文献翻译，水工建筑物，重力坝.doc

'Chapter5StaticandDynamicStressAnalysis第五章静态和动态应力分析5-1.StressAnalysis5-1.应力分析a.General.(1)Astressanalysisofgravitydamsisperformedtodeterminethemagnitudeanddistributionofstressesthroughoutthestructureforstaticanddynamicloadconditionsandtoinvestigatethestructuraladequacyofthesubstructanceandfoundation.LoadconditionsusuallyinvestigatedareoutlinedinChapter4.(2)Gravitydamstressesareanalyzedbyeitherapproximatesimplifiedmethodsorthefiniteelementmethoddependingontherefinementrequiredfortheparticularlevelofdesignandthetypeandconfigurationofthedam.Forpreliminarydesigns,simplifiedmethodsusingcantileverbeammodelsfortwo-dimensionalanalysisorthetrialloadtwistmethodforthree-dimensionalanalysisareappropriateasdescribedintheUSBureauofReclamation(USBR),“DesignofGravityDams”(1976).Thefiniteelementmethodisordinarilyusedforthefeatureandfinaldesignstagesifamoreexactstressinvestigationisrequired.a.普通方法(1)重力坝的应力分析是用以确定在静态和动态荷载作用下结构的应力分布和大小情况以及验证下部和基础的结构强度，荷载条件通常在第四章作了概述。(2)重力坝的应力分析通过基于满足坝体类型、构造和设计精度要求的近似的简化方法或有限单元法。初步设计时，根据美国垦务局（USBR）颁布的“重力坝设计规范（1976）”，可以使用二维的悬臂梁模型或者三维的模型试验的简化方法。有限单元法通常用于对应力精度要求更高的详细和最终设计阶段。b.Finiteelementanalysis.(1)Finiteelementmodelsareusedforlinearelasticstaticanddynamicanalysesandfornonlinearanalysesthataccountforinteractionofthedamandfoundation.Thefiniteelementmethodprovidesthecapabilityofmodelingcomplexgeometriesandwidevariationsinmaterialproperties.Thestressesatcorners,aroundopenings,andintensionzonescanbeapproximatedwithafiniteelementmodel.Itcanmodelconcretethermalbehaviorandcouplethermalstresseswithotherloads.Animportantadvantageofthismethodisthatcomplicatedfoundationsinvolvingvariousmaterials,weakjointsonseams,andfracturingcanbereadilymodeled.SpecialpurposecomputerprogramsdesignedspecificallyforanalysisofconcretegravitydamsareCG-DAMS(Anatech1993),whichperformsstatic,dynamic,andnonlinearanalysisandincludesasmearedcrackmodel,andMERLIN(Saouma1994),whichincludesadiscretecrackingfracturemechanicsmodel.b.有限元分析(1)有限元模型用于线性弹性的静态和动态分析以及坝体与基础相互影响的非线性分析。有限元方法具有模拟具有复杂几何形状和不同材料性能的能力。角落处，开口处和有张力处的应力可以用有限元模型来近似。它可以模拟混凝土的热行为和由其他荷载引起的温度应力。此方法的重要优点是对于涉及各种材料的复杂的基础，接缝薄弱处和断裂面能很容易模拟。专门设计用来对混泥土重力坝分析的专用计算机程序是CG-DAMS（Anatech1993年），它执行静态，动态和非线性分析，并包括一个弥散裂缝模型，梅兰（萨乌马1994年），其中包括离散裂缝断裂力学模型。 (2)Two-dimensional,finiteelementanalysisisgenerallyappropriateforconcretegravitydams.Thedesignershouldbeawarethatactualstructureresponseisthree-dimensionalandshouldreviewtheanalyticalandrealisticresultstoassurethatthetwo-dimensionapproximationisacceptableandrealistic.Forlongconventionalconcretedamswithtransversecontractionjointsandwithoutkeyedjoints,atwo-dimensionalanalysisshouldbereasonablycorrect.Structureslocatedinnarrowvalleysbetweensteepabutmentsanddamswithvaryingrockmoduliwhichvaryacrossthevalleyareconditionsthatnecessitatethree-dimensionalmodeling.(2)二维的有限元分析一般用于混凝土重力坝。但是设计者应该知道，实际的结构响应是三维的，应审查理论值和真实值以保证这二维近似方法是合理和有效的。对于较长的并设有横缝的常规混凝土大坝，二维的分析应是相当正确的。当结构位于陡峭的桥台之间的狭窄山谷和大坝在各处有不同的岩石模量时则需要使用三维建模。(3)ThespecialpurposeprogramsEarthquakeAnalysisofGravityDamsincludingHydrodynamicInteraction(EADHI)(ChakrabartiandChopra1973)andEarthquakeResponseofConcreteGravityDamsIncludingHydrodynamicandFoundationInteractionEffects(EAGD84)(Chopra,Chakrabarti,andGupta1980)areavailableformodelingthedynamicresponseoflineartwo-dimensionalstructures.Bothprogramsuseaccelerationtimerecordsfordynamicinput.TheprogramSDOFDAMisatwo-dimensionalfiniteelementmodel(ColeandCheek1986)thatcomputesthehydrodynamicloadingusingChopra’ssimplifiedprocedure.ThefiniteelementprogramssuchasGTSTRUDL,SAP,ANSYS,ADINA,andABAQUSprovidegeneralcapabilitiesformodelingstaticanddynamicresponses.(3)一些专用的程序如重力坝地震分析及水动力作用（EADHI）（查克拉巴蒂和乔普拉1973）、流体作用下的混凝土重力坝的地震响应分析和地基交互影响（EAGD84）（乔普拉，查克拉巴蒂，和Gupta1980年）可用于模拟线性二维结构的动力响应。这两个程序都对与动态输入使用加速度时间记录。SDOFDAM程序是用乔普拉简化程序计算水动力荷载的一个二维有限元模型。一些有限元程序如GTSTRUDL,SAP,ANSYS,ADINA,和ABAQUS提供了模拟静态和动态响应的能力。5-2.DynamicAnalysisThestructuralanalysisforearthquakeloadingsconsistsoftwoparts:anapproximateresultantlocationandslidingstabilityanalysisusinganappropriateseismiccoefficient(seeChapter4)andadynamicinternalstressanalysisusingsite-dependentearthquakegroundmotionsifthefollowingconditionsexist:5-2动态分析地震荷载的结构分析包括两部分：一个使用适当的抗震系数（见第4章）的位移和抗滑稳定的近似结果和一个满足下列条件的基于地震动的动态内应力分析：a.Thedamis100feetormoreinheightandthepeakgroundacceleration(PGA)atthesiteisgreaterthan0.2gforthemaximumcredibleearthquake.a.大坝高100英尺以上以及一点对于地震幅度的峰值加速度（PGA）大于0.2g。b.Thedamislessthan100feethighandthePGAatthesiteisgreaterthan0.4gforthemaximumcredibleearthquake.b.大坝高度低于100英尺且一点相对于地震幅度的峰值加速度PGA大于0.4g。c.Therearegatedspillwaymonoliths,wideroadways,intakestructures,orothermonolithsofunusualshapeorgeometry.c.有门控泄洪坝段，宽的通道，进水口，或其他有不寻常的几何形状的坝段。d.Thedamisinaweakenedconditionbecauseofaccident,aging,ordeterioration.The requirementsforadynamicstressanalysisinthiscasewillbedecidedonaproject-by-projectbasisinconsultantandapprovedbyCECW-ED.d.大坝由于意外情况，老化，或恶化而处于性能衰减的状况。在这种情况下的动态应力分析的要求将决定于专家的且被CECW-ED认可的项目标准。5-3.DynamicAnalysisProcessTheprocedureforperformingadynamicanalysisincludethefollowing:a.Reviewthegeology,seismology,andcontemporarytectonicsetting.b.Determinetheearthquakesources.c.Selectthecandidatemaximumcredibleandoperatingbasisearthquakemagnitudesandlocations.d.Selecttheattenuationrelationshipsforthecandidateearthquakes.e.Selectthecontrollingmaximumcredibleandoperatingbasisearthquakesfromthecandidateearthquakesbasedonthemostseveregroundmotionsatthesite.f.Selectthedesignresponsespectraforthecontrollingearthquakes.g.Selecttheappropriateacceleration-timerecordsthatarecompatiblewiththedesignresponsespectraifacceleration-timehistoryanalysesareneeded.h.Selectthedynamicmaterialpropertiesfortheconcreteandfoundation.i.Selectthedynamicmethodsofanalysistobeused.j.Performthedynamicanalysis.k.Evaluatethestressesfromthedynamicanalysis.5-3动态分析过程执行动态分析的过程包括以下内容：a.调查其地质学，地震学及当代构造环境。b.确定地震的来源。c.确定设计值、地震震级和位置。d.确定地震的衰减关系。e.确定基于最严重的地面运动的设计地震的最大可控值和操作标准。f.确定用于控制地震的设计反应谱。g.如果需要进行加速度-时间时程分析时，确定合适的满足设计反应谱的加速度-时间记录。h.确定混凝土和基础的动态材料属性。i.确定用来进行动力学分析的方法。j.进行动力学分析。k.通过动力学分析求得应力值。5-4.InterdisciplinaryCoordinationAdynamicanalysisrequiresateamofengineeringgeologists,seismologists,andstructuralengineers.Theymustworktogetherinanintegratedapproachsothatelementsofconservatismarenotundulycompounded.AnexampleofundueconservatismincludesusingarareeventastheMCE,upperboundvaluesforthePGA,upperboundvaluesforthedesignresponsespectra,andconservativecriteriafordeterminingtheearthquakeresistanceofthestructure.Thestepsinperformingadynamicanalysisshouldbefullycoordinatedtodevelopareasonablyconservativedesignwithrespecttotheassociatedrisks.Thestructuralengineersresponsibleforthedynamicstructuralanalysisshouldbeactivelyinvolvedintheprocessofcharacterizingtheearthquakegroundmotions(seeparagraph5-6)intheformrequiredforthemethodsofdynamicanalysistobeused. 5-4.各学科之间的相互配合动态分析需要工程地质学家，地震学家和结构工程师的合作。他们必须相互协调的工作在一起以便少部分的保守主义不会过度的复杂化。过分保守的例子包括使用如MCE的一个罕见事件，上界的PGA值，上界值的设计反应谱，以及确定结构抗震的保守标准。在进行动态分析的步骤应充分配合以得出在相关风险下相当保守的设计。负责结构动力分析的结构工程师应积极参与到所用的动态分析方法对地震地面运动特征（见第5-6）的形式要求的过程中。5-5.PerformanceCriteriaforResponsetoSite-DependentEarthquakesa.Maximumcredibleearthquake.GravitydamsshouldbecapableofsurvivingthecontrollingMCEwithoutacatastrophicfailurethatwouldresultinlossoflifeorsignificantdamagetoproperty.InelasticbehaviorwithassociateddamageispermissibleundertheMCE.b.Operatingbasisearthquake.GravitydamsshouldbecapableofresistingthecontrollingOBEwithintheelasticrange,remainoperational,andnotrequireextensiverepairs.5-5.某点的地震响应性能判别标准a.可信地震最大值。重力坝应具有继续控制MCE的能力而不会造成人员死亡或重大财产损失等灾难性后果。b.地震控制标准。重力坝应具有在弹性范围内抵抗控制OBE，保持运行且不用大修的能力。5-6.GeologicalandSeismologicalInvestigationAgeologicalandseismologicalinvestigationofalldamsitesisrequiredforprojectslocatedinseismiczones2through4.Theobjectivesoftheinvestigationaretoestablishcontrollingmaximumandcredibleoperatingbasisearthquakesandthecorrespondinggroundmotionsforeachandtoassessthepossibilityofearthquake-inducedfoundationdislocationatthesite.Selectingthecontrollingearthquakesisdiscussedbelow.AdditionalinformationisalsoavailableinTM5-809-10-1.5-6.地质和地震调查关于所有水库所在地地质和地震调查需要在地震带2到4个调查项目。调查的目的是为了对每个点建立控制最大值和可信的地震控制标准和相应的地震地面运动，并评估在当地由地震引起的地基错位的可能性。下面讨论了确定控制地震。其他信息也可在TM5-809-10-1找到。5-7.SelectingtheControllingEarthquakesa.Maximumcredibleearthquake.ThefirststepforselectingthecontrollingMCEistospecifythemagnitudeand/ormodifiedMercalli(MM)intensityoftheMCEforeachseismotectonicstructureorsourceareawithintheregionexaminedaroundthesite.ThesecondstepistoselectthecontrollingMCEbasedonthemostseverevibratorygroundmotionwithinthepredominantfrequencyrangeofthedamanddeterminethefoundationdislocation,ifany,capableofbeingproducedatthesitebythecandidateMCE’s.IfmorethanonecandidateMCEproducethelargestgroundmotionsindifferentfrequencybandssignificanttotheresponseofthedam,eachshouldbeconsideredacontrollingMCE.5-7.确定控制地震a.可信地震最大值。用于确定控制MCE的第一步是为在工地附近的检查区域内的每个地震构造结构或水源区指定MCE的大小和/或修改其麦加利（毫米）强度。第二步是选择建立在大坝内主要频率范围内最严重的地震动的控制MCE，并确定基础错位，即此处MCE的延展能力。如果有不止一个预选的MCE产生对大坝响应重大的在不同频段的最大地面运动，则每个都应看作一个控制MCE.b.Operatingbasisearthquake. (1)TheselectionoftheOBEisbaseduponthedesiredlevelofprotectionfortheprojectfromearthquake-induceddamageandlossofserviceprojectlife.Theprojectlifeofnewdamsisusuallytakenas100years.TheprobabilityofexceedanceoftheOBEduringtheprojectlifeshouldbenogreaterthan50percentunlessthecostsavingsindesigningforalesssevereearthquakeoutweighstheriskofincurringthecostofrepairsandlossofservicebecauseofamoresevereearthquake.b.地震设防标准。(1)OBE的确定是建立在工程在遭受地震破坏及超过使用年限时对工程期望得到的保护水平的基础之上的。新建的大坝的工程使用年限一般取为100年。在使用期限内的OBE的超越概率应不大于50%，除非在设计时冒花钱在修理上而降低防震要求以及由于更多的地震而丧失使用功能的风险节约成本。(2)TheprobabilisticanalysisfortheOBEinvolvesdevelopingamagnitudefrequencyorepicentralintensityfrequency(recurrence)relationshipofeachseismicsource;projectingtherecurrenceinformationfromregionalandpastdataintoforecastsconcerningfutureoccurrence;attenuatingtheseverityparameter,usuallyeitherPGAofMMintensity,tothesite;determiningthecontrollingrecurrencerelationshipforthesite;andfinally,selectingthedesignlevelofearthquakebasedupontheprobabilityofexceedanceandtheprojectlife.(2)对OBE的概率分析涉及到对每个震源研究其震级频率与震中频率（复发）之间的关系；通过对当地过去地震信息来预测将来的情况；当地的某些参数，通常是MM强度的PGA的衰减程度；确定此处的控制复发的关系；最后，依据超越频率及使用寿命确定抗震设防水平。5-8.CharacterizingGroundMotionsa.General.Afterspecifyingthelocationandmagnitude(orepicentralintensity)ofeachcandidateearthquakeandanappropriateregionalattenuationrelationship,thecharacteristicsofvibratorygroundmotionexpectedatthesitecanbedetermined.Vibratorygroundmotionshavebeendescribedinavarietyofways,suchaspeakgroundmotionparameters,acceleration-timerecords(accelerograms),orresponsespectra(Hayes1980,andKrinitzskyandMarcuson1983).Fortheanalysisanddesignofconcretedams,thecontrollingcharacterizationofvibratorygroundmotionshouldbeasite-dependentdesignresponsespectra..5-8.表征地震动a.一般地。当指定了位置以及每个预设地震的震级（或震中强度）且一个适当区域的衰减关系，则此处地面运动的震动特征即可确定。地震运动已经用很多方式进行了描述，如地面运动参数的峰值，加速度-时间记录（加速度），或反应谱（海斯1980年，Krinitzsky和马库森1983）。对于混凝土坝的分析和设计，对地震动的控制特征应基于此地的设计反应谱。b.Site-specificdesignresponsespectra.(1)Whereverpossible,site-specificdesignresponsespectrashouldbedevelopedstatisticallyfromresponsespectraofstrongmotionrecordsofearthquakesthathavesimilarsourceandpropagationpathpropertiesasthecontrollingearthquake(s)andarerecordedonafoundationsimilartothatofthedam.Importantsourcepropertiesincludemagnitudeand,ifpossible,faulttypeandtectonicenvironment.Propagationpathpropertiesincludedistance,depth,andattenuation.Asmanyaccelerogramsaspossiblethatarerecordedundercomparableconditionsandhaveapredominantfrequencysimilartothatselectedforthedesignearthquakeshouldbeincludedinthedevelopmentofthedesignresponsespectra.Also,accelerogramsshouldbeselectedthathavebeencorrectedforthetruebaselineofzeroacceleration,forerrorsindigitization,andforotherirregularities(SchiffandBogdanoff1967).b.特殊地点的设计反应谱 在任何可能的地方，特殊地点的设计反应谱都应从与控制地震一样有相似来源和传播途径的以及在与大坝相似的基础上记录下的强烈的地震运动记录的反应谱进行统计学的研究。重要的来源属性包括震级，如果可能的话，还包括断层类型和地质环境。传播路径属性包括距离，深度和衰减。在可比的条件下记录的且与设计地震有相似主频的尽可能多的加速度值应包括在设计反应谱的研究中。此外，应选择对真正的加速度基准线，对数字误差和对其他不规范的行为进行校正后的加速度值（Schiff和Bogdanoff1967）。(2)Wherealargeenoughensembleofsite-specificstrongmotionrecordsisnotavailable,designresponsespectramaybeapproximatedbyscalingthatensembleofrecordsthatrepresentsthebestestimateofsource,propagationpath,andsiteproperties.Scalingfactorscanbeobtainedinseveralways.Thescalingfactormaybedeterminedbydividingthepeakoreffectivepeakaccelerationspecifiedforthecontrollingearthquakebythepeakaccelerationoftherecordbeingrescaled.Thepeakvelocityoftherecordshouldfallwithintherangeofpeakvelocitiesspecifiedforthecontrollingearthquake,ortherecordshouldnotbeused.Spectrumintensitycanbeusedforscalingbyusingtheratioofthespectrumintensitydeterminedforthesiteandthespectrumintensityoftherecordbeingrescaled(USBR1978).Accelerationattenuationrelationshipscanbeusedforscalingbydividingtheaccelerationthatcorrespondstothesourcedistanceandmagnitudeofthecontrollingearthquakebytheaccelerationthatcorrespondstothesourcedistanceandmagnitudeoftherecordbeingrescaled(GuzmanandJennings1970).Becausethescalingofaccelerogramsisanapproximateoperationatbest,thecloserthecharacteristicsoftheactualearthquakearetothoseofthecontrollingearthquake,themorereliabletheresults.Forthisreason,thescalingfactorshouldbeheldtowithinarangeof0.33to3forgravitydam.(2)某地足够大的强震集合是不可能的，设计反应谱可能通过换算最具代表性的资料，传播路径，以及地貌的记录近似取得。换算因素包括多个方面。比例因数可通过区分峰值或由重新调整的记录的峰值加速度产生的为控制地震规定的有效加速度峰值确定。记录的速度峰值应在为控制地震而确定的速度峰值范围内，否则此记录是不能使用的。频谱强度能通过用某地的频谱强度与被重新评估的记录的频谱强度的比率来换算的到(USBR1978)。通过区分与换算后记录的震源矩和震级一致的加速度得到的控制地震的与换算后记录的震源矩和震级一致的加速度，加速度衰减关系可用来换算(GuzmanandJennings1970)。由于加速度按比例缩放充其量是一个近似运算，对于控制地震来说越接近实际地震的特点意味着更可靠的结果。因此，重力坝的比例因子的取值应在0.33～3的范围内。(3)Guidancefordevelopingdesignresponsespectra,statistically,fromstrongmotionrecordsisgiveninVanmarcke(1979).(3)从强震记录统计得到的设计反应谱的研究指导可参见Vanmarcke(1979)。(4)Site-dependentresponsespectradevelopedfromstrongmotionrecords,asdescribedinparagraphs5-8b,shouldhaveamplitudesequaltoorgreaterthanthemeanresponsespectrumfortheappropriatefoundationgivenbySeed,Ugas,andLysmer(1976),anchoredbythePGAdeterminedforthesite.ThisminimumresponsespectrummaybeanchoredbyaneffectivePGAdeterminedforthesite,butsupportingdocumentationfordeterminingtheeffectivePGAwillberequired(NewmarkandHall1982).(4)如在5-8段描述的那样，某地由强震记录得到的反应谱应该有振幅大于或等于Seed,Ugas,andLysmer(1976)所提出的恰当选择的且由对某点确定的PGA的固定基础的平均反应谱。反应谱的最小值可通过一个为某点确定的有影响的PGA值标记，但是必要条件是要有确定有影响的PGA值的文档(NewmarkandHall1982)。(5)Ameansmoothresponsespectrumoftheresponsespectraofrecordschosenshouldbe presentedforeachdampingvalueofinterest.Thestatisticallevelofresponsespectrausedshouldbejustifiedbasedonthedegreeofconservatismintheprecedingstepsoftheseismicdesignprocessandthethoroughnessofthedevelopmentofthedesignresponsespectra.Ifarareeventisusedasthecontrollingearthquakeandtheearthquakerecordsarescaledbyupperboundvaluesofgroundmotions,thenusearesponsespectrumcorrespondingtothemeanoftheamplificationfactorsiftheresponsespectrumisbasedonfiveormoreearthquakerecords.(5)一个从反应谱记录中选择的平滑的反应谱应能反应每个相关的阻尼值。反应谱的统计水平常应根据前面的抗震设计步骤和设计反应谱的所有情况的保守水平进行适当调整。如果一个罕见事件用来代表控制地震和由地震动的上限值换算得到的地震记录，那么当反应谱是根据五个或更多的地震记录得出的时要用一个与平均放大因子相适应的反应谱值。c.Accelerogramsforacceleration-timehistoryanalysis.Accelerogramsusedfordynamicinputshouldbecompatiblewiththedesignresponsespectrumandaccountforthepeakgroundmotionsparameters,spectrumintensity,anddurationofshaking.Compatibilityisdefinedastheenvelopeofallresponsespectraderivedfromtheselectedaccelerogramsthatliebelowthesmoothdesignresponsespectrumthroughoutthefrequencyrangeofstructuralsignificance.c.加速度-时间的加速度时程分析。用于动态输入的加速度应与设计反应谱和地震动峰值、光谱强度、震动持续时间的所占比例相匹配。匹配度是指由所有来源于比依照结构重要性确定的设计反应谱稍低而选择的加速度的反应谱的包络线。5-9.DynamicMethodsofStressAnalysisa.General.Adynamicanalysisdeterminesthestructuralresponsebasedonthecharacteristicsofthestructureandthenatureoftheearthquakeloading.Dynamicmethodsusuallyemploythemodalanalysistechnique.Thistechniqueisbasedonthesimplifyingassumptionthattheresponseineachnaturalmodeofvibrationcanbecomputedindependentlyandthemodalresponsescanbecombinedtodeterminethetotalresponse(Chopra1987).Modaltechniquesthatcanbeusedforgravitydamsincludeasimplifiedresponsespectrummethodandfiniteelementmethodsusingeitheraresponsespectrumoracceleration-timerecordsforthedynamicinput.Adynamicanalysisshouldbeginwiththeresponsespectrummethodandprogresstomorerefinedmethodsifneeded.Atime-historyanalysisisusedwhenyielding(cracking)ofthedamisindicatedbyaresponsespectrumanalysis.Thetime-historyanalysisallowsthedesignertodeterminethenumberofcyclesofnonlinearbehavior,themagnitudeofexcursionintothenonlinearrange,andthetimethestructureremainsnonlinear.5-9.动态应力分析方法a.常规方法。动态分析确定了建立在结构特征和地震荷载性质基础上的结构响应。动态方法通常采用模态分析技术。这种技术是基于简化假定，即在每一个固有模态的振动响应可以单独计算然后将模态响应结合起来确定总反应（乔普拉1987年）。对于动态输入，能用于重力坝的模态方法包括简化响应谱法和用响应谱或时间-加速度记录计算的有限元法。如果需要更细致的方法，动态分析应该从响应谱法和相关程序开始。通过响应谱分析，若大坝会出现屈服（开裂），则还应使用时程分析。时程分析允许设计者由决定非线性行为次数，在非线性范围内的偏移幅度，以及结构保持非线性的时间。b.Simplifiedresponsespectrummethod.(1)Thesimplifiedresponsespectrummethodcomputesthemaximumlinearresponseofanonoverflowsectioninitsfundamentalmodeofvibrationduetothehorizontalcomponentofgroundmotion(Chopra1987).Thedamismodeledasanelasticmassfullyrestrainedonarigidfoundation.Hydrodynamiceffectsaremodeledasanaddedmassofwatermovingwiththedam. Theamountoftheaddedwatermassdependsonthefundamentalfrequencyofvibrationandmodeshapeofthedamandtheeffectsofinteractionbetweenthedamandreservoir.Earthquakeloadingiscomputeddirectlyfromthespectralacceleration,obtainedfromthedesignearthquakeresponsespectrum,andthedynamicpropertiesofthestructuralsystem.b.简化反应谱法。(1)简化响应谱法计算非溢流坝段由于地面运动的水平分量产生的基本震动模式的线性响应最大值（乔普拉1987）。大坝被看做一个在刚性基础上受完全约束的弹性体。水的动力作用用作用在大坝上的流动水的质量模拟。附加水质量大小取决于震动基本频率，大坝模型尺寸，以及大坝与水库之间的相互影响。地震荷载可由从设计地震响应谱得到的加速度谱和结构的动力特性直接计算得出。(2)Thissimplifiedmethodcanbeusedalsoforanungatedspillwaymonoliththathasasectionsimilartoanonoverflowmonolith.AsimplifiedmethodforgatedspillwaymonolithsispresentedinWESTechnicalReportSL-89-4(ChopraandTan1989).(2)这种简化方法也可用于封闭的与非溢流坝段有相似截面的泄洪坝段。泄洪坝闸门的简化方法在饮水和环境卫生技术报告sl-89-4（乔普拉和Tan1989）中有介绍。(3)TheprogramSDOFDAMisavailabletoeasilymodeladamusingthefiniteelementmethodandChopra’ssimplifiedprocedureforestimatingthehydrodynamicloading.Thisanalysisprovidesareasonablefirstestimateofthetensilestressinthedam.Fromthatestimate,onecandecideifthedesignisadequateorifarefinedanalysisisneeded.(3)SDOFDAM程序可很容易的用有限元法及乔普拉简化程序模拟大坝并估算其动力荷载。这种分析方法提供了一个合理的大坝内的张应力第一估计值。设计者可通过估算值决定设计是否合理或是否需要精确计算分析。c.Finiteelementmethods.(1)General.Thefiniteelementmethodiscapableofmodelingthehorizontalandverticalstructuraldeformationsandtheexteriorandinteriorconcrete,anditincludestheresponseofthehighermodesofvibrations,theinteractioneffectsofthefoundationandanysurroundingsoil,andthehorizontalandverticalcomponentsofgroundmotion.c.有限元法(1)一般地。有限元法能模拟结构水平和垂直方向的变形以及内部和外部的混凝土，它包括高次振动模式的响应，基础与任何周围土壤的相互作用以及地震动的水平和垂直分量。(2)Finiteelementresponsespectrummethod.(a)Thefiniteelementresponsespectrummethodcanmodelthedynamicresponseoflineartwo-andthree-dimensionalstructures.ThehydrodynamiceffectsaremodeledasanaddedmassofwatermovingwiththedamusingWestergaard’sformula(Westergaard1933).Thefoundationsaremodeledasdiscreteelementsorahalfspace.(2)有限元响应谱法。(a)有限元响应谱法可用来模拟线性二维或三维结构的动力响应。水动力作用转化为用Westergaard的应力函数表示作用在大坝上的水荷载(Westergaard1933)。基础被看做分离的部分或只考虑一半空间。(b)SixgeneralpurposefiniteelementprogramsarecomparedbyHallandRadhakrishnan(1983).(b)霍尔和拉达克里希南（1983）比较了六个通用的有限元程序。(c)Afiniteelementprogramcomputesthenaturalfrequenciesofvibrationandcorrespondingmodeshapesforspecifiedmodes.Theearthquakeloadingiscomputedfromearthquakeresponsespectraforeachmodeofvibrationinducedbythehorizontalandverticalcomponentsofground motion.Thesemodalresponsesarecombinedtoobtainanestimateofthemaximumtotalresponse.Stressesarecomputedbyastaticanalysisofthedamusingtheearthquakeloadingasanequivalentstaticload.(c)有限元程序以规定的模式计算自振频率和相应的模态。由地震动的水平分量和垂直分量引起的每种振动模式的地震响应谱计算地震荷载。将这些模态响应组合可得到总响应的最大估计值。把地震荷载等价为作用于坝体相应的静态荷载，对其进行静力分析求出其应力值。(d)Thecompletequadraticcombination(CQC)method(DerKiureghian1979and1980)shouldbeusedtocombinethemodalresponses.TheCQCmethoddegeneratestothesquarerootofthesumofsquares(SRSS)methodfortwo-dimensionalstructuresinwhichthefrequenciesarewellseparated.CombiningmodalmaximabytheSRSSmethodcandramaticallyoverestimateorsignificantlyunderestimatethedynamicresponseforthree-dimensionalstructures.(d)完整二次型组合（CQC）方法（DerKiureghian1979年和1980年）应结合模态响应使用。当频率是完全分离的时，完整二次型组合（CQC）方法就变成对二维结构的平方和的平方根方法。用SRSS方法计算得到的组合模式极大值会大大高估或大幅低估三维结构的动力响应。(e)Thefiniteelementresponsespectrummethodshouldbeusedfordammonolithsthatcannotbemodeledtwodimensionallyorifthemaximumtensilestressfromthesimplifiedresponsespectrummethod(paragraph5-9b)exceeds15percentoftheunconfinedcompressivestrengthoftheconcrete.(e)有限元响应谱法应用于无法用二维模拟或通过简化响应谱法得到的张应力最大值超过了混凝土的无侧限抗压强度15%的坝段。(f)Normalstressesshouldbeusedforevaluatingtheresultsobtainedfromafiniteelementresponsespectrumanalysis.Finiteelementprogramscalculatenormalstressesthat,inturn,areusedtocomputeprincipalstresses.Theabsolutevaluesofthedynamicresponseatdifferenttimeintervalsareusedtocombinethemodalresponses.Thesecalculationsofprincipalstressoverestimatetheactualcondition.Principalstressesshouldbecalculatedusingthefiniteelementacceleration-timehistoryanalysisforaspecifictimeinterval.(f)正应力用于评估用有限元响应谱分析得到的结果。有限元程序依次计算用于主应力计算的正应力。在不同时间间隔的动力响应的绝对值用于与模态响应相结合。这些主应力运算结果比实际情况偏大。对于具体的时间间隔，主应力的计算应使用有限元加速度-时程分析。(3)Finiteelementacceleration-timehistorymethod.(a)Theacceleration-timehistorymethodrequiresageneralpurposefiniteelementprogramorthespecialpurposecomputerprogramcalledEADHI.EADHIcanmodelstaticanddynamicresponsesoflineartwo-dimensionaldams.Thehydrodynamiceffectsaremodeledusingthewaveequation.Thecompressibilityofwaterandstructuraldeformationeffectsareincludedincomputingthehydrodynamicpressures.EADHIwasdevelopedassumingafixedbaseforthedam.Themostcomprehensivetwo-dimensionalearthquakeanalysisprogramavailableforgravitydamsisEAGD84,whichcanmodelstaticanddynamicresponsesoflineartwo-dimensionaldams,includinghydrodynamicandfoundationinteraction.DynamicinputforEADHIandEAGD84isanaccelerationtimerecord.(3)有限元加速度时程分析法。(a)有限元加速度时程分析法需要一个通用的有限元程序或名叫EADHI的专用计算机程序。EADHI能模拟线性二维坝体的静态和动态响应。流体效应用波动方程模拟。动水压力的计算包括水的压缩系数和结构形变效应。EADHI 引用了大坝基础固定的假定。可用于重力坝的大型二维地震分析的程序是EAGD84，它能模拟包括流体动力学和基础相互作用的线性二维坝体的静态和动态响应。EADHI和EAGD84的动态输入是是加速度时间记录。(b)Theacceleration-timehistorymethodcomputesthenaturalfrequenciesofvibrationandcorrespondingmodeshapesforspecifiedmodes.Theresponseofeachmode,intheformofequivalentlateralloads,iscalculatedfortheentiredurationoftheearthquakeacceleration-timerecordstartingwithinitialconditions,takingasmalltimeinterval,andcomputingtheresponseattheendofeachtimeinterval.Themodalresponsesareaddedforeachtimeintervaltoyieldthetotalresponse.Thestressesarecomputedbyastaticanalysisforeachtimeinterval.(c)Anacceleration-timehistoryanalysisisappropriateifthevariationofstresseswithtimeisrequiredtoevaluatetheextentanddurationofahighlystressedcondition.(b)加速度时程分析法按规定的模式计算自振频率和相应的振型。以等效横向荷载的形式计算每种模式在地震加速度记录以初始条件开始的整个过程中的响应，经过短暂的时间间隔，计算每个时间间隔末尾的响应。将每个时间段的模态响应叠加得到总的响应值。对于每个时间段，通过静力分析计算出应力。(c)如果要评估在高应力状态下应力随时间的变化曲线的范围及持续时间，适当的方法是加速度时程分析。'