experimental study of the nonlinear effects generated in a concrete structure with damaged integrity

ISSN 1061�8309, Russian Journal of Nondestructive Testing, 2013, Vol. 49, No. 9, pp. 530–537. © Pleiades Publishing, Ltd., 2013.Original Russian Text © Marta Korenska, Monika Manychova, Lubos Pazdera, 2013, published in Defektoskopiya, 2013, Vol. 49, No. 9, pp. 47–55.

530

1 1. INTRODUCTION

Stability of building structures is one of very important issues in the field of nondestructive defectos�copy. Thanks to the stormy development of concrete and reinforced concrete buildings taking place in thelast century, the condition of concrete an reinforced concrete became a hot topic in the last decade. Con�crete proved to be a durable construction material in the recent years, however, concrete structures oftenexperience degradation after years of service. Structure rehabilitation techniques have reached a highstandard recently. However, the absence of an acceptable, relatively fast and cheap monitoring method,which would be capable of detecting structure faults at an early stage, thus making a simple and cost�effec�tive maintenance possible, is still persisting. Therefore, elaboration of new and simple defectoscopicmethods, capable of determining the integrity of a given structure or a building element is of sign impor�tance. It is also essential to develop and/or refine the methods designed to estimate the lifetime of buildingstructures.

Nonlinear ultrasonic spectroscopy represents new possibilities in acoustic nondestructive testing ofmaterial damage mentioned above. Experimental evidence for the highly nonlinear behaviour of microc�racked and damaged materials has existed for years from experiments of static stress�strain behaviour anddynamic nonlinear wave interaction. Recently, various papers on both the theoretical and experimentalexamination of diverse methods and their applicability in some fields have been published [1–4]. One ofthe fields in which a wide application range of nonlinear ultrasonic spectroscopy methods may beexpected is civil engineering. Poor material homogeneity and, in some cases, shape complexity of somecomponents used in the building industry, are heavily restricting the applicability of “classical” ultrasonicmethods [5]. Precisely these nonlinear ultrasonic defectoscopy methods are less susceptible to the men�tioned restrictions and one may expect them to contribute to a great deal to further improvement of thedefectoscopy and material testing in civil engineering.

1 The article is published in the original.

Experimental Study of the Nonlinear Effects Generatedin a Concrete Structure with Damaged Integrity1

Marta Korenskaa, Monika Manychovab, and Lubos Pazderaa

aBrno University of Technology, Faculty of Civil Engineering, Department of Physics, Veveri 95, 60200 Brno, Czech Republic

bBrno University of Technology, Faculty of Civil Engineering, Department of Building Structures, Veveri 95,60200 Brno, Czech Republic

Received November 27, 2012; in final form, December 08, 2012

Abstract—The paper deals with nonlinear interaction between elastic waves and structural defects inconcrete specimens. Three groups of concrete specimens which differed from each other in the struc�ture quality as a consequence of different ripening conditions were performed. Nonstandard concreteripening conditions resulted in the development of microcracks in the specimen structure. The non�linear elastic properties of the structure were tested by using the analysis of response frequency spec�trum generated from a continuous wave transmission through the concrete specimens. It was testedwhether or not the microcracks in the structure gave rise to parasitic components which were able togenerate nonlinear phenomena in the signal transmission. A single harmonic ultrasonic signal methodwas applied to the specimens and evaluation, especially of the second and third harmonic componentsas indicators of nonlinearity was carried out. Verification measurements which have been carried outin parallel with the ultrasonic ones, give evidence of the specimen structure integrity deteriorationsand confirm the correlation between the nonlinear effects on the transfer characteristics with the exist�ence of defects in the specimen internal structure.

Keywords: concrete, damage, structure interrogation, nonlinear elastic wave spectroscopy, parallelultrasonic and impact echo method.

DOI: 10.1134/S1061830913090040

ACOUSTIC METHODS

RUSSIAN JOURNAL OF NONDESTRUCTIVE TESTING Vol. 49 No. 9 2013

EXPERIMENTAL STUDY OF THE NONLINEAR EFFECTS GENERATED 531

2. NONLINEAR ULTRASONIC SPECTROSCOPY

Two groups of methods focusing on the material response nonlinearity have been dealt with until now,namely, resonance and non�resonance methods.

The first group of methods focuses on samples exhibiting strong resonance effects. It is of advantage tomake use of the resonance frequency shift versus the exciting signal intensity, which is a nonlinear effect.Resonance methods are hardly applicable to specimens in which the resonance effects are suppressed.Therefore, non�resonance methods are used in these cases. These methods analyse the effect of nonlin�earities on acoustic signals propagating through the specimens and methods can be split into two groups:measurements using a single harmonic ultrasonic signal (a single frequency f1) and measurements usingmultiple harmonic ultrasonic signals (usually two frequencies f1, f2).

In what follows, we describe a single harmonic ultrasonic signal measurement method which has beenapplied to the experiment. In this case, where the excitation is accomplished by a single frequency f1(Fig. 1) the nonlinearity gives rise to other harmonic signals, whose frequencies fn obey the Fourier seriesformulas:

(1)

In general, these frequency component amplitudes are falling when the harmonic order natural num�ber, n, is increasing:

(2)

If the nonlinearity effect is not entirely symmetrical, there can arise low�amplitude second and highereven�numbered harmonic components, whose amplitudes may be lower than those of the odd�numberedones. Among these emerging components, the third harmonic is the most distinctive one, see Fig. 1.Therefore, its amplitude is pursued by most researches, especially in electronics [6].

3. EXPERIMENTAL

Our research of the potential applicability of non�linear ultrasonic spectroscopy to the evaluation ofbuildingmaterial structural integrity focused first on ceramic elements [7, 8]. Having gained first results and experiencewe switched our focus on concrete structures, showing higher degree of inhomogeneity and roughness as com�pared with ceramic materials. As many as 21 specimens of dimensions 4 cm × 4 cm × 16 cm were preparedfrom a fine concrete mix. After the concrete hardening had been completed the specimens were dividedinto three groups. The first specimen group (denoted V) was kept, in accordance with standard conditions,in water for the entire ripening period (28 days). In this case no water content reduction took place. Thesecond specimen group was kept in air in laboratory environment conditions (denotation L). In conse�quence of water content reduction after ripening, the specimens shrank and microcracks arose in the spec�imen structure. The third specimen group (denoted S) was placed for twelve days of the ripening processinto a dryer in which the air temperature was 60°C in order to increase the specimen load and get heavierstructure deterioration. The experiment aimed at identifying the effect of non�standard conditions of theconcrete mix ripening on the structure integrity, by means of nonlinear ultrasonic spectroscopy. To verify

fn nf1 |n→ 0 1 2 … ∞., , , ,= =

An An 1–< |n→ 2 3 4 … ∞., , , ,=

Exciter Sensor

f1 f1 +nf1

f1 f f1 2f1 3f1 4f1 5f1 f00

S1(f) S0(f)

Specimen

Fig. 1. Frequency spectrum of a nonlinear medium response.

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MARTA KORENSKA et al.

the correlation of the nonlinear effects with structure defects, some other characteristics of concrete spec�imens, such as the ultrasonic wave propagation velocity and the predominant resonance frequency shift inthe frequency spectra of the specimen response to a mechanical impulse, were analyzed.

3.1. Measurements Using the Nonlinear Ultrasonic Spectroscopy Method

Single�harmonic�signal nonlinear ultrasonic spectroscopy method was applied to the tests of concretespecimens, the signal frequency equalled 30 kHz was used. The schema of the nonlinear ultrasonic equip�ment is showed in Fig. 2. The experimental set�up and testing of its component units have been describedin detail [9, 10] and is briefly described here. The measuring apparatus consists of two principal parts,namely, a transmitting section and a receiving and measuring section. The transmitting section consists offour functional blocks: a controlled�output�level harmonic signal generator, a low�distortion 100 W poweramplifier, an output low�pass filter to suppress higher harmonic components and ensure high purity of theexciting harmonic signal to exciter E. The main chain of the receiving section includes an input amplifierwith filters designed to minimize the receiving chain distortion and a bandpass filter amplifier. Havingbeen amplified, the sensor S output signal was fed into a THPS3�25 HandyScope3 measuring instrumentto be sampled and analyzed. For the purpose of improving the reliability and accuracy of the nonlinearexperiments and minimizing the error effects the attention was focused to transmission between exciter(E) and sensor (S). A program package to control the measuring process, the data processing and evalua�tion makes an indispensable tool.

The measurement results are shown in the form of transfer characteristic frequency spectrum diagrams(see Figs. 3 through 5). The frequency spectrum of Fig. 3 pertains to V12 specimen and represents theresults of the group of specimen which ripened under standard conditions in water. The diagram shows

Exciter ESensor S

Specimen

Flexible mounting

Amplifier

with BP�filters

Digital osciloscope

Output

LP filter f ≤ f1

Power

amplifilter

Signal source f1PC

Fig. 2. The schema of the nonlinear ultrasonic equipment.

0

2×104–120

–40

–80

40

5×104 105 2×105

1H2H 3H

4H

5H

Frequency, Hz

Am

plit

ude,

dB

Fig. 3. Transfer characteristic of intact V12 specimen.



clearly that the harmonic component amplitudes An decrease with the serial number n increase in goodagreement with Eq. (2), which gives evidence of a good structural integrity of these specimens.

Figure 4 shows the measurement results for No L3 specimen, which represents the specimen grouppartially stressed by shrinking. It is evident that higher harmonic component amplitudes are decreasingmore abruptly. At the same time, the fifth harmonic component’s amplitude, 3H, exceeds in magnitudethat of the fourth harmonic 2H. This change in the transfer characteristic appears to manifest the exist�ence of a nonlinearity in the specimen structure, which is due to insufficient specimen water content dur�ing the specimen ripening period.

The frequency spectrum shown in Fig. 5 pertains to S1 specimen. It represents the measurement resultsobtained from the group of specimens which were subjected to heavier stressing during the ripeningperiod, in order to trigger the microcrack generation. The diagram shows clearly a stronger non�linearity,which is due to the structure damage. A very abrupt drop of the second harmonic amplitude 2H is evident,amounting to almost 60 dB with respect to the first one 1H, thus manifesting a heavy deterioration of thespecimen structure.

To verify the correlation between the occurrence of non�linear effects and the specimen structuredefects, a number of further measurements were carried out using different methods.

3.2. Determination of Ultrasonic Wave Propagation Velocity

The propagation velocity of ultrasonic waves in the specimen in question was determined by means ofthe ultrasonic impulse method. This method is based on ultrasonic pulses being periodically sent into thematerial under investigation. The quantity to be measured is the impulse propagation velocity. This veloc�ity is different for various materials and varies with their properties. For example, a good�quality concretefeatures a higher ultrasound impulse propagation velocity than an inferior�quality one. The frequency oflongitudinal oscillations in the specimens was calculated using the well�known formula:

(3)

where: λ—ultrasonic wave wavelength [m], cl—velocity of ultrasonic waves [m s–1].

Table summarizes mean values of calculated ultrasonic wave propagation velocities and correspondingfrequencies of longitudinal oscillations for three different specimen groups. The summary of values givenin the table shows the effect of non�standard concrete specimen ripening conditions on their structuralintegrity. The ultrasonic wave propagation velocity drops with the specimen deterioration degree. Anothermethod used for specimen structure quality testing is a method called impact�echo.

f1λ

cl

��,=

0

2×104–120

–40

–80

40

5×104 105 2×105

1H

2H3H

4H

5H

Frequency, Hz

Am

plit

ude,

dB

Fig. 4. Transfer characteristic of L3 specimen which has been stressed by shrinking.

534



3.3. Impact�Echo Method

This method is used for non�destructive quality evaluation of building elements and concrete andmasonry structures. It is based on the propagation of stress waves, which are generated by a mechanicalimpulse (Fig. 6). A short�duration mechanical impact, produced by tapping a hammer or a small steel ballagainst the surface of concrete or masonry, produces low�frequency stress waves (from 1 to 60 kHz) thatpropagate into the structure and are reflected by flaws and/or external surfaces [11, 12]. Reflected wavesare recorded on the surface by a sensor in the form of a voltage signal. The resulting voltage versus timeplot (time�domain realization) is digitized and fed into the memory of a computer, which subsequentlycarries out the frequency analysis of it. A time realization and the corresponding frequency spectrum arethe results of this test. The predominant frequencies (which are represented by local maxima in the spec�trum) may be associated with multiple reflections within the structure, carrying information on the struc�ture integrity and defect localization. A mechanical impulse, provided in our case by a special hammer,

0

2×104–120

–40

–80

40

5×104 105 2×105

1H

2H

3H

4H

5H

Frequency, Hz

Am

plit

ude,

dB

Fig. 5. Transfer characteristic of S1 specimen which was subjected to stronger shrinking.

Values of verification physical quantities

Specimen group Velocity cl, m/s Frequency f, Hz

V—ripening in water 3410 10650

L—ripening in air 3060 9760

S—ripening in a dryer 2860 8970

Sensor S Mechanicalimpact

Specimen

Data processing

Time realization Frequency spectrum

Fig. 6. The schema of arrangement used in the impact echo method.



was applied at the exciter point E (see Fig. 2), a piezo�electric sensor S was used to pick up the response.The measurements gave rise to frequency spectra of the specimen response to a mechanical impulse, asshown in Figs. 7 through 9.

The diagram shown in Fig. 7 pertains to V12 specimen. This specimen ripened under standard condi�tions in water. The longitudinal direction predominant frequency equals 9700 Hz, whereas the calculationaccording Eq. (2) provides 10270 Hz. Slightly evident value 19400 Hz corresponds to the second har�monic component.

Figure 8 shows the response frequency spectrum for L2 specimen. This specimen underwent shrinkingdue to insufficient water content. It is seen that the predominant frequency shifted to 8 800 Hz, which cor�responds to a shift of 940 Hz. The diagram also shows the second (17.6 kHz) and third (26.4 kHz) har�monic components. According to Eq. (2), the longitudinal oscillation frequency was calculated to equal9500 Hz.

Figure 9 shows the behaviour of S1 specimen, which was subjected to stronger shrinkinginduced stress�ing, being placed in a dryer. In this case the predominant frequency shifted to 8000 Hz, which makes, in

0.8

1030

0.4

1.2

104 105

Frequency, Hz

Am

plit

ude,

arb

Fig. 8. Response frequency spectrum of L3 specimen, which was stressed by shrinking.

1.0

1030

0.5

1.5

104 105

Frequency, Hz

Am

plit

ude,

arb

Fig. 7. Response frequency spectrum of intact V12 specimen.

536



comparison with V12 specimen, a shift of 1740 Hz. The diagram also shows the second (16 kHz) andslightly third (24 kHz) harmonic components.

4. CONCLUSION

The purpose of this study was to experimentally investigate the nonlinear ultrasonic spectroscopypotential in order to evaluate the concrete specimen structure integrity. Three groups of specimens, madeof a fine concrete mix and differing in the structure integrity degree, were tested. The first specimen group,denoted V, was—after the specimen hardening had been completed—kept in water for 28 days, in orderto eliminate the shrinking induced stressing which would otherwise result from water content reduction.The second specimen group, denoted L, was kept in air at laboratory temperature. Water content reduc�tion resulted in shrinking and micro�cracks generation in these specimens. In the third specimen group,the shrinking process was increased by drying the specimens at a temperature of 60°C for 12 days duringthe ripening process.

Single�harmonic�signal nonlinear ultrasonic spectroscopy method was successful in investigatingwhether the specimen structure integrity was impaired due to shrinking�induced stressing. In the case ofstressed specimen groups (L and S), micro�cracks�induced nonlinear effects appeared in the frequencyspectra. They resulted in suppressing the even�numbered harmonic frequencies, especially the secondharmonic in the case of more heavily damaged specimens of the S group. In order to verify the correlationbetween the non�linear effect occurrence and the structure damage, verification measurements were car�ried out using two different methods.

Ultrasonic wave propagation velocity was determined. The value of the velocity decreased when theshrinking�induced specimen damage degree increased, which is accord with standard [13].

The results of the Impact�echo method proved a shift of predominant frequency components lowervalues in the case of the specimen shrinking�induced stressing.

ACKNOWLEDGMENTS

This research was supported by the Grant Agency of the Czech Republic by project No. P104/10/1430Damage Monitoring of Building Structure Components by Nonlinear Ultrasonic Spectroscopy.

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2. Lacouture, J., Johnson, P.A., and Cohen�Tenoudji, F., Study of critical behaviour in concrete during curing byapplication of dynamic linear and nonlinear means, J. Acoust. Soc. Am., 2003, vol. 113, no. 3, pp. 1325–1332.

1.2

1030

0.4

1.6

104 105

Frequency, Hz

Am

plit

ude,

arb

0.8

Fig. 9. Response frequency spectrum of S1 specimen which was subjected to stronger stressing.



3. Shui, G., Kim, J.Y., Qu, J., A new technique for measuring the acoustic nonlinearity of materials using Rayleighwaves, NDT and E International, 2008, vol. 41, no. 5, pp. 326–329.

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experimental study of the nonlinear effects generated in a concrete structure with damaged integrity

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