theory manual eng 2011

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


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


SectionA.3.3.5Table STRGEO 1.00 1.40 1

F_WaterDRSafetyfactoronDrivingWaterpressures(appliedin A G SectionA.3.1 STRGEO 1.30 1.00 1


A G TableA.3.pg130 STRGEO 1.00 1.00

F_HYDgDSTHydraulicCheckdestabilizationfactor A G;dst SectionA.5 HYD 1.35


TableA.17.pg136

HYD 0.90


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



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


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


A 0.00 1.00 1.00


R a;t SectionA.3.3.4

STRGEO 1.10 1.10 1.10


R a;p TableA.12.pg134 STRGEO 1.10 1.10 1.10


SectionA.3.3.5TableA.13pg.135

STRGEO 1.40 1.00 1.00


A G SectionA.3.1 STRGEO 1.35 1.35 1.00


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


TableA.17.pg136 HYD 0.90 0.90 0.90


UPL G;dst SectionA.4 UPL 1.10 1.10 1.10


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


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


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


R a;t SectionA.3.3.4 STRGEO 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10


R a;p TableA.12.pg134 STRGEO 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10


SectionA.3.3.5TableA.13pg.135

STRGEO 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00


A G SectionA.3.1 STRGEO 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00


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


TableA.17.pg136 HYD 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90


UPL G;dst SectionA.4 UPL 1.10 1.10 1.10 1.10 1.10 1.10 1.10 1.10


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


TypeEurocodeParameter

EurocodeReference

EurocodeChecks

XP240 XP220Fundamental Accidental

Note:Frenchcodestandardsareparticularlyimportantforsoilnailingwalls.


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Table2.5:PartialsafetyfactorsforstrengthdesignapproachwithGermanDIN2005



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


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


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


A G SectionA.3.1 STRGEO 1.00 1.35 1.00 1.20 1.00 1.00 1.00


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


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


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


R a;p TableA.12.pg134 STRGEO 1.00 1.11 1.11 1.11 1.11


SectionA.3.3.5TableA.13pg.

135STRGEO 1.00 1.33 1.33 1.33 1.00


A G SectionA.3.1 STRGEO 1.00 1.00 1.00 1.00 1.00


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


TableA.17.pg136

HYD 1.00 1.00 1.00 1.00 1.00


UPL G;dst SectionA.4 UPL 1.00 1.00 1.00 1.00 1.00


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.


Page|35

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


Page|37

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


WATER PRESSURE


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


WATER UNIT WEIGHT


(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.


UNFACTORED WATER

PRESSURE


Acive LATERAL

SOIL STRESS

Apparent Earth

Pressures

TOTAL LATERAL STRESS (factored

earth)


WATER PRESSURE


LATERAL SOIL

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







WATER TABLE ELEV.



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

)


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


WATER UNIT WEIGHT


(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.


UNFACTORED WATER

PRESSURE


Acive LATERAL

SOIL STRESS

Apparent Earth

Pressures

TOTAL LATERAL STRESS (factored

earth)


WATER PRESSURE


LATERAL SOIL

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





Safety factor on

earth pressures

Safety factor on Passive

Resistance

WATER TABLE ELEV.





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

)


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.


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).


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:


Page|63

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


Page|64

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.


Page|66

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

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