ACI Materials Journal/May-June 1999 291

ACI Materials Journal, V. 96, No. 3, May-June 1999.Received November 26, 1996, and reviewed under Institute publication policies.

Copyright © 1999, American Concrete Institute. All rights reserved, including the making ofcopies unless permission is obtained from the copyright proprietors. Pertinent discussionincluding author’s closure, if any, will be published in the March-April 2000 ACI MaterialsJournal if the discussion is received by December 1, 1999.

ACI MATERIALS JOURNAL TECHNICAL PAPER

An experimental study on the cracking behavior of steel fiber rein-forced concrete (SFRC) is reported. Third-point bend tests werecarried out on notched beams. Test setup enabled recording ofload, beam deflection, and crack mouth opening displacement.Simultaneously, acoustic waves caused by cracking were counted.At regular time intervals, ultrasonic compression waves wereinduced at one beam end and recorded at the other beam end afterpropagation through the sample. Both methods reveal the crackingbehavior of SFRC. A frequency analysis of the acoustic activityreveals that low-frequency events can be attributed to micro-cracking, while high-frequency emissions unveil macroscopichappenings such as macrocracks, load transfer from matrix tofibers, and fiber pullout. The ultrasonic waves can be interpretedfrom their energy or velocity. The wave energy is affected bymicrocracking, while the wave velocity exhibits a change when amacrocrack has developed over a certain beam depth. Theconjunction of both methods helps to determine, in an objectivemanner, the moment when the first macrocrack appears.

Keywords: acoustics; bending (reinforcing steels); concrete; cracking;fracturing; ultrasonic tests.

INTRODUCTIONConcrete is a brittle material having a very low fracture

strength and a low strain capacity. The tensile strain capacityof concrete can be improved by the addition of fibers (e.g.,steel fibers). Most of the steel fiber reinforced concrete(SFRC) used in practice contains low volume fractions offibers (< 1%). For such volume fractions, the tensile strengthof the composite is similar to that of the matrix, i.e., crackinginitiates essentially at the same stress and strain as in unrein-forced concrete. The benefit of the fibers is primarily evidentafter strain localization when fibers bridge cracks and restrainthem from opening, thus increasing the load-carrying abilityof the composite. This property of SFRC provides a largeimprovement in toughness compared to plain concrete.

As fibers are added to concrete to control the cracking ofFRC and to alter the postcracking behavior of the composite,a common way to characterize the composite material isthrough toughness tests.1 The most widely used approach inNorth America to quantify the toughness of fiber reinforcedconcrete is to define toughness indexes as described in ASTMC 1018.2 These indexes depend upon the energy absorbed bythe specimen up to the occurrence of the first macrocrack. Thisoccurrence is defined as the point on the load-deflection curveat which the form of the curve first becomes nonlinear.However, locating this point in an objective manner in theascending part of the load-deflection plot is almost impossibleand is always dependent on human judgment.3 The load-deflection plot of concrete is indeed nonlinear everywhere. Infact, even before it is loaded, concrete contains microcracks,

and some of these start to grow as soon as the concrete isloaded. Therefore, when talking about the first crackingstrength, one should understand the moment at which thosediffuse microcracks localize in a macrocrack.

In this paper, another method to locate the first crackingstrength of SFRC is shown, using acoustic emission andultrasonic wave propagation. The ability of the acousticemission and ultrasonic wave propagation to reveal crackingbehavior—and thus first cracking strength—of concrete canbe understood by the underlying physics. In concrete, adamage zone called fracture process zone (FPZ) forms aheadof any macrocrack tip. In this zone, microcracking anddebonding between the matrix and the aggregates cause thestress to decrease with further straining.4 The propagation ofa crack in SFRC further involves the formation of a fiberbridging zone (FBZ) in the wake of the macrocrack.5 Thesebridging fibers resist further crack extension. Withincreasing load, fiber debonding and pullout eventuallyoccur. All of these events—microcracking, fiber debonding,or macrocrack propagation—generate transient elastic stresswaves6 due to a rapid release of internal strain energy andthus can be detected by acoustic emission (AE). Furthermore,these incidents change the characteristics of the material sothat ultrasonic waves are attenuated as a result of increasingback-scattering,7 or slowed down due to an extendedpropagation path of the waves.

The combination of acoustic emission and ultrasonic wavepropagation offers a reliable tool for determining themoment at which macrocracking initiates, and for followingthe damage of the material during tests.

RESEARCH SIGNIFICANCEWhen comparing the performance of different kinds of

steel fiber reinforced concrete (SFRC), or when studying theenhanced performance of SFRC over its unreinforced coun-terpart, it is important to accurately assess the first crackingstrength, i.e., the moment at which diffuse microcrackslocalize in a macrocrack. The point where this first macro-cracking occurs is indeed the point where a distinction can bemade between the contribution of the fibers and that of thematrix. The ultimate strain of the matrix being smaller thanthat of the fibers, fiber reinforcement becomes effectivemainly after the matrix has cracked and the fibers are bridgingthese existing cracks.

Title no. 96-M36

Cracking Behavior of Steel Fiber Reinforced Concrete Revealed by Means of Acoustic Emission and Ultrasonic Wave Propagationby Anne Van Hauwaert, Francis Delannay, and Jean-François Thimus

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EXPERIMENTAL INVESTIGATIONMaterials and mixing

The concrete mix was composed of CEM I 42.5 R portlandcement (Type III portland cement), 0/5 river sand, and 2/8gravel. The proportions by weight were 1:2:2:0.5 (cement, fineaggregate, coarse aggregate, and water). This concrete presentsa compressive strength of approximately 41 MPa after 28 days.For the SFRC, use was made of hooked steel fibers having afiber length of 30 mm and a fiber diameter of 0.5 mm.

SpecimensBeams were cast in 600 x 150 x 150-mm3 wooden molds.

The central section of the molds was reduced with a plasticstrip of 100-µm thickness to create a notch and two semicircularwooden sticks to localize the crack-path (Fig. 1). After casting,the beams were left covered with a plastic sheet for 24 hr.Thereafter, they were unsealed and moist cured in a curingroom at 20 C in 90% humidity. After 28 days of aging, the

upper and lower faces of the specimens were ground parallelto one another, and the samples were tested as cast.

Different types of specimens were made: plain concretebeams, concrete beams reinforced with randomly distributedsteel fibers, and beams reinforced with aligned steel fibers inthe region above the notch.

The latter type of beam was made as follows (Fig. 2): 1) plainconcrete was poured until covering the plastic strip (±3 cm);2) fibers were aligned with tweezers along the longitudinaldirection in the plane of the notch and then covered with 1 cmof plain concrete; and 3) the mold was vibrated. Step 2 and 3were repeated 10 times until filling of the mold was completed.The number of fibers crossing the section of the beam above thenotch varied from 15 to 49 fibers on each line.

In this paper, a comparison is made among five samples,each being representative of one type of concrete, i.e., plainconcrete, concrete reinforced with 0.5% by volume ofrandom fibers, concrete reinforced with 1% by volume ofrandom fibers, concrete made of 10 layers of 15 alignedfibers, and concrete with 10 layers of 49 aligned fibers.

TestingThe beam specimens were tested in third-point bending.

The testing machine had a maximum load-capacity of 50 kNand was displacement-controlled. This device was verysilent, so as not to disturb acoustic emission measurements.It was not, however, stiff enough to prevent instabilities incertain configurations. The test setup complied with NBN B15-2388 (Fig. 3). It included a Japanese yoke,9 whichallowed for the elimination of extraneous support settlementsin such a way as to record only true specimen deflection.10 Alldata were electronically acquired using a 16-channel dataacquisition system (Fig. 4).

During tests, an accelerometer recorded the acoustic emissiongenerated inside the specimen. After amplification andfiltration in a conditioner (frequency band from 100 to 50 kHz),signals greater than a preset threshold were transformed intoimpulses and counted by a numeric counter. They werestored at regular time intervals. All events were consideredas having a duration of 1 ms, i.e., that even if the thresholdwas exceeded several times during this time lapse, only oneevent was considered to have occurred. An oscilloscopeallowed the acoustic activity to be followed.

At regular time-intervals during the tests, a PUNDIT unit(Portable Ultrasonic Non-destructive Digital IndicatingTester) generated electric impulses (100-V pulse amplitude,40 pulses/s, and 3 µs pulse width) to a crystal emitter, placed

ACI member Anne Van Hauwaert is a doctoral candidate in the Civil EngineeringDepartment of the Université catholique de Louvain, Belgium. Her research interestsinclude the interfacial fiber-matrix strength of fiber reinforced concrete using acousticemission, ultrasonics, microscopic analysis, and finite element techniques.

Francis Delannay is a professor in the Department of Materials and Processes of theUniversité catholique de Louvain. His research interests include relations betweenprocessing conditions and mechanical properties of engineering materials withspecial emphasis on interface phenomena in composites and multimaterials.

Jean-François Thimus is a professor and Head of the Architecture and CivilEngineering Department of the Université catholique de Louvain. His research interestsinclude microgravimetry, behavior of soils at low temperature (ground freezing) andat high temperature (nuclear waste disposal), as well as damage of natural or artificialrocks by use of acoustic and ultrasonic techniques.

Fig. 1—Beam geometry (dimensions in mm).

Fig. 2—Fibers aligned with tweezers in central part ofsample (dimensions in mm).

Fig. 3—Test setup.

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at one beam end. Only longitudinal compression waves wereused in this study. The receiver, placed at the other beam end,detected the signal deformed after traveling through thesample. This signal was then recorded by a numeric oscillo-scope and a computer with a frequency of 1024 points for500 µs. The two transducers had a diameter of 50 mm and afundamental rated frequency of 1 MHz. They were mountedon spring-frames to insure as constant a contact-stress aspossible. At the interface between the transducers and thesample, grease was used as a coupling agent to improvewave transmission.11 To allow for the time-consumingultrasonic acquisition, tests were performed at a jackdisplacement rate of 0.01 mm/min. During the ultrasonicwave propagation, the recording of acoustic emission wasinterrupted to prevent interference.

Interpretation toolsThe frequency components of the acoustic events were found

by calculating their power spectral density, by means of the FastFourier Transform. The frequency at which the power spectraldensity presented a maximum was termed fundamental. In thisstudy, low-frequency acoustic emissions have a fundamentalfrequency lower than 2 kHz, while high-frequency events havea fundamental frequency between 40 and 50 kHz.

The ultrasonic signals were processed by subtracting theirmean value calculated in the whole time-window (500 µs.Two parameters were measured from these processedwaves:

1. The propagation velocity

(m/s) (1)

where dstraight is the shortest distance between both trans-ducers, i.e., 600 mm in the experiments, and ta is the timeneeded for the wave to cross the whole specimen.

2. The ultrasonic energy

(V2 ⋅ s) (2)

where A(t) is the amplitude of the signal at time t, and ti is theend of the time-window as fixed in the experiments at 500 µs.

RESULTS AND DISCUSSIONIn the following, most plots present the load, the cumula-

tive acoustic events, and the ultrasonic parameters versus thebeam deflection. Similar plots were drawn versus the crackmouth opening displacement (CMOD), but such plots do notprovide any additional information and are therefore notreported in this paper. For the ultrasonic energy, it is importantto notice that only its relative variation has to be considered;the absolute value of the energy has no significance, giventhe dependence of the ultrasonic energy on the couplingbetween the transducers and the sample, which dependsitself on the amount of coupling grease and on the tension ofthe springs. This is why the scale of those measurements isgiven in percent on the various plots.

Figure 5(a) shows the load-deflection plot under third-point bending of a plain concrete specimen, a concretesample reinforced with randomly distributed fibers and aconcrete reinforced with aligned fibers. Due to the verybrittle nature of plain concrete, the first macrocrack corre-sponds to the maximum load for this specimen and leads tothe sudden fracture of the beam. At this scale, the load-deflection plot seems linear up to the first cracking strength.However, when visualized on a larger scale, as in Fig. 5(b),it appears that the plot for plain concrete is not linear up tothe maximum load, due to the development of inevitablemicrocracks. Thus, the first macrocrack does not concur withthe point on the load-deflection curve at which it firstbecomes nonlinear. In the same way, the plots for the fiberreinforced concretes are not linear up to their respective firstcracking load, and it is therefore very difficult to determinethe load corresponding to the first macrocrack for thosesamples, where the fibers enhance the load-carrying capacityof the composite after cracking has initiated. In thefollowing, the benefit of the use of acoustic emission andultrasonic wave propagation to locate the first crackingstrength in various configurations is outlined.

Figure 6 shows the load-deflection curve of a plainconcrete sample simultaneously with the cumulative acousticemission and the variation of the ultrasonic energy and

vpdstraight

ta

------------------=

E A t( )[ ]2 td

0

ti

∫=

Fig. 4—Acquisition setup.

ACI Materials Journal/May-June 1999294

propagation velocity. At maximum load (16.1 kN), the onsetof a macrocrack leads to sudden failure. Prior to collapse, adrop of the ultrasonic wave-energy and a low number of low-frequency acoustic events are observed. No high-frequencyemissions or changes in the propagation velocity are noticed.This first plot, therefore, shows that the existence anddevelopment of microcracks prior to collapse can be revealedby the attenuation of the ultrasonic waves and the occurrenceof low-frequency acoustic events.12

This can further be inferred from Fig. 7, where load,cumulative acoustic emission, ultrasonic propagationvelocity, and wave energy are shown as a function of beamdeflection for a concrete sample reinforced with 0.5% ofrandomly distributed fibers. The presence of an instability inthe load-deflection plot indicates that this volume fraction islower than the critical volume fraction Vc. Indeed, if thevolume fraction of the fibers is less than Vc , the stress sustain-able by the composite drops either when the matrix cracks, orwhen some stable debonding occurs immediately after theextension of the matrix crack.13 Prior to the considered insta-bility, the drop of ultrasonic energy and the occurrence oflow-frequency acoustic events confirm the development ofmicrocracks. At maximum load (15.9 kN), a significantdrop of the wave propagation velocity appears, and anincreasing amount of high-frequency events comes out asa result of macroscopic damage. At that moment, the dropof ultrasonic energy comes to an end and the energyreaches a bottom value. The maximum load of this sampleis, therefore, its first cracking strength. Why such variationscould not be recorded with the plain concrete sample, though

it also went to total collapse, is probably due to the fact that theextension of the macrocrack, which should induce a drop inthe ultrasonic propagation velocity and the occurrence ofhigh-frequency events, is followed by such a sudden failurethat there is no time to record whatsoever.

Armed with those findings, it is easy to find the first crackload for a SFRC, where the fibers enhance the load-carryingcapacity of the composite after cracking is initiated, as inFig. 8. In this figure, the load, cumulative acoustic emission,ultrasonic propagation velocity, and wave energy are givenas a function of beam deflection for a concrete beam rein-forced with 1% of randomly distributed fibers. No instabilityoccurs at this volume fraction, and the fracture toughnessand strength of the resultant composite are significantlyimproved. The fibers alone are capable of sustaining a stressgreater than that which causes matrix cracking, and thevolume fraction of the reinforcing fibers is thus greater thanthe critical value Vc.14 In Fig. 8, an instant decrease of theultrasonic energy with a nearly linear load-deflection curve isagain noticed for small deflections. The ultrasonic propaga-tion velocity stays steady and no high-frequency emissionsoccur. Thus, this confirms the existence and developmentof microcracks. Then, high-frequency acoustic activitysuddenly intensifies, and the load-deflection plot becomesincreasingly nonlinear. A change in the slope of the ultra-sonic energy is observed at that moment. Immediately after,the propagation velocity eases off, while the load-deflectionplot continues to rise. As opposed to Fig. 7, the drop of ultra-sonic propagation velocity does not coincide with theincrease of high-frequency acoustic activity. This is due to

Fig. 6—Load, acoustic emission, ultrasonic wave energy,and ultrasonic wave velocity versus beam deflection forplain concrete.

Fig. 7—Load, acoustic emission, ultrasonic wave energy,and ultrasonic wave velocity versus beam deflection forconcrete reinforced with 0.5% in volume of randomlydistributed fibers.

Fig. 5—(a) Load-deflection plots for plain concrete;concrete reinforced with 1% in volume of randomlydistributed fibers, and concrete reinforced with 10 layersof 49 aligned fibers on a scale of 5 mm; and (b) on a scaleof 0.5 mm.

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the fact that acoustic activity builds up as soon as the crackinitiates, whereas the velocity only drops when the direct pathbetween both transducers lengthens, i.e., when the crack ishalfway through the depth of the beam.15 This differenceis not perceived when the volume fraction of the reinforcingfibers is smaller than Vc , because crack propagation is, in thatcase, so fast that both events coincide. When the load-carrying capacity is brought up by a volume fraction of fibersthat is greater than Vc , first cracking strength is revealed bythe onset of high-frequency acoustic emission (in this case,16.2 kN), whereas the drop of ultrasonic propagationvelocity displays the progression of the crack halfwaythrough the depth of the beam.

The same behavior can be observed for aligned fibers.Figure 9 shows the results for a concrete beam reinforced with10 layers of 15 fibers aligned above the notch. This behavioris very similar to that of a concrete reinforced with 0.5% ofrandomly distributed fibers, as shown in Fig. 10. An instabilityis again observed, and the volume fraction is thus subcritical.At the beginning of loading, a drop of ultrasonic energy, aconstant ultrasonic propagation velocity, and the absence ofhigh-frequency activity is observed. Then, when the slope ofthe energy curve changes, high-frequency acoustic activitygrows, and the ultrasonic propagation velocity drops as amacrocrack forms. Both events coincide because the cracksuddenly crosses most of the beam depth. First crackingstrength occurs thus at maximum load, i.e., at 16 kN.

When the number of fibers exceeds the critical volumefraction, as in Fig. 11, where the results for a concretereinforced with 10 layers of 49 fibers are displayed, firstcracking occurs before the maximum load. The load-deflectionplot of this sample can be compared to that of a concretebeam reinforced with 1% of randomly distributed fibers, asillustrated in Fig. 12. At approximately 0.25 mm, the plot ofthe concrete with aligned fibers drops. This is due to the factthat a new crack was created outside the reinforced section,where less resistance was opposed to the progression of thecrack. In Fig. 11, one notices at low deflections, a constantultrasonic wave velocity, a slow drop of wave energy, andsome low-frequency acoustic activity. However, at a certainload (17.6 kN), the ultrasonic wave energy drops moresteeply, and high-frequency emissions progress, revealingthe onset of a macrocrack. First cracking strength has beenreached. As the progression of the crack is restrained by thebridging fibers, the ultrasonic velocity drops only later, whenthe crack has reached halfway through the beam depth.

In the previous examples, the alteration of concrete andSFRC samples, due to both microscopic and macroscopicevents, were followed by recording acoustic emission andultrasonic wave propagation.

For low deflections, the opening and extension of existingflaws alters the properties of the concrete, and the amplitudeand energy of the ultrasonic waveform gradually decline.16

This attenuation is dependent on the frequency of the transducerand on the size and number of flaws between the transmitterand the receiver. Some acoustic emissions might occur

Fig. 9—Load, acoustic emission, ultrasonic wave energy,and ultrasonic wave velocity versus beam deflection forconcrete reinforced with 10 layers of 15 fibers.

Fig. 10—Load-deflection plots for concrete reinforcedwith 0.5% of randomly distributed fibers and concretereinforced with 10 layers of 15 aligned fibers.

Fig. 8—Load, acoustic emission, ultrasonic wave energy,and ultrasonic wave velocity versus beam deflection forconcrete reinforced with 1% in volume of randomlydistributed fibers.

Fig. 11—Load, acoustic emission, ultrasonic wave energy,and ultrasonic wave velocity versus beam deflection forconcrete reinforced with 10 layers of 49 fibers.

296 ACI Materials Journal/May-June 1999

during the microcracking of the sample, but their frequencygenerally does not exceed 2 kHz.

Once a macrocrack initiates, acoustic emission is found togrow dramatically, especially events of frequencies rangingfrom 40 to 50 kHz, and the slope of the energy curve drops dueto macroscopic cracking of the matrix and load transfer frommatrix to fibers. Low-frequency acoustic emission may stilloccur, as the fracture process zone progresses. First crackloads based on those observations were found higher than thepoint on the load-deflection plot at which the form of the curvefirst becomes nonlinear, as shown in Table 1. An increase upto 50% of the first cracking strength can be observed.

Eventually, when the macrocrack has extended halfwaythrough the beam depth, the ultrasonic waves are forced totake a longer path to travel between both transducers and thepropagation velocity drops.

CONCLUSIONSIn this paper, a method to locate the first cracking strength

of concrete and SFRC samples was presented. Third-pointbending tests were performed, and the alteration of thematerial, due to both microscopic and macroscopic events,was followed by recording acoustic emission and ultrasonicwave propagation.

The microscopic damage of the material can be revealed bythe continuous decline of the ultrasonic wave energy and low-frequency acoustic emission; the initiation of a macroscopiccrack is revealed by a significant increase of high-frequencyacoustic events, whereas the extension of the crack halfwaythrough the beam depth and subsequent fiber pullout isdisclosed by the drop of the ultrasonic propagation velocity.

To make a distinction between high and low acousticevents, the signal must be recorded. An analysis based only oncounting of the events might lead to erroneous results. To havea reliable indication of the first cracking strength, acousticemission and ultrasonic wave propagation should be usedsimultaneously, as demonstrated in this paper.

ACKNOWLEDGMENTSThe authors thank the Laboratoire du Génie Civil for assistance with the

experimental and data-acquisition setup, and particularly G. Henriet, B.Hoet, and E. Bouchonville for their never-ending help. They thank J. Flemalfor his drawings. The financial support of N. V. Bekaert, S.A., is also grate-fully acknowledged. This research work was funded by the Fonds de Dével-oppement Scientifique of the Université catholique de Louvain.

NOTATIONA = amplitude of ultrasonic wavedstraight = straight path between ultrasonic emitter and receiverE = energy of ultrasonic wavet = timeta = arrival time of ultrasonic waveti = end of time-window of ultrasonic wavevp = propagation velocity of ultrasonic wave

CONVERSION FACTORS1 mm = 0.0394 in.

1 N = 0.255 lb1 MPa = 145 psi

1 deg C = (5/9)(deg F – 32)

REFERENCES1. Mindess, S. et al., “Standard Testing,” Preproceedings on High

Performance Fibre Reinforced Cement Composites, A. E. Naaman and H.W. Reinhardt, eds., 1995, 365 pp.

2. ASTM C 1018-94b, Standard Test Method for Flexural Toughnessand First-Crack Strength of FRC, ASTM Committee on Standards, Phila-delphia, 1994.

3. Mindess, S.; Chen, L.; and Morgan, D. R., “Determination of theFirst-Crack Strength and Flexural Toughness of Steel Fibre ReinforcedConcrete,” Advanced Cement-Based Materials, V. 1, 1994, pp. 201-208.

4. Cotterell, B., and Mai, Y. W., Fracture Mechanics of CementitiousMaterials, Chapman and Hall, London, 1991.

5. Cotterell, B., and Mai, Y. W., “Modeling Crack Growth in Fibre Rein-forced Cementitious Materials,” Materials Forum, V. 11, 1988a, pp. 341-351.

6. Ohtsu, M.; Shigeishi, M.; and Sakata, Y., “Nondestructive Evaluationof Defects in Concrete by Quantitative Acoustic Emission and Ultra-sonics,” Ultrasonics, V. 36, 1998, pp. 187-195.

7. Wu, T.-T., and Liu, P.-L., “Advancement on the Nondestructive Evalu-ation of Concrete Using Transient Elastic Waves,” Ultrasonics, V. 36,1998, pp. 197-204.

8. NBN B15-238, “Détermination de la Résistance à la Flexion et de laTénacité sous Flexion d'un Béton avec Fibres D’acier,” IBN, Bruxelles,Belgium, 1990. (in French)

9. JSCE-SF4, “Method of Tests for Flexural Strength and FlexuralToughness of Steel Fiber Reinforced Concrete,” Concrete Library of JSCE,V. 3, 1984, pp. 58-61.

10. Banthia, N., and Trottier, J.-F., “Discussion of Research Paper: Fiber—Types Effects on the Performance of Steel Fiber Reinforced Concrete,” ACIMaterials Journal, V. 89, No. 1, Jan.-Feb. 1992, pp. 106-107.

11. Couvreur, J.-F., and Thimus, J.-F., “The Properties of CouplingAgents in Improving Ultrasonic Transmission,” International Journal ofRock Mechanics and Mining Sciences and Geomechanical Abstracts, V. 33,No. 4, 1996, pp. 417-424.

12. Reymond, M. C.; Thimus, J.-F.; and Linze, Ph., “Acoustic EmissionCharacteristics of Schists and Sandstones,” Physical Acoustics: Fundamen-tals and Applications, O. Leroy and M. A. Breazeale, eds., Plenum Press,New York, 1990, pp. 591-598.

13. Hannant, D. J., Fiber Cements and Fiber Concretes, John Wiley andSons, Chichester, 1976.

14. Gopalaratnam, V. S. et al., “Fracture Toughness of Fiber ReinforcedConcrete,” ACI Materials Journal, V. 88, No. 4, July-Aug. 1991, pp. 339-353.

15. Van Hauwaert, A.; Thimus, J.-F.; and Delannay, F., “Use of Ultra-sonics to Follow Crack Growth,” Ultrasonics, V. 36, 1998, pp. 209-217.

16. Selleck, S. F. et al., “Ultrasonic Investigation of Concrete with Distrib-uted Damage,” ACI Materials Journal, V. 95, No. 1, Jan.-Feb. 1998, pp. 27-36.

Table 1—Comparison between first nonlinear load and first cracking strength

ASTM method,* kN

AE/US method,† kN

Difference,percent

Plain concrete 10.6 16.1 51.9

0.5% random fibers 10.4 15.9 52.9

1% random fibers 9.6 16.2 68.8

10 x 15 aligned fibers 10.4 16.0 53.8

10 x 49 aligned fibers 11.0 17.6 60.0*Load at which load-deflection plot first appears nonlinear.†Load at which significant high-frequency acoustic activity appears and slope of energy curve drops.

Fig. 12—Load-deflection plots for concrete reinforced with1% of randomly distributed fibers and concrete reinforcedwith 10 layers of 49 aligned fibers.