ACI 209.2R-2008 Guide for Modeling and Calculating Shrinkage and Creep in Hardened Concrete《建模和计算硬混凝土中的收缩和徐变指南》.pdf

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1、ACI 209.2R-08Reported by ACI Committee 209Guide for Modeling and CalculatingShrinkage and Creepin Hardened ConcreteGuide for Modeling and Calculating Shrinkage and Creepin Hardened ConcreteFirst PrintingMay 2008ISBN 978-0-87031-278-6American Concrete InstituteAdvancing concrete knowledgeCopyright by

2、 the American Concrete Institute, Farmington Hills, MI. All rights reserved. This materialmay not be reproduced or copied, in whole or part, in any printed, mechanical, electronic, film, or otherdistribution and storage media, without the written consent of ACI.The technical committees responsible f

3、or ACI committee reports and standards strive to avoid ambiguities,omissions, and errors in these documents. In spite of these efforts, the users of ACI documents occasionallyfind information or requirements that may be subject to more than one interpretation or may beincomplete or incorrect. Users

4、who have suggestions for the improvement of ACI documents arerequested to contact ACI. Proper use of this document includes periodically checking for errata atwww.concrete.org/committees/errata.asp for the most up-to-date revisions.ACI committee documents are intended for the use of individuals who

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6、f this information.All information in this publication is provided “as is” without warranty of any kind, either express or implied,including but not limited to, the implied warranties of merchantability, fitness for a particular purpose ornon-infringement.ACI and its members disclaim liability for d

7、amages of any kind, including any special, indirect, incidental,or consequential damages, including without limitation, lost revenues or lost profits, which may resultfrom the use of this publication.It is the responsibility of the user of this document to establish health and safety practices appro

8、priate tothe specific circumstances involved with its use. ACI does not make any representations with regard tohealth and safety issues and the use of this document. The user must determine the applicability of allregulatory limitations before applying the document and must comply with all applicabl

9、e laws and regulations,including but not limited to, United States Occupational Safety and Health Administration (OSHA) healthand safety standards.Order information: ACI documents are available in print, by download, on CD-ROM, through electronicsubscription, or reprint and may be obtained by contac

10、ting ACI.Most ACI standards and committee reports are gathered together in the annually revised ACI Manual ofConcrete Practice (MCP).American Concrete Institute38800 Country Club DriveFarmington Hills, MI 48331U.S.A.Phone: 248-848-3700Fax: 248-848-3701www.concrete.orgACI 209.2R-08 was adopted and pu

11、blished May 2008.Copyright 2008, American Concrete Institute.All rights reserved including rights of reproduction and use in any form or by anymeans, including the making of copies by any photo process, or by electronic ormechanical device, printed, written, or oral, or recording for sound or visual

12、 reproductionor for use in any knowledge or retrieval system or device, unless permission in writingis obtained from the copyright proprietors.209.2R-1ACI Committee Reports, Guides, Manuals, StandardPractices, and Commentaries are intended for guidance inplanning, designing, executing, and inspectin

13、g construction.This document is intended for the use of individuals who arecompetent to evaluate the significance and limitations of itscontent and recommendations and who will acceptresponsibility for the application of the material it contains.The American Concrete Institute disclaims any and allr

14、esponsibility for the stated principles. The Institute shall notbe liable for any loss or damage arising therefrom.Reference to this document shall not be made in contractdocuments. If items found in this document are desired by theArchitect/Engineer to be a part of the contract documents, theyshall

15、 be restated in mandatory language for incorporation bythe Architect/Engineer.Guide for Modeling and Calculating Shrinkageand Creep in Hardened ConcreteReported by ACI Committee 209ACI 209.2R-08This guide is intended for the prediction of shrinkage and creep incompression in hardened concrete. It ma

16、y be assumed that predictionsapply to concrete under tension and shear. It outlines the problems andlimitations in developing prediction equations for shrinkage and compressivecreep of hardened concrete. It also presents and compares the predictioncapabilities of four different numerical methods. Th

17、e models presented arevalid for hardened concrete moist cured for at least 1 day and loaded aftercuring or later. The models are intended for concretes with mean compressivecylindrical strengths at 28 days within a range of at least 20 to 70 MPa(3000 to 10,000 psi). This document is addressed to des

18、igners who wishto predict shrinkage and creep in concrete without testing. For structuresthat are sensitive to shrinkage and creep, the accuracy of an individualmodels predictions can be improved and their applicable rangeexpanded if the model is calibrated with test data of the actual concreteto be

19、 used in the project.Keywords: creep; drying shrinkage; prediction models; statistical indicators.CONTENTSChapter 1Introduction and scope, p. 209.2R-21.1Background1.2Scope1.3Basic assumptions for development of predictionmodelsChapter 2Notation and definitions, p. 209.2R-32.1Notation2.2DefinitionsCh

20、apter 3Prediction models, p. 209.2R-53.1Data used for evaluation of models3.2Statistical methods for comparing models3.3Criteria for prediction models3.4Identification of strains3.5Evaluation criteria for creep and shrinkage modelsChapter 4Model selection, p. 209.2R-74.1ACI 209R-92 model4.2Baant-Baw

21、eja B3 model4.3CEB MC90-99 model4.4GL2000 model4.5Statistical comparisons4.6Notes about modelsAkthem A. Al-Manaseer Marwan A. Daye David B. McDonald*Ian RobertsonZdenek P. Baant Walter H. Dilger Harald S. Mueller Kenji SakataJeffrey J. Brooks Noel J. Gardner*Hani H. A. Nassif K. Nam ShiuRonald G. Bu

22、rg Will Hansen Lawrence C. Novak W. Jason WeissMario Alberto Chiorino Hesham Marzouk Klaus Alexander Rieder*Members of the subcommittee that prepared this guide.Carlos C. Videla*ChairDomingo J. Carreira*Secretary209.2R-2 ACI COMMITTEE REPORTChapter 5References, p. 209.2R-135.1Referenced standards an

23、d reports5.2Cited referencesAppendix AModels, p. 209.2R-16A.1ACI 209R-92 modelA.2Baant-Baweja B3 modelA.3CEB MC90-99 modelA.4GL2000 modelAppendix BStatistical indicators, p. 209.2R-28B.1BP coefficient of variation (BP%) methodB.2CEB statistical indicatorsB.3The Gardner coefficient of variation (G)Ap

24、pendix CNumeric examples, p. 209.2R-30C.1ACI 209R-92 model solutionC.2Baant-Baweja B3 model solutionC.3CEB MC90-99 model solutionC.4GL2000 model solutionC.5Graphical comparison of model predictionsCHAPTER 1INTRODUCTION AND SCOPE1.1BackgroundTo predict the strength and serviceability of reinforced an

25、dprestressed concrete structures, the structural engineer requiresan appropriate description of the mechanical properties of thematerials, including the prediction of the time-dependantstrains of the hardened concrete. The prediction of shrinkageand creep is important to assess the risk of concrete

26、cracking,and deflections due to stripping-reshoring. As discussed inACI 209.1R, however, the mechanical properties of concreteare significantly affected by the temperature and availability ofwater during curing, the environmental humidity and temper-ature after curing, and the composition of the con

27、crete,including the mechanical properties of the aggregates.Among the time-dependant properties of concrete that are ofinterest to the structural engineer are the shrinkage due tocement hydration (self-desiccation), loss of moisture to theenvironment, and the creep under sustained loads. Dryingbefor

28、e loading significantly reduces creep, and is a majorcomplication in the prediction of creep, stress relaxation, andstrain recovery after unloading. While there is a lot of data onshrinkage and compressive creep, not much data are availablefor creep recovery, and very limited data are available forr

29、elaxation and tensile creep.Creep under variable stresses and the stress responsesunder constant or variable imposed strains are commonlydetermined adopting the principle of superposition. Thelimitations of this assumption are discussed in Section 1.3.Further, the experimental results of Gamble and

30、Parrott(1978) indicate that both drying and basic creep are onlypartially, not fully, recoverable. In general, provided thatwater migration does not occur as in sealed concrete or theinterior of large concrete elements, superposition can beused to calculate both recovery and relaxation.The use of th

31、e compressive creep to the tensile creep incalculation of beams time-dependant deflections has beensuccessfully applied in the work by Branson (1977), Baantand Ho (1984), and Carreira and Chu (1986).The variability of shrinkage and creep test measurementsprevents models from closely matching experim

32、ental data.The within-batch coefficient of variation for laboratory-measured shrinkage on a single mixture of concrete wasapproximately 8% (Baant et al. 1987). Hence, it would beunrealistic to expect results from prediction models to bewithin plus or minus 20% of the test data for shrinkage. Evenlar

33、ger differences occur for creep predictions. For structureswhere shrinkage and creep are deemed critical, material testingshould be undertaken and long-term behavior extrapolatedfrom the resulting data. For a discussion of testing forshrinkage and creep, refer to Acker (1993), Acker et al. (1998),an

34、d Carreira and Burg (2000).1.2ScopeThis document was developed to address the issues relatedto the prediction of creep under compression and shrinkage-induced strains in hardened concrete. It may be assumed,however, that predictions apply to concrete under tension andshear. It outlines the problems

35、and limitations in developingprediction equations, presents and compares the predictioncapabilities of the ACI 209R-92 (ACI Committee 209 1992),Baant-Baweja B3 (Baant and Baweja 1995, 2000), CEBMC90-99 (Muller and Hillsdorf 1990; CEB 1991, 1993,1999), and GL2000 (Gardner and Lockman 2001) models, an

36、dgives an extensive list of references. The models presented arevalid for hardened concrete moist cured for at least 1 day andloaded at the end of 1 day of curing or later. The modelsapply to concretes with mean compressive cylindricalstrengths at 28 days within a range of at least 20 to 70 MPa(3000

37、 to 10,000 psi). The prediction models were calibratedwith typical composition concretes, but not with concretescontaining silica fume, fly ash contents larger than 30%, ornatural pozzolans. Models should be calibrated by testingsuch concretes. This document does not provide informationon the evalua

38、tion of the effects of creep and shrinkage on thestructural performance of concrete structures.1.3Basic assumptions for developmentof prediction modelsVarious testing conditions have been established to stan-dardize the measurements of shrinkage and creep. Thefollowing simplifying assumptions are no

39、rmally adopted inthe development of prediction models.1.3.1 Shrinkage and creep are additiveTwo nominallyidentical sets of specimens are made and subjected to the samecuring and environment conditions. One set is not loaded and isused to determine shrinkage, while the other is generally loadedfrom 2

40、0 to 40% of the concrete compressive strength. Load-induced strains are determined by subtracting the measuredshrinkage strains on the nonloaded specimens from the strainsmeasured on the loaded specimens. Therefore, it is assumedthat the shrinkage and creep are independent of each other.Tests carrie

41、d out on sealed specimens, with no moisturemovement from or to the specimens, are used to determineautogenous shrinkage and basic creep.MODELING AND CALCULATING SHRINKAGE AND CREEP IN HARDENED CONCRETE 209.2R-31.3.2 Linear aging model for creepExperimentalresearch indicates that creep may be conside

42、red approxi-mately proportional to stress (LHermite et al. 1958; Keeton1965), provided that the applied stress is less than 40% of theconcrete compressive strength.The strain responses to stress increments applied atdifferent times may be added using the superposition principle(McHenry 1943) for inc

43、reasing and decreasing stresses,provided strain reversals are excluded (for example, as inrelaxation) and temperature and moisture content are keptconstant (Le Camus 1947; Hanson 1953; Davies 1957; Ross1958; Neville and Dilger 1970; Neville 1973; Baant 1975;Gamble and Parrot 1978; RILEM Technical Co

44、mmittee TC-691988). Major deviations from the principle of superpositionare caused by the neglect of the random scatter of the creepproperties, by hygrothermal effects, including water diffusionand time evolution of the distributions of pore moisturecontent and temperature, and by material damage, i

45、ncludingdistributed cracking and fracture, and also frictionalmicroslips. A comprehensive summary of the debate on theapplicability of the principle of superposition when dealingwith the evaluation of creep structural effects can be foundin the references (Baant 1975, 1999, 2000; CEB 1984;RILEM Tech

46、nical Committee TC-107 1995; Al Manaseer etal. 1999; Jirasek and Baant 2002; Gardner and Tsuruta2004; Baant 2007).1.3.3 Separation of creep into basic creep and dryingcreepBasic creep is measured on specimens that are sealedto prevent the ingress or egress of moisture from or to itsenvironment. It i

47、s considered a material constitutive propertyand independent of the specimen size and shape. Drying creepis the strain remaining after subtracting shrinkage, elastic, andbasic creep strains from the total measured strain on nominallyidentical specimens in a drying environment. The measuredaverage cr

48、eep of a cross section at drying is strongly size-dependant. Any effects of thermal strains have to be removedin all cases or are avoided by testing at constant temperature.In sealed concrete specimens, there is no moisture movementinto or out of the specimens. Low-water-cement-ratioconcretes self-d

49、esiccate, however, leading to autogenousshrinkage. Normal-strength concretes do not change volume atrelative humidity in the range 95 to 99%, whereas samplesstored in water swell (LHermite et al. 1958).1.3.4 Differential shrinkage and creep or shrinkage andcreep gradients are neglectedThe shrinkage strains deter-mined according to ASTM C157/C157M are measured alongthe longitudinal axis of prismatic specimens; however, themajority of reported creep and shrinkage data are based onsurface measurements of cylindrical specimens (AST