摘要本設計包括三個部分：一般部分、專題部分和翻譯部分。一般部分為張雙樓礦1.8Mt/a新井初步設計，共分10章：1.礦區(qū)概述及井田地質特征；2.井田境界和儲量；3.礦井工作制度、設計生產能力及服務年限；4.井田開拓；5.準備方式—采區(qū)巷道布置；6.采煤方法；7.井下運輸；8.礦井提升；9.礦井通風與安全技術；10.礦井基本技術經(jīng)濟指標。張雙樓煤礦位于徐州市西北，距徐州市約79km，在江蘇沛縣安國鎮(zhèn)境內。井田水平標高為-200m～-1200m，走向長8.47~10.79km，平均10.18km，傾斜寬平均為2.9km，水平面積約29.52km2。井田內可采煤層為9煤，煤層賦存穩(wěn)定，厚度平均4.5m，煤層傾角16~24°，平均22°。井田內工業(yè)儲量為192.36Mt，可采儲量為124.13Mt。礦井平均涌水量為300m3/h，相對瓦斯涌出量為0.77m3/t，屬低瓦斯礦井；煤塵有一定爆炸危險性，自燃發(fā)火期為3~6個月。張雙樓礦年設計生產能力為1.8Mt/a，服務年限為53.0年。礦井采用立井兩水平開拓暗立井直接延深開拓方式；采用中央并列與兩翼對角式混合通風方式；一水平標高-575m，二水平標高-950m。礦井采用走向長壁綜采一次采全厚采煤法；煤炭運輸采用膠帶與底卸式礦車，輔助運輸采用蓄電池電機車牽引礦車。礦井年工作日為330d，每天凈提升時間為16h，工作制度采用“三八”制。專題部分題目是：淺析礦井水的資源化。翻譯部分是一篇關于復合載荷下沙層地基運轉模型的論文，英文原文題目為：Aplasticitymodelforthebehaviouroffootingsonsandundercombinedloading。關鍵詞：立井；采區(qū)；綜采；中央并列式；兩翼對角式

ABSTRACTThisdesignincludesofthreeparts:thegeneralpart,specialsubjectpartandtranslatedpart.ThegeneralpartisanewpreliminarydesignofZhangshuanglouMinethatannualoutputis1.8Mt.Thedesignincludestenchapters:1.Mineandminegeologicalfeaturesoutlined;2.Waidarealmandreserves;3.Minesystem,designcapacityandlengthofservice;4.Waidadevelop;5.topreparetheway-withthedistrictroadwaylayout;6.miningmethods;7.undergroundtransport;8.minehoist;9.mineventilationandsecuritytechnologies;10.minethebasictechnicalandeconomicindicators.ZhangshuanglouMinelocatedintheCountytownofAnguowhichisinthenorthwestofXuzhouCity,anditisabout79kmawayfromXuzhou.Thelevelelevationoftheminefieldisfrom-200m~-1200m,thecoalfieldlengthonthestrikeis8.47kmto10.79km,average10.18km,thewidthonthedipis2.9kmonaverage,thetotalplaneareaofthemineisabout29.52km2.Thereisonlyoneexploringlayer_numbernine.Thecoalseamisstable,thecoalseamthicknessis4.5m.Itsdipangleis16to24degree,22degreeonaverage.Theindustryreservesoftheminefieldare192.36milliontonsandtheworkablereservesare124.13milliontons.TheaverageinflowrateinZhangshuangloumineis300m3/h.Therelativegasemissionis0.77m3/t,itisalowergassymine.Thecoaldusthavealittleexplosionhazardandself-combustiontendencyis3to6months.TheproductivecapacityofZhangshuanglouMineis1.8milliontonsperyear，andtheservicelifeis53.0years.Mineusesshaftandtwo-leveldevelopment.Thetypeofmineventilationsystemiscentralabreastandwingsdiagonal.Thefirstlevelisat-575m,Thesecondlevelisat-950m.Highcuttingminingmethodisusesbythemine.Mainroadwaymakesuseofbeltconveyorandbottom-dumpwagontotransportcoalresource,andminecartobeassistanttransport.Mineisworkingdaysfor330days,theneteverydaytoenhancethetime16hours.Minesystemis"3-8"structure.Thetitleofspecialsubjectis“Analysisofminewaterresourceutilization”.Thetranslationpartisatreatiseaboutaplasticitymodelforthebehaviouroffootingsonsandundercombinedloading.Keywords:shaft;panels;fullymechanizedmining;centralparallel;wingsdiagonalventilation

目錄一般部分1礦區(qū)概述及井田地質特征 頁英文原文AplasticitymodelforthebehaviouroffootingsonsandundercombinedloadingG.T.HOULSBY1,M.J.CASSIDY2(1.DepartmenofOffshoreEngineering,OxfordUniversity,UK;2.CenterforOffshoreFoundationSystems,UniversityofWesternAustralia(formerlyatOxfordUniversity))ABSTRACT：Acompletetheoreticalmodelisdescribedforthebehaviorofrigidcircularfootingsonsand,whensubjectedtocombinedvertical,horizontalandmomentloading.Themodel,whichisexpressedintermsofwork-hardeningplasticitytheory,isbasedonaseriesoftestsspecificallydesignedtoallowevaluationofthevariouscomponentsofthetheory.Themodelmakesuseoftheforceresultantsandthecorrespondingdisplacementsofthefooting,andallowspredictionsofresponsetobemadeforanyloadordisplacementcombination.Itisverifiedbycomparisonwiththedatabaseoftests.Theuseofthemodelisthenillustratedbysomedemonstrationcalculationsfortheresponseofajack-upunitonsand.Thisexampleillustratestheprincipalpurposeofthedevelopment,whichistoallowarealisticmodellingoffoundationbehaviourtobeincludedasanintegralpartofastructuralanalysis.KEYWORDS:footings/foundations;modeltests;numericalmodellingandanalysis;offshoreengineering;plasticity;sandsINTRODUCTIONThepurposeofthispaperistodescribeatheoreticalmodel,basedonstrain-hardeningplasticitytheory,whichiscapableofdescribingthebehaviourofacircularfootingonsandwhenitissubjectedtoallpossiblecombinationsofdrainedvertical,horizontalandmomentloading.Themotivationforthisworkcomesprincipallyfromtheoffshoreindustry,specificallyarisingfromtheproblemofassessmentofjack-upunitsunderextremeloading.Theapplicationsare,however,muchbroader,sincethemodelcouldbeappliedtomanyinstancesofcombinedloadingofafootingonsand.Structuralengineerscarryoutdetailedanalysesofjack-upunits,andaskgeotechnicalengineerstoprovidethemwiththevaluesofspringstiffnessestomodelthefoundations.Geotechnicalengineerstendtotaketheviewthatsuchasimplisticviewoffoundationbehaviourisunrealistic.Unfortunately,however,theyoftendescribethecomplexitiesandnon-linearitiesoffoundationbehaviourbyaseriesofadhocprocedures,whichastructuralengineercannotimplementwithinastandardanalysis.Thepurposeofthemodeldescribedhereistoprovideameansbywhichthestructuralandgeotechnicalengineerscancommunicate.Geotechnicalengineersmustbepreparedtore-casttheirknowledgeoffoundationbehaviourwithinaterminology(plasticitytheory)thatisamenabletonumericalanalysis.Structuralengineersmustacceptthatsoilbehaviourcannotbedescribedmerelyby‘springs’,butcanbeaccommodatediftheyarepreparedtousestrain-hardeningplasticitytheorywithintheiranalyses.TheadhocproceduresfordescribingfoundationbehaviorundercombinedloadinghavetheirrootsintheworkonbearingcapacitybyMeyerhof(1953),andaretypifiedbytheproceduresdescribedbyBrinchHansen(1970)andVesic(1973).Thesemethodsareadequateforpredictingfailureundercombinedloads,buttheyareunsuitablefornumericalanalysis,principallybecausetheyformulatetheproblemusingaseriesoffactorsappliedtothebearingcapacityformulaforverticalloading,modifyingittoaccountforhorizontalandmomentloading.Thisrenderstheanalysisunsuitablefordirectinclusioninnumericalanalysisprograms.Furthermoretheconventionalanalysespaynoattentiontotheissueofplasticstrainspre-failure,sincetheytreatonlythefailureproblem.Analternativeistoaddresstheproblemdirectlyasoneofloadingwithinathree-dimensional(V,M,H)loadspace,andtoexplore,forinstance,theshapeoftheyieldsurfaceinthisspace.ThisapproachwaspioneeredbyRoscoe&Schofield(1956),whowerealsoconcernedwithaproblemofsoilstructureinteraction:thatofcalculatingthefullyplasticmomentresistanceofashortpierfoundationforasteelframework.Thegeneralframeworkofplottingloadpathsin(V,M,H)spacehasbeenadoptedbytheoffshoreindustry,buttheformulaeusedtoderivethefailuresurfacesareoftenbasedontheshapeandinclinationfactorapproach(seee.g.Hambly&Nicholson,1991).Recentlytherehasbeenconsiderableinterestinthedevelopmentofmodelsbasedonplasticitytheory,andontheexperimentalworknecessarytosupportthisapproach(e.g.Schotmann,1989;Nova&Montrasio,1991:Gottardi&Butterfield,1993,1995;Houlsby&Martin,1992;Martin,1994).Themodeldescribedhereisintendedforthedescriptionofdrainedloadingofacircularfoundationondensesand,subjectedtoanarbitrarycombinationofvertical,horizontalandmomentloads.Itiscompleteinthesensethatanyloadordeformationpathcanbeappliedtothefootingandthecorrespondingunknowns(deformationsorloads)calculated.ThemodelisbasedonexperimentaldatabyGottardi&Houlsby(1995)andGottardietal.(1999).Theloadingofafootingclearlyresultsinacomplexstateofstressesinthesoil.Intheapproachusedheretheresponseofthefoundationis,however,expressedpurelyintermsofforceresultants(V,M,H)onthefooting.Thissimplificationisveryconvenient,especiallyasitallowsthemodeltobecoupleddirectlytoanumericalanalysisofastructure.Itisdirectlyanalogoustotheuseofforceresultants(tension,bendingmomentandshearforce)intheanalysisofbeamsandcolumns.However,itobscuressomeofthedetailedresponseofthefooting—forinstancethefactthatarealfootingprobablydoesnotexhibitatruly`elastic'responseofthesortemployedwithinthemodelforcertainloadcombinations.Nevertheless,itprovestobeausefulidealisation.OUTLINEOFTHEMODELBeforegivingthedetailedmathematicalformoftheexpressionsused(seethenextsection),itisworthdescribingthemodelinoutline.Theprincipalconceptadoptedisthatatanypenetrationofafoundationintothesoil,ayieldsurfacein(V,M,H)spacewillbeestablished.Anychangesofloadwithinthissurfacewillresultonlyinelasticdeformation.Loadpointsthattouchthesurfacecanalsoresultinplasticdeformation.Althoughtheshapeofthissurfaceisassumedconstant,thesizemayvary,withtheyieldsurfaceexpandingasthefootingispushedfurtherintothesoil.Forsimplicitytheexpansionoftheyieldsurfaceistakensolelyasafunctionoftheplasticcomponentoftheverticaldeformation.Themodelisthusoneofthestrain-hardeningplasticitytype.Thepreciseformofthehardeninglawisspecifiedbyarelationshipbetweenthesizeoftheyieldsurfaceandtheplasticverticaldeformation.Withintheyieldsurface,wherethedeformationisassumedaselastic,thebehaviourisspecifiedbyasetofelasticconstants.Finallyastatementmustbemadeabouttheflowrule,whichdeterminestheratiobetweentheplasticstrains.Thesimplesttypeofflowruleis‘associatedflow’,inwhichtheplasticpotentialisthesameastheyieldsurface.Inthismodelaslightvariationisusedinthattheshapeoftheyieldsurfaceandplasticpotentialaredescribedbysimilarmathematicalexpressionsbutwithdifferentparametervalues.Itisnecessarytointroducetheseparametersifthemodellingofplasticverticaldeformationsistobeatallreasonable.Thereisastrikinganalogybetweenthestructureoftheproposedmodelandthatofconstitutivemodelsbasedoncritical-stateconcepts.Intheanalogytheverticalloadplaysthesameroleasthemeannormalstress,p’,thehorizontalloadorthemomentareequivalenttodeviatorstress,q,andtheverticalpenetrationplaysthesamerole(withachangeofsign)asthevoidsratioorspecificvolume.TheanalogyispursuedinmoredetailbyHoulsby&Martin(1992)andMartin(1994).DETAILSOFTHEMODELThemodeldescribedhereisknownasModelC(ModelsAandBweredevelopedbyMartin(1994)forfootingsonclay).ThesignconventionsandnomenclatureusedinthefollowingarethosesuggestedbyButterfieldetal.(1997)andareshowninFig.1.TypicalparametervaluesforModelCarepresentedinTable1. Fig.1.Signconventionsforloadanddisplacement. Fig.2.ShapeofyieldsurfaceTable1. PropertiesusedinModelCConstantdimensionExplanationConstrainsTypicalvalueNotesRLFootingradiusVariousγF/L3Unitweightofsoil20kN/m3gShearmodulusfactor400Forequation(2)kvElasticstiffnessfactor(vertical)2.65khElasticstiffnessfactor(horizontal)2.3kmElasticstiffnessfactor(moment)0.46kcElasticstiffnessfactor(horizontal/momentcoupling)-0.14h0Dimensionofyieldsurface(horizontal)0.116MaximumvalueofH/V0onM=0m0Dimensionofyieldsurface(moment)0.086MaximumvalueofM/2RV0onH=0αEccentricityofyieldsurface1.0<α<1.0-0.2β1Curvaturefactorforyieldsurface(lowstress)≦1.00.9β1=β2=1givesparabolicsectionβ2Curvaturefactorforyieldsurface(highstress)≦1.00.99β1=β2=1givesparabolicsectionβ3Curvaturefactorforplasticpotential(lowstress)≦1.00.55β4Curvaturefactorforplasticpotential(highstress)≦1.00.65αhAssociationfactor(horizontal)1.0-2.5Variationaccordingtoequation(9)andαh∞=2.5αmAssociationfactor(moment)1.0-2.15Variationaccordingtoequation(9)andαm∞=2.15k'Rateofchangeinassociationfactors0.125fInitialplasticstiffnessfactor0.144NγBearingcapacityfactor(peak)150-300δpDimensionlessplasticpenetrationatpeak0.0136ElasticbehaviourTheelasticrelationshipbetweentheincrementsofload(dV,dM,dH)andthecorrespondingelasticdisplacements(dwe,dθe,due)is dVdMwhereRistheradiusofthefooting,Gisarepresentativeshearmodulus,andkv,km,kh,kcaredimensionlessconstants.Thevaluesoftheseconstantsmaybederivedusing,forinstance,finiteelementanalysisofafooting(Bell,1991;NgoTran,1996),andtypicalvaluesaregiveninTable1.Thevaluesofthedimensionlessconstantsdependonthegeometryofthefooting(e.g.coneangleanddepthofembedment)aswellasthePoisson'sratioforthesand.AnappropriatevalueofGisoneofthemostdifficultparameterstoestablishforthemodel.Recognisingthatthemobilisedshearstiffnessisstronglydependentontheshearstrain,thevaluehastobeacompromiseonethatisrepresentativeoftypicalstrainsinthesoil.Ithasbeendeterminedherebyfittingofoverallcurvestoexperimentaldata.Theshearmodulusalsodependsonstresslevel,andistypicallyproportionaltoapproximatelythesquarerootofthemeaneffectivestress.Itisconvenientthereforetoestimatetheshearmodulusthroughuseofaformulasuchas GPwherePaisatmosphericpressure,Visarepresentativeverticalloadonthefoundation,A=πr2istheplanareaofthefoundation,andgisadimensionlessconstant.Atypicalvalueofgisapproximately400formediumdensesand,butwouldbeexpectedtodependmildlyontherelativedensity.Notethatequation(2)representsadifferentscalingrelationshipthanwasusedinCassidy(1999),andissuggestedonthebasisofmorerecentwork.YieldsurfaceTheyieldsurfaceismostconvenientlyexpressedindimensionlessterms,usingthevariablesv=V/V0,m=M/2RV0,h=H/V0,whereV0istheparameterthatdefinesthesizeoftheyieldsurface.ThechosenformofthesurfacethatfitstheobservedbehaviouroffootingswellisthatusedbyMartin(1994): f=hwherethefactorβisintroducedsothath0andm0havesimplephysicalinterpretations.Thissurfacemayseemunnecessarilycomplicated,anditisperhapsusefultoconsiderasimplifiedforminwhicha=0andβ1=β2=1: f=hh0Itisstraightforwardtoshowthatthisisa‘rugbyball’shapedsurfacethatisellipticalinsectiononplanesatconstantV,andparaboliconanysectionincludingtheV-axis:seeFig.2.Althoughthereissometheoreticaljustificationforthischoiceofshape(particularlyinthe(V,M)plane),itislargelychosenempirically.ThesizeofthesurfaceisdeterminedbythepointonthesurfaceatmaximumVvalue,whichisgivenby(V,M,H)=(V0,0,0).Theshapeofthesurfaceisdeterminedbythetwoparametersh0andm0,whichdeterminetheratiosofH/VandM/2RVatthewidestsectionofthesurface,whichoccursatV=V0/2.Thefactorainequation(3)allowstheellipsetobecomeeccentric(thatis,theprincipalaxesarenolongeralignedwiththeH-andM-axes).Thisisnecessaryforaccuratemodelingoftheexperimentaldata,andaccountsforthefactthatif,forinstance,thefootingissubjectedtoahorizontalloadfromlefttoright,aclockwisemomentwillproduceadifferentresponsefromananticlockwisemoment.Thefactorsβ1andβ2areintroducedfollowingNova&Montrasio(1991).Theyhavetwoadvantages:(a)thepositionofthemaximumsizeoftheellipticalsectioncanbemovedfromV=V0/2toV=β2V0/(β1+β2),thusfittingexperimentaldatabetter;and(b)bychoosingβ1﹤1andβ2﹤1thesharppointsonthesurfaceatV=0andV=V0canbeeliminated,whichhasadvantagesinthenumericalimplementationofthemodel.Ifβ1=β2=0.5,theyieldsurfacebecomesanellipsoid.Thefactorβ12inequation(3)issimplysothath0andm0retaintheiroriginalmeanings.StrainhardeningTheformofthestrain-hardeningexpressioncanbedeterminedfromaverticalload-penetrationcurve,sinceforpureverticalloadingV0=V.Typicalload-penetrationcurvesareshowninFig.3,showingapeakintheload-penetrationcurveforthedensesandtestedbyGottardi&Houlsby(1995).Anexpressionthatfittsthedatawell,andwhichisshowninFig.3,is V0wherekisaninitialplasticstiffness,wpistheplasticcomponentoftheverticalpenetration,V0misthepeakvalueofV0,andwpmisthevalueofwpatthispeak.Nospecialsignificanceisattachedtothisparticularformofthefittotheverticalload-penetrationresponse,andalternativeexpressionsthatfittedotherexperimentaldatacouldalsobeappropriate.Aformulathatmodelspost-peakworksofteningaswellaspre-peakperformancewasessential.However,equation(5)unrealisticallyimpliesV0→0aswp→∞.Thereforeitcanbeusedonlyforalimitedrangeofpenetrations.Itisassumedthatformostproperlydesignedfoundationsondensesand,loadingpost-peakwouldnotbeexpected;however,foracompletemodelcapableoffittingpost-peakbehaviourmorerealistically,equation(5)canbealteredto V0wherefpisadimensionlessconstantthatdescribesthelimitingmagnitudeofverticalloadasaproportionofV0m(thatis,V0→fpV0maswp→∞).Itispossibletousethesameparametricvaluesofk,V0mandwpmasinequation(5).Forrealisticfootingdesignsinwhichitwasnotrequiredtodescribesoftening,amuchsimplerequationthanequation(6)couldbeused.Thepreciseformofthisequationisnotinfactcentraltothemodel;allthatisrequiredisaconvenientexpressionthatfitsobserveddataanddefinesV0asafunctionofwp.Fig.3.TheoreticalfitoftheverticalloadtestsPlasticpotentialInthe(M/2R,H)planeanassociatedflowruleisfoundtomodeltheratiosbetweentheplasticdisplacementswell,butthisisnotthecaseinthe(V,M/2R)or(V,H)planes,forwhichanassociatedflowruleisfoundtopredictunrealisticallylargeverticaldisplacements.Aplasticpotentialdifferentfromtheyieldsurfacemustthereforebespecified.Aconvenientexpressionis,however,verysimilartothatusedfortheyieldsurface: g=hWhereβandαvisanassociationparameter(associatedflowisgivenbyαv=1.0).Notethattheconditiong=0isusedtodefineadummyparameterV0’whichgivestheintersectionoftheplasticpotentialwiththeV-axis.Theprimedparametersaredefinedbyv’=V/V0’,m’=M/2RV0’andh’=H/V0’.Factorsβ3andβ4havebeenintroduced,whichcanbechosenindependentlyfromβ1andβ2.Theassociationparameterαvallowsforvariationoftheverticaldisplacementmagnitude,withvaluesgreaterthan1.0resultingintheincreaseoftheverticaldisplacements.Italsocontrolsthepositionofthe‘parallelpoint’asdefinedbyTan(1990),whichisthepointontheyieldlocusatwhichthefootingcouldrotate(ormovesideways)atconstantverticalloadandwithnofurtherverticaldeformation.Accuratepredictionofthispointisimportantasitdescribesthetransitionbetweensettlementandheaveofthefootingandwhereslidingfailureswilloccur.Intheanalogywithcritical-statemodels,thispointplaysthesameroleasthecriticalstate.Whenassociatedflowisused(αv=1,β3=β1,β4=β2)theparallelpointoccursatv=β2/(β1+β2):thatis,thelargestconstantverticalloadsectionoftheyieldsurface.Asαvisdecreased,thepositionoftheparallelpointmovestoalowervalueofverticalload,buttheexactexpressionforthevalueofvbecomesverycomplex.Themodellingofrealisticverticaldisplacementsandofthepositionoftheparallelpointarelinked,andwithonlyoneparameteritisdifficulttomodelbothadequately.Increasingh0orm0withtwoassociationfactors,ratherthanscalingtheverticalcomponent,enablestheplasticpotential'sshapetochangeintheradialplane.Thisconsequentlychangesradialplasticdisplacements.Thismethodhastheadvantageofmoreflexibilityinmodellingsubtledifferencesbetweenhorizontalandmomentloadingresults.Usingtwoassociationfactorstheplasticpotentialmaybedefinedas g=hIfαhandαmareconstantandequal,equation(7)isequivalenttoequation(8)forthesamevalueofαv.Infactitwasfoundthatexperimentaldatacanbefittedwellonlyiftheαhandαmfactorsarethemselvestakenasvariable.ThevaluesofαhandαmthatbestfitboththeradialdisplacementandconstantVtestsofGottardi&Houlsby(1995)werefoundtobehyperbolicfunctionsofplasticdisplacementhistories: αh αm=wherek’determinestherateofchangeoftheassociationfactors.Fornopreviousradialdisplacements,αhandαmequateto1andassociatedflowisassumed.TheratesatwhichαhandαmvaryinModelCaredepictedinFig.4.Withtheplasticpotentialdefinedasinequation(6),thefollowingvalueswereevaluated:β3=0.55;β4=0.65;αh∞=2.5;αm∞=2.15;k’=0.125.Furtherdetailsofthedevelopmentoftheplasticpotentialinequation(8)andcomparisonsbetweenthetheoryandexperimentaldatacanbefoundinCassidy(1999).PartiallydrainedbehaviourThemodeldescribedaboveisbasedondatafromtestsondrysand,andthusdescribesfullydrainedbehaviour.Forrealisticloadingtimesoflargeoffshorefoundations,partiallydrainedbehaviourisexpected,andtheabovemodelwouldneedtobemodifiedtotakeintoaccountthetransientporepressuresbeneaththefoundation.BothMangal(1999)andByrne(2000)havecarriedoutmodeltestsequivalenttothoseusedhere,butonsaturatedsandandatloadingrateswherepartiallydrainedbehaviouroccurs.Theyrecordthatloadingratehasremarkablylittleeffectontheload-deformationresponse,sothatthecurrentmodelprovidesareasonablestartingpointfordescriptionofpartiallydrainedbehaviour.Somecautionisofcoursenecessaryifthereisanypossibilitythatthemagnitudeofthetransientporepressuresmightbesufficienttoinduceliquefactionphenomena.Fig.4.RatesofvariationofαhandαminModelCRETROSPECTIVEMODELLINGOFEXPERIMENTSToinvestigatethecapabilitiesofModelCtomodelfootingbehaviour,numericalsimulationswerecarriedoutforanumberofrepresentativeexperiments.Ineachofthesesimulationsthemeasuredvaluesofthreeofthemeasuredquantities(e.g.thedisplacements)weretakenasinput,andtheotherthreequantities(e.g.theloads)werecalculatedasoutputforcomparisonwiththeexperiments.Noidealisationoftheexperimentalinputdatawascarriedout,sothattheinputvaluescontainalltheminorfluctuationsassociatedwithexperimentalmeasurements.TheprogramusedtoimplementModelCisabletohandlesuchperturbations.ThesimulationsarecarriedoutforthetestsreportedbyGottardi&Houlsby(1995),usinga100mmdiameterfootingonmediumdenseLeightonBuzzardsand.ThesearethesameteststhatwereusedforthedevelopmentofModelC,sothatthequalityofthefitisofcourseexpectedtobegood.Thepurposeofthisexerciseis,however,twofold:(a)todemonstratethatModelCcanbeimplementednumerically,andusedtosimulatefootingbehaviour;and(b)toassesstheoverallcapabilityofthemodeltocapturethesalientfeaturesoftheoriginaldata.VerticalpenetrationtestFigure5(a)showstheexperimentalresultsforaverticalpenetrationtest.Fig.5(b)isasimulationofthissametestinwhichthemeasureddisplacementistakenasinput,andtheverticalloadcalculated.ModelCgivesloadsthataccuratelyrepresenttheoriginaltest,andthisisprincipallyatestofthechosenstrain-hardeninglaw.Thethreeverticalunload/reloadloopspre-peakaremodelledwell,althoughModelCdoesnotreflectthehysteresisthatoccursintheexperimentalresults.Thisdoesmakeaslight,butnottoosignificant,reductioninthedisplacementscomparedwiththeircorrespondingloads.TheModelCprogrampredictsthelocationoftheexistingyieldsurfacewhenbeingreloadedinanunload-reloadloop.Itdoesnotovershoottheyieldsurfacebecauseofabisectionalgorithmusedtodeterminetheproportionoftheincrementthatiselastic,withtheremainingproportionallocatedaselastoplastic.IneachofFigs6—Fig.11following,(a)and(b)representthemeasuredexperimentaldata,and(c)and(d)representtheModelCsimulation.MomentandhorizontalswipetestsfromV≈1600NInaswipetestthefootingisload-controlledintheverticaldirectionuntilitreachesaprescribedload,inthiscaseV≈1600N.Rotationorhorizontaldisplacementisthenappliedtothefootingwiththetracecorrespondingtoatrackalongtheyieldsurface,appropriateforthatembedment.Figure6representsamomentswipestartingatV≈1600N.Priortotheswipethefootingisloadedinthepurelyverticaldirectionwithonlysmallamountsofhorizontalandmomentloadbeingdeveloped.However,forclarity,onlytheswipehasbeenplotted.ModelCsimulatesthemagnitudeofpeakmomentadequately,reachingavaluejustoverM/2R=150N.ThenumericalpeakmomentinFig.6(d)andtheexperimentalpeakmomentinFig.6(b)occurredatthesameverticalload.Additionally,Figs6(a)and(c)showthattheamountofrotationbeforethepeakwasmodelledaccurately.However,inthistestModelClocatesthe`parallelpoint'slightlylowerthantheexperiment(pointAinFig.6(d)).IntheModelCsimulationinFig.6(d)movementbackalongtheyieldsurfacecanbeseentooccur,forinstanceatV≈800NandagainatV≈600N.Figure7representsanequivalentswipe,butinthehorizontaldirection,withModelCload-controlledtoV≈1600Nandthendisplacement-controlledfortheswipe.Theprogrammodelsthetrackalongtheyieldsurfaceverywell,withthepeakhorizontalloadalmostexactlymatchingthatoftheexperimentatjustover200N.Fig.7(c)showsModelCpredictingaverysimilardisplacementpathtotheexperiments(Fig.7(a)),verifyingtheflowruleforthiscase.Thesimulationstopstrackingataroundthesamehorizontalandverticalloadlevels,indicatingaccuratepredictionofthe‘parallelpoint’inthehorizontalplane.Furtherjustificationoftheuseoftwoindependentassociationfactors(αhandαm)intheflowru