Non-linear Ultrasonic Evaluation of Damaged Concrete Based on Higher Order

Materials and Design 30 (2009) 4095–4102

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Materials and Design

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Non-linear ultrasonic evaluation of damaged concrete based on higher orderharmonic generation

A.A. Shah a, Y. Ribakov b,*

a Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology, 2-12-1, W8-22, O-okayama, Meguro-ku, Tokyo 152-8552, Japanb Department of Civil Engineering, Ariel University Center of Samaria, 44837 Ariel, Israel

a r t i c l e i n f o

Article history:Received 22 March 2009Accepted 7 May 2009Available online 12 May 2009

Keywords:A. ConcreteE. MechanicalG. Non-destructive testingG. Ultrasonic analysis

0261-3069/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.matdes.2009.05.009

* Corresponding author. Tel.: +972 546 431 385; faE-mail address: [email protected] (Y. Ribakov).

a b s t r a c t

Non-linear ultrasonic testing, based on higher order harmonic generation, is a true mean for nondestruc-tive evaluation of concrete allowing damage detection at early stages of damage. Using conventional non-destructive testing methods like pulse echo, velocity and impact echo for evaluation of such damages isdifficult because poor sensitivity of these methods to early damage occurrence. In this paper an experi-mental investigation of 18 cubic concrete specimens, caste with three different water–cement ratios,using non-linear ultrasonic technique is presented. The specimens were ultrasonically evaluated bothin damaged and undamaged conditions. The specimens were damaged progressively by loading themunder compression in several steps up to their ultimate load bearing capacity. At the end of each loadingstep ultrasonic evaluation was performed and time domain waveforms were recorded at different powerlevels. Frequency spectra were prepared by performing Fast Fourier Transformation of the recorded timedomain waveforms. The frequency spectra were used to obtain the first three harmonic amplitudes. Thecaptured harmonic amplitudes were used to calculate the second and third harmonic ratios. Comparisonof the harmonic ratios has shown the extraordinary sensitivity of the non-linear ultrasonic method, usedin this study, to early damage detection. It was also observed that this sensitivity further increases aswater cement ratio increases.

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1. Introduction

Concrete is known as a heterogeneous material including vari-ous constituents (sand, aggregates, cement, etc.). The dimensions,and geometry of the constituents are different and their locationsare randomly distributed in the body of concrete. Hence it is highlypossible that defects and damages should exist in concrete evenbefore it is mechanically loaded. Non Destructive Evaluation(NDE) of concrete has motivated a lot of research works.

Several NDE methods such as acoustic emission, electricalmethods, impact-echo, magnetic methods, radar, sonic methods,surface hardness methods, thermography, acoustic tomography,and ultrasonic methods are used for concrete inspection. NDE tech-niques have several advantages when compared to conventionaldestructive techniques, for example, use for in-place inspectionof structures and noninvasive properties. Of all these techniques,ultrasonic methods are commonly used to evaluate mechanicaland environmental damage in concrete because their relativelylow cost, flexibility, and ability to reveal microscopic changes inthe inspected material’s structure.

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One of the earliest studies on cracks formation in loaded con-crete with ultrasound was performed by Jones in 1952 [1]. A morecomplete study of ultrasonic applications in concrete was carriedout by Jones and Facaoaru in 1969 [2]. They have developed rec-ommendations dealing with the application of the ultrasonic pulsemethod to derive the elastic properties, strength and homogeneityof structural concrete, and for identify locations of internal defects.They have also discussed methods for measuring the pulse veloc-ity, and the influence of test conditions on the accuracy of the mea-surements. While both works have historical importance, theresults presented are limited to a few specimens and loading cases.

In 1970 Shah and Chandra [3] examined several different con-crete mixtures using four different types of transducers. The reso-nant frequency of the transducers that were used in theexperiments was: 25, 250, 750, and 2250 kHz. Three different load-ing cases were considered in the experiments: pushover, cyclic andsustained compression. Changes in ultrasonic attenuation andvelocity were correlated to micro-crack growth, and the findingswere substantiated by scrutinizing the damaged specimens micro-scopically. Although some of the observations contradict laterexperiments (for example, during pushover loading of the hard-ened cement paste specimens no changes in pulse velocity wereobserved), it was reported that ultrasonic measurements can pro-vide a good indicator of micro-crack growth in the three loading

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4096 A.A. Shah, Y. Ribakov / Materials and Design 30 (2009) 4095–4102

cases considered. It was also concluded that an increase in the res-onant frequency of the transducers concomitantly increases sensi-tivity to crack growth and the initial velocity in the unloaded stage.

Traditional ultrasonic methods are based on measurements ofthe propagating pulse velocity, that is, the time ultrasonic pulsesneed to travel through a concrete member. Thereby piezoelectrictransducers are used to generate and receive a wave signal. Thedetection of cracks and voids depends upon the lengthening ofthe travel path between the transducers. Application of this meth-od for concrete is described in detail in the ASTM standard (C 597-83) [4]. The measurements of the pulse velocity may be used todetermine the quality of concrete and its compressive strength[5]. Methods based only on the propagating wave velocity arecalled pulse velocity or linear ultrasonic methods. They have beenused to evaluate the quality of concrete and to estimate the dete-rioration and cracking of concrete members. Additionally, pulsevelocity has been used to evaluate the compressive strength ofconcrete through experimental correlation of strength and stiffness[6]. A major issue, however, is that P-wave velocity is not sensitiveto microstructural changes such as internal microcraks andmicrovoids in concrete materials.

An important ultrasonic study was conducted by Berthaud [7,8]to assess damage in concrete correlating the mechanical andacoustical consequences of compression loading. It was consideredthat the anisotropy induced by the degradation of concretethrough axial loading. Based on the argument that the ultrasonicexperiments cannot differentiate between tensile cracks in a con-crete specimen due to compressive or tensile loading, a plangentskepticism was expressed with respect to the value of ultrasonicassessment of damage in concrete [7]. In the conclusion of model-ing the experiments, it was reported [8] that it is always difficult toobtain mechanical information from ultrasonic waves.

2. Literature review on non-linear ultrasonic techniques

Some investigators report that the decrease in the pulse ampli-tude (ultrasonic pulse attenuation) and shifts in the peak fre-quency are more sensitive and more reliable measures tocharacterize distributed damage and diffuse cracking in the con-crete than pulse velocity [9,10]. Selleck et al. used ultrasonic longi-tudinal pulses to evaluate damage on concrete due to freeze–thawcycles and salt scaling [9]. They have studied changes in the pulsevelocity, peak-to-peak attenuation, and peak frequency. It was ob-served that peak-to-peak amplitude and peak frequency weremore sensitive to concrete damage induced by freeze–thaw cyclesand salt scaling than pulse velocity. Both peak-to-peak amplitudeand peak frequency, however, showed a large scatter during theexperiments.

Ultrasonic techniques, investigating non-linear response ofmaterials, offer a potential for measuring certain concrete proper-ties more effectively than methods, assuming linear behavior [11].That is why, the use of linear non-destructive testing methods, likepulse echo or velocity and impact echo, in damage evaluation atmicro level has low efficiency [12]. They can provide very littleindication of the damage in concrete until it progresses to the pointof causing failure [13].

Non-linear ultrasound, on the other hand, has shown increasedsensitivity to early damage detection over linear methods [14].This sensitivity extends from very low to very high damage levelscorresponding to strain localization and fracture [15]. Materialdeterioration or degradation can also be effectively evaluated byusing non-destructive ultrasonic waves, because their propagationcharacteristics are directly related to the material properties. How-ever, generally strength degradation is often found in apparentlyflawless material. As a consequence, the conventional linear non-

destructive testing methods, as stated earlier, are highly sensitiveto gross defects only and less sensitive to evenly distributed mi-cro-cracks. Non-linear ultrasound can be applied for damagedetection at any level, including micro-cracks. It is thus essentialto use non-linear ultrasonic test for effective assessment of mate-rial’s degradation when the damages in concrete appear under ini-tial level of load applied. Defects in concrete at these initial loadingconditions will further be called in this paper as early stagedamages.

Non-linear ultrasonic measurements often use the phenome-non of harmonic generation [16]. Following this phenomenon, alongitudinal ultrasonic tone burst of amplitude A0 at frequencyx0 is launched on one side of the specimen under examination.If A0 is large enough, the wave detected on the other side of thespecimen contains harmonic components. Hence, the detectedwave possesses a component of amplitude A1 at the fundamentalfrequency x0, a component of amplitude A2 at the second-har-monic frequency 2x0, a component of amplitude A3 at the thirdharmonic frequency 3x0, and so on.

Harmonic generation results from the non-linear interactionbetween the ultrasonic wave and the material [17]. As damage in-creases, the magnitude of the non-linear interaction also increases.It causes a greater portion of the fundamental frequency to be con-verted to higher harmonics. Therefore, it can be expected that thedegree of material degradation can be evaluated by measuring thenon-linearity of the ultrasonic wave propagated through the targetmaterial.

3. Significance of the current research

The current study is focused on non-linearity of concrete inview of the second and third-order or higher frequency compo-nents occurrence in addition to the fundamental one. In order toevaluate the higher harmonic generation, transmitting transduceris usually excited by a high power electrical signal [18–21]. A ro-bust experimental procedure to track the material’s non-linearitywas developed. The procedure was based on conventional piezo-electric contact transducers offering the potential to be used infield applications. The burst signal excitations, using this method,gave higher power than the impedance increase method. Theseburst excitations prevented the transducers from overheatingand guaranteed better non-linear characterization compared tothe method, employing free oscillations at the tail end of the burst.The method has an additional advantage that the work frequencyis imposed on the transducer and free oscillations of other vibra-tion modes are limited. Further, it allowed the user to isolate thesample’s non-linearity from the non-linearity of the measurementsystem. After the signal time history is recorded, frequency spectraare prepared by applying Fast Fourier Transformation (FFT). Thesespectra are used to track Fourier amplitudes of fundamental, sec-ond and third harmonic.

The ratios of second and third harmonic amplitudes to thesquare and cube of the fundamental one, commonly called as thesecond and third harmonic ratios, were calculated at differentdamage and power levels similar to the preliminary research car-ried out by the authors for cylindrical specimens [22]. It allowedmeasuring the damage growth in concrete in view of the genera-tion of higher harmonic components. Sensitivity of higher har-monic to changes in damage and power levels was also studied.

Albeit the modeling of the ultrasonic experiments, conducted inthis research, differs and is in some ways considerably simplerthan the model, described in Berthaud’s works [7,8], as it will beshown below, the results are fairly encouraging and indicate thatultrasonic measurements can be used to assess damage in con-crete. The main goal of the experimental program presented herein

A.A. Shah, Y. Ribakov / Materials and Design 30 (2009) 4095–4102 4097

is to apply non-linear ultrasonic testing for evaluation of distrib-uted mechanical damage in concrete, thereby enhancing ultrasonicNDE capabilities to extract quantitative information about thedamage. In contrast to the previous ultrasonic studies [1–3,9,10],longitudinal non-linear ultrasonic wave propagation in thethrough transmission mode was explored. The variations in theamplitude and frequency components with the increasingmechanical damage in concrete and input power level changeswere correlated to the damage growth-defined as the concretedegradation.

4. Non-linear ultrasound equations

Nonlinear interaction of an ultrasonic wave with concrete maytake several forms. In the current study the nonlinear property ofharmonic generation as a means for evaluating distributed damageis used. As it was shown by the authors in a previous study, carriedout for cylindrical specimens [22], initially this damage begins asdegradation and micro-cracking in the interfacial transition zone.As damage progresses, micro-cracks grow and coalesce to form alarger crack that eventually lead to ultimate failure. The ultrasonicwave interacts with these micro structural changes and micro-cracking and, as a result of this interaction, part of the wave is con-verted into harmonics. As damage progresses, larger amplitudes ofharmonics are generated.

The non-linear wave equation, used in this research for describ-ing the observed behavior of the material, is:

@2PW

@t2 ¼ c2W 1� CW

@PW

@a1

� �� @2PW

@a21

ð1Þ

Here PW is the displacement of the waveform with respect to time;cW is the linear wave velocity; CW is the non-linearity parameter; a1

is the wave propagation distance.It is expedient to employ a perturbation expansion of the dis-

placement in the following form:

PW ¼ Pð1ÞW þ Pð2ÞW þ � � � ð2Þ

where Pð1ÞW is the solution of the linear differential equation describ-ing the wave

@2Pð1ÞW

@t2 ¼ c2W

@2Pð1ÞW

@a21

ð3Þ

The solution of linear wave Eq. (3) at a1 = 0, is

Pð1ÞW ¼ PW1 cosðkWa1 �xtÞ ð4Þ

where kW is the mode wave number.Substituting Eq. (4) into Eq. (1) leads

@2Pð2ÞW

@t2 ¼ c2W

@2Pð2ÞW

@a21

� 12

c2WCWk3

W PW1ð Þ2 sin 2 kWa1 �xtð Þ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}Non-linear term¼second harmonic sinusiod

ð5Þ

Solution to Eq. (5) is obtained by assuming a general solution in thefollowing form [23]:

Pð2ÞW ¼ f a1ð Þ sin 2 kWa1 �xtð Þ þ g a1ð Þ cos 2 kWa1 �xtð Þ ð6Þ

Substitution of Eq. (6) into Eq. (5) yields

4kWdf

da1þ d2g

da21

!cos 2 kWa1 �xtð Þ

� 4kWdgda1� d2f

da21

!sin 2 kWa1 �xtð Þ

¼ 12

CWk3W PW1ð Þ2 sin 2 kWa1 �xtð Þ ð7Þ

By equating coefficients of the sinusoidal terms in Eq. (7) it can befollowed that

4kWdf

da1þ d2g

da21

¼ 0 ð8Þ

and

4kWdgda1� d2f

da21

¼ �12

CWk3W PW1ð Þ2 ð9Þ

Assuming that df/da1 and d2g=da21 are zero, turns Eqs. (8) and (9)

into consistent solution.A solution to Eq. (1) can be found using Eqs. (2), (4), and (5) i.e.

PW ¼ PW1 cos kWa1 �xtð Þ � 18

CWk2W PW1ð Þ2a1 sin 2 kWa1 �xtð Þ þ � � �

ð10Þ

This equation shows that a second harmonic signal of amplitudePW2 ¼ 1=8CWk2

WP2W1a1 is generated. Eq. (10) also suggests that CW

may be obtained experimentally by measuring the absolute ampli-tudes of the fundamental and second harmonic signals as

CW ¼ 8PW2

k2WP2

W1a1

ð11Þ

The non-linearity n-th order parameter (CWn) is assumed to charac-terize the efficiency of the n-th harmonic generation and to bedependent on the tested material’s linear and non-linear–elasticproperties only. For n = 2 the following relation is usually used forCW2 definition [24]

PW2 ¼ CW2=4ð Þk2WP2

W1a1 ð12Þ

Let u1 = PW1, u2 ¼ PW2 and a1 = x. In this case Eq. (12) implies that

u2 ¼ ðC2=4Þk2u21x ð13Þ

where k ¼ x=c is the wave number and x is the wave propagationdistance.

To determine C2 the second harmonic amplitude u2 for the gi-ven fundamental amplitude u1 should be measured.

For pure and flawless materials, the third harmonic is typicallygenerated by two subsequent three-wave interactions:xþx! 2x and 2xþx! 3x, [24] that leads to the followingrelation

u3 ¼ C22=8

� �k4u3

1x2 ð14Þ

From Eqs. (13) and (14) yields that

u3=u2 ¼ 2u2=u1 or u3=u1 ¼ 2 u2=u1ð Þ2 ð15Þ

Since normally in an experiment u2/u1 ffi 1% the third harmonic isnegligible for most of the flawless materials.

Recently, abnormally high level of the third harmonic has beenrevealed in the presence of cracks [25] and grain boundaries [26].That could be explained by unusually high forth-order non-linear-ity of defective materials permitting the third harmonic to be gen-erated by direct four-wave process: xþxþx! 3x. In this caseEq. (14) is substituted by

u3 ¼ C3=6ð Þk3u31x ð16Þ

where C3 is the third-order non-linearity parameter depending onthe effective elasticity modules of the order of up to four.

Eq. (13) shows that the displacement of the second harmonic u2

varies as the square of the fundamental frequency displacement,u1. Letting A1 and A2 to be signal amplitudes of the fundamentaland second harmonic frequencies obtained from the receivingtransducer, and using the approximation of u1 = A1 and u2 = A2,the equation becomes


A2 ¼ C2=4ð Þk2A21x or A2=A2

1 ¼ C2=4ð Þk2x ð17Þ

Since k and x are constant for a given testing situation, the harmonicratio of A2=ðA1Þ2 is a direct measure of the level of damage in thetested concrete. It should be noted that the second harmonic ampli-tude, and thus, the degree of second harmonic generation, is relatedto the square of the fundamental amplitude. Therefore, higher lev-els of harmonic generation occur as input amplitude (power) of thefundamental increases.

Similarly, for the third harmonic Eq. (16) can also be written bysubstituting the measured amplitudes of displacements as

A3 ¼ C3=6ð Þk3A31x or A3=A3

1 ¼ C3=6ð Þk3x ð18Þ

In general, the harmonic ratio, A2=ðA1Þ2 is sensitive to micro struc-tural changes and micro-cracking in the interfacial transition zonewhile the third harmonic ratio, A3=ðA1Þ3 is more sensitive to mi-cro-cracking. These are not mutually exclusive; however, both dete-rioration mechanisms contribute to both harmonic ratios.

5. Experimental setup and program

Analyzing the outcomes of the experimental results, obtainedby the authors in the previous study [22], new experiments werecarried out in this research. The new tests were aimed at observingthe performance of non-linear ultrasonic testing method in evalu-ating concrete cubes that were progressively damaged under axialcompression loading. The results obtained from this investigationshould be considered as a useful source in examining the defectsor damages in concrete at early stages, which can be very helpfulin making accurate maintenance and repair decisions in a timelymanner.

For non-linear ultrasonic testing a high power tone burst gatedamplifier having output, concentrated at one frequency, which isnecessary to drive the response of the specimen into the nonlinearrange; a broadband receiver; a transmitting and receiving wavetransducers; a function generator; and an oscilloscope with abuilt-in PC were used. Both transmitting and receiving wave trans-ducers were broad-banded operating at central frequencies of100 kHz and 200 kHz, respectively. The waveform of the transmit-ted signal was a tone burst with 10 cycles. Fig. 1 shows examples oftransmitted and received signals.

In the experiments, a thin layer of silicone gel was used as cou-plant between the transducers and the concrete surfaces. In addi-

Fig. 1. Examples of (a) transmitted signal (b) received signal.

tion, two rubber bands were tightly rapped around thetransducers (Fig. 2). The rubber bands together with the couplantprovided excellent conductivity for ultrasonic signals and consid-erably improved the local contact conditions between the trans-ducers and the concrete surfaces.

The pulser/receiver section of the ultrasonic equipment, used inthis research, allows the user to control gain, high-pass, and low-pass filters in order to improve the signal–noise ratio as much aspossible. A PC based oscilloscope reads the signal from the pul-ser/receiver and stores it in a file.

The non-linear ultrasonic tests were performed simultaneouslywith uni-axial compression loading. The axial compressive loadwas gradually applied to each specimen in several steps (up tothe ultimate level) using a closed loop servo-hydraulic universaltesting machine with a capacity of 2000 kN. At the end of eachloading step a non-linear ultrasonic test was performed and thetime domain waveforms were recorded.

Damages to each test specimen were induced in compression inincrements of 20% of the ultimate strength of the specimen. Aftereach loading increment, the specimen was ultrasonically evaluatedusing a high power tone burst ultrasonic unit in the through trans-mission mode. Each specimen was carried through cycles of load-ing, and NDT analysis for loads of 0%, 20%, 40%, 60%, and 80% of theestimated failure load. The ultrasonic testing paths through theconcrete were normal to the loading direction. The tests were alsorun at five output power levels of the pulser, corresponding to 10%,30%, 50%, 70%, and 90% of the maximum possible output of 1800 V.

The undamaged specimens, representing 0% of the applied ulti-mate load, were initially evaluated using nonlinear ultrasound atall power levels to establish a baseline value for the nonlinearparameters A2=ðA1Þ2 and A3=ðA1Þ3. The ultrasonic data, associatedwith the nonlinear parameters A2=ðA1Þ2 and A3=ðA1Þ3, recorded athigher loading stages and different input power levels, was com-pared with the baseline value in order to measure the change inoccurrence of higher order frequency components, caused by thechange in damage level and input power.

6. Materials characterization

Eighteen cubic specimens, 150 � 150 � 150 mm in size, wereprepared from three concrete batches with water cement (w/c) ra-tios of 40%, 50%, and 60%, respectively. The w/c were selectedbased on improved workability of the mix and achieving the de-sired concrete strength as well as according to the ASTM standards[27]. For each concrete batch six specimens were prepared. Threespecimens from each batch were tested for measuring compressivestrength. The remaining three specimens from the same concretebatch were used for non-linear ultrasonic evaluation. The meancompressive strength of the cubes was used as the compressivestrength of the test specimens in selecting the load steps for ultra-sonic testing. The average 28-day compressive strength obtainedfor 40%, 50% and 60% w/c concretes was 53 MPa, 41 MPa and30 MPa, respectively.

Type I Portland cement, locally available well grinded riversand, and crushed stones as coarse aggregates with maximumaggregate size of 12 mm were used in the concrete mix. In addi-tion, a high range water reducing admixture, air entraining agentand internal rod vibrator were used to improve workability andconsolidation of concrete. After casting, all the specimens werekept under ambient conditions for 24 h, covered with a polythenesheet. The moulds were opened and the hardened concrete cubeswere stored in a humidity room for 28-day moist curing beforesubjecting to axial compression and non-linear ultrasonic tests.The materials selection and casting procedure were made follow-ing the Japanese Standard for concrete construction [28] and the

Fig. 2. Test specimen with transducers for ultrasonic evaluation and compression testing (a) before loading, (b) after loading.

0

500

1000

1500

2000

2500

0 20 40 60 80 100Damage, Percent of Ultimate Strength

Cha

nge

inA

2/A

12(%

)

10% of Max Power Level30% of Max Power Level50% of Max Power Level70% of Max Power Level90% of Max Power Level

Fig. 3. Percent change in 2nd harmonic ratio, A2=A21 with damage level at various

input power levels (w/c = 40%).

0

1000

2000

3000

4000

5000


Cha

nge

inA

3/A13

(%)


Fig. 4. Percent change in 3rd harmonic ratio, A3=A31 with damage level at various



rules specified by the Concrete Laboratory at Tokyo Institute ofTechnology.

We obtained reasonably good quality concrete that is normallyproduced for concrete construction throughout Japan. During non-destructive evaluation of concrete specimens under compressionthe aim was not to break the specimens completely, but ratherto induce distributed internal damages under progressive loadapplication. The nonlinear ultrasound setup was arranged in amanner to detect the damages or defects present in concrete dueto compression loading.

7. Discussion of results

Application of non-linear ultrasonic testing technique to a solidmaterial is considered to be difficult because a non-linear ultra-sonic wave is not easily generated in solids. However, by using ahigh power tone burst ultrasonic wave drive device and excellentcoupling conditions, a nondestructive inspection method can effec-tively realize the non-linear behavior of a material. With this tech-nique, when a high power ultrasonic wave, having large amplitude,is injected into the material, the waveform of the incident ultra-sonic wave is considered to be distorted. As a result, the waveformof the penetrated ultrasonic wave is different from that of the in-jected one. Therefore, unlike the incident ultrasonic wave, the pen-etrated one has harmonic frequency components.

In this experimental investigation the results of non-linearultrasonic tests on the first three specimens with w/c of 40%showed that the nonlinear parameters as measured by the 2ndand 3rd harmonic ratios A2=ðA1Þ2 and A3=ðA1Þ3 increased signifi-cantly as the damage level and the input power increased. Theaverage results for three tests are shown in Figs. 3 and 4. Fig. 3shows that the 2nd harmonic ratio increases significantly for dam-age levels above 40%. As power level is increased a greater increasein the second harmonic ratio is observed, as predicted by Eq. (13).At damage level corresponding to 80% of the ultimate strength andat the 90% power level, the second harmonic ratio increased byover 2000% over the undamaged condition.

Similar results were observed for the third harmonic ratio (seeFig. 4). As it can be followed from this figure, the change in thethird harmonic ratio was even greater than that observed for thesecond one. At a damage level of 80% of the ultimate strengthand at 90% power, this ratio changed by over 4200% compared tothe undamaged state. Clearly, both of these harmonic ratios areextraordinarily sensitive to damage.

Figs. 5 and 6 show similar results for specimens that were castewith w/c of 50%. Average values of test results for three specimensare plotted. The trend of increasing the 2nd and 3rd harmonic ra-

tios is apparent in these figures. The increase in 2nd and 3rd har-monic ratios with damage was even greater than that in thespecimens with w/c of 40%. At a damage level of 80% of the ulti-mate strength and 90% input power, the change in second har-monic ratio is over 3000% compared to the undamaged condition(see Fig. 5). Fig. 6 shows the increase in 3rd harmonic ratio fromundamaged to damaged state as damage and input power increase.At 80% of the estimated failure load using 90% power level, the 3rdharmonic ratio is raised by about 7500% over the undamaged state.

The average changes in higher harmonic generation for the nextthree tests of w/c of 60% with different damage and power levelsare shown in Figs. 7 and 8. In both graphs the 2nd and 3rd har-monic ratios increased with increasing damage. This change in


the harmonic ratios from the undamaged state appears to be sig-nificant as the damage level exceeds 40% of the ultimate strength.For second harmonic ratio, as shown in Fig. 7, the change at 80% ofthe failure load and 90% of the input power is over 4000%. In case ofthird harmonic ratio the change observed was much greater thanthat of the second one. The 3rd harmonic ratio increased by about11,300% at the damage level, corresponding to 80% of the failureload with 90% of the maximum power input compared to the levelof undamaged condition. Both graphs showed evidence that thesensitivity of non-linear ultrasonic testing technique to damagedetection in concrete increases as w/c increases.

Figs. 3–8 show that the change in the second and third har-monic ratios from the baseline value increased with increasing

0

700

1400

2100

2800

3500

0 20 40 60 80 100

Damage, Percent of Ultimate Strength

Ch

ang

e in

A2/A

12(%

)




0

2000

4000

6000

8000


Cha

nge

inA

3/A

13(%

)




0

1000

2000

3000

4000

5000


Cha

nge

inA

2/A12

(%)




the w/c. This is because concrete with high w/c has more defectsand, as a result of these defects, it is more damaged than that withlow w/c. On the other hand, the magnitude of higher harmonicgeneration increases as damage increases. Thus, the increase insecond and third harmonics from undamaged state to damagedstate was greater for concrete with high w/c. As it was mentionedabove, the third harmonic ratio has shown higher sensitivity todamage than the second one for concretes with all w/c, used in thisstudy.

Following Figs. 9–11, the third harmonic ratio is also extremelysensitive to lower levels of damage. These figures are the modifiedversions of Figs. 4, 6 and 8 with the scale expanded to show in de-tail the changes in third harmonic ratio for damage levels of 20 and40%.

Power levels of 10% and 30% in each graph have shown poorsensitivity to low levels of damage. The changes in the third har-monic ratio at the 20% damage level are small and consideredinsignificant compared to the large ones observed at higher dam-age levels. These changes may indicate that the shrinkage stresses,present in the specimen at the undamaged condition are relievedwhen the specimen is subjected to 20% of ultimate strength. Thisis illustrated by the drop in the harmonic ratio in each of the fig-ures at the 20% damage level using lower input power, i.e. 10, 30,or 50%. At higher power levels of 70 and 90% there is sufficient en-ergy present to stimulate sufficient harmonic generation to over-come the effects of residual shrinkage stresses (see Figs. 9–11).

At damage levels, corresponding to 40% of ultimate strength,significant changes to the second and third harmonic ratios are ob-served. The stress produced at this damage level correspondsapproximately to the stresses a concrete structure experiences un-der normal service loads. As it was shown by Mindess et al. [29],

0

3000

6000

9000

12000


Cha

nge

inA

3/A13

(%)




-30

0

30

60

90


Cha

nge

inA

3/A

13(%

)


Fig. 9. Percent change in 3rd harmonic ratio, A3=A31 with damage levels of 20% and

40% (w/c = 40%).

-25

0

25

50

75

100

125


Cha

nge

inA

3/A

13(%

)



40% (w/c = 50%).

-25

0

25

50

75

100

125


Cha

nge

inA

3/A13

(%)



40% (w/c = 60%).


micro-crack formation starts to increase when the compressivestresses are about 30–40% of ultimate strength. The data associatedwith third harmonic ratio, plotted in Figs. 9–11, clearly indicatesthat some damage occurs under service loads.

Attenuation has been found to be a major factor influencing themagnitude of the second and third harmonic ratios. The amplitudeof the fundamental frequency, A1, is measured after it has passedthrough the damaged specimen and experiences increasing atten-uation as the damage level increases. Since this term is squared inthe second harmonic ratio and cubed in the third one, it has a ma-jor effect on the changes in harmonic ratios as damage progresses.Similarly, the amplitudes of the second and third harmonics (A2

and A3, respectively) generated within the specimen by the nonlin-ear process, also experience attenuation, which further affects theharmonic ratios. Further investigation of the influence of attenua-tion on measuring the damage growth in concrete will be done infuture research.

8. Conclusions

The study was aimed at evaluation of progressive damages inconcrete using non-linear ultrasonic technique, based on higher or-der harmonic generation. Eighteen cubic specimens were preparedfrom three concrete batches with three distinct water cement(w/c) ratios. The specimens were initially evaluated in undamagedconditions using non-linear ultrasound to establish a baseline va-lue for the second and third harmonic ratios. Damages were in-duced in the specimens by loading them in compression withload increments of 20% of their ultimate strength until failure oc-curred. At the end of each loading step non-linear ultrasonic eval-uation of the specimens was performed and the time domainwaveforms were recorded. Frequency spectra were prepared using

Fast Fourier Transformation of the time domain waveforms. FromFrequency spectra the fundamental, second, and third harmonicamplitudes were obtained and used for estimating the secondand third harmonic ratios.

It was shown that non-linear ultrasonic testing method, basedon higher order harmonic generation, is highly effective in damagedetection in concrete. The second and third harmonic ratios haveshown to be very sensitive to compression induced damage in con-crete. Their sensitivity increased as w/c increased. Additionally, thethird harmonic has shown higher sensitivity to damage detectionthan the second one.

At higher power and damage levels generation of higher orderfrequency components in the test specimens, independent of thew/c were evident. Moreover, as the magnitude of these higher or-der components is related to the concrete material behavior andpulse power output, the magnitude of the higher order frequencycomponents was different in undamaged and damaged concretes.It shows the sensitivity of higher harmonic generation, basednon-linear ultrasonic testing method, to the change in damageand power levels.

It was demonstrated that increasing the input power levelsyields increased sensitivity to damage. At the higher input powerlevels the damage, associated with service load stresses, is alsoclearly indicated.

The results of this study form a way for effective damage detec-tion in concrete structures even at early stage damages, allowingundertaking proper measures for retrofitting and preventing ofstructures’ failure. In our opinion, with appropriate minor modifi-cations the methodology, used in this research for concrete dam-ages evaluation, can also be applied for detection of early stagedamages in other materials.

Acknowledgement

The research grant for conducting this research was provided byJapan Society for the Promotion of Science (JSPS), which is grate-fully acknowledged by the first author.

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Non-linear Ultrasonic Evaluation of Damaged Concrete Based on Higher Order

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