PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Use of Higher-Harmonic Generation To Detecting Cracks due To
Steel Corrosion In Reinforced Concrete
Jaime RAMIS1; Marina MIRÓ2; Jesús CARBAJO2; Pedro POVEDA1; Guillem de Vera2; Miguel ÁngelCLIMENT212DFISTS, University of Alicante, 03690 Sant Vicent del Raspeig, Alicante, Spain

Civil Engineering Department, University of Alicante, 03690 Sant Vicent del Raspeig, Alicante, Spain;

ABSTRACTReinforced concrete is of vital importance in many civil and industrial structural applications. Corrosion orother interface deboning in steel-concrete is a typical failure mode during the long service period of thestructures, which can severely reduce the load-bearing capacity. Higher-Harmonic-Generation (HHG) havebeen used to detecting the onset of microcracking due to steel corrosion in model reinforced concreteelements. The specimens were of prismatic shape with a single steel rebar. The corrosion was forced byadmixing an appropriate amount of sodium chloride at the moment of preparing the concrete mix, and by theapplication of an electric field, using a constant current density power source. The results indicate that theonset of cracking seems to be accompanied by the appearance of higher-harmonic generation at the output
signal, when the system is excited by means of an ultrasound wave.
Keywords: Non-Linear Ultrasonic Test, Cracks, Corrosion

1. INTRODUCTION
A review on non-linear ultrasonic techniques for non-destructive assessment of micro-damage in amaterial can be found in [1]. Some of these techniques are based on changes in the resonancefrequency (spectroscopy) [2] or on the generation of higher order harmonics [3]. In particular,
harmonic generation relies on the generation of higher harmonics whose amplitude is directly linked tothe damage occurrence. In brief, the degradation of a material is linked to a non -linear mechanicalbehavior of it so that as the micro-damage grows, non-linearity increases. As a result, when an
ultrasonic wave propagates through the material an interaction with these microstructural changes
induces the generation of nonlinear terms linked to these higher order waves. Many authors havesuccessfully used this technique to characterize the damage of granite samples subjected tocompressive loadings [4], to investigate thermal damage in sandstone [5], or for in situ real time
monitoring of load-induced damage in concrete [6]. Accordingly, given the potential of this techniquein terms of early damage detection it was found worth investigating its applicability to the study of
micro-cracking induced by corrosion processes in concrete.
This work shows some preliminary results on the use of a non-linear ultrasonic technique based on
harmonic generation to study the micro-cracks produced in reinforced cement mortar under forced
steel corrosion. For this purpose, several prismatic reinforced cement mortar s pecimens were preparedand subjected to a forced corrosion test that accelerated the damage.
Preliminary results indicate that the use of a non-linear ultrasonic technique can be very useful forthe early damage detection and durability assessment of corro ded cement-based structures.
This paper is organized as follows: Firstly, the materials used in this work and how they areprepared and damaged (corrosion test) are described. Secondly, the ultrasonic methods (linear andnonlinear) and the experimental setup are explained. Finally, some results are exposed and discussed
and at the end a brief conclusion is presented.

1jramis@ua.es4761

2. MATERIAL
2.1 Sample preparation
The experimental tests were performed over two sets of three prismatic reinforced cement mortar
specimens having the same dimensions and composition. The choice of cement mortar instead ofconcrete as experimental basis was expected to ensure a better adhesion in the steel -mortar interface
besides reducing the heterogeneities different that the micro -cracking to be induced by the corrosion
phenomena.
First, the cement mortar was prepared mixing a standard siliceous sand aggregate and a sulphate
resisting ordinary Portland cement, CEM I 52.5 R-SR 3, in accordance with the UNE-EN 197-1
standard [7]. A kneading process was then performed mixing the cement mortar with sodium chloride
dissolved in water, being the Water/Cement (W/C) ratio used 0.5. The chloride sodium let obtain a 2%
Cl- relative to the cement weight in the hardened mortar and thereby accelerate the corrosion process.
In a following step, the cement mortar mix was arranged in 100 x 100 x 350 mm3 plastic moulds for 24hours before being extracted for mechanical compaction and curing during 7 days in a hum idity
chamber at 20 ºC and 95 % relative humidity. Each of these moulds allowed centre -crossing a steel
rebar of 12 mm in diameter along each sample 10 mm beneath its upper surface. The steel rebars werepreviously weighted and cleaned from native corrosion products following a recommendation
procedure [8], covering the ends with vinyl electric tape to avoid the steel-mortar-air interaction. Thislayout was chosen so as to favour the micro-cracking produced by the corrosion process to emerge on
the upper surface of the samples and thus ease the monitoring of the micro -crack width growth overtime using a microscope. The preparation data of the cement mortar mix is given in Table 1.
Table 1 – Composition of the Cement Mortar
Material

Amount (g)Cement (CEM I 52,5 R SR(3))

450Standard siliceous sand

1350

Deionized water

225 (w/c = 0.5)

NaCl

14.8 (2% Cl- relative to cement weight)

Photographs of the sample preparation process and the final process are shown in Fig. 1 and 2.

Figure 1 – Left: Preparation process. Right: Sample prepared.

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Figure 2 – Dimensions of samples
2.2 Forced Corrosion Test
The forced corrosion test was performed by using an electrophoretic power source that applied of aconstant current density of 40 μA/cm2 between the steel rebar (anode) and an external galvanized steel
grid (cathode) placed in the bottom of the specimens. Samples were partially submerged (5 mm height)
in a recipient filled with tap water so as to keep an appropriate electric conductivity throughout thematerial, a polypropylene sponge being used between these and the steel grid. The forced corrosion
test was then performed over each of the sets above described, the duration of the experiment being of
23 days for each set. Given that the electrophoretic power source provided a constant current density,
it was possible to corrode three specimens simultaneously in a single test by connecting these in series.
The tests were performed under pseudo-controlled conditions with a relative humidity of 84±4% and atemperature of 23±1ºC to minimize the influence of additional factors on the measurements. Fig. 3
shows an image of the forced corrosion test.

Figure 3 – Experimental setup of the forced corrosion test

3. METHODS
3.1 Ultrasonic Pulse Velocity (UPV) test
Ultrasonic Pulse Velocity (UPV) test is a linear technique that allows determining the ultrasonicwave velocity through a given material from the transit time of a pulse between separate emitting andreceiving transducers. This test is normally used to detect the presence of defects or cracks in concrete
in a simple manner: the lowering of the velocity of the ultrasonic pulse relative to a reference state (i.
e. undamaged conditions) indicates the presence of cracks. Moreover, this method can also provide
information regarding the attenuation of concrete and be helpful in the determination of its elasticproperties. A detailed description on the application of this measurement procedure to concretematerials can be found in the standard ASTM C597-16 [9].
Despite being considered a very extended technique to assess the quality of concrete, it is lesssensitive to micro-cracks and therefore to early damage detection that the non -linear technique to bedescribed next.

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3.2 Non-linear Ultrasonic Test
The non-linear technique used in the present study is based on the harmonic generation in standing
waves [5]. In this test, two transducers are placed opposite each other on both sides of a finite solidmaterial, a purely sinusoidal wave being generated until standing wave conditions are achieved. The
non-linear elastic response of the solid medium is responsible for the distortion of this wave and thehigher harmonic generation, whose magnitude depends on the elastic properties thereof. Whil e theseelastic properties slightly change in the early stage of a damage process, the harmonic generation issensitive to defects whose sizes are smaller than the wavelength of the emitted signal (e. g.
micro-cracks), thus making this method more useful when compared to the UPV test.
Harmonic generation can be determined by examining the amplitudes of the fundamental andharmonic frequencies in the frequency spectrum of the received signal. Assuming that the changes inthe wave propagation velocity and the attenuation are small, the parameters of non-linearity can beapproximated as Bn = A 2 /A 1 2, and Bpn = A 3 /A1 3 A 1 ,A3 and A 2being the amplitudes of thefundamental and second harmonic waves, respectively. In practice, the variation of this ratio relative toinitial undamaged conditions is used as an indicator of the micro -structural damage [3]. The main
advantage of the standing wave method when compared to the propagative one is that it can be usedeven for specimens whose thickness is smaller than the wavelengths of the fundamental and second
harmonic waves. In short, this non-linear technique is expected to be more sensitive to microscale
damage than the linear method above described, as it will be shown in section 3 (results) .
3.3 Experimental Setup
The experimental setup developed to perform both the linear and non-linear ultrasonic tests overthe prepared specimens is described next. A custom-made application was implemented using thesystem-design development software LabVIEW© (see fig.4).

Figure 4 – Custom-made application implemented using software LabVIEW™
The application was run using the acquisition platform NI USB 6361, whose samp ling frequency
was set to 2 MHz.
Figure 5 shows the positions of the transducers transmitters and receivers used. Table 2 completes
the information indicating which transducer acts as an emitter and as a receiver.

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Figure 5 – Position of the transducers in each of the configurations studied
Table 2 – Configurations studied
Configuration

Transducer
E/R

C1

E1/R1

C1I

E1/R1

C2

E2/R2

C3

E3/R3

C4

E4/R4

For each configuration a 30 kHz sinusoidal signal was sent to a FS WMA-100 amplifier and then tothe emitter transducer, using different peak input voltages from 120 to 200 V in 10 V steps to fed thetransducer. Both the emitter and the receiver transducers (Dakel IDK-09) [10] were glued to each endof the reinforced cement mortar specimens, the received signal being amplified using the signal
conditioner B&K 2693-A-0F4 and sent to the acquisition platform.
For the CiI configuration, the emitter transducer was supplied with two tones at the same time (f1 =30kHZ, f2 = 2kHz). A scheme of the experimental setup used for the ultrasonic measurements is shownin Fig. 6.

Figure 6 – Experimental setup used for the ultrasonic measurements
A Hanning/Hann/rectangular window was applied to the steady state interval of the received
signal, the Fourier transform being used to obtain the frequency spectrum of the windowed signal. It isthen straightforward to obtain the amplitudes of the fundamental (30 kHz) and second harmonic (60kHz) from this spectrum
Both the linear and non-linear ultrasonic measurements were performed at intervals of 12 hours
over the 23 days that the forced corrosion test lasted (except weekends).

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4. RESULTS
4.1 Microscopic Data
In addition to the ultrasonic tests, microscopic photographs on the upper surface of the samples
were taken throughout the whole experiment so as to assess the crack width growth as a function of thecorrosion rate. Evolution of the size of the crack is shown in Fig. 7.

20 μm
30 μm

40 μm

60 μm
Figure 7 – Evolution of the size of the crack

4.2 Ultrasonic Test
Some significant results are shown. Figure 8 -Left shows the frequency response of the records
made with the configuration C1 in measures 1, 10 and 11, when the transducer is excited whit 120 V. It
can be seen that the fundamental amplitude (A1) decreases at the same time as the amplitude of thesecond and third harmonics (A2 and A3) decreases. In the 7-Right figure, the variation of theparameters Bn and Bpn with the measurements is shown. An increase of these parameters in the M9 isnoticed. Since the fissure becomes visible one or two days after this growth, it can be assumed th at it
has been caused by the damage of the material related to the corrosion process. In figures 9 the same
representations are made for a voltage of 190 V.

Figure 8 –Left: Frequency response of the records made with the configuration C1 in measures 1,10and 11, when the transducer is excited whit 120 V. Right : Evolution of the parameters Bn and Bpn

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Figure 9 –Left: Frequency response of the records made with the configuration C1 in measures 1,10and 11, when the transducer is excited whit 180 V. Right : Evolution of the parameters Bn and Bpn
Figure 10 presents the frequency response for the CiI configuration when the emitter transducer
was supplied with two tones at the same time (f1 = 30kHZ, f2 = 2kHz) being excited with 180 volts. It
can be seen that the amplitude of the products of intermodulation distortion (frequencies 32, 28, 34 and26 KHz) increases from measure M1 to M12

Figure 10 – Frequency response for the CII configuration: The emitter transducer was supplied with twotones at the same time (f1 = 30kHZ, f2 = 2kHz) being excited with 180 volts

5. CONCLUSIONSThe preliminary results that are obtained in this work indicate that it is possible to detectmicro-cracking of reinforced mortar specimens due to corrosion using higher-harmonic generation.
The non-linear ultrasonic measurements yield similar values of times for cracking, as compared to themicroscopic observations of the mortar surface. However, these are preliminary results and it isnecessary further research.

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ACKNOWLEDGEMENTS
This research was funded by the Spanish Agencia Estatal de Investigación (grant codeBIA2016-80982-R) and by the European Regional Development Fund (grant code BIA2016-80982-R).
M. M. acknowledges a pre-doctoral fellowship from the Spanish Ministerio de Educación, Cultura yDeporte (FPU16/04078).
We would like to thank Carmen Andrade for advice on the details of the corrosion testing. We thankalso Lafarge-Holcim Spain for providing the cement samples for preparing the reinforced mortar
specimens.

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