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K e y s t o n e R e t ai n i n g W al l U n i t s
G e o s y n t h e t i c S oi l R ei nf o r c e m e n t
R e t ai n i n g W al l D es i g n T h e o r y
T h e D esi g n P r o c es s
K e y W al l O p e r a ti n g I n s t r u c ti o n s
A p p e n di c es
2011 KeystoneRetainingWallSystems, Inc
OriginalMarch2001
RevisedAugust2001
ReprintedJuly 2006
Revised&ReprintedFebruary, 2011
& K E Y W ALL O PERA T I N G G U ID E
Keystone
D ES I G N M A N U AL
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i
I N TR O D U C T I O N
TableofContents
PART ONE KeystoneRetainingWallUnits
KeystoneRetainingWallUnits.................................................................... ..................................................................... . 1.1
KeystoneMaterials................................................................... ...................................................................... ....................... 1.2
StandardUnit................................................................ ..................................................................... ................................... 1.2
CompacUnit.................................................................. ..................................................................... ................................... 1.3
KeystoneCenturyW
allU
nits............................................................ ..................................................................... ............ 1.3133EliteUnit.................................................................. ..................................................................... ................................... 1.4
UnitShearResistance.............................................................. ...................................................................... ....................... 1.4
BaseShearResistance.............................................................. ...................................................................... ....................... 1.4
Inter-UnitShearResistance................................................................ ..................................................................... ............ 1.5
ShearData&Analysis............................................................. ...................................................................... ....................... 1.5
TypicalShearResistanceBetweenUnits................................................................ ........................................................... 1.6
PART TWO GeosyntheticSoilReinforcement
GeosyntheticSoilReinforcement.................................................................. ..................................................................... . 2.1
DesignStrength............................................................. ..................................................................... ................................... 2.2
ReductionFactors.................................................................... ..................................................................... ........................ 2.3
ConnectionStrength .......................................................................................................................................................2.4-2.5
GeosyntheticSoilInteractionCoefficient ......................................................................................................................2.5-2.6
GeogridManufacturersData............................................................ ..................................................................... ............ 2.6
PART THREE RetainingWallDesignTheory
RetainingWallDesignTheory .......................................................... ..................................................................... ............ 3.1
ImportantTechnicalDefinitions.................................................................. ...................................................................... 3.2
LateralEarthPressureTheories................................................................... ..................................................................... . 3.3
CoulombEarthPressureTheory .................................................................. ..................................................................... . 3.4
CoulombEarthPressureEquation ..............................................................................................................................3.4-3.5
CoulombFailurePlaneLocation.................................................................. ..................................................................... . 3.6
RankineEarthPressureTheory ................................................................... ..................................................................... . 3.6
RankineEarthPressureEquations ..............................................................................................................................3.6-3.7
RankineFailurePlaneLocation................................................................... ..................................................................... . 3.7
TrialWedgeAnalysis.............................................................. ..................................................................... ........................ 3.8
BearingCapacity ........................................................... ..................................................................... ................................... 3.9AppliedBearingPressure.................................................................. ...................................................................... ............ 3.9
CalculatedBearingCapacity .............................................................. ..................................................................... .......... 3.10
BearingCapacity Factors ...........................................................................................................................................3.10-3.11
Settlement........................................................... ...................................................................... ............................................ 3.11
GlobalStability .............................................................. ..................................................................... ................................. 3.12
SeismicAnalysis............................................................ ..................................................................... ................................. 3.13
In troduc t ion......................................................................................................................................... iv
D esign Manual&KeyWall Operat ing Guide ..................................................................................... v
G e o t echn ica l R esp on s i b i l i ty............................................................................................................. vi
References.......................................................................................................................................... vii
TA B L E O F C O N T E N T S
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D ES I G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
ii
TA B L E O F C O N T E N T S
PART FO UR TheDesignProcess
Introduction ..........................................................................................................................................................4.1
DesignMethodology ...............................................................................................................................................................4.2
UnitSelection...........................................................................................................................................................................4.2
WallBatter ...............................................................................................................................................................................4.3
HingeHeight...........................................................................................................................................................................4.3
WallGeometry ........................................................................................................................................................................4.4
WallEmbedment ....................................................................................................................................................................4.4
SlopingToe ..............................................................................................................................................................................4.5
SoilProperties................................................................... ..................................................................... ........................... 4.5-4.6
Surcharge..................................................................................................................................................................................4.6
ReinforcementType&Properties ........................................................................................................................................4.7
SoilReinforcementLength....................................................................................................................................................4.7
ExternalStability Analysis.....................................................................................................................................................4.8
BatteredWallDesignOptions ..............................................................................................................................................4.9
AASHTOLRFD............................................................. ...................................................................... ........................ 4.9-4.10
SlidingAnalysis .....................................................................................................................................................................4.11
Coulomb-NCMASliding ..................................................................................................................................................4.12
Rankine-AASHTOSliding ..............................................................................................................................................4.12
OverturningAnalysis ...........................................................................................................................................................4.13
Coulomb-NCMAOverturning ........................................................................................................................................4.14
Rankine-AASHTOOverturning.................................................................. ...................................................................4.14
Overturning ...........................................................................................................................................................................4.14
BearingCapacity ...................................................................................................................................................................4.14
UltimateBearingCapacity ..................................................................................................................................................4.15
InternalStability ....................................................................................................................................................................4.15TensileCapacity ....................................................................................................................................................................4.16
TensionLevelCalculation...................................................................................................................................................4.17
AASHTOInternalTension................................................................................................................................................4.18
ConnectionCapacity .............................................................................................................................................................4.18
PulloutCapacity ............................................................... ..................................................................... ....................... 4.19-4.20
Stability ofFacing .................................................................................................................................................................4.20
P A R T FI V E KeyWallOperatingInstructions
Installation&UsersGuide ....................................................................................................................................................5.1
Installation ...............................................................................................................................................................................5.2
Registration ..............................................................................................................................................................................5.3
KeywallInstallation&Setup .................................................................................................................................................5.4
LaunchingtheKeywallProgram .........................................................................................................................................5.5KeywallWindowsInterface..................................................................................................................................................5.6
KeywallInterfaceOptions......................................................... ...................................................................... ............... 5.7-5.8
KeywallRegistrationDetails.................................................................................................................................................5.8
GeneralInput.................................................................... ..................................................................... ......................... 5.9-5.10
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PA RT O N E
K E Y S T O N E R E T AI NI N G W A L L U N I T S
Fordland, Lakewood, Colorado;KeystoneCentury&HalfCenturyWall
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D ES I G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
eystoneretainingwallunitsareazero-slumpconcretemasonry productdevelopedspecifically
foruseinearthretainingwallstructures. Keystonehasdevelopedawidevariety ofshapesand
designstoaccommodatemostarchitecturalandstructuralrequirements. Localproducersof
theKeystoneproductshaveavariety ofcolorsavailable, complementingmostlandscapingand
structuralretainingwallapplications.
Keystonestructuralproductscurrently availableinclude:
StandardI/StandardII, Figure1:1
CompacI/CompacII/CompacIII, Figure1:2
KeystoneCentury Wall, Figure1:3
133Elite
, Figure1:4
TheKeystoneunitslistedabovearedesignedforuseasstructuralretainingwalls, i.e., thoseexceeding6.5 feet
(2m)inheightand/orsupportingstructuresorhighway loading.
Inadditiontotheaboveunits,Keystonehasacompletelineofsmallerlandscapeproductsthataremarketedand
soldthroughretaildistributionandlandscapesupply outlets. Theseproductsaregenerally notconsideredfor
structuralapplicationsandarenotdiscussedfurtherinthismanual.
KEYSTONE RETAIN ING WALL UN ITS
K
Brentwood Gate, Burnaby, BritishColumbia;Keystone133Elite
1.1
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1.2
P ART O N E
RetainingWallUnits
P ART O N E
RetainingWallUnits
Keystoneunitsaretypicallymanufacturedof concretewithaminimumcompressivestrengthof3000 psi
(21MPa)at28 daysandamaximumabsorptionof8%. Alldimensionsareplusorminus18inch(3mm)
exceptfortheunitdepth, whichvariesduetothesplitrockfinish. Themanufacturingprocessisautomated,
sothemixing, compaction, andcuringareperformedundercontrolledconditionsandprovideconsistent
quality.Theunitshavevariousfacetexturesavailable, dependingonyourlocalmanufacturer. Someofour
mostpopulartexturesaremoldedorsplit-rockfinishinvariousnaturalcolors. Faceshapescanbetri-plane,
straight, Victorian, orSculpterramoldedfacesuchasHewnstone.
Standard, Compac,KeystoneCentury Wall&133Elitearevertically interconnectedusinghigh-strength
pultrudedfiberglasspins.TheKeystoneunitshavecoresthatarefilledwithcleancrushedstonetoprovide
additionalmechanicalinterlockandinternaldrainage.Thepinsassurearunningbondconfigurationof
theunitsandprovidesignificantlateralconnectionstrengthbetweenunits.Thepinsimprovetheconnection
betweentheunitsandthestructuralsoilreinforcementwhileassuringproperplacementofthe
reinforcementmaterials.
Theconnectionpinsareavailableinstraightandshouldereddesigns. Straightpinsare5inches(133mm)
longandinch(12.7mm)indiameter. TheStandardandCompacunitsusestraightpins. Shoulderedpins
are3inches(95mm)longandinch(12.7mm)indiameter.Theshoulderedlengthis78inch(22mm)
andtheshouldereddiameterisinch(20mm). TheCentury Walland133Eliteunitsuseshoulderedpins.
Theminimumpinstrengthis6,400 psi(44MPa)shortbeamshearstrengthand110,000 psi(750MPa)tensile
strength. Thepinsaremanufacturedofpultrudedfiberglassandwillnotcorrodeordeteriorate. Inaddition,
thefiberglasspindoesnotchangeproperties(softenorbecomebrittle)duetothetemperaturechanges
typicalinretainingwallapplications.
TheStandardunitvariesduetomanufacturingconsiderationsfrom18 to24 inches(457 to600mm)in
depth, withatypicalfacewidthof18 inches(457mm)andheightof8 inches(203mm).Thegeometry yields
exactly 1 squarefoot(0.09m)offaceareaperunit. Unitsweighfrom95 to125 pounds(43 to56kg)each,
varyingwithlocalmanufacturingandaggregates.Thecentroidoftheunitisslightly forwardofcenter
towardtheface, butfordesignpurposes, itistakenatthecenter. Fordesignpurposes, thein-placedensity
oftheaggregatefilledunitis120 pcf(18.85 kN /m ).
Standardunitsaremanufacturedwithadualpinholeconfiguration.Thefrontpinsettingallowstheunits
tobeplacedataminimumsetbackofapproximately 18-inch(3.2mm)per8 inch(203mm)unitheight
(1batter, fordesignpurposesuse0). Therearpinsettingallowsplacementoftheunitsataminimum
1-inch(31.7mm)setbackper8 inch(203mm)unitheight(8batter). Analternateplacementoffront/back
pinholeallowsasetbackof58-inch(15.9mm)per8 inch(203mm)unitheight(4batter).
Note:
Notallunitstypes,
facetreatmentsand
colorsareavailable
atallmanufacturing
locations. Please
check withyourlocal
manufactureror
Keystonesupplierfor
availability.
KEYSTONE MATERIALS
STAN D ARD UN IT
F igure 1:1 Standard/Standard IIU n it
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1.3
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
TheKeystoneCompacunitisa12 inch(305mm)deepunitwithatypicalfacewidthof18 inches(457mm)
by 8 inches(203mm)high. Thisgeometry yieldsexactly 1 squarefoot(0.09m)offaceareaperunit.Depth
may vary from11 to12.5 inches(280 to317mm)dependinguponlocalmanufacturingandsplitting
requirements.Unitsweighfrom70 to95 pounds(32 to43kg)each, varyingwithlocalmanufacturingand
aggregates. Fordesignpurposes, thein-placedensity oftheaggregatefilledunitis120 pcf(18.85 kN/m).
Thedualpinholeconfigurationallowsthesame1(0fordesignpurposes), 4, and8setbackasthe
Standardunit.
Century Wallisathreepiecesystemthatconsistsofasmall,medium, andlargeunit.Thewidthofthe
unitsisthevaryingdimensionthatdictatesthesize. Thesmallunitis7 inches(178mm)wide, themedium
unitis11 inches(279mm)wide, andthelargeunitis18 inches(457mm)wide.ThethreeCentury Wall
unitsare12 inches(305mm)deepand8 inches(203mm)high.Thesmallunitweighs45 pounds(20kg), the
mediumunitweighs58 pounds(26kg), andthelargeunitweighs90 pounds(41kg). Weightsmay vary with
localmanufacturingandaggregates.
SimilartotheCompacandStandardunits, adualpinholeconfigurationallows1(0fordesignpurposes),
4, and8setback.
CO MPAC UN IT
KEYSTONE CENTURY WALLUN ITS
F igure 1:3 Century Wa llU n its
F igure 1:2 Compac / CompacII / CompacIIIU n it
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1.4
P ART O N E
RetainingWallUnits
P ART O N E
RetainingWallUnits
133Eliteunitsare8 inches(203mm)highand24 inches(610mm)widetocreateafaceareaof1.33 square
feet(0.124m), hencethename133Elite.Thedepthoftheunitis11.5 inches(292mm).Dependingonface
treatment, theweightofthe133Eliteunitisapproximately 100 pounds(45kg).
133Eliteunitsaremanufacturedwithonepinpositionthatcreatesanearverticalsetbackequalto38
inch(9.6mm)per8 inches(203mm)ofunitheight(2.5batter).
Therearetwoareaswheretheshearresistanceisimportant:
Levelingpadshearresistance
Inter-unitshearresistance
Bothareimportanttothewallsability toresistlateralmovementsduringconstructionandtoholdtheretained
soilinplace.Theshearandmomentcapacity ofthewallfacingpreventsbulgingofthewallface.
Apreparedlevelingpadisrequiredtoprovideafirm, levelsurfaceonwhichtoplacethebasecourseunits
atthedesignelevationsandprovidelocalizedbearingcapacity fortheunits.
Levelingpadsmay beconstructedofwell-compactedgravel/crushedstoneorunreinforcedconcrete.Formost
walls, thegravel/crushedstonelevelingpadisadequate.Fortallerwalls(over15 feetor5m), contractorshave
foundthatconcretecanleadtofasterwallinstallationandiseasiertouseonthelargerprojects.Theconcrete
padrequiresmorecareinplacementandmoreexpensivematerials(concreteversusaggregate), butthespeedof
placingthefirstcoursegenerally offsetstheextracostofmaterials.
InKeystonewallswithnoearthreinforcement(gravity walls), thetotalresistanceofthewalltolateral
movement(sliding)isprovidedby thefrictionalongthebaseoftheunits. InsoilreinforcedKeystonewalls,
unitbasefrictionisalessercomponentoftheslidingcalculationasthereinforcedzoneprovidesmostof
theresistancealongthebase. Sincethelevelingpadmay beconstructedofvariousmaterials, thefrictional
resistancevarieswiththeroughnessandshearstrengthofthematerials.
133ELITEUN IT
UN ITSHEARRESISTANCE
BASE SHEARRESISTANCE
F igure 1:4 133E li te U n it
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1.5
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
Laboratory testinghasbeenperformedtodeterminetheinter-unitshearresistanceofthevariousKeystone
units. Theinter-unitshearresistanceistheinternalshearcapacity ofthewallfacing. Withoutadequate
shearresistancebetweenunits, awallcouldbulgebetweenlayersofreinforcing, shearduringconstruction,
orinthecaseofagravity wall, shearbetweenany unitabovethebase.
Forgravity walls, theinter-unitshearcapacity isobtainedbasedonthecalculatednormalforce. Whena
layerofgeogridreinforcingisincludedinthewallsystem, theshearingresistancebetweenunitsmay be
reducedbecausethereinforcingcanreducefrictionbetweenunits.Thegranularinterlockisdecreasedand
theunit-to-unitfrictionmay bereduced. Formany systems, reinforcingmay actually decreasethestability
ofthefacewhileprovidingstability totheoverallearthmass.
Inter-unitsheartestinghasbeenperformedonallKeystonestructuralunits. Testingwasinitially doneat
UtahStateUniversity ontheCompacandStandardunits. Theinter-unitsheartestingontheremainderof
theunitshasbeencompletedby Bathurst, ClarabutGeotechnicalTestingInc.Theresultsofthetestforthe
CompacandStandardunitsaregraphically depictedinFigures1:5 and1:6. Laboratory testingprovidesthe
followingderivedequationsforshearresistancebasedonatotalcalculatednormalforce, N , inlbs/lf.
N =
h Wuunitwhere:
h = DepthtoInterface
Wu = Widthofunitface
un it = Unitweightofunitface
AdditionaldirectsheartestswerecompletedatUtahStateUniversity toevaluatebaseshearusingthree
typesoflevelingpadmaterials.Theresultsofthattestingislistedbelow:
TodeterminemetricequivalentsinkN /m , dividethey-interceptby 68.5. Forexample, theStandardunit
tounitshearequationwouldbeF=35.43+Ntan17.4. SheartestreportsareavailablefromKeystone.
INTER-UN ITSHEARRESISTANCE
SHEARD ATA AND ANALYSIS
Un it to UnitUn it to Unit
w/geogrid
Standard F=2427+Ntan17.4 F =1550+ Ntan17.4
Standard II F =1375 +N tan35 F =1556 +N tan19
Compac F=769+Ntan26.9 F =769+ Ntan26.9
CompacII F =1475 +N tan29 F =1250 +N tan29
CompacIII F =1393+ Ntan34 F =900+ Ntan34
Century Wall F =900+ Ntan30 F =900+ Ntan30
133E lite F =1100 +N tan29 F =1100 +N tan29
Standard Compac
Crushed Stone Pad F=995+0.31N F=0.92 N
Concrete Pad F=205+0.30N F=0.90 N
Sand Pad F=290+0.29N F=0.49 N
INTER-UNIT SHE AR TABLE
BASE SHEAR TABLE
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1.6
P ART O N E
RetainingWallUnits
P ART O N E
RetainingWallUnits
Inter-Un it Shear Strength
0
1000
2000
3000
4000
5000
6000
0 2000 4000 6000 8000 10000
NormalF orce (p lf)
S
hear
Force
(
pl
f)
Standard
Standard
w/geog
rid
1000 3000 5000 7000 9000 11000
Un it to Unit
Un it to Unitw/Geogrid
TYP ICALSHEARRESISTAN CE BETWEEN UN ITS
Un it to Un it
Un it to Un itw/Geogrid
Inter-Unit Shear Strength
0
1000
2000
3000
4000
0 2000 4000 6000
NormalF orce (p lf)
Shear
Forc
e
(
pl
f)
1000 3000 5000
Comp
acII
Comp
acIIwi
thGe
ogrid
F igure 1:5 Standard Un it Inter-unit Shear Strength
F igure 1:6 CompacIIU n it Inter-unit Shear Strength
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PA RT T W O
G E O S Y N T H E T I C S O I L R E I N F O R C E M E N T
MartinStreetImprovements, Fredonia, Wisconsin;KeystoneCompacHewnstone
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D ES I G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
eystoneretainingwallsmay performasgravity retainingwallsforheightsupto6 ft(1.8m)forStandardunits
and3.3ft(1m)forCompacunits, dependingongeometry, soiltype, andspecificloading. Whenawallexceeds
safegravity heights, soilreinforcementisrequiredtoprovidestability againstoverturningandsliding. The
majority ofKeystoneretainingwallsareconstructedusinggeosyntheticreinforcement, whichisthefocusofthis
manualandtheKeyWallprogram.DesignforinextensiblesteelreinforcementisdiscussedintheKeystoneKeySystem
designmanualandHITECEvaluation, August2000.
Soil-reinforcedwallstypically consistofgeosyntheticmaterials, primarily geogrids, whichareconnectedtothe
Keystoneunitsandplacedinhorizontallayersinthecompactedbackfill. Alimitequilibriumdesignprocedureisused
todeterminethenumber, strength, length, anddistributionofgeosyntheticreinforcementlayersrequiredtoforma
stablesoil-reinforcedmass.
Geosyntheticmaterialdesignparametersinthelimitequilibriumanalysisare:
Long-TermDesignStrength(LTDS)andallowablestrength, Tal
Geosynthetic-Keystoneunitconnectionstrength, Tcl, Tsc
Geosynthetic-soilpulloutinteractioncoefficient, C i
Geosynthetic-soildirectshearcoefficient, Cds
Terminology usedtodefinegeosyntheticsoilreinforcementtensilestrengthvariessomewhatbetweenauthors,
specifiers, andsuppliers. Theterminology usedwithinthissectionisconsistentwiththatofNCMAandAASHTO/
FHWA, unlessotherwisenoted.
GEOSYNTHETIC SO ILREINFORCEMENT
WallconstructionwithGeogrid Reinforcement.
K
2.1
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2.2
P ART T W O
GeosyntheticSoilReinforcement
Thepracticefordeterminingtheallowabletensilestrengthofgeosyntheticreinforcement, (Tal), isbased
upontheU.S. FederalHighway Administrationguidelines. ThismethodestablishestheLongTerm
DesignStrength(LTDS), bebasedonsustainedloadtesting, extrapolatedtoadesignlifeforthestructure.
TheLong-TermDesignStrength(LTDS), forgeogridreinforcementutilizedintheKeystoneRetaining
Walldesignis:
Equation(2a) LTDS =
Therearetwodesignphilosophiescurrently employedinretainingwalldesignandanalysis. AllowableStress
Design(ASD)istheconventionalworkingstressandfactorofsafetymethodofanalysisthathasbeenused
foryears. LimitStateDesign(LSD)orLoadandResistanceFactorDesign(LRFD)isthenewermethodthat
comparesfactoredloadstofactoredresistances.
Allowable StressD esign
Thelong-termdesignstrength(LTDS), isreducedby anoverallsafety factor(FS), inAllowableStress
designtoaccountforallfactorsonloads, uncertainties, etc.
Equation(2b) Tal =
Limit State Design (LRFD)
TheLongTermDesignStrength(LTDS)isreducedby aresistancefactor()inLimitStateDesign/
(LRFD)toaccountformaterialuncertainty.
Equation(2c) Tal = GE OLTDS
TheNCMA, Rankine, AASHTO96, andAASHTOSimplifieddesignmethodsinKeyWallemploy
AllowableStressdesignprocedures.TheAASHTOLRFD, CanadianLRFDandAustraliandesignmethods
inKeyWallemployLimitStatedesignprocedures.
Tensile Strength (Tult)
TultistheultimatestrengthofgeosyntheticreinforcingwhentestedinawidewidthtestperASTMD4595(geotextile)orD6637 (geogrid).ThisvalueisreportedastheMeanAverageRollValue(MARV),
asdeterminedby themanufacturersquality controlprocessandaccountingforstatisticalvariation.
DESIG N STREN GTH
LTDS
FS
Tult
RFcrx RF idx RFd
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2.3
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
Note:
KeyWallpermitsthe
choiceofthreediffer
backfillmaterials
(fine-grained soils,
34-inch(20 mm)mi
and 2 inch(50 mm)
minus), whichestabl
adefaultvalueforth
installationdamage
factorsused inthe
LTDSdetermination
based onthe
manufacturers
recommendations
and testing.
REDUCTION FACTORS
RFcr
RFcristhereductionfactortoaccountforthelong-termcreepcharacteristicofpolymetricmaterials. The
long-termtension-strain-timebehaviorofpolymericreinforcementisdeterminedfromresultsofcontrolled
laboratory creeptestsconductedonfinished-productspecimensforperiodsupto10,000 hoursperASTM
D5262 andD6992.Thedataisthenextrapolatedtotheprojectdesignlifeofthestructure, 75 yearsor100
years. Creeprupturetestingissimilartotheproceduredescribedabove, however, theloadatwhichrupture
may occurattheendofthedesignlifeispredicted. Acombinationof10,000 hourtestingandcreeprupture
testingappearstobethecurrentstandardforevaluatinggeosyntheticmaterialcreep.TypicalrangeofRFcr
is1.4 to5.0.
RF id
RFidisthereductionfactorforinstallationdamage(i.e., cuts, nicks, tears, etc.)createdby fillplacementand
constructionequipmentoperationswithvariousbackfillmaterialthatcanpotentially reducereinforcing
strengthandperformance. Therecommendedreductionfactorforreinforcementinstallationdamageis
basedonresultsoffull-scaleconstructiondamagetests. Sitespecificvaluesmay bedeterminedby
performingconstructiondamagetestsfortheselectedgeosyntheticmaterialwithprojectspecific
backfillandequipment. TypicalrangeofRFidis1.05 to2.00.
RFd
RFdisthereductionfactortoaccountfortheeffectsofchemicalandbiologicalexposuretothe
reinforcementthataredependentonmaterialcomposition, includingresintype, resingrade, additives,
manufacturingprocess, andfinalproductphysicalstructure. FormostsoilsusedwiththeKeystoneSystem,
themanufacturershaveincludedrecommendedfactorstoaccountforpossiblechemicalandbiologicaldegradation. Insoilswherehighalkalinity orotheraggressivefactors(ph9)may bepresent, the
manufacturershouldbecontactedforspecificrecommendations.TypicalrangeofRFdis1.0 to2.0.
Forfurtherinformationonthechemicalandbiologicaldurability ofareinforcement, areviewofdurability
ispresentedinFHWA-NHI-09-087 Corrosion/DegradationofSoilReiforcementforMSEWallsand
ReinforcedSoilSlopes.
FS
FSistheoveralltensionsafety factorformaterial, geometric, andloadinguncertaintiesthatcannotbe
specifically accountedfor. FSissimilartootheroverallsafety factorsinAllowableStressdesign. A
minimumfactorofsafety of1.5 isrequiredformostpermanentapplications. Forunusualloading
conditions, variableorpoorly definedsoilconditions, thisfactormay beincreasedatthediscretionof
thedesigner.
GE OGE O isthegeosyntheticresistancefactorformaterialuncertainty usedinLimitStateDesign. TheUSAASHTOLRFDCodeuses0.90 forthetensileresistancefactor. Resistancefactorswillvary inLimit
StateDesignbasedontheload/resistancefactorsystemadoptedby specificdesigncodes.
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2.4
P ART T W O
GeosyntheticSoilReinforcement
Theconnectionstrengthisthestrengthstatereinforcement-facingconnectionstrength. Thecapacity is
dependentupontheverticaldepthtothereinforcement, wallgeometry, typeofKeystoneunitutilized, and
thespecificgeosyntheticutilized.
Laboratory testingisrequiredtodefinetheconnectionstrengthforspecificunitsandgeosyntheticmaterials
atvaryingnormalpressures.Typicalgraphsforanindividualstress-straintestandcompleteseriesplotis
showninFigure2:1 andFigure2:2 perNCMATestMethodSRWU-1/ASTMD6638.
Note:
Reinforced soilwall
designsareuniqueto
thespecificKeystone
unitsandgeosynthetic
reinforcementused.
Connectiondatais
specifictoeach
combinationand
reinforcementlevel.
Substitutionofany
materialsinvalidatesa
givenwalldesign.
F igure 2:1 Load Test at one Norma lF orce
F igure 2:2 Connect ion Load P lotsa t D iff erent Norma lF orces
CONNECTIO N STREN GTH
Peak Load
Failure
3 / 4 " De formation
Load at 3/4"
Stress/strain p lot
D isp lacement
C
onnecti
on
Load
Norma lF orce
C
onne
cti
on
Load
Peak Load Plot
3/4" Load Plot
Tconn = y + N tan Max
y
Max
Max
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2.5
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
InAllowableStressdesign, thecalculatedtensileloadateachreinforcementlevelinthegeosyntheticmust
belessthan1)theallowablegeosyntheticdesignstrength, Tal, and2)anultimateconnectionstrengthlimit,
Tcl, dividedby asafety factor(Tcl/FS).Therecommendedminimumfactorofsafety ontheultimate
connectionstrengthis1.5.
InLimitState/LRFDdesign, thefactoredtensileloadateachreinforcementlevelinthegeosyntheticmust
belessthan1)theallowablegeosyntheticdesignstsrength, Tal, and2)theultimateconnectionstrengthlimit,
Tcl, timestheappropriateresistancefactor().
Serviceability strength, Tsc, isdefinedastheconnectionstrengthatamaximum0.75-inch(20mm)
movement, asdeterminedwiththeNCMATestMethodSRWU-1/ASTMD6638. Serviceability criteriais
only consideredwhenaservicestateanalysisisbeingperformed. Thisisrarely consideredincurrentMSE
walldesignasservicestatedeformationisnotwellundersood.NCMAandAASHTOdesigncodes
generally ignoretheservicestateconditionandrequireastrengthanalysisonly.
Twotypesofsoil-reinforcementinteractioncoefficientsorinterfaceshearstrengthparametersareusedfor
designofsoilreinforcedstructures:pulloutinteractioncoefficient, C i,anddirectshearcoefficient, Cds.
Thepulloutinteractioncoefficientisusedinstability analysistocomputethefrictionalresistancealong
thereinforcement/soilinterfaceinthezonebeyondadefinedplaneoffailure.
Thecalculationyieldsthe
capacity toresistpulloutofthereinforcementfromthesoil.
Thedirectshearcoefficientisusedtodeterminethefactorofsafety againstoutwardslidingofthewallmass
alongthelayersofreinforcement.Thecoefficientsaredeterminedinthelaboratory andareafunctionof
soilandgeosyntheticmaterialtypes.
Designpulloutresistanceofthegeosyntheticreinforcementisdefinedastheultimatetensileload
requiredtogeneratemovementofthereinforcementthroughthesoilmassmeasuredatamaximum
inch(19mm)displacement. Therecommendedminimumfactorofsafety againstgeosyntheticpulloutis
1.5. Equivalentresistancefactorsareusedinlimitstatedesign. ASTMD6706may beusedtodetermine
pulloutcoefficientsforgeogrids.
Note:AASHTO requiresthat1000 hoursustained load testingbeperformed onallgeosyntheticconnection
schemesforMSEwallsperFHWAguidelines. Thistestingcanresultinanadditionalreductionfactorthat
reducesconnectioncapacityoverthelifeofthestructure. Thereisnoevidencethatconnectioncreep isalongterm
performanceconsiderationbased onthethousandsofwallsconstructed sincethe1980s. NCMAdoesnotrecognize
theconceptintheirDesignManualforSegmentalRetainingWallsand Keystonehasnotobserved thisin
practice. ThemostprobableexplanationisthattheDesignloadsnevermaterializeattheconnectionasextensible
reinforcementcanyieldtoreleaseanystressbuild up whilethesurroundingsoiland reinforcementpicksup the
load (ie, arching). CurrentUSpracticeistoanalyzetheconnectionat100%ofthetheoreticaldesignload inthe
reinforcementwhichoverstatestheload and probablyexplainsthelack ofcreep related connectionisuses.
CONNECTIO N STREN GTH
GEOSYNTHETIC-SO ILINTERACTION COEFFICIENT
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2.6
P ART T W O
GeosyntheticSoilReinforcement
KeyWall2010 usesthefollowingdefaultvaluesforC iandC dsbaseduponthephiangleinputtedforthe
reinforcedfillmaterial.
* (USCistheUnifiedSoilClassificationSystemperASTMD-2487)
** (Consultgeogridmanufacturer)
GEOGRID MANUFACTURERS DATA
GeogridmanufacturerswerecontactedduringthedevelopmentofthisKeystoneDesignManualandasked
toprovidetherequiredinformationtoevaluatetheirdesignparameters.Thematerialprovidedandtesting
performedbyKeystoneisthebasisforthevaluesprogrammedintoKeyWall. Informationprovidedto
Keystoneby thegeogridmanufacturers/suppliersisavailabledirectly fromthegeogridmanufacturers.
Note:
Asnewmaterialsare
developed ornewdatais
provided, KeyWallsdata
fileswillbeupdated.
Keystoneprovidesthe
dataasaservicetoits
customersand toensure
datauniformityfor
Keystonedesign. This
informationisprovided
withnowrittenor
implied warrantyasto
theaccuracyofthedata
supplied. Datavalues
should beverified with
themanufacturers.
Note:
Thesecoefficientsdonot
applytoGeotextilesor
fatsoils.So ilType (USC*) A N GLE C i Cd
Crushed Stone ,Grave l(G W ,GM) > 32 0.9 0.9
Sand ,Grave l,Silty Sands(SW ,SM ,SP) > 28 0.8 0.8
Sandy Silt,Lean C lay (SC ,ML,CL) > 25 0.7 0.7
Other clay (CL/CH) < 25 0.6** 0.6**
GEOSYNTHETIC-SO ILINTERACTION COEFFICIENT
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P A RT T H R E E
R E T AI NI N G W A L L D E S I G N T H E O R Y
ArborLakes, Beaverton, Oregon;KeystoneCenturyWall
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D ES I G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
3.1
arthretainingwallstructuresrequirethreeprimary areasofdesignanalysis:1)lateralearthpressures
2)foundationbearingcapacity, and3)globaloroverallstability.Theanalysisofeachisbasedonthe
followingengineeringpropertiesofthesoil(s):angleofinternalfriction(), soilcohesion(c), andthe
density ()ofthesoils.
Inthischapter, thebasicmechanismsoflateralearthpressuresandstability offoundationsarepresented.Global
stability andseismicanalysisarebeyondthescopeofthisdesignmanualbutabriefdescriptionisprovided.Once
thebasicconceptsandmechanismsofearthpressuresareunderstood, simplificationofthecalculationstodevelop
theCoulombandRankineearthpressuretheoriescanbeexamined.Therearefurthersimplificationsmadetothe
theorieswhenadaptedfordesignofmechanically stabilizedearth(MSE)structures. By startingwiththebasictheory,
itiseasiertounderstandthemechanismsofperformanceandfailureandadaptthedesigntospecialconditionsnot
directly addressedby thesimplifiedmethods.
Theusershouldrefertorecentgeotechnicaltextbooks, theNCMADesignManualforSegmentalRetaining
Walls,FHWADesignand ConstructionofMechanicallyStabilized EarthWallsand Slopes, andAASHTOStandard
SpecificationsforHighwayBridges,foradditionalmaterialandinformationonsoilsandMSEstructures. Thismanual
issolely intendedtoprovideinsightintotheKeyWalldesignsoftwareandthegeneralprinciplesofmodularwall
designwithoutbeinganexhaustivesummary ofsoilmechanics.
RETA IN ING WALL DESIG N THEORY
E
Thurgood MarshallMiddleSchool, SanDiego, California;KeystoneStandard &Compac
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3.2
P ART T HR E E
RetainingWallDesignTheory
Effective StressD esign
Thesoilstrengthparametersarebasedondrainedconditionsthatareapplicabletogranularsoilsandfine
grainedsoilsforlongterm, drainedconditions. (Note:thesepropertiesarereferredtoasandcinmost
textbooks. Inthismanual, andcwillbeusedforsimplicity andrepresentseffectivestressanalysis.)
Angle of InternalFriction ()Thisvaluerepresentsthefrictionalshearstrengthofthesoilwhentestedundercompactedandconfined
conditions.Thisvalueshouldnotbeconfusedwithasoilangleofrepose,whichreflectstheanglethata
pileofloosesoilwillnaturally stand.
Peak Strength
Thepeakshearstrengthofasoilisthemaximumloadmeasuredduringatestatanominaldisplacement.
Thismanualwillutilizepeakshearstrengthvaluesineffectivestressanalysisunlessotherwisenoted.
Residualstrengthvaluesrequiregreatermovementofthesoilthanisintendedby thedesignofreinforced
soilstructuresbutmay beappropriateinsomecaseswithcohesivesoils.
Globa lStabili ty
Conventionalretainingwalldesignonly looksatsimplesliding, overturning, andbearingasfailuremodes.
Thismanualreferstoglobalstability asallothercombinationsofinternalandexternalstability, slope
stability, andcompoundfailureplanesthatmay compromisethewallstructure.
Fa ilure Plane
Soilfailureplanesaretypically non-linearandareoftenrepresentedby alog-spiralcurve. Internally, thefailureplane(locusofmaximumstresspoints)ismodeledasastraightlinefollowingtheappropriate
RankineorCoulombdefinitionoftheslopeangleforsimplification.
Bearing Capacity Factors
Thegeneralbearingcapacity formulaasproposedbyTerzaghiisused.However, differentbearingcapacity
factorshavebeenpublishedby Meyerhof,Hansen, andVesicovertheyears. Thismanualusesthefactors
proposedby Vesic(1975), whichisconsistentwiththeotherdocumentsdiscussingMSEwalls. (Note:All
factorsassumelevelgroundandmustbeadjustedforslopinggroundconditions.)
Soilmechanicstextbooksincludesectionsonpassiveandactiveearthpressures. They describethe
theoriesofCoulombandRankineandmethodsofsolutionviaformulas, graphicalmethods, and
computeranalysis. Thismanualwillbriefly discussthemethodsofactiveearthpressurecalculation
asitrelatestoreinforcedsoilstructuresandaccepteddesignprincipals. Passivepressuresaretypically
neglectedandnotcoveredinthismanual.
IMPORTA NTTECHNICALDEFIN ITIO NS
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3.3
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
TheNCMADesignManualforSegmentalRetainingWalls, Second and Third editions, isbasedonCoulomb
earthpressuretheory.Thebasicassumptionsforthisactivewedgetheory weredevelopedby Coulomb
(1776).Theothermajormethodology isRankineearthpressuretheory (1857), whichisbasedonthestate
ofstressthatexistsintheretainedsoilmass. Boththeoriesessentiallymodeltheweightofthesoilmass
slidingalongatheoreticalplaneoffailure(Figure3.2 and3.3). Thelateralearthpressure, Pa, isthenetforce
requiredtoholdthewedgeofsoilinplaceandsatisfy equilibrium.
ThemajordifferencebetweenthetwotheoriesisthattheCoulombmodelandequationsaccount
forfrictionbetweenthebackofthewallandthesoilmassaswellaswallbatter. Rankineequations
moreconservatively assumenowallfrictionatthesoil-wallinterfaceandaverticalwallstructure
whichgreatly simplifiesthemathematicsoftheproblem. Thefrictionatthebackofthewallfaceand
atthebackofthereinforcedzoneforexternalstability computations, providesanadditionalforce
componentthathelpssupporttheunstablewedgeofsoil. Becauseoftheseadditionalresistingforces,
thelateralearthpressurecalculatedby Coulombisgenerally lessthantheearthpressurethatwouldbe
predictedby theRankineequations.
AASHTOdesignmethodologiesgenerally appliesRankineearthpressuretheory forearthreinforced
structures. AASHTOdesignmethodology isrequiredonmosttransportationrelatedprojectsoperating
underthismoreconservativedesigncriteria.
LATERALEARTH PRESSURE THEORIES
Note:
Whenthebackslope
equaltotheassumed
frictionattheback
ofthewall(=),
Coulomband Ranki
formulasprovide
identicalearthpressu
coefficientsand resul
forcesforverticalwa
Note:
Forthoseinterested i
comparingCoulomb
versusRankineversu
AASHTO, KeyWall
allowstheuserto
selecteachdesign
methodology. NCMA
istheCoulombanaly
pertheNCMAdesign
manual;Rankinean
AASHTOuseaRan
approach, butwill
accountforwallbatt
entered intheKeyWa
Geometryselection
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3.4
P ART T HR E E
RetainingWallDesignTheory
Thereadershouldnotethatforhorizontalsurfaces(levelsurcharge)orinfiniteslopingsurfaces(extending
beyondthetheoreticalCoulombfailureplane), aclosed-formequationsolutionisapplicableandeasily
derived. Forgeometrieswheretheslopechangeswithinthezoneoffailure(brokenbackslope), thesimple
equationsarenolongerapplicableandmay beunnecessarily conservative. Forexample, ifashortbroken
backslopeismodeledasaninfiniteslope, thedesignmay requiresignificantlymorereinforcementand
excavationthanifmodeledcorrectly. Fortheseconditions, thetrialwedgemethodisusedintheanalysis.
Thisisaniterativetrialwedgeprocesswheresuccessivefailuresurfacesaremodeleduntilamaximum
earthpressureforceiscalculatedforthegeometry andloadinggiven(SeeFigure3:4).
Theearthpressurebehindthewallfaceoratthebackofthereinforcedzoneisrepresentedby atriangular
pressuredistributionforactivesoilpressureandarectangulardistributionforuniformsurchargepressure
asisshowninFigure3:1.
TheappropriateCoulombearthpressureequationsforearthandsurchargepressureareasfollows:
Equation(3a) Pa =H ka
Equation(3b) Pq =q Hka
where:
ka = coefficientofactiveearthpressure
= moistunitweightofthesoil
H = totaldesignheightofthewall
q = uniformsurcharge
COULOMB EARTH PRESSURE THEORY
H/3H/2
H Pa
Pq
q
F igure 3:1 Earth Pressure D iagram
COULOMB EARTH PRESSURE EQUATIO N
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3.5
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
COULOMB EARTH PRESSURE EQUATIO N
Theactiveearthpressurecoefficient, ka, isdeterminedfromanevaluationoftheCoulombwedgegeometry
showninFigure3:2 andresultsinthefollowingkacoefficient:
Equation(3c) ka =
where:
= angleofbatterfromhorizontal
= angleofinternalfrictionofsoil
=
slopeangleabovewall = angleoffrictionatbackofwall
Thisequationisfoundindifferingformsinothertextsduetothetrigonometricassumptionsmadeinthe
formuladerivation.ThederivationofthisCoulombformulacanbefoundingeotechnicaltextbookssuchas
FoundationAnalysisand Designby Bowles(1996).
H
R
W
Pa
F igure 3:2 Cou lomb Wedge D iagram
sin(+ )
sinsin () 1 +
sin(+ )sin()sin()sin(+ )
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3.6
P ART T HR E E
RetainingWallDesignTheory
TheCoulombfailureplanevariesasafunctionofthewallgeometry andfrictionanglesforboththesoils
andthesoil/wallinterface. Forlevelsurchargeandinfiniteslopeconditions, therelationshipforis:
Equation(3d) tan (- ) =
where:
= angleofinternalfriction
= batterofwallmeasuredfromvertical(-90)
= slopeangleabovethewall
= angleoffrictionatbackofwall
(orreinforcedmass)
TablesareavailableintheNCMADesignManualandelsewherethattabulatethesevaluesandassistin
determiningtheappropriateCoulombearthpressurecoefficientsandfailureplaneorientationbasedupon
thewallgeometry andsoilparameters. TheKeyWallprogramcalculatesthesevaluesforeachgeometry.
Forbrokenbackconditions, atrialwedgecalculationisusedinsteadoftheformulas.
Rankineearthpressureisastateofstressevaluationofthesoilbehindaretainingstructurethattraditionally
assumesaverticalwallandnofrictionbetweenthesoil/wallinterface.Theorientationoftheresultantearth
pressureisparalleltothebackslopesurface.
Theearthpressurebehindthewallfaceoratthebackofthereinforcedzoneisrepresentedby a
triangularpressuredistributionsimilartothatshowninFigure3:1.Theearthpressureequations
arethesameasCoulomb:
Equation(3e) Pa =H k a
Equation(3f) Pq =q Hka
where:
ka = coefficientofactiveearthpressure
= moistunitweightofthesoil
h = totaldesignheightofthewall
q = uniformliveloadsurcharge
RA NKINE EARTH PRESSURE EQUATIO NS
RA NKINE EARTH PRESSURE THEORY
COULOMB FA ILURE PLANE LOCATIO N
tan"#$tan"#%tan"# $ cot"+ #&%' $ tan"# cot"+ #&
1 + tan"#%tan "# $ cot "+ #&
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3.7
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
kacandeterminedfromanevaluationoftheRankinewedgegeometry similartotheCoulombwedge
analysisasshowninFigure3:3.
Thisresultsinthefollowingequationsforka:
Verticalwall, levelbackslope
Equation(3g)
ka=
tan(45 -2)
Verticalwall, backslope
Equation(3g) ka = cos
where:
= angleofinternalfrictionofsoil = slopeangleabovewall
TheRankinefailureplanelocationistypically assumedtobeat:
Equation(3h) = 45+2
Whereisfixedandmeasuredfromhorizontalunderalldesignscenarios, whichisonly technically correct
forlevelsurchargeapplicationsandminimalwallbatter. Intheory, theRankinefailureplanevariesunder
backslopeconditions.However, itiscustomary tofixthefailureplaneat45+2inearthreinforcement
design, thusbestrepresentingthecurvedfailuresurfaceandlocusofmaximumstresspointsfora
reinforcedsoilmass.
Note:
TheCoulombearth
pressureequation
willprovideidentica
Rankineearthpressu
coefficientsbysetting
theinterfacefriction
angle, , equaltothe
backslope, , fora
specificdesigncase.
TheKeyWallprogra
actuallyusesthis
method tocalculate
Rankineearthpressu
coefficientsasit
permitswallbatter
tobeincluded in
thecalculation
whenrequired.
RA NKINE FAILURE PLANE LOCATIO N
H
= 45 + /2
W
R
Pa
F igure 3:3 Rank ine Wedge D iagram
RA NKINE EARTH PRESSURE EQUATIO NS
cos coscos
cos $coscos
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3.8
P ART T HR E E
RetainingWallDesignTheory
Thelimitationofclosedformsolutions, suchastheCoulombandRankineequations, isthatonly simple
levelandinfiniteslopingsurchargeswithuniformloadingscanbeanalyzed. Itisnecessary tolookata
trialwedgemethodorapproximationmethodwhenattemptingtoanalyzebrokenbackslopesorother
slope/loadcombinations.
AASHTOandNCMAsuggestanapproximationmethodforbroken-backslopeconditionsthatdefines
equivalentdesignslopesfortheexternalanalysis.However, theinternalanalysisisnotwelldefinedfor
unusualslopesandloadingconditionsandthedesignerisexpectedtouseengineeringjudgementwiththe
simplifiedmethods.
TheKeyWallprogramusesatrialwedgeanalysisfordeterminingtheinternalandexternalforces
inordertoprovidethecorrectresultsformorecomplicateddesigngeometries.Thetrialwedge
calculationisaniterativeprocessthatdeterminestheloadingatsuccessivefailureplaneorientationsuntil
amaximumloadingisdeterminedforthegeometry andsurchargeloading(SeeFigure3:4).
TheKeyWalltrialwedgeanalysisusedisconsistentwiththefundamentalassumptionsoftheapplicable
Coulomband Rankinetheoriesby setting=. Trialwedgeresultsmatchtheequationsolutionsfor
thelevelandinfiniteslopeconditions, butwilldeterminethecorrectinternalandexternalvaluesfor
brokenbackslopeconditionsandoffsetliveanddeadloads. Thismethodofanalysispermitsthedesigner
toproperlymodelmany typicaldesignconditionsandnotoverly simplify theanalysisduetolimitationsof
equationsolutionsandotherdesignsoftware.
F igure 3:4 Tr ia lWedge D iagram
H
R
W
WR
ForceD iagram
W1W2
W3 W4 W5 W6
Wedges
TRIALWEDGE ANALYSIS
Note:
TheAASHTO
Simplified, AASHTO
LRFD, and CAN
LRFDmethodsusethe
AASHTO Simplified
method forcalculatinginternalpressuresand
thetrialwedgefor
calculatingexternal
loadingconditions.
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3.9
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
Bearingcapacity istheability ofthefoundationsoiltosupportadditionalloadingimposedonthesurface
fromthecompletedwallsystem. Bearingcapacity isanalyzedconsideringtwocriteria:
Shearcapacity ofthesoil
Totalanddifferentialsettlement
Shearcapacity ofthesoilisafunctionofthefoundationsoilstrength, thesoilmassequivalentfootingsize,
thedepthofembedment, andany groundwaterconditionsasdeterminedby thegeotechnicalinvestigation.
Figure3:5 showstheMeyerhofdistributionofappliedbearingpressureforflexiblefoundationsystemsthat
istypically utilizedwithearthreinforcementstructures.
Theequivalentfootingwidthandappliedbearingpressurearecalculatedasfollows:
Equation(3i) e = B 2- (Mr- M o)/Rv
Equation(3j) v = Rv(B - 2e)
where: e = eccentricity ofreaction
B = totallengthofbase
Mr = sumofresistingmoments
Mo = sumofoverturningmoments
Rv = sumofverticalreactions
BEARING CAPACITY
W
q
e
D
R
v
B-2e
B
Foundation So
il
- shear strengthc- coh esion- un it w e ight
F igure 3:5 App li ed Bearing Pressure D iagram
APPLIED BEARIN G PRESSURE
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3.10
P ART T HR E E
RetainingWallDesignTheory
Qultistheultimatebearingcapacity ofthefoundationsoilsbasedonthesoilandgeometry parameters.
Theultimatefoundationbearingcapacity canbecalculatedfromthefollowingMeyerhofequation:
Q ult = cNcscdc+ D N qsqdq+ 0.5BNsd
Forwhichinfinitely longstripfootingwithshapeanddepthfactors=1.0, andeffectivebasewidthof
B - 2e, simplifiesto:
Equation(3k) Q ult = cN c+D N q+ 0.5(B - 2e)N
where:
c = cohesionoffoundationsoil
= unitweightoffoundationsoil
D = depthofembedmentbelowgrade
B-2e = effectivefootingwidth
Nc = bearingcapacity factorforcohesion
N q = bearingcapacity factorforembedment
N = bearingcapacity forfootingwidth
Bearingcapacity factorsforthebearingcapacity equation(throughVesic1975)areasfollows:
Nc = (N q- 1)cot N q = e
tantan(45+2) N = 2(N q +1)t an
Thefactorofsafety forbearingcapacity istheratioofultimatebearingcapacity tothecalculated
appliedbearingpressure.
Equation(3l) FSbearing = Q ult/ v
Aminimumsafety factorof2.0 (NCMA)and2.5 (AASHTOASD)againstbearingcapacity failureis
consideredacceptableforflexibleearthreinforcedstructures.
AASHTOLRFDcomputesacapacity demandratio(CDR)forbearingcapacity usingtheequationbelow:
Equation(3m) C DRbearing = Q ultRFb/v(factored loa ds)
TheMSEwallbearingresistancefactorisRFb=0.65. Asisalwaysthecase, thebearingcapacity
demandratiois(1.0.
CALCULATED BEARING CAPACITY
BEARING CAPACITY FACTORS
Note:
Insomecases, bearing
capacityisdetermined
withoutconsideringthe
wallembedment
portionoftheequation,
D N q. SeeKeyWall
DesignPreferences
forthisoption.
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3.11
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
Note:
Thedesigneris
cautioned about
spanningboxculvert
constructingwallsov
uncompacted utility
trenches,goingdirect
fromarock foundati
toasoilfoundation,
transitioningfroman
elasticbearingsurfac
toarigid foundation
surface. Differential
settlementsinsuch
ashortdistancewill
bedetrimentaltoany
structure, and vertica
constructionslipjoin
arerecommended.
BEARING CAPACITY FACTORS
Bearingcapacity inKeyWallisbasedsolely onthesoilparametersinputforthefoundationsoilandthe
embedmentdepthassumingthatthegroundislevelinfrontofthewall.Thedesignermay checkforatotal
stressconditionby insertingtotalstressparametersforthefoundationsoil.
Settlementcriteriamay limitdesignbearingpressuresforstructureshavinglargefootingareas, suchas
mat-typefoundationsandbearingareasunderMSEwallsystems. By reviewingequation(3k), itiseasy
toseethatwithalargeB, theshearcapacity ofthefoundationisusually sufficient.However, with
largerfootingwidths, theareaofinfluencebelowtheloadedareabecomesquitelarge, typically 2B, and
theadditionofthisverticalstressoveralargeareacaninducesignificantsettlement. Itisimportantthat
thedesignerdistinguishesbetweenallowablebearingcapacity forshearfailure(acatastrophicfailure
mechanism)andasettlementcriterion(anon-catastrophicevent).
Totalsettlementislimitedby thedesignersperformancecriteriaandimpactonadjacentstructuresor
tolerancesonverticalmovements. Aslongasthestructuresettlesuniformly, thereisnosignificant
structuraleffectonthewallsystem.Differentialsettlement, however, willcauseaflexuralmovementin
thewallfaceandmay leadtounitrealignmentandcrackstorelievetensilestressesintheconcrete.
Differentialsettlementstypically shouldbelimitedto1%(i.e., 1 footin100 feet)(NCMA)or%
(i.e., 1 footin200 feet)(AASHTO).
Settlementanalysisisbeyondthescopeofthisdocument, andisnotincludedintheKeyWallanalysis.
Duetothevariability offoundationconditions, potentialinfluencesofgroundwater, andother
subsurfaceconditions, itisrecommendedtoconsultaqualifiedgeotechnicalengineerforproper
analysisandspecifications.
SETTLEMENT
Bearing Capac ity Facto rs (Vesic1975)
N c Nq N
0 5.14 1.00 0.00
5 6.49 1.57 0.45
10 8.34 2.47 1.22
15 10.98 3.94 2.65
20 14.83 6.40 5.39
25 20.72 10.66 10.88
30 30.14 18.40 22.40
35 46.12 33.30 48.03
40 75.31 64.20 109.41
Note:
LimitStateorLRFD
analysisrequiresa
servicestateanalysis
inadditiontothe
strengthanalysis.
KeyWallprovidesth
bearingpressurein
additiontothefactor
bearingpressurefor
comparison.
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3.12
P ART T HR E E
RetainingWallDesignTheory
Globalstability analysisisbeyondthescopeofthisdocumentandisnotincludedintheKeyWallprogram.
However, itcanbeanecessary partofacomprehensivedesignanalysisonlargerprojectsandisbest
performedby thesitegeotechnicalengineer.
Globalstability shouldbeinvestigatedany timethefollowingsituationsoccur:
Steepslopesaway fromthetoeofwall
Steepslopesabovethetopofwall
T
ieredwallconstruction Poorfoundationsoils
Slopestability isacomplicatedanalysisthatdependsonsitegeometry, constructionmethods, testedsoil
parametersandpotentialinfluenceofgroundwater. Itisrecommendedthataqualifiedgeotechnical
engineerbeconsultedforproperanalysisandrecommendations.
AminimumFactorofSafety of1.3 isrequiredbyNCMAandAASHTO. Ahigherfactor(FS = 1.5)may
berequiredforcriticalstructuressuchasbridgeabutments. AASHTOLRFDrequiressimilarratios.
NCMA'sDesignManual, 3rdEdition, introducedtheconceptofinternalcompoundstability (ICS)whichisalimitedformofglobalstability analysisthatcheckscircularfailureplanesthroughthereinforced
zoneforalimitedsetofconditions.Keystonebelievesthatglobalstability analysisshouldbedoneona
comprehensivebasis, whenrequired, toavoidthelimitationsoftheICSanalysisanddoesnotcurrently
includethatfunctioninKeyWall.
ExternalG lob alStabili ty S lid ing Surface
InternalG lob a l
Stabili ty S lid ing Surface
2nd Tier Load ing
Method ofSlices
W
E1E2
T1
T2
N
L
FS = 1.30 m i
F igure 3:7 G loba lStab il i ty Section
GLOBALSTABILITY
INTERN ALCOMPOUND STABILITY ANALYSIS
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3.13
D ESI G N M A N U AL& K E Y W A L L O P E R A T I N G G U I D E
Keystoneretainingwallstructureshaveproventobeearthquakeresistantduetothesystemsinherent
flexibility thatpermitsminoryieldingduringamajorseismicevent.
ThemostrecentseismicdesignstandardsarecontainedintheAASHTOStandardSpecificationsforHighway
Bridges(Chapter11)andinthe3rdeditionoftheNCMADesignManual, whichdescribeapseudo-static
methodofanalysisbasedontheMononobe-Okabeapplicationofconventionalearthpressuretheory.
Aschematicofpseudo-staticanalysisconsiderationsisshowninFigure3:8 belowasitpertainsto
reinforcedsoilstructures.
Thedetailsofseismicanalysisarebeyondthescopeofthismanualandotherdocumentsshouldbe
consulted.Therearemany waystoevaluateseismicforces, whicharequitecomplicated.TheKeyWall
programusesthreedifferentmethodsthatparallelthethreedifferentdesignmethodologiesofCoulomb,
Rankine, andAASHTO.
SEISM IC ANALYSIS
Peak Ground Acce leration ,A
LateralInert ialForce
StaticEarthPressure
DynamicEarthPressure
EXTERN AL STABILITY
Structure Acce leration ,Am
Act iveZone
Active WedgeInert ialF orce
FacingInert ialF orce
INTERNAL STABILITY
F igure 3:8 Externa lStab il ity
F igure 3:9 InternalStab il ity
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