Article

Corrosion Assessment of Steel Bars Used in Reinforced Concrete Structures by Means of Eddy Current Testing Naasson P. de Alcantara Jr. *, Felipe M. da Silva, Mateus T. Guimarães and Matheus D. Pereira Received: 25 September 2015; Accepted: 19 December 2015; Published: 24 December 2015 Academic Editor: Piervincenzo Rizzo Department of Electrical Engineering, São Paulo State University—Unesp, Bauru 17033-360, Brazil; [email protected] (F.M.S.); [email protected] (M.T.G.); [email protected] (M.D.P.) * Correspondence: [email protected]; Tel.: +55-14-3013-6115; Fax:+55-14-3231-2820

Abstract: This paper presents a theoretical and experimental study on the use of Eddy Current Testing (ECT) to evaluate corrosion processes in steel bars used in reinforced concrete structures. The paper presents the mathematical basis of the ECT sensor built by the authors; followed by a finite element analysis. The results obtained in the simulations are compared with those obtained in experimental tests performed by the authors. Effective resistances and inductances; voltage drops and phase angles of wound coil are calculated using both; simulated and experimental data; and demonstrate a strong correlation. The production of samples of corroded steel bars; by using an impressed current technique is also presented. The authors performed experimental tests in the laboratory using handmade sensors; and the corroded samples. In the tests four gauges; with five levels of loss-of-mass references for each one were used. The results are analyzed in the light of the loss-of-mass and show a strong linear behavior for the analyzed parameters. The conclusions emphasize the feasibility of the proposed technique and highlight opportunities for future works. Keywords: reinforced concrete structures; corrosion process; nondestructive testing; eddy current testing; accelerated corrosion techniques

1. Introduction Reinforced concrete structures are, nowadays, the main construction element in most countries. However, despite flexibility and other construction advantages, reinforced concrete presents some problems that need constant monitoring. One of the main problems that fall within this scope is the process of corrosion of the reinforcements. In fact, the corrosion process dramatically affects the long-term performance of reinforced concrete structures, because it affects the flexural strength, deformation behavior, ductility, bond strength and mode of failure of the structures (El Maaddawy and Soudky [1]). Corrosion of steel in concrete structures is as an oxidation process, followed by the breakdown of the passive film of the steel, due to the entry of chloride ions or carbon dioxide. In the initial phase the corrosion crack doesn’t happen directly on the surface of the concrete structure, but only shows up when the corrosion product reaches its threshold value. In addition, after the appearance of corrosion cracks on the surface, the rate of corrosion increases significantly due to the increased inflow of chloride ions or carbon dioxide through the cracks. In conclusion, this acceleration of the corrosion process threatens the safety of reinforced concrete structure (Maruya et al. [2]).

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As a result of the corrosion process, the corrosion product volume is two to six times greater than theSensors original volume of the steel bar; so, this volume expansion causes cracking and spalling of 2015, 15, page–page the concrete cover, reduction of the cross-sectional area of the reinforcing steel volume, beyond that the already mentioned negativeeffects. effects. Consequently, Consequently, the corrosion reduces the the of theofalready mentioned negative thereinforcement reinforcement corrosion reduces load-carrying capacity of the structure,and andbrittle brittle failure without warning. According to load-carrying capacity of the structure, failuremay mayoccur occur without warning. According to Roqueta et al. [3], quoting Arndt and Jalinoos [4], there are six phases in the concrete corrosion Roqueta et al. [3], quoting Arndt and Jalinoos [4], there are six phases in the concrete corrosion process process for nondestructive monitoring of the service life of a concrete structure, as depicted in Figure 1. for nondestructive monitoring of the service life of a concrete structure, as depicted in Figure 1. CORROSION LEVEL DURING THE CONCRETE STRUCTURE SERVICE LIFE

Free rust

Stress

Concrete

expansion

initiation

cracking

Chloride penetration and corrosion initiation

O2

Cl-

HO2

Figure 1. Schematic illustration ofofthe ofthe theconcrete concrete deterioration tocorrosion the corrosion Figure 1. Schematic illustration thevarious various steps steps of deterioration duedue to the the reinforcement (adapted from [3]). of theofreinforcement (adapted from [3]).

The aim of this paper is to present an experimental study on the use of Eddy Current Testing

The aim of this paper is to present an experimental study on the use of Eddy Current Testing (ECT) to evaluate corrosion processes in the steel bars used in reinforced concrete structures. The (ECT) to evaluate corrosion processes in the steel bars used in reinforced concrete structures. following sections will present a survey of the techniques used to evaluate the corrosion in The following sections will a survey thedetails techniques to evaluate thethe corrosion in reinforced structures, the present mathematical basis,ofand of the used ECT sensors built for tests, reinforced structures, the mathematical basis,with and details of results, the ECT built for the tests, computational simulations and comparisons experimental thesensors production of corroded computational simulations and comparisons with experimental results, the production of corroded samples of steel bars, results of experimental tests and their analysis. samples of steel bars, results of experimental tests and their analysis. 2. A very Brief Survey of the Corrosion Assessment of Reinforced Concrete Structures

2. A very Brief Survey of the Corrosion Assessment of Reinforced Concrete Structures 2.1. Electrochemical Techniques

Although, Techniques in general, visual inspection is the most common practice for the evaluation of the 2.1. Electrochemical conservation status of reinforced concrete structures, it is an inappropriate choice for checking the

Although, general, visual Signs inspection is thesuch most common for the evaluation of existence of in corrosion processes. of damage, as cracks and practice spalling, when they appear, the conservation status of reinforced concrete structures, it is an inappropriate choice for checking are indicative of an extensive corrosion process, so it is desirable to monitor the corrosion process in the existence of corrosionstarung processes. damage, such as cracks andby spalling, when periodic they appear, the reinforcement, withSigns the of structure construction phase, conducting are indicative ofand an extensive corrosion process, so it is desirable to monitor the corrosion process in inspections, keeping a record of data. There are different assess theconstruction reinforcementphase, corrosion on existing structures as: the reinforcement, starung methods with thetostructure by conducting periodic such inspections, (1) open circuit potential measurements; (2) surface potential measurements; (3) linear polarization and keeping a record of data. resistance (4) galvanostatic transient methods; (5) on electrochemical impedance There are measurements; different methods to assess thepulse reinforcement corrosion existing structures such as: spectroscopy; (6) harmonic analysis and (7) noise analysis. This is not an exhaustive list, but it (1) open circuit potential measurements; (2) surface potential measurements; (3) linear polarization reflects the most common methods studied and used in recent years. Their basic principles remain resistance measurements; (4) galvanostatic pulse transient methods; (5) electrochemical impedance unchanged, but some new technological contributions have been added over time. Below there is a spectroscopy; (6) harmonic analysis and (7) noise analysis. This is not an exhaustive list, but it reflects brief description of each cited method: the most common methods studied and used in recent years. Their basic principles remain (1) A metal body in contact with the surrounding media develops an electric potential. In unchanged, but some new technological contributions have been added over time. Below there is reinforced concrete structures, the concrete acts as an electrolyte, generating an electrostatic a brief description of each cited method: potential, which can vary from place to place, depending on the state of the concrete. The

(1)

A metal bodyinvolved in contact with thecircuit surrounding developsisan electric the potential. In reinforced principle in the open potentialmedia measurements essentially measurement of the corrosion potential of the rebar a standard referencegenerating electrode. This is the most typical concrete structures, the concrete actsto as an electrolyte, an electrostatic potential, procedure for from the routine reinforced concrete (Erdogdu et al. [5]). which can vary placeinspection to place,ofdepending on the structures state of the concrete. The principle (2) During the corrosion process, an electrical current flows through the concrete between the of involved in the open circuit potential measurements is essentially the measurement anodic and cathodic regions. Measurements of the difference of potential at the concrete surface the corrosion potential of the rebar to a standard reference electrode. This is the most typical procedure for the routine inspection of reinforced concrete structures (Erdogdu et al. [5]). 2

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(3)

(4)

(5)

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During the corrosion process, an electrical current flows through the concrete between the anodic and cathodic regions. Measurements of the difference of potential at the concrete surface detect this current flow. Surface potential measurements are a non-destructive test to identify anodic and cathodic regions in concrete structures and, indirectly, to detect corrosion processes of the reinforcement. Two reference electrodes are used for the measurements, and no electrical connection to the rebar is required. An electrode is held fixed on the structure in a symmetrical point. The other electrode, called moving electrode, is moved to the nodal points of a grid, along the structure. The measurements are done using a high-impedance voltmeter. A positive reading of the voltage represents an anodic area where corrosion is possible. The higher the potential difference between the anodic and cathodic areas, the higher is the probability of corrosion (Song and Saraswathy [6]). The unique electrochemical technique with quantitative ability regarding the corrosion rate is the so-called polarization resistance, Rp . This technique is based on the application of a small electrical perturbation to the rebar by using a counter electrode and a reference electrode. If the electrical signal is uniformly distributed throughout the reinforcement, the ∆E/∆I ratio defines Rp . The corrosion current, Icorr , is inversely proportional to Rp , or, Icorr = B/Rp , where B is a constant. Rp can be measured employing direct current or alternating current techniques (Andrade and Alonso [7]). The galvanostatic pulse method is a transient polarization technique working in the time domain. A short time anodic current pulse is impressed galvanostatically on the reinforcement from a counterelectrode placed on the concrete surface. The reinforcement is polarized in the anodic direction compared to its free corrosion potential. A reference electrode records the resulting change of the electrochemical potential of the reinforcement. Applying a constant current to the system, an intermediate ohmic potential jumps, and a slight polarization of the rebars occur. Under the assumption that a simple Randles circuit describes the transient behavior of the rebars, the potential of the reinforcement, V(t), at a given time t, can be expressed by an exponential expression, plus a constant resistance (Sathiyanarayanan et al. [8]). Measurement of the electrochemical impedance is done by imposing a sinusoidal voltage (or current) signal of small amplitude, and by measuring the response signal of voltage and current. The amplitudes and the phase difference between the two signals are then analyzed. The frequencies vary between 10´5 and 105 Hz, and the amplitudes between 10 mV and 10 V (MacDonald et al. [9]). The harmonic analysis method is an extension of the impedance method. Its execution is faster and leads to results that are more straightforward than those of the electrochemical impedance method. This technique is carried out by imposing an A.C. voltage perturbation at a single frequency and measuring the A.C. current density, i1 . Two higher harmonics i2 and i3 are also measured. The harmonic analysis uses the fact that the corroding interface acts as a rectifier, in that the second harmonic current response is not linear about the free corrosion potential (Vedalakshmi et al. [10]). In the electrochemical noise method, measurements of the spontaneous fluctuations of the corrosion potentials and currents, which are observed as electrically coupled pairs, are taken. This method is random in nature. The range of frequency is typically from 10´3 to 1.0 Hz. Typical amplitudes are of the order of µV to mV, for voltage, and from nA to µA, for current. Electrochemical noise is a low-cost nondestructive technique reasonably straightforward, although attention must be paid to avoid problems, such as instrument noise, extraneous noise, aliasing, and quantization (Sheng et al. [11]).

2.2. Electromagnetic Techniques The previous section presented some techniques for the identification of corrosion process in reinforced concrete structures, based on electrochemical phenomena. In this section, we present

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the use of techniques for rebar inspection, as well as to detect corrosion processes, based on electromagnetic phenomena. Of course, this is not a state-of-the-art review, but it will serve to contextualize the present work in this scenario. Electromagnetic fields are classified in stationary fields, low-frequency varying fields, and high-frequency varying fields. These three types of electromagnetic fields are used to develop non-destructive technology (NDT) techniques to assess the reinforcement of concrete structures. Makar and Desnoyer [12], and Wolf and Vogel [13] presented examples of the use of magnetic flux leakage (MFL) method, produced by magnetostatic fields, to detect failures in concrete rebars. In both papers, the MFL method was used to detect breaks in steel tendons of prestressed structures. Eddy current testing (ECT) is the best known technique in the NDT area based on low-frequency electromagnetic fields. Shull [14] and Garcia-Martin et al. [15] have presented very well the principles of ECT. In the reinforced concrete inspection context, Rubinacci et al. [16] presented an example of the use of this technique. They used the ECT principles to develop a numerical model, based on the finite element method, to locate and identify the size of steel bars under the concrete. Alcantara [17], built differential electromagnetic sensors, produced dozens of reinforced concrete samples, and performed laboratory tests, using the results to construct ANN training vectors, to locate and identify steel bars under the concrete cover. Ground penetrating radar (GPR) is the best known technique in the NDT area based on high-frequency electromagnetic fields. Annan [18] and Blindow [19] are good references to understand the principles of GPR. Farnoosh et al. [20] presented electromagnetic and computational aspects of the technique, using a numerical analysis. According to these authors, one of the biggest difficulties in the use of the GPR technique is that skilled personnel should analyze the results, and it involves a considerable amount of post-processing work. Shaw et al. [21] used GPR results to construct ANN training vectors to locate and identify steel bars in reinforced concrete structures. Concerning corrosion assessment in the reinforcement of concrete structures, there are few works using GPR techniques. In [22] the authors describe laboratory experiments on the influence of moisture and chloride contents on the amplitude of radar signals. In reference [3], the authors used low-profile ultra-wide-band antennas and twelve concrete samples with induced corrosion, to correlate electromagnetic signatures with the corrosion level of the steel bars. The results were compared with numerical simulations, to verify their consistency. Radiography is one of the earliest NDT techniques used for imaging the steel reinforcements immersed in the concrete. Due to their very small wavelengths, they propagate through the material along straight paths without any significant diffraction. X- and gamma-ray methods are capable of producing accurate two-dimensional images of the concrete interior. However, their use in concrete testing is limited, due to their high initial costs, relatively low speed, heavy and expensive equipment, need for extensive safety precautions and highly skilled operators, and perhaps most important of all, the requirement of accessing both sides of the structure (Buyukozturk [23]). Thermography is another NDT technique based on electromagnetic principles used in the inspection of rebar-reinforced concrete structures. Baek et al. [24] proposed an integration of electromagnetic heat induction and infrared thermography to detect steel corrosion in concrete. They used an inductive heater to heat the steel rebar remotely from the concrete structure surface, integrated with an IR camera to capture the heat signatures. 3. Description and Basics of the Developed ECT Sensors for Steel Bar Inspections 3.1. Mathematical Basics The sensors developed in this work use the eddy current principles. Their electromagnetic parts are, basically, RLC series circuits. An RLC series circuit is an association in series of a resistor, an inductor, and a capacitor. In this case, L is the inductance of a sensor coil, Lc , R is the sum of the coil resistance Rc and any other additional resistances Ra , and C is the capacitance of an external

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capacitive array, Ca , placed in series with the coil. Figure 2 shows an electrical equivalent circuit for the sensor. The following simplifying assumptions limit the use of this equivalent circuit: (1) the capacitors Sensors 2015, 15, page–page do not present electrical resistances; in other words, only displacement currents are considered within the capacitors; (2) if external resistors are added to the sensor, they do not present both inductive and inductive and capacitive effects and only conduction current will present in these (3) the capacitive effects and only conduction current will be present in be these resistors; (3) resistors; the operational operational frequency of the sensors will be in the range of 7.5–15 kHz, so no capacitive effects will frequency of the sensors will be in the range of 7.5–15 kHz, so no capacitive effects will be considered be considered in the sensor coil; (4) the model does not consider parasitic capacitances; (5) if contact in the sensor coil; (4) the model does not consider parasitic capacitances; (5) if contact resistances are resistances known, theytocan added to the model. known, theyare can be added thebe model.

Rc + jωLc

1/(jωCa)

Ra

isensor Vcap Vsource

~ Figure 2. The electrical equivalent circuit of the ECT sensor for reinforcement inspections. Figure 2. The electrical equivalent circuit of the ECT sensor for reinforcement inspections.

In Figure 2, 2, an an input input VVsource , with angular frequency = 2πf, is the voltage applied to source In Figure , with angular frequency ω ω = 2πf, is the voltage applied to the the terminals of the RLC circuit, V is the voltage at the capacitive array terminals, and i is cap voltage at the capacitive array terminals, and isensor is the sensor terminals of the RLC circuit, Vcap is the loop the loopincurrent in theInitially, sensor. Initially, the analysis of the electrical of 2Figure current the sensor. the analysis of the electrical circuit ofcircuit Figure will be2 will donebefordone the for the no-load condition (no ferromagnetic material placed under the sensor). The second law of no-load condition (no ferromagnetic material placed under the sensor). The second law of Kirchoff Kirchoff allows to express, for the voltage at the source terminals: allows to express, for the voltage at the source terminals:

and for the current: and for the current:

ˆ ˙ 11 ) 𝑖 (𝑅 )𝑖 𝑉 = + 𝑅 + 𝑗 (𝜔𝐿 − 𝑠𝑜𝑢𝑟𝑐𝑒 𝑐 R a q𝑎i sensor 𝑠𝑒𝑛𝑠𝑜𝑟 𝑐 𝑠𝑒𝑛𝑠𝑜𝑟 Vsource “ pRc ` ` j ωLc ´ 𝜔𝐶a𝑎 isensor ωC

(1) (1)

Vsource 𝑉𝑠𝑜𝑢𝑟𝑐𝑒 ˆ ˙ isensor “ = 𝑖𝑠𝑒𝑛𝑠𝑜𝑟 11 pR(𝑅 R a𝑅 q 𝑎`) + j 𝑗ωL c `𝑐 + c´ (𝜔𝐿 − ) 𝑐 ωC 𝜔𝐶 a𝑎

(2) (2)

Before proceeding with with the the analysis analysisofofthe theequivalent equivalentcircuit circuitit it necessary carry is is necessary to to carry outout an an analysis of the behavior of the electromagnetic field region interest, with presence analysis of the behavior of the electromagnetic field in in thethe region of of interest, with thethe presence ofof a asteel steelbar. bar.As Asthe thesensor sensorisisfed fedby byaatime-varying time-varyingvoltage voltageat at its its terminals, terminals, the the resultant time-varying electromagnetic field will induce eddy current current loops loops in in the the conducting conducting body. body. The magnitude and behavior of the eddy current will depend on the magnetic flux density distribution, the metal conductivity, thethe electrical frequency. The The induced eddy eddy currents will create conductivity, metal metalpermeability, permeability,and and electrical frequency. induced currents will acreate counter time-varying magnetic field that will disturb the original field. As an illustration, Figure a counter time-varying magnetic field that will disturb the original field. As an illustration,3 shows mapping a 900 turn fedturn by a coil, voltage of 5.0 Vrms , withofa 5.0 frequency equala Figure a3field shows a fieldfor mapping forcoil, a 900 fedsource by a voltage source Vrms, with to 8.05 kHz. Thetonon-commercial FEMM software [25] was used [25] to perform the simulations. frequency equal 8.05 kHz. The non-commercial FEMM software was used to 2D perform the 2D Figure 3a shows the3a flux distribution in the regioninunder the coil, without thewithout presencethe of presence the steel simulations. Figure shows the flux distribution the region under the coil, bar. Figure 3b shows distribution in the region the coil withthe thecoil presence of presence the steel of the steel bar. Figurethe 3bflux shows the flux distribution inunder the region under with the bar, and Figure 3c shows of the flux of within the within bar andthe inbar the and region surrounding it. of the steel bar, and Figuredetails 3c shows details the flux in the region surrounding it. Inspecting the the maps maps of of Figure Figure3,3,it itis is possible some expected phenomena possible to to seesee some expected phenomena fromfrom the the electromagnetic theory: (1)high the permeability high permeability thedistorts steel distorts the of flux the around electromagnetic theory: (1) the of the of steel the lines of lines flux around bar; the as isinknown, in a magnetic/non-magnetic theare lines of flux are to perpendicular as isbar; known, a magnetic/non-magnetic interface, theinterface, lines of flux perpendicular the interface to the non-magnetic interface in the non-magnetic medium; (2) theofhigh of steel does not permit in the medium; (2) the high conductivity steelconductivity does not permit the penetration of the the penetration of thethe magnetic bar; the flux density (andcurrents) consequently the eddy magnetic flux within bar; the flux flux within densitythe (and consequently the eddy is confined to a currents) is around confinedthe tointerface a tiny region around the and interface between thenon-conductor bar and the surrounding tiny region between the bar the surrounding medium; in fact, the skin depth for the steel bar (calculated using the formula 𝛿 = 1/√𝜇𝑓𝜎), considering a relative permeability, 𝜇𝑟 , equal to 1000, electric conductivity, 𝜎, equal to 5.9 MS/m [16], and frequency 𝑓 equal to 8.05 kHz is about 0.13 mm, is very consistent with the figures in Figure 3. Finally, magnitude and phase of the flux density are disturbed point by point. Table 1 shows the components of the magnetic induction vector at the center of the red line in Figure 3b.

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non-conductor medium; in fact, the skin depth for the steel bar (calculated using the formula a δ “ 1{ µ f σ), considering a relative permeability, µr , equal to 1000, electric conductivity, σ, equal to 5.9 MS/m [16], and frequency f equal to 8.05 kHz is about 0.13 mm, is very consistent with the figures in Figure 3. Finally, magnitude and phase of the flux density are disturbed point by point. Table 1 shows the2015, components of the magnetic induction vector at the center of the red line in Figure 3b. Sensors 15, page–page

(a)

(b)

(c) Figure 3. of of thethe fluxflux distribution under an ECT (a) Without the steelthe bar;steel (b) With Figure 3. Simulation Simulation distribution under an sensor. ECT sensor. (a) Without bar; the steel bar; (c) Details of the flux in the steel bar and region around it. (b) With the steel bar; (c) Details of the flux in the steel bar and region around it. Table with and and without without the the steel steel bar. bar. Table 1. 1. 2D 2D components components of of the the magnetic magnetic induction induction vector, vector, with

Without the bar Without With thethe barbar With the bar

Bx (Wb/m2) Bx (Wb/m2 ) −3.665 × 10−6 − j6.346 × 10−7 ´7 ´3.665 10´6 j6.346׈10 10−11 −8 −´ −4.240 ˆ × 10 j5.172

´4.240 ˆ 10´8 ´ j5.172 ˆ 10´11

By (Wb/m2) 2.526 × 10 − j1.224 × 10−6 ´4 ´6 2.526 ˆ 10 2.522 × 10−4´+j1.224 j1.815ˆ×10 10−7 2) By (Wb/m −4

2.522 ˆ 10´4 + j1.815 ˆ 10´7

As a result of the above discussion, the parameters of the electrical equivalent circuit will be affected the following way: discussion, (1) ohmic losses will occur in bar; this fact cancircuit be taken As ainresult of the above the parameters of the steel electrical equivalent willinto be account by adding a resistance ∆Rohmic e in thelosses equivalent circuit; (2) The is no the affected in the following way: (1) will occur in the steelcoil bar;inductance this fact can be longer taken into original value, 𝐿𝑐 . A new effective 𝐿𝑒𝑓 will be defined account by adding a resistance ∆Reinductance in the equivalent circuit; (2) Theas:coil inductance is no longer the original value, Lc . A new effective inductance Le f will be defined as: 𝐿𝑒𝑓 = 𝐿𝑐 + ∆𝐿𝑒 (3) Le f “ Lc `caused ∆Le by the changes in the original magnetic (3) where ∆𝐿𝑒 is a little change of the coil inductance, field, by the presence of eddy currents in the steel bar. where ∆Lvoltage change the coil inductance, by theas: changes in the original magnetic e is a little The at the sensorofterminals will be now caused be expressed field, by the presence of eddy currents in the steel bar. 1 𝑉𝑠𝑜𝑢𝑟𝑐𝑒 = (𝑅𝑐 + 𝑅𝑎 + ∆𝑅𝑒 )𝑖𝑠𝑒𝑛𝑠𝑜𝑟 + 𝑗 (𝜔(𝐿𝑐 + ∆𝐿𝑒 ) + )𝑖 (4) 𝑗𝜔𝐶𝑎 𝑠𝑒𝑛𝑠𝑜𝑟

or: 1 (5) )𝑖 + 𝑗𝜔∆𝐿𝑒 𝑖𝑠𝑒𝑛𝑠𝑜𝑟 𝜔𝐶𝑎 𝑠𝑒𝑛𝑠𝑜𝑟 The sensor is designed to operate at its resonant frequency at no load. In other words, the inductive and capacitive reactances within the parentheses in Equation (5) will have the same value. 𝑉𝑠𝑜𝑢𝑟𝑐𝑒 = (𝑅𝑐 + 𝑅𝑎 + ∆𝑅𝑒 )𝑖𝑠𝑒𝑛𝑠𝑜𝑟 + 𝑗 (𝜔𝐿𝑐 −

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The voltage at the sensor terminals will be now be expressed as: ˆ Vsource “ pRc ` R a ` ∆Re q isensor ` j ω pLc ` ∆Le q ` or:

ˆ

Vsource

1 “ pRc ` R a ` ∆Re q isensor ` j ωLc ´ ωCa

1 jωCa

˙ isensor

(4)

˙ isensor ` jω∆Le isensor

(5)

The sensor is designed to operate at its resonant frequency at no load. In other words, the inductive and capacitive reactances within the parentheses in Equation (5) will have the same value. or: 1 ωLc “ (6) ωCa and: f “

ω 1 ? “ 2π 2π Lc Ca

(7)

At the resonant frequency, the current in the sensor is: isensor “

Vsource pRc ` R a ` ∆Re q ` jω∆Le

(8)

which after some algebraic operations are expressed as the sum of a real and an imaginary parts: isensor “

Vsource pRc ` R a ` ∆Re q2 ` pω∆Le q2

pRc ` R a ` ∆Re ´ jω∆Le q

(9)

The voltage at the capacitor (after some algebraic operations) is: Vcap “ ´

Vsource ı rω∆Le ` j pRc ` R a ` ∆Re qs ” ωCa pRc ` R a ` ∆Re q2 ` pω∆Le q2

(10)

The phase angle for the sensor current, φc , is tg´1 p´ω∆Le { pRc ` R a ` ∆Re qq, and phase angle for the voltage at the capacitor, φv , is tg´1 ppRc ` R a ` ∆Re q {ω∆Le q. The phase angle for the relation Vcap {isensor will be always φ “ ´π{2. At no-load condition, ∆Le “ ∆Re “ 0, and Equations (9) and (10) become: Vsource Rc ` R a

(11)

Vsource ωCa pRc ` R a q

(12)

isensor “ and: Vcap “ ´j

Equations (11) and (12) express the maximum values of the current at the sensor, and of the voltage at the probe capacitor, respectively. Connecting a potentiometer in series with the sensor coil, the no-load condition (values of isensor and Vcap without the presence of a steel bar under the sensor) can be periodically calibrated. 3.2. The Frequency-Adjustment Method to Calculate the Effective Resistance and Inductance The mathematical development presented in the previous subsection shows that the current in the sensor and the voltage drop at the terminals of the capacitive array depend on variations of both resistance and inductance. Therefore, for a better use of the results obtained, it is important to have a way to calculate the resistances and inductances explicitly, after the measurements. From finite element simulations, the authors observed that variations on the effective inductances between the load and no-load condition are less than 0.5%. Including this variation in

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the calculation of a new resonant frequency, the frequency variation is less than 0.25%. Based on this fact, the authors propose a simple method to extract the resistance and inductance values from the measurements. After reaching the resonant frequency of the no-load condition, the sensor is placed on the steel bar, and the frequency is adjusted until the new resonant condition is attained: Lc ` ∆Le “

1

(13)

p2π f n q2 Ca

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and:

Vsource pRc ` R a ` ∆Re q “ where fn is the new resonant frequency. 2π f n Ca Vcap

(14)

where fn isElement the newSimulations resonant frequency. 3.3. Finite and Experimental Comparisons for an ECT Sensor 3.3. Finite Simulations Experimental Comparisons for an ECTthe Sensor FiniteElement element analysis isand a very interesting way to investigate behavior of electromagnetic devices. Through it, a good understanding of the phenomena involved can be obtained, in addition Finite element analysis is a very interesting way to investigate the behavior of electromagnetic to the mathematical modeling of the problem. Moreover, prototypes are built with more confidence, devices. Through it, a good understanding of the phenomena involved can be obtained, in addition if the expected results for their operation can be accurately predicted. to the mathematical modeling of the problem. Moreover, prototypes are built with more confidence, This subsection will present the construction details of an ECT sensor built from the if the expected results for their operation can be accurately predicted. mathematical model presented in the previous section. Figure 4 shows the electromagnetic This subsection will present the construction details of an ECT sensor built from component of this sensor. It is composed of a multi-turn coil with 900 turns of 24 AWG wire, the mathematical model presented in the previous section. Figure 4 shows the electromagnetic connected in series with a capacitive array with capacitance equal to 5 nF and an additional component of this sensor. It is composed of a multi-turn coil with 900 turns of 24 AWG wire, resistance of 50 Ω (not shown in the figure for clarity). The dimensions of the coil are also provided connected in series with a capacitive array with capacitance equal to 5 nF and an additional resistance in this figure. of 50 Ω (not shown in the figure for clarity). The dimensions of the coil are also provided in this figure. The authors performed 3D finite element frequency-domain simulations for this sensor using The authors performed 3D finite element frequency-domain simulations for this sensor using the commercial software COMSOL Multiphysics [26]. Figure 5 shows the magnetic flux density at the commercial software COMSOL Multiphysics [26]. Figure 5 shows the magnetic flux density at the coil surface and the steel bar surface. The gauge of the bar is 20 mm, and the distance between the the coil surface and the steel bar surface. The gauge of the bar is 20 mm, and the distance between top of the bar and the sensor is 25 mm. Figure 6 shows the mapping of the eddy current induced in the top of the bar and the sensor is 25 mm. Figure 6 shows the mapping of the eddy current induced the steel bar. As can be seen from these pictures, the magnetic induction is very low elsewhere in the steel bar. As can be seen from these pictures, the magnetic induction is very low elsewhere (magnetic saturation is not present), and the eddy currents are concentrated in the region of the steel (magnetic saturation is not present), and the eddy currents are concentrated in the region of the steel bar right below of the sensor. bar right below of the sensor. 70 mm 40 mm

110 mm

140 mm

Winding height: 20 mm

(a)

(b)

Figure 4. 4. The The electromagnetic electromagnetic components components of of an an ECT ECT sensor sensor to to inspect inspect the the reinforcement reinforcement of of concrete concrete Figure structures. (a) Perspective view; (b) Coil dimensions. structures. (a) Perspective view; (b) Coil dimensions.

Winding height: 20 mm

(a)

(b)c

4. 15 The electromagnetic components of an ECT sensor to inspect the reinforcement of concrete SensorsFigure 2016, 16, 9 of 18 structures. (a) Perspective view; (b) Coil dimensions.

Figure 5. 5. Magnetic Magnetic flux flux density density at at the the surface surface of of the the coil coil and and the the steel steel bar. bar. Figure Sensors 2015, 15, page–page

8

(a)

(b)

(c)

Figure 6. Induced current in the steel bar represented by the red arrows. (a) Perspective view; (b) Top Figure 6. Induced current in the steel bar represented by the red arrows. (a) Perspective view; view; side (c) view. (b) Top(c)view; side view.

These figures are very interesting to understand the behavior of the field quantities involved. These figures are very interesting to understand the behavior of the field quantities involved. However, to evaluate if this sensor will produce the expected results other variables should be However, to evaluate if this sensor will produce the expected results other variables should be analyzed, such as the effective resistance and inductance of the winding, changes in the phase angle analyzed, such as the effective resistance and inductance of the winding, changes in the phase angle of the current in the sensor, and the voltage drop at the capacitive array. COMSOL Multiphysics was of the current in the sensor,perform and the simulations voltage dropfor at two the capacitive array. COMSOL Multiphysics was prepared to automatically bar gauges, as well as for different positions prepared to automatically perform simulations for two bar gauges, as well as for different positions of the steel bar in relation to the sensor. of theSimulations steel bar in were relation to the done for asensor. steel bar with gauge of 20.0 mm, placed at 25.0 and 45.0 mm under Simulations done a steel gauge of resistance, 20.0 mm, effective placed atcoil 25.0inductance, and 45.0 mm the sensor. Figurewere 7 show theforresults forbar thewith effective coil the under the sensor. Figure 7 show the results for the effective coil resistance, effective coil inductance, voltage at the capacitive array and phase angle of the current in the sensor. The graphics also present the voltage at thevalues capacitive arrayforand angle current in the graphics the experimental obtained thisphase sensor, but of thethe methodology usedsensor. for the The experimental also experimental values obtained butthe thesimulated methodology used for the tests present will be the present in the subsequent sections.forAsthis cansensor, be seen, and experimental results agree very well each other. Resistance (Simulated and Measured) 86 85 84

Inductance (Simulated and Measured) 78.9

of the current in the sensor, and the voltage drop at the capacitive array. COMSOL Multiphysics was prepared to automatically perform simulations for two bar gauges, as well as for different positions of the steel bar in relation to the sensor. Simulations were done for a steel bar with gauge of 20.0 mm, placed at 25.0 and 45.0 mm under the sensor. Figure 7 show the results for the effective coil resistance, effective coil inductance, the Sensors 2016, 16, 15 10 of 18 voltage at the capacitive array and phase angle of the current in the sensor. The graphics also present the experimental values obtained for this sensor, but the methodology used for the experimental tests will be present in be thepresent subsequent As can be seen, andsimulated experimental experimental tests will in thesections. subsequent sections. Asthe cansimulated be seen, the and results agree very well eachvery other. experimental results agree well each other. Resistance (Simulated and Measured)

Inductance (Simulated and Measured)

86

78.9

85

78.8

83

Inductance (mH)

Resistance (Ohm)

84 82 81 80 79 78

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Figure Figure 7. 7. Simulated Simulated(color (colormarks) marks)and andexperimental experimentalresults results(hollow (hollowblack blackmarks) marks)for for the the effective effective resistance resistance (a), (a); effective effective inductance inductance (b), (b); voltage voltage (c) (c);and andphase phaseangle angle (d) (d) for for aa 20 20 mm mm steel steel bar. bar. Red Red marks: Steel bar placed 25 mm under the sensor. Blue marks: Steel bar placed 45 mm under the sensor. marks: Steel bar placed 25 mm under the sensor. Blue marks: Steel bar placed 45 mm under the sensor.

4. The Production of Corroded Samples of Steel Bars 4. The Production of Corroded Samples of Steel Bars The The corrosion corrosion process process of of the the reinforcement reinforcement of of concrete concrete structures structures is, is, in in general, general, quite quite slow. slow. Corrosion acceleration techniques are an important part of the studies on this subject. The impressed Corrosion acceleration techniques are an important part of the studies on this subject. The impressed current technique is the most suitable one for this purpose. References [1–4,27,28] describe some current technique is the most suitable one for this purpose. References [1–4,27,28] describe some research on this technique. research on this technique. In this work, the impressed current technique was used to produce corroded samples of steel In this work, the impressed current technique was used to produce corroded samples of steel bars. Figure 8 shows the schematic arrangement of the experiment and Figure 9 shows four concrete bars. Figure 8 shows the schematic arrangement of the experiment and Figure 9 shows four concrete samples in the laboratory during the corrosion process. samples in the laboratory during the corrosion process. The purpose of the experiment was to obtain corroded samples of steel bars, with different levels of corrosion. In the context of this paper, corrosion level is correlated with the loss-of-mass of the steel sample. The concrete samples were immersed 12Vin a solution composed of 5 g of NaCl for each liter of water. A 12V DC battery was used to provide current. Care was taken to not allow DC the electricalanode the current in each tank to exceed 1.0 A, renewing the saline solution periodically. The concrete flex cables between A between one and two months, to achieve different samples remained within the solution for periods the steel bars levels of corrosion. After the period of corrosion, the bars were removed from the concrete and the cathod rust carefully cleaned. Finally, the bars were weighed, and their weight compared with the weight of e samples of the same gauge and length, but not corroded. (steel bar)

Figure 8. Schematic arrangement for the corrosion process.

Corrosionacceleration accelerationtechniques techniquesare arean animportant importantpart partofofthe thestudies studieson onthis thissubject. subject.The Theimpressed impressed Corrosion currenttechnique techniqueisisthe themost mostsuitable suitableone onefor forthis thispurpose. purpose.References References[1–4,27,28] [1–4,27,28]describe describesome some current research on this technique. research on this technique. thiswork, work,the theimpressed impressedcurrent currenttechnique techniquewas wasused usedtotoproduce producecorroded corrodedsamples samplesofofsteel steel InInthis bars.Figure Figure 8 shows the schematic arrangement of the experiment and Figure 9 shows four concrete bars. Sensors 2016, 16,815shows the schematic arrangement of the experiment and Figure 9 shows four concrete 11 of 18 samples thelaboratory laboratoryduring duringthe thecorrosion corrosionprocess. process. samples ininthe

12V 12V DC DC AA cathod cathod e

anode anode flex cables between flex cables between the steel bars the steel bars

e (steel (steel

bar) bar)

Figure8. Schematicarrangement arrangementfor forthe thecorrosion corrosionprocess. process. Figure Schematic arrangement for the Figure 8.8.Schematic corrosion process.

Sensors 2015, 15, page–page

The purpose of the experiment was to obtain corroded samples of steel bars, with different levels of corrosion. In the context of this paper, corrosion level is correlated with the loss-of-mass of the steel sample. The concrete samples were in immersed inofacorrosion, solution at composed of 5 g of NaCl for Figure 9. Fourconcrete concrete samples the process corrosion, thelaboratory. laboratory. Figure Figure 9. 9. Four Four concrete samples samples in in the the process process of of corrosion, at at the the laboratory. each liter of water. A 12V DC battery was used to provide the electrical current. Care was taken to not allow the current in each tank to exceed 1.0 A, renewing the saline solution periodically. The 10 From the produced sixteen samples of corroded barstwo andmonths, four samples of concrete samples remainedmaterial, within the solution for 10 periods betweensteel one and to achieve non-corroded bars wereAfter chosen this paper. The gauges used were: 10.0, 12.5, 20.0 different levelssteel of corrosion. thefor period of corrosion, the bars were removed from16.0 the and concrete mm. For each bar gauge, bars were chosen with corrosion levels close to 10%, 15%, 20% and 25%. and the rust carefully cleaned. Finally, the bars were weighed, and their weight compared with the Figure 10 theof16.0 samples. weight of shows samples the mm samegauge gaugesteel andbar length, but not corroded.

(a)

(b)

Figure steel bars. bars. Figure 10. 10. (a) (a) Concrete Concrete debris; debris; (b) (b) Samples Samples of of corroded corroded steel

From the produced material, sixteen samples of corroded steel bars and four samples of It should be pointed out that in the context of this work corrosion level is correlated with non-corroded steel bars were chosen for this paper. The gauges used were: 10.0, 12.5, 16.0 and 20.0 the loss-of-mass of the steel samples, but according to the simulations presented in the previous mm. For each bar gauge, bars were chosen with corrosion levels close to 10%, 15%, 20% and 25%. section, a more tighter correlation would be with the loss-of-cross-section-area of the bar, Figure 10 shows the 16.0 mm gauge steel bar samples. since the electro-magnetic field does not penetrate into the body of the samples. It should be pointed out that in the context of this work corrosion level is correlated with the loss-of-mass of the steel samples, but according to the simulations presented in the previous section, a more tighter correlation would be with the loss-of-cross-section-area of the bar, since the electro-magnetic field does not penetrate into the body of the samples. 5. Results

Sensors 2016, 16, 15

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5. Results 5.1. Experimental Setup For this paper, an ECT-RLC sensor, similar to those presented in Section 4, was built. The capacitive array is a 3 ˆ 3 array of 5.0 nF capacitors connected series-parallel, resulting in an equivalent capacitance of 5.0 nF. The winding and the capacitive array were connected in series, inserted in a plastic box especially built for this, and after the internal connections, its interior was filled with a plastic resin. A U1733C handheld LCR meter (Agilent, São Paulo, Brazil) was used to measure the resistance, inductance and capacitance of the sensor at 10 kHz, and the measured values were: 73 Ω, 78.31 mH and 5.0 nF, respectively. Figure 11a shows a picture of the prototype used in the measurements. Figure 11b shows the experimental set-up used for this paper. It is composed of a signal generator to excite the probe at desired values of voltage and frequency, a digital desk-multimeter to measure the voltage at the capacitive array, an oscilloscope to inspect the quality of the signals and a laptop with a LabView application to control all the equipment. Sensorsequipped 2015, 15, page–page

(a)

(b) Figure (b) Experimental Experimental setup setup for for the the measurements. measurements. Figure 11. 11. (a) (a) An An ECT ECT sensor sensor for for corrosion corrosion inspection; inspection; (b)

5.2. The Sensor 5.2. The Movement Movement of of the the Sensor The measurements for two between the sensor the bars = 25 bars and The measurementswere weretaken taken for distances two distances between theand sensor and(e the 45 mm). For the measurements already shown in Figure 7, the sensor was placed at nine positions (e = 25 and 45 mm). For the measurements already shown in Figure 7, the sensor was placed at (d = 0, 10, 20, 30, 40, 50, 60, 70, and 80 mm), in relation to the bar axis, as illustrated in Figure 12. The nine positions (d = 0, 10, 20, 30, 40, 50, 60, 70, and 80 mm), in relation to the bar axis, as illustrated base frequency used in the test was 8043 Hz, the measured resonant frequency of the sensor. in Figure 12. The base frequency used in the test was 8043 Hz, the measured resonant frequency of the sensor.

sensor movement

e d

sensor movement

5.2. The Movement of the Sensor The measurements were taken for two distances between the sensor and the bars (e = 25 and 45 mm). For the measurements already shown in Figure 7, the sensor was placed at nine positions (d = 0, 10, 20, 30, 40, 50, 60, 70, and 80 mm), in relation to the bar axis, as illustrated in Figure 12. The Sensors 2016, 16, 15 13 of 18 base frequency used in the test was 8043 Hz, the measured resonant frequency of the sensor.

sensor movement

e d

sensor movement

(a)

(b)

Figure 12. Schematic representation of the movement of the sensor: (a) top view; (b) side view.

Figure 12. Schematic representation of the movement of the sensor: (a) top view; (b) side view.

5.3. The Procedure for the Measurements

5.3. The Procedure for the Measurements

The procedure for the measurements was as follows:

The procedure for the measurements was as follows: At no-load condition (no steel bar under the sensor):

-

-

At no-load (nois steel baron, under the sensor): (1) Thecondition equipment turned the resonant frequency is set in the signal generator and Sensors 2015, 15, page–page

(1)

-

-

slightly changed until to reach the real resonant frequency for the sensor, 8043 Hz in this

The equipment is turned on, the resonant frequency is set in the signal generator and slightly reach the realfrequency resonant for frequency for the sensor, 8043 Hz in case. This changed frequencyuntil was to used as starting all measurements with corroded or 12 this case. This used on. as starting frequency for all measurements with non-corroded steel frequency bars, from was this point corroded or non-corroded steel bars, from this point on. (2) The coil inductance is calculated, using Equation (13). (2) The coil inductance is calculated, using Equation (13). (3) The coil resistance is calculated, using Equation (14). (3) The coil resistance is calculated, using Equation (14). At load condition: At load condition: (4) A steel bar is placed under the sensor aligned with its main axis. The voltage at the (4) capacitive A steel bar is is placed underand therecorded. sensor aligned withthe its frequency main axis.slightly The voltage at the array measured After this, changed, up capacitive array is measured and recorded. After this, the frequency slightly changed, to the new resonance condition, and steps (2) and (3) are repeated, to calculate the effective up to the new resonance condition, and steps (2) and (3) are repeated, to calculate resistance and effective inductance. the effective resistance and effective inductance. (5) phase of (5) The The phaseangle angleofofthe thecurrent currentininthe thesensor sensorisis calculated calculated using using the the extracted extracted values values of resistance and inductance. resistance and inductance.

Figure 13 13 shows shows the the voltage voltage at at the the capacitive capacitive arrays arrays when when the the bars bars are are placed placed at at the the reference reference Figure levels of of 5, 5, 25 25 and and 45 45 mm mm to to the the sensor. sensor. Circle Circle marks marks are are the the results results obtained obtained before before the the adjustment adjustment of of levels the frequency, and square marks are the results recorded after this adjustment. the frequency, and square marks are the results recorded after this adjustment. Distance to Sensor: 25 mm Voltage at the Capacitor (V)

52 51 50 49 48 47 46 0

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15 Loss of Mass (%)

20

25

Figure 13. Measured voltage voltage at at the the capacitive capacitive array array for for corroded corroded (loss of mass equal zero) and 13. Measured non-corroded steel bars, as a function of the distance of the non-corroded steel bars, as of the bar to the sensor. sensor. Red curves—20.0 mm bar gauge; gauge. Blue curves—16.0 mm mm bar bar gauge, gauge, magenta magenta curves—12.5 curves—12.5 mm mm bar bar gauge; gauge and black curves—10.0 mm bar bar gauge. gauge. Distance to Sensor: 25 mm 6

rence (V)

5 4

Distance to Sensor: 25 mm Voltage at the Capacitor (V)

52

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49 48

As can be seen, the differences 47 between the values measured before and after the frequency adjustment become smaller, as the 46distance from the sensor increases. For a better understanding of 0 10 20 25 the behavior of the sensor as a function of the barof15 gauge, Loss Mass (%) corrosion level and distance from the bar to the sensor, Figure 14 shows the difference between the voltage at no load condition and the voltage the can capacitive array forvoltage corroded (loss of mass equal well zero)stratified, and with Figure a steel 13. barMeasured under thevoltage sensor.at As be seen, these differences are very non-corroded steel bars, as a function of the distance of the bar to the sensor. Red curves—20.0 mm both in relation to the distance from the bar to the sensor, as in relation to the bar gauge. In a real gauge. Blue gauge, the magenta curves—12.5 gauge of and field bar inspection, if thecurves—16.0 gauge of themm bar bar is known, corrosion level andmm the bar thickness theblack concrete curves—10.0 mm bar gauge. cover can be identified with enough confidence. Distance to Sensor: 25 mm 6

Voltage Difference (V)

5 4 3 2 1 0 0

10

15 Loss of Mass (%)

20

25

Figure 14. 14. Voltage Voltagedifference, difference,asasa afunction function gauge, of mass reference distance. of of thethe barbar gauge, lossloss of mass and and reference distance. Red Red curves—20 mmgauge. bar gauge; Blue curves—16.0 mmgauge, bar gauge; magenta curves—12.5 mm bar curves—20 mm bar Blue curves—16.0 mm bar magenta curves—12.5 mm bar gauge gauge; and black curves—10.0 mm bar gauge. and black curves—10.0 mm bar gauge.

As can be seen, differences between theshow valuesthe measured and after frequency To complete thistheanalysis, Figures 15–17 effectivebefore resistances andthe inductances, adjustment become smaller, as the distance from the sensor increases. For a better understanding of calculated according to the procedure shown in the beginning of this section when the bars are placed thethe behavior of distances the sensorofas5,a25 function of theThe barcode gauge, corrosion level and is: distance from the bar to at reference and 45 mm. color for these graphic red curves—20.0 mm the sensor, Figure 14 shows the difference between the voltage at no load condition and the voltage bar gauge; blue curves—16.0 mm bar gauge; magenta—12.5 mm bar gauge; black curves—10.0 mm Sensors 2015, 15, page–page withgauge. a steel bar under the sensor. As can be seen, these voltage differences are very well stratified, bar Concerning thedistance resistance, the variations depending on:to(1)the thebar corrosion both in relation to the from the bar toare thesignificant sensor, as in relation gauge.level; In a real 13 (2) the gauge of the steel bar and; (3) the distance of the bar to the sensor. Concerning the inductance, field inspection, if the gauge of the bar is known, the corrosion level and the thickness of the concrete the variations are insignificant, depending on: (1) the corrosion level; (2) the gauge of the steel bar cover can be identified with enough confidence. and (3) the distance of the bar to the sensor. The most significant changes occur for the distance of To complete this analysis, Figures 15–17 show the effective resistances and inductances, 5 mm. However, this would not be a usual distance between the bar and the sensor in a field test. calculated according toconcrete the procedure shown theequal beginning of this the bars The thickness of the cover must be at in least to the gauge of section the bar, when which does not are placed at the reference distances 5, 25 and 45 mm. code color changes, for thesedepending graphic on is: red happen in this case. With regard of to the distance of 25 mm,The there are slight curves—20.0 barbar, gauge; blueremains curves—16.0 mm bar gauge; magenta—12.5 mmWith bar regard gauge;toblack the gaugemm of the but that constant, regardless of the corrosion level. curves—10.0 mm gauge. the distance of bar 45 mm, apparently there is no significant change in the inductance values.

(a)

(b)

Figure 15. Resistance (a)(a) and inductance steelbars barsatatthe the reference distance 5 mm. Figure 15. Resistance and inductance(b) (b) for for the the steel reference distance of 5 of mm.

uctance (mH)

Distance to Sensor: 25 mm

78.65

(a)

(b)

Figure 15. Resistance (a) and (a) inductance (b) for the steel bars at(b) the reference distance of 5 mm. Sensors 2016, 16, 15

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Figure 15. Resistance (a) and inductance (b) for the steel bars at the reference distance of 5 mm. Distance to Sensor: 25 mm

Effective Inductance (mH)(mH) Effective Inductance

Distance to Sensor: 25 mm

78.65 78.65

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20 Loss15 of Mass (%) Loss of Mass (%)

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Figure 16.16. Resistance (a)(a) and inductance (b) for thesteel steel bars atthe the reference distance ofmm. 25 mm. Figure 16.Resistance Resistance (a) and inductance(b) (b)for forthe steel bars reference distance Figure and inductance bars atatthe reference distance ofof2525mm.

Effective Inductance (mH) Effective Inductance (mH)

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Figure 17. Resistance (a) and inductance (b) for the steel bars at the reference distance of 45 mm.

Figure 17.17. Resistance (b)for forthe thesteel steel bars reference distance 45 mm. Figure Resistance(a) (a)and andinductance inductance (b) bars at at thethe reference distance of 45 of mm. Concerning the resistance, the variations are significant depending on: (1) the corrosion level; (2) the gauge of the steel bar and; (3) the distance of the bar to the sensor. Concerning the inductance, Concerning the resistance, the variations are significant depending on: effective (1) the corrosion level; a conclusion of this analysis it is apparently calculate the resistance, the As variations are insignificant, depending on: (1) thesufficient corrosiontolevel; (2) the gauge of the steel bar (2) the gaugedata of the steel bar and; (3) the distance of the bar to the sensor. inductance, from obtained to develop a method for the Concerning inspection of the reinforced and the (3) the distance of in thethe barmeasurements, to the sensor. The most significant changes occur for the distance of the concrete variations are insignificant, depending on: (1) the corrosion level; (2) the gauge of the bar structures,this both as regards identification and location of the for steel the 5 mm. However, would not be the a usual distance between the bar andreinforcement, the sensor in aasfield test. anddetection (3) the distance of the bar of to the thesteel sensor. of corrosion process bars.The most significant changes occur for the distance of

5 mm. However, this would not be a usual distance 14 between the bar and the sensor in a field test. 5.4. The Lift-Off Effect

14the effects caused by undesired variations of In eddy current NDT tests, “lift-off effects” are the distance between the sensor and the specimen, and can easily mask the test results. In this article, a fast investigation was conducted to evaluate the lift-off effect on the resistance and inductance values. The experiment to investigate the lift-off effects was done with non-corroded bars with a gauge of 20 and 16 mm. The bars were placed at the reference distance of 25 and 45 mm, and for each one, four lift-off values were used: 2, 4, 6 and 8 mm. The results were compared with those obtained for the original distance. Figure 18 shows the effect of the lift-off on the resistance values, and Figure 19 shows the effect on the inductance values. Again, red curves stand for 20 mm bar gauge and blue curves stand for 16 mm bar gauge. Circle marks stand for 25 mm, and square marks stand for 45 mm between the sensor and the bar. As can be seen, the effects are greater for the resistance. However, in a real field inspection, if the measures are taken with the sensor performing small offsets in the axial direction, probably the lift-off should not affect the results substantially. However, this is an issue that must be carefully considered in the development of a real system for the inspection of concrete structures.

distance between the sensor and the specimen, and can easily mask the test results. In this article, a distance between the sensor and the specimen, and can easily mask the test results. In this article, a fast investigation was conducted to evaluate the lift-off effect on the resistance and inductance fast investigation was conducted to evaluate the lift-off effect on the resistance and inductance values. The experiment to investigate the lift-off effects was done with non-corroded bars with a values. The experiment to investigate the lift-off effects was done with non-corroded bars with a gauge of 20 and 16 mm. The bars were placed at the reference distance of 25 and 45 mm, and for each gauge of 20 and 16 mm. The bars were placed at the reference distance of 25 and 45 mm, and for each one, four lift-off values were used: 2, 4, 6 and 8 mm. The results were compared with those obtained one,2016, four16, lift-off values were used: 2, 4, 6 and 8 mm. The results were compared with those obtained Sensors 15 16 of 18 for the original distance. for the original distance.

(a) (a)

(b) (b)

Figure 18. Lift-off effects on the resistance values. (a) absolute values; values; (b) (b) Percent Percent variation. variation. Figure 18.18. Lift-off effects onon thethe resistance values. (a)(a) absolute Figure Lift-off effects resistance values. absolute values; (b) Percent variation. 79

Variation of the Inductance in Function of the Lift-off

Inductance in Function of the Lift-off Inductance in Function of the Lift-off

0.25Variation of the Inductance in Function of the Lift-off 0.25

79

0.2 0.2

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Percent Variation (%) Percent Variation (%)

78.9 78.9

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4mm/0 6 mm/0 4mm/0 Lift-off relation 6 mm/0 Lift-off relation

8 mm/0 8 mm/0

(b) (b)

Figure 19. Lift-off effects on the inductance values. (a) absolute values; (b) Percent variation. Figure Lift-off effects inductance values. absolute values; Percent variation. Figure 19.19. Lift-off effects onon thethe inductance values. (a)(a) absolute values; (b)(b) Percent variation.

Figure 18 shows the effect of the lift-off on the resistance values, and Figure 19 shows the effect Figure 18 shows the effect of the lift-off on the resistance values, and Figure 19 shows the effect 5.5. Discussion on the inductance values. Again, red curves stand for 20 mm bar gauge and blue curves stand for 16 on the inductance values. Again, red curves stand for 20 mm bar gauge and blue curves stand for 16 mm bar gauge. Circle marks standthe forconclusion 25 mm, andissquare marks for current 45 mm betweento theidentify sensor analyzing these results, the use stand ofstand eddy mmBybar gauge. Circle marks stand for 25 mm, andthat square marks for 45 mmtesting between the sensor and the bar. As can be seen, the effects are greater for the resistance. However, in a real field the process of corrosion in the reinforcement of concrete structures can lead However, to a reasonable level of and the bar. As can be seen, the effects are greater for the resistance. in a real field inspection, if the measures are taken with the sensor performing small offsets in the axial direction, success. The experimental results presented here are the first approach of the authors, and of course, inspection, if the measures are taken with the sensor performing small offsets in the axial direction, they can be improved. The sensor was taken to operate in its frequency of resonance and minor 15 15 proposed in the mathematical development variations around it. The frequency-adjustment method was successful. In a general way, the results showed a consistent behavior, with the highest values being obtained for the highest levels of corrosion. Comparing the results on the gauge of the bars, was possible to perceive a logical sequence, with the lowest values for the gauge of 10 mm, and the highest values for the gauge of 20 mm. A practical methodology for the use of ECT in the identification of corrosion processes in the reinforcement of concrete structures can be outlined as follows: first, measurements can be made over non-corroded parts of the reinforcement. In this way, the gauge and concrete cover (if not yet known) can be determined. After, measurements can be made successively along the reinforcement, comparing the results between then and with those for the non-corroded parts. The way forward is now to conduct extensive laboratory and field measurements, to establish large datasets that can be used to feed artificial intelligent tools, like artificial neural networks or fuzzy logic, to develop expert systems for the detection of corrosion in the reinforcement of concrete structures.

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6. Conclusions A theoretical and experimental study was carried out for determining the corrosion level of steel bars used in reinforced concrete structures, using eddy current testing. The following steps were followed: theoretical review, with an overview of the main types of methods in the analysis of the corrosion of reinforcement of concrete structures; mathematical development of the circuit theory, to obtain expressions for the parameters and electrical variables of interest for the problem.; finite element simulations to understanding the electromagnetic phenomena involved in the analysis, and to predict the behavior of the parameters and electrical variables of the proposed sensors; experimental tests for the acceleration of the corrosion of steel bars in reinforced concrete structures; experimental measurements with the sensor using corroded and non-corroded samples; comparisons between simulated and experimental results; analysis of the results obtained for the corroded samples. All these steps were successful. The methodology presented here is not a substitute for the well-established electrochemical methods already in use. It can be used as a preliminary assessment of the reinforcement of concrete structures in search of corrosion processes, and further work can be done, using other methods, to obtain a more comprehensive diagnosis of the problem. ECT sensors based on the principles presented here can be easily built, and operated by personnel with basic professional training, without the need for further knowledge in electrochemistry, for example. Finally, there is a wide field to be explored on this subject, as new levels of frequencies, multi-frequency sensors, improvement in the dimensions of the sensors, sensors with ferrite cores, etc., are all topics worth pursuing. Acknowledgments: The authors express their gratitude to the FAPESP – São Paulo Research Foundation, for the financial support of this research, under the grants number 2014/08797-8, 2014/09622-7, 2014/09624-0 and 2014/09609-0. Author Contributions: Naasson P. de Alcantara Jr.: Supervision of the research. Definition of the system for the process of acceleration of corrosion of steel bars, idealization of the ECT sensors, Conduction of the experimental tests. Analysis of the experimental results. Wrote the article. Felipe M. da Silva: Built the electromagnetic sensors and electronic circuits, performed experimental measurements. Mateus T. Guimarães: Performed the experiments for the acceleration of the corrosion of the steel bars in the concrete samples and experimental measurements. Matheus D. Pereira: Performed computational simulations and experimental measurements. Conflicts of Interest: The authors declare no conflict of interest.

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