水平偏心受荷群桩群桩效应的广义p乘子经验算法

水平偏心受荷群桩群桩效应的广义p乘子经验算法

1pole-soel-pilein回采后,清理剂为自溶液coel-lahens,性别干部可培养清真人内皮细胞的非全日制预算是由预算削减而非全日制预算削减的。whereβThepurposeofthisstudyistodevelopnewp-multipliersforgroupeffectinpilegroupssubjectedtoeccentriclateralloading.Thenewlydevelopedp-multipliersarecalledgeneralizedp-multipliersinordertodifferentiatefromthoseforpilegroupsunderlateralloading.Inthispaper,tostudypile-soil-pileinteractionduetohorizontalmotionsoftwoindividualpilesinapilegroupsubjectedtoeccentriclateralloading,themotionfeatureoftwo-pilegroupssubjectedtoeccentriclateralloadingisanalyzedindetail.Then,centrifugemodeltests,numericalanalysis,andanewlydevelopedsoilfailuremodelonpile-soil-pileinteractionbetweentwopilesareintroduced.Finally,empiricalequationsforreductionfactorsandaprocedureareproposedtocalculatep-multiplierofeachpileinapilegroupundereccentriclateralloading.Datafromreportedmodelpilegrouptestsareusedtoverifytheaccuracyoftheproposedapproach.2内皮拉赫病例的皮埃罗夫2.1清三单.4insi供热体可靠性模型Forapilegroupundereccentriclateralloading,ifitscapisstiffenoughtobeconsideredasrigidandtheoverturninganglesofthepilecapintwohorizontaldirectionsarenegligible,themotionofthepilecapisconsideredasaplanemotionofarigidbody.Thus,thereexistsatwistcenterinthemotionplaneofthecapatanytime,calledtheinstantaneouscenter,andthedirectionoftheinstantaneousvelocityofapointinthecapisperpendiculartotheconnectionlinebetweenthepointandtheinstantaneouscenter.Fig.1illustratesthemotionofapileinapilegroupsubjectedtoalateralloadwithaneccentricity.Assumethattheinstantaneouscenterofthepilegroupisunchangedunderthegivenloading.Thepilerotatesfromtheinitialpositionthroughanangleδtothefinalposition.Thepiledisplacementissandtheinstantaneousvelocityofthepileattheinitialpositionisv.Theanglebetweensandvishalfoftherotationangleδ.Ifδissmall,thedirectionofscanbeapproximatedtothatofv.Infact,thetestsconductedby2.2entwellsofaafigSincebothpilegroupconfigurationandappliedforcestransferredtopilegroupsbyeccentriclateralloadingarearbitrary,theinstantaneouscentersofthepilegroupscouldbeanywhereintheplaneofthepilecaps.Providedthatatwo-pilegroupsubjectedtoeccentriclateralloadingrotatesclockwiseaboutaninstantaneouscenter,asshowninFig.2,theplanethattheinstantaneouscenterlocates,isdividedintosixsectionsbyaa′,bb′,andcc′.AnarrowatapilecenterinFig.2representsthevectorofinstantaneousvelocityofthepile.Astheinstantaneouscenterisinthesectionsbetweenbb′andcc′(e.g.pointsAandB),thetwopilesmovetodifferentsidesofaa′(Fig.2);whilethetwopilesmovetothesamesideofaa′iftheinstantaneouscenterisintheleftsideofbb′ortherightsideofcc′(e.g.pointsA′andB′).Astheinstantaneouscenterislocatedatbb′orcc′,oneofthetwopilesmovesparalleltoaa′orhasnomotion,whileanothercanmovetoeithersideofaa′accordingtothepositionoftheinstantaneouscenter.Whendrawingbothvectorsinax-ycoordinatesystem,wherethexaxisisparalleltoaa′,asshowninFig.2,thetwovectorsareeitherinthesamequadrantordistributeinthetwoadjacentquadrantssymmetricaboutthexaxis.Afeatureisthatboththecomponentvectorsoftheinstantaneousvelocitiesalongaa′areinthesamedirectionifbotharenon-zero.Iftherotationdirectionofthetwo-pilegroupisassumedanticlockwise,thesamefeaturecanbeobtainedthroughasimilaranalysis.TodescribethemotionsofthetwopilesshowninFig.2inaconvenientway,thetwopilesaredefinedasaleadingpileandatrailingpile.Takingthedirectionsofbothcomponentvectorsalongtheconnectionlinebetweenthetwopilesasareference,ifoneofthetwocomponentsalongtheconnectionlineisanon-zerovectorandpointstoapile,thepilepointedtoiscalledtheleadingpilewhiletheotherpileisthetrailingpile.Conversely,ifapileislocatedattheoppositedirectionofthenon-zerocomponentvector,thepileisthetrailingpile,andtheotheristheleadingpile.Ifthecomponentsofbothinstantaneousvelocitiesalongtheconnectionlinearezerovectors,thetwopilescanbedesignatedarbitrarily.TakingthetwopilesinFig.2asanexample,Pile1istheleadingpileandPile2isthetrailingpileastheirinstantaneouscenterisaboveaa′;conversely,Pile1becomesthetrailingpileandPile2istheleadingpileasthecenterisbelowaa′.Therefore,apileinapilegroupcouldbeboththeleadingpilerelativetoanadjacentpileandthetrailingpilerelativetoanother.Supposeηistheanglebetweenthemotiondirectionoftheleadingpileandthelineconnectingtheleadingpileandthetrailingpile,asshowninFig.3.Regardlessofitsrotationdirection,ηisdesignatedaspositiveandvariesintherangeof0°–90°.Defineθastheanglebetweenthemotiondirectionofthetrailingpileandtheconnectionline(Fig.3).ReferringtoFig.2,ifthevectorsoftheleadingpileandthetrailingpileareatthesamesideoftheconnectionline,θisdefinedaspositive;whileθisnegativeiftheyareatdifferentsides,sothevalueofθvariesbetween-90°and90°.Anyconditionofmotiondirectionsoftwopilesinapilegroupsubjectedtoeccentriclateralloadingcanberepresentedbyacombinationofηandθ.3co起源测试3.1驳岸相关概念分析Centrifugemodeltestswereperformedtoinvestigatepile-soil-pileinteractionsbetweentwopilessimultaneouslysubjectedtolateralloadsindifferentdirectionsintheZJU-400geotechnicalcentrifuge.Atestsystemwasdevelopedwhichincludedtwolateralloadingdevicesanddisplacementmeasurementdevices.Thesystemwasarrangedinalargerigidmodelcontainerwithinsidedimensionsof1.2m×0.95m×1.0m,asshowninFig.4.Alateralloadingdeviceincludedanelectricmotor,areductiongearbox,adirectioncontroller,anEntran-typeloadcell,anextensionbar,andaloadingring.Thedirectioncontrollerconnectedtheelectricmotorandthegearbox.Themotiondirectionoftheoutputshaftofthegearboxwasadjustablebymeansofthedirectioncontrollertoenablehorizontallyloadingamodelpileinadesireddirection.Thedirectioncontrollerwasfixedatthebottomofadoublebeamfixingframe,whichtransferredthehorizontalreactionforcestothecontainer(Fig.4a).Aloadcellwasusedtomeasuretheloadappliedonthemodelpilehead,andanaluminumbarwasusedtoconnecttheoutputshaftandtheloadcell.Thelengthofthebarwasadjustablesothattheloadingdevicecouldbeusedindifferentloadingcases.AsshowninFig.4b,aloadingringwithaninternaldiameterof15mmwasfixedinfrontoftheloadcell,andwascapableofhorizontallypushingorpullingamodelpilebasedonthetestrequirements.Tomounttheloadingringonamodelpile,themodelpilewasfirstpassedthroughtheloadingring,thentheextensionbarwasadjustedtohavetheinnersideoftheloadingringjusttouchtheoutsidesurfaceofthemodelpile.Twolateralloadingdeviceswereneededinatwo-piletest.Alasersensorwasusedtomeasurethepileheadhorizontaldisplacementofeachmodelpile.AsshowninFig.4b,analuminumplanefixedoneachloadingringwasutilizedasthelaserreflectivesurface;thedatameasuredfromthelasersensorrepresentedthelateraldisplacementofthepile.3.2dedlegregaceSevenmodelpilesweremadeusingaluminumtubes850mminlength,14mminoutsidediameter,and1.5mminwallthickness.Thepiletoeswerecirculartruncatedcones2mminbottomdiameterand7mminlength.Theembeddedlengthwas700mm.Themodelpilesweretestedat40gtosimulateprototypeconcretepileswithdimensions0.56by28mindiameterandembeddedlengthandflexuralstiffnessof203MN·mThesandexaminedcanbeclassifiedaspoorlygradedsandaccordingtotheunifiedsoilclassificationsystem,withaspecificgravityof2.633.Theparticle-sizediameterscorrespondingto10%,30%,and60%passingonthecumulativeparticle-sizedistributioncurveare0.11,0.14,and0.19mm,respectively.Thecriticalfrictionanglemeasuredbythesandpiletestis32°.Asingle-hoserainingmethodwasusedtopreparethesampleswithadepthof750mm(Kongand3.3astg/tg-3,soeldensityofficiensossofficienssolid标准Sixloadingcases,asshowninFig.5,wereselectedforthepresentstudy.Thespacingofthetwopilesinthesixcasesisthreetimesthepilediameter(3D).Thesixloadingcaseswereequallydividedintotwoloadingseriesbytwovaluesofη,0°and45°,respectively.Eighttwo-piletestswereconductedsuccessfully.Table1summarizestheeighttestsinthreetestgroups,denotedasTG-1,TG-2,andTG-3,basedontheloadingseriesandsoildensities.TG-1andTG-2wereconductedinsandwitharelativedensityof60%,whileTG-3wasinsandwitharelativedensityof45%.ThetwoloadingcasesinTG-2werethesameasthecorrespondingcasesinTG-3asacomparisontostudytheeffectofsoildensityonpile-soil-pileinteraction.Fig.4ashowsthetestconfigurationofTG-3(correspondingtotheloadingserieswithη=45°).Threetwo-pilegroupsandasinglepileweretestedinTG-3.ThesolidpointsinFig.4arepresentthepositionsofthemodelpilesandthearrowsindicatetheloadingdirections.Toavoidboundaryeffectsandsoildisturbance,thedistancesbetweenanytwotestspotsandbetweenthetestspotsandthecontainerboundarieswereatleast10timesthepilediameter(Craigand4通过meining反应表ABAQUSwasemployedtofurtherinvestigatetheinfluenceofηandθonpile-soil-pileinteractionsbetweentwopiles.Boththepileshaftsandthesoildomaininthenumericalmodelwererepresentedby3Dsolidelementswith8-nodelinearbrick,andameshrefinementwasperformedinthepositionswherehighlevelsofstrainwereexpectedtooccur.Asingle-pilemodelandadouble-pilemodelwerebuilttosimulatetheprototypepilesinthepresenttests.ThepileshaftswereassumedtobeelasticwithaYoung’smodulusof42GPaandaPoisson’sratioof0.33.ThesoilwasmodeledwithaMohr–Coulombconstitutivemodel.Thepeakfrictionangleofthemodelsandwastakenasthesoilfrictionangleinthemodel,whichwascalculatedbythefollowingempiricalcorrelationproposedbywhereφBesidesthesixloadingcasesinTable1,anothertenloadingconditions,θ=0°and90°inthecaseofη=45°,andθ=-75°,-30°,-15°,0°,15°,30°,60°,and90°inthecaseofη=90°,weresimulatedbythedevelopednumericalmodel.Soilparametersinthecaseofη=90°wereinaccordancewiththoseinTG-1.5pile使用—ExperimentalandnumericalresultsFig.5showstheload-displacementcurvesobtainedfromthemodeltests.ItisfoundthattheresistancesoftheleadingandtrailingpilesarelowerthanthatofthesinglepileinallloadingcasesexceptCase3(η=0°andθ=90°),whichdemonstratesthatthereexistsignificantpile-soil-pileinteractionsinallthecasesexceptCase3.InCase3,thecurvesoftheleadingandtrailingpilesalmostcoincidewiththatofthesinglepile(Fig.5c).Inaddition,thelateralresistanceofthetrailingpileissmallerthanthatofthecorrespondingleadingpileinallthecasesexceptCase3,whichimpliesthatthepilepositionalsoaffectsthepile-soil-pileinteractions.NumericalresultsarealsoshowninFig.5forcomparison.Mostofthenumericalcurvesmatchthecorrespondingtestdatawell.ThemostsignificantdifferencebetweenbothresultsisobservedinCase3.Thenumericalcurveoftheleadingpilematchesthetestcurvewell,butthatofthetrailingpileislowerthanthetestcurve.Itdemonstratesthatthenumericalmodelslightlyoverestimatedthesoilresponseinfrontofthetrailingpile,especiallyinthecaseswheresmallornopile-soil-pileinteractionexistsbetweenthetwopiles.Fig.6showsthereductionfactorsβobtainedfromtheexperimentalandnumericalcurvesinFig.5.LetβComparingTG-2insandwitharelativedensityof60%andTG-3insandwitharelativedensityof45%,bothβFig.4bshowsaphotographofsoilsurfacecollapsearoundtwomodelpiles.Thefailurezoneattheoppositesideoftheloadingdirectionbehindeachmodelpileformedanarchcontour.Thefailurezone,causedbystressrelaxationgeneratingactiveearthpressurealongthepileshaft(6项目interityTakingηandθastwoaxes,arectangularcoordinatesystemisformedbyηandθ,calledtheη-θplane.ThetestdatafromCase3indicatethatatleastaregionexistsontheη-θplane,wherenopile-soil-pileinteractionbetweentwopilesexists,soasoilfailuremodelwasdevelopedtofindtheboundarybetweentheregionswithandwithoutinteraction.Apassivewedge-typefailuremodelproposedbyBrownetal.(1988)isemployedtoillustratethefailurezonesinfrontofbothpiles,asshowninFig.7a.Forconvenienceandaconservativeview,thespreadingangleofthewedgeistakenastheinternalfrictionangleφalthoughitisprobablyrelatedtosoildensity(Reeseetal.,1974).Theactivefailurezonesbehindbothpilesareassumedtobe“U”shapewitharadiusR(Fig.7a).Itisassumedthatthepassivezoneofthetrailingpileoverlapswithbothofthefailurezonesoftheleadingpilebuttheactivezoneofthetrailingpileneveroverlapswithboth.Employingthedevelopedsoilfailuremodeltoanalyzetheoverlappingofthefailurezonesbetweentwopiles,threepossiblecriticalconditionsweredetermined(Fig.7).Intheregionof90°≥η≥0°and90°≥θ≥0°(theupperhalfoftheη-θplane),asshowninFig.7a,foragivenvalueofη,thecriticalconditionisthattheleftsideofthewedgefailurezoneofthetrailingpileisparalleltotherightsideofthewedgefailurezoneoftheleadingpile.ThecorrespondingvalueofθiscalledthecriticalangleanddenotedasθFigs.7band7cshowtwocriticalconditionsintherangeof90uf0b0≥η>0uf0b0and0uf0b0>θ≥-90uf0b0(thelowerhalfoftheη-θplane).Asη≥φ-ξ,whereξistheanglebetweenthelineconnectingthetwopilesandthecommontangentbetweenthetrailingpileandtheactivefailurezoneoftheleadingpile(Fig.7b),thecriticalconditionisthepositionwheretherightsideofthewedgezoneofthetrailingpiletouchestheedgeoftheactivefailurezoneoftheleadingpile,wherethecriticalangleisθReferringtoFig.7b,ξcanbecalculatedbywhereListhepilespacing.Ifassumingthesliplinesoftheactivefailurezonearestraight,theanglebetweenthesliplinesandverticaldirectionis45°-φ/2(ChengandwhereHisthedepthoftheactivefailurezone,which,asmentionedbefore,isapproximatelyequaltothewedgedepthofthepassivefailurezone.Reeseetal.(2006)plottedHvaryingwithφ.ItisfoundfromEq.(4)thatRisnotsensitivetoφ.Forinstance,Rincreasesfrom9.2Dto10.2Dasφincreasesfrom30°to45uf0b0.AspointedoutbyReeseetal.(2006),thesignificantdifferencebetweenthecalculatedresultandthetestdatamaycomefromtheelementarynatureofthemodelsusedinthecomputation;evenso,theequationservesausefulpurposeinindicatingtheformifnotthemagnitude.Acorrectioncoefficient0.16isintroducedintothefirstphaseinEq.(4),whichwasback-calculatedbasedontheobservedradiusoftheactivefailurezoneinthepresenttests.Fig.8alsoshowsvariationsofθIntheinterestingrangeofφfrom30°to45°,theradiusoftheactivefailurezoneRisaround1.5D.Ifthepilespacingislessthan3D,overlappingwilloccurbetweentheactivefailurezonescausedbytheleadingandtrailingpiles.TheanalysisinFig.7ignorestheoverlappingbetweentheactivefailurezones,sothedevelopedapproachissuitableforpilegroupswithpilespacingofapproximately3Dorlarger.Inaddition,themaximumpilespacingisthedistanceatwhichtheinteractionisignoredasthetwopilesareinanin-linearrangement.Rollinsetal.(2005)andAshourandArdalan(2011)summarizedthevariationsofp-multiplierwithpilespacingfromdifferentresearchersandagencies,whichindicatesthattheutmostpilespacingis8D.Conservatively,8Distakenasthemaximumpilespacing.Table2summarizestheequationsofθ7Calculationofp-multiplier7.1quara品牌形词AsshowninFig.6,bothβwhereaFig.9illustratesthevariationsofβwithηatθ=0°obtainedfromthemodeltests,numericalresults,andreferences.Functionsofquadraticparabolawereemployedtobestfitthedatapointsoftheleadingandtrailingpiles,whicharewhereabFig.6showsthecomparisonofthepredictedcurvesbytheproposedempiricalequationswiththepresentdatapoints.Thepredictedcurvesfitthedatapointsfairlywell.Particularly,thecurvesgiveanindicationofthecriticalanglesandthezoneswithandwithoutinteractions.7.2pileinde都以公物理论指导下的calciateGivenapilegroupwithnpilessubjectedtoeccentriclateralloading,asthegroupconfigurationandthemotiondirectionsofallthepilesinthegroupareknown,thep-multiplierforeachpilecanbecalculatedbyEq.(1).Fig.11showsthedetailedprocess.Intheproposedprocedure,onlytheinfluenceofmotiondirectionsonthereductionfactorsandpmultiplierswasconsidered.Infact,thepilesinthegroupdiffernotonlyinmotiondirectionsbutalsoinmagnitudes.Previousstudiesontheresponseoflaterallyloadedpilegroups(8产品类别8.12trclateralmoading,flusrace-silization,flusrace-silization,flusrace的stiff见表1Gu(2014)conductedcentrifugemodeltestsonthree-diameterspaced2×2pilegroupssubjectedtoeccentriclateralloading.Modelsoilwassilicasandwithrelativedensityof55%.Modelpilesweremanufacturedusingaluminumtubestosimulateclosedendpipepileswithanoutsidediameterof1.78mandanembeddedpilelengthof69.7m.Theflexuralstiffnessofthepilesintheprototypescalewas20.72GN·m8.23pilewrececeTwolarge-scalemodeltestsonathree-diameterspaced3×3pilegroupundereccentriclateralloadingwithdifferenteccentricities(e=6Dand11D)insaturatedsandysiltwereconductedbyKongetal.(2015).Themodelpileswerefabricatedusingsteeltubes114mmindiameter,4.5mminthickness,and5.95minlength.Thepileswerejackedintothesoilandfixedbyarigidcap,thenhorizontallyloadedonthepilecapbyahydraulicactuator.GROUPandLPILEwerealsoadoptedtosimulatetheresponseofthepilegroupsandback-analyzethesoilparametersfromasingle