1、ACI 446.4R-04 became effective April 21, 2004.Copyright 2004, 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
2、recording for sound or visual reproductionor for use in any knowledge or retrieval system or device, unless permission in writingis obtained from the copyright proprietors.ACI Committee Reports, Guides, Standard Practices, andCommentaries are intended for guidance in planning,designing, executing, a
3、nd inspecting construction. Thisdocument 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
4、any and allresponsibility 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 document
5、s, theyshall be restated in mandatory language for incorporation bythe Architect/Engineer.446.4R-1It is the responsibility of the user of this document toestablish health and safety practices appropriate to the specificcircumstances involved with its use. ACI does not make anyrepresentations with re
6、gard to health and safety issues and theuse of this document. The user must determine theapplicability of all regulatory limitations before applying thedocument and must comply with all applicable laws andregulations, including but not limited to, United StatesOccupational Safety and Health Administ
7、ration (OSHA)health and safety standards.Report on Dynamic Fractureof ConcreteACI 446.4R-04This report summarizes information regarding the analysis of concrete systemssubjected to rapid loading. Engineers will obtain an overview of the subjectmatter along with recommended approaches for analysis an
8、d selection ofmaterial properties. Researchers will obtain a concise source of informationfrom leading authorities in the field conducting research and applying theseconcepts in practice. This report describes how, as strain rates increase above104to 103s1, concrete in tension and compression become
9、s stronger andstiffer, with less prepeak crack growth and less ductile behavior in thepostpeak region. The rate dependence of bond is shown to be due tolocal crushing around deformations of the bar and to have the samerelationship to rate as compressive strength. The practical effect of thislocal cr
10、ushing is to concentrate strains in a small number of cracks,thus lowering the overall ductility of reinforced members. Finally, it isconcluded that computational models of postpeak behavior undereither dynamic or static load should use a localization limiter so thatstrain softening into arbitrarily
11、 small regions is prevented. The modelsshould also properly pose the equations of motion; one appropriateway to do this is to represent softening through rate dependence, suchas viscoplasticity.Keywords: computational modeling; concrete-reinforcement bond; cracking;fracture energy; fracture mechanic
12、s; fracture toughness; size effect; strain rate;stress-intensity factor; stress rate.CONTENTSChapter 1Introduction, p. 446.4R-21.1General1.2Conceptual models1.3Scope1.4AbbreviationsReported by ACI Committee 446Farhad Ansari Y.-S. Jenq Philip C. PerdikarisZdenek P. Bazant N. Krstulovic-Opara G. Pijau
13、dier-CabotOral Buyukozturk C. K. Y. Leung Victor E. SaoumaIgnacio Carol Victor C. Li Surendra P. ShahDavid Darwin F.-B. Lin R. Sierakowski*Manuel Elices J. Mazars Wimal Suaris*Rolf Eligehausen Steven L. McCabe S. SwartzS.-J. Fang Christian Meyer Tianxi TangR. Gettu Hirozo Mihashi Tatsuya TsubakiTosh
14、iaki Hasegawa Richard A. Miller C. VipulanandanNeil Hawkins*Sidney MindessMethi WecharatanaAnthony R. Ingraffea Barzin Mobasher Yunping XiJeremy IsenbergCharles D. NormanVellore S. GopalaratnamChairWalter H. Gerstle*Secretary*Members of subcommittee who prepared this document.Co-chair of subcommitte
15、e who prepared this document.446.4R-2 ACI COMMITTEE REPORTChapter 2Experimental evidence of rate effects, p. 446.4R-52.1Mode I failure: plain concrete and mortar2.2Failure under compressive stress2.3Mixed-mode failure2.4Bond failure2.5Concluding remarksChapter 3Analytical modeling of strain-rate eff
16、ects, p. 446.4R-173.1Models for rate dependence of fracture based onmicromechanics3.2Rate-sensitive damage models that incorporatemicrocracking phenomena3.3Strain-rate-dependent fracture modelChapter 4Computational modeling of localized failure under dynamic loading, p. 446.4R-214.1Model of fracture
17、 process zone4.2Nonlocal continuum modelsChapter 5Summary, p. 446.4R-23Chapter 6References, p. 446.4R-246.1Referenced standards and reports6.2Other referencesCHAPTER 1INTRODUCTION1.1 GeneralImpact, explosions, and earthquakes impose dynamiceffects on concrete structures. Impact loading on a parapetc
18、an occur if it is struck accidentally by a crane. Seismicloading produces significant strain rates in concrete shear-walls and other lateral force-resisting elements. Explosiveloading, due to accidental detonation of industrial vaporclouds or terrorist bombing, produces high strain rates infloor sla
19、bs and columns. These possibilities have promptedexperiments on plain concrete specimens to investigate basicproperties of concrete under various states and rates of loading.Under dynamic loading (rapidly applied loads of shortduration), both structural and material responses depend on theapplied lo
20、ading rate. Although both the geometry of thestructure and the material properties control the rate of cracking,this report is concerned primarily with the material effects.Common practice for evaluating the resistance of concretestructures to dynamic loading is to:a) Estimate the transient state of
21、 stress in the structureusing an elastodynamic analysis; andb) Evaluate the resistance of the structure using strengthproperties for the concrete and steel that are enhanced bystrain-rate-dependent factors. For the failure modes of aconcrete structure controlled by yielding of the reinforce-ment or
22、crushing of the concrete, common practice usuallyprovides reliable design information. For those failuremodes controlled by crack propagation, however, such asdiagonal tension or splitting failures, and where resistance tofracture is of fundamental importance for computations ofenergy absorption and
23、 energy dissipation, common practicedoes not usually yield reliable information. This inadequacyis due primarily to the fact that dynamic fracture of concretestructures does not involve instantaneous fracture, butcontinuous dynamic crack propagation under dynamicloading. Reliable dynamic failure ana
24、lyses of concrete structuresrequires knowledge of the dynamic fracture properties of theconcrete as well as its strain-rate-dependent properties.Therefore, this report concerns not only strain rate effectsbut also consideration of the dynamic fracture propertiesof concrete in general.As shown in Fig
25、. 1.1, the strength of concrete in tension,flexure, and compression increases with an increase in theloading rate. The strain corresponding to the maximumstrength also increases with an increase in the loading rate.The increase in strain is due to the development of multiplecracks in the failure zon
26、e, and the value of the maximumstrain is strongly dependent on the width assumed for thefailure zone.The differing rates of increase in tensile, flexural, andcompressive strengths with increasing loading rates, and thecrack propagation effects that cause failure, can result in themode of failure of
27、a concrete member changing from flexureto shear with an increase in the loading rate. Consequently, adynamically loaded beam may require more shear reinforcementto ensure ductile behavior than the same beam loaded statically.Characterization of the rate effects for the materials of thebeam, its iner
28、tial effects, and how those effects combine tocontrol crack propagation, are essential to successful designsto resist high strain-rate loadings.Inertial effects are involved in any impact loading of astructure or in any impact testing in a laboratory. In the lattercase, many efforts have been devote
29、d to reducing this effectso that dynamic test data can be used to evaluate the dynamicstrength of concrete by static analysis. Inertial effects,however, are inherent in any dynamic event of materialdeformation or fracture. The inertial effect of a large mass ofmaterial, such as concrete, considerabl
30、y increases the impactresistance of the structure. This effect occurs because theinput energy should be transformed into kinetic energy,which is directly proportional to the mass, for moving theFig. 1.1Strain rate behaviors of plain concrete in differentsimple response modes (Suaris and Shah 1983).R
31、EPORT ON DYNAMIC FRACTURE OF CONCRETE 446.4R-3material necessary for crack formation and propagation.Therefore, any dynamic loading analysis should incorporateinertial effects rather than avoid them. Fortunately, currentdynamic finite-element computer programs can readilyhandle this problem.Because
32、of inertial and crack propagation considerations,it is not possible to directly link strain rates and loading rates.The test method used in the laboratory to investigatedynamic effects for a given type of loading is usually relatedto a given strain rate range. As indicated in Fig. 1.1, thelowest str
33、ain rate at which testing is performed is approximately107s1. That rate, which corresponds to static loading, alsohas creep associated with it. The next higher strain rateregion, up to 106 s1, is a quasistatic loading regime and isthe rate commonly involved in laboratory testing to investigateseismi
34、c effects using servocontrolled hydraulic jacks. In thethird region, up to 103or 102s1, mechanical resonance inthe specimen and testing apparatus may need to be considered toproperly interpret the response of the concrete within thecomplex specimen-machine interaction that occurs. Suchhigher rates c
35、an occur in shaketable experiments and instructures dynamically loaded by earthquakes. Rates up to 1 s1can be achieved in the laboratory using special hydraulictesting machines equipped with high-capacity servo-valves.Loading rates between 102and 1 s1correspond to thoseimposed by impact loadings suc
36、h as vehicles hitting bridgepiers or aircraft landing on airport runways. Finally, ratesabove 102s1cannot be readily achieved with a hydraulictesting machine. Impact or drop weight machines should beused or wave propagation utilized (Split-Hopkinson pressurebar device) to induce rate effects in smal
37、l volumes of material.Loadings in this region correspond to those that can occur inbombing adjacent to or within the building, and service system andother explosions that occur within the building. Rate dependence is thought to have a microstructuralorigin in the viscoelastic character of the harden
38、ed cementpaste. Rate dependence probably originates from the abilityof the bonds in calcium silicate hydrates to break and reformin a process governed by their thermal activation energy. Asecond origin of rate dependence is thought to be the time-dependent nature of crack growth, which originates in
39、 thesuccessive ruptures of interparticle bonds in the hardenedcement paste or concrete. Those ruptures cause growth of thefracture crack, an effect that is also a thermally activatedprocess (Bazant, Gu, and Faber 1995; Bazant and Prat 1988).This report examines the factors that cause strain-rateeffe
40、cts on concrete properties such as elastic modulus andtensile strength, and on fracture properties such as crackinitiation, crack propagation, critical stress-intensity factor,and fracture energy. The effects of strain rates between106to 104s1are considered. The primary focus is onunreinforced speci
41、mens because the vast majority of the datareported in the literature deal with such specimens. Rela-tively little unclassified work has been reported on thedynamic fracture of reinforced concrete structures. Therefore,some interpretation is needed to apply the work summarizedherein directly to reinf
42、orced structures.1.2Conceptual modelsAny conceptual model that takes into account static andquasistatic as well as strain-rate effects in concrete dependson the scale of observation. The use of Wittmanns (1983)approach of studying concrete on three levels (macro, meso,and micro) helps to clarify the
43、 origins of rate effects.1.2.1 MacrolevelAt the macrolevel, concrete is idealized ashomogeneous and isotropic. For very large structures withdimensions measured in meters, linear elastic fracturemechanics (LEFM) may be used; a single crack can beassumed, and a critical combination of crack length an
44、dapplied boundary conditions can then lead to crack growth.Growth can be locally stable (slow) or unstable (fast),depending on the stress gradients that the growing crackencounters. A critical value of K1(the stress intensity factor)should be reached as a necessary condition for crack growthto occur
45、. This critical value of stress intensity, also referredto as the fracture toughness, has been measured and found tobe much larger under dynamic loading than under staticloading, (Mindess, Banthia, and Yan 1987; John and Shah1986). Macrolevel models regard the cause of strain-rateeffects as a transf
46、er of strain energy at finite velocity fromthe structure surrounding the crack to the newly formedcracked surfaces. If the velocity of the advancing crack islow, strain-energy transport from the remainder of thestressed body along the crack surfaces to the crack tip iscommunicated via Rayleigh waves
47、 that travel at the Rayleighwave velocity Cr. In tests carried out by Mindess, Banthia, andYan (1987), John and Shah (1986), and Ross, Tedesco, andKuennen (1995), crack velocities at strain rates in the rangeof 0.1 to 1 s1were of the order of 100 ms1, or less than 10%of the Rayleigh wave velocity. Y
48、on, Hawkins, and Kobayshi(1991a) measured somewhat higher crack velocities of 132 and250 ms1but again, their values are considerably less thanthe Rayleigh wave velocity. On the other hand, Ross, Tedesco,and Kuennen (1995) have suggested that the crack velocityincreases linearly with an increasing st
49、rain rate on a log-log plot.They report experimentally measured crack velocities well inexcess of 100 ms1at strain rates greater than 1 s1. Curbachand Eibl (1989) have measured crack-tip velocities in therange of 120 to 540 ms1, and Takeda (1986) has reportedcrack-tip velocities as high as 1000 ms1using an extremelyhigh loading rate. In theory, however, as the crack velocity Vapproaches the Rayleigh wave velocity Cr, crack faces do notmove apart fast enough to provide the localized strains necessaryfor a high crack tip stress-intensity f
