technical standards and commentaries for … · technical standards and commentaries for port and...

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TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN

[5] Consideration of Pile Group Action

(1)Whenpilesareusedasapilegroup,theeffectofpilegroupactiononthebehaviorofindividualpilesisnecessarytobeconsidered.

(2)WhenthecenterintervalofdrivenpilesexceedsthevaluesinTable 2.4.10,theactionofthepilegrouponlateralresistancemaybeignored.

Table 2.4.10 Center Intervals of Piles

SandysoilTransverse Pilediameterx1.5Longitudinal Pilediameterx2.5

CohesivesoilTransverse Pilediameterx3.0Longitudinal Pilediameterx4.0

[6] Lateral Bearing Capacity of Coupled Piles

(1)Thelateralbearingcapacityofafoundationofthestructurewithcoupledpilesisnecessarytobedeterminedasappropriateinviewofstructuralcharacteristicsofthefoundation.

(2)DistributionofHorizontalForceinFoundationwithaCombinationofVerticalandCoupledPilesWhenahorizontalforceactsonafoundationwithacombinationofverticalandcoupledpiles,theforcebornebyverticalpilesisfarsmallerthanthatbornebycoupledpilesundertheconditionofequalhorizontaldisplacement.Itmaygenerallybeassumedthatallofthehorizontalforceisbornebythecoupledpiles.

(3)LateralBearingCapacityofCoupledPilesThere are two calculationmethods for the lateral bearing capacity of coupled piles. The first method onlytakes account of the resistanceof the axial bearing capacity of eachpile. The secondmethod takes accountoftheresistanceoftheaxialbearingcapacityofeachpileaswellasthelateralbearingcapacityofeachpileinconsiderationofthebendingresistanceofpiles.

(4)CasewhenOnlyAxialResistanceofIndividualPilesisConsideredasResistingHorizontalForce

Whenonlytheaxialresistanceisconsideredasresistance,asshowninFig. 2.4.19,theverticalandhorizontalactionsactingontheheadofapairofcoupledpilesshallbedividedintotheaxialforceofeachpile.Thecoupledpilesshallbedesignedinawaythattheaxialforceoneachpileislessthanthedesignvaluesoftheaxialresistanceordesignvaluesoftheaxialpullingresistanceoftherespectivepiles.Theaxialforcecanbecalculatedusingequation(2.4.46)oragraphicsolution(seeFig. 2.4.19)

(2.4.46)

where P1,P2:pushingforceactingoneachpileorpullingforcewhenthevalueisnegative(kN)θ1,θ2 :inclinationangleofeachpile(º) Vi :verticalforceactingoncoupledpiles(kN) Hi :horizontalforceactingoncoupledpiles(kN)

PART III FACILITIES, CHAPTER 2 ITEMS COMMON TO FACILITIES SUBJECT TO TECHNICAL STANDARDS

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Hi

Hi

Vi

P1

P1

P2

P2

Vi

θ1 θ2

Fig. 2.4.19 Axial Forces of Coupled Piles

(5)Method of Calculating Horizontal Resistance of Coupled Piles Considering Lateral Resistance of individualPilesVariousmethodsofcalculatingthehorizontalresistanceofcoupledpilesbyconsideringthelateralresistanceofindividualpilesareavailable.Forexample;

①Method of solution based on a conditionwhereby the displacement of each pile is always the same at theintersectionofthecoupledpiles,ontheassumptionthatthespringcharacteristicsofthepileheadintheaxialandlateraldirectionsareelastic.

②Methodofobtainingtheultimateresistanceofthecoupledpilesontheassumptionthattheaxialandlateralresistancesofthepilesshowelasto-plasticproperties.

③Methodofcalculatingtheloadanddisplacementatthepileheads,orthesettlementandtheupwarddisplacementofpilesbypullinginthecaseof(b)onthebasisofempiricalequations.110)

④Methodofusingtheresultsofloadingtestsonsinglepiles.111)

⑤Methodofsolutionassumingthattheyieldstateofeachpilewilloccursuccessivelyandtheresistanceofeachmembertogreaterforceswillbeconstantuntiltheresistanceofthecoupledpilesreachestheultimatebearingcapacity.Thefollowingpresentsanoutlineofmethod①.

Themethod①aboveistocalculatethedistributionofhorizontalforcetoeachpileontheassumptionthattheaxialandlateralresistancesofapilehaveelasticproperties112) InthecoupledpilesshowninFig.2.4.20,thesettlementofeachpileatthepileheadisproportionaltotheaxialforceactingonthatpileandalsothelateraldisplacementisproportionaltothelateralforceactingonthatpile.Onthisassumption,theaxialandlateralforcesactingoneachpileofthecoupledpilescanbecalculatedusingequation(2.4.47),derivedfromtheconditionsofforceequilibriumandcompatibilityofdisplacements.

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(2.4.47)

Verticalandhorizontaldisplacementsofthepileheadcanbecalculatedbyequation(2.4.48)

(2.4.48)

where

N1,N2 :axialforceactingoneachpile,compressiveforceisindicatedbypositivevalue(kN) H1,H2 :lateralforceactingoneachpile(kN) V :verticalloadperpairofcoupledpiles(kN) H :horizontalloadperapairofcoupledpiles(kN) θ1,θ2 :inclinationangletoverticallineofeachpile(°) ω1,ω2 :axialspringconstantofeachpilehead(kN/m) µ1,µ2 :lateralspringconstantofeachpilehead(kN/m) δ'1,δ'2 :verticaldisplacementofeachpilehead(m) η'1,η'2 :horizontaldisplacementofeachpilehead(m)

Thesubscriptnumbersattachedtothesymbols,asshowninFig. 2.4.20,are“1”forthepushedpileand“2”forthepulledpileifonlyahorizontalloadacts. ThevalueslistedinTable 2.4.11 maybeusedforthespringconstantsofpilehead.ThesymbolsusedinTable 2.4.11aredefinedbelow

(2.4.49)

where :penetrationlengthofpiles(m) λ :exposedlengthofpiles(m) E :Young’smodulusofpilematerial(kN/m2) A :pilesectionarea(m2) I :momentofinertiaofpile(m4) Es :elasticmodulusofsubsoil(kN/m2)Es=kCH B B :pilewidth(m) κCH :coefficientoflateralsubgradereaction(kN/m3)

ThecoefficientoflateralsubgradereactionkCH maybecalculatedbymultiplyingthevalueofkCH obtained


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in[4] Estimation of Pile Behavior using Analytical Methods, (5) ② Chang’s Method bythefactorobtainedfromFig. 2.4.17,inaccordancewiththeinclinationofpiles.

V

HN1 N2

H1

H2

(Out-batter pile) (In-batter pile)

l1 l2

λ1 λ2

δ1

δ2

δ'1δ'2

η1 η2

η'1 η'2θ1 θ2

Fig. 2.4.20 Coupled Piles Considering Pile Bending and Soil Resistance due to Deflection

Table 2.4.11 Spring Constants of Pile Head

Axialspringconstantofpilehead(ω)

EndBearingpiles

Frictionpiles

Cohesivesoil

Sandysoil

Lateralaxialspringconstantofpilehead(µ)

Pileheadhinged

Withoutexposedsection(λ=0)

Withexposedsection(λ≠0)

Pileheadfixed

Withoutexposedsection(λ=0)

Withexposedsection(λ≠0)

2.4.6 General Considerations of Performance Verification of Pile Foundations

Performanceverificationofpilefoundationscanbeconductedasfollows.

[1] Load Sharing

(1)Verticalloadsareconsideredtobesupportedbypilesalone.Ingeneral,nobearingcapacityshallbeexpectedfor thegroundincontactwith thebottomof thesuperstructure. Evenif thegroundunder thebottomslabofthesuperstructurewhichissupportedbythepilesisincontactwiththebottomoftheslabwhenconstructioniscompleted,voidsundertheslabwillappearovertime;therefore,fromtheviewpointofsafety,itispreferabletoignorethebearingcapacityofthegroundundertheslab.

(2)Horizontalactionsaregenerallysupportedbypilesalone.However,ifpassiveearthpressureresistanceatthefrontoftheembeddedpartofthesuperstructurecanbeexpected,thisresistancemayalsobeincluded.However,itisgenerallydifficulttocalculatetheresistanceduetopassiveearthpressureinthiscase.Itisnotnecessarilypossible todeterminewhether thepassiveearthpressureof theground reaches itsultimatevalue in response

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to thepileheaddisplacement corresponding to the staticmaximum lateral resistanceof thepiles. When thesuperstructureisdisplaceduntilthepassiveearthpressurereachesthevalueobtainedusingCoulomb’sequation,thereisadangerofthepileundergoingbendingfailure.Therefore,whenconsideringinclusionofthepassiveearthpressureresistanceat thefrontof thisembeddedsection, itshallnotbeincludedincalculationswithoutadequateexaminationofthesefacts.

(3)Forstructuraltypesinwhichsettlementoffacilitiesiscontrolledbyemployingpilesasfrictionpiles,forexample,piled-raftfoundations,122)orsoftlandingmoundlessstructureswithpiles,therearecasesinwhichitisreasonabletoconsiderthebearingcapacityundertheslabbottom. In case of the performance verification of the facilities above, it is necessary to confirm sufficiently thebehaviorcharacteristicsofthefacilities.

(4)ProcedureofperformanceverificationforpilefoundationsItisgenerallypreferablethatperformanceverificationofpilefoundationsbeconductedbytheprocedureshowninFig. 2.4.21.

Type of pilesShape of pilesDimensions of pilesArrangement of piles

Assumptions :

Type of pilesShape of pilesDimensions of piles (diameter, wall thickness, and length)Arrangement of pilesNumber of pilesPile driving angle

Determination :

Estimation of bearing capacity of pilesLoading testsStatic bearing capacity formulas

Displacement of single pile

Ultimate bearing capacity of single pile

Allowable bearing capacity of single pile

Stress generated in piles

Displacement of pile group

Ultimate bearing capacity of pile group

Allowable bearing capacity of pile group

Stress generated in piles

Soil conditionsLoad conditions Allowable displacement

Economy

End

Axial bearing capacity Axial pulling forceHorizontal resistance Negative skin frictionBucklingJoint efficiencyVibration and earthquake

Fig. 2.4.21 Example of Procedure of Performance Verification Procedure

[2] Distance between Centers of Piles

Whendeterminingthedistancebetweenthecentersofpilestobedriven,theworkability,deformationbehaviorofsurroundingground,andbehaviorasapilegroupisnecessarytobetakenintoaccount.

[3] Performance Verification of Pile Foundations during Construction

(1)ExaminationofLoadsduringConstruction

① Inperformanceverificationofpiles,itispreferabletoexaminenotonlytheloadsactingaftercompletionofconstructionbutalsothoseduringtransportation,positioning,anddriving.


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② DrivingsuspensioncontrolbypiledrivingformulasPile driving formulas, designed to calculate the static maximum bearing capacity of piles from dynamicpenetrationresistance,aredifficulttomakegooduseinprinciple.Althoughestimationsofthestaticmaximumbearingcapacityusingpiledrivingformulashavetheadvantageofbeingverysimple,theproblemliesintheiraccuracy.InFig. 2.4.22 bySawaguchi,23)thestaticmaximumbearingcapacityobtainedfromthepiledrivingformulaforsteelpilesiscomparedwiththeresultsofloadingtestsinaformoftheratiooftheformertothelatter.Thefigurerevealsmajordiscrepancyanddispersionbetweenthetwo.Inclayeysoil,soilisdisturbedduringpiledrivingandskinfrictiontemporarilydecreases.Therefore,thestaticmaximumbearingcapacitycannotbeestimatedbypiledrivingformulas. Insandysoil,piledrivingformulasaresaidtobeinaccurateforestimatingthebearingcapacityoffrictionpiles. Thelimitsofapplicabilityofpiledrivingformulasarediscussedinreference24). Nevertheless,whendrivingalargenumberofpilesintoalmostidenticalground,piledrivingformulascanbeusedasareferenceforestimatingtherelativedifferencesinbearingcapacitypereachdrivenpile.Thus,theapplicationoftheseformulasshouldberestrictedtoconstructionmanagementpurposes. However,theymayalsobeusedasreferencetoconfirmvariationinthebearingcapacityofeachpileortofinishthedrivingofeachpilesothattheyareallgovernedbythesamecondition. Ithasbecomepossible toseparate theresistanceof thepileshaftandresistanceat theendof thepilebyperformingandynamicpileloadingtest;moreaccuratedrivingsuspensioncontrolcanbeexpectedthanbydependingsolelyonpiledrivingformulas.

10 20 40 60 100 200 400 600 1,000%

Hiley’s equationHiley’s equation

Weisbach’s equationWeisbach’s equation

Denmark’s equationDenmark’s equation

Smith’s equationSmith’s equation

Janbu’s equationJanbu’s equation

Fig. 2.4.22 Distribution of Results of Pile Driving Formulas and Loading Tests

(a) Hiley’sequationHiley’sequationisthemostcommonpiledrivingformulaandisexpressedbyequations(2.4.50)and(2.4.51).

(2.4.50)Energy required for penetration of pile

Impulsiveloss

Loss due to elasticdeformation of pile

Loss due to elasticdeformation of ground

Loss due to cushion

(2.4.51)

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where Rdu :ultimatepile-drivingresistance;i.e.,dynamicmaximumbearingcapacity(kN) WH :weightofhammer(kN) WP :weightofpileincludingpileheadattachments(kN) F :impactenergy(kJ) ef :efficiencyofhammer,rangingfrom0.6to1.0,dependingonthetypeofhammer126) e :reboundcoefficient(e =1ifcompletelyelastic,ande =0ifcompletelynon-elastic) S :finalsettlementofpile(m) C1 :elasticdeformationofpile(m) C2 :elasticdeformationofground(m) C3 :elasticdeformationofpileheadcushion(m)

MostpiledrivingformulasareobtainedbyreplacingC1,C2,C3,ef,e,etc.inequation(2.4.51)withappropriatevalues. Equation (2.4.52) is considered relativelywell-suited to steel piles. Assuming the impact betweenhammerandpiletobeelastic,i.e., e =1,thefollowingisderived:

(2.4.52)

ThetermC1+C2+C3intheaboveisthesumofelasticdeformationofground,pile,andpileheadcushion.

Ofthese,thetermC1+C2areequaltothereboundK measuredatthepileheadinpiledrivingtests(seeFig. 2.4.23).Withsteelpiles,elasticdeformationC1isdominant,whileC3isgenerallysmaller.Thus,ifC3isneglected,thefollowingcanbeassumed:

(2.4.53)

thus, (2.4.54)

where Rdu :dynamicmaximumbearingcapacityofpile(kN) ef :efficiencyofhammer,setat0.5incaseofequation(2.4.54) S :settlementofpile(m) drophammers:meansettlementperblowforthefinal5–10strikes(m) otherhammers:meansettlementperblowforthefinal10–20strikes(m) K :valueofrebound(m) F :impactenergy(kN·m) drophammer: Singleactionsteamhammer: F=WH H

doubleactionsteamhammer:F=(ap+WH )H dieselhammer: F=2 WH H H :dropheightofhammer(m) WH :weightofhammer(kN) a :cross-sectionalareaofcylinder(m2) p :steampressureorairpressure(kN/m2)

ThedesignvalueofaxialresistanceRdadisobtainedbymultiplyingRdubythepartialfactorγ.Here,apartialfactorγof0.33cangenerallybeused.

(2.4.55)


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PencilPencil

Metal clamp

Pile

Penetration of pile (s)

Elastic compression of pile and ground (K)

(a) (b)

Fig. 2.4.23 Rebound Measurement

[4] Joints of Piles

(1) Jointsofpilesshallbesufficientlysafeagainstactionsaftercompletionaswellasduringconstruction.

(2)Jointsshallbeplacedatthepositionwherethereisasufficientmarginincross-sectionalstrengthandrelativelyfreefromcorrosion.

(3)Dependingon thepositionof joints, the forcesactingon jointsaftercompletionofa structurearesometimesfarsmallerthanthestrengthofthepiles.However,considerationsshouldbetakentoensurethesafetyofjointsagainstthepile-drivingstressduringconstruction,loadincreasesinfuture,andunexpectedstressesarisingwithinthecrosssectionofjoints.

(4)PositionofJointsExecutionofjointpartsisnecessarilyaccompaniedbyworkattheconstructionsite.Therefore,unlikefabricationinafactory,supervisionofconstructionworktendstobeinadequate.Accordingly,inperformanceverificationofjoints,caredifferentfromthatforthepileproperisnecessary.Evenindeepsectionswhicharenotaffectedbybendingstressunderordinaryconditions,thereareexamplesofbucklingofpilesatjointsandatpointswherethepilewallthicknesschangesbelowajoint.Thus,adequateexaminationisnecessary. Indeterminingthepositionofjoints,itisnecessarytoselectthejointpositionbasedonagoodunderstandingofthejointstructure,consideringallofthefactorsofbending,shear,compression,andtension.Apositionwheretheflexuralmomentissmallshallbeselectedifthejointstructureisweakagainstbending,andapositionwhereshearissmallshallbeselectedifthestructureisweakagainstshear. Thedurabilityofjointsisconsideredtobesmallincomparisonwiththepile.Forexample,insteelpiles,variouskindsofcorrosioncontroltreatmentareconsideredtocauseareductionoffunctionsduetoweldingatthispart.Therefore,jointpositionswherecorrosionisslightshallbeselected,andinparticular,positionswhicharesubjecttorepeatedwettinganddryingduetochangingwaterlevelsshallbeavoided. The lengthallotted toelements inonepile isdeterminedby thepositionof joints. Limitations related totransportation,constructionequipment,andworkspacefactorsshallbeconsideredindeterminingthelengthoftheelement.Itisconsideredadvantageoustoreducethenumberofjointstotheminimumanduselongelementsasmuchaspossible.Giventhepresenttransportationconditions,themaximumlengthsthatcanbetransportedare13mbyroadand20mbyrail.

(5)JointsinSteelPilesInsteelpiles, arcwelded joints shouldgenerallybeused,as this is themost reliable typeof joint. However,becausegas-pressureweldingandothernewmethodsarebeingdeveloped,whensufficientsafetyisconfirmedbytheresponsibleengineerbasedonadequatestudybytesting,theseothermethodsmayalsobeused.

(6)WoodPileJointsItisnotpreferabletousethewoodenjointswhenhorizontalforceorpullingforcedoesnotact.

(7)ReinforcedConcretePileJointsandPrestressedConcretePileJointsWhenreinforcedconcretepileandprestressedconcretepileareused to thestructurewherehorizontal forceorpullingforceacts,jointstructurewhichhasbeenconfirmedwithhighreliabilityshallbeselected.

[5] Change of Plate Thickness or Material Type of Steel Pipe Piles

(1)Whenchangingplatethicknessormaterialtypeofsteelpipepiles,alldueconsiderationsshallbegiventotheworkabilityandthedistributionofsectionforceonpiles.

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(2)Thesectionforceofsteelpipepilesvarieswithdepth,generallydecreasingasthedepthbecomeslarge.Therefore,platethicknessormaterialtypeofsteelpipepilesissometimeschangedoverthetotallengthfromtheeconomicalpointofview.

(3)Whenchangingplatethicknessormaterialtypeofsteelpipepiles,thepositionofthechangeshouldbeatthedepthwherethesectionforcearisinginthepilesdoesnotincrease.Cautionisalsorequiredbecausesuchachangemaynotbeallowedifalargenegativeskinfrictionisactive.

(4)Jointingpileswithdifferentthicknessandmaterialtypeshouldbedonebyshopcircularwelding.TheshapeoftheweldedsectionshouldcomplywithJISA5525.

[6] Other Notes regarding Performance Verification

(1)SteelPiles

① RadialbucklingofsteelpipepilesWhenusingclosedendedpilesandwhenusingopenendedpilesfromwhichthesoilistoberemovedforfillingwithconcrete, if thewall thicknessof thepile is extremely thin relative to thepilediameterorpenetrationlengthisextremelylarge,thereisadangerofbucklingintheradialdirectionduetotheearthpressureandwaterpressureactingonthepilesurface.Therefore,cautionisnecessary. Theexternalpressureatwhichbucklingoccurswhenasteelpipeissubjectedtouniformexternalpressurecangenerallybeexpressedasshowninequation(2.4.56).

(2.4.56)

where pk :externalpressurecausingbuckling(kN/m2) E :modulusofelasticityofsteel(kN/m2)E=2.1x108kN/m2

v :Poisson’sratioofsteelv=0.3 t :wallthicknessofcylinder(mm) r :radiusofcylinder(mm)

② AxialbucklingofsteelpipepilesInsteelpipepileswhichhaveathinwallthicknessrelativetothepilediameter,asinlargediameterpiles,thereisadangeroflocalbucklingduetoaxialloading. Thereisnodangerthatbucklingwilloccurduringpiledrivingprovidedtheimpactstressislessthantheyieldstressofthesteelpile.134)KishidaandTakanoproposedequation (2.4.57) toexpresstheeffectofwallthicknessonyieldstress.

(2.4.57)

where σpy :yieldstressofsteelpileconsideringeffectofwallthickness(kN/m2) σy :yieldstressofsteelpileagainststaticload(kN/m2)


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2.5 Settlement of Foundations2.5.1 Ground Stress

(1) Itispreferablethatthestressinducedinagroundduetoloadonafoundationisestimatedbyassumingthatthegroundisanelasticbody.However,foruniformlydistributedload,thestressinthegroundmaybeestimatedbysimplyassumingthatthestressdisperseslinearlywithdepth.

(2)Whena structurebuilton thegroundwhichhasa sufficientmarginof safety factoragainst shear failure, thestressdistributioninthegroundcanberationallyapproximatedbyassumingthegroundtobeanelasticbody.TheelasticsolutionobtainedbyBoussinesqiscommonlyusedincalculationofstressdistributioninaground.Boussinesq’ssolution isbasedonthecase thataverticalconcentrated loadactsonthesurfaceofanisotropicandhomogeneoussemi-infiniteelasticbody.Bysuperposingthissolution,itispossibletocalculatethestressdistributioninthegroundwhenalineloadorspatially-distributedloadactsonthegroundsurface.Inadditiontothiselasticsolution,theKoeglermethodthatassumesthestresstodisperselinearlywithdepthcanbeusedforestimatingthestressinthegroundwhenastriploadorarectangularloadactsontheground.137)

2.5.2 Immediate Settlement

(1) Inestimationofimmediatesettlement,itispreferabletoapplythetheoryofelasticitybyappropriatelysettingthemodulusofelasticityoftheground.

(2)Immediatesettlement,unlikeconsolidationsettlement,whichwillbedescribed in the following, iscausedbysheardeformationandoccurssimultaneouslywithloading.Becausesandygrounddoesnotundergolong-termconsolidationsettlementlikethatincohesivesoilground,immediatesettlementinsandyground,asdescribedhere, canbe considered tobe total settlement. On theotherhand, the immediate settlementof cohesive soilgroundisaphenomenonwhichiscausedbysettlementduetoundrainedsheardeformationandplasticflowinthelateraldirection.Insoftcohesivesoilground,therearecasesinwhichimmediatesettlementmaybeignoredinperformanceverificationbecauseitissmallerthantheconsolidationsettlementdescribedbelow. Incalculationsofimmediatesettlement,thegroundisusuallyassumedtobeanelasticbody,andthetheoryofelasticityandthemodulusofelasticityE andPoisson’sratiov areused.Asthemodulusofelasticityofsoilvariesgreatlydependingonthestrainlevel,itisimportanttomakecalculationsusingamodulusofelasticitythatcorrespondstotheactualstrainlevel.Forexample,thestraininsoftgroundwithasmallsafetyfactorisontheorderof0.5%to1.5%,whilethatinexcavationofhardgroundanddeformationoffoundationsisnomorethan0.1%.TherelationshipbetweenthestrainlevelandtheelasticmodulusshallfollowPart II,Chapter 3, 2.3.1 Elastic Constants.

2.5.3 Consolidation Settlement

(1)Settlementsoffoundationsthatarecausedbyconsolidationofgroundshallbeexaminedinaccordancewiththeproceduresdescribed inPart II, Chapter 3,2.3.2 Compression and Consolidation Characteristics. Designparametersforthegroundisnecessarytobedeterminedbyusinganappropriatemethodbasedontheresultsofconsolidationtests.

(2)Calculationsofsettlementsduetoconsolidationcanbeperformedbasedontheresultsofconsolidationtestsonundisturbed samplesof cohesive soils. Thefinal consolidation settlement,which is the amountof settlementwhenconsolidationcausedbyaloadhasfinallycompleted,isdeterminedbythecompressibilitypropertiesofthesoilskeleton,andcanbeestimateddirectlyfromtheresultsofconsolidationtests.Time-dependentchangesinsettlementuptothefinalconsolidationsettlementofafoundationarenecessarytobecalculatedbasedonthetheoryofconsolidation.

(3)CalculationMethodsofFinalConsolidationSettlementofFoundationFinalconsolidation settlementof foundationcanbecalculatedbyusing the followingequationsdescribed inPart II, Chapter 3,2.3.2 Compression and Consolidation Characteristics.

①Whenusinge-logp curve:

(2.5.1)

where S :finalconsolidationsettlementduetopressureincrementΔp(m) h :layerthickness(m) Δe :changeinvoidratioforpressureincrementΔp

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e0 :initialvoidratio

②WhenobtainedfromCc:Applicationofthismethodislimitedmainlytothecasesinwhichconsolidationofthenormalconsolidationareaisconsidered.

(2.5.2)

where S :finalconsolidationsettlementduetopressureincrementΔp(m) h :layerthickness(m) Cc :compressionindex e0 :initialvoidratio p0 :overburdenpressure(kN/m2) Δp :pressureincrement(kN/m2)

③ whenobtainedfrommv:Applicationofthismethodislimitedtocasesinwhichtheincrementofconsolidationpressureissufficientlysmallthatmvcanbeconsideredconstant.

(2.5.3)

where S :finalconsolidationsettlementduetopressureincrementΔp(m) mv :coefficientofvolumecompressibilitywhenconsolidationloadis (m2/kN) p0 :overburdenpressure(kN/m2) Δp :pressureincrement(kN/m2) h :layerthickness(m)

(4)CalculationMethodofTime-SettlementRelationshipTherateofconsolidationsettlementiscalculatedfromtherelationshipbetweentheaveragedegreeofconsolidationU andthe timefactorT that isobtainedfromTerzaghi’sconsolidation theory,where thedissipationofexcessporewaterpressureisexpressedasapartialdifferentialequationofthermalconductivitytype.Theamountofsettlements(t)atagiventimet canbecalculatedfromtheaveragedegreeofconsolidationU(t)bythefollowingequation:

(2.5.4)

Thefiniteelementanalysiswithvisco-elasto-plasticitymodelforcohesivesoilcanbeutilizedforaccurateanalysisoftheconsolidationsettlementthattakesaccountofinhomogeneityonconsolidationpropertiesoftheground,theeffectofselfweightofcohesivesoillayerandtime-relatedchangesinconsolidationload.

(5)DivisionofCohesiveSoilLayersubjecttoConsolidationWhen calculating the final consolidation settlement, the cohesive soil layer is usually divided into a numberofsub-layersasshowninFig. 2.5.1. Thisisbecausetheconsolidationpressureandthecoefficientofvolumecompressibilitymv varywithdepth.Withthemv method,thefinalconsolidationsettlementoffoundationmaybecalculatedusingequation(2.5.5).

(2.5.5)

where S0 :finalconsolidationsettlement(m) ∆σz :incrementsofconsolidationpressureatthecenterofasub-layer(kN/m2) mv :coefficientofvolumecompressibilityfortheconsolidationpressureatthecenterofeachsub-

layerequalto ,(m2/kN) whereσz0istheeffectiveoverburdenpressureatthecenterofasub-layerbeforeconsolidation ∆h :thicknessofasub-layerintheconsolidatedlayer(m)


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mv1

mv

Z

ΔσZ

ΔσZ1

Δh1

Z Z

Z1

Z2

Fig. 2.5.1 Calculation of Consolidation Settlement

Sincemvand∆σzgenerallydecreasewithdepth,thecompressionineachsub-layerbecomessmallerasthedepthincreases.Thethicknessofsub-layerΔhisusuallysetat3to5m.ItshouldbenotedthattheconsolidationsettlementofsoftcohesivesoilwillbeunderestimatedwhenΔhistakentoolarge,becausethevalueofmνofthesurfacelayerisverylargeanditgovernsthetotalsettlement.Theincrementofconsolidationpressure∆σziscalculatedatthecenterofeachsub-layerusingtheverticalstressdistributionwithdepth,whichisdescribedin2.5.1 Ground Stress.Theterm∆σzistheincrementinverticalstressduetoloading.Inthenaturalground,itisusuallyassumedthatconsolidationduetotheexistingoverburdenpressurehascompletelyfinished. Althoughthedistributionofsubgradereactionatthebottomoffoundationisnotthesameasthatoftheactingloadduetotherigidityoffoundation,therigidfoundationsettlesunifomlyandthestressdistributionofsubsoilatacertaindepthbecomesirrelevanttothedistributionofreactionimmediatelybelowthefoundationbottom.

(6)VerticalCoefficientofConsolidationcv andHorizontalCoefficientofConsolidationchWhenporewaterofgroundflowsverticallyduringconsolidation,theverticalcoefficientofconsolidationcvisused.Butwhenverticaldrainsareinstalled,drainedwaterofgroundflowsmainlytothehorizontaldirectionandthehorizontalcoefficientofconsolidationchshouldbeused.ThevalueofchobtainedfromexperimentsontheclayinJapaneseportareasrangesfrom1.0to2.0timesthevalueofcv.140)However,inperformanceverificationch≒cvisacceptablewhenconsideringadecreaseinchduetodisturbancecausedbyinstallationofverticaldrains,inhomogeneousconsolidationpropertiesintheground,andothers.

(7)CoefficientofConsolidationcv ofOverconsolidatedClay141)Thecoefficientofconsolidationofcohesivesoilinovercosolidatedstateisgenerallylargerthanthatinnormallyconsolidatedstate. Whenthecohesivesoilseemstobeclearlyinoverconsolidatedstate,thevalueofcv usedforperformanceverificationshouldbetheoneatthemeanconsolidationpressurebetweentheexistingeffectiveoverburdenpressure and thefinalpressure after consolidation. However, rather than simplycalculatingcv atthemeanconsolidationpressure, itwouldbebetter todetermineaweightedmeanvalueofcv considering thesettlement.

(8)RateofConsolidationSettlementinInhomogeneousGroundWhen the ground consists of alternate layers with different cv values, the rate of consolidation settlement isanalyzedusingtheequivalent-thicknessmethod142)ornumericalanalysissuchasthefinitedifferencemethod143)or thefiniteelementmethod.144),145),146) Theequivalent-thicknessmethodisusedasasimplifiedmethod,butit sometimesyields significanterrors. When theground is inhomogenous toa largeextentorwhenaccurateestimationisrequired,itisrecommendedtousethefiniteelementmethod.

(9)SettlementduetoSecondaryConsolidationThe shape of the settlement - time curve in long-term consolidation tests on cohesive soil is consistentwithTerzaghi’sconsolidationtheoryuptothedegreeofconsolidationofaround80%.Whentheconsolidationpassesthislevel,thesettlementincreaseslinearlywithlogarithmoftime.Thisisduetothesecondaryconsolidationthat arises with the time-dependent properties of soil skeleton under consolidation load, beside the primaryconsolidationthatcausesthesettlementaccompanyingdissipationofexcessporewaterpressureinducedinthecohesivesoilduetoconsolidationload. Thesettlementduetosecondaryconsolidationisparticularlysignificantinpeatandotherorganicsoils.Inordinaryalluvialclaylayers,theconsolidationpressurecausedbyloadingisoftenseveraltimesgreaterthantheconsolidationyieldstressofthesubsoil.Undersuchconditions,thesettlementduetosecondaryconsolidationissmallerthanthatduetotheprimaryconsolidation,andisnotsignificantintheperformanceverification.Butwhentheconsolidationpressureactingonthegroundduetoloadingdoesnotgreatlyexceedconsolidationyieldstress,thesettlementduetosecondaryconsolidationtendstocontinueoveralongtime,eventhoughthesettlementduetoprimaryconsolidationmaybesmall.Inthiscase,thesecondaryconsolidationsettlementmustbefullytakenintoaccountintheperformanceverification.

–478–


Thesettlementduetosecondaryconsolidationmaybegenerallycalculatedusingthefollowingequation:

(2.5.6)

where Ss :settlementduetosecondaryconsolidation(m) Cα :coefficientofsecondarycompression t :time(d) t0 :starttimeofsecondaryconsolidation(d) h :claylayerthickness(m)

Thecoefficientofsecondarycompressionisobtainedfromconventionalconsolidationtests.ItcanalsobeestimatedfromtherelationshipbetweenandthecompressionindexCc thatisgenerallyexpressedinthefollowingequation147)

(2.5.7)

2.5.4 Lateral Displacement

(1) In quaywalls or seawalls constructed on soft cohesive ground, countermeasures are preferable when lateraldisplacementsduetosheardeformationofthegroundhaveanadverseeffectonstructures.

(2)Inquaywallsorseawallsonsoftground,therearecasesinwhichitisnecessarytoestimatelateraldisplacementscausedbysheardeformationoftheground.Lateraldisplacementsincludedisplacementaccompanyingimmediatesettlementoccurringimmediatelyafterloading,anddisplacementwhichoccurscontinuouslyovertimethereafter.In cases where the imposed load is significantly smaller than the ultimate resistance of the ground, lateraldisplacementaccompanyingimmediatesettlementcanbepredictedbyanalyzingthegroundasanelasticbody.

(3)Afrequentproblemwithsoftgroundislateraldisplacementsoccurringasacombinationofconsolidationandcreepdeformationduetoshearwhentheratiooftheresistanceofthegroundasawholetothemomentduetoactionsislow,beingontheorderof1.3.Amethodofpredictingwhetherthiskindoflateraldisplacementwilloccur or not using a simple constant based on past experience has been proposed.148)Whenmaking amoredetailed analysis, computer programswhich obtain changes over time in settlement and lateral displacementbyfiniteelementanalysisarewidelyused,applyinganelasto-plasticmodeloranelasto-viscoplasticmodel tocohesivesoilground.Becausetheimportanceoflateraldisplacementdiffersgreatlydependingonthefunctionsofthefacilities,itisnecessarytoselectanappropriatecalculationmethodconsideringthesefunctions.

2.5.5 Differential Settlements

(1)Whenconstructingstructuresonasoftcohesiveground,unevensettlementsofthegroundshallbetakenintoaccount and appropriate countermeasures are preferable when uneven settlements have an adverse effect onstructures.

(2)Asimplifiedmethodisproposedforestimatingunevensettlementinreclaimedlandinportareas.Thismethodclassifiesthegroundofreclaimedlandintothefollowingfourtypes;

① Extremelyinhomogeneousground② Inhomogeneousground③ Ordinaryground④ Homogeneousground

Fig. 2.5.2 showsthemeanunevensettlementratiosforeachtypeofground. Theunevensettlementratiomeanstheratioofthedifferenceintheaveragesettlementoccurringbetweentwoarbitrarypointstothetotalsettlement.Forexample,becausethemeanunevensettlementratiofortwopointsseparatedbyadistanceof50mingroundoftype(b)is0.11,whensettlementofxcmoccursfromacertainreferencetime,theaverageunevensettlementoccurringin thedistanceof50mcanbecalculatedas0.11x. Whenapplyingthismethodtoactualproblems,itispreferabletocorrectthevaluesinFig. 2.5.2forthereferencetimeandthedepthofthegroundwhichistheobjecttosettlement.150),151)


–479–

Extremely inhomogeneous ground Inhomogeneous groundOrdinary groundHomogeneous ground

Mea

n un

even

settl

emen

t rat

io

Distance between 2 points 0 20 50 100

0.5

0.4

0.3

0.2

0.1

0

Fig. 2.5.2 Relationship between Distance and Uneven Settlement Ratio in Reclaimed Land

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–483–

147) Mesri,G.:Coefficientofsecondarycompression,Proc.A.S.C.E,Vol.99,SM1,pp.123-137,1973148) Kasugai,Y.,K.MinamiandH.Tanaka:ThePredictionoftheLateralFlowofPortandHarbourStructures,TechnicalNote

ofPHRINo.726,1992149) Okumura,T.andT.Tsuchida:PredictionofDifferentialSettlementwithSpecialReferencetoVariabilityofSoilParameters,

Rept.ofPHRIVol.20,No.3,1981150) Tsuchida,T.andK.Ono:EvaluationofDifferentialSettlementswithNumericalSimulationandItsApplicationtoAirport

PavementDesign,Rept.ofPHRIVol.27,No.4,1988151) Tsuchida,T.:Estimationofdifferentialsettlementinreclaimedland,ProceedingsofAnnualConferenceofPHRI,1989

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3 Stability of Slopes3.1 General

(1)Stability of slopes against slip failure caused by selfweight of soil or surchargemay be analyzed as a two-dimensionalproblem,assumingacirculararcslipsurfaceorastraightslidingsurface.

(2)Itisnecessarytoperformslopestabilityanalysisforthecaseinwhichaslopebecomesleaststable.

(3)Inslopestabilityanalysis,incaseswherethestabilityofthesoilmasscomprisingaslopeisreducedbytheselfweightofthesoilorsurcharge,astheultimateequilibriumstate,itisnecessarytoconfirmthatthedesignvalueofshearingresistanceexceedsthedesignvalueofshearingforcebasedonactions.Calculationmethodsusedintheslopestabilityanalysiscanalsobeusedtocalculatethebearingcapacityoffoundations,inadditiontothestabilityofslopes,asthesecalculationmethodsareusedtoexaminethestabilityofsoilmasses.ThemethoddescribedbelowcanbeusedinverificationofstabilityagainstvariablesituationsinrespectofLevel1earthquakegroundmotioninadditiontothePermanentsituation.

(4)ShapesofSlipSurface

① TypesofshapesofslipsurfacesTheoretically,shapesofslipsurfacesinslopestabilityanalysisarecombinationsoflinear,logarithmicspiral,and/orcirculararcshapes1).Inpractice,however,linearorcirculararcslipsurfacesareassumed.Whenthereisaparticularlyweaklayerandaslipsurfaceisexpectedtopassoverit,thatslipsurfaceorotherappropriateslipsurfacesmaysometimesbeassumed.Anassumedslipsurfaceingeneralshouldbetheonealongwhichtheslipofthesoilmasssmoothlytakesplace.Thus,aslipsurfacewithsharpbendsorcurvesthatseemstobekinematicallyunnaturalshouldnotbeused.

② SlipfailureofslopeonsandysoilgroundSlipfailureofslopesofdrysandorsaturatedsandusuallytakesaforminwhichtheslopecollapses,andasa result, its inclinationdecreases. Therefore, it ismore appropriate to consider a slopeof these types as astraightslidingsurface thanasacircularslipfailuresurface. Evenwhenconsideringacircularslipfailuresurface,theformisclosetoastraightlinepassingthroughthevicinityofthesurfacelayer.Theinclinationofasandyslopewhentheslopeisinastateofequilibriumistermedtheangleofrepose.Thisangleofreposeisequivalenttotheangleofshearresistance,whichcorrespondstothevoidratioofthesandcomprisingtheslope.Inthecaseofunsaturatedsand,theslopepossessesapparentcohesionresistancecausedbythesuctionduetothesurfacetensionofthewaterinthesand.Asaresult,itsangleofreposeisfarlargerthaninthecasesofdrysandandsaturatedsand.However,saturationmayincreaseduetoinfiltrationofrainwaterorariseinthegroundwaterlevel,causingasuddendecreaseinapparentcohesionresistance,orangleofrepose.Therefore,adequateconsiderationisnecessary.

③ SlopefailureofcohesivesoilgroundTheactualslipfailuresurfaceofcohesivesoilgroundisclosetoacirculararc,andadeepslipcalledthebasefailureoftentakesplace,whileashallowslipappearsnearthesurfacelayerinsandyslope. Slopestabilityanalysis isusually treatedasa two-dimensionalproblem. Althoughactualslipsurface inslopeswith longextention takes theformof three-dimensionalcurvedsurfaces,a twodimensionalanalysisgivesasolutionon thesaferside. When thestability isexpected todecreasedue tosurchargeoverafiniteextention,however,theresistanceofbothsidesofacylindricalfailuresurfacemaybetakenintoaccount.

(5)ActionsinSlopeStabilityAnalysisImportant causes of slip failures are selfweight of soil, surcharge,water pressure and others. Beside them,repeatedactionssuchasseismicforce,waveforce,andothersmaybeincluded.Resistanceagainsttheslipisgivenbyshearresistanceofsoilandcounterweight.Becausetheshearstrengthofsoilisrelatedwithtime,thestabilityproblemsonsoilmassareclassifiedintotwocases;loadingonthegroundinnormallyconsolidatedstate,andunloadingbyexcavation.Theformerisreferredtoasashort-periodstabilityproblemandthelatteralong-period.Itispreferabletouseshearstrengthappropriatetoeachcase(seePart II, Chapter 3, 2.3.3 Shear Characteristics).

(6)Stability verification in slope stability problems can be performed by confirming that the ratio of the shearstrength of soil to the shear stress in an assumed slip surface is greater than1.0. Thevalue of the obtainedratiowilldifferdependingontheassumedslipsurface.However,theresultwiththesmallestratioof“shearingresistance”/”shearing force” among the shearing resistance and shearing forceobtained assuming several slipsurfacesbasedonthegivenconditionsshallberegardedasthelimitstateforslipfailureoftheslopeunderstudy.


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(7)PartialFactorsInexaminationofthestabilityofslopes,thepartialfactorsforeachstructuraltypeoffacilitiesorpartialfactorsbytypeofimprovedsoilcangenerallybeused.Inperformanceverificationofstructuraltypesandembankmentsforwhichnopartialfactorsareparticularlyspecified,thevaluesshowninthissectioncanbeused.ThepartstobereferencedonpartialfactorsareasshowninTable 3.1.1.Becausethepositionoftheslipsurfacewilldifferdependingonhowthepartialfactorsforthesoilparameterandtheanalysismethodaredetermined,cautionisnecessarywhentherangeofsoilimprovementistobedeterminedbasedonthestabilityverification.Forexample,ifthepartialfactorofthesoilparameteroftheresistancesideissetsmall,therangeofslipfailure,whichisthelimitstate,willbenarrow.Thismeansthatthenecessaryrangeofsoilimprovementwillbeunderestimated.

Table 3.1.1 Parts to be Referenced on Partial Factors for Use in Verification of Slip Failure

Applicablefacilitiesforpartialfactors Partstobereferenced Applicablefacilities

Compositebreakwater Chapter 4 Protective Facilities for Harbors3.1 Gravity-type Breakwaters (Composite Breakwaters), Table 3.1.1

Uprightbreakwater,slopingcaissonbreakwater,uprightwave-dissipatingblocktypebreakwater,wave-dissipatingcaissontypebreakwater

Breakwaterarmoredwithwave-dissipatingblocks

Chapter 4 Protective Facilities for Harbors3.4 Gravity-type Breakwaters (Breakwaters Covered with Wave-dissipating Blocks), Table 3.4.1

Slopingtopcaissonbreakwaterarmoredwithwave-dissipatingblocks

Gravity-typequaywall Chapter 5 Mooring Facilities2.2 Gravity-type Quaywalls, Table 2.2.2

Gravity-typerevetment,placement-typecellular-bulkheadquaywall

Sheetpilequaywall Chapter 5 Mooring Facilities2.3 Sheet Pile Quaywalls, Table 2.3.3

Sheetpilerevetment,cantileveredsheetpilequaywall

SCPimprovedsoil Chapter 2, 4 Soil Improvement Methods4.10 Sand Compaction Pile Method for Cohesive Soil Ground, Table 4.10.2

Gravity-typequaywallorsheetpilequaywallapplyingSCPimprovement

Others Inaccordancewiththissection(3 Stability of Slopes)

Slopingbreakwaterandothersimilarfacilities

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3.2 Examination of Stability3.2.1 Stability Analysis by Circular Slip Failure Surface

(1)ExaminationofthestabilityofslopescanbeperformedbycircularslipfailureanalysiswiththemodifiedFelleniusmethod,whichisgivenbythefollowingequation,orbyanappropriatemethodequivalenttothebearingforcein2.2.5 Bearing Capacity for Eccentric and Inclined Actions,dependingonthecharacteristicsoftheground.Inequation(3.2.1),thepartialfactorγafortheanalysismethodshouldbeanappropriatevaluecorrespondingtothecharacteristicsofthegroundandcharacteristicsofthefacilities.Ingeneral,γacanbesetat1.30orhigherforpermanentsituations,butincaseswherethereliabilityoftheconstantsusedinverificationcanbeconsideredhighbasedonactualdataforthesameground,andincaseswheremonitoringworkiscarriedoutbyobservingthedisplacementandstressofthegroundduringconstruction,valuesfromoflargerthan1.10andlessthan1.30canbeused.2)Incaseswherepartialfactorsaregivenforthestructuraltypeofthefacilitiesorbytypeofimprovedsoil,asshownin3.1(7) Partial Factors,thepartialfactorsgivenattheobjectivepartsshallbeused.

(3.2.1)

where R :radiusofcircularslipfailure(m) cd :incaseofcohesionsoilground,designvalueofundrainedshearstrength,andincaseofsandy

ground,designvalueofapparentcohesionindrainedcondition(kN/m2) l :lengthofbottomofslicesegment(m) W’d :design value of effective weight of slice segment per unit of length (weight of soil.When

submerged,unitweightinwater)(kN/m) qd :designvalueofverticalactionfromtopofslicesegment(kN/m) θ :angleofbottomofslicesegmenttohorizontal(º) φd :incaseofcohesionsoilground,0,andincaseofsandyground,designvalueofangleofshear

resistanceindrainedcondition(º) Wd :designvalueoftotalweightofslicesegmentperunitoflength,totalweightofsoilandwater

(kN/m) x :horizontaldistancebetweencenterofgravityofslicesegmentandcenterofcircularslipfailure

(m) PHd :designvalueofhorizontalactiononsoilmassofslicesegmentincircularslip(kN/m) a :lengthofarmfromcenterofcircularslipfailureatpositionofactionofPHd(m) S :widthofslicesegment(m) γa :partialfactorforanalysismethod

The design values in equation (3.2.1) can be calculated using the following equation bymultiplying thecharacteristicvaluebythepartialfactor.Ifpartialfactorsarenotparticularlydesignated,1.00canbeusedforallpartialfactorsinequation (3.2.2).

cd =γc ck ,W'd =γW' W'k ,qd =γq qk ,φd =tan–1(γtanφ tanφk),PHd =γPH PHk (3.2.2)

(2)Inslopestabilityanalysis,thecausesofslipfailureincludetheselfweightofthesoil,surcharge,waterpressure,wavepressure,andactionduetogroundmotion.Elementswhichresistslipfailureincludetheshearingresistanceofthesoilandcounterweight.Verificationofsafetyagainstslipfailureofslopesisperformedassumingthattheshearingresistanceofthesoilexceedstheshearingforceintheassumedslipsurface.Whenassumingacircularslipfailuresurface,thisisequivalenttoverifyingthatthemomentswhichworktoresistslipexceedthemomentswhichcauseslipforthecenterofthecircle.

(3)Intheslicemethodusedincircularslipfailuresurfaces,thesoilmassinsidetheslipcircleisdividedintoanumberofslicesbyverticalplanes,theshearingforceatthebottomsurfaceofeachsliceandtheresistantstressofthesoilarecalculatedconsideringthebalanceofforcesineachslice.Thefactthatthedesignvalueoftheshearingresistanceobtainedbyaddingthestressesforalloftheslicesexceedsthedesignvalueoftheshearingforcealongthesliplineisthenverified.Inordertosolvetheinter-slicebalanceofforcesintheslicemethod,itisnecessarytoassumestaticallythedeterminateconditions.Variousmethodshavebeenproposed,whichvarydependingontheassumptionsused.Ingeneral,themodifiedFelleniusmethodandthesimplifiedBishopmethodareused.


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(4)StabilityAnalysisMethodusingModifiedFelleniusMethod1),3),4)Variouscalculationmethodshavebeenproposedfortheslicemethod,dependingonhowtheforcesactingontheverticalplanesbetweentheslicesareassumed.ThemodifiedFelleniusmethodassumesthatthedirectionoftheresultantforceactingonverticalplanesbetweenslicesisparalleltothebaseoftheslices.ThismethodisalsoreferredtoasthesimplifiedmethodorTschbotarioffmethod.WhenacirculararcandasliceareasshowninFig. 3.2.1,equation(3.2.1)accordingtothemodifiedFelleniusmethodisapplicable. Inperformingslopestabilityanalysis,first,thecenteroftheslipcircleisassumed.Oftheslipcirclesthattakethispointastheircenter,theonewiththesmallestratioexpressedby“thedesignvalueofshearingresistance”/”designvalueofshearingforcebasedonloading”isobtained,anditsvalueisusedastheminimumratioforthatcenterpoint.Theminimumratioof“designvalueofshearingresistance”/”designvalueofshearingforce”forothercenterpointsisthenobtainedbythesamemethod.Verificationcanbeperformedforthelimitstateforslipfailureoftheslopeusingtheminimumvalueoftheminimumratiosobtainedbythecontourfortheminimumratios.

Fig.3.2.1 Circular Slip Failure Analysis using Modified Fellenius Method

(5)StabilityAnalysisbyBishopMethod3),5) Bishop5)proposesanequationwhichconsiderstheverticalshearingforceandhorizontalforceactingintheverticalplaneofaslice. Inactualcalculations,acalculationmethodwhichassumesthattheverticalshearingforcesareinbalanceisoftenused.ThismethodiscalledthesimplifiedBishopmethod.InthesimplifiedBishopmethod,γFfFfiscalculatedbasedonequation(3.2.3),5)andstabilitycanbeverifiedbytheverificationparameterFf≥1. In this equation, the symbolγ is thepartial factor for its subscript, and the subscriptsk andd are thecharacteristicvalueanddesignvalue,respectively.

(3.2.3)

where Ff :verificationparameter γFf :partialfactorforanalysismethod cd :incaseofcohesionsoilground,designvalueofundrainedshearstrength,andincaseofsandy

ground,designvalueofapparentcohesionindrainedcondition(kN/m2) S :widthofslicesegment(m) W’d :design value of effectiveweight of slice segment per unit of length (weight of soil. When

submerged,unitweightinwater)(kN/m) ød :incaseofcohesionsoilground,0,andincaseofsandyground,designvalueofangleofshear

resistanceindrainedcondition(º) qd :designvalueofverticalactionfromtopofslicesegment(kN/m) θ :angleofbottomofslicesegmenttohorizontal(º) Wd :designvalueoftotalweightofslicesegmentperunitoflength,totalweightofsoilandwater

(kN/m) PHd :designvalueofhorizontalactiononsoilmassofslicesegmentincircularslip(kN/m) a :lengthofarmfromcenterofcircularslipfailureatpositionofactionofPHd(m) R :radiusofcircularslipfailure(m)

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The design values in the equation can be calculated using the following equation by multiplying thecharacteristicvaluebythepartialfactor.Provided,however,thatWdshallbeexpressedbythesumofW’dandtheweightofwater,becauseitisnotnecessarytomultiplytheweightofwaterbyapartialfactor.Ifpartialfactorsarenotparticularlydesignated,1.00canbeusedforallpartialfactorsinequation (3.2.4).

cd =γc ck,W'd =γW' W'k,qd =γq qk,φd =tan–1(γtanφ' tanφk ),PHd =γPH PHk (3.2.4)

(6)ApplicabilityofStabilityAnalysisMethods6),7)SolutionsinstabilityanalysisbythemodifiedFelleniusmethodandthesimplifiedBishopmethodareinagreementforcohesivesoilinwhichφ=0,whenallpartialfactorare1.00,butdifferwhenthecirculararcpassesthroughsandyground.InJapan,circularslipfailureanalysisbythemodifiedFelleniusmethodiswidelyused.ThisisbecauseithasbeenreportedthatthemodifiedFelleniusmethodreasonablyexplainstheactualbehaviorsofslopefailurebasedontheresultsofanalysisofcasehistoriesofslipfailuresinportareasinJapan,4)andalsogivesasafetysidesolutionforsandyground. However,whenthefoundationgroundconsistsentirelyofsandysoillayers,orwhenaslipcirclecutsthroughground consisting of an upper thick sandy layer and lower cohesive soil layer, it is known that themodifiedFellenius method underestimates stability evaluated by the ratio expressed by the design value of shearingresistance/designvaluebasedonactions.7)Fromtheviewpointofthebasicprinciplesofthestabilitycalculationmethod,thesimplifiedBishopmethodismoreaccurateundersuchconditions.Therefore,thesimplifiedBishopmethodisgenerallyusedincaseofeccentricandinclinedloads,whichareparticularlyaproblemwhenexaminingthebearingcapacityofmounds(see2.2.5 Bearing Capacity for Eccentric and Inclined Actions).ItshouldbenotedthatthesimplifiedBishopmethodhastheproblemofoverestimatingtheratioexpressedby“designvalueofshearingresistance”/“designvalueofshearingforcesbasedonactions”whenactionsonnear-horizontalsandygroundapplyverticalloads.Insuchcases,amethodofstabilitycalculationcanbeusedwhichassumesthattheratiooftheverticaltothehorizontalforcesbetweenslicesis1/3.5oftheangleofsliceinclination.8)Instabilityverificationinthiscase,calculationsaremadeusingthefollowingequation.Inthisequation,thesymbolγisthepartialfactorforitssubscript,andthesubscriptskanddarethecharacteristicvalueanddesignvalue,respectively.

(3.2.5)

n

Basedonequation (3.2.5),γFfFfiscalculated,andstabilitycanbeverifiedbytheverificationparameterFf≥1.Thedesignvaluesinthisequationcanbecalculatedusingthefollowingequation.Provided,however,thatWdshallbeexpressedbythesumofW’dandtheweightofwater,becauseitisnotnecessarytomultiplytheweightofwaterbyapartialfactor.Ifpartialfactorsarenotparticularlydesignated,1.00canbeusedforallpartialfactorsinequation(3.2.6).

cd =γc ck,W'd=γW' W'k,qd=γq qk,φd=tan–1(γtanφ tanφk),PHd=γPH PHk (3.2.6)

wheren =1+tanθtan(βθ),β isaparameterwhichprovidestheratiooftheverticalforcetothehorizontalforceactingonthesidesoftheslice,andcanbeassumedtobeβ=1/3.5.Theothersymbolsarethesameasthoseinequation(3.2.3).

3.2.2 Stability Analysis Assuming Slip Surfaces other than Circular Slip Surface

(1)Despitetheprovisionsstatedintheprevioussections,alinearoracompoundedslipsurfaceshallbeassumedinstabilityanalysiswhenitismoreappropriatetoassumeaslipsurfaceotherthanacirculararcslipsurfacesaccordingtothegroundconditions.

(2)Whenlinearslipisassumed,examinationofstabilityagainstslipfailureofaslopewithastraightslidingsurfaceiscalculatedusingthefollowingequation.

(3.2.7)

where cd :designvalueofcohesionofsoil(kN/m2) φd :designvalueofangleofshearingresistanceofsoil(º) :lengthofbaseofslice(m) W'd :designvalueofeffectiveweightofsliceperunitoflength(kN/m)


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Wd :designvalueoftotalweightofsliceperunitoflength(kN/m) θ :inclinationofbaseofslice,assumedtobepositiveinthecaseshowninFig. 3.2.2(º) PHd :designvalueofhorizontalactionperunitoflengthappliedtoslicesegmentofslope,actions

includewaterpressure,actionsduetowavesandactionsduetogroundmotion(kN/m) γa :partialfactorforanalysismethod

ThepartialfactorγRfortheanalysismethodforslipfailurecanbe≧1.2inthepermanentsituationand≧1.00forvariablesituationsinrespectofLevel1earthquakegroundmotion. Thedesignvaluesinthisequationcanbecalculatedusingthefollowingequation.Provided,however,thatWdshallbeexpressedbythesumofW’dandtheweightofwater,becauseitisnotnecessarytomultiplytheweightofwaterbyapartialfactor.Ifpartialfactorsarenotparticularlydesignated,1.00canbeusedforallpartialfactorsinequation (3.2.8).

cd =γc ck,W'd =γW' W'k,φd =tan–1(γtanφ tanφk), PHd =γPH PHk (3.2.8)

Fig. 3.2.2 Examination of Slope Stability Analysis using Linear Sliding Surface

References

1) R.F,Scott:PrincipleofSoilmechanics,AddisonWesley,p.431,19722) Tsuchida,T.andTANGYiXin:TheOptimumSafetyFactor forStabilityAnalysesofHarbourStructuresbyUseof the

CircularArcSlipMethod,Rept.ofPHRIVol.5、No.1、pp.117-146,19963) Yamaguchi,K.:SoilMechanics(FullyRevisedEdition)Chapter7,Stabilityanalysisofearthstructure,Giho-doPublishing,

pp.197-223,19694) Nakase,A.：Theφ=0analysisofstabilityandunconfinedcompressionstrength,SiolandFoundation,Vol.7,No.2,pp.33-50,

19675) A.W.Bishop:Theuseoftheslipcircleinthestabilityanalysisofslopes,Geotechnique,Vol.5,No.1,pp.7-17.19556) Nomura,K.,T.Hayafuji andF.Nagatomo:ComparisonbetweenBishop’smethod andTschebotarioff’smethod in slope

stabilityanalysis,Rept.ofPHRIVol.7No.4,pp.133-175,19687) Kobayashi,M.:Outstandingissuesinstabilityanalysisofground,ProceedingsofAnnualConferenceofPHRI1976,pp.73-

93,19768) Tsuchida,T.,M.KobayashiandT.Fukuhara:Calculationmethodforbearingcapacitybycircularslipanalysisutilizingslice

method,Proceedingsof33rdConferenceonGeotechnicalEngineering,pp.1371-1372,1998

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4 Soil Improvement Methods4.1 General

Whencarryingoutsoilimprovementasacountermeasureagainstpossiblefailuresofsoftground,anappropriatemethodshallbeselectedinviewofthecharacteristicsoffoundationsubsoil,typeandscaleofstructure,easeandperiodofconstruction,economicfactorsandinfluenceontheenvironment.

4.2 Liquefaction Countermeasure Works

Incarryingoutliquefactioncountermeasureworks,itispreferabletoconductanappropriateexaminationofthefollowingitemsinordertomaintainthefunctionsofthefacilities.

①Methodofcountermeasureworks② Scopeofexecutionofcountermeasureworks(executionareaanddepth)③ Concreteperformanceverificationofcountermeasureworks

4.3 Replacement Methods

(1) Intheperformanceverificationofthereplacementmethod,itisnecessarytoconsiderstabilityagainstcircularslipfailure,settlementofsubsoil,andconstructabilityofreplacement.

(2)Replacement methods can be divided into two methods including the replacement of subsoil by excavation(foundationreplacementbyexcavation)andtheforcedreplacement.Inthereplacementofsubsoilbyexcavationmethod,softsoilisexcavatedandremovedbyasuctiondredgeroragrabdredgerandreplacedbyfillingwithgoodqualitysoil. Thismethod iswidelyused inoffshoreworks. On theotherhand, theforcedreplacementmethodisamethodinwhichsoftsoilisforciblypushedoutbyembankmentload,sandcompactionpiles,blasting,orothermethods,andisthenreplacedwithgoodqualitysoil.39)

(3)The following presents the performance verification method for the replacement of subsoil by excavation(foundationreplacementbyexcavation),whichiswidelyusedinoffshoreworks.

① ProcedureofperformanceverificationIntheperformanceverificationofthereplacementmethods,asshowninFig. 4.3.1,itisgenerallypreferabletocarryouttheperformanceverificationbyaprocedureofassumptionoftheverificationconditions,assumptionof the verification cross section including replacement depth, replacement width, and slope of excavation,examinationofcircularslipfailure,examinationofsettlement,andselectionofthereplacedsand.AlthoughnotshowninFig. 4.3.1,itisalsonecessarytoexaminethepossibilityofliquefactionofthereplacedsandandtheevaluationoftheeffectthereof.

Examination of circular slip failure

Examination of settlement

Permanent state

Setting of design conditions

Assumption of cross-sectional dimensions

Evaluation of actions

Selection of replaced sand

Performance verification Performance verification

Fig. 4.3.1 Example of Performance Verification Procedure for Replacement Method


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② ExaminationofslipfailureIn theexaminationof slip failurebycircular slip failure calculations,3 Stability of Slopes canbeusedasa reference. For partial factors, related provisions inPart III of thisTechnical Standard can be used as areference,asnecessary. Incalculatingtheearthpressureonsheetpilesoranchorageworksinsidethereplacedsection,itispreferabletoconductanexaminationof thecompositeslipinadditiontotheconventionalearthpressurecalculations.Incaseswheretheentirelayeristobereplacedandthebaserockstratumisinclined,itispreferabletoconductanexaminationforacompositeslipwhichincludesslipfailureonthebaserock.

③ ExaminationofsettlementWhencohesivesoilremainsbeneaththereplacedcrosssection,suchasbeneathpartialreplacementortheslopeoffoundationexcavation,consolidationsettlementcanbeexpectedinthecohesivesoilportion.Therefore,itispreferabletoconductanexaminationoftheeffectofthisconsolidationsettlementonthesuperstructure.

④ SelectionofreplacedsandItispreferablethatthereplacedsandhasagoodgrainsizedistributionandhasalowcontentofsiltcontent.Ingeneral,theratiooffinescontentisfrequentlyspecifiedasnomorethan15%.Theangleofshearresistanceofreplacedsandcangenerallybeassumedtobearound30º.However,thisvalueisaffectedbytheparticlesize,sizedistribution,placementmethod,sequenceofplacement,elapsedtime,surcharge,andotherfactors.Thereisacasewheretheangleofshearresistanceisextremelylow,andthereforecautionisnecessary.

⑤ ExaminationofLiquefactionLiquefactionisgenerallyassessedbasedonthegrainsizedistributionandtheN-valuesofthereplacedsand.Whendifficulttoevaluate,theliquefactionshouldbeexaminedbycyclictriaxialtest41)(seePart II, Chapter 6 Ground Liquefaction).Whenliquefactionisoneofcriticalfactorsinthedeterminationofthereplacementsectionandthecharacteristicsofthereplacementsand,itshouldbeconsideredatselectingthereplacedmaterial.Ifinsufficientstrengthofthereplacedsandisexpected,itispreferabletocompactthereplacedsandafterfilling.

⑥ TheN-valuesofthereplacedsandareaffectedbyitsgrainsizeandgrainsizedistribution,placementmethodand sequence of placement, elapsed time and surcharge. According to some case studies, theN-values ofthereplacedsandwerearound10whensandwasinstantaneouslyplacedinlargevolumefromlarge-capacityhopperbargeswithbottomdoors,around5whensandwasplacedbygrabbucketsfromsandcarriers,andevensmallervalueswhensandwasspreadbysuctiondredger.SeveralcasestudiesshowthattheN-valuesoftheloosereplacedsandincreasedwiththeapplicationofsurchargeandtheelapsedtimeafterplacingthereplacedsandorrubblestonesorplacingcaisson.

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4.4 Vertical Drain Method4.4.1 Fundamentals of Performance Verification

(1) Intheverticaldrainmethod,itisnecessarytosecurethefollowingperformancecorrespondingtothepurposesofimprovement.

① Assuretargetedstrengthincrease.② Assurethatresidualsettlementshouldbewithintheallowablevalue.③ Securethenecessarystabilityofthefacilities.

(2)AnexampleoftheperformanceverificationprocedurefortheverticaldrainmethodisshowninFig. 4.4.1.

Constructionperiod

Determination of type,diameter, and spacing of drains

Allowablesettlement

Bearingcapacity

of groundAssumption of target strength increase

Verification of stabilityagainst circular slip failure

Determination of embankmentwidth and shape

in each stage of construction

Assumption of necessaryconsolidation load

Assumption of sectionto be improved

Assumption of height, weight,and shape of embankment

Determination of embankmentheight and consolidation period in

each stage of construction

Verification of stability againstcircular slip failure

Comparison of economy

Fig. 4.4.1 Example of Performance Verification Procedure for Vertical Drain Method

4.4.2 Performance Verification

(1)DeterminationofHeightandWidthofEmbankment

① Heightandwidthofembankmentnecessaryinsoilimprovement

(a) Theheightandwidthoftheembankmentwhenanembankmentistobeusedasconsolidationloadbythepreloadmethodor surchargemethod shall bedeterminedconsidering the strength increasenecessary forstability of the embankment during and after construction, the stability and allowable settlement of thefacilitiestobeconstructed,theeffectonthesurroundingarea,andotherrelevantfactors.

(b)Itispreferabletosetthetopwidthoftheembankmentlargerthanthewidthrequiredforsoilimprovement(seeFig. 4.4.2).


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H

h

Mean widthMean width

Fill top width (Fill)

Fill top width (Fill)

Drain areaDrain area

(Permeable layer)(Permeable layer)

Fig. 4.4.2 Width of Embankment for Vertical Drain Method

(c) Inexaminationofthestrengthincrease(Δc)oftheoriginalground,equation (4.4.1)canbeused.

(4.4.1)where

Ca :targetstrengthincrease(kN/m2) h :heightofembankment(m) p0′ :initialpressure(verticalpressurebeforestartofconstruction)(kN/m2) pc′ :preconsolidationpressure(kN/m2) U :degreeofconsolidation α :coefficientofstressdistribution,namelyratioofdistributedstressingroundandconsolidation

load(embankmentload) γ′ :effectiveunitweightofembankment(kN/m3) Δc :strengthincrease(kN/m2)Δc/Δp:increaserateofstrength

② Evaluationofstabilityofembankment

(a) It isnecessarytoverifythestabilityofembankmentsbycircularslipfailureanalysisorotherappropriatemethodsfortheheightandwidthoftheembankmentdeterminedbytheaboveexplanationof① Height and width of the embankment necessary in soil improvement.Incaseswhereitisnotpossibletosecurethestabilityof theembankment itself, it isnecessary todivide thefinal embankment into several stagesandperformverificationofthestabilityineachoftheembankmentstages.

(b)EvaluationofstabilityofembankmentagainstslipfailureIn the examination of the stability of an embankment by circular slip failure calculations,3 Stability of Slopescanbeusedasareference.Forthepartialfactorstobeusedinthecalculations,thepartialsafetyfactorsforthecircularslipfailurecalculationsinconnectionwithrespectivefacilitiescanbeused.Inthiscase,thestrengthofthegroundmustconsiderthestrengthincreasecalculatedbyequation(4.4.1).

(c) RoughestimationofstrengthincreaseSincesurchargeisusuallyappliedinseveralstagesintheverticaldrainmethod,thedegreeofconsolidationU tobeusedinequations(4.4.1)and(4.4.2)differsateachsurchargestage.However,strengthincrementmayoftenbecalculatedbyassumingauniformdegreeofconsolidationofapproximately80%.

(2)PerformanceVerificationofDrainsIntheperformanceverificationofdrains,itisnecessarytomakecalculationswhichconsiderthepermeabilitycharacteristicsofthedrainmaterial,andpermeabilitycharacteristicsandthicknessofthesandmat,inadditiontothedraininterval,draindiameter,anddrainageconditionsatthetopandbottomofthelayertobeconsolidated.

① Drainsandsandmats

(a) Drainsandsandmatsshallpossesstherequireddrainagefunctions.

(b)ConsolidationrateanddraindiameterTheconsolidationrateisapproximatelyproportionaltothedraindiameterandinverselyproportionaltothesquareofthedraininterval.Generally,theamountofdrainmaterialcanbereducedbyplacingsmalldiameter

–494–


drainsatsmallintervalsratherthanbyplacinglargediameterdrainsatwideintervals.However,inthesanddrainmethod,useofsandpileswithanexcessivelysmalldiametermayresultincloggingduetoinfiltrationofclayeyparticles,andthereisadangerofbreakageofthesandpilesifthepilesareunabletofollowdeformationbyloadingorconsolidationsettlementduringtheconsolidationperiod.Constructionrecordsofsanddrainmethodtodateshowthat themostfrequentlyuseddiameter is40cm,anddiametersnormallyrangefrom30-50cm.Inthesmalldiameterfabri-packeddrainmethod,43)sandpileswithadiameterof12cmarepackedintosyntheticfiberbags,andfoursandpilesareinstalledsimultaneouslyusingalightweightpiledriver.Thismethodisfrequentlyusedwithextremelysoftsubsoilonland.Afabri-packeddrainmethodwithadiameteroftheorderof40cmhasalsobeendevelopedforimprovementofextremelysoftsubsoilattheseabottom.44),45)

(c)MaterialsforsandpilesSandusedforsandpilesshouldhavehighpermeabilityaswellasasuitablegrainsizetopreventcloggingwithclayeyparticles.ThegrainsizedistributionsofsandusedinworksareshowninFig. 4.4.3.However,casesinwhichsandwithasomewhathigherfinescontentisusedhavealsoincreasedinrecentyears.

Grain size(mm)

1

2

3 4

56

7

B

9

1011

12

A

0

20

40

60

80

100

0.1 1 10

Silt Fine sand Coarse sand Gravel

Examples in Japan121

8New YorkA B

Pass

ing

wei

ght p

erce

ntag

e (%

)

Fig. 4.4.3 Examples of Sand Used in Sand Piles

(d)PrefabricateddrainsandrelatedmaterialsIntheperformanceverificationoftheprefabricationdraintypeofstrip-shapeddrain,thewidthandthicknessofapproximately10cmand5cmrespectively,theobjectdrainisconvertedtoacirculardrainhavingthesamecircumferentiallength.Inpracticalcases,however,theperformanceverificationisconductedasequivalenttoasanddrainhavingadiameterof5cm.42)Cautionisnecessaryincaseswherethedrainagecapacityofthedrainislow,asthereisatimelaginconsolidationattheendoftheverticaldrain(i.e.,lowerpartoftheconsolidationlayer).

(e) SandmatsThethicknessofthesandmatlayerisusuallysettobeapproximately1.0mto1.5mformarineworksand0.5mto1.0mforlandworks.Athicksandmatlayermaycausedifficultyindrainpiledriving.Ontheotherhand,athinsandmatlayermayshowreducedpermeabilityduetoinfiltrationofclayeyparticles. Wherethethicknessofthesandmatlayerisconcerned,whenthedrainagecapacityofthesandmatlayerislow,adelayinconsolidationmayoccurduetoheadloss.Inthiscase,itispreferabletoimprovepermeabilitybyinstallingdrainagepipesinthesandmatlayer.Inrecentyears,amethodwhichdoesnotrequireasandmathasbeendevelopedbyconnectingtheexcesslengthsofdrainsinagrid-likeshapetosecuredrainagepathsinthehorizontaldirection.50)

② Draininterval

(a) Intervalofdrainpilesshallbesodeterminedthattherequireddegreeofconsolidationcanbeobtainedinagivenconstructionperiod.

(b)GeneralTheverticaldrainmethodcanbeappliedwhentherateofconsolidationbythepreloadingmethod,surchargemethod,vacuumconsolidationmethod,orsimilarmethodsisslowconsideringthetimeconstraintsof theconstructionperiod.Fig. 4.4.4 showstherelationshipbetweentherequiredconsolidationtimet80,drainage


–495–

distanceH,andcoefficientofconsolidationcvofaclayeylayerbythepreloadingmethod,surchargemethod,andvacuumconsolidationmethod. Note)InFig. 4.4.4,theunitsusedareconsolidationtimet80(day),drainagedistanceH(m),andcoefficientofconsolidationcv(cm2/min).

1 5 10 50H(m)

U10%20%30%40%50%

60%

70%80%90%

T/T800.0130.0550.1250.222

0.348

0.507

0.7111.0001.497

6months

1year

3years

2years

4years5years

10

50

100

500

1000

5000

10000

Permeable layerPermeable layer



Impermeable layerImpermeable layer

Clay

Clay

0.2

2H

H

(d)

10years

t 80

c ν=0

.01c

m /m

in2

c ν=0

.01c

m /m

in2

0.3 0.4

0.60.8

1.0

0.10.08

0.06

0.04

0.03

0.02

Fig. 4.4.4 Required Days for 80% Consolidation of Clay Layer

(c) DeterminationofdrainInterval ThedrainintervalcanbeobtainedfromFig. 4.4.5 andequation (4.4.3)basedontheBarrontheoryorBiotheory.51)Ithasbeenpointedoutthatconsolidationmaybedelayedduetotheeffectofthesmear,whichmeansthedisturbanceofcohesivesoilgroundbydraindriving,ifthedrainintervalisexcessivelysmall52),53),54),55).

(4.4.3)where

D :draininterval(cm) β :factorrelatedtoarrangementofdrains

withsquarearrangement,β=0.886,andwithatriangulararrangement,β=0.952.

n : (n canbeobtainedfromFig. 4.4.5)

De :effectivediameterofdrain(cm) Dw :diameterofdrain(cm)

Th’ :parametersimilartotimefactor

cvh :coefficientofconsolidationrelatedtoflowofwaterinhorizontaldirection(cm2/min) t :consolidationtime(min)

Note)Theunitusedfortime(t) inFig. 4.4.5 andFig. 4.4.6 isdays.

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Fig. 4.4.5 Calculation Chart for N-value

(d)FlowofwaterinverticaldirectionIntheverticaldrainmethod,consolidationbyflowofwaterinthehorizontaldirectionisexpected.However,whenthe thicknessof the layer tobeconsolidated iscomparativelysmall incomparisonwith the intervalbetweenthedrains,progressofconsolidationduetoflowofwaterintheverticaldirectioncannotbeignored.Fortheperformanceverificationofthepileintervalconsideringconsolidationduetoverticalflowofwater,Reference49)canbeusedasareference.

(e) CoefficientofconsolidationinhorizontaldirectionNoappropriatetestmethodhasbeenestablishedforthecoefficientofconsolidation(cvh)forflowofwaterinthehorizontaldirectionofcohesivesoillayers.Ingeneral,thecoefficientofconsolidationinthehorizontaldirectionisconsideredtobe5-10timesgreaterthanthatintheverticaldirection,butsomereportssaythattheyare equivalent. If the effectsofhead loss in thedrains and theeffectof smear are considered, it isnotnecessarilyadvisabletousetheresultsofconsolidationtestswhichreproducetheflowofwaterinthehorizontal direction. According to examples of construction to date, there are no practical objections tosubstitutionofthecoefficientofconsolidation(cv)forflowofwaterinthehorizontaldirectionofclayeysoillayers.

(f) CalculationofdegreeofconsolidationAfterdeterminingthedraininterval,therelationshipbetweenthedegreeofconsolidationandelapsedtimecanbeobtainedusingequations (4.4.4)and(4.4.5)andFig. 4.4.6.

(4.4.4)

(4.4.5)

where Th :timefactorofconsolidationforflowofwaterinhorizontaldirection cvh :coefficientofconsolidationforflowofwaterinhorizontaldirection(cm2/min) t :elapsedtimefromstartofconsolidation(min) De :effectivediameterofdrainarea(cm) Dw :diameterofdrain(cm)

Note)InFig. 4.4.6,theunitsusedarecoefficientofconsolidationcvh(cm2/min),effectivediameterofdrainareaDe(cm),andelapsedtimet (day).


–497–

Fig. 4.4.6 Calculation Chart for Degree of Consolidation

(g)EffectivediameterofdrainareaTheeffectivediameterofdrainareaDe isthediameterofanequivalentcirclethathasthesameareaasthesoilbeingdrainedbyasandpile.TherelationshipbetweenDe andintervalofthedrainpileD isasfollows:

De =1.128D forsquaregridpattern. (4.4.6)De =1.050D forequilateraltriangulargridpattern. (4.4.7)

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4.5 Deep Mixing Method4.5.1 Fundamentals of Performance Verification

[1] Scope of Application

(1)Thedeepmixingmethoddealtwithinthissectionistheoneinwhichthesoilin-situismixedmechanicallywithcement.

(2)Themajorityofexamplesofapplicationofsoilimprovementbythedeepmixingmethodinportsarebreakwaters,revetments including partition dikes, and quaywalls having caissons or the like as their superstructure. Theperformanceverificationmethodpresentedherecanbeappliedtoimprovedsoilwhenagravity-typebreakwaterrevetmentorquaywallistobeusedasthesuperstructure.

(3)When applying the deepmixingmethod to port facilities, a high rigidity subsurface structure is formed bymutuallyoverlappingstabilizedsoilhavingapileshapeinthegroundusingamixingmachine.Thepatternofthissubsurfacestructureisdetermineddependingonthepropertiesofthegroundandthetypeandscaleofthesuperstructure.Ingeneral,however,theblocktypeandthewalltypeshowninFig. 4.5.1arefrequentlyused.Accordingly,blocktypeimprovementandwalltypeimprovementwillbediscussedherewhicharerepresentativeformsofimprovementinthefieldofportengineering.

(4)ThewalltypeimprovementconsistsoflongandshortwallsasshowninFig. 4.5.1(b).Thebasicconceptofthedesignisthatthelongwallsfunctiontotransmittheexternalactionstothefoundationground,whiletheshortwallsfunctiontoincreasetheintegrityoftheimprovedground.

Long wallShort wall

Soft subsoil Improved subsoilImproved subsoil

Seabed

Sea surfaceSea surface

Sea surface

Soft subsoilSoft subsoilSoft subsoilSoft subsoil

Sea surface

Sea surfaceSea surface

Seabed

Soft subsoil Improved subsoilImproved subsoil

(a)blocktypeimprovement (b)walltypeimprovement

Fig. 4.5.1 Typical Improvement Patterns in the Deep Mixing Method

[2] Basic Concept

(1)Definitionsofthetermsareasfollows;

① Stabilizedsoil:Improvedsoilproducedbythedeepmixingmethod.

② Stabilizedbody:Akindofstructureformedundergroundwithstabilizedsoil.

③ Improved ground: Portion in which the stabilized body and untreated soil is combined. In the wall typeimprovement,theuntreatedsoilbetweenthelongwallsisinclusive.

④ Improvedsubsoilsystem:Portionabovethebottomoftheimprovedsubsoil,betweentheverticalplanespassingthroughthefronttoeandheeloftheimprovedsubsoil.

⑤ Externalstability:Examinationofstabilityofunifiedbodyconsistingofimprovedsubsoilandsuperstructureasarigidbodyintheprocessuptofailure.

⑥ Internalstability:Examinationofinternalfailureofthestabilizedbodywhichisstableexternally.


–499–

⑦ Bottomseatedtype:Structuraltypeinwhichthestabilizedbodyisseateddirectlyonthebearingstratum;inthistypeofimprovement,actionsaretransmittedtothebearingstratumbyimprovementofthesoftgroundreachingasfarasthebearingstratum.

⑧ Floatingtype:Structuraltypeinwhichthestabilizedbodytakesaformthatfloatsinthesoftground;inthistypeofimprovement,thestabilizedbodyisnotseatedonthebearingstratum,butsoftgroundisallowedtoremainunderneaththestabilizedbody.

(2)Stabilizedsoilbythedeepmixingmethodgenerallyhasextremelyhighstrengthanddeformationmodulusandextremelysmallstrainatfailureincomparisonwiththesoiloftheoriginalground.60)Accordingly,astabilizedbody formedwith stabilized soil can be regarded as a kind of structure. Therefore, examination of externalstabilityofthestructureasawhole,examinationoftheresistanceofthestructureitself,andwhenparticularlynecessary,examinationofthesettlement,horizontaldisplacement,androtationofthestabilizedbodyasarigidbodyshallbeperformed.

(3)Intheperformanceverificationofthedeepmixingmethod,theTechnical Manual for the Deep Mixing Method in Marine Construction Works 61)canbeusedasareference.

(4)An example of the procedure of the performance verification for the deep mixing method for gravity-typestructuresisshowninFig. 4.5.2.

Permanent state

Variable states in respect of Level 1 earthquake ground motion

Permanent state

Accidental states in respect ofLevel 2 earthquake ground motion

Determination of design conditions

Assumption of dimensions of stabilized body

Evaluation of actions including setting of seismic coefficient for verification

Determination of dimensions of stabilized body

Performance verificationPerformance verification

*2

*1

Verification of external stability such as sliding, overturning and bearing capacity

Verification of external stability such as sliding, overturning and bearing capacity

Verification of internal stability such as toe pressure, shear stress and dislodging

Verification of internal stability such as toe pressure, shear stress and dislodging

Examination of deformation by dynamic analysis

Examination of deformation by dynamic analysis

Examination of circular slip failure and settlement

*1:Whennecessary,examinationofdeformationbydynamicanalysiscanbeperformedforLevel1earthquakegroundmotion.Incaseswhere thewidthoftheimprovedsubsoilissmallerthanthewidthofthefoundationmound,itispreferabletoconductanexaminationof deformationbydynamicanalysis.*2Dependingontheperformancerequirementsofthemainbody,examinationforLevel2earthquakegroundmotionshallbeperformed.

Fig. 4.5.2 Example of Procedure of Performance Verification of Deep Mixing Method

–500–


(5)TheperformanceverificationofvariablesituationsinrespectofLevel1earthquakegroundmotioninthedeepmixingmethodcanbeconducted,equivalenttogravity-typequaywalls,byeitherthesimplifiedmethod(seismiccoefficientmethod),orbyadetailedmethod(nonlinearseismicresponseanalysisconsideringdynamicinteractionofthegroundandstructures)presentedinPart III, Chapter 5, 2.2.3 Performance Verification.Incaseswherethewidthoftheimprovedsubsoilissmallerthanthewidthofthefoundationmoundintheresultsofverificationbythesimplifiedmethod,itisnecessarytocarryoutanexaminationofdeformationoftheimprovedsubsoilandmainbodybyadetailedmethod.ExaminationofaccidentalsituationsinrespectofLevel2earthquakegroundmotionmayalsobenecessarydependingontheperformancerequirementsofthefacilities.

(6)Intheperformanceverificationofthedeepmixingmethod,itisnecessarytoconsiderthefollowingitems.

① Becausethereisnomethodforthedeepmixingmethodtodeterminethedimensionsofthestabilizedbodyatonce,theverificationcalculationisperformedrepeatedlyuntilstabilityconditionsaresatisfiedandthemosteconomicalcrosssectionisobtained.

② Inimprovedsubsoilbywall-typeimprovement,itisnecessarytodeterminethedimensionsofboththelongwallsand theshortwalls. Because the longwallsandshortwallsareconstructedbymutuallyoverlappingpilebodiesofstabilizedsoil,thecross-sectionalshapesofthewallscannotbedeterminedarbitrarilyanditisnecessarytoconsiderthedimensionsofthemixingmachinewhichisexpectedtobeused.

③ Inimprovedsubsoilbywall-typeimprovement,untreatedsoilbetweenthelongwallsexistsintheimprovedsubsoil;therefore,intheexaminationoftheinternalstability,itisnecessarytoexaminetheextrusionoftheuntreatedsoilbetweenthelongwalls,inadditiontotheexaminationoftheinternalstressinthestabilizedbody.

④ Thelimitvaluesofdeformationinthevariablesituationsandtheaccidentalsituationscanbesetcorrespondingtotheperformancerequirementsofthefacilities,usingdeformationofthemainstructuretobesupportedbythedeepmixingmethodasanindex.

⑤ IntheverificationofdeformationofLevel1earthquakegroundmotionandLevel2earthquakegroundmotion,it ispreferable touseanumericalmodelorresultsofshakingtable testswhichcanappropriatelyassess theresidualdeformationoftheimprovedsubsoilcausedbygroundmotion.

4.5.2 Assumption of Dimensions of Stabilized Body

[1] Mixing Design Method for Stabilized Subsoil

Itisnecessarytodeterminethemixingdesignofthestabilizedsubsoilbyperforminglaboratorymixingtestsorin-situtestsunderthesameconditionsasinactualconstruction.

[2] Material Strength of Stabilized Body

(1)Allowablestressofthestabilizedbodyneedstobeappropriatelydeterminedfortheexaminationoftheinternalstability.

(2)Design compressive strength fc can be obtained using equation (4.5.1) based on the standard design strengthquc. Inthisequation, thesymbolγ is thepartialfactorfor itssubscript,andthesubscriptskandddenotethecharacteristicvalueanddesignvalue,respectively.

(4.5.1)where

fc :designcompressivestrengthofstabilizedbody(kN/m2) α :factorforeffectivecross-sectionalarea β :reliabilityindexofoverlap quc :designstandardstrength(kN/m2)

Thedesignvaluesintheequationcanbecalculatedusingthefollowingequation.

qucd=γ quc quck

Forthepartialfactorγqucofdesignstandardstrength,thevaluesmentionedin4.5.4 Performance Verification, [2] Examination of Internal Stability maybeused.

(3)Thedesignshearstrengthfshanddesigntensilestrengthft ofthestabilizedbodycanbeobtainedfromequation (4.5.2) andequation(4.5.3)usingthedesigncompressivestrengthfc.


–501–

(4.5.2)

(4.5.3)where

fsh :designshearstrengthofstabilizedbody(kN/m2) ft :designtensilestrengthofstabilizedbody(kN/m2)

(4)In the performance verification of the stabilized body, the stabilized body is assumed to be amaterial withhomogeneousstrength.However,inactualconstructionwork,becausethestabilizedbodyisformedbymutualoverlappingofpilesofstabilizedsubsoil,therearecasesinwhichinhomogeneousbystabilizedsoilremains,forexample,containingresidualuntreatedsoilorhavingstrengthdifferencesinoverlappedparts,dependingonthemixingmachineusedandthemethodofoverlapping.Thefactorsαandβshowninequation(4.5.1)arefactorsfortreatingstabilizedsubsoilasmaterialhavinghomogeneousstrength.Theconceptswhensettingthesefactorsarepresentedinthefollowing.

① Factorforeffectivecross-sectionalareaαWhenconstructioniscarriedoutusingmachineswithmultiplemixingblades,thecrosssectionofthestabilizedbodyconsistsofmultiplecylindersasshowninFig. 4.5.4.Inblock-typeandwall-typeimprovement,the stabilizedbody is formedbyoverlapping stabilized subsoil havingapile shapeas shown inFig. 4.5.5.Therefore,unimprovedportionsremainaroundtheoverlappingparts,andtheareaoccupiedbythestabilizedsubsoilissmallerthaninotherareas.Thefactorforeffectivecross-sectionalareaαisafactorforcorrectingthisunimprovedpart. Thevalueofthefactorforeffectivecross-sectionalareawilldifferdependingonthedirectionandtypeoftheactionssuchascompressive,tensileandshearwhicharetheobjectoftheperformanceverification.Forexample,whenconsideringshearforceintheverticaldirectionofthestabilizedbodyorstressactingperpendiculartooverlappingparts,examinationonthenarrowestconnectingsectiongivessafesideresults.Ontheotherhand,whenconsideringnormalstressintheverticalplaneofthestabilizedbody,theentireareaofthestabilizedbodymaybeconsideredasactingeffectively.Here,thefactoraccordingtotheformerconceptisusedasthefactorforeffectivecross-sectionalareafortheeffectivewidthα1,andthefactoraccordingtothelatterconceptisusedasthefactorforeffectivecross-sectionalareafortheeffectiveareaα2.

Dx

x

Dy

y

D

R

L

d

Connecting surface

Width ofoverlapping

Fig. 4.5.3 Effective Width inherent in Deep Mixing Machine Fig.4.5.4 Connecting Surfaces

(a) Factorforeffectivecross-sectionalareaforeffectivewidthα1Thefactorforeffectivecross-sectionalareaforeffectivewidthα1shallgenerallybethesmallerofthevaluesobtainedusingequation(4.5.4)andequation(4.5.5).

1) FactorformixingmachinesInFig. 4.5.3,assumingtheintervalbetweenthemixingshaftsofthemixingmachinesisDxandDyandtheoverlappedlengthoftheimprovedpilesislxandly,thecoefficientα1determinedbythemixingmachinescanbeobtainedusingequation (4.5.4).

–502–


(4.5.4)

2) FactorforoverlapInFig. 4.5.4,assumingtheintervalbetweenthemixingshaftsisD,theradiusofthemixingbladeisR,andtheoverlapwidthisd,thefactorα1foroverlapcanbeobtainedusingequation(4.5.5).

(4.5.5)

Inmanyexamples,theminimumoverlapwidthdisassumedtobe25cm,consideringexecutionaccuracyandcapacity.

(b)Factorforeffectivecross-sectionalareaforeffectiveareaα2Thefactorfortheeffectiveareaα2canbeobtainedusingequation(4.5.6).

(4.5.6)where

A1 :areaenclosedbyboldlineinFig. 4.5.4 A2 :areashownbyhatchedlinesinFig. 4.5.4

② ReliabilityindexofoverlapβAtoverlappedparts,anewimprovedpileisjoinedtotheexistingimprovedpileofstabilizedsubsoilwhichhasalreadybeguntoharden.Therefore,thereisapossibilitythatthestrengthofthispartmaybesmallerthanthatofotherparts.Thereliabilityindexofoverlapβisdefinedastheratioofthestrengthofoverlappedparttothatofotherimprovedpiles.Itsvaluewilldifferdependingontheelapsedtimeuntilthenewpileisjoinedtotheexistingpile,themixingcapacityofthemachine,thestabilizerfeedmethod.However,ingeneral,βmaybesettoapproximatelyβ=0.8–0.9.

(5)Relationshipbetweenstandarddesignstrengthandin-situandlaboratorymixingstrength Therelationshipbetweentheaveragevaluequf oftheunconfinedcompressivestrengthqufofin-situstabilizedsubsoilandthecharacteristicvaluequckofthestandarddesignstrengthisgivenbyequation (4.5.7).

(4.5.7)where

K :coefficientshowingnormaldeviation,namelymultiplierforstandarddeviationσ.Ingeneral, K =1.0canbeadopted. V :coefficientofvariationofunconfinedcompressivestrengthqufofin-situstabilizedsoil.

BecausethevalueofVisgreatlyaffectedbythemixingmachineandmixingtechnology,itispreferablethatVbesetindividuallyforeachcase.However,basedonthepastexamples,V =33(%)canbeused.

SettingofthevalueofthecoefficientKas1.0whenthevariationoftheunconfinedcompressivestrengthqufofin-situstabilizedsubsoilfollowsanormaldistributionmeansthatthecharacteristicvaluequckofthestandarddesignstrengthissetatastrengthwherethedefectoccurrenceratiois15.9%(seeFig. 4.5.5). Therelationshipbetweentheaveragevaluequf oftheunconfinedcompressivestrengthqufofin-situstabilizedsubsoilandtheaveragevaluequl oftheunconfinedcompressivestrengthqulofsamplesmixedinthelaboratoryisgivenbyequation (4.5.8).

(4.5.8)

Thevalueofλisaffectedbynumerousfactors,includingthemixingmachineandconstructionconditions,typeofsoilwhichistheobjectofimprovement,typeofstabilizer,thecuringenvironment,andage.Asaguideline,inoffshoreworks,λ=1canbeassumedwhenconstructionisperformedbylarge-ormedium-scaleworkingcrafts,andλ=0.5–1canbeassumedforsmall-scaleworkingcrafts.Provided,however,thatthevalueofλmayalsobedeterminedbasedontestsorthepastrecordsofconstruction. Aschematicdiagramoftherelationshipbetweendesignstandardstrengthquckandtheaveragevaluequl oftheunconfinedcompressivestrengthofsamplesmixedinthelaboratoryandtheaveragevaluequf oftheunconfinedcompressivestrengthofin-situstabilizedsoilisshowninFig. 4.5.5.


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0.0 0.5 1.0 1.5 2.0 2.5 3.0

quck qut = λ quck

15.9%15.9%

kσ=σ

Fig. 4.5.5 Relationship between quck, , and quck (schematic diagram)

4.5.3 Conditions of Actions on Stabilized Body 68)

(1)Fig. 4.5.6 shows a schematic diagram of the loads acting on the stabilized body in the case of gravity-typerevetmentsandquaywalls.

(2)Becauseimprovedsubsoilofwall-typeimprovementcontainsuntreatedsoilintheimprovedsubsoil,dependingontheperformanceverificationitems,itmaybenecessarytosettheloadconditionsbyseparatingtheuntreatedandstabilizedsubsoils.

(3)Fortheexaminationontheexternalstabilityofimprovedsubsoilsystems,PaorPpcanbedeterminedusingtheactiveandpassiveearthpressuresspecifiedinPart II, Chapter 5, 1 Earth Pressure.Whenexamininginternalstability,Pamaybeconsideredasactiveearthpressure. However, it ispreferable thatPpbesetappropriatelywithintherangefromearthpressureatrest topassiveearthpressure,consideringtheexternalstabilityof theimprovedsubsoilsystem.

(4)In caseswhere a certain amount of displacement of the improved subsoil is expected, it has been confirmedexperimentallythatadhesionofuntreatedsoilactsontheverticalplanesoftheactiveandpassivesidesofthestabilizedbody.Inthecaseofembankmentandreclamationbehindtheimprovedsubsoil,downwardnegativeskinfrictionaccompaniedbyconsolidationsettlementoftheuntreatedsoilactsontheverticalplaneoftheactivesideofthestabilizedbody.Therefore,thesetypesofadhesionshouldbeconsideredintheexaminationofthePermanentsituation.69)Ontheotherhand,intheexaminationofactionsassociatedwithgroundmotion,safetysideassumptions,forexample,thattheinertiaforceofthestabilizedbodyandtheearthpressureduringgroundmotionwillactsimultaneously,areadopted.Therefore,CuaasadownwardactionandCupasanupwardactionmaybeassumedintheexaminationofbothexternalandinternalstability.ThevalueofCuaandCupinthiscaseareobtainedfromtheundrainedshearstrengthoftheuntreatedsoilundertheseconditions.

(5)Inthecaseofimprovedsubsoilbywall-typeimprovement,itmaybeassumedthatbothPaandPpactuniformlyonthe longwalls and the untreated soil between the longwalls. Provided, however, thatwhen the subgradereactionTatthebottomofthestabilizedbodyisobtained,itisassumedthattheloadsactingonthestabilizedbody,suchastheweightofthemainbody,areconcentratedonthelongwalls,andonlytheself-weightoftheuntreatedsoilactsontheuntreatedsoilbetweenthelongwalls. TheshearresistanceforceRshallbethesumoftheshearresistanceforcesactingonthestabilizedbodyandthebottomoftheuntreatedsoil.

(6)Deformationofthesuperstructureduringactionofgroundmotiontendstobereducedbysoilimprovementbythedeepmixingmethod.Therefore,whensettingtheseismiccoefficientfortheverificationofthesuperstructureandtheimprovedsubsoilsystem,itispossibletosetarationalseismiccoefficientfortheverificationbasedonanappropriateevaluationofthisreductioneffect.

When soil improvement is performedby the deepmixingmethod the characteristic valuekh1k of the seismiccoefficientfortheverificationofthesuperstructureandthestructuralelementsofimprovedsubsoilsystemsuchassuperstructure,foundationmound,backfill,reclamationandsurchargecanbecalculatedbymultiplyingthemaximumvalueofcorrectedaccelerationαcobtainedfortheuntreatedgroundbythereductioncoefficient0.64,asshowninequation (4.5.9) 61).

(4.5.9)

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where kh1k :characteristic value of seismic coefficient for verification of superstructure and structural

elements of improved subsoil system such as superstructure, foundation mound, backfill,reclamationandsurcharge

Da :allowabledeformation(cm) Dr :standarddeformation(=10cm) αc :maximumvalueofcorrectedacceleration(cm/s2) g :gravitationalacceleration(=980cm/s2)

This reductioncoefficientwasobtainedbasedon the resultsofa2-dimensionalnonlineareffective stressanalysis for untreated soil and improved subsoil. For details, Reference 61) can be used as a reference. Incalculatingthemaximumvalueofcorrectedaccelerationαcforuntreatedsoil,Chapter 5, 2.2.2 (1) S e i s m i c coefficient for verification used in verification of damage due to sliding and overturning of wall body and insufficient bearing capacity of foundation ground in variable situations in respect of Level 1 earthquake ground motion canbeusedasareference. Thecharacteristicvalueoftheseismiccoefficientforverificationofimprovedsubsoilkh2kcanbecalculatedbymultiplyingtheseismiccoefficientforverificationkh1kobtainedusingequation (4.5.9)bythereductioncoefficient0.65(kh2k=0.65xkh1k). Provided, however, that in the characteristic value of the seismic coefficient for verification kh3k used incalculations of the earth pressure during earthquakes for improved subsoil systems, in equation (4.5.9), themaximumvalueofcorrectedaccelerationshallnotbemultipliedbyareductioncoefficient.

L.W.L. R.W.L.

T

H

HW

C

P

C

P

tt

1

2

P

4

H6

55

W6

4

W

W8H8

H9 W9Pah

w

ua

pv

up * In case of wall-type improvement

dw

W1

H7

W7

H1

W2

H2

H3 W3

Untreated part

Stabilized part

<Vertical component><Vertical component>

Pph

Passive earth pressurePp

Pav

<Horizontal component><Horizontal component>

<Verticalcomponent><Verticalcomponent>

<Horizontalcomponent><Horizontalcomponent>

Waterpressure

Active earthpressure

Pa

Subgrade reaction

R* Block-type, wall-type (depend on slip pattern)

Fig. 4.5.6 External Forces Acting on Stabilized Body

Pa :resultantearthpressureperunitoflengthactingonverticalplaneofactiveside(kN/m) Pah :horizontalcomponentofresultantearthpressureperunitoflengthactingonverticalplaneof

activeside(kN/m) Pav :vertical componentof resultant earthpressureperunitof lengthactingonverticalplaneof

activeside(kN/m) Pp :resultantearthpressureperunitoflengthactingonverticalplaneofpassiveside(kN/m) Pph :horizontalcomponentofresultantearthpressureperunitoflengthactingonverticalplaneof

passiveside(kN/m) Ppv :vertical componentof resultant earthpressureperunitof lengthactingonverticalplaneof

passiveside(kN/m) Pw :resultantresidualwaterpressureperunitoflength(kN/m) Pdw :resultantdynamicwaterpressureperunitoflength(kN/m)

W1-W9 :weightperunitoflengthofeachpart(kN/m) H1-H9 :inertiaforceperunitoflengthofeachpart(kN/m)


–505–

Cua :resultantadhesionofverticalplaneperunitof lengthactingonverticalplaneofactiveside(kN/m)

Cup :resultantadhesionofverticalplaneperunitoflengthactingonverticalplaneofpassiveside(kN/m)

R :shearresistanceperunitoflengthactingonbottomofimprovedsubsoil(kN/m) T :resultantofsubgradereactionperunitoflengthactingonthebottomofimprovedsoil(kN/m) t1,t2 :intensityofsubgradereactionattoesofstabilizedbody(kN/m)

Intheperformanceverificationofactionsduringgroundmotionofstratawhicharesubjecttoliquefaction,itisnecessarytoconsiderthedynamicwaterpressureduringtheactionofgroundmotionontheimprovedbody.Forcalculationofdynamicwaterpressure,Part II, Chapter 5, 2 Water Pressurecanbeusedasareference.

4.5.4 Performance Verification

[1] External Stability of Improved Subsoil

Fortheexternalstabilityofimprovedsubsoil,thefollowingitemsshallbeexamined,assumingthatthestabilizedbodyandthesuperstructurebehaveintegrally.Itshouldbenotedthatthefollowingdescribesthecasesofgravity-typerevetmentsandquaywalls;however,thesamedescriptioncanalsobeappliedtobreakwatersbyappropriatelysettingactionsduetowavesandotherrelevantfactors.

(1)ExaminationofSliding61)

① Theimprovedsubsoilshallsecuretherequiredstabilityagainstslipfailure.

② Itisnecessarytoconductperformanceverificationofimprovedsubsoilbywall-typeimprovementfortwocases,namely, theslippattern1casewhichconsiders thefrictionalresistanceofthebottomoftheimprovedsubsoilasawholeasresistancetoslipfailure,andtheslippattern2casewhichconsiderstheresultantofthefrictionalresistancedirectlyunderthelongwallsandtheshearingresistanceoftheunimprovedsubsoilbetweenthewalls,consideringtheimprovedgroundtobeastructureinwhichthestabilizedsubsoillongwallsfullydemonstratesshearstrength.Intheexaminationofthestabilityagainstslipfailure,equation (4.5.10)canbeused.Thesymbolγintheequationisthepartialfactorforitssubscript,andthesubscriptskandddenotethecharacteristicvalueanddesignvalue,respectively.

(Slippattern1)

(Slippattern2)

(4.5.10)Provided,however,that

where R1 :frictionalresistanceofbearinggroundperunitoflengthactingonbottomofstabilizedbody

(kN/m) R2 :frictional resistanceofbearinggroundperunitof lengthactingonbottomofuntreatedsoil

(kN/m)

–506–


R3 :shearingresistanceperunitoflengthactingonbottomofuntreatedsoil(kN/m) Pw :resultantofresidualwaterpressureperunitoflength(kN/m) Pdw :resultantofdynamicwaterpressureduringearthquakeperunitoflength(kN/m) Hi :inertiaforceperunitoflengthactingonrespectiveparts(kN/m) Wi :weightperunitoflengthofsurcharge,superstructure,foundationmound,backfill,reclamation

onimprovedsubsoilcomprisingimprovedsubsoilsystem(kN/m) Ws :weightperunitoflengthofstabilizedbody(kN/m) W9 :weightperunitoflengthofuntreatedsoilbetweenlongwalls(kN/m) B :improvedwidthofstabilizedbody(m) Rl :ratiooflongwallinstabilizedbody Rs :ratioofshortwallinstabilizedbody μ :staticfrictioncoefficient Cu :shearstrengthofbottomofuntreatedsoil(kN/m2) Pah :horizontalcomponentofresultantearthpressureperunitoflengthactingonverticalplaneof

activeside(kN/m) Pav :vertical componentof resultant earthpressureperunitof lengthactingonverticalplaneof

activeside(kN/m) Pph :horizontalcomponentofresultantearthpressureperunitoflengthactingonverticalplaneof

passiveside(kN/m) Ppv :vertical componentof resultant earthpressureperunitof lengthactingonverticalplaneof

passiveside(kN/m) Cua :resultantadhesionofverticalplaneperunitof lengthactingonverticalplaneofactiveside

(kN/m) Cup :resultantadhesionofverticalplaneperunitoflengthactingonverticalplaneofpassiveside

(kN/m) ρwg :unitweightofseawater(kN/m3) RWL :residualwaterlevel(m) WL :waterlevelatfrontside(m) hL :waterdepthatbottomofstabilizedbody(m) h1 :waterdepthatfrontsideofstructure(m) kh1 :seismic coefficient for verification when calculating inertia force acting on surcharge,

superstructure, foundationmound,backfillandreclamationon improvedsubsoilcomprisingimprovedsubsoilsystem(kN/m)

kh2 :seismiccoefficientforverificationwhencalculatinginertiaforceactingonimprovedsubsoil kh3 :seismiccoefficientforverificationwhencalculatingearthpressureanddynamicwaterpressure

actingonimprovedsubsoilsystem Wni :weightperunitoflengthofsurcharge,superstructure,mainbody,foundationmound,backfill

andreclamationonimprovedsubsoilcomprisingimprovedsubsoilsystem.Ifsubmerged,theweightinairwhensaturatedwithwatershallbeused.(kN/m)

Wn8 :weightperunitoflengthofstabilizedbody.Ifsubmerged,theweightinairwhensaturatedwithwatershallbeused.(kN/m)

Wn9 :weightperunitoflengthofuntreatedsoilbetweenlongwalls.Ifsubmerged,theweightinairwhensaturatedwithwatershallbeused.(kN/m)

γi :structuralfactor,generallybeassumedtobe1.0 γa :structuralanalysisfactor,generallybeassumedtobe1.0

③ Thesystemreliability indexβT is setdependingon the individual facilitiesand improvedsubsoil. Incaseswheresoilimprovementiscarriedoutbythedeepmixingmethod,thesystemreliabilityindexβTforslidingandoverturningofthewallbody,failureduetoinsufficientbearingcapacityofthefoundationgroundofgravity-typequaywalls,failureduetotoepressure,verticalshearfailureofthelongwallpart,verticalshearfailureoftheshortwallpartandfailureduetoextrusionofuntreatedsubsoilbetweenthtelongwallswas2.9(failureprobabilityof2.1x10–3)forthePermanentsituation.Thiswastheresultofassessment,byreliabilitytheory,oftheaveragesafetylevelofgravity-typequaywallsforsoilimprovementbythedeepmixingmethodintheconventionaldesignmethod.Intheperformanceverificationdescribedhere,thetargetreliabilityindexofβT '=3.0foreachlimitstateissetsoastoexceedthesystemreliabilityindex.ThepartialfactorsdeterminedonthisbasisareasshowninTable 4.5.1throughTable 4.5.6.Forpartialfactorsforuseintheexaminationofslipfailureofimprovedsubsoil,thevaluesshowninTable 4.5.1maybeused.Forpartialfactorswhicharenotlistedinthetable,1.00maybeused.


–507–

Table 4.5.1 Standard Values of Partial Factors for Use in Examination of Slip Failure(a) Permanent situation

AllfacilitiesTargetreliabilityindexβT 2.9

TargetsystemfailureprobabilityPfT 2.1×10–3

Reliabilityindexβusedincalculationofγ 3.0γ α µ/Xk V

Slippattern1 γW1-γW9 Weight 1.00 0.131 1.00 0.03γPah Horizontalresultantofactiveearthpressure 1.15 –0.519 1.00 0.10γPav Verticalresultantofactiveearthpressure 1.00 0.000 1.00 –γPph Horizontalresultantofpassiveearth

pressure0.90 0.277 1.00 0.10

γPpv Verticalresultantofpassiveearthpressure 1.00 0.000 1.00 –γCua Adhesionofverticalplane(activeside) 1.00 0.000 1.00 –γCup Adhesionofverticalplane(passiveside) 1.00 0.000 1.00 –γµ Staticfrictioncoefficient 0.70 1.000 1.00 0.10γa Structuralanalysisfactor 1.00 – – –

Slippattern2 γW1-γW9 Weight 1.00 0.000 1.00 –γPah Horizontalresultantofactiveearthpressure 1.15 –0.461 1.00 0.10γPav Verticalresultantofactiveearthpressure 1.00 0.000 1.00 –γPph Horizontalresultantofpassiveearth

pressure0.85 0.454 1.00 0.10

γPpv Verticalresultantofpassiveearthpressure 1.00 0.000 1.00 –γCua Adhesionofverticalplane(activeside) 1.00 0.000 1.00 –γCup Adhesionofverticalplane(passiveside) 1.00 0.000 1.00 –γµ Staticfrictioncoefficient 0.75 0.831 1.00 0.10γcu Shearstrengthofbottomofunimproved

subsoil0.80 0.202 1.00 0.33

γa Structuralanalysisfactor 1.00 – – –

–508–


(b) Variable situations in respect of Level 1 earthquake ground motion

AllfacilitiesPerformancerequirement Serviceability

γ α µ/Xk VSlippattern1 γW1-γW9 Weight 1.00 – – –

γPah Horizontalresultantofactiveearthpressure 1.00 – – –γPav Verticalresultantofactiveearthpressure 1.00 – – –γPph Horizontalresultantofpassiveearth

pressure1.00 – – –

γPpv Verticalresultantofpassiveearthpressure 1.00 – – –γCua Adhesionofverticalplane(activeside) 1.00 – – –γCup Adhesionofverticalplane(passiveside) 1.00 – – –γµ Staticfrictioncoefficient 1.00 – – –γa Structuralanalysisfactor 1.00 – – –

Slippattern2 γW1-γW9 Weight 1.00 – – –γPah Horizontalresultantofactiveearthpressure 1.00 – – –γPav Verticalresultantofactiveearthpressure 1.00 – – –γPph Horizontalresultantofpassiveearth


γPpv Verticalresultantofpassiveearthpressure 1.00 – – –γCua Adhesionofverticalplane(activeside) 1.00 – – –γCup Adhesionofverticalplane(passiveside) 1.00 – – –γµ Staticfrictioncoefficient 1.00 – – –γcu Shearstrengthofbottomofunimproved

subsoil1.00 – – –


(2)ExaminationofOverturning61)

① Itisnecessarythatimprovedsubsoilsecuretherequiredstabilityagainstoverturning.Intheexaminationofthestabilityagainstoverturningofimprovedsubsoilbywall-typeimprovement,equation (4.5.11)andequation (4.5.12)canbeused.Intheseequations,thesymbolγisthepartialfactorforitssubscript,andthesubscriptskandddenotethecharacteristicvalueanddesignvalue,respectively.

(a) Permanentsituation

(4.5.11)

(b)VariablesituationsinrespectofLevel1earthquakegroundmotion

(4.5.12)Provided,however,that


–509–

whereItemsrelatedtoresistance

Pph :horizontalcomponentofresultantofearthpressureperunitoflengthactingonverticalplaneofpassiveside(kN/m)

Wi :weight per unit of length of surcharge, superstructure, foundation rubble, backfill andreclamationonimprovedsubsoilcomprisingimprovedsubsoilsystem(kN/m)

W8 :weightperunitoflengthofstabilizedbody(kN/m) W9 :weightperunitoflengthofuntreatedsoilbetweenlongwalls(kN/m) Pav :verticalcomponentofresultantofearthpressureperunitoflengthactingonverticalplaneof

activeside(kN/m) Cua :adhesionofverticalsideperunitoflengthactingonverticalplaneofactiveside(kN/m)

Itemsrelatedtoloads Pw :residualwaterpressureperunitoflengthactingonverticalplaneofactiveside(kN/m) Pah :horizontalcomponentofresultantofearthpressureperunitoflengthactingonverticalplaneof

activeside(kN/m) Hi :inertiaforceperunitoflengthactingonrespectivepartsofimprovedsubsoilsystem(kN/m) Wni :weight per unit of length of surcharge, superstructure, foundation mound, backfill and

reclamation on improved subsoil comprising improved subsoil system. If submerged, theweightinairwhensaturatedwithwatershallbeused.(kN/m)

Wn8 :weightperunitoflengthofstabilizedbody.Ifsubmerged,theweightinairwhensaturatedwithwatershallbeused.(kN/m)

Wn9 :weightperunitoflengthofuntreatedsoilbetweenlongwalls.Ifsubmerged,theweightinairwhensaturatedwithwatershallbeused.(kN/m)

kh1 :seismic coefficient for verification when calculating inertia force acting on surcharge,superstructure,foundationmound,backfill,back–pluggingandsurchargeonimprovedsubsoilcomprisingimprovedsubsoilsystem

kh2 :seismiccoefficientforverificationwhencalculatinginertiaforceactingonimprovedsubsoil kh3 :seismiccoefficientforverificationwhencalculatingearthpressureandactivewaterpressure

actingonimprovedsubsoil Pdw :dynamicwaterpressureperunitoflengthactingonverticalplaneofactiveside(kN/m)

xi,xav,xcua:distancefromactionlineofverticalforceactingonimprovedsubsoiltofronttoeofstabilized body(m)

γi,γp, γw, γdw :heightfromactionlineofhorizontalforceactingonimprovedsubsoiltobottomofstabilized body(m) γi :structuralfactor,generallybeassumedtobe1.0 γa :structuralanalysisfactor(see Table 4.5.2)

② Forpartialfactorsforuseintheexaminationofoverturningofimprovedsubsoil,thevaluesshowninTable 4.5.2maybeused.Forpartialfactorsnotlistedinthetable,1.00maybeused.

–510–


Table 4.5.2 Standard Values of Partial Factors for Use in Examination of Overturning (a) Permanent situation




Overturning γPph Horizontalresultantofpassiveearthpressure

0.85 0.382 1.00 0.10

γW6 Weight(foundationmound) 1.00 0.030 1.00 0.03γW7 Weight(backfillsoil) 1.00 0.055 1.00 0.03γW8 Weight(stabilizedbody) 1.00 0.102 1.00 0.03γW9 Weight(untreatedsoil) 1.00 0.074 1.00 0.03γCua Adhesionofverticalplane(stabilizedbody

part:activeside)1.00 0.102 1.00 0.10

γPah Horizontalresultantofactiveearthpressure 1.25 –0.882 1.00 0.10γPav Verticalresultantofactiveearthpressure 1.00 0.029 1.00 0.10γa Structuralanalysisfactor 1.00 – – –



γ α µ/Xk VOverturning γPph Horizontalresultantofpassiveearth


γW6 Weight(foundationmound) 1.00 – – –γW7 Weight(backfillsoil) 1.00 – – –γW8 Weight(stabilizedbody) 1.00 – – –γW9 Weight(untreatedsoil) 1.00 – – –γCua Adhesionofverticalplane(stabilizedbody

part:activeside)1.00 – – –

γPah Horizontalresultantofactiveearthpressure 1.00 – – –γPav Verticalresultantofactiveearthpressure 1.00 – – –γa Structuralanalysisfactor 1.10 – – –

(3)ExaminationofBearingCapacity61)

① Improvedsubsoilshallsecuretherequiredstabilityagainstfailureofbearingcapacityoftheoriginalgroundunderthebottomoftheimprovedsubsoil.Intheexaminationofthebearingcapacityofblock-typeimprovedsubsoil,2.2 Shallow Spread Foundationscanbeusedasareference.

② For thebearing capacityof improved subsoil bywall-type improvementwhen thebearingground is sandyground,verificationcanbeperformedusingequation(4.5.13) fortoepressurest1andt2,consideringtheeffectofmutualinterferencebetweenthelongwalls.Inthisequation,thesymbolγisthepartialfactorforitssubscript,andthesubscriptskandddenotethecharacteristicvalueanddesignvalue,respectively.

Inthecaseof (4.5.13)inthecaseof

where


–511–

γR :partialfactorforbearingcapacityofsandyground(see2.2.2 Bearing Capacity of Foundations on Sandy Ground)

Nq,Nr:bearingcapacitycoefficients(see2.2.2 Bearing Capacity of Foundations on Sandy Ground) p0 :effectiveoverburdenpressuretobearingsandlayer(kN/m2) ρg :unitweightofbearingground,whensubmerged,unitweightinwater(kN/m3)

Ll :lengthoflongwallindirectionoffaceline(m)(seeFig. 4.5.9) Ls :lengthofshortwallindirectionoffaceline(m)(seeFig. 4.5.9) B :improvementwidth(m)(seeFig. 4.5.9)

[2] Examination of Internal Stability

(1)Forthecharacteristicvalueofthematerialstrengthofthestabilizedbody,4.5.2 Assumption of Dimensions of Stabilized Body canbeusedasareference.

(2)Thestressgeneratedinthestabilizedbodycanbeobtainedbyassumingthatthestabilizedbodyisanelasticbodyundertheconditionsspecifiedin4.5.3 Conditions of Actions on Stabilized Body.

(3)In block-type improved subsoil and improved subsoil by wall-type improvement, internal stability can beexaminedbythemethodpresentedbelow.Provided,however,thatincaseswheretheshapeofthestabilizedbodyiscomplexorthedepthofthestabilizedbodyislargeincomparisonwithitswidth,examinationbyFEManalysisispreferable.

(4)ExaminationofToePressure61)

① Examinationof internal stabilitydue to toepressureat thebottomof thestabilizedbodycanbeperformedusingequation(4.5.14),consideringtheeffectoftheconfiningpressureactingontheimprovedsubsoil.Inthisequation,thesymbolγisthepartialfactorforitssubscript,andthesubscriptskandddenotethecharacteristicvalueanddesignvalue,respectively.

(4.5.14)

where fc :designcompressivestrength(kN/m2) t1, 2 :toepressures(kN/m2) K :coefficientofearthpressure wi :unitweightofuntreatedsoil,whensubmerged,unitweightinwater(kN/m3) hi :layerthicknessofuntreatedsubsoil(m) γi :structuralfactor,generallybeassumedtobe1.0 γa :structuralanalysisfactor,generallybeassumedtobe1.0

Thedesignvaluesintheequationcanbeobtainedusingthefollowingequations.

Provided,however,thatitisnecessarytodeterminethevalueoftheconfiningpressureKΣ(widhi)actingonthebottomedgeofthestabilizedbodyfromtheuntreatedsubsoilconsideringtheimprovementpatternandexternalstabilityoftheimprovedsubsoil.

② Forthepartialfactorsforuseinexaminationoftoepressure,thevaluesshowninTable 4.5.3maybeused.Forpartialfactorsnotlistedinthetable,1.00maybeused.

–512–


Table 4.5.3 Standard Values of Partial Factors for Use in Examination of Toe Pressure

(a) Permanent situation




Toepressure γquc Standarddesignstrength 0.55 – – –γt1,2 Toepressure 1.05 –0.116 1.00 0.03γwi Unitweightofuntreatedsoil 1.00 0.001 1.00 0.03γa Structuralanalysisfactor 1.00 – – –



γ α µ/Xk VToepressure γquc Standarddesignstrength 0.67 – – –

γt1,2 Toepressure 1.00 – – –

γwi Unitweightofuntreatedsoil 1.00 – – –γa Structuralanalysisfactor 1.00 – – –

(5)ExaminationofShearingStressatVerticalPlaneUnderFaceLineofSuperstructure61)

① Examinationofinternalstabilityagainstshearingstressalongtheverticalplanebeneaththefacelineofthesuperstructurecanbeperformedforthelongwallpartandshortwallpartusingequation (4.5.15)andequation (4.5.16),respectively.Intheseequations,thesymbolγisthepartialfactorforitssubscript,andthesubscriptskandddenotethecharacteristicvalueanddesignvalue,respectively.

(a) Longwall

(4.5.15)where

α :factorforeffectivecross-sectionalarea β :reliabilityindexofoverlapbetweenimprovedpiles Tl :resultantofsubgradereactionactingfromfronttoeofimprovedsubsoiltopositionofBl(kN)

(Tld=γTTl) quc :standarddesignstrength(kN/m2)(qucd = γqucquck) Wl :effectiveweightofstabilizedbodyfromfronttoeofimprovedsubsoiltopositionofBl(kN)(Wld

=γwWl) A :cross-sectionalareaofstabilizedbody,incaseoflongwallA=DlLl +DsLs(m2)(seeFig. 7.5.7)

Dl,Ds :verticallengthoflongwall,namelyimproveddepth,andverticallengthofshortwall(m)Ll,Ls :lengthsoflongwallandshortwallindirectionoffaceline,respectively(m) γi :structuralfactor,generallybeassumedtobe1.0 γa :structuralanalysisfactor,generallybeassumedtobe1.0

Whena rubblemoundexistsbetween the stabilizedbodyand the superstructure, examinationmaybeperformedusinganexaminationplanewhichconsidersloaddispersioninthemoundfromthepositionofthefacelineofthesuperstructure.(SeeFig. 4.5.7;θistheangleofloaddispersioninthemound.)


–513–

B

D

DD

θsA

LsT

B

W

L

Fig. 4.5.7 Schematic Diagram of Vertical Shear Stress (Long Wall)

Forthepartialfactorsforuseintheexaminationofverticalshearfailureofthelongwallpart,thevaluesshowninTable 4.5.4canbeused.Forpartialfactorswhicharenotlistedinthetable,1.00maybeused.

Table 4.5.4 Standard Values of Partial Factors for Use in Examination of Vertical Shear Failure of Long Wall





Verticalshearfailureoflongwall

γquc Standarddesignstrength 0.55 – – –γT Resultantofsubgradereaction 1.05 –0.115 1.00 0.03γW Effectiveweightofstabilizedbody 1.00 0.005 1.00 0.03γa Structuralanalysisfactor 1.00 – – –



γ α µ/Xk VVerticalshearfailureoflongwall

γquc Standarddesignstrength 0.67 – – –γT Resultantofsubgradereaction 1.00 – – –γWℓ Effectiveweightofstabilizedbody 1.00 – – –γa Structuralanalysisfactor 1.00 – – –

(b)Shortwall

(4.5.16)where

α : factorforeffectivecross-sectionalareaβ : reliabilityindexofoverlapbetweenimprovedpilesTl’: toepressureafterdispersioninmound,notincludingself–weightofmound(kN/m2)(Tl’d=γT lT’l’k) (seeFig. 4.5.8)(kN)

–514–


quc :standarddesignstrength(kN/m2)(qucd = γqucquck) wm :unitweightofmound,whensubmerged,unitweightinwater(kN/m3) hm :thicknessofmound(m) Wl :effectiveweightofstabilizedbody,whensubmerged,unitweightinwater(kN/m3) Ds :verticallengthofshortwall(m) Ls :lengthofshortwallindirectionoffaceline(m) γi :structuralfactor,generallybeassumedtobe1.0 γa :structuralanalysisfactor,generallybeassumedtobe1.0

Fig. 4.5.8 Schematic Diagram of Calculation of Vertical Shear Stress (Short Wall)

Forthepartialfactorsforuseinexaminationofverticalshearfailureoftheshortwall,thevaluesshowninTable 4.5.5canbeused.Forpartialfactorswhicharenotlistedinthetable,1.00maybeused.

Table 4.5.5 Standard Values of Partial Factors for Use in Examination of Vertical Shear Failure of Short Wall





Verticalshearfailureofshortwall

γquc Standarddesignstrength 0.55 – – –γT1' Toepressure 1.05 –0.091 1.00 0.03γwi Unitweightofstabilizedbody 1.00 –0.006 1.00 0.03γwm Unitweightofmound 1.00 –0.006 1.00 0.03γa Structuralanalysisfactor 1.00 – – –



γ α µ/Xk VVerticalshearfailureofshortwall

γquc Standarddesignstrength 0.67 – – –γT1' Toepressure 1.00 – – –γwi Unitweightofstabilizedbody 1.00 – – –γwm Unitweightofmound 1.00 – – –γa Structuralanalysisfactor 1.00 – – –


–515–

(6)ExaminationofExtrusion61)

① Becauseimprovedsubsoilbywall-typeimprovementcomprisesalargenumberoflongwallsandashortwallconnecting the longwalls,untreatedsubsoil is leftbetween the longwalls. Failures inwhich theuntreatedsubsoil between the longwalls is dislodged are conceivable, depending on conditions such as the spacingbetweenthelongwalls,thestrengthoftheuntreatedsubsoil,thethicknessofthebackfilllayer.Therefore,itisnecessarytoexamineextrusionoftheuntreatedsoilbetweenthelongwalls.71)

② Aschematicdiagramofextrusionoftheuntreatedsoilinimprovedsubsoilbywall-typeimprovementisshowninFig. 4.5.9.

Fig. 4.5.9 Schematic Diagram of Extrusion of Untreated Subsoil

③ Examinationofextrusionofuntreatedsubsoilbetweenlongwallscanbeperformedbyrepeatedcalculationsusingequation(4.5.17),usingvariousvaluesofDiinthecalculations.

(4.5.17)where

Ls :lengthofshortwallindirectionoffaceline(m) Di :depthfrombottomedgeofshortwalltocross–sectionbeingexamined(m) Cu :averageshearstrengthofuntreatedsubsoilatintermediatedepthbetweenbottomedgeofshort

wallandcrosssectionbeingexamined(kN/m2)(C=γcuCuk) B :improvedwidth(m)

Pah’,Pph’:horizontalcomponentsofresultantofactiveearthpressureandpassiveearthpressureactingonuntreatedsubsoilbetweenlongwalls,respectively,downtothedepthofDifrombottomofshortwall(kN)(Pph’d=γPphPph’d,Pah’d =γPahPah’k)

kh2 :seismiccoefficientforverificationwhencalculatinginertiaforceactingonimprovedsubsoil(kh2d=γkh2kh2k)

hw :headbetweenresidualwaterlevelandwaterlevelatfrontofstructure(m)(hwd=γhwhwk) wi :unitweightinairofuntreatedsubsoilwhensaturatedwithwater(kN/m3)ρwg :unitweightofseawater(kN/m3) γi :structuralfactor,generallyassumedtobe1.0 γa :structuralanalysisfactor,generallyassumedtobe1.0

–516–


④ Forthepartialfactorsforuseintheexaminationoftheextrusionoftheuntreatedsubsoilbetweenlongwalls,thevaluesshowninTable 4.5.6canbeused.Forpartialfactorswhicharenotlistedinthetable,1.00maybeused.

Table 4.5.6 Standard Values of Partial Factors for Use in Examination of Extrusion(a) Permanent situation




Extrusionfailure

γCu Averageshearstrengthofuntreatedsoil 0.75 0.955 1.00 0.10γPah' Horizontalcomponentofresultantofactive

earthpressureactingonuntreatedsoilbetweenlongwalls

1.05 –0.190 1.00 0.10

γPph' Horizontalcomponentofresultantofpassiveearthpressureactingonuntreatedsoilbetweenlongwalls

0.95 0.182 1.00 0.10

γwi Unitweightinairofuntreatedsoilwhensaturatedwithwater

1.00 0.000 1.00 0.10


* Thepartialfactorsforuseinexaminationofextrusionweredeterminedbyreliabilityanalysisoftheexaminationposition(Di)atwhichthereliabilityindexβshowsitsminimumvalue.



γ α µ/Xk VExtrusionfailure

γCu Averageshearstrengthofuntreatedsoil 1.00 – – –γPah' Horizontalcomponentofresultantofactive

earthpressureactingonuntreatedsoilbetweenlongwalls

1.00 – – –

γPph' Horizontalcomponentofresultantofpassiveearthpressureactingonuntreatedsoilbetweenlongwalls

1.00 – – –

γwi Unitweightinairofuntreatedsoilwhensaturatedwithwater

1.00 – – –


* Thepartialfactorsforuseinexaminationofextrusionweredeterminedbyreliabilityanalysisoftheexaminationposition(Di)atwhichthereliabilityindexβshowsitsminimumvalue.

(7)ExaminationofCircularSlipFailure

① Intheexaminationofthecircularslipfailure,3 Stability of Slopescanbeusedasareference.

② Becausethestrengthofthestabilizedbodyissufficientlygreaterthanthatofordinarysoil,examinationofslipcirclespassingthroughthestabilizedbodymaybeomitted.

(8)ExaminationofDisplacement

①Whentheimprovedsubsoilisofthefloatingtype,lateraldisplacementduetoactionsinrespectofreclamationand waves and actions in respect of ground motion, and vertical displacement due to consolidation areconceivable.Therefore,advanceexaminationonmeasurescapableofsatisfyingtheperformancerequirementsofthefacilitiesisnecessary,basedonestimationsofthesedisplacements.

② Inslidingfailureandcircularslipfailureofimprovedsubsoil,thereisacertaindegreeofrelationshipbetweentheratioofthedesignvalueofresistanceanddesignvalueoftheeffectsofactions,andtheamountofimmediatedisplacementduetolateraldisplacementofthestabilizedbody.Therefore,itispossibletojudgethenecessityofexaminationoflateraldisplacementofthestabilizedbodydependingonthesafetymargininthesefactors.Furthermore,whenthelayerthicknessoftheuntreatedsubsoilunderneaththestabilizedbodyisconstant,and


–517–

itisjudgedthattheestimateddisplacementinthehorizontaldirectioncansatisfytheperformancerequirementsofthefacilities,theexaminationoftheconsolidationsettlementisonlynecessary.

③ Even inbottom seated-type improved subsoil,when a cohesive soil layer exists under thebearing stratum,the examination of the amount of consolidation settlement is necessary, as there is a possibility of verticaldisplacementofthestabilizedbodyduetoconsolidationsettlement.

④ It is preferable to determine the allowable displacement of improved subsoil appropriately, considering theperformancerequirementsofthefacilities.

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