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Evaluating the damage in reinforced concrete slabs under bending test

with the energy of ultrasonic waves

Farid Moradi-Marani, Patrice Rivard ⇑, Charles-Philippe Lamarche, Serge Apedovi Kodjo

Civil Engineering Department, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada

h i g h l i g h t s

High deformations of concrete distort acoustic waves and change the waveform. We proposed an approach based on energy loss of ultrasonic probe signals. This approach appears to be more effective to monitor the crack propagation.

a r t i c l e i n f o

 Article history:

Received 12 May 2014Received in revised form 3 September 2014Accepted 24 September 2014Available online 27 October 2014

Keywords:

UltrasonicEnergy loss

Damage evaluationReinforced concreteAlkali–silica reactionNon destructive testing

a b s t r a c t

This paper deals with the feasibility and sensitivity of ultrasonic probe waves for characterizing themechanical damage of reinforced concrete slabs during bending tests either in sound concrete or in con-crete affected by alkali–silica reaction (ASR). The results show that the ultrasonic probe waves are capa-ble of distinguishing between the damage phases in the concrete elements (initial structural cracking andbars yielding phases). Three reinforced concrete slabs with dimension of 1.40 0.75 0.3 m3 (made withnonreactive aggregates and ASR-reactive aggregate) were used in this experiment. Both the conventionalmethod of load–deflection measurements and the nondestructive testing based on ultrasonic probe sig-nals were applied in order to evaluate the feasibility of ultrasonic testing for tracking crack growth in thereinforced concrete elements. These slabs were assessed under four-point monotonic bending tests over aspan of 1400 mm and were subjected to step-loading until failure. The ultrasonic probe signals wererecorded at the each step-load and then energy of received signals were extracted in order to evaluatethe energy loss of the signals due to the mechanical cracking. Changes in the energy contents of the sig-nals fairly correlate with the increase of the loads. The results show that the ultrasonic testing is a morerobust approach for distinguishing the sound concrete slab from the damaged concrete.

 2014 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Background review

Traditionally, the mechanical behavior of concrete elements isevaluated by analyzing the load–deflection or stress–strain behav-iors from various types of mechanical tests. These tests have beenstandardized and have been presented as means of evaluating var-ious static and dynamic properties of the concrete elements. Thesemechanical testing methods assess the general macro-behavior of concrete elements by measuring the response of concrete elementsto external loads. These methods are often not enough robust todetect small changes in concrete properties, such as micro-crackgrowth. Although these small anomalies typically do no threaten

the general serviceability of reinforced concrete elements, theymay jeopardize the long-term performance of the structures froma durability point of view. It may also intensify the rate of otherchemical and physical damage mechanisms such as the corrosionof the steel bars and tendons [28]. Therefore, the development of methods that allow accurate tracking of the stress changes andconcrete cracking would be extremely useful.

It has been demonstrated that acoustoelasticity methods arepotentially efficient to monitor the stress changes in concrete withan accuracy far superior to the common structural measurements[15,27,33,30,40]. Indeed, thorough studies conducted on the prop-agation of the acoustoelastic waves into media showed that thereis an analytical expression between the principal stresses and theacoustic wave velocities for an isotopic medium   [16,14,8]. Lilla-mand et al.   [15], Schurr et al.   [27], Stähler et al.   [33], Shokouhiand Niederleithinger [30] applied this physical expression to eval-uate small stress-induced changes in uniaxial static compression

http://dx.doi.org/10.1016/j.conbuildmat.2014.09.050

0950-0618/ 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 819 821 8000x63378; fax: +1 819 821 7974.

E-mail address:  Patrice.Rivard@Usherbrooke.ca (P. Rivard).

Construction and Building Materials 73 (2014) 663–673

Contents lists available at   ScienceDirect

Construction and Building Materials

j o u r n a l h o m e p a g e :   w w w . e l s e v i e r . c o m / l o c a t e / c o n b u i l d m a t

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tests. Although there were some differences between the measure-ments, good correlations were obtained for the small stress-induced changes in concrete specimens and acoustoelastic wavevelocity changes based on Murnaghan  [16]. A similar study wascarried out by Zhang et al. [40] on concrete specimens tested underdirect tensile forces, where the results proved to be in agreementwith studies performed under uniaxial compressive loads despitethe limitations associated with the direct tensile strength of con-crete. Acoustoelastic methods are precise in monitoring smallstress-induced changes. These methods are more accurate priorto the development of mechanical macro-cracks within the con-crete matrix. These methods are based on the assumption of apath-independency of the acoustic waves; whereas the trajectoriesand paths of the acoustic waves change with the extent of macro-cracks through the medium. This may cause frequency attenua-tions, absorption of signal energy, and some variations of thewaveform [1,24,34,37]. Therefore, these methods would not reli-able for tracking stress changes in the case of reinforced concrete;because the reinforced concrete elements are serviceable althoughthe macro-cracks develop within the concrete and the elements gounder high deformations. Moreover, Stähler et al.  [33], in a fieldexperiment, reported that the attenuation associated with thestress changes in service structures can distort the waveformsbecause of the high heterogeneity of the concrete. Similar resultswere observed by Grêt et al.  [11], through an experimental studyconducted in order to monitor the in-situ stress changes in a hardrock mine. This phenomenon may also limit the implementation of the acoustoelastic approaches for evaluating the stress changes infield experiments.

Nogueira and Willam [17] and Qasrawi and Marie [20] used theUltrasonic Pulse Velocity (UPV) method to monitor the crack devel-opment in a concrete sample under uniaxial compression. Thismethod has two important limitations concerning the monitoringof crack growth: (1) it is difficult to measure the velocity changesat low-levels of damage (micro-crack development phase); (2)there are limitations for distinguishing between the damage

phases (i.e. closure of inherent micro-defects at the initial stageof loading, micro-cracking/cracking development, yielding and fail-ure) by tracking stress-induced changes within heterogeneouscementitious materials. Their results showed that there was abouta 5% drop in pulse velocity when the stress-strength ratio was of 80%. Generally, the results show no significant variation of thepulse velocity until around 90% of the failure strength. This findingis in agreement with results obtained by Van Den Abeele et al. [36]and Sargolzahi et al.  [26], where it was demonstrated that linearacoustical methods, like UPV, are not sensitive enough withregards to the development of damage features (e.g. cracks andflaws) in heterogeneous cementitious materials. The resultsobtained by Shiotani and Aggelis   [29]   and Van Hauwaert et al.[37] also showed that the UPV is not sensitive enough to evaluate

distributed damage.

1.2. Scope of work

A major challenge addressed in this article is the evaluation of the bending stresses in reinforced concrete slabs using ultrasonicwaves. A sound concrete slab and the concrete slabs damaged byalkali–silica reaction (ASR) were selected to assess the effective-ness of the ultrasonic waves to monitor the stress evolutions inboth slabs. The attenuation of the frequencies and the distortionof the waveforms in reinforced concrete elements can limit theapplication of common methods like acoustoelastic-stress changemethods. Therefore, the approach of the energy loss of ultrasonicwaves is considered in this paper, and applied to track the mechan-

ical behavior of concrete slabs over four-point bending tests. To doso, a step-loading protocol was performed, and the concrete

condition was evaluated by computing the energy loss of the ultra-sonic waves recorded at each step.

Hu et al. [12] and Song et al.  [32] applied the same concept forhealth monitoring concrete elements in bending test using embed-ded piezoceramic transducers. Although this method is also usefulfor long term measurements to track the history of stress change inconcrete structures, it is not suitable for service concrete structuresthat are not pre-instrumented. This research relies on externaltransducers attached to the concrete surface for evaluating stressevolution, which represent a convenient approach to the monitor-ing of existing structure.

The energy loss measurements using coherent ultrasonic wavesinclude intrinsic absorption and scattering contributions. Diffusiontheory can separate the energy loss contributions due to absorp-tion and scattering [3,18,38]. Quiviger et al.  [21], Deroo et al. [7],Punurai et al. [19], Becker et al. [4] and Anugonda et al.  [3] appliedthe diffuse ultrasound in small size cement paste and concretespecimens (not more than few centimeters). Due to the heteroge-neous nature of concrete, Punurai et al. [19] suggest taking a build-ing block approach even for small size concrete specimens. Withthis method, it should be possible to characterize the energy lossdue to absorption and scattering from individual elements (i.e.cement paste, aggregate, inherent micro-cracks, etc.). Then, itmay be possible to combine into a unified description. For this rea-son, it is still complicated to apply diffusion theory in large-scalereinforced concrete elements in the field to uncouple the loss con-tributions due to absorption and scattering. It should be mentionedthat, during a mechanical loading test, the heterogeneity of con-crete increase dramatically due to the development of macro-cracking. This can limit the application of the diffusion theory inlarge-scale reinforced concrete elements during a structural test.

2. Experimental program

 2.1. S ampling and materials

Tests were conducted on three concrete slabs with dimension of 1.40 0.75 0.3 m3. Two slabs were fabricated with alkali–silica reactive coarseaggregates. To boost the reaction, pellets of NaOH were added to the mixing waterof the reactive concrete in order to increase the total alkali content of the concreteto 5.0 kg/m3 Na2Oeq. The third slab was fabricated with nonreactive aggregates. Thecomposition of the concrete is provided in Table 1. The concrete slabs were rein-forced with seven 20M (nominal diameter = 19.5 mm) at the tension face and seven10M (nominal diameter = 11.3 mm) at the compression face, which both werehooked at the ends. Rebars are made of G30.18-M92 (R2002) grade 400W Canadiansteel with nominal yield strength of 400 MPa [6]. The slabs were also reinforcedwith 10M stirrups at a 100 mm center-to-center constant spacing. The reinforce-ment layout in both plan and elevation view is illustrated in Fig. 1. The measuredsteel properties are also given in  Table 2.

All concrete slabs went through a 28-day moist curing at normal temperatures.Table 3 shows the average compressive and tensile strengths, as well as the averagemodulus of elasticity at the 28 days and at the test time (800 days). The nonreactivereinforced concrete slab is referred to as NS and the reactive reinforced concreteslabs to as RS1 and RS2.

 2.2. Load testing and acoustic measurements

Fig. 2 shows a sketch of the test set-up with the configuration of the acoustictransducer located both on the tension and compression faces. This configurationenables the generation and measurement of the required ultrasonic waves at

 Table 1

Mix design of the concrete slabs for 1.0 m 3.

Components Values

Water/cement 0.50Cement 400 kg/m3

Na2Oeq   5.0 kg/m3

Coarse aggregate (5–14 mm) 864 kg/m3

Coarse aggregate (10–20 mm) 216 kg/m3

Fine aggregate 730 kg/m3

Water 200 kg/m3

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each load-step. The slabs were tested under four-point loading at room temper-ature to investigate the degree of damage using the energy loss approach. Thetests were conducted using a 12 MN capacity hydraulic MTS testing machineat a load rate of 0.5 kN/s. A loading protocol with 30 kN load-steps was usedto perform the tests where acoustic measurements were taken at each load

level. Two external LVDTs, with a range of 19 mm, were used to measure theoverall deflections of the concrete slabs. To measure the concrete and steel barsdeformations, two strain gages were placed on the steel bars on the tension side(extrados). Two strain gages were also installed on the concrete on the compres-sion side (intrados).

1400 mm

750

mm

Y

X

75 mm

100 mm

75 mm 100 mm

1400 mm

30

0

m

m

Z

X

10M

20M

10M

Fig. 1.  Reinforcement layout in both plan and elevation view.

 Table 2

Mechanical properties of steel bars.

Steel bar Yielding strength (MPa) Yielding strain (l) Young modulus (GPa) Tensile strength (MPa)

D10 505 2579 196 624D20 489 2431 201 595

 Table 3Mechanical properties of concrete at 28-day and at 800 days (testing time). Each value is the average of three specimens.

Slab Compressive strength (MPa) Indirect tensile strength (MPa) Young modulus elasticity (GPa)

28-day 800 days 28-day 800 days 28-day 800 days

NS 36.5 62.2 – 5.8 35.9 37.1RS1 39.5 46.7 – 4.9 39.1 23.7RS2 38.8 46.9 – 4.6 33.8 25.3

Load

30

0

m

m

Z

X

Signal

Generator

1400 mm

LVDTTransducer Transducer

TransducerTransducer

Fig. 2.  Sketch of test set-up and instrumentation for acoustoelastic response of the concrete slabs at each step loading.

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The loading was maintained constant for 2 min at each load step, so the non-destructive measurements could be performed with the transducers placed on boththe compression and tension faces. For the acoustoelastic measurements, a four-channel signal generator was used to generate the required acoustic waves duringthe tests. The signals excited two Panametrics piezoelectric transducer with a250-kHz central frequency. Then, the generated signals were detected by similartransducer placed on the same face (indirect configuration of transducers), andthe measured signals were amplified before being sent to the data acquisitionsystem. Each propagated signal response was recorded at a sampling rate of 

60 MHz during 1.667 ms (100,000 data points). The signals were not simulta-neously emitted by the transducers placed on the compression and tension faces;they were generated one after another in order to prevent the receiver transducersfrom acquiring mixed signals.

An indirect configuration of transducers was chosen to perform the tests,because Yaman et al.   [39] showed that more parts within concrete slabs wouldbe monitored using indirect configuration of transducers. With this configuration,the propagated signals are reflected at the boundaries and pass through a larger vol-ume in comparison with the direct transducer configuration.

 2.3. Data processing 

At each load step, the acoustic signals were recorded by each transducer pairplaced on each side. Then, the recorded signals were averaged to reduce noiseand other unbiased random spurious effects. The recorded signals at 0.5 kN loadingwere considered as the reference state.

As mentioned previously, an energy loss approach of ultrasonic waves was used

to evaluate the damage growth in the concrete slabs due to loading. Therefore, theenergy (E t ) of each signal was calculated according to Eq.  (1):

E t  ¼XN 

i¼1

½0:5ð Ai þ Aiþ1Þ2 Dt    ð1Þ

where N  = 100,000 is the number of samples that corresponds to a recording time of 1.667 ms for the response of the concrete slabs;  A i   is defined as the amplitude of recorded signals; and  Dt  = 3.334 108 s is the time window.

In addition to the energy of signals in time-domain, energy spectral density of each time window was calculated by summing the power spectrum in a bandwidthof 300 kHz using Eq. (2):

E  f   ¼XN 2ð Þ1

 f ¼1

½0:5ð A f  þ  A f þ1Þ2 D f    ð2Þ

where E  f  is energy spectral density;  A f  is defined as the amplitude value in a certainfrequency measured from power spectrum of signals; and  D f  = 600 Hz.In order to find the power spectrum of a signal, the time-domain signal was

divided into overlapping time window. The signal was multiplied with a Hammingwindow to smooth the signal edges which led to good properties for frequencyanalysis, and then frequency spectrum was determined by performing the discretetime Fourier transform (DTFT) operation.

Centroid frequency shift approach was also considered to assess the mechanicaldamage developed in the concrete slabs during the bending test. This value was cal-culated as a weighted mean of the frequencies found in the signals using Eq.  (3):

 f c  ¼XN 2ð Þ1

n¼0

ð f n   A fnÞ

0@

1A, XN 1

n¼0

 A fn

!  ð3Þ

where f c  is the centroid frequency of a spectrum;  f n and  A fn are frequency and mag-nitude of events, respectively.

3. Test results and discussion

Before performing the structural tests and acoustic measure-ments, microscopic examinations were carried out 75-mm coresdrilled from the slab in order to confirm that damage to the con-crete slabs was primarily associated with ASR. The Damage RatingIndex (DRI) [10,13] was calculated on sections polished from thedrilled cores. Basically, the DRI consists of a petrographic examina-tion performed on a polished concrete section using a stereo-microscope at a magnification of 16. In this study, the modifiedDRI method, proposed by Villeneuve et al. [13], was used to countsdefects in the aggregates, the cement pate and at the transitionzone between aggregates and cement paste. Table 4 presents theASR damage feature and weighing factors, which were used toevaluate the DRI. Although there is no consensus about a thresholdvalue, it might be considered that a DRI value above 30 would indi-cate that ASR is a likely cause of damage [23]. DRI number greater

 Table 4

Microscopic features and weighing factors for modified DRI method [13].

Petrographic features measured Symbols Weighingfactors

Closed and tight cracks in coarse aggregates CC   0.25Opened cracks or network cracks in coarse

aggregatesOC   2

Cracks and network cracks with reaction by-product in coarse aggregates

OC + R    2

Disaggregated and corroded aggregates DA   2Coarse aggregate debonded CD   3Cracks in cement paste CP   3Cracks with reaction by-products in cement paste CP + R    3

DRI

RS1 - expansion 0.14%CC

OC

OC + R

CP

CP + R

CD

0 200 400 600 800

0 200 400 600 800

DRI

RS2 - expansion 0.19%CC

OC

OC + R

CP

CP + R

CD

5 mm

RS2

RS15 mm

Fig. 3.  DRI values and microscopic images from ASR-cracking for the RS1 at an expansion of 0.14% and for the RS2 at an expansion of 0.19%. The cracks are filled by ASR-gel.

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than 300 indicates that the concrete is suffering from severe dete-rioration level associated with ASR.

As shown in Fig. 3, DRI numbers along with microscopic imagesconfirm that the RS1 and RS2 are suffering from ASR and it is theprimary cause of the damage. DRI values that were recorded forNS are far lower, and are in the order of 25. This can be attributedto inherent defects of the concrete specimens as well as pre-exist-ing cracks in the aggregate particles [22].

It should be mentioned that the ASR expansion was monitoredby Demec gauges, which had been installed on both compressionand tension faces of the slabs. Then the average values measuredbetween Demec gauges were reported as the ASR expansion of the concrete slabs.  Fig. 4  shows a layout of the Demec points inthe concrete slabs.

 3.1. Mechanical testing 

Fig. 5 shows the crack propagation observed for the concreteslabs. The damage development and cracking growth are dividedin three zones: (1) initial structural cracking; (2) main bars yield-ing; and (3) failure strength. Crack propagation in RS1 and RS2was nearly the same as that observed in NS. For the NS slab, asthe load increased, flexural cracks propagated through the tensionzone (extrados) to the compression zone (intrados). Shear cracksalso developed outside the constant pure moment section (centralpart).

Fig. 6 shows the relationships between the load and deflectionat mid-span that were measured in the tension zone, load andstrain in tensile reinforcing bars, and load and strain in compres-sive zone. A similar behavior was observed for all concrete slabs.The three defined zones of initial structural tensile cracks, rein-forcement yielding and failure (Figs. 5 and 6) are identical in allcases.

The influence of ASR on the mechanical response of concretebeams and slabs has been studied before [5,9,35]. Fan and Hanson[9] showed that the flexural loading capacity of ASR-affected rein-forced beams was nearly the same as that of the nonreactivebeams, even though the levels of expansion were significant andthere were visual ASR-cracks at the surface. Clark  [5]  reported asummary of a vast number of studies carried out on the structuraleffects of ASR in reinforced concrete beams. A wide range of resultswere reported from negligible changes to significant improves forfailure loads of reinforced ASR-affected reinforced beams in com-parison with non-ASR beams (i.e. load failure from 0.93 to 1.47times of non-ASR reinforced beams). Indeed, in reinforced concretebeams, the longitudinal expansions cause a hogging effect (self-prestressing effect) because the expansion in the tension zoneswith tensile reinforcement is more confined compared with thecompression zones   [35]. Therefore, this hogging effect mayincrease the failure strength of ASR-affected reinforced beams.

Z

Y

Z

X

Y

X

Demec point Demec point on the opposite side

Fig. 4.   Layout of the Demec points installed on both compression and tension faces.

Fig. 5.   Cracking development for NR concrete slabs; (a) initial visual cracks during the load process; (b) main bars yielding point; (c) ultimate load capacity (failure strength).

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Fig. 7 schematically shows the hogging effect associated with ASR in concrete beams and slabs. It should be mentioned that the hog-ging effect depends on the reinforcement ratio in both the tensionand compression zones. For instance, the beams could have beenover-reinforced in the study by Swamy and Al-Asali  [35], causing15% and 26% dissipation in failure loads with expansion levels of 0.25% and 1.7%, respectively. The ratio of tensile and compressivesteel bars in the concrete beam sections was 1.8% and 1.0%, respec-tively, which are much higher than those of the concrete slabs

tested in this research. Indeed, high ratio of reinforcement in thetension and compression zones of a concrete beam or slab mayreduce the hogging effect despite significant ASR-expansion inthe concrete element. In this paper, these ratios are 1.1% and0.4%, respectively. Thus, more support from the hogging effectcan be expected in the concrete slabs of this research. A detailedinterpretation of the ASR-expansion results confirms the hoggingeffect for the reactive concrete slabs. The results show that a differ-ential expansion occurred between compression and tension faces.This differential expansion was 0.04% for RS1 and 0.08% for RS2 atthe test time.

 3.2. Energy loss of ultrasonic waves

The acoustic waves were distorted during the tests and theirenergy was absorbed by macro-cracks that developed in the con-crete slabs. Fig. 8 shows the distortion and the dissipation of theacoustic waves with regards to crack development observed atboth the compression and tensile faces. The amplitude of the sig-nals recorded at the tension face clearly decreases with higher ratedue to the absorption and multiple-diffusion by the crack develop-ments. The signals of the compression face should be separatelystudied for early arrival waves and late arrival waves (coda waves).In the compression face, early arrival waves, which are mostly highfrequency waves, propagate through near-to-surface parts andgenerally pass through the compression zone. Thus, early arrivalwaves are amplified by stress development because the concrete

in the compression zone is gradually compressed, and micro-defects generally decrease in size. As shear cracks are generated

a

b

c

Steel bars

Steel bars

Steel barsConcrete

Concrete

Concrete

Inial structural cracks

Bars yielding Failure strength

Inial structural cracks

Bars yielding Failure strength

Inial structural cracks

Bars yielding Failure strength

Fig. 6.  Typical response of concrete and reinforcing bars to applied loads (a) nonreactive slab; (b) reactive slab 1 (expansion 0.14%); (c) reactive slab 2 (expansion 0.19%).

Self prestressed

element – inial

state

Released

prestressing

related to ASR

Loading progress

before structural

cracking

Fig. 7.  Variations of ASR-crack widths in the reinforced concrete slabs to loading.ASR-cracks are presented schematically for clarifying the hogging effect.

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in the compression zone at higher loads, these high frequency

waves moderately decline in amplitude. The amplitude of the sec-ond part, the coda waves, decreases due to the propagation of 

cracks through the concrete slabs. Let us recall that the coda waves

travel deeply through the medium and are scattered multipletimes by the acoustical heterogeneities in the concrete  [31]. The

Inial structural cracks

Bars yielding

Failure

Zero load

Early arrival

Late arrival

Early arrival

Late arrival

Early arrival

Late arrival

Early arrival

Late arrival

Early arrival

Late arrival

Early arrival

Late arrival

Early arrival

Late arrival

Early arrival

Late arrival

Fig. 8.  Signal distortion and dissipation at both the compression and tension faces with regards to crack development in the nonreactive concrete slabs (NS).

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coda waves can be associated with the reflection of the probewaves that are diffused into the tension zone. Thus, the coda wavesrapidly decayed due to the generation of macro-cracks in the ten-sion zone; whereas the amplitudes of the early arrival waves firstlyincrease and then decline due to crack propagation. Similar behav-ior was observed for the three concrete slabs.

This distortion and the dissipation of the probe signals due tothe loading may limit the application of the methods based onthe velocity variations of acoustoelastic waves, which has beenproposed in the literature for the investigation of the stresschanges in concrete [15,27,30,33,40]. To eliminate this restriction,the energy loss approach to acoustic waves and centroid frequencyshift were considered to track the stress–strain development andthe crack propagation within the concrete slabs.  Fig. 9 illustratesthe evolution of the normalized energy loss and the normalizedapplied loads versus the deflections measured at the mid-span.Both graphs show a similar trend; however, the energy loss of the acoustic waves is generally more sensitive with regards tothe evolution of the damage.

For the NS slab:   as depicted in  Fig. 6, the deflection of about2.5 mm corresponds to the initial structural cracking zone, whilethe 5.0-mm deflection corresponds to the tensile bars yieldingzone. As shown in Fig. 9a, the energy of the signals recorded at bothfaces linearly decreased by 80% for a 2.5-mm deflection (initialstructural cracks zone). This reduction of the energy correspondsto 35% of the failure load in the load–deflection graph. Such behav-ior indicates that the energy loss approach to acoustic waves is def-initely more sensitive to crack initiation in comparison withcommon measurements of load–deflection. The rate of the energyloss significantly decreases between deflections of 2.5 mm and5.0 mm. Therefore, it is difficult to identify the state of the slabbetween main bars yielding and total failure using the energy lossgraph.

For RS1: as shown in Fig. 9b, the rate of the energy loss at thecompression face is different from that at the tension face. At thetension face, the energy of the recorded signals linearly decreasesby about 80% for the 2.5-mm deflection (initial structural crackszone); then, it continues with a similar behavior as for NS up to

Energy evoluon of me-amplitude domain

a

b

c

Fig. 9.  Energy loss for signals recorded at the compression and the tension faces of (a) nonreactive slab; (b) reactive slab 1 (expansion 0.14%); (c) reactive slab 2 (expansion0.19%). Deflections were measured at mid-span of the tension face.

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the main bars yielding point. At the compression face, the responseof the concrete slabs to the acoustic waves is fairly similar to theload–deflection graphs. The energy loss for the initial cracks zoneis about 30% and about 70% for the bars yielding. This lower rateof the energy reduction may be related to the hogging effect dueto ASR-expansion.

For RS2: as shown in Fig. 9c, in comparison with RS1, the initialstructural cracks zone occurred at higher loading for the signalsrecorded at the compression face. This can be due to the higherexpansion level of RS2 (0.19%), which can increase the hoggingeffect in the slab. The initial structural cracks zone is given bythe energy loss 50%, which is at higher loads than that of theRS1; and the main bars yielding zone is given by the energy loss70%. The general behavior of the signals recorded at the tensionface is fairly the same as that in the RS1. However, there is a greaterloss for the RS2, followed by a sharp recovery of about 10% of theenergy. Then the energy of signals decreases with lower rate bydeflection. It may be related to hogging effect that is more signifi-cant in RS2 due to higher ASR-expansion.

Fig. 10 compares all the signals recorded at both the compres-sion and tension faces for the nonreactive and reactive slabs. Theenergy reduction of the signals recorded at the tension faces doesnot seem to be a robust criterion that allows distinguishingbetween ASR-affected and non-ASR slabs (Fig. 10). This limitationFig. 10.  Energy evolution of the received acoustic signals in the concrete slabs.

Energy evoluon of frequency-amplitude domain

Fig. 11. Spectral energy density reduction at the compression and the tension faces of (a) nonreactive slab; (b) reactive slab 1 (expansion 0.14%); (c) reactive slab 2 (expansion0.19%). Deflections were measured at mid-span of the tension face.

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may be related to concrete natural weakness in tension regardlessof the concrete state. In this study, the indirect tensile strength of concrete at the test time was respectively 5.8, 4.9 and 4.6 MPa forthe NS, RS1 and RS2, which are relatively close values despiteexpansion levels of 0.14% (RS1) and 0.19% (RS2). In Fig. 10, the sig-nals recorded at the compression faces can clearly differentiate theASR-damaged slabs from the nonreactive one. However, the energyreduction of RS2 is lower than RS1 prior to the 5.0-mm deflection,because the expansion levels are nearly the same from a structuralpoint of view. Despite the difficulty associated with the energy lossmeasurements at the tension faces, this method appears to be suf-ficiently sensitive to detect the damage evolution stage (crack ini-tiation and main bars yielding) in the concrete slabs. The resultsfound by Van Hauwaert et al.   [37]   also showed that the energyreduction of waveform is a better indicator for tracking crackgrowth in reinforced concrete specimens.

Fig. 11 shows the spectral energy density reduction of signals,calculated from Eq. (2). It is demonstrated that this parameter isvery high sensitive to the initial structural crack propagations.According to the figure, more than 90% of the energy decreasesin both nonreactive and reactive concrete slabs as soon as the ini-tial structural cracks appeared around the 2.5-mm deflection. Allcases show the same behavior, except the NS at the tension facewith a post-peak after the 2.5-mm deflection. It is not generallyeasy to distinguish between the different phases of the damagepropagation using the spectral energy density reduction, whereasthe energy reduction of time-domain signals showed fairly similarbehavior for load–deflection curves. However, the spectral energymeasurements showed that the decrease in the signal energywas accompanied with a reduction in the spectral energy density.Akhras [2]  reported similar behavior when both parameters wereapplied to characterize increasing deterioration in concrete dueto freezing and thawing cycles.

The spectral analysis of the recorded signals was also performedin order to define the centroid frequencies of each signals and theirshift associated with cracking induced by the step loadings. The

robustness of the centroid frequency analysis for tracking crackdevelopment in ASR-affected concrete has been shown by Saint-Pierre  [25].  Fig. 12 illustrates the centroid frequency shift for allconcrete slabs. This parameter, measured at the tension faces,appears to be a more accurate indicator to distinguish betweenthe undamaged slab, and the moderately and highly damaged slabsdue to ASR-expansion. The rate of frequency shift is nearly thesame for all concrete slabs before initial structural cracks zone(deflection 2.5 mm); and then, this parameter shows higher shiftsfor ASR-affected slabs. These results also indicate that it is possibleto clearly make a distinction between RS1 (expansion 0.14%) andRS2 (expansion 0.19%).

4. Conclusions

The feasibility of an energy approach to acoustic waves wasassessed in order to evaluate the mechanical damage growth inreinforced concrete slabs. The high ductility of the reinforced con-crete provides the required serviceability despite cracks and anom-alies growth within the concrete. This ductility property of reinforced concrete, which is associated with high deformations,

distorts acoustic waves and changes the waveform. Therefore,the velocity variations and time shift methods, which are consid-ered to be robust methods for tracking stress changes in concrete,are not applicable in this case. It was found that the energyapproach to time-domain and frequency-domain signals are moresensitive to assess the stress evolution and cracking propagation inthe reinforced concrete slabs, either in the sound concrete slab orin the ASR-damaged concrete slabs. The results showed that theenergy loss approach is more sensitive to the structural crack ini-tiation. This is supported by the rapid dissipation of energy. Theproposed method is promising for structural testing of reinforcedconcrete elements and assemblies.

The moderate trend of the energy reduction of the ultrasonicwaves recorded at the compression faces of the ASR-affected slabs

was found to be a good indicator to distinguish between the soundand ASR-affected concrete. This is supported by the fact that theload–deflection measurements were not robust enough to distin-guish between the sound and ASR-damaged slabs. For instance,despite the fact that RS1 and RS2 had reached expansion levelsof 0.14% and 0.19% prior to testing, no significant difference wasobserved between the structural behavior of the ASR-affected slabsand the sound slab. This observation is explained by the hoggingeffect. The main conclusions of this study are derived from asfollow:

  The energy reduction curves at the tension face can clearlyidentify the initial structural cracks zones (deflection around2.5 mm) and yielding of the steel bars (deflection of about

5.0 mm). However, most of the energy of the acoustic signalsdecreased as the initial structural cracks occurred in theconcrete.

 The energy reduction of the NS slab measured at the compres-sion face is the same as that measured at the tension face. How-ever, this reduction was lower for the RS1 and the RS2, and theload–deflection changes and signal energy variation showedsimilar trends. This phenomenon can be explained by the hog-ging effect in the ASR-damaged concrete slabs. A more detailedevaluation of the signals recorded at the compression facespointed out a clear difference between ASR and non-ASR slabs.

 The spectral energy density of the acoustic signals showed highsensitivity to the damage development in the concrete slabs,and most of the energy of the frequency-domain spectrums

drop as initial structural cracks occurred in the concrete.

Fig. 12.  Central frequency shift versus mid-span deflection during load test for the

signals recorded at the tension faces.

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However, the analysis of the energy of the time-domain signalsenables more effective tracking of the stress changes in the con-crete slabs compared with the spectral energy densities.

 The centroid frequency shifts calculated from the signalsrecorded at the tension faces clearly distinguish ASR-affectedconcrete from the non-reactive concrete. Moreover, the cen-troid frequencies showed an increase of the shift with to theexpansion level.

Future studies using energy loss approach should be conductedon large-scale concrete elements to address the uncertainties asso-ciated with the ultrasonic evaluation of ASR-affected concrete, hog-ging effects (self-prestressing effect), etc. The complementarity of the approach can provide civil structural researchers and engineerswith an alternative method capable of monitoring crack initiationand propagation in concrete elements during structural tests.

 Acknowledgements

The investigation was carried out with financial supports forthis research by the Natural Science and Engineering ResearchCouncil of Canada (NSERC – grant RGPIN-283240-2009), by theFonds Québécois de Recherche sur la Nature et les Technologies(FQRNT), by the Federal Highway Administration (FHWA). Thesesupports are greatly acknowledged by the authors. We also thankDanick Charbonneau, Georges Lalonde and Claude Aubé for theirtechnical support.

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