
PPE=equivalentpassiveearthpressureduringanearthquake
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AdditionalInformation
1992AASHTODiv.IAEqns.C65and
C66
AdditionalInformation
AASHTO5.5.2B
where:
KPE=seismicpassivepressurecoefficient
=unitweightofsoil
H=heightofsoilatthelocationwheretheearthpressureistobefound
kV=verticalaccelerationcoefficient
=angleofinternalfrictionofsoil
kH=horizontalaccelerationcoefficient
=slopeofsoilfaceindegrees
i=backfillslopeangleindegrees
=angleoffrictionbetweensoilandwall
SpecialSoilConditions
Duetocreep,somesoftclaysoilshavenopassiveresistanceunderacontinuingload.Removalofundesirablematerialandreplacementwithsuitablematerialsuchassandorcrushedstoneisnecessaryinsuchcases.Generally,thisconditionisindicatedbyavoidratioabove0.9,anangleofinternalfriction( )lessthan22,orasoilshearlessthan0.8ksf.Soilshearisdeterminedfromastandardpenetrationtest.
SoilShear
Friction
Intheabsenceoftests,thetotalshearingresistancetolateralloadsbetweenthefootingandasoilthatderivesmostofitsstrengthfrominternalfrictionmaybetakenasthenormalforcetimesacoefficientoffriction.Iftheplaneatwhichfrictionalresistanceisevaluatedisnotbelowthefrostlinethenthisresistancemustbeneglected.
WhenAShearKeyIsNotUsed
Slidingisresistedbythefrictionforcedevelopedattheinterfacebetweenthesoilandtheconcretefootingalongthefailureplane.Thecoefficientoffrictionforsoilagainstconcretecanbetakenfromthetablebelow.Ifsoildataisnotreadilyavailableorisinconsistent,thefrictionfactor(f)canbetakenas
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AdditionalInformation
AASHTO4.4.7.1.2&4.4.8.1.3
AdditionalInformation
AASHTODiv.IA6.3.1(B)and
AASHTO5.5.6.2
AdditionalInformation
f= where istheangleofinternalfrictionofthesoil(CivilEngineeringReferenceManualbyMichaelR.Lindeburg,6thed.,
1992).
CoefficientofFrictionValuesforSoilAgainstConcrete
SoilTypea CoefficientofFrictioncoarsegrainedsoilwithoutsilt 0.55coarsegrainedsoilwithsilt 0.45
silt(only) 0.35clay 0.30b
aItisnotnecessarytocheckrockorshaleforslidingduetoembedment.bCautionshouldbeusedwithsoilswith
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AASHTO5.5.6.1criticalsectionforbendingmomentsshallbetakenatthefrontfaceofthestem.Thecriticalsectionforshearshallbetakenatadistanced(d=effectivedepth)fromthefrontfaceofthestem.
Heel
Therearprojection(heel)ofthebaseslabshallbedesignedtosupporttheentireweightofthesuperimposedmaterials,unlessamoreexactmethodisused.Theheelshallbedesignedasacantileversupportedbythewall.Thecriticalsectionforbendingmomentsandshearshallbetakenatthebackfaceofthestem.
ShearKeyDesign
Theshearkeyshallbedesignedasacantileversupportedatthebottomofthefooting.
751.24.3.2.2PileFootings
Footingsshallbecastonpileswhenspecifiedonthe"DesignLayoutSheet".Ifthehorizontalforceagainsttheretainingwallcannototherwiseberesisted,someofthepilesshallbedrivenonabatter.
PileArrangement
Forretainingwallssubjecttomoderatehorizontalloads(walls15to20ft.tall),thefollowinglayoutissuggested.
Section
Plan
Forhigherwallsandmoreextremeconditionsofloading,itmaybenecessaryto:
usethesamenumberofpilesalongallrows
usethreerowsofpiles
providebatterpilesinmorethanonerow
LoadingCombinationsforStabilityandBearing
Thefollowingtablegivestheloadingcombinationstobecheckedforstabilityandpileloads.Theseabbreviationsareusedinthetable:
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DL=deadloadweightofthewallelements
SUR=twofeetofliveloadsurcharge
E=earthweight
EP=equivalentfluidearthpressure
COL=collisionforce
EQ=earthquakeinertialforceoffailurewedge
LoadingCase VerticalLoads HorizontalLoads OverturningFactorofSafetySlidingFactorofSafety
BatteredToePiles VerticalToePiles
Ia DL+SUR+E EP+SUR 1.5 1.5 2.0II DL+SUR+E EP+SUR+COL 1.2 1.2 1.2III DL+E EP 1.5 1.5 2.0
IVb DL+E None
Vc DL+E EP+EQ 1.125 1.125 1.5aLoadCaseIshouldbecheckedwithandwithouttheverticalsurcharge.bA25%overstressisallowedontheheelpileinLoadCaseIV.cThefactorsofsafetyforearthquakeloadingare75%ofthatusedinLoadCaseIII.BatteredpilesarenotrecommendedforuseinseismicperformancecategoriesB,C,andD.SeismicdesignofretainingwallsisnotrequiredinSPCAandB.RetainingwallsinSPCBlocatedunderabridgeabutmentshallbedesignedtoAASHTOSpecificationsforSPCB.
PilePropertiesandCapacities
ForLoadCasesIIVinthetableabove,theallowablecompressivepileforcemaybetakenfromthepilecapacitytableinthePilingSectionoftheBridgeManualwhichisbasedinpartonAASHTO4.5.7.3.Alternatively,theallowablecompressivepilecapacityofafrictionpilemaybedeterminedfromtheultimatefrictionalandbearingcapacitybetweenthesoilandpiledividedbyasafetyfactorof3.5(AASHTOTable4.5.6.2.A).Themaximumamountoftensionallowedonaheelpileis3tons.
ForLoadCaseVinthetableabove,theallowablecompressivepileforcemaybetakenfromthepilecapacitytableinthePilingSectionoftheBridgeManualmultipliedbytheappropriatefactor(2.0forsteelbearingpiles,1.5forfrictionpiles).Alternatively,theallowablecompressivepilecapacityofafrictionpilemaybedeterminedfromtheultimatefrictionalandbearingcapacitybetweenthesoilandpiledividedbyasafetyfactorof2.0.Theallowabletensionforceonabearingorfrictionpilewillbeequaltotheultimatefrictioncapacitybetweenthesoilandpiledividedbyasafetyfactorof2.0.
TocalculatetheultimatecompressiveortensilecapacitybetweenthesoilandpilerequirestheboringdatawhichincludestheSPTblowcounts,thefrictionangle,thewaterlevel,andthesoillayerdescriptions.
Assumetheverticalloadcarriedbybatteredpilesisthesameasitwouldbeifthepilewerevertical.ThepropertiesofpilesmaybefoundinthePilingSectionoftheBridgeManual.
NeutralAxisofPileGroup
Locatetheneutralaxisofthepilegroupintherepetitivestripfromthetoeofthefootingatthebottomofthefooting.
MomentofInertiaofPileGroup
Themomentofinertiaofthepilegroupintherepetitivestripabouttheneutralaxisofthesectionmaybedeterminedusingtheparallelaxistheorem:
I=(IA)+(Ad2)where:
IA=momentofinertiaofapileaboutitsneutralaxis
A=areaofapile
d=distancefromapile'sneutralaxistopilegroup'sneutralaxis
IAmaybeneglectedsotheequationreducesto:
I=(Ad2)
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ResistanceToSliding
Anyfrictionalresistancetoslidingshallbeignored,suchaswouldoccurbetweenthebottomofthefootingandthesoilonaspreadfooting.
FrictionorBearingPilesWithBatter(Case1)
Retainingwallsusingfrictionorbearingpileswithbattershoulddeveloplateralstrength(resistancetosliding)firstfromthebattercomponentofthepileandsecondfromthepassivepressureagainsttheshearkeyandthepiles.
FrictionorBearingPilesWithoutBatter(Case2)
Retainingwallsusingfrictionorbearingpileswithoutbatterduetositeconstrictionsshoulddeveloplateralstrengthfirstfromthepassivepressureagainsttheshearkeyandsecondfromthepassivepressureagainstthepilebelowthebottomoffooting.Inthiscase,theshearkeyshallbeplacedatthefrontfaceofthefooting.
ConcretePedestalPilesorDrilledShafts(Case3)
Retainingwallsusingconcretepedestalpilesshoulddeveloplateralstrengthfirstfrompassivepressureagainsttheshearkeyandsecondfrompassivepressureagainstthepilebelowthebottomofthefooting.Inthiscase,theshearkeyshallbeplacedatthefrontofthefooting.Donotbatterconcretepedestalpiles.
ResistanceDuetoPassivePressureAgainstPile
Theprocedurebelowmaybeusedtodeterminethepassivepressureresistancedevelopedinthesoilagainstthepiles.Theprocedureassumesthatthepilesdevelopalocalfailureplane.
F=thelateralforceduetopassivepressureonpile
,where:
=unitweightofsoil
H=depthofpileconsideredforlateralresistance(Hmax=6B)
CP=coefficientofactiveearthpressure
B=widthofpile
=angleofinternalfrictionofsoil
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ResistanceDuetoPileBatter
Usethehorizontalcomponent(duetopilebatter)oftheallowablepileloadasthelateralresistanceofthebatteredpile.(Thispresupposesthatsufficientlateralmovementofthewallcantakeplacebeforefailuretodeveloptheultimatestrengthofbothelements.)
b=theamountofbatterper12inches.
(#ofbatteredpiles)where:
PHBatter=thehorizontalforceduetothebatteredpiles
PT=theallowablepileload
Maximumbatteris4"per12".
ResistanceDuetoShearKeys
Ashearkeymaybeneededifthepassivepressureagainstthepilesandthehorizontalforceduetobatterisnotsufficienttoattainthefactorofsafetyagainstsliding.Thepassivepressureagainsttheshearkeyonapilefootingisfoundinthesamemannerasforspreadfootings.
ResistancetoOverturning
Theresistingandoverturningmomentsshallbecomputedatthecenterlineofthetoepileatadistanceof6B(whereBisthewidthofthepile)belowthebottomofthefooting.Amaximumof3tonsoftensiononeachheelpilemaybeassumedtoresistoverturning.Anyeffectsofpassivepressure,eitherontheshearkeyoronthepiles,whichresistoverturning,shallbeignored.
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AdditionalInformation
AASHTO5.5.6.2
AdditionalInformation
AASHTO5.5.6.1
PileProperties
LocationofResultant
Thelocationoftheresultantshallbeevaluatedatthebottomofthefootingandcanbedeterminedbytheequationbelow:
where:
e=thedistancebetweentheresultantandtheneutralaxisofthepilegroup
M=thesumofthemomentstakenabouttheneutralaxisofthepilegroupatthebottomofthefooting
V=thesumoftheverticalloadsusedincalculatingthemoment
PileLoads
Theloadsonthepilecanbedeterminedasfollows:
where:
P=theforceonthepile
A=theareasofallthepilesbeingconsidered
M=themomentoftheresultantabouttheneutralaxis
c=distancefromtheneutralaxistothecenterlineofthepilebeinginvestigated
I=themomentofinertiaofthepilegroup
StemDesign
Theverticalstem(thewallportion)ofacantileverretainingwallshallbedesignedasacantileversupportedatthebase.
FootingDesign
Toe
Thetoeofthebaseslabofacantileverwallshallbedesignedasacantileversupportedbythewall.Thecriticalsectionforbendingmomentsshallbetakenatthefrontfaceofthestem.Thecriticalsectionforshearshallbetakenatadistanced(d=effectivedepth)fromthefrontfaceofthestem.
HeelThetopreinforcementintherearprojection(heel)ofthebaseslabshallbedesignedtosupporttheentireweightofthesuperimposedmaterialsplusanytensionloadintheheelpiles(neglectcompressionloadsinthepile),unlessamoreexactmethodisused.Thebottomreinforcementintheheelofthebaseslabshallbedesignedtosupportthemaximum
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compressionloadinthepileneglectingtheweightofthesuperimposedmaterials.Theheelshallbedesignedasacantileversupportedbythewall.Thecriticalsectionsforbendingmomentsandshearshallbetakenatthebackfaceofthestem.
ShearKeyDesignTheshearkeyshallbedesignedasacantileversupportedatthebottomofthefooting.
751.24.3.2.3CounterfortWalls
Assumptions:
(1)StabilityTheexternalstabilityofacounterfortretainingwallshallbedeterminedinthesamemannerasdescribedforcantileverretainingwalls.Thereforerefertopreviouspagesforthecriteriaforlocationofresultant,factorofsafetyforslidingandbearingpressures.
(2)Stem
where:
Ca=coefficientofactiveearthpressure
=unitweigtofsoil
Designthewalltosupporthorizontalloadfromtheearthpressureandtheliveloadsurcharge(ifapplicable)asoutlinedonthepreviouspagesandasdesignatedinAASHTDSection3.20,exceptthatmaximumhorizontalloadsshallbethecalculatedequivalentfluidpressureat3/4heightofwall[(0.75H)P]whichshallbeconsideredapplieduniformlyfromthelowerquarterpointtothebottomofwall.
Inaddition,verticalsteelInthefillfaceofthebottomquarterofthewallshallbethatrequiredbytheverticalcantileverwallwiththeequivalentfluidpressureofthat(0.25H)height.
Maximumconcretestressshallbeassumedasthegreaterofthetwothusobtained.
Theapplicationofthesehorizontalpressuresshallbeasfollows:
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CounterfortWallSectionMomentsaretobedeterminedbyanalysisasacontinuousbeam.Thecounterfortsaretobespacedsoastoproduce
approximatelyequalpositiveandnegativemoments.
(3)CounterfortCounterfortsshallbedesignedasTbeams,ofwhichthewallistheflangeandthecounterfortisthestem.Forthisreasontheconcretestressesanenormallylowandwillnotcontrol.
Forthedesignofreinforcingsteelinthebackofthecounterfort,theeffectivedshallbetheperpendiculardistancefromthefrontfaceofthewall(atpointthatmomentisconsidered),tocenterofreinforcingsteel.
(4)Footing
Thefootingofthecounterfortwallsshallbedesignedasacontinuousbeamofspansequaltothedistancebetweenthecounterforts.
Therearprojectionorheelshallbedesignedtosupporttheentireweightofthesuperimposedmaterials,unlessamoreexactmethodisused.RefertoAASHTDSection5.5.6.
Dividefooting(transversely)intofour(4)equalsectionsfordesignfootingpressures.
Counterfortwallsonpileareveryrareandaretobetreatedasspecialcases.SeeStructuralProjectManager.
(5)SignBoardtypewalls
TheSignBoardtypeofretainingwallsareaspecialcaseofthecounterfortretainingwalls.ThistypeofwallisusedwherethesoiIconditionsaresuchthatthefootingsmustbeplacedagreatdistancebelowthefinishedgroundline.Forthissituation,thewallisdiscontinuedapproximately12in.belowthefinishedgroundlineorbelowthefrostline.
Duetothelargedepthofthecounterforts,itmaybemoreeconomicaltouseasmallernumberofcounterfortsthanwouldotherwisebeused.
Alldesignassumptionsthatapplytocounterfortwallswillapplytosignboardwallswiththeexceptionoftheapplicationofhorizontalforcesforthestem(orwalldesign),andthefootingdesignwhichshallbeasfollows:
Wall
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Footing
Theindividualfootingsshallbedesignedtransverselyascantileverssupportedbythewall.RefertoAASHTOSection5.
751.24.3.3Example1:SpreadFootingCantileverWall
TypicalSectionthruWall(SpreadFooting)
f'c=3,000psify=60,000psi=24in.s=120pcf(unitwgtofsoil)Allowablesoilpressure=2tsfc=150pcf(unitwgtofconcr.)RetainingwallislocatedinSeismicPerformanceCategory(SPC)B.A=0.1(A=seismicaccelerationcoefficient)
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Assumptions
Retainingwallisunderanabutmentorinalocationwherefailureofthewallmayaffectthestructuralintegrityofabridge.Therefore,itmustbedesignedforSPCB.
Designisforaunitlength(1ft.)ofwall.
Summomentsaboutthetoeatthebottomofthefootingforoverturning.
ForGroupLoadsIVIloading:
F.S.foroverturning2.0forfootingsonsoil.F.S.forsliding1.5.
Resultanttobewithinmiddle1/3offooting.
Forearthquakeloading:
F.S.foroverturning0.75(2.0)=1.5.F.S.forsliding0.75(1.5)=1.125.Resultanttobewithinmiddle1/2offooting.
Baseoffootingisbelowthefrostline.
Neglecttoponefootoffillovertoewhendeterminingpassivepressureandsoilweight.
Useofashearkeyshiftsthefailureplaneto"B"whereresistancetoslidingisprovidedbypassivepressureagainsttheshearkey,frictionofsoilalongfailureplane"B"infrontofthekey,andfrictionbetweensoilandconcretealongthefootingbehindthekey.
Soilcohesionalongfailureplaneisneglected.
Footingsaredesignedascantileverssupportedbythewall.
Criticalsectionsforbendingareatthefrontandbackfacesofthewall.Criticalsectionsforshearareatthebackfaceofthewallfortheheelandatadistanced(effectivedepth)fromthefrontfaceforthetoe.
Neglectsoilweightabovetoeoffootingindesignofthetoe.
Thewallisdesignedasacantileversupportedbythefooting.
LoadfactorsforAASHTOGroupsIVIfordesignofconcrete:
=1.3.E=1.3forhorizontalearthpressureonretainingwalls.E=1.0forverticalearthpressure.
Loadfactorforearthquakeloads=1.0.
LateralPressuresWithoutEarthquake
Ca=
Ca= =0.546
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Load Area(ft2) Force(k)=(UnitWgt.)(Area) Arm(ft.) Moment(ftk)(1) (0.5)(6.667ft)(2.222ft)=7.407 0.889 7.278 6.469(2) (6.667ft)(6.944ft)=46.296 5.556 6.167 34.259(3) (0.833ft)(8.000ft)+(0.5)(0.083ft)(8.000ft)=7.000 1.050 2.396 2.515(4) (1.500ft)(9.500ft)=14.250 2.138 4.750 10.153(5) (2.500ft)(1.000ft)=2.500 0.375 2.500 0.938(6) (1.000ft)(1.917ft)+(0.5)(0.010ft)(1.000ft)=1.922 0.231 0.961 0.222 V=10.239 MR=54.556
PAV 1.178 9.500 11.192
resisting V=11.417 MR=65.748
PAH 3.534 3.556 12.567PP 2.668 1.3891
1Thepassivecapacityattheshearkeyisignoredinoverturningchecks,sincethiscapacityisconsideredinthefactorofsafetyagainstsliding.Itisassumedthataslidingandoverturningfailurewillnotoccursimultaneously.Thepassivecapacityattheshearkeyisdevelopedonlyifthewalldoesslide.
Overturning
F.S.= o.k.
where:MOT=overturningmomentMR=resistingmoment
ResultantEccentricity
=4.658ft.
o.k.
Sliding
CheckifshearkeyisrequiredforGroupLoadsIVI:
F.S.= =0.896nogoodshearkeyreq'd
where:sc=angleoffrictionbetweensoilandconcrete=(2/3)ss
F.S.=
where:ss=angleofinternalfrictionofsoil
F.S.= =1.7891.5o.k.
FootingPressure
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PH=pressureatheel =1.132k/ft2
PT=pressureattoe =1.272k/ft2
Allowablepressure=2tons/ft2=4k/ft21.272k/ft2o.k.
LateralPressuresWithEarthquake
kh=0.5A=0.5(0.1)=0.05
kv=0
ActivePressureonPsuedoWall
==24(istheangleoffrictionbetweenthesoilandthewall.Inthiscase,==becausethesoilwedgeconsideredisnexttothesoilabovethefooting.)
i=18.435
=0
KAE=0.674
PAE=sH2(1kv)KAE
PAE=[0.120k/ft3](10.667ft)2(1ft.)(10)(0.674)=4.602k
PAEV=PAE(sin)=4.602k(sin24)=1.872k
PAEH=PAE(cos)=4.602k(cos24)=4.204k
P'AH=PAEHPAH=4.204k3.534k=0.670k
P'AV=PAEVPAV=1.872k1.178k=0.694k
where:P'AHandP'AVaretheseismiccomponentsoftheactiveforce.
PassivePressureonShearKey
==24(=becausethesoilwedgeconsideredisassumedtoforminfrontofthefooting.)
i=0
=0
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KPE=0.976
PPE=sH2(1kv)KPE
PPE=[0.120k/ft3][(5.0ft)2(2.5ft2)](1ft.)(10)(0.976)=1.098k
Load Force(k) Arm(ft) Moment(ftk)(1)thru(6) 10.239 54.556
PAV 1.178 9.500 11.192P'AV 0.694 9.500 6.593
resisting V=12.111 MR=72.341
PAH 3.534 3.556 12.567P'AH 0.670 6.400a 4.288PPEV 0.447b 0.000 0.000PPEH 1.003b 1.389c 0.000
MOT=16.855aP'AHactsat0.6Hofthewedgeface(1992AASHTODiv.IACommentary).bPPEHandPPEHarethecomponentsofPPEwithrespectto(thefrictionangle).PPEdoesnotcontributetooverturning.cThelineofactionofPPEHcanbelocatedaswasdoneforPP.
Overturning
o.k.
ResultantEccentricity
o.k.
Sliding
o.k.
FootingPressure
foreL/6:
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AdditionalInformation
1992AASHTODiv.IACommentary
=1.139k/ft2
=1.411k/ft2
Allowablesoilpressureforearthquake=2(allowablesoilpressure)
(2)[4k/ft2]=8k/ft2>1.411k/ft2o.k.
ReinforcementStem
d=11"2"(1/2)(0.5")=8.75"
b=12"
f'c=3,000psi
WithoutEarthquake
PAH=[0.120k/ft3](0.546)(6.944ft.)2(1ft.)(cos18.435)=1.499k
=1.3
E=1.3(activelateralearthpressure)
Mu=(1.3)(1.3)(1.499k)(2.315ft)=5.865(ftk)
WithEarthquake
kh=0.05
kv=0
=2.862
=/2=24/2=12forangleoffrictionbetweensoilandwall.Thiscriteriaisusedonlyforseismicloadingiftheangleoffrictionisnotknown.
=24
i=18.435
=0
KAE=0.654
PAEH=1/2sKAEH2cos
PAEH=1/2[0.120k/ft](0.654)(6.944ft.)2(1ft.)cos(12)=1.851k
Mu=(1.499k)(2.315ft.)+(1.851k1.499k)(0.6(6.944ft.))=4.936(ftk)
Themomentwithoutearthquakecontrols:
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AdditionalInformation
AASHTO8.17.1.1&8.15.2.1.1
=85.116psi
=
= =0.00144
min= =0.00245
Use=4/3=4/3(0.00144)=0.00192
ASReq=bd=0.00192(12in.)(8.75in.)=0.202in.2/ft
One#4barhasAS=0.196in2
s=11.64in.
Use#4's@10"cts.
CheckShear
VuVn
WithoutEarthquake
Vu,=(1.3)(1.3)(1.499k)=2.533k
WithEarthquake
Vu=1.851k
Theshearforcewithoutearthquakecontrols.
=28.4psi
=109.5psi>28.4psio.k.
ReinforcementFootingHeel
Note:Earthquakewillnotcontrolandwillnotbechecked.
E=1.0(verticalearthpressure)
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d=18"3"(1/2)(0.750")=14.625"
b=12"
f'c=3,000psi
Mu=1.3[(5.556k+1.500k)(3.333ft)+0.889k(4.444ft)+1.178k(6.667ft)]
Mu=45.919(ftk)
=238.5psi
= =0.00418
min= =0.00235
ASReq=0.00418(12in.)(14.625in.)=0.734in2/ft.
Use#6's@7"cts.
CheckShear
Shearshallbecheckedatbackfaceofstem.
Vu=1.3(5.556k+1.500k+0.889k+1.178k)=11.860k
=109.5psio.k.
ReinforcementFootingToe
d=18"4"=14"
b=12"
WithoutEarthquake
ApplyLoadFactors
load4(weight)=0.431k(1.3)(1.0)=0.560k
E=1.3forlateralearthpressureforretainingwalls.
E=1.0forverticalearthpressure.
MOT=12.567(ftk)(1.3)(1.3)=21.238(ftk)
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MR=[54.556(ftk)+11.192(ftk)](1.3)(1.0)=85.472(ftk)
V=11.417k(1.3)(1.0)=14.842k
=4.328ft.
e=(9.5ft./2)4.328ft.=0.422ft.
=1.146k/ft2
=1.979k/ft2
=1.811k/ft.
Mu=2.997(ftk)
WithEarthquake
PH=1.139k/ft
PT=1.411k/ft
=1.356k/ft
Mu=2.146(ftk)
Themomentwithoutearthquakecontrols.
=16.990psi
= =0.000284
min= =0.00257
Use=4/3= =0.000379
ASReq=0.000379(12in.)(14.0in.)=0.064in.2/ft.
s=36.8in.
Minimumis#4barsat12inches.Thesewillbethesamebarsthatareinthebackofthestem.Usethesmallerofthetwospacings.
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Use#4's@10"cts.
CheckShear
Shearshallbecheckedatadistance"d"fromthefaceofthestem.
WithoutEarthquake
=1.913k/ft.
=1.240k
WithEarthquake
=1390k/ft.
=0.788k
Shearwithoutearthquakecontrols.
=109.5psio.k.
ReinforcementShearKey
Thepassivepressureishigherwithoutearthquakeloads.
=1.3
E=1.3(lateralearthpressure)
d=12"3"(1/2)(0.5")=8.75"
b=12"
Mu=(3.379k)(1.360ft.)(1.3)(1.3)=7.764(ftk)
=112.677psi
= =0.00192
min= =0.00292
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Use=4/3=4/3(0.00192)=0.00256
ASReq=0.00256(12in.)(8.75in.)=0.269in.2/ft.
Use#[email protected].
CheckShear
=109.5psio.k.
ReinforcementSummary
751.24.3.4Example2:LShapedCantileverWall
TypicalSectionthruWall(SpreadFooting)
f'c=4000psi
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fy=60,000psi
=29
s=120pcf
Allowablesoilpressure=1.5tsf=3.0ksf
RetainingwallislocatedinSeismicPerformanceCategory(SPC)A.
=21.801
=0.462
=2.882
PA=1/2sCaH2=1/2(0.120k/ft3)(0.462)(4.958ft.)2=0.681k
Forsliding,PPisassumedtoactonlyontheportionofkeybelowthefrostlinethatissetatan18in.depthonthesouthernborder.
PP=1/2(0.120k/ft3)(2.882)[(2.458ft.)2(1.500ft.)2]=0.656k
Assumptions
Designisforaunitlength(1ft.)ofwall.
Summomentsaboutthetoeatthebottomofthefootingforoverturning.
F.S.foroverturning2.0forfootingsonsoil.
F.S.forsliding1.5forfootingsonsoil.
Resultantofdeadloadandearthpressuretobeinbackhalfofthemiddlethirdofthefootingifsubjectedtofrostheave.
Forallloadingcombinationstheresultantmustbeinthemiddlethirdofthefootingexceptforcollisionloads.
Thetop12in.ofthesoilisnotneglectedindeterminingthepassivepressurebecausethesoiltherewillbemaintained.
Frostlineissetat18in.atthesouthborderforMissouri.
Portionsofshearkeywhichareabovethefrostlineareassumednottoresistslidingbypassivepressure.
Useofashearkeyshiftsthefailureplaneto"B"whereresistancetoslidingisalsoprovidedbyfrictionofsoilalongthefailureplaneinfrontoftheshearkey.Frictionbetweenthesoilandconcretebehindtheshearkeywillbeneglected.
Soilcohesionalongthefailureplaneisneglected.
Liveloadscanmovetowithin1ft.ofthestemfaceand1ft.fromthetoe.
Thewallisdesignedasacantileversupportedbythefooting.
Footingisdesignedasacantileversupportedbythewall.Criticalsectionsforbendingandshearwillbetakenatthefaceofthewall.
LoadfactorsforAASHTOGroupsIVIfordesignofconcreteare:
=1.3.
E=1.3forhorizontalearthpressureonretainingwalls.
E=1.0forverticalearthpressure.
LL=1.67forliveloadsandcollisionloads.
DeadLoadandEarthPressureStabiltyandPressureChecks
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DeadLoadandEarthPressureStabiltyandPressureChecksLoad Force(k) Arm(in.) Moment(ftk)(1) (0.833ft.)(5.167ft.)(0.150k/ft3)=0.646 5.333 3.444(2) (0.958ft)(5.750ft)(0.150k/ft3)=0.827 2.875 2.376(3) (1.000ft)(1.500ft)(0.150k/ft3)=0.22534.259 4.250 0.956
V=1.698 MR=6.776
PAV 0.253 5.750 1.455
V=1.951 MR=8.231
PAH 0.633 1.653 1.045PP 0.656 1.061
MOT=1.0451Thepassivepressureattheshearkeyisignoredinoverturningchecks.
Overturning
=7.8772.0o.k.
LocationofResultant
MoDOTpolicyisthattheresultantmustbeinthebackhalfofthemiddlethirdofthefootingwhenconsideringdeadandearthloads:
=3.683ft.o.k.
Sliding
where:
ss=angleofinternalfrictionofsoil
sc=angleoffrictionbetweensoilandconcrete=(2/3)ss
=2.3391.5o.k.
FootingPressure
=0.808ft.
Heel: =0.625ksf
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Stabilityisnotanissuebecausetheliveloadresistsoverturningandincreasestheslidingfrictionforce.
Theliveloadwillbedistributedas:
whereE=0.8X+3.75
X=distanceinfeetfromtheloadtothefrontfaceofwall
Theliveloadwillbepositionedasshownbythedashedlinesabove.Thebearingpressureandresultantlocationwillbedeterminedforthesetwopositions.
LiveLoad1ftFromStemFace
ResultantEccentricity
X=1ft.
E=0.8(1ft.)+3.75=4.55ft.
=3.516k
=3.834ft.
=5.75ft.o.k.
FootingPressure
AllowablePressure=3.0ksf
Heel: =1.902ksf
Toe: =0.000ksf
LiveLoad1ftFromToe
ResultantEccentricity
X=3.917ft.
E=0.8(3.917ft.)+3.75=6.883ft.
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=2.324k
=2.225ft.
=0.958ft.o.k.
FootingPressure
AllowablePressure=3.0ksf
Heel: =0.239ksfo.k.
Toe: =1.248ksfo.k.
DeadLoad,EarthPressure,CollisionLoad,andLiveLoadStabilityandPressureChecks
Duringacollision,theliveloadwillbeclosetothewallsocheckthiscombinationwhentheliveloadisonefootfromthefaceofthestem.Sliding(ineitherdirection)willnotbeanissue.Stabilityabouttheheelshouldbecheckedalthoughitisunlikelytobeaproblem.Therearenocriteriaforthelocationoftheresultant,solongasthefootingpressuredoesnotexceed125%oftheallowable.Itisassumedthatthedistributedcollisionforcewilldevelopanequalandoppositeforceonthefillfaceofthebackwallunlessitexceedsthepassivepressurethatcanbedevelopedbysoilbehindthewall.
FLL=3.516k
FCOLL= =1.667k
=1.867
PPH=2.556k>FCOLLThusthesoilwilldevelopanequalbutopp.force.
OverturningAbouttheHeel
F.S.=
F.S.= =1.8471.2o.k.
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FootingPressure
=1.022ft.fromheel
e= =1.853ft.
AllowablePressure=(1.25)(3.0ksf)=3.75ksf
Heel: =3.566ksfo.k.
StemDesignSteelinRearFace
=1.3
E=1.3(activelateralearthpressure)
d=10in.2in.(0.5in./2)=7.75in.
PAH=0.412k
Mu=(1.333ft.)(0.412k)(1.3)(1.3)=0.928(ftk)
=17.160psi
=0.000287
=0.00298
Use=(4/3)=(4/3)(0.000287)=0.000382
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One#4barhasAS=0.196in2,sotherequiredminimumofone#4barevery12in.controls.
Use#4's@12in.(min)
(Thesebarsarealsothebarsinthebottomofthefootingsothesmallerofthetworequiredspacingswillbeused.)
CheckShear
=8.8psi
=126.5psi>8.8psio.k.
StemDesignSteelinFrontFace(CollisionLoads)
Thesoilpressureonthebackofthestembecomespassivesoilpressureduringacollision,howeverthispressureisignoredforreinforcementdesign.
=1.3
LL=1.67
=7.75in.
=1.667k/ft.
Mu=1.667k/ft.(1ft.)(3ft.)(1.3)(1.67)=10.855(ftk)
=200.809psi
=0.00345
=0.00298
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One#4barhasAS=0.196in2.
s=7.3in.
Use#4's@7in.
CheckShear
=45.8psi
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=0.653ksf
MomentatWallFace:
=1.524(ftk)
DeadLoad,EarthPressure,andLiveLoad
LiveLoad1ft.FromStemFace
E=1.3(lateralearthpressure)
LL=1.67
=1.3
ApplyLoadFactors:
FLL=3.516k(1.3)(1.67)=7.633k
V=7.633k+1.951k(1.3)=10.169k
MOT=1.045(ftk)(1.3)(1.3)=1.766(ftk)
MR=8.231(ftk)(1.3)+3.917ft.(7.633k)=40.599(ftk)
=3.819ft.
e=3.819ft.(5.75ft./2)=0.944ft.
=0.026ksf
=3.511ksf
=3.006ksf
=2.400ksf
Footingwt.fromfaceofwalltotoe:
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Footingwt.= =0.919k
Footingwt.fromLLWLtotoe:
Footingwt.= =0.732k
MomentatWallFace:
MW=
MW=2.430(ftk)
MomentatLLWL:
MLL= =4.837(ftk)
LiveLoad1ft.FromToe
ApplyLoadFactors:
FLL=2.324k(1.3)(1.67)=5.045k
V=5.045k+1.951k(1.3)=7.581k
MOT=1.045(ftk)(1.3)(1.3)=1.766(ftk)
MR=8.231(ftk)(1.3)+5.045k(1ft.)=15.745(ftk)
=1.844ft.
=1.031ft.
PH=0ksf
=2.741ksf
L1=3[(L/2)e]
L1=3[(5.75ft./2)1.031ft.]=5.532ft.
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=0.305ksf
=2.196ksf
MomentatWallFace:
MW=
=1.298(ftk)
MomentatLLWL:
MLL= =1.186(ftk)
DesignFlexuralSteelinBottomofFooting
d=11.5in.4in.=7.500in.
Mu=4.837(ftk)(controllingmoment)
=0.096ksi
=0.00162
=0.00421
Use=(4/3)=(4/3)(0.00162)=0.00216
ASReq=0.00216(12in.)(7.5in.)=0.194in2/ft.
s=12.1in.
Use#4'[email protected].(Alsousethisspacinginthebackofthestem.)
CheckShear
DeadLoadandEarthPressureOnly
VW=1.038k
LiveLoad1ft.FromStemFace
Shearatthewallcanbeneglectedforthisloadingcase.
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VLL=4.019k
LiveLoad1ft.FromToe
VW=1.525k
VLL=2.282k
UseVU=4.019k
=126.5psi
ShearKeyDesign
Forconcretecastagainstandpermanentlyexposedtoearth,minimumcoverforreinforcementis3inches.
=8.75in.
=0.331k/ft.
=0.850k/ft.
Mu=1.287(ftk)
=0.0187ksi
=0.000312
=0.00337
Use=(4/3)=(4/3)(0.000312)=0.000416
ASReq=0.000416(12in.)(8.75in.)=0.0437in2/ft.
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s=53.8in.
Use#4'[email protected].(min)
CheckShear
V=0.886k
=16.8psi
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fc=3,000psi
fy=60,000psi
=27
s=120pcf
Piletype:HP10x42
Allowablepilebearing=56tons
Pilewidth=10inches
Toepilebatter=1:3
Barriercurbweight=340lbs/ft.oflength
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Barriercurbresultant=0.375ft.fromitsflatback
Assumptions
Retainingwallislocatedsuchthattrafficcancomewithinhalfofthewallheighttotheplanewhereearthpressureisapplied.
Reinforcementdesignisforonefootofwalllength.
Summomentsaboutthecenterlineofthetoepileatadistanceof6B(whereBisthepilewidth)belowthebottomofthefootingforoverturning.
Neglecttoponefootoffillovertoeindeterminingsoilweightandpassivepressureonshearkey.
Neglectallfillovertoeindesigningstemreinforcement.
Thewallisdesignedasacantileversupportedbythefooting.
Footingisdesignedasacantileversupportedbythewall.
Criticalsectionsforbendingareatthefrontandbackfacesofthewall.
Criticalsectionsforshearareatthebackfaceofthewallfortheheelandatadistanced(effectivedepth)fromthefrontfaceforthetoe.
Forloadfactorsfordesignofconcrete,seeEPG751.24.1.2GroupLoads.
=0,=27soCAreducesto:
=0.376
=2.663
Table751.24.3.5.1isforstabilitycheck(momentstakenaboutC.L.oftoepileatadepthof6Bbelowthebottomofthefooting).
Table751.24.3.5.1
Load Force(kips/ft) ArmaboutC.L.oftoepileat6Bbelowfooting(ft.)Moment(ftkips)perfootof
walllength
DeadLoad
(1) 0.340 2.542 0.864
(2) (1.333ft.)(7.000ft.)(0.150k/ft3)=
1.4002.833 3.966
(3) (3.000ft.)(8.500ft.)(0.150k/ft3)=
3.8254.417 16.895
(4) (1.000ft.)(1.750ft.)(0.150k/ft3)=
0.2634.417 1.162
V=5.828 MR=22.887
EarthLoad
(5) (7.000ft.)(5.167ft.)(0.120k/ft3)=
4.3406.083 26.400
(6) (2.000ft.)(2.000ft.)(0.120k/ft3)=
0.4801.167 0.560
V=4.820 MR=26.960
LiveLoadSurcharge
PSV(2.000ft.)(5.167ft.)(0.120k/ft3)=
1.2406.083 MR=7.543
PSH(2.000ft.)(0.376)(10.000ft.)
(0.120k/ft3)=0.90210.000 MOT=9.020
EarthPressurePA 2.2561 8.333 MOT=18.799
PP 3.2852
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CollisionForce(FCOL)
(10.000k)/[2(7.000ft.)]=0.714 18.000 MOT=12.852
HeelPileTension(PHV)
(3.000tons)(2k/ton)(1pile)/(12.000ft.)=0.500 7.167
MR=3.584
ToePileBatter(PBH) 5.9033 PassivePilePressure
(Ppp) 0.8324
1
2
3
4
Table751.24.3.5.2isforbearingpressurechecks(momentstakenaboutC.Loftoepileatthebottomofthefooting).
Table751.24.3.5.2
Load Force(kips/ft) ArmaboutC.L.oftoepileat6Bbelowfooting(ft.)Moment(ftkips)perfootof
walllength
DeadLoad
(1) 0.340 0.875 0.298
(2) (1.333ft.)(7.000ft.)(0.150k/ft3)=
1.4001.167 1.634
(3) (3.000ft.)(8.500ft.)(0.150k/ft3)=
3.8252.750 10.519
(4) (1.000ft.)(1.750ft.)(0.150k/ft3)=
0.2632.750 0.723
V=5.828 MR=13.174
EarthLoad
(5) (7.000ft.)(5.167ft.)(0.120k/ft3)=
4.3404.417 19.170
(6) (2.000ft.)(2.000ft.)(0.120k/ft3)=
0.4800.500 0.240
V=4.820 MR=18.930
LiveLoadSurcharge
PSV(2.000ft.)(5.167ft.)(0.120k/ft3)=
1.2404.417 MR=5.477
PSH(2.000ft.)(0.376)(10.000ft.)
(0.120k/ft3)=0.9025.000 MOT=4.510
EarthPressurePA 2.256 3.333 MOT=7.519
PP 3.285 CollisionForce
(FCOL)(10.000k)/[2(7.000ft.)]=0.714 13.000 MOT=9.282
HeelPileTension(PHV)
(3.000tons)(2k/ton)(1pile)/(12.000ft.)=0.500 5.500
MR=2.750
ToePileBatter(PBH) 5.903 PassivePilePressure
(Ppp)0.832
Investigatearepresentative12ft.strip.Thiswillincludeoneheelpileandtwotoepiles.Theassumptionismadethatthestiffnessofabatterpileintheverticaldirectionisthesameasthatofaverticalpile.
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NeutralAxisLocation=[2piles(1.5ft.)+1pile(7ft.)]/(3piles)=3.333ft.fromthetoe.
I=Ad2
Forrepetitive12ft.strip:
Totalpilearea=3A
I=2A(1.833ft.)2+A(3.667ft.)2=20.167(A)ft.2
Fora1ft.unitstrip:
Totalpilearea=(3A/12ft.)=0.250A
CaseI
F.S.foroverturning1.5
F.S.forsliding1.5
CheckOverturning
NeglectresistingmomentduetoPSVforthischeck.
MR=22.887(ftk)+26.960(ftk)+3.584(ftk)
MR=53.431(ftk)
MOT=9.020(ftk)+18.799(ftk)=27.819(ftk)
F.S.OT= =1.921>1.5o.k.
CheckPileBearing
WithoutPSV:
V=5.828k+4.820k=10.648k
e= =1.885ft.
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Momentarm=1.885ft.1.833ft.=0.052ft.
Allowablepileload=56tons/pile.EachpilehasareaA,so:
o.k.
o.k.
WithPSV:
V=5.828k+4.820k+1.240k=11.888k
=2.149ft.
Momentarm=2.149ft.1.833ft.=0.316ft.
o.k.
o.k.
CheckSliding
=3.1731.5o.k.
CaseII
F.S.foroverturning1.2
F.S.forsliding1.2
CheckOverturning
MR=(22.887+26.960+7.543+3.584)(ftk)=60.974(ftk)
MOT=(9.020+18.799+12.852)(ftk)=40.671(ftk)
=1.4991.2o.k.
CheckPileBearing
=1.369ft.
Momentarm=1.833ft.1.369ft.=0.464ft.
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o.k.
=35.519k
o.k.
CheckSliding
=2.5881.2o.k.
CaseIII
F.S.foroverturning1.5
F.S.forsliding1.5
CheckOverturning
MR=(22.887+26.960+3.584)(ftk)=53.431(ftk)
MOT=18.799(ftk)
=2.8421.5o.k.
CheckPileBearing
=2.309ft.
Momentarm=2.309ft.1.833ft.=0.476ft.
=37.065k
o.k.
=53.649k
o.k.
CheckSliding
=4.4411.5o.k.
CaseIV
CheckPileBearing
=3.015ft.
Momentarm=3.015ft.1.833ft.=1.182ft.
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25%overstressisallowedontheheelpile:
o.k.
=28.868k
o.k.
ReinforcementStem
b=12in.
cover=2in.
h=16in.
d=16in.2in.0.5(0.625in.)=13.688in.
FCollision=0.714k/ft
ApplyLoadFactors
FCol.=LL(0.714k)=(1.3)(1.67)(0.714k)=1.550k
PLL=E(0.632k)=(1.3)(1.67)(0.632k)=1.372k
PAStem=E(1.105k)=(1.3)(1.3)(1.105k)=1.867k
Mu=(10.00ft.)(1.550k)+(3.500ft.)(1.372k)+(2.333ft.)(1.867k)
Mu=24.658(ftk)
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=0.146ksi
=0.00251
=0.00212
=0.00251
One#5barhasAS=0.307in2
s=8.9in.
Use#[email protected].
CheckShear
VuVn
Vu=FCollision+PLL+PAStem=1.550k+1.372k+1.867k=4.789k
=34.301psi
=109.5psi>34.3psio.k.
ReinforcementFootingTopSteel
b=12in.
cover=3in.
h=36in.
d=36in.3in.0.5(0.5in.)=32.750in.
Designtheheeltosupporttheentireweightofthesuperimposedmaterials.
Soil(1)=4.340k/ft.
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LLs=1.240k/ft.
=2.325k/ft.
ApplyLoadFactors
Soil(1)=E(4.340k)=(1.3)(1.0)(4.340k)=5.642k
LLs=E(1.240k)=(1.3)(1.67)(1.240k)=2.692k
Slabwt.=D(2.325k)=(1.3)(1.0)(2.325k)=3.023k
Mu=(2.583ft.)(5.642k+2.692k+3.023k)=29.335(ftk)
=0.0304ksi
=0.000510
=0.00188
Use=4/3=4/3(0.000510)=0.000680
One#4barhasAs=0.196in.2
s=8.8in.
Use#[email protected].
CheckShear
=33.998psi109.5psi=co.k.
ReinforcementFootingBottomSteel
Designtheflexuralsteelinthebottomofthefootingtoresistthelargestmomentthattheheelpilecouldexertonthefooting.ThelargestheelpilebearingforcewasinCaseIV.Theheelpilewillcausealargermomentaboutthestemfacethanthetoepile(eventhoughtherearetwotoepilesforeveryoneheelpile)becauseithasamuchlongermomentarmaboutthestemface.
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Pileisembeddedintofooting12inches.
b=12in.
h=36in.
d=36in.4in.=32in.
ApplyLoadFactorstoCaseIVLoads
V=13.842k/ft.
M=41.735(ftk)/ft.
e= =3.015ft.
Momentarm=3.015ft.1.833ft.=1.182ft.
=7.588k/ft.
=27.825(ftk)/ft.
=0.0301ksi
=0.000505
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=0.00196
Use=4/3=4/3(0.000505)=0.000673
ASReq=bd=(0.000673)(12in.)(32in.)=0.258in2/ft.
One#4barhasAs=0.196in2.
s=9.1in.
Use#[email protected].
CheckShear
Thecriticalsectionforshearforthetoeisatadistanced=21.75inchesfromthefaceofthestem.Thetoepileis6inchesfromthestemfacesothetoepilesheardoesnotaffecttheshearatthecriticalsection.Thecriticalsectionforshearisatthestemfacefortheheelsoalloftheforceoftheheelpileaffectstheshearatthecriticalsection.TheworstcaseforshearisCaseIV.
Vu=7.588k
=23.248psi109.5psi=co.k.
ReinforcementShearKey
b=12in.
h=12in.
cover=3in.
d=12in.3in.0.5(0.5in.)=8.75in.
ApplyLoadFactors
PP=E(3.845k)=(1.3)(1.3)(3.845k)=6.498k
Mu=(0.912ft.)(6.498k)=5.926(ftk)
=0.0860ksi
=0.00146
=0.00292
Use=4/3=4/3(0.00146)=0.00195
ASReq=bd=(0.00195)(12in.)(8.75in.)=0.205in.2/ft.
One#4barhasAs=0.196in2
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s=11.5in.
Use#[email protected].
CheckShear
=72.807psi
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Eachsectionofwallshallbeinincrementsof4ft.withamaximumlengthof28'0".
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CantileverWallsLShaped
Eachsectionofwallshallbeinincrementsof4ft.withamaximumlengthof28'0".
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CounterfortWalls
Notes:Dimension"A"
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*Maximumlength=28'0".*Eachsectiontobein4'0"increments.
*(Seerusticationrecessdetails.)Dimensions"B"&"C"
*Asrequiredbythedesigntobalancethenegativeandpositivemoments.(Seethedesignassumptions).
Notes:Batter"D":
*Asrequiredtomaintain9"minimumatthetopofthecounterfortand12"minimumedgedistanceatthetopofthefooting,betweencounterfortandfootingedge.
*Battertobegivenaneighthofaninchperfootofcounterfortheight.Dimension"L":
*Asrequiredforstability.*Asanestimate,use"L"equalto1/2theheightof"H".
SignBoardTypeCounterfortWalls
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Notes:Dimension"A"
*Maximumlength=28'0".*Eachsectiontobein4'0"increments.
*(Seerusticationrecessdetails.)Dimensions"B"&"C"
*Asrequiredbythedesigntobalancethenegativeandpositivemoments.(Seethedesignassumptions).
Dimension"E"*(Signboardtypeonly)
*Asrequiredtomaintainfootingpressurewithintheallowableforexistingfoundationmaterial.12"minimum.
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Notes:Batter"D":
*Asrequiredtomaintain9"minimumatthetopofthecounterfortand12"minimumedgedistanceatthetopofthefooting,betweencounterfortandfootingedge.
*Battertobegivenaneighthofaninchperfootofcounterfortheight.Dimension"L":
*Asrequiredforstability.*Asanestimate,use"L"equalto1/2theheightof"H".
751.24.3.7Reinforcement
CantileverWalls
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(*)Alternatelongandshortbarsatequalspaces.(**)Ifcollisionfrocesareassumed,use#4@12"cts.min.andextendatleastdevelopmentlengthintofooting.(SeeSection
2.4)(***)Theo.cutoffforbending+developmentlength.(Wallheightover10'only.)
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(*)Alternatelongandshortbarsatequalspaces.(**)Ifcollisionfrocesareassumed,use#4@12"cts.min.andextendatleastdevelopmentlengthintofooting.(SeeSection
2.4)(***)Theo.cutoffforbending+developmentlength.(Wallheightover10'only.)
(****)Duetositeconstriction.
CantileverWallsLShaped
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(*)Donotsplicestressbarsinthefillfaceattopoffooting.(**)Ifcollisionfrocesareassumed,use#4@12"cts.min.andextendatleastdevelopmentlengthintofooting.(SeeSection2.4)
CounterfortWalls
WallandStem
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(Forfootingreinforcement,seethe"Footing"diagram,below)(*)Usedevelopmentlength(otherthantopbar)orstandardhookwith(Min.)tensionembedment"E"(SeeManualSection2.4).
(**)SeelapsplicesClassB(otherthantopbars).(SeeManualSection2.4.)
Footing
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(*)Bydesignforloadsandfootingpressuresonsectionunderconsideration.(#5@12"cts.istheminimum.)
CounterfortWallsSignBoardType
WallandStemReferto"CounterfortWalls,WallandStem",above.
SpreadFooting
Iftheshearlineiswithinthecounterfortprojected(longitudinallyortransversely),thefootingmaybeconsideredsatisfactoryforallconditions.Ifoutsideofthecounterfortprojected,thefootingmustbeanalyzedandreinforcedforbendingandcheckedforbondstressandfordiagonaltensionstress.
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751.24.3.8Details
NonKeyedJoints
Eachsectionofwallshallbeinincrementsof4ft.withamaximumlengthof28'0".
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SeeManualSection4.0forappropriatenotes.
KeyedJoints
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SeeManualSection4.0forappropriatenotes.
RusticationRecess
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Drains
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Note:Frenchdrainsshallbeusedonallretainingwalls,unlessotherwisespecifiedontheDesignLayout.
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ConstructionJointKeys:
CantileverWalls
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CounterfortWalls
Keylength:Dividethelength"A"intoanoddnumberofspacesofequallengths.Eachspaceshallnotexceedalengthof24inches.Useasfewspacesaspossiblewiththeminimumnumberofspacesequaltothree(oronekey).
Keywidth=Counterfortwidth/3(tothenearestinch)
Keydepth=2"(nominal)
SignBoardWalls
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Keylength=dividelength"A"or"B"intoanoddnumberofspacesofequallengths.Eachspacelengthshallnotexceed24inches.Useasfewspacesaspossiblewiththeminimumnumberofspacesequaltothree(oronekey).
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