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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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(2)
(3)
(4)
(5)
(6)
(7)
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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
Sensors 2016, 16, 15
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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.
Sensors 2016, 16, 15
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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 −
Sensors 2016, 16, 15
7 of 18
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
Sensors 2016, 16, 15
8 of 18
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
Sensors 2015, 15, page–page
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
78.7
78.6
78.5
77
76
75
0
10
20
30
40
50
60
70
78.4
80
0
Sensor Displacement (mm)
10
20
Sensors 2015, 15, page–page
(a)
40
50
60
70
80
(b)
Voltage at the Capacitive Array
52
9
51
50
49
48
Phase Angle (deg)
Figure 7. Cont.
53
Voltage (V)
30
Sensor Displacement (mm)
Phase Angle for the Current at the Sensor
83.2
83
82.8
82.6
82.4
47
46
0
10
20
30
40
50
60
70
80
Sensor Displacement (mm)
(c)
82.2
0
10
20
30
40
50
60
70
80
Sensor Displacement (mm)
(d)
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
12 of 18
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
10
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
Sensors 2016, 16, 15
51
50
14 of 18
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
15 of 18
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
78.6
78.6
78.55
78.55
0
0
10
10
(a)(a)
15
20
Loss15
of Mass (%)
Loss of Mass (%)
20
25
25
(b)
(b)
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)
79.5
79.5
79
79
78.5
78.5
78
78
77.5
77.5
77
0
77
0
(a)
(a)
Distance
to Sensor:
45 mm
Distance
to Sensor:
45 mm
10
15
Loss of Mass (%)
10
20
15
Loss of Mass (%)
25
20
25
(b)
(b)
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
Inductance (mH)
Inductance (mH)
Percent Variation (%)
Percent Variation (%)
78.9
78.9
0.15
0.15
78.8
78.8
0.1
0.1
78.7
78.7
0.05
0.05
78.6
78.6
78.5
0.0
78.5
0.0
2.0
4.0
2.0 Lift-off (mm)
4.0
Lift-off (mm)
(a)
(a)
6.0
6.0
8.0
8.0
0
2 mm/0
0
2 mm/0
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.
Sensors 2016, 16, 15
17 of 18
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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