CONCRETE LIBRARY OF JSCE NO. 39, JUNE 2002
ESTIMATING THE CORROSION RATE OF REINFORCING STEEL IN CONCRETE BY
MEASURING POLARISATION RESISTANCE
(Translation from Proceedings of JSCE, No. 669/V-50, February 2001)
Koichi KOBAYASHI
Toyo MIYAGAWA
This study looks into polarisation resistance methods. Based on a better understanding of these methods, the
aim is to clarify the relationship between corrosion loss and polarisation resistance in reinforced concrete
beams that suffer deterioration due to chloride induced corrosion, thus leading to quantitative estimates of
steel bar corrosion loss from the polarisation resistance. The results obtained in this study can be summarised
as follows: (1) The current flowing upon polarisation flows into the steel bar largely from the inner side of
specimen irrespective of the type of counter electrode. (2) Where a double-disk counter electrode is used, the
amount of current flowing out from the main counter electrode approximately corresponds to that flowing into
the cover side of the steel bar. (3) The amount of corrosion can be calculated more precisely from the polarisation
resistance by combining the measurements obtained using the double-pulse method with a large counter electrode
and those obtained using the AC impedance method with a double-disk counter electrode. (4) The constant K
in the Stern-Geary formula is obtained as 0.0296V in this study.
Keywords: chloride induced corrosion, polarization resistance, macro-cell corrosion, double rectangular
pulse method, AC impedance method
Koichi Kobayashi is an Assistant Professor in the Department of Civil Engineering, Chubu University, Kasugai,
Japan. He obtained his Dr. Eng. from Kyoto University in 1999. His research interests relate to chloride
induced corrosion of reinforcing steel in concrete. He is a member of JSMS, JCI, and JSCE.
Toyo Miyagawa is a Professor in the Department of Civil Engineering, Kyoto University, Kyoto, Japan. He
received his Dr. Eng. from Kyoto University in 1985. He is the author of a number of papers dealing with
durability, maintenance and repair of reinforced concrete structures. He is a member of ACI, RILEM, CEB,
JSMS, JCI and JSCE.
- 103 -
1. INTRODUCTION
Reinforced concrete structures are intrinsically durable as long as they are properly designed and constructed.
In fact, they were once regarded as semi-permanent and maintenance-free. However, it is now known that
certain properties of a concrete structure, such as load bearing capacity, deteriorate as time passes. In some
cases, the deterioration occurs prematurely and causes many serious problems. In other cases, it progresses
slowly over several decades of service.
While it is certainly important to construct structures that are durable, it is also essential to provide proper
maintenance such that a long service life is achieved. There are several factors which cause deterioration of
reinforced concrete structures, one of the major ones being corrosion of the reinforcing steel. To prevent this
type of deterioration, it is important to use dense and durable concrete so as to prevent the penetration of
chloride ions and carbon dioxide gas, which break down the passive film that forms on the reinforcing steel.
Corrosion of steel bars can be recognised when the cover concrete cracks in the direction of the reinforcement.
However, by the time a crack is observed, corrosion has already progressed to a significant degree. Moreover,
the corrosion reaction accelerates once the cover concrete has cracked, so repairs become more difficult.
Accordingly, it is important to properly monitor a reinforced concrete structure and to detect steel corrosion at
an early stage.
Among various techniques for non-destructive testing, electrochemical test methods are considered most
effective for inspecting reinforcing steel corrosion, because the steel corrosion process is an electrochemical
reaction. The polarisation resistance method, for instance, is particularly suitable for evaluating the corrosion
rate of steel bars. It utilises a relationship between corrosion current and polarisation resistance. More
specifically, when the electric potential of a steel bar is forced to change, i. e., when the steel bar is "polarised",
the polarisation resistance Rp is equal to the ratio of ∆E to ∆I, where ∆E represents the change in potential of
the steel and ∆I represents the change in current.
Within reinforced concrete, at the interface between the steel and the pore solution, there exists an electric
doublelayer consisting of a Helmholtz layer and a diffusion boundary layer. The pore solution and electric
doublelayer can most simply be considered equivalent to an electric circuit, as shown in Fig. 1, consisting of
the polarisation resistance Rp, a capacitor Cd, and a resistor representing the resistivity of the concrete Rc. As the
response of this circuit, when the steel is polarised, depends on a resistive component and a capacitative
component, it is necessary to isolate the polarisation resistance component alone in order to determine the exact
corrosion rate.
The prevailing methodology in Japan for determining polarisation resistance includes the AC impedance method
and the two frequencies method [1]~[5]. The two frequencies method works as follows. When voltage ∆E or
current ∆I is applied to the circuit at very high frequency, the reactance of the capacitor becomes negligible
and the electric current flows almost entirely through the resistor Rc and the capacitor Cd. In this situation, the
response of the circuit can be regarded as that of the resistor alone. On the contrary, when voltage ∆E or
current ∆I is applied at very low frequency, the reactance of the capacitor becomes infinite. Therefore, the
circuit can be treated as consisting only of the resistor Rc and the polarisation resistance Rp connected in series.
Thus, the response of the circuit when high-frequency voltage or current is applied represents the resistance of
the resistor, while the response when a low frequency is applied represents the resistance of the resistor and
the polarisation resistance. Accordingly, the polarisation resistance is obtained by subtracting the high-frequency
result from the low frequency result. In practice, the two frequencies method is often implemented as a
double-pulse method, in which two different frequency waveforms
are superposed and applied simultaneously.
Rp
The actual electrochemical state of the steel embedded in the concrete
is of course much more complex than that represented by the circuit
model because of various factors affecting the electrochemical
properties of the steel. These include the Warburg impedance, or
resistivity to the diffusion of gases and ions, and the mill scale formed
on the surface of the steel bar. Thus the results obtained by the two
- 104 -
Rc
Cd
Fig. 1 Equivalent electric circuit model
frequency method are only approximate values.
The AC impedance method involves applying a voltage to the steel bar at varying frequencies and expressing
the electrochemical properties of the steel bar in either the complex-plane presentation or the Bode presentation.
While the double-pulse method offers easy measurement and good applicability to actual concrete structures,
the results obtained are not necessarily reliable due to the various factors mentioned above. On the other hand,
the AC impedance method permits much more precise measurement of the polarisation resistance and thereby
makes possible evaluation of the corrosion rate of the steel bar. However, it entails a complex, time-consuming
measurement procedure. Since estimating corrosion loss necessitates a large number of measurements over
time, it is not instantly practicable, either. Another problem to be resolved before precise evaluations of
corrosion rate are possible is that the electrochemical behaviour of a steel bar while polarised is not always
uniform, because electric current flows through the cover concrete which may have various shapes and consist
of various different mixtures.
This study looks further into polarisation resistance methods. Based on a better understanding of these methods,
the aim is to clarify the relationship between corrosion loss and polarisation resistance in reinforced concrete
beams that suffer deterioration due to chloride induced corrosion, thus leading to quantitative estimates of
steel bar corrosion loss from the polarisation resistance.
2. EXPERIMENTAL PROCEDURE
2.1 Materials and Mixtures
Table 1 shows the mix proportions used for the experimental specimens and Table 2 the materials employed
in these mixtures.
Three types of ordinary concrete were prepared. In two cases, N15 and N30, chloride ions were added (at
1.5% and 3.0% per unit mass of water, corresponding to 2.75kg and 5.5kg per unit volume of concrete,
respectively) to ordinary concrete to simulate chloride-induced corrosion, while no chloride ions were added
to mixture NN. The concentration of chloride ions in mixture N15 slightly exceeded the 1.2~2.5kg/m3 threshold
for corrosion of reinforcing steel as reported by some researchers [6][7]. These chloride ions were added by
blending sodium chloride into the concrete during mixing, and the same mass of sand was removed from the
specified mix proportions.
Two types of powder-type self-compacting concrete containing limestone powder were prepared: mixture SL
(W/C=0.6) had the same water-binder ratio as ordinary concrete so as to obtain normal strength, and mixture
SH (W/C=0.4) had a lower water-binder ratio so as to obtain higher strength. Self-compacting concrete was
developed to offer superior self-compactability for filling all corners of the formwork without the need for
vibration. Thus, it is considered to have advantage for repair work, which often requires injection of concrete
into confined spaces.
Table 1 Mix proportions
NN
N15
N30
SL
SH
W/C
(%)
W/(C+ Lp)
(%)
60
60
60
45
32.4
33.1
s/a
(%)
50.0
49.9
49.7
50.0
50.1
Unit mass (kg/m3)
W
C
Lp
183
305
0
170
174
283
387
242
138
S
867
863
858
780
783
- 105 -
G
891
800
Air
Compressive
Water
entraining
strength
reducing agent
agent
at 28 days
NaCl (C+Lp) x % (C+Lp) x % (N/mm2)
0
32.4
4.575
0.25*
0.0053
30.1
9.15
29.2
2.1**
0.01
34.9
0
2.2**
0.01
49.0
* Water-reducing agent
** High-range water-reducing agent
Table 2 Materials
Ordinary Portland cement ; Specific gravity : 3.15;
Cement
Blane fineness : 3260cm2/g
Limestone powder
CaCO3 >95% ; Specific gravity : 2.73; Blane fineness : 6770cm2/g
River sand ; Specific gravity : 2.57; Water absorption : 1.80%;
Fine aggregate
Fineness modulus : 2.63
Crushed stone ; Specific gravity : 2.64; Maximum size : 15mm;
Coarse aggregate
Fineness modulus : 6.18
Water-reducing agent
Lignosulfonic acid
High-range water reducing agent Polycarboxylic acid
Air-entraining agent
Rosin-based anionic surfactant
2.2 Specimens
Two types of beam were prepared for this study.
The vertical-jointed specimen shown in Fig. 2 was constructed with vertical joints to simulate an uneven
chloride ion distribution, causing a macro-cell corrosion circuit to be formed, in a case where the bottom
surface of a beam is repaired by patching. Two deformed reinforcing steel bars 10mm in diameter and 700mm
in length with mill scale were embedded in these specimens with 20mm of concrete cover (twice the bar
diameter). Electrical cables rated at 100 volts and with a resistance of 14Ω/m were soldered to one end of each
steel bar after exposing the bare steel by grinding off the mill scale. These connections were used for measuring
half-cell potentials and polarisation resistance. The exposed ends of the steel bars were then wrapped with a
self-bonding insulating tape and further covered with epoxy resin to prevent the ingress of water.
Mixtures NN, SL, and SH were placed as the central part of the vertical-jointed specimen, corresponding to
the repaired part of the structure, and mixtures NN, N15, and N30 were placed to form the left and right parts
of the specimen, corresponding to the chloride-contaminated part of the structure. The central part was placed
on the first day. Water was then sprayed over the joint surfaces, and the left and right parts were placed on the
next day. The specimen was demolded on the third day.
Table 3 shows the combination of mixtures used in each type of vertical-jointed specimens. Two beams of
each discrete type were prepared. In order to investigate the effects of the actual joints, into which chloride
ions might penetrate, monolithic specimens using each type of concrete alone were also prepared: specimens
NN, N15, N30, SL, and SH. Further, specimens with two joints were prepared using the same concrete
throughout: specimens NN-NN-NN, N30-N30-N30, and SL-SL-SL. In this case also, the left and right parts
were placed on the second day.
Cable
30
40
Placed from this side
250
800
300
L part
C part
30
80
250
R part
20
D10
0
100
Distance from left end
200
250
300
700
400
500
550
600
700
Halfcell potential
Polarization resistance
(Double-pulse method)
(
)
(
Polarization resistance
(AC impedance method)
Fig. 2 Vertical-jointed specimen (unit: mm)
- 106 -
)
Table 3 Vertical-jointed specimens
The horizontal-jointed specimen shown in Fig. 3 was constructed with
a horizontal joint for the investigation of macro-cell corrosion and
micro-cell corrosion. Four deformed reinforcing steel bars 10mm in
diameter and 300mm in length with mill scale were embedded in the
specimens with a concrete cover of thickness 20mm. Cables were
attached as with the vertical-jointed specimens. Mixtures NN, SL,
and SH were placed as the bottom layer of the horizontal-jointed
specimen on the first day. Water was sprayed over the joint surface,
after which mixtures NN, N15, and N30 were placed as the upper
layer of the specimen on the next day. The specimen was demolded
on the third day.
Table 4 shows the combination of mixtures used in each type of
horizontal-jointed specimen. Two beams of each discrete type were
prepared. Monolithic specimens, NN and N30, were also prepared as
with the vertical-jointed specimens.
Both vertical-jointed specimens and horizontal-jointed specimens were
left in a laboratory at ambient temperature after demolding, and 5%
chloride sodium solution was sprayed on them once a day. After
demolding, all specimens were held on wood spacers with the
placement surface upwards, while their bottom surfaces were kept wet.
The compressive strength values of the concrete at the age of 28 days,
as given in Table 1, were obtained from cylindrical specimens with a
diameter of 100mm and a height of 200mm. These were cured in the
same way as the beam specimens.
Part
C
L
N15-NN-N15
N15-NN-N30
N30-NN-N30
NN-SL-N15
N15-SL-N15
NN-SL-N30
N15-SL-N30
N30-SL-N30
NN-SH-N15
N15-SH-N15
NN-SH-N30
N15-SH-N30
N30-SH-N30
NN
NN-NN-NN
N15
N30
N30-N30-N30
SL
SL-SL-SL
SH
N15
NN
N30
NN
N15
NN
N15
N30
NN
N15
NN
N15
N30
R
N15
N30
N15
SL
N30
N15
SH
N30
NN
NN
N15
N30
N30
SL
SL
SH
NN
N30
SL
NN
N30
SL
2.3 Test procedure
Also shown in Fig. 2 are the half-cell potential measuring points for the steel bars in the vertical-jointed
specimens. Measurements at these points were made using a reference electrode of saturated silver chloride
through the 20mm concrete cover at intervals of 100mm and at the joints.
The polarisation resistance of the steel bars and the electrical resistivity of the cover concrete were measured
by applying a double rectangular pulse at a voltage of ±2~20mVp-p and at frequencies of 0.1Hz and 800Hz. A
copper plate 100mm in width and 800mm in length was placed in close contact with the cover concrete and
used as the counter electrode. The reference electrode, consisting of saturated silver chloride, was attached to
the side of the specimen at the bar midpoint in the longitudinal direction. These measurements were made at
the ages of 3, 5, 7, and 14 days, and thereafter every one or two weeks.
The polarisation resistance of the steel bars was also measured at the age of 160 days using an AC impedance
Cable
400
300
30 40 30
20
10
20
20
10
20
Placed from
this side
T part
B part
D10
Fig. 3 Horizontal-jointed specimen (unit: mm)
- 107 -
Table 4 Horizontal-jointed specimens
Part
T
N30-SL
N30-SH
N30-NN
NN
N30
N30
B
SL
SH
NN
NN
N30
Counter electrode
8
40
45
106
Fig. 4 Double-disk counter electrode
(unit: mm)
0.03
0.02
0.01
0
R part
C part
L part
N15-NN-N15
N15-NN-N30
N30-NN-N30
NN-SL-N15
N15-SL-N15
NN-SL-N30
N15-SL-N30
N30-SL-N30
NN-SH-N15
N15-SH-N15
NN-SH-N30
N15-SH-N30
N30-SH-N30
NN
NN-NN-NN
N15
N30
N30-N30-N30
SL
SL-SL-SL
SH
Reference electrode
Corrosion loss of steel bar (g/cm2)
Guard counter electrode
Repaired Repaired
with NN with SL
Repaired
with SH
For investigation of
influence of joints
method with a voltage of ±1~10mV p-p and a
Fig. 5 Corrosion loss of steel bars
frequency ranging from 10mHz to 10Hz at the
(vertical-jointed specimens)
points shown in Fig. 2 through the 20mm
concrete cover. The counter electrode used for
the AC impedance method was a double-disk [10] consisting of a main centre disk 40mm in diameter and an
enclosing guard disk 108mm in diameter, as shown in Fig. 4. Polarisation resistance in this case was calculated
only from the current between the steel bar and the main centre counter-disk.
In addition to the measurements carried out with the reference electrode attached to the centre of the specimen,
polarisation resistance was measured using the double-pulse method with the reference electrode attached to
the left part or to the right part of the specimen denoted by (O) in Fig. 2. In these measurements, a copper plate
measuring 100mm in width and 800mm in length was used as the counter electrode.
The four cables connected to the steel bars in the horizontal-jointed specimens were bound into a single
bundle to allow macro-cell corrosion current to flow among the steel bars. Further, the macro-cell corrosion
current flowing from the bottom bars to the top bars was measured with a amperemeter.
One of each type of vertical- and horizontal-jointed specimens was broken up for removal of the steel bars at
the age of 160 days. The state of steel corrosion of each steel bar was sketched and the corroded area on the
surface was calculated. The corrosion loss of these steel bars was estimated according to a JCI method [8].
3. CORROSION OF STEEL BARS
Fig. 5 shows the average values of corrosion loss over the whole surface area of the two steel bars in each
vertical-jointed specimen per unit surface area. Fig. 6 similarly shows the corrosion loss of the steel bars in
each horizontal-jointed specimen per unit surface area. Fig. 7 shows macro-cell corrosion losses calculated
from macro-cell current in the horizontal-jointed specimens. As can be seen from Fig. 6, uneven chloride ion
distribution caused the formation of macro-cell corrosion circuit in the horizontal-jointed specimens. The
results shown in Figs. 5 to 7 are discussed in detail in a previous report [9].
4. POLARISATION AREA DEFINITION
4.1 Basic assumptions for simulation
Assuming that iron is completely turned into divalent ions during the corrosion reaction, the following theoretical
- 108 -
0.010
T part
Calculated macro-cell corrosion
loss of steel bar (g/cm2)
Corrosion loss of steel bar (g/cm2)
0.03
B part
0.02
0.01
0
T part N30 N30 N30
NN
B part -NN -SL -SH
Repaired
N30
0.009
T part
0.008
0.001
0
T part N30 N30 N30
NN
B part -NN -SL -SH
Repaired
Not repaired
B part
N30
Not repaired
Fig. 7 Calculated macro-cell corrosion loss of
steel bars (horizontal-jointed specimens)
Fig. 6 Corrosion loss of steel bars
(horizontal-jointed specimens)
correlation exists between corrosion loss and the polarisation resistance of the steel bars:
G=
M
2 Fa
M
1
∫ Icorr dt = K × 2 Fa × ∫ Rp dt
Eq. (1)
where:
G : corrosion loss (g/cm2)
M : atomic mass of iron (= 55.8)
Fa : Faraday constant (= 96,500C)
Icorr : corrosion current density per unit surface area of steel bar (A/cm2)
Rp : polarisation resistance (Ωcm2)
K : Stern-Geary constant (V)
Using this relationship, the corrosion loss G can be calculated from the polarisation resistance Rp per unit
surface area of steel bar if the Stern-Geary constant K is known. However, in order to obtain the polarisation
resistance of steel bars embedded in concrete, the polarised area must be determined appropriately, taking into
consideration the uneven flow of the polarising current into the steel bars. In order to determine the polarised
area, the distributions of electric potential and current flow were simulated using a two-dimensional finite
differential method under the following conditions with respect to both longitudinal and cross sections of the
specimen being polarised.
a. For the sake of simplicity, it was supposed that the concrete was evenly dense and that the distributions
of electric potential u(x,y) in the model specimen satisfied the following Laplace equation:
∂ 2u ∂ 2u
+
=0
∂x 2 ∂y 2
Eq. (2)
b. The analysing models had the same dimensions as the vertical-jointed specimen, and one reinforcing
steel bar 10mm in diameter and 700mm in length was embedded in the model with 20mm of concrete
cover.
c. Polarisations were made with both types of counter electrode mentioned above: one was a rectangular
copper sheet covering the entire cover surface of the model, and the other was a double structure 40mm
and 108mm in width with an 8mm hole.
d. For the sake of simplicity, it was supposed that the potential of the counter electrode was equal to the
half-cell potential of the steel bar, E0mV, and that the steel bar was polarised to (E0-10) mV, assuming
- 109 -
that each of them bore uniform electric potential in themselves respectively, with the potential difference
between them being 10mV.
e. It was supposed that current flowed from each nodal point in four directions: up, down, left and right.
Each flow was through a resistor reflecting the electric resistivity of the concrete. Hence, current was
calculated from the electric potential difference between adjacent nodal points, taking account these
resistor values.
f. It was supposed that the electric potential of the nodal points at the end of the analysing model that were
not in contact with the counter electrode was equal to the electric potential of adjacent nodal points
inside the specimen.
g. Calculation of the electric potential was repeated until the electric potential of all the nodal points
reached a state of convergence; that is, when the change in electric potential fell below 0.0001mV.
In analysing the 100mm x 100mm lateral cross section, the distance between adjacent nodal points was set at
1mm. The actual electrical resistivity of the cover concrete between the steel bar and the rectangular counter
electrode, as obtained in measurements of polarisation resistance in vertical-jointed specimens at the age of
160 days, ranged approximately from 20 to 60Ω. To calculate simply the resistivity between nodal points in
the analysing model, it was assumed that a 100mm wide counter electrode lay beneath the bottom of the cover
concrete 100mm in width and 20mm in height, while reinforcing steel plate 100mm in width was in contact
with the top of the cover concrete, and that the cover concrete consisted of a grid of electrical resistors.
Assuming that the resistivity of the concrete between the reinforcing steel plate and the counter electrode was
40Ω based on the actual results mentioned above, the resistivity R between each pair of nodal points was taken
to be 200Ω (= 40Ω x (100mm / 1mm) ÷ (20mm / 1mm), where 100mm and 20mm respectively are the width
and height of the cover concrete, and 1mm is the distance between nodal points).
In analysing the 100mm x 800mm longitudinal section, the distance between adjacent nodal points was set at
2.5mm. As above, it was supposed that a 700mm wide reinforcing steel plate and a 700mm wide counter
electrode were in contact with the top and bottom of the cover concrete 700mm in width and 20mm in height,
and that the concrete consisted of a grid of resistors. In this case, the concrete resistivity R between each two
nodal points was calculated as 1,400Ω (= 40Ω x (700mm / 2.5mm) ÷ (20mm / 2.5mm), where 700mm and
20mm respectively are the width and height of the cover concrete, and 2.5mm is the distance between nodal
points).
4.2 Analysis of lateral cross section
Figs. 8 (a)-(c) show potential distributions in the 100mm x 100mm lateral cross section of the analysing
-6
-8
-8
-4
-8
-6
-4
-2
-2
-2
Counter electrode
100mm
100mm
-6
100mm
100mm
100mm
100mm
-2 -4
Counter electrode
Guard counter electrode
Counter electrode
(b)
(c)
(a)
Fig. 8 Electric potential distribution in lateral section (unit: mV): (a) with large rectangular counter electrode,
(b) with double-disk counter electrode, and (c) with main electrode of double-disk counter electrode
- 110 -
35.2µA
(40.1%)
35.0µA
(40.5%)
28.1µA
(38.5%)
52.7µA
(59.9%)
51.3µA
(59.5%)
45.0µA
(61.5%)
(a)
(b)
(c)
Fig. 9 Electric current distribution around steel bar in lateral section: (a) with large rectangular counter electrode,
(b) with double-disk counter electrode, and (c) with main electrode of double-disk counter electrode
model obtained by the analysis. Fig. 8 (a) illustrates the case where the counter electrode is 100mm wide, as
used in the double-pulse method measurement. Fig. 8 (b) illustrates the case where the counter electrode has
a double structure, as used in the AC impedance method (see Fig. 4). Fig. 8 (c) is a cross sectional illustration
of another analysing model in which only the main counter electrode of the double-disk counter electrode is
used for polarisation. (No actual measurements were carried out in this case.)
Figs. 9 (a)-(c) are diagrams showing the current flows into the steel bars. The length and direction of each
arrow represent the amount and direction of the current.
As these diagrams make clear, the distribution of electric potential in the analysing model with the rectangular
counter electrode is very similar to that of the model with the double structure counter electrode. The current
flow distributions in the three analysing models are also similar to each other, with current flowing into the
steel bar not only from the cover concrete side but also from the upper side. The ratio of current flowing into
the steel bar from the upper side of the cross section to the entire current flow is as high as 40% in all cases (see
Fig. 9).
With respect to the model specimen with the double structure electrode, the current flowing from the main
electrode accounts for 59.6% of all current from the counter electrode, including the guard electrode, almost
matching the 59.5% (see Fig. 9 (b)) of current flowing into the steel bar from the cover concrete side relative
to the entire current flow. Consequently, it is assumed that all current from the main counter electrode flows
into the cover concrete side of the steel bar, and that only this side is polarised by the main counter electrode.
Based on this assumption, one-half of the nominal circumference of the steel bar is used in calculating the
polarised area of the steel bar in the case of specimens with the double-disk electrode.
Regarding the analysing model with the large rectangular counter electrode that covers the entire surface of
the specimen, the current flowing into the steel bar from the upper part of the analysing model is significant,
and therefore the entire circumference of the steel bar is taken account in calculating the polarised area of the
steel bar.
With respect to the analysing model with only the main counter electrode of the double-disk, the ratio of the
current flowing into the steel bar from the upper part of the specimen is 38.5%, as shown in Fig. 9 (c), almost
the same as in the other two cases, although the width of the counter electrode is less. This implies that the
guard electrode restrains current from scattering.
4.3 Analysis of longitudinal section
Fig. 10 (a) shows the potential distribution in a longitudinal section of the analysing model with the 800mm
long rectangular counter electrode while Fig. 10 (b) shows the model with the double structure counter electrode
at the center of the model. As can be seen, the potential distributions in these two specimens differ from each
other. Fig. 11 shows the intensity and direction of current in the vicinity of the double-disk electrode. Current
from the main counter electrode flows up vertically into the steel bar, while the current from the guard electrode
tends to diverge.
- 111 -
C
L
C
L
800mm
100mm
800mm
Counter electrode
Guard counter electrode
Counter electrode
(a)
(b)
Fig. 10 Electric potential distribution in longitudinal section; (a) with large rectangular counter electrode,
(b) with double-disk counter electrode
Distance from centre of specimen (cm)
8
6
4
2
C
L
0
2.0
1.5
1.0
0.5
0
Guard counter electrode
Counter electrode
Fig. 11 Electric potential and current distribution in
longitudinal section around double-disk counter
electrode
Location of steel bar
Current into steel bar or
from counter electrode (µA)
Distance from top surface
of specimen (cm)
Steel bar
C
L
2.0
33.3%
1.5
1.0
0.5
31.7%
0
40
30
20
10
0
Distance from centre of specimen (cm)
Location of
Location of double-disk
rectangular electrode
electrode
Type of counter electrode
Double-disk Rectangular
Current into steel bar
Current from
counter electrode
Fig. 12 shows the intensity of current flowing from or
Fig. 12 Current flows out from the counter electrodes
and into the steel bar in the longitudinal section
into the nodal points which represent the counter
electrode or steel bar. In the case of the double-disc
counter electrode, 33.3% of all current originates from
the main counter electrode. Meanwhile, the current flowing into the steel bar just above the main counter
electrode including the center hole accounts for 31.7% of the current flowing into the whole surface area of the
steel bar. Thus the intensity of current flowing out from the main counter electrode almost matches the
intensity of current flowing into the steel bar just over the main counter electrode. Therefore, in conjunction
with the assumption mentioned above with respect to the analysis of the lateral section, it can be considered
that the polarised area of the steel bar is equal to half the surface area of the steel bar over the main counter
electrode. In this study, the polarised area of the steel bar is calculated as 4cm x 3cm / 2 = 6cm2 , where 4cm is
the diameter of the main counter electrode, and 3cm is the nominal circumference of the steel bar. It should be
noted, however, that this result may lack precision, because it is obtained from two- dimensional analysis
while the double-disk counter electrode is actually circular.
On the other hand, in the case of the counter electrode measuring 800mm in length, the current intensity is
distributed almost evenly along the steel bar, except for areas at its ends, as shown in Fig. 12. The ratio of
current flowing into the steel bar from upper side of analysing model is only a few percent in the analysis of
the longitudinal section. However, it was ascertained from analysis of the lateral section that a considerable
amount of current does flow into the steel bar from the upper side of analysing model, and therefore it must be
taken into consideration. Thus the polarized area of the steel bar in the specimen with the rectangular counter
- 112 -
Corrosion rate index of steel bar
by AC impedance method (1/kΩ/cm2)
1
0.1
● ●
●● ●
●
●
●
●
●● ●●
●
●●
●●
●
●
●●
●●
●●❍
■
■■
■■■
● **-SL-**
❍ SL
(Vertical joint)
0.01 ❍
❍
❍
❍
0.01
❍
0.1
■■
■■ ■■
■■
■ ■
■■ ■
■
■ ■■
■
✩
✩
★★
★
✩
★
★✩
★
✩
✩✩
★★
★
★
✩
★
★★★
★
★
★✩
■ **-SH-**
❏ SH
(Vertical joint)
✩
✩
★ **-NN-**,
✩ NN, N15, N30
(Vertical joint)
■
❏❏■
✩
✩✩
✩
✩
1 0.01
0.1
0.1
1 0.01
Corrosion rate index of steel bar by rectangular pulse method (1/kΩ/cm2)
1
Fig. 13 Relationships between corrosion rate indexes by the two methods
electrode was considered to be 70cm x 3cm = 210cm2, where 70cm is the length of the steel bar, and 3cm is the
nominal circumference of the steel bar.
5. COMPARISON OF POLARISATION RESISTANCE MEASURED BY TWO METHODS
5.1 Estimation of corrosion rate
Using the polarised areas thus obtained, the polarisation resistance and corrosion rate index can be calculated
in accordance with Eq. (1). In this study, the reciprocal of the polarisation resistance, 1/Rp (1/Ω/cm 2), is
defined as the corrosion rate index, because it is proportional to the corrosion current density (which corresponds
to the corrosion rate).
With the AC impedance method, it was difficult to determine the exact polarisation resistance from the
incomplete circle obtained in the complex-plane presentation when the corrosion rate was very low. Since
hardly any corrosion has occurred in a steel bar with a corrosion rate index under 0.01 (1/Ω/cm2), it is safe to
regard the corrosion rate index as 0.01 (1/Ω/cm2) in such cases, if 1/ Rp < 0.01 (1/Ω/cm2 ).
The corrosion rate indexes obtained by the double-pulse method and the AC impedance method are plotted in
Fig. 13. As can be seen, they differ greatly from each other. The reason for these large differences is that
although the polarisation resistance distribution in the vertical-joint specimens is non-uniform because of the
uneven chloride concentration, this was not taken into account in the analysis of polarisation area in the
previous section.
In this section, the effects of polarisation resistance will also be taken into account so as to obtain more precise
distributions of electric potential and current in the specimens.
5.2 Simulation for determining effect of polarisation resistance
The following condition was added to a~g listed in the section 4.1 above.
h. Left and right parts of the analysing model measuring 250mm each from either end consist of chloride
contaminated concrete, while the 300mm long central part consists of sound concrete.
Specimen N30-SH-N30, which conforms to this condition, was used in analysing the potential and current
distributions in a longitudinal section of the analysing model under polarisation. The distance between nodal
points representing concrete and the steel bar was set at 2.5mm. The electrical resistivity of the cover concrete
between the steel bar and the large rectangular counter electrode of vertical- jointed specimen N30 was measured
as 40Ω by the double-pulse method. Based on this value, the resistance between nodal points in the left and
right parts of the model, consisting of mixture N30, was calculated as R1=1,400Ω as in the analysis in the
- 113 -
previous section. As for the resistance between nodal points
representing concrete in the central part of the model, this was
calculated as R2=1.5R1 because the electrical resistivity of the
cover concrete in vertical-jointed specimen SH was 60Ω.
Table 5 Resistivity between nodal points
Specimen
N30-SH-N30
Part
L&R
C
Electrical
resistivity (Ω)
R
1.5R
Current into steel bar or
from counter electrode (µA)
1
1
Furthermore, additional nodal points were allotted to the
interface between the concrete and the steel bar, and the electrical
Polarization
4R1
13R1
resistivity between these points and points in the neighboring
resistance (Ω)
concrete was treated as the polarisation resistance.
The polarisation resistance of the steel bar in the
C
Location of steel bar
L
left and right parts of specimen N30-SH-N30
obtained by actual measurements using the AC
1.6
impedance method was about 2,000Ωcm2. Based
on this value, the resistivity between nodal points
1.2
representing polarisation resistance and nodal
31.8%
points in the neighboring concrete was calculated
with sound
0.8
as Rp1=5,333Ω (=2,000Ωcm2 x (1cm ÷ 2.5mm) ÷
36.2%
Cl1.5cm (= one-half of the nominal circumference
of the steel bar)) ≈ 4R1 . As for the central part of
0.4
the model, the resistivity was calculated as Rp2 ≈
31.1%
27.8%
33.4%
13R1 , based on the measured value, 7,000Ωcm2,
0
of polarisation resistance in the central part of
40
30
20
10
0
specimen N30-SH-30.
Distance from centre of specimen (cm)
Location of
rectangular electrode
5.3 Polarisation behaviour of steel bar
It was supposed that the steel bar uniformly
polarises to (E0 -10)mV when polarised by an
external voltage source, because the potential of
the steel bar evens out although the half-cell
potential is distributed unevenly along the
reinforcing steel. The concrete resistivity and
polarisation resistance used for calculation by a
finite differential method are as shown in Table 5.
Location of double-disk
electrode
Type of counter electrode
Double-disk Rectangular
Current into steel bar
Current from
counter electrode
Fig. 14 Distributions of current flows out from the
counter electrodes and into the steel bar
considering the effect of polarization resistance
Fig. 14 shows the calculated current distributions flowing from the counter electrode and into the steel bar for
three cases: one using the large rectangular counter electrode, and two using the double-disk electrode located
to the left or in the centre.
In the case with the rectangular counter electrode, less current flowed into the steel bar in the central higher
resistivity and polarisation resistance section than in the left part, where the chloride-contaminated concrete
was. Moreover, the intensity of current flowing into steel bar was smaller in all three cases than shown in Fig.
12, where the effect of polarisation resistance was not taken into account, despite the use of an identical value
of electric resistivity for chloride-contaminated concrete. This difference is attributable to the effect of the
polarisation resistance, which was larger than the concrete resistivity. The effect of polarisation resistance is
considered to be even more significant in the part consisting of sound concrete, where the polarisation resistance
of the steel bar was relatively larger. Accordingly, it is assumed that the polarisation resistance should be
taken into consideration in order to obtain more precise determinations of the electric potential distribution in
a specimen.
With the 800mm long counter electrode, current flowing from the upper side of the specimen into the steel bar
was negligible in the analysis of longitudinal section. Thus, the entire model specimen can be treated as an
electrical circuit consisting of a resistor R' representing the concrete resistivity and a polarisation resistance
Rp' connected in series. The total amount of current flowing into all nodal points in the steel bar was 68.6µA.
Hence, Rp'=E ÷ I -R'=10mV ÷ 68.6µA - 40Ω (or 60Ω) = 106Ω (or 86Ω). In turn, the polarisation resistance Rp
- 114 -
between the nodal points was calculated as follows: Rp=106Ω
(or 86Ω) x (steel surface area on the cover concrete side
52.5cm2) ≈5,600Ωcm 2 (or 4,500Ωcm 2). These values are
smaller than 7,000Ωcm2, which is the assumed polarisation
resistance of the sound concrete part, and are 2.5 to 2.8 times
larger than 2,000Ωcm2, which is the polarisation resistance
of the chloride-contaminated part.
0.5
-iZ" (kΩ)
10Hz
❍ ❍ ❍ ❍
❍
❍ ❍
❍
0.01Hz
❍
▲❍▲
N30-SH-N30
❍
◆◆▲◆▲◆
◆◆
▲
❍
▲▲
▲
❍
◆
◆
◆
◆
◆◆◆
▲
▲
▲
▲
▲
0
0
This leads to a conclusion that, when evaluating the
deterioration of an RC member subjected to macro-cell
corrosion where a corroded area and a sound area coexist,
the polarisation resistance cannot be determined precisely if
a large rectangular counter electrode is used.
0.01Hz
0.1Hz
100mHz
0.1Hz 0.5
Z' (k Ω)
1
◆ 100mm ❍ 400mm
▲ 700mm
Fig. 15 Examples of complex-plane
presentation of electrochemical
proprieties of steel bars obtained in this
study
It should be noted, however, that this study is based on the
assumption that the electric potential distribution when the
bar is in a polarised state is uniform in the longitudinal
direction of the steel bar, and that the actual electrical behaviour of the steel bar being polarised is not known.
In fact, the actual values of polarisation resistance measured by the double-pulse method with the reference
electrode on the sound part differed from the results when the reference electrode was on the chloridecontaminated part. Furthermore, it has been reported that the polarisation resistance of the cathode region in
a macro-cell corrosion circuit is small even in the absence of corrosion [10]. Thus, further investigation will
be necessary to clarify the electrochemical behaviour of reinforcing steel bars in concrete suffering macrocell corrosion.
In the case in which the double structure counter electrode was placed at the centre of the specimen, the
current flowing out from the main counter electrode accounted for 31.8% of the total current from the entire
counter electrode, while the ratio of the current flowing into the steel bar just above the main counter electrode
(including the centre hole) to the total current flow into the steel bar was 31.1%. In the case in which the
counter electrode was placed on the left part of the specimen, these ratios were 36.2% and 33.4%, respectively.
From these results, it can be concluded that almost all of the current flowing out from the main counter
electrode flows into the part of the steel bar just above it.
In summary, polarisation resistance can be measured
more precisely by the AC impedance method using a
double-disk counter electrode.
6. STUDY OF CONSTANT K
As mentioned in Section 4, in order to calculate the
amount of corrosion loss from the polarisation resistance,
constant K must be given.
The measured polarisation resistance of the anode region
is affected not only by the anode reaction of the macrocell circuit but also by both the anode and cathode
reactions of micro-cell corrosion. Moreover, the
polarisation resistance obtained with the use of the
rectangular counter electrode is influenced by the macrocell cathode reaction. However, it is impossible in
- 115 -
Corrosion loss of steel bar (g/cm2)
Furthermore, as is obvious from the examples of steel bar electrochemical properties in complex-plane
presentation as shown in Fig. 15, the polarisation resistance obtained by the double-pulse method at two
frequencies (0.1 and 800Hz in this study) differs considerably from the result obtained by the AC impedance
method, particularly when the polarisation resistance is large.
0.025
0.020
0.015
0.010
0.005
0
●
❍
❍
❍
●
●
●●
❍
●
●
●●
●
●
● with two or three
●●
concrete mixtures
❍❍
●
with
one concrete
❍
●
mixture
●
●
❍
❍
❍●
❍
❍
❍●●
❍●
0
0.2
0.4
0.6
0.8
1.0
2
1
M
)
(g/V/cm
×∫
dt
2Fa
Rp
Fig. 16 Relationship between corrosion loss and
corrosion rate index by double-pulse method
Specimen
Ratio
**-SL-N30
6.47 (2.15)
**-SH-N30
5.31 (1.76)
**-NN-N30
5.75 (1.91)
N30, N30-N30-N30
3.01 (1.00)
Corrosion loss of steel bar (g/cm2)
Table 6 Ratios of corrosion rate index in verticaljointed specimens (Results by AC
impedance method/those by double-pulse
method; Values in brackets are normalized
ratios divided by the ratio for specimens N30
and N30-N30-N30)
0.025
●
●
●
0.020
●●●
●
●
●●●
●
●●
●
●
0.015
0.010
●
0.005
●
y = 0.0296x
R =0.8776
0
0
** =NN, N15,N30
0.2
0.4
0.6
0.8
1.0
M
1
2
dt (g/V/cm )
×∫
′
2 Fa
Rp
Fig. 17 Relationship between corrosion loss and
practice to precisely isolate these component effects
corrosion rate index by double-pulse method
from the measured polarisation resistance so as to
modified by considering the results obtained
obtain the micro-cell corrosion loss and macro-cell
by AC impedance method
corrosion loss independently. Further investigation
needs to be carried out to clarify the implications of
the physical and electrochemical properties of steel bars in macro-cell corrosion circuits. As for the possibility
of estimating corrosion loss by the AC impedance method using a double-disk counter electrode, this is not
practical, because it would require measurement of the polarisation resistance at a large number of points.
With the above in view, the overall corrosion loss of the steel bar as a whole was calculated first from the
polarisation resistance measured by the simple double-pulse method with the use of the large rectangular
counter electrode. Fig. 16 shows the relationship between corrosion loss and integrated corrosion rate index
up to the age of 160 days. This index is the reciprocal of polarisation resistance obtained by the double-pulse
method using the large rectangular counter electrode multiplied by M/2Fa. The corrosion loss per unit surface
area was obtained by dividing the total corrosion loss caused by both macro-cell corrosion and micro-cell
corrosion with the surface area of the steel bar (210cm2).
The gradient of this graph corresponds to constant K in Eq.(1). However, there are large variations in this
gradient between specimens of different types. Specifically, constant K was 0.0566(V) in the case of jointed
specimens with uneven chloride distribution, whereas it was 0.0252(V) in the case of specimens with an
uniform chloride distribution. This difference is attributable to the use of a counter electrode covering the
entire surface of the cover concrete, which results in both anode and cathode regions of the macro-cell being
polarised together.
Table 6, derived from Fig. 13, shows the ratios of corrosion rate index according to the AC impedance method
to that according to the double-pulse method for specimens that include an N30 part at 160 days. As this
shows, the results obtained by the two methods differed greatly, even in the case of specimens consisting only
of N30 and considered to have an even chloride distribution in the longitudinal direction.
The reasons for these large discrepancies are discussed here. First, the underside of the steel bar is more likely
to corrode because of the formation of a water membrane caused by bleeding. Further, the lower part of the
specimens was kept wet by water spraying in the experiments, leading to the formation of an anode on the
lower half of the steel bar on the cover concrete side and an cathode on the upper half of the steel bar.
Accordingly, the corrosion rate index obtained by the AC impedance method was larger than the mean value
of corrosion of the entire circumference of the steel bar, because of use of the double-disk counter electrode
with which only the lower half of the steel bar is polarised. The large difference between the two methods is
also attributable to same degree to the difference in frequency used for measuring the polarisation resistance.
Assuming that the corrosion rates are overestimated equally in all specimens when the double-disk counter
electrode was used, the ratios shown in Table 6 can be normalised, as shown in brackets, by dividing by 3.01
- 116 -
double-pulse method
(rectangular electrode)
AC impedance method
(double-disk electrode)
defining
polarisation area
Rp1 (Icorr1)
defining
polarisation area
Rp2 (Icorr)
ratio
effect of
circumferential
distribution of
corrosion
corrosion loss
nomalised
ratio
constant
K
Rp' (I corr')
effect of
macro-cell and
applied frequency
Fig. 18 Flow chart representing this study
(the value obtained for specimens N30 and N30-N30-N30 with most even chloride distributions).
As mentioned above, the overall polarisation resistance of a specimen with macro-cell corrosion measured
with the large rectangular counter electrode was calculated to be 2.5 to 2.8 times larger than the polarisation
resistance of the corroded area alone. The normalised ratios in Table 6 for the jointed specimens are about
twice as large for the specimens consisting of N30 alone. This confirms, therefore, that in addition to the
difference in frequency used for polarisation resistance measurements and the circumferentially uneven
distribution of corrosion rate around the steel bar, the large difference between polarisation resistance values
obtained by the two methods with the two different counter electrodes contributes to the uneven distribution
of corrosion rate along the steel bar due to macro-cell corrosion.
Based on the assumptions made here, the corrosion rate indexes in Fig. 16 are corrected by multiplying them
with the normalised ratios shown in brackets in Table 6, and the results are re-plotted in Fig. 17. This figure
shows only the results for specimens using mixture N30. As can be seen, the variations were reduced to an
insignificant level, with the constant K being 0.0296(V). It is thus demonstrated that the "apparent" polarisation
resistance obtained using the double-pulse method with the large rectangular counter electrode can be corrected
to a more realistic value by integrating the results obtained using the AC impedance method with the doubledisk counter electrode. This means it is possible to predict corrosion loss more accurately from the polarisation
resistance. The constant K obtained in this study also falls within the range 0.017 to 0.050(V), which has
previously been reported as a reasonable range [11].
The procedure followed in this study is summarised in the form of a flow chart in Fig. 18.
7. CONCLUSION
The results obtained in this study can be summarised as follows:
(1) The current flowing upon polarisation flows into the steel bar largely into the side of the steel bar not
facing the counter electrode, irrespective of the type of electrode.
- 117 -
(2) Where a double-disk counter electrode is used, the amount of current flowing out from the main counter
electrode approximately corresponds to that flowing into the cover side of the steel bar.
(3) The amount of corrosion can be calculated more precisely from the polarisation resistance by combining
the measurements obtained using the double-pulse method with a large counter electrode and those obtained
using the AC impedance method with a double-disk counter electrode.
(4) The constant K in the Stern-Geary formula is obtained as 0.0296V in this study.
The AC impedance method, which uses low frequencies for measurement, together with the double-disk
counter electrode, which restricts diffusion of the polarisation current, gives results that accurately reflect the
polarisation resistance of the steel bar. On the other hand, it entails time-consuming measurements at a large
number of measuring points, and is not immediately applicable to the actual maintenance of RC structures.
However, as demonstrated in this study, it can be used to advantage if combined with the more simple doublepulse method. For example, it can be used to add corrections to the results obtained by the double-pulse
method with a large counter electrode, so as to obtain a more precise corrosion rate whenever necessary.
It should be noted that the relationship between the polarisation resistance values obtained respectively by the
two methods varies depending on the corrosion distribution, half cell potential, age of the concrete, and various
other factors. Therefore, the electrochemical properties of a reinforcing steel bar suffering macro-cell corrosion
should further be investigated, and the constant K in the Stern-Geary formula considered further.
References
[1] Okada, K., Kobayashi, K., Miyagawa, T., and Honda, T., "Basis for Repair by Corrosion Monitoring of
Steel Bar with Polarisation Resistance Method", Proceedings of the JCI, Vol. 5, pp. 249-252, 1983 (in
Japanese)
[2] Yokota, M., "Estimation of Corrosion Behaviour for Steel Rebar in Concrete by Electrochemical Methods",
Proceedings of the JCI, Vol. 12, No. 1, pp. 545-550, 1990 (in Japanese)
[3] Takewaka, K., "Corrosion of Reinforcement", Concrete Journal, JCI, Vol. 33, No. 3, pp. 123-128, 1995 (in
Japanese)
[4] Matsumura, T., Kanazu, T., and Nishiuchi, T., "Corrosion Detection Using AC Impedance Method for
Reinforcing Steel in Specimens Exposed Seashore Environment", Proceedings of the JCI, Vol. 19, No. 1,
pp. 1309-1314, 1997 (in Japanese)
[5] Araki, K., Seki, H., and Kaneko, Y., "Theoretical and Experimental Studies of Current Distribution in NonDestructive Inspection Method of Reinforcements Embedded in Concrete", Journal of Materials, Concrete
Structures and Pavements, No. 592/V-39, pp. 53-62, 1998 (in Japanese)
[6] Otsuki, N., Yokoi, T., and Shimozawa, O., "The Influence of Chloride on the Passivation Film of Steel Bars
in Mortar", JSCE Journal of Materials, Concrete Structures and Pavements, No. 360/V-3, pp. 111-118,
1985 (in Japanese)
[7] Miyagawa, T., "Early Chloride Corrosion on Reinforcing Steel in Concrete", Doctoral Thesis, Kyoto
University, 1985
[8] JCI Technical Committee on Steel Corrosion and Corrosion Protection, "Test Methods and Standards for
Steel Corrosion and Corrosion Protection in Concrete Structures (Draft)", 1987 (in Japanese)
[9] Kobayashi, K., Watanabe, Y., Hattori, A., and Miyagawa, T., "Corrosion of Steel Bars in Chloridecontaminated Concrete Member Patched with Self-compacting Concrete", Concrete Library of JSCE, No.
35, pp. 169-183, 2000
[10] Yokota, M., "Estimation of Macro-cell Corrosion Rate of Reinforcing Steel in Concrete by AC Impedance
Method", Shikoku Research Institute Inc. Reports, No. 68, pp. 42-47, 1997 (in Japanese)
[11] JSCE Subcommittee for Studies on Steel Corrosion and Corrosion Protection in Concrete, "State of the
art and future trends related to steel corrosion, corrosion protection and repair", Concrete Engineering
Series, 1997 (in Japanese)
- 118 -