theory manual eng 2011
DESCRIPTION
asdasdTRANSCRIPT
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DeepXcav theory manual: Developed by Ce.A.S. srl, Italy and Deep Excavation LLC, U.S.A.
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DEEPXCAV
A SOFTWARE FOR ANALYSIS AND DESIGN OF RETAINING WALLS
THEORY MANUAL
RELEASE 9.1.1.9 - November 2011
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TableofContentsSection Title Page1 Introduction 42 GeneralAnalysisMethods 43 Groundwateranalysismethods 44 UndrainedDrainedAnalysisforclays 45 ActiveandPassiveCoefficientsofLateralEarthPressures 55.1 ActiveandPassiveLateralEarthPressuresinConventional
Analyses6
5.2 ActiveandPassiveLateralEarthPressuresinPARATIEmodule 65.3 PassivePressureEquations 105.4 ClassicalEarthPressureOptions 115.4.1 Active&PassivePressuresfornonLevelGround 115.4.2 Peck1969EarthPressureEnvelopes 135.4.3 FHWAApparentEarthPressures 145.4.4 FHWARecommendedApparentEarthPressureDiagramfor
SofttoMediumClays16
5.4.5 FHWALoadingforStratifiedSoilProfiles 165.4.6 ModificationstostiffclayandFHWAdiagrams 195.4.7 VerificationExampleforSoftClayandFHWAApproach 225.4.8 CustomTrapezoidalPressureDiagrams 245.4.9 TwoStepRectangularPressureDiagrams 255.5 Verticalwalladhesioninundrainedloading 266 Eurocode7analysismethods 276.1 SafetyParametersforUltimateLimitStateCombinations 286.2 Automaticgenerationofactiveandpassivelateralearth
pressurefactorsinEC7typeapproaches.35
6.3 DeterminationofWaterPressures&NetWaterPressureActionsinthenewsoftware(ConventionalLimitEquilibriumAnalysis)
36
6.4 Surcharges 376.5 LineLoadSurcharges 386.6 StripSurcharges 406.7 Other3Dsurchargeloads 407 AnalysisExamplewithEC7 428 Groundanchorandhelicalanchorcapacitycalculations
GroundAnchorCapacityCalculations61
8.1 GroundAnchorCapacityCalculations 618.2 Helicalanchorcapacitycalculations 67
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Section Title Page9 GeotechnicalSafetyFactors 719.1 Introduction 719.1.1 Introduction 719.1.2 CantileverWalls(conventionalanalysis) 729.1.3 Wallssupportedbyasinglebracinglevelinconventional
analyses.73
9.1.4 Wallssupportedbyamultiplebracinglevels(conventionalanalysis)
739.2 CloughPredictions&BasalStabilityIndex 749.3 Groundsurfacesettlementestimation 7610 HandlingunbalancedwaterpressuresinParatie 7811 WallTypesStiffnessandCapacityCalculations 7912 SeismicPressureOptions 8312.1 Selectionofbaseaccelerationandsiteeffects 8412.2 DeterminationofretainingstructureresponsefactorR 8512.3 SeismicThrustOptions 8712.3.1 Semirigidpressuremethod 8712.3.2 MononobeOkabe 8812.3.3 RichardsShimethod 8912.3.4 Userspecifiedexternal 8912.3.5 WoodAutomaticmethod 9012.3.6 WoodManual 9012.4 WaterBehaviorduringearthquakes 9012.5 WallInertiaSeismicEffects 9112.6 VerificationExample 92
13 Verificationoffreeearthmethodfora10ftcantileverexcavation
9614 Verificationof20ftdeepsinglelevelsupportedexcavation 10015 Verificationof30ftexcavationwithtwosupportlevels 105 AppendixA APPENDIX:VerificationofPassivePressureCoefficient
Calculations109
AppendixB APPENDIX:SampleParatieInputFileGeneratedbyNewSoftwareProgram
113
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1. Introduction
ThisdocumentbrieflyintroducesthenewDeepXcavParatiecombinedsoftwarefeatures,analysismethods,andtheoreticalbackground.ThehandlingofEurocode7isemphasizedthroughanexampleofasimplesingleanchorwall.
2. GeneralAnalysisMethodsThecombinedDeepXcavParatiesoftwareiscapableofanalyzingbracedexcavationswithconventionallimitequilibriummethodsandbeamonelasticfoundations(i.e.thetraditionalPARATIEengine).Anexcavationcanbeanalyzedinoneofthefollowingsequences:
a) Conventionalanalysisonlyb) Paratieanalysisonlyc) CombinedConventionalParatieAnalysis: 1stConventionalanalysiswithtraditionalsafety
factorsstoredinmemory.Oncethetraditionalanalysisiscompleted,thentheParatieanalysisislaunched.
3. GroundwateranalysismethodsThesoftwareoffersthefollowingoptionsformodelinggroundwater:
a) Hydrostatic: ApplicableforbothconventionalandParatieanalysis.InParatie,hydrostaticconditionsaremodeledbyextendingthewallliningeffectto100timesthewalllengthbelowthewallbottom.
b) Simplifiedflow: ApplicableforbothconventionalandParatieanalysis.Thisisasimplified1Dflowaroundthewall.IntheParatieanalysismode,thetraditionalParatiewaterflowoptionisemployed.
c) FullFlowNetanalysis: ApplicableforbothconventionalandParatieanalysis.Waterpressuresaredeterminedbyperforminga2Dfinitedifferenceflowanalysis.InPARATIE,waterpressuresarethenaddedbytheUTABcommand.Theflownetanalysisdoesnotaccountforadropinthephreaticline.
d) Userpressures: ApplicableforbothconventionalandParatieanalysis.Waterpressuresdefinedbytheuserareassumed.InPARATIE,waterpressuresarethenaddedbytheUTABcommand.
IncontrasttoPARATIE,conventionalanalysesdonotgenerateexcessporepressuresduringundrainedconditionsforclays.
4. UndrainedDrainedAnalysisforclaysClaybehaviordependsontherateofloading(orunloading).WhenfaststresschangestakeplacethenclaybehavioristypicallymodeledasUndrainedwhileslowstresschangesorlongtermconditionsaretypicallymodeledasDrained.
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Inthesoftware,thedefaultbehaviorofaclaytypesoilissetasUndrained.However,thefinalDrained/UndrainedanalysismodeiscontrolledfromtheAnalysistab.ThesoftwareoffersthefollowingDrained/UndrainedAnalysisOptions:a) Drained: Allclaysaremodeledasdrained. In thismode,conventionalanalysismethods
use theeffectivecohesioncand theeffective frictionangle todetermine theappropriatelateralearthpressures.Forclays, thePARATIEanalysisautomaticallydetermines theeffectivecohesionfromthestressstatehistoryandfromthepeakandconstantvolumeshearingfrictionangles(peakandcvrespectively)anditdoesnotusethedefinedcinthesoilstab.
b) Undrained: Allclaysaremodeledasundrained.Inthismode,conventionalanalysismethodsusetheUndrainedShearStrengthSuandassumeaneffectivefrictionangle=0otodeterminethe appropriate lateral earth pressures. For clays, the PARATIE analysis automaticallydeterminestheUndrainedShearStrengthfromthestressstatehistoryoftheclayelementandfrom thepeakand constantvolume shearing frictionangles (peakandcv respectively),butlimitstheupperSutothevalueinthesoilstab.
c) Undrainedforonlyinitiallyundrainedclays: Onlyclayswhoseinitialbehaviorissettoundrained(Soilsform)aremodeledasundrainedasdescribedinitemb)above.Allotherclaysaremodeledasdrained.
IncontrasttoPARATIE,conventionalanalysesdonotgenerateexcessporepressuresduringundrainedconditionsforclays.
5. ActiveandPassiveCoefficientsofLateralEarthPressuresThenewsoftwareoffersanumberofoptionsforevaluatingtheActiveandPassivecoefficientsthatdependon theanalysismethodemployed (ParatieorConventional).An importantdifferencewithPARATIE isthattheoldconceptofUphillandDownhillsidehasbeenchangedtoDrivingsideandResistingSide.Sections5.1and5.2presentthemethodsemployedindeterminingactiveandpassivecoefficients/pressuresinConventionalandParatieanalysesrespectively.However,inallcasesthemethodslistedinTable1availableforcomputingactiveandpassivecoefficients.Table1:AvailableExactSolutionsforActiveandPassiveLateralEarthPressureCoefficients
MethodActiveCoefficient PassiveCoefficient
AvailableSurfaceangle
WallFriction EQ.2 Available
Surfaceangle
WallFriction EQ.
Rankine Yes No1 No1 No Yes No1 No1 NoCoulomb Yes Yes Yes No Yes Yes Yes YesCaquotKeriselTabulated No Yes Yes Yes NoCaquotKeriselTabulated No Yes Yes Yes NoLancellota No Yes Yes Yes YesNotes: 1. RankinemethodautomaticallyconvertstoCoulombifasurfaceangleorwallfrictionisincluded.2. Seismiceffectsareaddedasseparately.
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5.1 ActiveandPassiveLateralEarthPressuresinConventionalAnalysesIn theconventionalanalysis thesoftware firstdetermineswhichside isgeneratingdrivingearthpressures.Oncethedrivingside isdetermined,thesoftwareexamines ifasinglegroundsurfaceangleisassumedonthedrivingandontheresistingsides.Ifasinglesurfaceangleisusedthentheexact theoretical equation is employed as outlined in. If an irregular ground surface angle isdetectedthentheprogramstartsperformingawedgeanalysisontheappropriateside.Horizontalground earth pressures are then prorated to account for all applicable effects including wallfriction.Itshouldbenotedthattheactive/passivewedgeanalysescantakeintoaccountflownetwaterpressuresifaflownetiscalculated.Thecomputedactiveandpassiveearthpressuresarethenmodified iftheuserassumesanothertypeof lateralearthpressuredistribution (i.e.apparentearthpressurediagramcomputed fromactiveearthpressuresabovesubgrade,dividepassiveearthpressuresbyasafetyfactor,etc.).Allof theaboveKa/Kpcomputationsareperformedautomatically foreach stage.Theuserhasonlytoselecttheappropriatewallfrictionbehaviorandearthpressuredistribution.
5.2 ActiveandPassiveLateralEarthPressuresinPARATIEmoduleParatie7.0 incorporates theactiveandpassiveearthpressure coefficientswithin the soildata.Hence,intheexistingParatie7.0eventhoughKa/Kpareinthesoilpropertiesdialog,theuserhastomanuallycomputeKa/Kpand includewallfrictionandothereffects(suchasslopeangle,wallfriction). If a slope angle surface change takes place on a subsequent stage, then the existingParatie user has tomanually compute and change Ka/Kp to properly account for all requiredeffects.Thenewsoftwareoffersadifferent,morerationalizedapproach.
InthenewSWthedefaultKa/Kp(forbothpeakandcv)defined inthesoilstabarebydefaultcomputedwithnowallfrictionandforahorizontalgroundsurface.TheuserstillhastheabilitytousethedefaultPARATIEengineKa/Kpbyselectingacheckbox inthesettings (TabulatedButeevalues). This new approach offers the benefit that the same soil type can easily be reused indifferent design sectionswithout having tomodify the base soil properties. Otherwise, whilestronglynotrecommended,wallfrictionandgroundsurfaceanglecanbeincorporatedwithinthedefaultKa/KpvaluesintheSoilDataDialog.IngeneralthelayoutlogicindeterminingKaandKpisdescribedinFigure1.
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Options 1 2 3Default Ka, Kp = Rankine
(RECOMMENDED)Default engine Ka/Kp (Butee) for zero
wall friction and horizontal ground gives same numbers as Rankine
User defined Ka/Kp that can include slope and wall friction (NOT
RECOMMENDED)
Default KaBase, KpBase defined for each soil type
(Performed for each stage)
1. Default Option (YES) 2. NoSW automatically determines slope angle, wall friction, and other effects KaBaseOptions: A. Enable Kp changes for seismic effects (Default = Yes) KpBase
B. Enable Ka/Kp changes for slope angle (Default = Yes)C. Enable wall friction adjustments (Default = Yes)
For each stage then Options 1.1 and 1.2 are available:
Ka= Kabase x Ka(selected method, slope angle, wall friction)Ka Rankine (i.e. ground slope =0, wall friction = 0)
Kp= Kpbase x Kp(selected method, slope angle, wall friction, EQ)Kp Rankine (i.e. ground slope =0, wall friction = 0)
Ka= Ka(selected method, slope angle, wall friction)
Kp= Kp(selected method, slope angle, wall friction, EQ)
IMPORTANT LIMITATIONSA) Ka/Kp for irregular surfaces is not computed and is treated as horizontal.B) Seismic thrusts are not included in the default Ka calculations.
Sub option 1.2: Use Actual Ka/Kp as determined from Stage Methods and Equations (see Table 1)
3. Examine material changes. The latest Material change property will always override the above equations.
Soil Type Dialog/Base Ka-Kp
Enable automatic readjustment of Ka/Kp for slope angle, wall friction etc?
Sub option 1.1: Prorate base Ka/Kp for slope and other effects (Default)
*notewallfrictioncanbeindependentlyselectedonthedrivingortheresistingside.However,basicwall frictionmodeling is limited to threeoptionsa)Zerowall friction,b)%ofavailablesoil friction,andc)setwallfrictionangle.
Figure1:Ka/KpdeterminationoptionsforParatiemoduleinnewsoftware
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When thesoftwaredetectsthattheuser isrunningananalysiswithnonhorizontalsoil layers(i.e. custom linemode is turned on), the softwarewill calculate the appropriate active and passivelateral earth pressure coefficients by performing a series ofwedge analysis. Eachwedge analysis isperformed at the bottom elevation of each layer by assuming a linearwedge failure with nowallfriction.Then,ifwallfrictionisassumed,theKaandKpvaluesareproratedbytheratioofthehorizontallayerKawith the selectedmethod (Coulomb,Caquot, etc) to theRankineKaorKp values. Last, thecomputedKaandKpcoefficientsaremultipliedordividedbytheappropriatepartialsafetyfactors ifaEC7 typeapproach is selected.For clays, thewedgeanalysis isperformed forboth thepeakand theconstantvolumefrictionangleKaandKpvalues(KaCV,KpCV,KaPeak,KpPeak).Moreinformationaboutthewedgeanalysisequationsispresentedinsections5.4and5.5. InmostcasesthisapproachyieldsgoodroughapproximationstotheactualKaandKpvaluesincomplex geological stratigraphies. However, results should be more closely inspected as in someconditionsmoreconservativecoefficientsmaybegeneratedwhenblock type failuresare initiated. Inthesecases, itmightbemoreappropriatetodefineacustom increasedKaanddecreasedKpfromthesoilsinputdialogandtheResistanceTab.Theprogramoffersawaytoquicklyinspectthewedgeanalysisvalues(withoutthewallfrictionprorating)bytypingthefollowingcommandsintheCommandPrompttextbox: GENWEDGES0LEFT =GeneratestheequivalentKaandKpfortheleftsideoftheleftwall GENWEDGES0RIGHT =GeneratestheequivalentKaandKpfortherightsideoftheleftwall GENWEDGES1LEFT =GeneratestheequivalentKaandKpfortheleftsideoftherightwall GENWEDGES1RIGHT =GeneratestheequivalentKaandKpfortherightsideoftherightwallNote: Thecommandscanbeexecutedonlywhen theexcavationsectionhasbeenanalyzedatleast once.The following example presents a case where the previous commands were verified with no wallfriction.
Figure2.1.a:Wedgeanalysisexamplefornonlinearanalysis
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Inthisexamplethelayerpropertiesare:
FortheGenWedges0Rightcommandthefollowingmessagewillbeproduced:
Forsand layers the reportedKaWedgeandKpWedge isalso reported in theCVandPeakValues.Forclays,theKaWedgeandKpWedgerepresentthevaluesusedinthelimitequilibriumanalysis,whiletheKaCV,KpCV,KaPK,KpPKrepresentthevaluesusedinthenonlinearanalysis(Paratieengine).Negativeandzerovaluesarereportedwhenalayerisnotintersectedbythewall.Uponcloserinspectionofthepreviouslypresented resultsone can see that the calculated Ka and Kp values are very close to thetheoreticalhorizontalKaandKpRankinevalues.SomeexpectedsmalldifferencesarealsoobservedbuttheseareexpectedbecausethetypicallyusedKaandKpequationsformultilayeredsoilsassumeastepwisewedgefailure(whichisalsoaroughapproximation)whereasthewedgeanalysisassumesasingleanglefromthewalltothesurface.
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5.3 PassivePressureEquationsThis sectionoutlines the specific theoreticalequationsused fordetermining thepassive lateralearthpressurecoefficientswithinthesoftware.a) Rankinepassiveearthpressurecoefficient:Thiscoefficient isapplicableonlywhennowall
frictionisusedwithaflatpassivegroundsurface.Thisequationdoesnotaccountforseismiceffects.
b) Coulomb passive earth pressure coefficient: This coefficient can include effects of wall
friction,inclinedgroundsurface,andseismiceffects.TheequationisdescribedbyDasonhisbook Principles of Geotechnical Engineering, 3rd Edition, pg. 430 and in many othertextbooks:
Where = Slopeangle(positiveupwards) = Seismiceffects= with
ax= horizontalacceleration(relativetog)ay= verticalacceleration,+upwards(relativetog)= Wallanglefromvertical(0radianswallfaceisvertical)
c) Lancellotta:Accordingtothismethodthepassive lateralearthpressurecoefficient isgiven
by:
Where And
d) CaquotKerisel(Tabbuttee):RefertomanualbyParatieandtabulatedvalues.
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5.4 ClassicalEarthPressureOptions5.4.1 Active&PassivePressuresfornonLevelGround
Occasionallynonlevelgroundsurfacesandbencheshavetobeconstructed.ThecurrentversionofDeepXcavcanhandleboth singleangle sloped surfaces (i.e single10degree slopeangle)andcomplexbencheswithmultiplepoints.DeepXcavautomaticallydetectswhichconditionapplies.Forsingleangleslopes,DeepXcavwilldetermineusethetheoreticalRankine,Coulomb,orCaquotKeriselactive,orpassivelateralthrustcoefficients(dependingonuserpreference).For non level ground that does not meet the single slope criteria, DeepXcav combines thesolutionsfroma levelgroundwithawedgeanalysisapproach.Pressuresaregenerated inatwostepapproach:a)first,soilpressuresaregeneratedpretendingthatthesurfaceislevel,andthenb)soilpressuresaremultipliedbytheratioofthetotalhorizontalforcecalculatedwiththewedgemethoddividedby the totalhorizontal forcegenerated fora levelgroundsolution.This isdoneincrementallyatallnodes throughout thewalldepth summing forces from the topof thewall.Wall friction is ignored in the wedge solution but pressures with wall friction according toCoulombforlevelgroundareproratedasdiscussed.This approach does not exactly match theoretical wedge solutions. However, it is employedbecauseitisveryeasywiththeiterativewedgesearch(asshowninthefigurebelow)tomissthemostcriticalwedge.Thus,when lateralactiveorpassivepressureshave tobebackfigured fromthetotal lateralforcechangeaspike in lateralpressurecaneasilyoccur(whilethetotalforce isstill the same). Hence, by prorating the activepassive pressure solution a much smootherpressure envelope is generated. Inmost cases this soil pressure envelope is very close to theactual critical wedge solution. The wedgemethods employed are illustrated in the followingfigures.Surcharge loadsarenotconsidered inthewedgeanalysessincesurchargepressuresarederivedseparatelyusingwellacceptedlinearelasticityequations.
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Figure 2.1: Active force wedge search solution according to Coulomb.
Figure 2.2: Passive force wedge search solution according to Coulomb.
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5.4.2 Peck1969EarthPressureEnvelopesAfterobservationofseveralbracedcutsPeck(1969)suggestedusingapparentpressureenvelopeswiththefollowingguidelines:
istaken astheeffectiveunitweightwhilewaterpressuresareaddedseparately(privatecommunicationwithDr.Peck).
Figure2.3:ApparentEarthPressuresasOutlinedbyPeck,1969
Formixedsoilprofiles(withmultiplesoil layers)DeepXcavcomputesthesoilpressureas ifeachlayeractedonlybyitself.AfterprivatecommunicationwithDr.Peck,theunitweightgrepresentseither the totalweight (forsoilabove thewater table)or theeffectiveweightbelow thewatertable.For soilswithboth frictionalandundrainedbehavior,DeepXcavaverages the"Sand"and"Soft clay" or "Stiff Clay" solutions.Note that the Ka used inDeepXcav is only for flat groundsolutions. The same effect for different Ka (such as for sloped surfaces), can be replicated bycreatingacustomtrapezoidalredistributionofactivesoilpressures.
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5.4.3 FHWAApparentEarthPressuresThe current version of DeepXcav also includes apparent earth pressurewith FHWA standards
(Federal Highway Administration). The following few pages are reproduced from applicable FHWAstandards.
Figure2.4:RecommendedapparentearthpressurediagramforsandsaccordingtoFHWA
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TOTALLOAD(kN/m/meterofwall)=3H2to6H2(Hinmeters)
Figure2.5:RecommendedapparentearthpressurediagramforstifftohardclaysaccordingtoFHWA.Inbothcasesforfigures2.4and2.5,themaximumpressurecanbecalculatedfromthetotalforceas:a. Forwallswithonesupport:p=2xLoad/(H+H/3)b. Forwallswithmorethanonesupport:p=2xLoad/{2H2(H1+Hn+1)/3)}
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5.4.4 FHWARecommendedApparentEarthPressureDiagramforSofttoMediumClays
Temporaryandpermanentanchoredwallsmaybeconstructedinsofttomediumclays(i.e.Ns>4)if a competent layer of forming the anchor bond zone iswithin reasonable depth below theexcavation. Permanently anchoredwalls are seldom usedwhere soft clay extends significantlybelowtheexcavationbase.Forsofttomediumclaysandfordeepexcavations(andundrainedconditions),theTerzaghiPeckdiagram shown in figure2.5hasbeenused toevaluateapparentearthpressures fordesignoftemporarywalls insofttomediumclays.Forthisdiagramapparentsoilpressuresarecomputedwithacoefficient:
Where m is an empirical factor that accounts for potential base instability effects in deepexcavationsissoftclays.WhentheexcavationisunderlainbydeepsoftclayandNsexceeds6,misset to0.4.Otherwise,m is takenas1.0 (Peck,1969).Using theTerzaghiandPeckdiagramwithm=0.4incaseswhereNs>6mayresultinanunderestimationofloadsonthewallandisthereforenot conservative. In this case, the softwareusesHenkelsequationasoutlined in the followingsection.An importantrealization isthatwhenNs>6thentheexcavationbaseessentiallyundergoesbasalfailure as the basal stability safety factor is smaller than 1.0. In this case, significant soilmovementsshouldbeexpectedbelowtheexcavationthatarenotcapturedbyconventionallimitequilibriumanalysesandmaynotbeincludedinthebeamonelastoplasticsimulation(Paratie).
ThesoftwareinthecaseofasinglesoillayerwillusethethisequationifNs>4andNs
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Distribute the factored total force into an apparent pressure diagram using the trapezoidaldistributionshowninFigure2.4.
Wherepotentialfailuresurfacesaredeepseated, limitequilibriummethodsusingslopestabilitymaybeusedtocalculateearthpressureloadings.TheTerzaghiandPeck(1967)diagramsdidnotaccountforthedevelopmentofsoilfailurebelowthebottomof theexcavation.Observationsand finiteelement studieshavedemonstrated thatsoil failure below the excavation bottom can lead to very large movements for temporaryretainingwallsinsoftclays.ForNs>6,relativelargeareasofretainedsoilneartheexcavationbaseare expected to yield significantly as the excavation progresses resulting in largemovementsbelowtheexcavation,increasedloadsontheexposedportionofthewall,andpotentialinstabilityoftheexcavationbase.Inthiscase,Henkel(1971)developedanequationtodirectlyobtainKAforobtaining themaximum pressure ordinate for soft tomedium clays apparent earth pressurediagrams (thisequation isappliedwhenFHWAdiagramsareusedand theprogramexamines ifNs>6):
Wherem=1accordingtoHenkel(1971).Thetotalloadisthentakenas:
Figure2.6:Henkelsmechanismofbasefailure
Figure2.7showsvaluesofKAcalculatedusingHenkelsmethodforvariousd/Hratios.ForresultsinthisfigureSu=Sub.This figure indicatesthatfor4
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usingthesofttomediumapparentearthpressurediagramwithKa=0.22is0.193H2resultinginamaximumpressurep=0.26H.UseofKa=0.22,accordingtoFHWA,representarationaltransitionvalueforthesecases.Henkelsmethod is limitedtocaseswheretheclayssoilsontheretainedsideoftheexcavationand below the excavation can each be reasonably characterized using a constant value forundrained shear strength. Where a more detailed shear strength profile is required, limitequilibriummethodsmaybeusedtoevaluatetheearthpressureloadingsonthewalldescribedinsection5.7.3oftheFHWAmanual(notperformedwithinthesoftware).
Figure2.7:Comparisonofapparentlateralearthpressurecoefficientswithbasalstabilityindex(FHWA2004).Forclaysthestabilitynumberisdefinedas:
Pleasenotethatsoftwareusestheeffectiveverticalstressatsubgradetofindanequivalentsoilunitweight,Waterpressuresareaddedseparatelydependingonwaterconditionassumptions.This is slightlydifferent from theapproach recommendedby FHWA,however,afterpersonalcommunicationwith the lateDr.Peck,has confirmed thatusersof apparent earthpressuresshouldusetheeffectivestressatsubgradeandaddwaterpressuresseparately.By ignoring thewater table, or by using customwater pressures, the exact same numericalsolutionaswiththeoriginalFHWAmethodcanbeobtained.
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5.4.6 ModificationstostiffclayandFHWAdiagramsOvertheyearsvariousresearchersandengineershaveproposednumerousapparentlateralearthpressure diagrams for braced excavations. Unfortunately, most lateral apparent pressurediagramshavebeentakenoutofcontextormisused.Historically,apparentlateralearthpressurediagrams have been developed from measured brace reactions. However, apparent earthpressurediagramsareoftenarbitrarilyusedtoalsocalculatebendingmomentsinthewall.In excavations supporting stiff clays, many researchers have observed that the lower bracescarriedsmallerloads.Thishasmisledengineerstoextrapolatetheapparentlateralearthpressuretozeroatsubgrade. In thisrespect,manyapparent lateralearthpressurediagramscarrywithinthemahistoricalunconservativeoversight inthefactthatthe lateralearthpressureatsubgradewasneverdirectlyorindirectlymeasured.Konstantakos(2010)hasproventhatthezeroapparentlateral earth pressure at the subgrade level assumption is incorrect, unconservative, andmostimportantlyunsubstantiated.Thishistoricaloversight,can leadtosevereunderestimationoftherequiredwallembedmentlengthandoftheexperiencedwallbendingmoments.Iflargerdisplacementscanbetoleratedordrainedconditionsareexperiencedtheapparentearthpressurediagramsmustnot,ataminimum,dropbelowthetheoreticalactivepressure,unlesssoilarching iscarefullyevaluated.Alternatively, in thesecases, for fastcalculationsorestimates,anengineer can increase the apparent earth pressure from 50% atmidway between the lowestsupport leveland the subgrade to the full theoreticalapparentpressureor theactivepressurelimitatthesubgradelevel(seeFigure2.8).Asalways,theseequationsrepresentasimplificationofcomplexconditions.Iftighterdeformationcontrol isrequiredorwhenfullyundrainedconditionsaretobeexpected,then the virtual reaction at the subgrade levelhas to take intoaccount increased lateralearthpressures that caneven reach close to fiftypercentof the totalvertical stressat the subgradelevel.The initialstateofstresshastobetaken intoconsiderationasoverconsolidatedsoilstratawill tend to induce larger lateral earth stresses on the retainingwalls. In such critical cases, adesignengineermustalwayscomplimentapparentearthpressurediagramcalculationswithmoreadvancedandwellsubstantiatedanalysismethods.TheabovemodificationscanbeappliedwithinthesoftwarebydoubleclickingonthedrivingearthpressurebuttonwhentheFHWAorPeckmethodisselected.
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Figure2.8:MinimumlateralpressureoptionforFHWAandPeckapparentpressurediagrams(check
box).
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Figure 2.9: Proposed modifications to stiff clay and FHWA apparent lateral earth pressure diagrams (Konstantakos 2010).
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5.4.7 VerificationExampleforSoftClayandFHWAApproachA10mdeepexcavationisconstructedinsoftclaysandthewallisembedded2minasecondsoftclaylayer.Thewallissupportedbythreesupportsatdepthsof2m,5m,and8mfromthewalltop.Assumedsoilpropertiesare:
Clay1: From0to10mdepth, Su=50kPa 20kN/m3Clay2: From10mdepthandbelow Su=30kPa 20kN/m3Thedepthtothefirmlayerfromtheexcavationsubgradeisassumedasd=10m(whichisthe
modelbase,i.e.thebottommodelcoordinate)
Figure2.10:VerificationexampleforFHWAapparentpressureswithasoftclay
Thetotalverticalstressattheexcavationsubgradeis:v20kN/m3x10m=200kPa
Thebasalstabilitysafetyfactoristhen:
FS=5.7x30kPa/200kPa=0.855(verifiedfromFig.2.10)
ThenaccordingtoHenkelKaiscalculatedas(m=1):
Thetotalthrustabovetheexcavationisthen:Ptotal=0.5KAvxH=647kN/mThemaximumearthpressureordinateisthen:
p=2xLoad/{2H2(H1+Hn+1)/3)}=2x647kN/m/{2x10m2x(2m+2m)/3}=74.65kPa
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Thesoftwarecalculates74.3kPaandessentiallyconfirmstheresultsasdifferencesareattributedtoroundingerrors.Thetributaryloadinthemiddlesupportisthen3mx74,3kPa=222.9kN/m(whichisconfirmedbythe program).When performing only conventional limit equilibrium analysis it is important toproperlyselect thenumberofwallelements thatwillgenerateasufficientnumberofnodes. Inthisexample,195wallnodesareassumed.Ingeneralitisrecommendedtouseatleast100nodeswhenperformingconventionalcalculationswhile200nodeswillproducemoreaccurateresults.
Nowexaminethecaseifthesoilwasasandwithafrictionangleof30degrees.
Figure2.11:VerificationexampleforFHWAsoftclayanalysis
Inthiscase,thetotalactivethrustiscalculatedas:Ptotal=0.65KAvxH=432.9kN/mThemaximumearthpressureordinateisthen:
p=2xLoad/{2H2(H1+Hn+1)/3)}=2x432.9kN/m/{2x10m2x(2m+2m)/3}=49.95kPaThisapparentearthpressurevalueisconfirmedbythesoftware.
Next,wewillexaminethesameexcavationwithamixedsandandclayprofile.Sand: From0to5mdepth, =30o 20kN/m3 Clay1: From5to10mdepth, Su=50kPa 20kN/m3Clay2: From10mdepthandbelow Su=30kPa 20kN/m3
Inthisexample,Ns=6.67.AsaresultwewillhavetouseHenkelsequationbutaveragetheeffectsofsoilfrictionandcohesion.Thismethodisaroughapproximationandshouldbeusedwithcaution.
From0mto5mthefrictionforceonaverticalfaceinSand1canbecalculatedas:Ffriction=0.5x20kN/m3x5mxtan(30degrees)x5m=144.5kN/m
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TheavailablesidecohesiononlayerClay1is:5mx50kPa=250kN/mThetotalsideresistanceontheverticalfaceisthen:250kN/m+144.5kN/m=395.5kN/mTheaverageequivalentcohesioncanbecomputedas:
Su.ave=395.5kN/m/10m=39.55kPa
ThenaccordingtoHenkelKaiscalculatedas(m=1):
Thetotalthrustabovetheexcavationisthen:Ptotal=0.5KAvxH=849kN/mThemaximumearthpressureordinateisthen:
p=2xLoad/{2H2(H1+Hn+1)/3)}=2x647kN/m/{2x10m2x(2m+2m)/3}=98kPaThisresultisconfirmedbythesoftwarethatproduces99.2kPa.
Figure2.12:VerificationexampleforFHWAmixedsoilprofilewithsoftclayandsand
5.4.8 CustomTrapezoidalPressureDiagrams Withthisoptiontheapparentearthpressurediagram isdeterminedastheproductoftheactive
soilthrusttimesauserdefinedfactor.Thefactorshouldrangetypicallyfrom1.1to1.4dependingon the user preferences and the presence of a permanent structure. The resulting horizontalthrust is then redistributed as a trapezoidal pressure diagram where the top and bottomtriangularpressureheightsaredefinedasapercentageoftheexcavationheight.
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5.4.9 TwoStepRectangularPressureDiagramsVeryoften,especially in theUS,engineersareprovidedwith rectangularapparent lateralearthpressuresthataredefinedwiththeproductofafactortimestheexcavationheight.TwofactorsareusuallydefinedM1forpressuresabovethewatertableandM2forpressuresbelowthewatertable.M1andM2shouldalreadyincorporatethesoiltotalandeffectiveweight.Useofthisoptionshould be carried with extreme caution. The following dialog will appear if the rectangularpressureoptionisselectedinthedrivingpressuresbutton.
Figure2.10:Twosteprectangularearthpressurecoefficients.
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5.5 VerticalwalladhesioninundrainedloadingShorttermtotalstressconditions(i.e.undrainedloading)representthestateinthesoilbeforetheporewaterpressureshavehadtimetodissipatei.e.immediatelyafterconstructioninacohesivesoil.Fortotalstressthehorizontalactiveandpassivepressuresarecalculatedusingthefollowingequations:pa=Ka(z+q)SuKacpp=Kp(z+q)+SuKpc
Where:(z+q)representsthetotaloverburdenpressureKa=Kp=1.0forcohesivesoils.
Designsu=sud=sumc/FSsuwhereFssuistypically1.5.Theearthpressurecoefficients,KacandKpc,makeanallowanceforwall/soiladhesionandarederivedasfollows:
Kac=Kpc=2(1+Swmax/Sud)0.5
AccordingtothePilingHandbookbyArcelor(2005),the limitingvalueofwalladhesionSwmaxatthe soil/sheet pile interface is generally taken to be smaller than the design undrained shearstrengthofthesoil,sud,byafactorof2forstiffclays.i.e.Swmax=xSud,where=0.5.Lowervaluesofwalladhesion,however,mayberealized insoftclays. Inanycase,thedesignershouldrefertothedesigncodetheyareworkingtoforadviceonthemaximumvalueofwalladhesiontheymayuse.Currently, thesemodificationscanbeusedonly inconventional limitequilibriumanalyses.
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6. Eurocode7analysismethods
In the US practice excavations are typically designed with a service design approach while aStrengthReductionApproachisusedinEuropeandinmanyotherpartsoftheworld.Eurocode7(strength design, herein EC7) recommends that the designer examines a number of differentDesign Approaches (DA1, DA2, DA3) so that the most critical condition is determined. InEurocode 7 soil strengths are readjusted according to thematerial M tables, surcharges andpermanentactionsarereadjustedaccordingtotheactionAtables,andresistancesaremodifiedaccordingto theR tabulatedvalues. Hence, inacasethatmaybeoutlinedasA2+M2+R2onewouldhavetoapplyalltherelevantfactorstoActions,Materials,andResistances.A designer still has to perform a service check in addition to all the ultimate design approachcases.Hence,aconsiderablenumberofcaseswillhave tobeexaminedunless themostcriticalcondition canbeeasilyestablishedby anexperiencedengineer. In summary,EC7provides thefollowingcombinationswherethefactorscanbepickedfromthetablesinsection6.1:DesignApproach1,Combination1: A1+M1+R1DesignApproach1,Combination2: A2+M2+R1DesignApproach2: A1*+M1+R2DesignApproach3: A1*+A2++M2+R3
A1*=Forstructuralactionsorexternalloads,andA2+=forgeotechnicalactions EQK(fromEC8): M2+R1 (TheItaliancodeDM08usesDA11,DA12,andEQKdesignapproachmethodsonly).IntheoldParatie(version7andbefore),thedifferentcaseswouldhavebeenexaminedinmanyLoadHistories.ThetermLoadHistoryhasbeenreplacedinthenewsoftwarewiththeconceptofDesignSection.EachdesignsectioncanbeindependentfromeachotheroraDesignSectioncanbe linkedtoaBaseDesignSection.Whenadesignsection is linked, themodelandanalysisoptions are directly copied from the BaseDesign Sectionwith the exception of the Soil CodeOptions(i.e,Eurocode7,DM08etc).InEurocode7,variousequilibriumandothertypechecksareexamined:a) STR: Structuraldesign/equilibriumchecksb) GEO: Geotechnicalequilibriumchecksc) HYD: Hydraulicheavecasesd) UPL: Uplift(onastructure)e) EQU: Equilibriumstates(applicabletoseismicconditions?)
Thenew softwarehandles anumberof STR,GEO, andHYD checkswhile it gives the ability toautomaticallygenerateallEurocode7casesforamodel.Unfortunately,Eurocode7asawholeismostlygearedtowardstraditionallimitequilibriumanalysis.Inmoreadvancedanalysismethods(suchas inParatie),Eurocode7canbehandledaccordingtothe letterofthecodeonlywhenequalgroundwater levelsareassumed inbothwallsides.However,muchdoubtexistsastothe
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mostappropriatemethodtobeemployedwhendifferentgroundwaterlevelshavetobemodeled.Section6.1presentsthesafety/strengthreductionparametersthatthenewsoftwareuses.
6.1 SafetyParametersforUltimateLimitStateCombinationsTable 2.1 lists all safety factors that areused in thenew software and alsoprovides theusedsafetyfactorsaccordingtoEC72008.Thelast4tablecolumnslistthecodesafetyfactorsforeachcodecase/scenario(i.e. inthefirstrowCase1referstoM1,Case2referstoM2).Table2.2 liststhesamefactorsfortheItaliancodeNTC08,whiletables2.3,2.4,and2.5listthesafetyfactorsfortheGreek,theFrench,andtheGermancodesrespectively.Last, table 2.6 presents the load combinations employed byAASHTO LRFD 5th edition (2010).AASHTOslightlydiffersfromEuropeanstandardsinthatsoilstrengthisnotfactored.
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Table2.1:ListofsafetyfactorsforstrengthdesignapproachaccordingtoEurocode7
InternalSWParameter Description
Type EurocodeParameter
EurocodeReference
EurocodeChecks
Case1DA1:comb1.
A1+M1+R1
Case2DA1:comb2.
A2+M2+R1
Case3DA2:
A1+M1+R2
Case4DA1:
A1+M1+R1
EQU:M2+R1
F_Fr SafetyfactorontanFR M M SectionA.3.2 STRGEO 1.00 1.25 1.00 1.25 1.25F_C Safetyfactorc' M M STRGEO 1.00 1.25 1.00 1.25 1.25F_Su SafetyfactoronSu M M STRGEO 1.00 1.40 1.00 1.40 1.40
F_LV Safetyfactorforvariablesurcharges(unfavorable) A Q SectionA.3.1 STRGEO 1.50 1.30 1.50 1.50 0.00
F_LP Safetyfactorforpermanentsurcharges(unfavorable) A G TableA.3.pg130 STRGEO 1.35 1.00 1.35 1.35 1.00
F_LvfavorSafetyfactorforvariablesurcharges(favorable) A Q SectionA.3.1 STRGEO 0.00 0.00 0.00 0.00 1.00
F_Lpfavor Safetyfactorforpermanentsurcharges(favorable) A G TableA.3.pg130 STRGEO 1.00 1.00 1.00 1.00 1.00
F_EQ Safetyfactorforseismicpressures
A 0.00 0.00 0.00 0.00 1.00
F_ANCH_T Safetyfactorfortemporaryanchors
R a;t SectionA.3.3.4 STRGEO 1.10 1.10 1.10 1.00 1.10
F_ANCH_P Safetyfactorforpermanentanchors
R a;p TableA.12.pg134 STRGEO 1.10 1.10 1.10 1.00 1.10
F_RESSafetyfactorearthresistancei.e.Kp R R;e
SectionA.3.3.5TableA.13pg.
135STRGEO 1.00 1.00 1.40 1.00 1.00
F_WaterDRSafetyfactoronDrivingWaterpressures(appliedinBeamANALYSISONLYtoaction)
A G SectionA.3.1 STRGEO 1.35 1.00 1.35 1.00 1.00
F_WaterRESSafetyfactoronResistingwaterpressures(appliedinBeamAnalysistoaction)
A G TableA.3.pg130 STRGEO 1.00 1.00 1.00 1.00 1.00
F_HYDgDST HydraulicCheckdestabilizationfactor A G;dst SectionA.5 HYD 1.35 1.35 1.35 1.35 1.00
F_HYDgSTABSafetyfactoronHydrauliccheckstabilizingaction A G;stb
TableA.17.pg136
HYD 0.90 0.90 0.90 0.90 0.90
F_gDSTABFactorforUNFAVORABLEpermanentDESTABILIZINGACTION
UPL G;dst SectionA.4 UPL 1.10 1.10 1.10 1.10 1.10
F_gSTABFactorforfavorablepermanentSTABILIZINGaction UPL G;stb
TableA.15.pg136
UPL 0.90 0.90 0.90 0.90 0.90
F_DriveEarthmultiplicationfactorappliedtodrivingearthpressures A Gonactions TableA.3 STRGEO 1.35 1.00 1.35 1.00 1.00
F_DriveActive N/A N/A N/A N/A N/AF_DriveAtRest N/A N/A N/A N/A N/A
F_Wall Safetyfactorforwallcapacity STR Modelfactorforwallcapacity 1.00 1.00 1.00 1.00 1.00
TableA.4pg.130
EUROCODE7,EN19971:2004(2007) CodeCase
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Table2.2:ListofsafetyfactorsforstrengthdesignapproachaccordingtoItalianNTC2008code
InternalSWParameter Description
TypeEurocodeParameter
EurocodeReference
EurocodeChecks
Case1 Case2 Case3* Case4 EQK
F_Fr SafetyfactorontanFR M M SectionA.3.2 STRGEO 1.00 1.25 1.25
F_C Safetyfactorc' M M STRGEO 1.00 1.25 1.25
F_Su SafetyfactoronSu M M STRGEO 1.00 1.40 1.4
F_LVSafetyfactorforvariablesurcharges(unfavorable) A Q SectionA.3.1 STRGEO 1.50 1.30 1
F_LPSafetyfactorforpermanentsurcharges(unfavorable) A G
TableA.3.pg130
STRGEO 1.30 1.00 1
F_LvfavorSafetyfactorforvariablesurcharges(favorable) A Q SectionA.3.1 STRGEO 0.00 0.00 1
F_Lpfavor Safetyfactorforpermanentsurcharges(favorable) A G
TableA.3.pg130
STRGEO 1.00 1.00 1
F_EQSafetyfactorforseismicpressures
A 0.00 0.00 1
F_ANCH_TSafetyfactorfortemporaryanchors
R a;t SectionA.3.3.4 STRGEO 1.10 1.10 1.10 1.1
F_ANCH_PSafetyfactorforpermanentanchors
R a;p TableA.12.pg134 STRGEO 1.20 1.20 1.20 1.2
F_RESSafetyfactorearthresistancei.e.Kp R R;e
SectionA.3.3.5Table STRGEO 1.00 1.40 1
F_WaterDRSafetyfactoronDrivingWaterpressures(appliedin A G SectionA.3.1 STRGEO 1.30 1.00 1
F_WaterRESSafetyfactoronResistingwaterpressures(appliedinBeamAnalysistoaction)
A G TableA.3.pg130 STRGEO 1.00 1.00
F_HYDgDSTHydraulicCheckdestabilizationfactor A G;dst SectionA.5 HYD 1.35
F_HYDgSTABSafetyfactoronHydrauliccheckstabilizingaction A G;stb
TableA.17.pg136
HYD 0.90
F_gDSTABFactorforUNFAVORABLEpermanentDESTABILIZINGACTION
UPL G;dst SectionA.4 UPL 1.10
F_gSTABFactorforfavorablepermanentSTABILIZINGaction
UPL G;stb TableA.15.pg136 UPL 0.90
F_DriveEarthmultiplicationfactorappliedtodrivingearthpressures A Gonactions TableA.3 STRGEO 1.30 1.00 1
F_Wall Safetyfactorforwallcapacity STR Modelfactorforwallcapacity 1.00 1.00 1
TableA.4pg.130
ITALIAN,NTC2008 CodeCase
Note: F_WallisnotdefinedinEC7.TheseparameterscanbeusedinanLRFDapproachconsistentwithUSAcodes.
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Table2.3:ListofsafetyfactorsforstrengthdesignapproachGreekdesigncode2007
InternalSWParameter Description
Type EurocodeParameter
EurocodeReference
EurocodeChecks
Case1DA2*:
A1+M1+R2
Case2DA3:A1A2+M2+R1
EQU:M2+R1
F_Fr SafetyfactorontanFR M M SectionA.3.2 STRGEO 1.00 1.25 1.25F_C Safetyfactorc' M M STRGEO 1.00 1.25 1.25F_Su SafetyfactoronSu M M STRGEO 1.00 1.40 1.40
F_LVSafetyfactorforvariablesurcharges(unfavorable) A Q
SectionA.3.1
STRGEO 1.50 1.50 1.00
F_LPSafetyfactorforpermanentsurcharges(unfavorable) A G
TableA.3.pg130
STRGEO 1.35 1.35 1.00
F_LvfavorSafetyfactorforvariablesurcharges(favorable) A Q
SectionA.3.1
STRGEO 0.00 0.00 0.00
F_LpfavorSafetyfactorforpermanentsurcharges(favorable) A G
TableA.3.pg130
STRGEO 1.00 1.00 1.00
F_EQSafetyfactorforseismicpressures
A 0.00 1.00 1.00
F_ANCH_T Safetyfactorfortemporaryanchors
R a;t SectionA.3.3.4
STRGEO 1.10 1.10 1.10
F_ANCH_PSafetyfactorforpermanentanchors
R a;p TableA.12.pg134 STRGEO 1.10 1.10 1.10
F_RESSafetyfactorearthresistancei.e.Kp R R;e
SectionA.3.3.5TableA.13pg.135
STRGEO 1.40 1.00 1.00
F_WaterDRSafetyfactoronDrivingWaterpressures(appliedinBeamANALYSISONLYtoaction)
A G SectionA.3.1 STRGEO 1.35 1.35 1.00
F_WaterRESSafetyfactoronResistingwaterpressures(appliedinBeamAnalysistoaction)
A G TableA.3.pg130 STRGEO 1.00 1.00 1.00
F_HYDgDSTHydraulicCheckdestabilizationfactor A G;dst SectionA.5 HYD 1.35 1.00 1.00
F_HYDgSTABSafetyfactoronHydrauliccheckstabilizingaction A G;stb
TableA.17.pg136 HYD 0.90 0.90 0.90
F_gDSTABFactorforUNFAVORABLEpermanentDESTABILIZINGACTION
UPL G;dst SectionA.4 UPL 1.10 1.10 1.10
F_gSTABFactorforfavorablepermanentSTABILIZINGaction UPL G;stb
TableA.15.pg136 UPL 0.90 0.90 0.90
F_DriveEarthmultiplicationfactorappliedtodrivingearthpressures A Gonactions TableA.3 STRGEO 1.35 1.35 1.00
F_DriveActive N/A N/A N/A
F_DriveAtRest N/A N/A N/A
F_Wall Safetyfactorforwallcapacity STR Modelfactorforwallcapacity 1.00 1.00 1.00
EUROCODE7,GREEK2007 CodeCase
TableA.4pg.130
Note:ForslopestabilitythedesignapproachisequivalenttoEQU
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Table2.4:PartialsafetyfactorsforstrengthdesignapproachwithFrenchcodesXP240andXP220
Case1 Case2 Case3 Case4 Case5 Case6 Case7 Case812a
(stand)2b
(sens)12a
(stand)2b
(sens)12a
(stand)2b
(sens)12a
(stand)2b
(sens)
F_Fr SafetyfactorontanFR M M SectionA.3.2 STRGEO 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25F_C Safetyfactorc' M M STRGEO 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25F_Su SafetyfactoronSu M M STRGEO 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40
F_LVSafetyfactorforvariablesurcharges(unfavorable) A Q
SectionA.3.1
STRGEO 1.33 1.33 1.00 1.00 1.33 1.33 0.00 0.00
F_LPSafetyfactorforpermanentsurcharges(unfavorable) A G
TableA.3.pg130
STRGEO 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_LvfavorSafetyfactorforvariablesurcharges(favorable) A Q
SectionA.3.1
STRGEO 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
F_LpfavorSafetyfactorforpermanentsurcharges(favorable) A G
TableA.3.pg130
STRGEO 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90
F_EQ Safetyfactorforseismicpressures
A 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_ANCH_T Safetyfactorfortemporaryanchors
R a;t SectionA.3.3.4 STRGEO 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10
F_ANCH_PSafetyfactorforpermanentanchors
R a;p TableA.12.pg134 STRGEO 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10
F_RESSafetyfactorearthresistancei.e.Kp R R;e
SectionA.3.3.5TableA.13pg.135
STRGEO 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_WaterDRSafetyfactoronDrivingWaterpressures(appliedinBeamANALYSISONLYtoaction)
A G SectionA.3.1 STRGEO 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_WaterRESSafetyfactoronResistingwaterpressures(appliedinBeamAnalysistoaction)
A G TableA.3.pg130 STRGEO 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_HYDgDSTHydraulicCheckdestabilizationfactor
A G;dst SectionA.5 HYD 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35
F_HYDgSTABSafetyfactoronHydrauliccheckstabilizingaction A G;stb
TableA.17.pg136 HYD 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90
F_gDSTABFactorforUNFAVORABLEpermanentDESTABILIZINGACTION
UPL G;dst SectionA.4 UPL 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10
F_gSTABFactorforfavorablepermanentSTABILIZINGaction UPL G;stb
TableA.15.pg136 UPL 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90
F_DriveEarthmultiplicationfactorappliedtodrivingearthpressures A GonactionsTableA.3 STRGEO 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_DriveActive N/A N/A N/A N/A N/A N/A N/A N/A
F_DriveAtRest N/A N/A N/A N/A N/A N/A N/A N/A
F_Wall Safetyfactorforwallcapacity STR Modelfactorforwallcapacity 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
Fundamental Accidental
TableA.4pg.130
EUROCODE7,FRENCH2007 CodeCase
InternalSWParameter Description
TypeEurocodeParameter
EurocodeReference
EurocodeChecks
XP240 XP220Fundamental Accidental
Note:Frenchcodestandardsareparticularlyimportantforsoilnailingwalls.
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Table2.5:PartialsafetyfactorsforstrengthdesignapproachwithGermanDIN2005
InternalSWParameter Description
Type EurocodeParameter
EurocodeReference
EurocodeChecks
Case1GZ2(SLS)
Case2GZ1B(LC1)
Case3GZ1B(LC2)
Case4GZ1B(LC3)
Case5GZ1C(LC1)
Case6GZ1C(LC2)
Case7GZ1C(LC3)
F_Fr SafetyfactorontanFR M M SectionA.3.2 STRGEO 1.00 1.00 1.00 1.00 1.25 1.15 1.10F_C Safetyfactorc' M M STRGEO 1.00 1.25 1.15 1.10 1.25 1.15 1.10F_Su SafetyfactoronSu M M STRGEO 1.00 1.25 1.15 1.10 1.25 1.15 1.10F_LV Safetyfactorforvariablesurcharges
(unfavorable)A Q SectionA.3.1 STRGEO 1.00 1.50 1.30 1.00 1.30 1.20 1.00
F_LPSafetyfactorforpermanentsurcharges(unfavorable) A G
TableA.3.pg130 STRGEO 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_LvfavorSafetyfactorforvariablesurcharges(favorable)
A Q SectionA.3.1 STRGEO 0.00 0.00 0.00 0.00 0.00 0.00 0.00
F_LpfavorSafetyfactorforpermanentsurcharges(favorable) A G
TableA.3.pg130 STRGEO 1.00 0.90 0.90 0.90 0.90 0.90 0.90
F_EQ Safetyfactorforseismicpressures A 1.00 0.00 0.00 0.00 1.00 1.00 1.00
F_ANCH_T Safetyfactorfortemporaryanchors R a;t SectionA.3.3.4 STRGEO 1.00 1.10 1.10 1.10 1.10 1.10 1.10
F_ANCH_P Safetyfactorforpermanentanchors R a;p TableA.12.pg134 STRGEO 1.00 1.10 1.10 1.10 1.10 1.10 1.10
F_RES Safetyfactorearthresistancei.e.Kp R R;eSectionA.3.3.5
TableA.13STRGEO 1.00 1.40 1.30 1.20 1.40 1.00 1.00
F_WaterDRSafetyfactoronDrivingWaterpressures(appliedinBeamANALYSISONLYtoaction)
A G SectionA.3.1 STRGEO 1.00 1.35 1.00 1.20 1.00 1.00 1.00
F_WaterRESSafetyfactoronResistingwaterpressures(appliedinBeamAnalysistoaction)
A G TableA.3.pg130 STRGEO 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_HYDgDSTHydraulicCheckdestabilizationfactor
A G;dst SectionA.5 HYD 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_HYDgSTABSafetyfactoronHydrauliccheckstabilizingaction A G;stb
TableA.17.pg136 HYD 1.00 0.90 0.95 0.90 0.90 0.95 0.90
F_gDSTABFactorforUNFAVORABLEpermanentDESTABILIZINGACTION UPL G;dst
SectionA.4
UPL 1.00 1.00 1.00 1.00 1.00 1.00 1.00
F_gSTAB FactorforfavorablepermanentSTABILIZINGaction UPL G;stb
TableA.15.pg136 UPL 1.00 0.90 0.95 0.90 0.90 0.95 0.90
F_DriveEarthmultiplicationfactorappliedtodrivingearthpressures A Gonactions TableA.3 STRGEO 1.00 1.35 1.20 1.00 1.00 1.00 1.00
F_DriveActive N/A N/A N/A N/A N/A N/A N/A
F_DriveAtRest N/A 1.20 1.10 N/A N/A N/A N/A
F_Wall Safetyfactorforwallcapacity STR Modelfactorforwallcapacity 1.00 1.00 1.00 1.00 1.00 1.00 1.00
EUROCODE7,GERMAN2005
TableA.4pg.130
CodeCase
Note: 1.Case5,6,and7areonlyusedinslopestabilityanalysisinconjunctionwithcases1,2,and3respectively. 2.Atrestearthpressurefactorisusedinmultiplyingearthpressuresonlyinlimitequilibriumanalyses.
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Table2.6:PartialsafetyfactorsforstrengthdesignapproachwithAASHTOLRFD5thedition2010
InternalSWParameter Description Type
EurocodeParameter
EurocodeReference
EurocodeChecks
ServiceI
StrengthIa
StrengthIb
StrengthII
ExtremeI
F_Fr SafetyfactorontanFR M M SectionA.3.2 STRGEO 1.00 1.00 1.00 1.00 1.00F_C Safetyfactorc' M M STRGEO 1.00 1.00 1.00 1.00 1.00F_Su SafetyfactoronSu M M STRGEO 1.00 1.00 1.00 1.00 1.00F_LV
Safetyfactorforvariablesurcharges(unfavorable) A Q SectionA.3.1 STRGEO 1.00 1.75 1.75 1.35 0.50
F_LPSafetyfactorforpermanentsurcharges(unfavorable) A G TableA.3.pg130 STRGEO 1.00 1.00 1.35 1.35 1.35
F_LvfavorSafetyfactorforvariablesurcharges(favorable) A Q SectionA.3.1 STRGEO 1.00 0.00 0.00 0.00 0.00
F_LpfavorSafetyfactorforpermanentsurcharges(favorable) A G TableA.3.pg130 STRGEO 1.00 0.90 1.00 1.00 1.00
F_EQSafetyfactorforseismicpressures
A 1.00 1.00 1.00 1.00 1.00
F_ANCH_TSafetyfactorfortemporaryanchors
R a;t SectionA.3.3.4 STRGEO 1.00 1.00 1.00 1.00 1.00
F_ANCH_PSafetyfactorforpermanentanchors
R a;p TableA.12.pg134 STRGEO 1.00 1.11 1.11 1.11 1.11
F_RESSafetyfactorearthresistancei.e.Kp R R;e
SectionA.3.3.5TableA.13pg.
135STRGEO 1.00 1.33 1.33 1.33 1.00
F_WaterDRSafetyfactoronDrivingWaterpressures(appliedinBeamANALYSISONLYtoaction)
A G SectionA.3.1 STRGEO 1.00 1.00 1.00 1.00 1.00
F_WaterRESSafetyfactoronResistingwaterpressures(appliedinBeamAnalysistoaction)
A G TableA.3.pg130 STRGEO 1.00 1.00 1.00 1.00 1.00
F_HYDgDSTHydraulicCheckdestabilizationfactor A G;dst SectionA.5 HYD 1.00 1.00 1.00 1.00 1.00
F_HYDgSTABSafetyfactoronHydrauliccheckstabilizingaction A G;stb
TableA.17.pg136
HYD 1.00 1.00 1.00 1.00 1.00
F_gDSTABFactorforUNFAVORABLEpermanentDESTABILIZINGACTION
UPL G;dst SectionA.4 UPL 1.00 1.00 1.00 1.00 1.00
F_gSTABFactorforfavorablepermanentSTABILIZINGaction UPL G;stb
TableA.15.pg136
UPL 11.00 1.00 1.00 1.00 1.00
F_DriveEarthmultiplicationfactorappliedtodrivingearthpressures A Gonactions TableA.3 STRGEO 1.00 1,35 1.35 1.35 1.35
F_DriveActive N/A 1.50 1.50 1.50 1.50F_DriveAtRest N/A 1.35 1.35 1.35 1.35
F_Wall Safetyfactorforwallcapacity STR Modelfactorforwallcapacity 1.00 1.00 1.00 1.00 1.00
AASHTOLRFD(2010)5thEdition CodeCase
TableA.4pg.130
Note: 1. AASHTOrecommendsthatslopestabilityanalysisisperformedonlywiththeServiceI combination. 2. Atrestandactiveearthpressurefactorsareusedinmultiplyingearthpressuresonlyinlimitequilibrium analyseswhentheuserhasselectedarelevantmethod.
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6.2 Automatic generation of active and passive lateral earth pressure factors in EC7 typeapproaches.Figure3outlinesthecalculationlogicfordeterminingtheactiveandpassivelateralearthpressurecoefficients. In conventional analyses, the resistance factor is applied by dividing the resistinglateralearthpressureswithasafetyfactor.
1:GetBasesoilstrengthparameters(Slope,wallfriction,etc)
2.Modifysoilpropertiesaccordingtothecode'M"case
3:DeterminebaseKa&KpaccordingSection5.1forConventionalAnalysis
Section5.2forParatieAnalysis
4.Multiply/DivideKaandKpbyAppropriateFactor4.1PARATIEANALYSIS
Kp.BaseF_RES
InDA11thesoftwareusesinternallyFS_DriveEarth=1andstandardizestheexternalloadsbyFS_DriveEarth.Then,attheendoftheanalysis,wallmoments,shearforces,andsupportreactionsaremultipliedbyFS_DriveEarthandtheultimatedesignvaluesareobtained:
WallmomentMULT=MCALCxFS_DriveEarthWallShearVULT=VCALCxFS_DriveEarthSupportReactionRULT=RCALCxFS_DriveEarth
4.2CONVENTIONALANALYSISKa.used=Ka.BaseKp.used=Kp.BaseDetermineInitialDrivingandResistingLateralEarthPressures
4.2.a: FinalDrivingLateralEarthPressures=InitialxFS_DriveEarth(FS_DriveEarth=1EC7,DM08)
4.2.b: FinalResistingLateralEarthPressures=Initial/F_RES
Kp.used=Ka.used= Ka.BasexFS_DriveEarth
Figure3:CalculationlogicfordeterminingKaandKpanddrivingandresistinglateralearthpressures.
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6.3 Determination of Water Pressures & Net Water Pressure Actions in the new software
(ConventionalLimitEquilibriumAnalysis)ThesoftwareprogramofferstwopossibilitiesfordeterminingwateractionsonawallwhenEC7isemployed.Inthecurrentapproach,theactualwaterpressuresorwaterlevelsarenotmodified.Option1(Default):NetwaterpressuremethodInthedefaultoption,theprogramdeterminesthenetwaterpressuresonthewall.Subsequently,the net water pressures aremultiplied by F_WaterDR and then the net water pressures areappliedonthebeamaction.Thenetwaterpressureresultsarethenstoredforreferencechecks.Hence,thismethodcanbeoutlinedwiththefollowingequation:
Wnet=(WdriveWresist)xF_WaterDROption 2: Water pressures multiplied on driving and resisting sides (This Option is not yetenabled.)Inthisoption,theprogramfirstdeterminesinitialnetwaterpressuresonthewall.Subsequently,thenetwaterpressuresaredeterminedbymultiplyingthedrivingwaterpressuresbyF_WaterDRandbymultiplyingtheresistingwaterpressures.Thenetwaterpressureresultsarethenstoredforreferencechecks.Hence,thismethodcanbeoutlinedwiththefollowingequation:
Wnet=WdrivexF_WaterDRWresistxF_WaterRES
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6.4 Surcharges
Thenewsoftwareenablestheusertouseanumberofdifferentsurchargetypes.SomeofthesesurchargesarecommonwithPARATIE,however,mostsurchargetypesarenotcurrentlyincludedintheParatieEngine.Table3liststheavailabletypesofsurcharges.
Table3:Availablesurchargetypes
SurchargeTypePermanent/Temporary
(P/T)ExistsinParatieEngine
ExistsinConventional
AnalysisConventionalAnalysis
CommentsSurfaceLineload P&T No Yes
Theoryofelasticity.CanincludebothHorizontalandVerticalcomponents.
Lineload P&T No Yes SameasaboveWallLineLoad P&T No Yes SameasaboveSurfaceStripSurcharge P&T Yes Yes SameasaboveWallstripSurcharge P&T Yes Yes Sameasabove
ArbitraryStripSurcharge P&T No Yes
Theoryofelasticity.VerticalDirectiononly.
Footing(3D) P No YesBuilding(3D) P No Yes3DPointLoad P&T No YesVehicle(3D) T No Yes
AreaLoad(3D) P&T No YesMoment/Rotation Yes No WhenEC7(orDM08)isutilized,thefollowingitemsareworthnoting:a) In the PARATIE module: In the default option the program does not use the Default
ParatieEngine fordeterminingsurchargeactions,butcalculatesallsurchargesaccordingtotheconventionalmethods.IftheParatieSimplifiedLoadOptionsareenabled(Figure4.1),thenallconventionalloadsareignored.OnlyloadsthatmatchtheParatieenginecriteriaareutilized.
b) UnfavorablePermanent loadsaremultipliedbyF_LPwhile favorablepermanent loadsaremultipliedby1.0.
c) UnfavorableTemporary loadsaremultipliedbyF_LVwhile favorable temporary loadsaremultipliedby0.
Thesoftwareoffersgreatversatilityforcalculatingsurchargeloadsonawall.Surchargesthataredirectlyonthewallarealwaysaddeddirectlytothewall.Inthedefaultsetting,externalloadsthatarenotdirectlylocatedonthewallarealwayscalculatedusingtheoryofelasticityequations.Mostformulasusedaretrulyapplicableforcertaincaseswheregroundisflatortheloadiswithinaninfiniteelasticmass.However,theformulasprovidereasonableapproximationstootherwise
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extremelycomplicatedelasticsolutions.WhenPoison'sratioisusedthesoftwarefindsandusestheapplicablePoissonratioofvateachelevation.
Figure4.1:SimplifiedParatieloadoptions Figure4.2:Elasticitysurchargeoptions
6.5 LineLoadSurcharges
Lineloadsaredefinedwithtwocomponents:a)averticalPy,andb)ahorizontalPx.Itisimportanttonotethatthemanyoftheequationslistedbeloware,onlybythemselves,applicableforaloadinaninfinitesoilmass.Forthisreason,thesoftwaremultipliestheobtainedsurchargebyafactormthataccountsforwallrigidity.Thesoftwareassumesadefaultvaluem=2thataccountsforfullsurchargereflectionfromarigidbehavior.However,avaluem=1.5mightbeareasonably lessconservativeassumptionthatcanaccountforlimitedwalldisplacement.For line loads thatare locatedon the surface (or theverticalcomponentstrip loads,sincestriploadsarefoundbyintegratingwithlineloadcalculations),equationsthatincludefullwallrigiditycan be included. This behavior can be selected from the Loads/Supports tab as Figure 4.2illustrates.Inthiscase,thecalculatedloadsarenotmultipliedbythemfactor.Forverticallineloadsonthesurface:WhentheUseEquationswithWallRigidityoptionisnotselected,thesoftwareusestheBoussinesqequationlistedinPoulosandDavis,1974,Equation2.7a
HorizontalSurcharge
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Foraverticalsurfacelineload,whentheUseEquationswithWallRigidityoptionisselected,thesoftwareusestheBoussinesqequationasmodifiedbyexperimentforridigwalls(Terzaghi,1954).
Forverticallineloadswithinthesoilmass:ThesoftwareusestheMelansequationlistedinPoulosandDavis,1974,Equation2.10bpg.27
andm=(1v)/vHorizontalSurcharge
Forthehorizontalcomponentofasurfacelineload:ThesoftwareusestheintegratedCerrutiproblemfromPoulosandDavisEquation2.9b
HorizontalSurcharge
Forthehorizontalcomponentofalineloadwithinthesoilmass:ThesoftwareusesMelansproblemEquation2.11bpg.27,fromPoulos&Davis
HorizontalSurcharge
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6.6 StripSurchargesStrip loads inthenewsoftwarecanbedefinedwith linearlyvaryingmagnitudes inbothverticaland horizontal directions.Hence, complicated surcharge patterns can be simulated. Surchargepressuresarecalculatedbydividingthestriploadintoincrementswhereanequivalentlineloadisconsidered.Thenthelineloadsolutionsareemployedandnumericallyintegratedtogivethetotalsurchargeat thedesiredelevation.The software subdivideseach strip load into50 incrementswhere it performs the integration of both horizontal and vertical loads.On surface loads, theverticalloadiscalculatedfromintegrationalongxandnotalongthesurfaceline.
6.7 Other3DsurchargeloadsThesoftwareoffersthepossibilitytoincludeother3dimensionalsurcharges.Inessence,alltheseloadsareextensions/integrationsofthe3Dpointverticalloadsolution.For3Dfootings,thesurchargeonthewallcanbecalculatedintwoways:a) Byintegratingthefootingbearingpressureoversmallersegmentsonthefootingfootprint.In
thiscasethefootingissubdividedintoanumberofsegmentsandthesurchargecalculationsareslightlymoretimeconsuming.
b) Byassumingthatthefootingloadactsasa3Dpointloadatthefootingcentercoordinates.Forloadsthatarelocatedonthesurface:ThesoftwareprogramusestheBoussinesqequation.Resultsfromthefollowingequationsaremultipliedbytheelasticloadadjustmentfactormaspreviouslydescribed.
Theradialstressincrementisthencalculatedas:
Thehoopstressisdefinedas:
Withtheanglesdefinedas:
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Then,thehorizontalcomponentsurchargeis:
Forverticalpointloadswithinthesoilmass:ThesoftwareusestheMindlinsolutionasoutlinedbyPoulosandDavis,1974equations2.4.a,and2.4.g
6.8 LoadbehaviorandfactorswhenadesignapproachisusedWhenananalysisusesdesignapproachsuchasEC7,eachexternal loadmustbecategorizedasfavorableorunfavorable. In thedefaultmodewhenno loadcombination isused, the softwareprogramautomaticallycategorizes loadsasfavorableorunfavorablebasedontheir locationanddirection relative to thewall and the excavation.Hence, loads thatpush thewall towards theexcavationaretreatedasunfavorable,whileloadsthatpushthewalltowardstheretainedsoilaretreatedasfavorable. Inalldesignapproachmethods,favorablevariable loadsare ignored intheanalysiswhilefavorablepermanentloadsaremultipliedbyasafetyfactorequalto1.Unfavorableloadsgettypicallymultipliedwithfactorsrangingfrom1to1.5dependingontheexamineddesignapproachandtheloadnature(permanentvs.variable).Whenaloadcombinationisused,theuserhastheoptiontomanuallyselectthebehaviorofeachload.
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7. AnalysisExamplewithEC7
Asimplifiedanalysisexample ispresented inthissectionforthepurposeof illustratinguseofEC7methods.Theexample involves theanalysisofsteelsheetpilewallsupportedbyasingle leveloftiebackswiththefollowingassumptions: Retainedgroundsurfacelevel(uphillside)El.+200 Maximumexcavationlevel(downhillside)El.+191 WaterlevelonretainedsideEl.+195 WaterlevelonexcavatedsideEl.+191 Waterdensity WATER=10kN/m3 Soilproperties: TOTAL=20kN/m3,DRY=19kN/m3,c=3kPa,=32deg,
Exponentialsoilmodel:Eload=15000kPa,Ereload=45000kPa,ah=1,av=0KpBase=3.225(Rankine),KaBase=0.307(Rankine)UltimateTiebackbondcapacityqult=150kPaUserspecifiedsafetyonbondvaluesFSGeo=1.5
TiebackData: ElevationEl.+197,Horizontalspacing=2mAngle=30degfromhorizontalPrestress=400kN(i.e.200kN/m)StructuralProperties:4strands/1.375cmdiametereach,
Thus ASTEEL = 5.94cm2 Steelyieldstrength Fy = 1862MPa
FixedbodylengthLFIX = 9m FixedbodyDiameterDFIX = 0.15m
WallData: SteelSheetpileAZ36,Fy=355MPa
Walltop.El.+200Walllength18mMomentofInertiaIxx=82795.6cm4/mSectionModulusSxx=3600cm3/m
Surcharge: VariabletriangularsurchargeonwallPressure5kPaatEl.+200(topofwall)Pressure0kPaatEl.+195
The construction sequence is illustrated in Figures 4.1 through 4.4. For the classical analysis thefollowingassumptionswillbemade:RankinepassivepressuresonresistingsideCantileverexcavation: Activepressures(Freeearthanalysis)
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Finalstage: Apparentearthpressuresfromactivex1.3,redistributedtopfrom0kPaatwalltoptofullpressureat25%ofHexc.,Activepressuresbeneathsubgrade.
Freeearthanalysisforsingleleveloftiebackanalysis.Waterpressures: Simplifiedflow
Figure5.1:InitialStage(Stage0,DistortedScales)
Figure5.2:Stage1,cantileverexcavationtoEl.+196.5(tiebackisinactive)
Figure5.3:Stage2,activateandprestressgroundanchoratEl.+197
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Figure5.4:Stage3,excavatetofinalsubgradeatEl.+191
ThefirststepwillbetoevaluatetheactiveandpassiveearthpressuresfortheservicecaseasillustratedinFigure5.
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Top triangular pressure height= 0.25 Hexc = 2.25 m Hexc= 9 mApparent Earth Pressure Factor: 1.3 (times active)
Eurocode Safety factors 1 1 1SOIL UNIT
WEIGHTDRY UNIT WEIGHT
WATER UNIT WEIGHT
WATER TABLE ELEV. Ka Kp c'
(kPa) (kPa) (kPa) (m) (deg) (kPa) (m) m m/m32 0.307 3.255 3 195 22 0.1818
20 19 10 195 32.00 0.307 3.255 3.000
ELEV.
TOTAL VERTICAL STRESS
WATER PRESSURE
EFFECTIVE VERTICAL STRESS
Acive LATERAL
SOIL STRESS
Apparent Earth
Pressures
TOTAL LATERAL STRESS
TOTAL VERTICAL STRESS
WATER PRESSURE
EFFECTIVE VERTICAL STRESS
LATERAL SOIL
STRESS
TOTAL LATERAL STRESS NET
(m) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)
200 0 0 0 0 0.00 0.00 0.00
199.43 10.82 0.00 10.82 0.00 -7.93 -7.93 -7.93
197.75 42.75 0.00 42.75 -9.81 -31.33 -31.33 -31.33
195 95 0 95 -25.86 -31.33 -31.33 -31.33
191 175 -32.7 142.3 -40.39 -31.33 -64.06 -64.06
191 175 -32.7 142.3 -40.39 -40.39 -73.12 0 0 0 10.82 10.82429 -62.3
182 355 -106.4 248.64 -73.07 -73.07 -179.43 180 106.4 73.64 250.48 356.84 177.4
Total active earth force above subgrade:Fx
From El. 200.00 to El. 199.43 0.0 kN/mFrom El. 199.43 to El. 197.75 8.2 kN/mFrom El. 197.75 to El. 195.00 49.1 kN/mFrom El. 195.00 to El. 191.00 132.5 kN/m
Sum= 189.8 kN/mFactored Forc 246.7
Max. Apparent Earth Pressure= 31.3 kPa
LEFT EXCAVATION SIDE PRESSURES RIGHT SIDE PRESSURES (PASSIVE)
Modified for calculation/Strength Reductions
Hydraulic travel length
Hydraulic loss gradient i
WATER TABLE ELEV.
180
182
184
186
188
190
192
194
196
198
200
202
-200 -100 0 100 200 300 400
ELEV
ATIO
N (m
)
LATERAL STRESS (kPa)
LEFT LAT SOILLEFT WATERLEFT TOTALRIGHT LAT SOILRIGHT WATERRIGHT TOTALNET
Figure6:Calculationoflateralearthandwaterpressuresforservicecase
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AsFigure6shows,thecalculatedmaximumapparentearthpressureis31.3kPawhichisveryclosetothe31.4kPaapparentearthpressureenvelopecalculatedfromthesoftware(Figure7.1).Allotherpressurecalculationsarealsoverywellconfirmed(withinroundingerroraccuracy).
Figure7.1:Apparentlateralearthpressuresfromconventionalanalysis
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Figure7.2:Simplifiedflowgroundwaterpressuresfromconventionalanalysis
Figure7.3:Simplifiedflownetgroundwaterpressuresfromconventionalanalysis
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Figure7.4:Wallsurchargepressures(unfactored)
Figure7.5:Walldisplacementsfromconventionalanalysis(laststage)
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Figure7.6:Shearandmomentdiagramswithsupportreactionandstresschecksdrawn(redlineson
momentdiagramshowwallcapacity).
Figure7.7:Shearandmomentdiagramenvelopes(forcurrentdesignsectiononly)
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Next,theEC7combinationDA3approachwillbeexaminedindetail.However,allEC7designapproacheswillbeanalyzedsimultaneously.Themodelislinkedtothebasedesignsection.
Figure8.1:GeneralmodelforEC7DA3Approach
Thecorrespondingsafetyfactorsare:
FS(tan())= 1.25FS(c)= 1.25FS(Su)= 1.5(thisisalsousedfortheultimatebondresistance)FS(Actionstemp)= 1.3FS(Anchors)= 1.1FS(WaterDrive)= 1.0FS(Drive_Earth)= 1.0
Nexttheactiveandpassiveearthpressures,aswellasthenetwaterpressuresfortheDA3approachwillbecalculatedasillustratedinFigure8.2.AsFigures8.3through8.4demonstrate,thesoftwarecalculatesessentiallythesamelateralearthpressuresasthespreadsheetshowninFigure8.2.
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Top triangular pressure height= 0.25 Hexc = 2.25 m Hexc= 9 m
Apparent Earth Pressure Factor: 1.3 (times active)
Eurocode Safety factors 1.25 1 1.25SOIL UNIT
WEIGHTDRY UNIT WEIGHT
WATER UNIT WEIGHT
WATER TABLE ELEV. Ka Kp c'
(kPa) (kPa) (kPa) (m) (deg) (kPa) (m) m m/m32 0.307 3.255 3 195 22 0.1818 1 1 1
20 19 10 195 26.56 0.382 2.618 2.400
ELEV.
TOTAL VERTICAL STRESS
UNFACTORED WATER
PRESSURE
EFFECTIVE VERTICAL STRESS
Acive LATERAL
SOIL STRESS
Apparent Earth
Pressures
TOTAL LATERAL STRESS (factored
earth)
TOTAL VERTICAL STRESS
WATER PRESSURE
EFFECTIVE VERTICAL STRESS
LATERAL SOIL
STRESS
TOTAL LATERAL STRESS
Net water pressure (factored) NET
(m) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)
200 0 0 0 0 0.00 0.00 0 0.00
199.59 7.77 0.00 7.77 0.00 -7.37 -7.37 0 -7.37
197.75 42.75 0.00 42.75 -13.37 -40.60 -40.60 0 -40.60
195 95 0 95 -33.33 -40.60 -40.60 0 -40.60
191 175 -32.7 142.3 -51.39 -40.60 -73.33 -32.73 -73.3
191 175 -32.7 142.3 -51.39 -51.39 -84.11 0 0 0 7.77 7.765837 -32.73 -76.3
182 355 -106.4 248.64 -92.02 -92.02 -198.39 180 106.4 73.64 200.51 306.88 0.00 108.5
Total active earth force above subgrade:Fx
From El. 200.00 to El. 199.59 0.0 kN/mFrom El. 199.59 to El. 197.75 12.3 kN/mFrom El. 197.75 to El. 195.00 64.2 kN/mFrom El. 195.00 to El. 191.00 169.4 kN/m
Sum= 245.9 kN/mFactored Forc 319.7
Max. Apparent Earth Pressure= 40.60 kPa
Modified for calculation/Strength Reductions
LEFT EXCAVATION SIDE PRESSURES RIGHT SIDE PRESSURES (PASSIVE)
WATER TABLE ELEV.
Hydraulic travel length
Hydraulic loss gradient i
Safety factor on net water pressures
Safety factor on
earth pressures
Safety factor on Passive
Resistance
180
182
184
186
188
190
192
194
196
198
200
202
-300 -200 -100 0 100 200 300 400
ELEV
ATIO
N (m
)
LATERAL STRESS (kPa)
LEFT LAT SOILLEFT WATERLEFT TOTALRIGHT LAT SOILRIGHT WATERRIGHT TOTALNET WaterNet
Figure8.2:CalculationoflateralearthandwaterpressuresforDA3Approach
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Figure8.2:ApparentlateralearthpressuresforDA3Approach(40.7kPapressureverifiedspreadsheet
calculations)
Figure8.3:FactoredlateralsurchargepressuresforDA3Approach(7.5kPapressure=5kPax1.5)
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Figure8.4:NetFactoredwaterpressuresforDA3Approach
32.73kPapressure=32.73kPax1.0 ,32.7kPafromFigure6.3Spreadsheetcalculation32.7kPa
Figure8.5:WallshearandmomentforDA3Approach
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NextweexaminethecaseofDA11whereearthandwaterpressuresaremultipliedbysafetyfactorswhilethesoilstrengthparametersaremaintained.
Top triangular pressure height= 0.25 Hexc = 2.25 m Hexc= 9 mApparent Earth Pressure Factor: 1.3 (times active)
Eurocode Safety factors 1 1 1SOIL UNIT
WEIGHTDRY UNIT WEIGHT
WATER UNIT WEIGHT
WATER TABLE ELEV. Ka Kp c'
(kPa) (kPa) (kPa) (m) (deg) (kPa) (m) m m/m32 0.307 3.255 3 195 22 0.1818 1.35 1.35 1
20 19 10 195 32.00 0.307 3.255 3.000
ELEV.
TOTAL VERTICAL STRESS
UNFACTORED WATER
PRESSURE
EFFECTIVE VERTICAL STRESS
Acive LATERAL
SOIL STRESS
Apparent Earth
Pressures
TOTAL LATERAL STRESS (factored
earth)
TOTAL VERTICAL STRESS
WATER PRESSURE
EFFECTIVE VERTICAL STRESS
LATERAL SOIL
STRESS
TOTAL LATERAL STRESS
Net water pressure (factored) NET
(m) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)
200 0 0 0 0 0.00 0.00 0 0.00
199.43 10.82 0.00 10.82 0.00 -7.93 -10.71 0 -10.71
197.75 42.75 0.00 42.75 -9.81 -31.33 -42.30 0 -42.30
195 95 0 95 -25.86 -31.33 -42.30 0 -42.30
191 175 -32.7 142.3 -40.39 -31.33 -75.02 -44.18 -86.5
191 175 -32.7 142.3 -40.39 -40.39 -87.25 0 0 0 10.82 10.82429 -44.18 -87.9
182 355 -106.4 248.64 -73.07 -73.07 -205.01 180 106.4 73.64 250.48 356.84 0.00 151.8
Total active earth force above subgrade:Fx
From El. 200.00 to El. 199.43 0.0 kN/mFrom El. 199.43 to El. 197.75 8.2 kN/mFrom El. 197.75 to El. 195.00 49.1 kN/mFrom El. 195.00 to El. 191.00 132.5 kN/m
Sum= 189.8 kN/mFactored Forc 246.7
Max. Apparent Earth Pressure= 31.33 kPa
Safety factor on
earth pressures
Safety factor on Passive
Resistance
WATER TABLE ELEV.
Hydraulic travel length
Hydraulic loss gradient i
Modified for calculation/Strength Reductions
LEFT EXCAVATION SIDE PRESSURES RIGHT SIDE PRESSURES (PASSIVE)
Safety factor on net water pressures
180
182
184
186
188
190
192
194
196
198
200
202
-300 -200 -100 0 100 200 300 400
ELEV
ATIO
N (m
)
LATERAL STRESS (kPa)
LEFT LAT SOILLEFT WATERLEFT TOTALRIGHT LAT SOILRIGHT WATERRIGHT TOTALNET WaterNet
Figure8.6:CalculationoflateralearthandwaterpressuresforDA11Approach
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Figure8.7:ApparentlateralearthpressuresforDA11Approach(42.4kPapressureverified
spreadsheetcalculations)
Figure8.8:NetFactoredwaterpressuresforDA11Approach
44.18kPapressure=32.73kPax1.35 ,32.7kPafromFigure6.3Spreadsheetcalculation44.18kPa
Inthefollowingpages,thenonlinearsolutiontothesameproblemisbrieflypresented.
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Figure9.1:WallbendingmomentsandshearforcesforParatieSolutionforservicecase.
Figure9.2:WallbendingmomentsandshearforcesforParatieSolutionforDA3case.
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Figure9.3:NetwaterpressuresforParatieSolutionforDA3case(notyetfactored)
Figure9.4:WallbendingmomentsandshearforcesforParatieSolutionforDA11case.
IMPORTANTForDA11:InParatiewhenWaterUnfavorableorEarthUnfavorablearegreaterthan1,wallbending,wallshear,and support reaction results are obtained from an equivalent service analysis approach. In thisapproach, all surcharge magnitudes are standardized by Earth Unfavorable (1.35 in DA11), thus,unfavorablevariableloadswillbemultipliedby1.5/1.35=1.111whilepermanentloadsby1.35/1.35=1.Whentheanalysisiscompletedthewallmoment,wallshear,andsupportreactionresultsaremultipliedx1.35.Thedisplacementshoweverarenotmultiplied.
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ThetiebackSTR&GEOcapacitycalculationswillbeperformedforCaseDA11:
R = 1.1(temporarytieback)SU = 1(Shearstrengthalsousedforbondvalues)FSGeo= 1.0Userspecifiedsafetyfactorinthisexample,
recommendedvalue1.35inotherconditions.
FixedbodylengthLFIX = 9m FixedbodyDiameterDFIX = 0.15m
UltimateSkinfrictionqULT = 150kPaThentheultimategeotechnicalcapacityis:
RULT.GEO=LFIXxxDFIXxqULT/R)RULT.GEO=578.33kNpergroundanchor
Thedesigngeotechnicalcapacity(forstresscheckratios)iscalculatedas:RDES.GEO=LFIXxxDFIXxqULT/RxSUxFSGeo)=578.33kN
TheUltimateStructuralcapacitycanbecalculatedas:RULT.STR=AFIX.STEELxFy/M)
Notethat1/M=intheEC=0.87RULT.STR=0.87AFIX.STEELxFy
RULT.STR=0.87x5.94cm2x1862MPa=961.8kNTheseresultsareverifiedbythesoftwareprogram:
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Figure9.6:Individualsupportreactions/capacity
ThetiebackGEOcapacitycalculationsforCaseDA12:
R = 1.1(temporarytieback)SU = 1.4(Shearstrengthalsousedforbondvalues)FSGeo = 1.0InM2casesthisfactorisautomaticallysetto1.0in
ordertoproduceconsistentcapacitieswithavailabledesignchartsforbondresistanceofgroundanchors(whereanFS=2.0).
FixedbodylengthLFIX = 9m FixedbodyDiameterDFIX = 0.15m
UltimateSkinfrictionqULT = 150kPaThentheultimategeotechnicalcapacityis:
RULT.GEO=LFIXxxDFIXxqULT/RxSUxFSGeo)RULT.GEO=578.33kNpergroundanchor
Thedesigngeotechnicalcapacity(forstresscheckratios)iscalculatedas:RDES.GEO=LFIXxxDFIXxqULT/RxSUxFSGeo)=413.1kN
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Figure9.7:Individualsupportreactions/capacityforDA12
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8. Groundanchorandhelicalanchorcapacitycalculations8.1 GroundAnchorCapacityCalculations
A ground anchor has two forms of capacity, a geotechnical and a structural resistance. ThestructuralresistanceofthetendonsisdefinedbyECsteelstandardswhilethebondedzonehasto be examined for its pullout capacity (geotechnical check). The new software includes anumberofgroundanchor(tieback)sections.Hence,agroundanchorsectioncanbereusedoverand over inmany different support levels and inmany different design sections (the sameapproachisalsoutilizedforsteelstruts,rakers(inclinedstruts),andconcreteslabs).Thetiebackcapacities(ultimateandpermissible)canbecalculatedusingthefollowingequations:a) Ultimategeotechnicalcapacityusedforthegeotechnicalyieldingis:
RULT.GEO=LFIXxxDFIXxqULT/R)b) Thedesigngeotechnicalcapacity(forstresscheckratios)iscalculatedas:
RDES.GEO=LFIXxxDFIXxqULT/RxSUxFSGeo)Where:
qULT = UltimateSkinfriction(optionsavailable)LFIX = Fixedbodylength
DFIX = Fixedbodydiameter(0.09mto0.15mtypically)FSGeo = 1.0to2.0userspecifiedsafetyfactor.
FSGeo=1.0inM2designapproachmethods.R = 1to1.2ResistancefactorgeotechnicalcapacitySU = 1to1.4(Shearstrength,usedforbondvalues)
Note that Rand SUarebydefault1,but takeEurocodeorDM08 specified valueswhenadesignapproachisused.c) TheultimateanddesignStructuralcapacitycanbecalculatedas:
PULT.STR=ULT.CODEx(AreaofTendons)xFyULT.CODE=Materialstrengthreductionfactortypically0.9
PDES.STR=DESx(AreaofTendons)xFy
DES=Materialstrengthreductionfactor0.6to0.9Theultimatecapacity isusedtodeterminethestructuralyieldingoftheelementwhilethepermissible isused for thestresschecks.ULT.CODE isalwayspickedup from thestructuralcode that isused.DEScanbespecifiedby theuserorcanbesetautomaticallywhen thesome code settings are specified.When Eurocodes are used ALL should be the same asULT.CODE.
Notethat=1/M
InthedefaultsettingduringaParatieanalysis,thenewsoftwaremodelsatiebackautomaticallyasayieldingelement (Wirewithyieldingproperties)with itsyielding forcedeterminedas the
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minimum STRorGEO capacity.Agroundanchor canalsobemodeledasanonyieldingwireelement by selecting the appropriate option in the Advanced Tab of the Tieback dialog.However,itisfeltthatduetolegalreasonsitisbettertoincludeatiebackasyieldingelementbydefault.Figure10.1showsthemaintiebacksectiondialog.Themainparametersofinterestarethesteelmaterial,thecrosssectionalareaofthesteeltendons,andthefixedbodydiameter(Dfix).
Figure10.1:Maintiebacksectiondialog(ElasticWirecommandinRed)
The geotechnical capacity represents the capacity of the soil to resist the tensile forcestransferredby the steel strands to the groutedbody.Thenew software subdivides the fixedbodyintoanumberofelementsweresoilresistanceiscomputed.Aspreviouslymentioned,thegeotechnicaltiebackcapacityisevaluatedforeverystage.WithinthecurrentParatieengine,itiscurrentlypossibletochangetheyield limitofanELPLspringfromstagetostage. Initially, inthe Paratiemode the software uses the capacity at the stage of installation. The capacity isadjustedateachstageandthefinalsupportcheckisperformedfortheactualcapacityforeachstage.Anumberofoptionsexistfordefiningthegeotechnicalcapacityofatieback:
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a) Soil resistance is computed from frictional and cohesive components. For the frictionalcomponent,DeepXcavuses theaverageof theverticaland lateralatreststress times thetangentofthefrictionangle.Forthecohesivecomponent,adhesionfactorscanbeapplied.Furthermore,individualdensificationfactorscanbeappliedseparatelytothefrictionalandcohesivecomponentstosimulatetheeffectofpressuregrouting.Endbearingatthestartofthe grouted body is ignored. These calculations should be considered as a first orderestimate.Hence,inthiscasetheultimateskinfrictioncanbedefinedas:
tULT=F1x0.5x(V+HKo)xtan()+F2xx(corSU)
In an undrained analysis the software will use SU and =0. For a drained analysis theprogramwilluseandc.Where:
F1= Frictionaldensificationfactor(default1)F2= Cohesionaldensificationfactor(default1)= Adhesion factor (default =1), but program also offers a dynamic trilinear
approachfordefiningthisparameterbasedoncorSu.Inthisapproach: =Value1=0.8ifcorSu=Climit2=LinearinterpolationforcorSubetweenClim1andClim2.
b) Userdefinedgeotechnicalcapacity(andstructural)definedfromtheadvancedtiebacktab.
Figure10.2:Advancedtiebackdialogtab
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c) Ultimatespecificbondresistancefortiebacksection.tULT=qULTinGeotechnicaltaboftiebacksection
Figure10.3:Geotechnicaltiebackdialogtab(WirecommandinRed)
d) Ultimatebondresistancedeterminedfromintegratingsoilultimateskinfrictionresistances
overthefixedlength.tULT=qULTfromSoiltype(BondTab)
In this case, the skin friction canbedetermined from theBustamantedesign charts (Fig.10.5.1,10.5.2)whenpressuremetertestdataareavailable.
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Figure10.4:BondtabinSoiltypedialog(>buttonoffersabilitytoestimatefrom
Pressuremetertests).
e) WhenaEurocodedesignapproachisappliedultimatepulloutresistanceiscalculatedfrombondvaluesbyapplyingthesamesafetyfactor(incombinationwithallothersafetyfactors)asfortheundrainedshearstrengthSu.However, incertaincases liketheM2theprogramdoesnotapply theUserSpecifiedFS_geo inorder toproduceconsistentcapacity results.Thus,whenEurocode7orNTCsettingsareapplied,theuserspecifiedFS_GeoisonlyusedincaseswhereM1factorsareapplied.When the pullout resistance is calculated from soil cohesion and friction, then the skinfriction iscalculateddirectly from theadjusted frictionangleandshearstrength/cohesionvaluesaccordingtheMsafetyfactors.
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Figure10.5.1:EstimationofbondresistancefortiebacksfromTA95accordingtoBustamante.
Figure10.5.2:EstimationofbondresistancefortiebacksfromPressuremetertestsFHWAand
Frenchrecommendations.
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8.2 HelicalanchorcapacitycalculationsAhelicalanchor/pileconsistsofoneormorehelixshapedbearingplatesattachedtoacentralshaft,whichisinstalledbyrotatingor"torqueing"intotheground.Eachhelixisattachednearthetip,isgenerallycircularinplan,andformedintoahelixwithadefinedpitch.Helicalanchors/pilesderivetheirloadcarryingcapacitythroughbothendbearingonthehelixplatesandskinfrictionontheshaft(Figure10.6.1).
Figure10.6.1:Typicalhelicalanchordetailandgeotechnicalcapacitybehavior
AccordingtoIBC2009,theallowableaxialdesignload,Pa,ofhelicalpilesshallbedeterminedasfollows:
Pa=0.5Pu (IBC2009Equation184)WherePuistheleastvalueof:
1.Sumoftheareasofthehelicalbearingplatestimestheultimatebearingcapacityofthesoilorrockcomprisingthebearingstratum.2.Ultimatecapacitydeterminedfromwelldocumentedcorrelationswithinstallationtorque.3.Ultimatecapacitydeterminedfromloadtests.4.Ultimateaxialcapacityofpileshaft.5.Ultimatecapacityofpileshaftcouplings.6.Sumoftheultimateaxialcapacityofhelicalbearingplatesaffixedtopile.
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AnexplanationandsummaryofeachofthesixdesigncriterionsrequiredpertheIBCforhelicalpiledesignhavebeenlistedbelowtobetterexplainthedesignprocessandintentofthecode.Item1isin reference to the IndividualBearingMethod. Thismethod requiresprior knowledgeof the soilpropertiesatthesiteviaasoilsreportorboringlogs.Pleasenotethatmostsoilreportsonlyreporttheallowablebearing capacityofa soilor stratum.Thisallowable capacitynormallyhasa safetyfactoroftwoorthreeapplied.Item1 is inreference to the IndividualBearingMethod.Thismethodrequirespriorknowledgeofthesoilpropertiesatthesiteviaasoilsreportorboringlogs.Pleasenotethatmostsoilreportsonlyreport theallowablebearingcapacityofa soilor stratum.Thisallowablecapacitynormallyhasasafetyfactoroftwoorthreeapplied.ApplyinganotherfactorofsafetyoftwopertheIBCwouldbeextremelyconservative.Typicalhelicalplatesizesare8,10,12,14and16indiameter.Themaximumnumberofhelicalplates placed on a single pile is normally set at six (6). The central area of the shaft is typicallyomittedfromtheeffectiveareaofthehelicalplatewhenusingtheIndividualBearingMethod.Thetotalcapacityoftheanchorcanbecalculatedas:
Qult=Qshaft+Qhwhere:Qult=TotalMultihelixAnchor/PileUltimateCapacityQh=IndividualHelixUltimateCapacity
Qh=Ah(Ncc+DNq)Qh.strQh=Ah(9c+DNq)Qh.str
where:Ah= ProjectedeffectiveareaofhelixNc= 9forratiooftophelixdepthtohelixdia.>5(programassumesvalue=9)D= DepthofhelixplatebelowgroundlineNq= BearingcapacityfactorforsandQh.str= UppermechanicallimitdeterminedbyhelixstrengthQshaft= Geotechnical shaft resistance can be also included. Within the program, the shaft
resistance is calculatedonlywithin from the startingpointof the fixed lengthof theanchor to the first encountered helical plate. Inmost cases, the shaft resistance isconservativelyignored.
ThesoftwareprogramreplacestheaboveDtermwiththeverticaleffectivestressateachhelix.Accordingtoastandardpractice(ABChancecorporationpresentation),NqcanbecalculatedasadaptedfromG.G.MeyerhofFactorsforDrivenPilesinhispaperBearingCapacityandSettlementofPileFoundations,1976Equation:
Nq=0.5(12*)/54Withafewexceptions,theshaftresistancecanbecalculatedinasimilarmannerasthegeotechnicalcapacity of ground anchors. When the capacity is calculated with side frictional methods, adistinctioncanbemadebetweenagroutedanongroutedshaft(i.e.agroutedshafthasfrictionofcementgroutwithsoilwhileanongroutedshaftbetweensteelandsoil).
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Item 2 is in reference to the Torque CorrelationMethod. The Torque CorrelationMethod is anempiricalmethod thatdistinguishes the relationshipbetweenhelicalpilecapacityand installationtorqueandhasbeenwidelyusedsincethe1960s.Theprocessofahelicalplateshearingthroughthesoilorweatheredbedrock inacircularmotion isequivalenttoaplatepenetrometertest.ThemethodgainednotorietybasedonthestudyperformedbyHoytandClemence(1989).Theirstudyanalyzed91helicalpile loadtestsat24differentsiteswithinvarioussoiltypesrangingfromsand,siltan