estimating the corrosion rate of...
TRANSCRIPT
ESTIMATING THE CORROSION RATE OF REINFORCING STEEL IN CONCRETE BYMEASURING 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, theaim is to clarify the relationship between corrosion loss and polarisation resistance in reinforced concretebeams that suffer deterioration due to chloride induced corrosion, thus leading to quantitative estimates ofsteel bar corrosion loss from the polarisation resistance. The results obtained in this study can be summarisedas follows: (1) The current flowing upon polarisation flows into the steel bar largely from the inner side ofspecimen irrespective of the type of counter electrode. (2) Where a double-disk counter electrode is used, theamount of current flowing out from the main counter electrode approximately corresponds to that flowing intothe cover side of the steel bar. (3) The amount of corrosion can be calculated more precisely from the polarisationresistance by combining the measurements obtained using the double-pulse method with a large counter electrodeand those obtained using the AC impedance method with a double-disk counter electrode. (4) The constant Kin the Stern-Geary formula is obtained as 0.0296V in this study.
Keywords: chloride induced corrosion, polarization resistance, macro-cell corrosion, double rectangularpulse 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 chlorideinduced 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. Hereceived his Dr. Eng. from Kyoto University in 1985. He is the author of a number of papers dealing withdurability, maintenance and repair of reinforced concrete structures. He is a member of ACI, RILEM, CEB,JSMS, JCI and JSCE.
CONCRETE LIBRARY OF JSCE NO. 39, JUNE 2002
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Rc
Rp
Cd
Fig. 1 Equivalent electric circuit model
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 thatcertain properties of a concrete structure, such as load bearing capacity, deteriorate as time passes. In somecases, the deterioration occurs prematurely and causes many serious problems. In other cases, it progressesslowly over several decades of service.
While it is certainly important to construct structures that are durable, it is also essential to provide propermaintenance such that a long service life is achieved. There are several factors which cause deterioration ofreinforced concrete structures, one of the major ones being corrosion of the reinforcing steel. To prevent thistype of deterioration, it is important to use dense and durable concrete so as to prevent the penetration ofchloride 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 atan early stage.
Among various techniques for non-destructive testing, electrochemical test methods are considered mosteffective for inspecting reinforcing steel corrosion, because the steel corrosion process is an electrochemicalreaction. The polarisation resistance method, for instance, is particularly suitable for evaluating the corrosionrate of steel bars. It utilises a relationship between corrosion current and polarisation resistance. Morespecifically, 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 ofthe steel and ∆I represents the change in current.
Within reinforced concrete, at the interface between the steel and the pore solution, there exists an electricdoublelayer consisting of a Helmholtz layer and a diffusion boundary layer. The pore solution and electricdoublelayer can most simply be considered equivalent to an electric circuit, as shown in Fig. 1, consisting ofthe polarisation resistance Rp, a capacitor Cd, and a resistor representing the resistivity of the concrete Rc. As theresponse of this circuit, when the steel is polarised, depends on a resistive component and a capacitativecomponent, it is necessary to isolate the polarisation resistance component alone in order to determine the exactcorrosion rate.
The prevailing methodology in Japan for determining polarisation resistance includes the AC impedance methodand the two frequencies method [1]~[5]. The two frequencies method works as follows. When voltage ∆E orcurrent ∆I is applied to the circuit at very high frequency, the reactance of the capacitor becomes negligibleand the electric current flows almost entirely through the resistor Rc and the capacitor Cd. In this situation, theresponse of the circuit can be regarded as that of the resistor alone. On the contrary, when voltage ∆E orcurrent ∆I is applied at very low frequency, the reactance of the capacitor becomes infinite. Therefore, thecircuit 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 ofthe resistor, while the response when a low frequency is applied represents the resistance of the resistor andthe polarisation resistance. Accordingly, the polarisation resistance is obtained by subtracting the high-frequencyresult from the low frequency result. In practice, the two frequencies method is often implemented as adouble-pulse method, in which two different frequency waveformsare superposed and applied simultaneously.
The actual electrochemical state of the steel embedded in the concreteis of course much more complex than that represented by the circuitmodel because of various factors affecting the electrochemicalproperties of the steel. These include the Warburg impedance, orresistivity to the diffusion of gases and ions, and the mill scale formedon the surface of the steel bar. Thus the results obtained by the two
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frequency method are only approximate values.
The AC impedance method involves applying a voltage to the steel bar at varying frequencies and expressingthe 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 therebymakes possible evaluation of the corrosion rate of the steel bar. However, it entails a complex, time-consumingmeasurement procedure. Since estimating corrosion loss necessitates a large number of measurements overtime, it is not instantly practicable, either. Another problem to be resolved before precise evaluations ofcorrosion rate are possible is that the electrochemical behaviour of a steel bar while polarised is not alwaysuniform, because electric current flows through the cover concrete which may have various shapes and consistof 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 concretebeams that suffer deterioration due to chloride induced corrosion, thus leading to quantitative estimates ofsteel 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 employedin these mixtures.
Three types of ordinary concrete were prepared. In two cases, N15 and N30, chloride ions were added (at1.5% 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 addedto mixture NN. The concentration of chloride ions in mixture N15 slightly exceeded the 1.2~2.5kg/m3 thresholdfor corrosion of reinforcing steel as reported by some researchers [6][7]. These chloride ions were added byblending sodium chloride into the concrete during mixing, and the same mass of sand was removed from thespecified 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 mixtureSH (W/C=0.4) had a lower water-binder ratio so as to obtain higher strength. Self-compacting concrete wasdeveloped to offer superior self-compactability for filling all corners of the formwork without the need forvibration. Thus, it is considered to have advantage for repair work, which often requires injection of concreteinto confined spaces.
Table 1 Mix proportions
* Water-reducing agent** High-range water-reducing agent
C/W)%(
)pL+C(/W)%(
a/s)%(
m/gk(ssamtinU 3) retaWtnegagnicuder
)pL+C( x %
riAgniniartne
tnega)pL+C( x %
evisserpmoChtgnerts
syad82tamm/N( 2)W C pL S G lCaN
NN
06 06
0.05
381 503 0
768
198
0
*52.0 3500.0
4.23
51N 9.94 368 575.4 1.03
03N 7.94 858 51.9 2.92
LS 06 4.23 0.05 071 382 242 087008 0
**1.2 10.0 9.43HS 54 1.33 1.05 471 783 831 387 **2.2 10.0 0.94
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Fig. 2 Vertical-jointed specimen (unit: mm)
300
800
700100 200
250 550300 400 500 600 7000
25025030 30
40
20
80
Halfcell potential
Distance from left end
Polarization resistance (AC impedance method)
Polarization resistance(Double-pulse method)
D10
Cable
C part R partL part
Placed from this side
( ) ( )
Table 2 Materials
tnemeC;51.3:ytivargcificepS;tnemecdnaltroPyranidrO
mc0623:ssenenifenalB 2 g/
redwopenotsemiL OCaC 3 ;37.2:ytivargcificepS;%59> :ssenenifenalB mc0776 2 g/
etagerggaeniF;%08.1:noitprosbaretaW;75.2:ytivargcificepS;dnasreviR
36.2:suludomsseneniF
etagerggaesraoC;mm51:ezismumixaM;46.2:ytivargcificepS;enotsdehsurC
81.6:suludomsseneniFtnegagnicuder-retaW dicacinoflusongiL
tnegagnicuderretawegnar-hgiH dicacilyxobracyloP
tnegagniniartne-riA tnatcafruscinoinadesab-nisoR
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 unevenchloride ion distribution, causing a macro-cell corrosion circuit to be formed, in a case where the bottomsurface of a beam is repaired by patching. Two deformed reinforcing steel bars 10mm in diameter and 700mmin length with mill scale were embedded in these specimens with 20mm of concrete cover (twice the bardiameter). Electrical cables rated at 100 volts and with a resistance of 14Ω/m were soldered to one end of eachsteel bar after exposing the bare steel by grinding off the mill scale. These connections were used for measuringhalf-cell potentials and polarisation resistance. The exposed ends of the steel bars were then wrapped with aself-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 tothe repaired part of the structure, and mixtures NN, N15, and N30 were placed to form the left and right partsof the specimen, corresponding to the chloride-contaminated part of the structure. The central part was placedon the first day. Water was then sprayed over the joint surfaces, and the left and right parts were placed on thenext 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 ofeach discrete type were prepared. In order to investigate the effects of the actual joints, into which chlorideions might penetrate, monolithic specimens using each type of concrete alone were also prepared: specimensNN, N15, N30, SL, and SH. Further, specimens with two joints were prepared using the same concretethroughout: specimens NN-NN-NN, N30-N30-N30, and SL-SL-SL. In this case also, the left and right partswere placed on the second day.
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40040
20
202020
10
10
30 30300
D10
Cable Placed from this side
T part
B part
Fig. 3 Horizontal-jointed specimen (unit: mm)
traPL C R
51N-NN-51N51N
NN
51N
03N-NN-51N03N
03N-NN-03N 03N
51N-LS-NN NN
LS
51N51N-LS-51N 51N
03N-LS-NN NN
03N03N-LS-51N 51N
03N-LS-03N 03N
51N-HS-NN NN
HS
51N51N-HS-51N 51N
03N-HS-NN NN
03N03N-HS-51N 51N
03N-HS-03N 03N
NN NN
NN-NN-NN NN NN NN
51N 51N
03N 03N
03N-03N-03N 03N 03N 03N
LS LS
LS-LS-LS LS LS LS
HS HS
traPT B
LS-03N03N
LS
HS-03N HSNN-03N NN
NN NN
03N 03N
Table 3 Vertical-jointed specimens
Table 4 Horizontal-jointed specimens
The horizontal-jointed specimen shown in Fig. 3 was constructed witha horizontal joint for the investigation of macro-cell corrosion andmicro-cell corrosion. Four deformed reinforcing steel bars 10mm indiameter and 300mm in length with mill scale were embedded in thespecimens with a concrete cover of thickness 20mm. Cables wereattached as with the vertical-jointed specimens. Mixtures NN, SL,and SH were placed as the bottom layer of the horizontal-jointedspecimen on the first day. Water was sprayed over the joint surface,after which mixtures NN, N15, and N30 were placed as the upperlayer of the specimen on the next day. The specimen was demoldedon the third day.
Table 4 shows the combination of mixtures used in each type ofhorizontal-jointed specimen. Two beams of each discrete type wereprepared. Monolithic specimens, NN and N30, were also prepared aswith the vertical-jointed specimens.
Both vertical-jointed specimens and horizontal-jointed specimens wereleft in a laboratory at ambient temperature after demolding, and 5%chloride sodium solution was sprayed on them once a day. Afterdemolding, all specimens were held on wood spacers with theplacement 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 adiameter of 100mm and a height of 200mm. These were cured in thesame way as the beam specimens.
2.3 Test procedure
Also shown in Fig. 2 are the half-cell potential measuring points for the steel bars in the vertical-jointedspecimens. Measurements at these points were made using a reference electrode of saturated silver chloridethrough 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 measuredby applying a double rectangular pulse at a voltage of ±2~20mVp-p and at frequencies of 0.1Hz and 800Hz. Acopper plate 100mm in width and 800mm in length was placed in close contact with the cover concrete andused as the counter electrode. The reference electrode, consisting of saturated silver chloride, was attached tothe side of the specimen at the bar midpoint in the longitudinal direction. These measurements were made atthe 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
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Counter electrodeCounter electrode
Guard counter electrode
Reference electrodeReference electrode
84045106
Fig. 4 Double-disk counter electrode(unit: mm)
Fig. 5 Corrosion loss of steel bars(vertical-jointed specimens)
0
0.01
0.02
0.03
Cor
rosi
on lo
ss o
f st
eel b
ar (
g/cm
2 )Repaired with NN
Repaired with SH
Repaired with SL
For investigation of influence of joints
L part
C part
R part
SHSLSL
-SL
-SL
N30
-N30
-N30
N30
N15
NN
-NN
-NN
NN
N30
-SH
-N30
N15
-SH
-N30
NN
-SH
-N30
N15
-SH
-N15
NN
-SH
-N15
N30
-SL
-N30
N15
-SL
-N30
NN
-SL
-N30
N15
-SL
-N15
NN
-SL
-N15
N30
-NN
-N30
N15
-NN
-N30
N15
-NN
-N15
method with a voltage of ±1~10mVp-p and afrequency ranging from 10mHz to 10Hz at thepoints shown in Fig. 2 through the 20mmconcrete cover. The counter electrode used forthe AC impedance method was a double-disk [10] consisting of a main centre disk 40mm in diameter and anenclosing guard disk 108mm in diameter, as shown in Fig. 4. Polarisation resistance in this case was calculatedonly 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 tothe left part or to the right part of the specimen denoted by (O) in Fig. 2. In these measurements, a copper platemeasuring 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 singlebundle to allow macro-cell corrosion current to flow among the steel bars. Further, the macro-cell corrosioncurrent 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 atthe age of 160 days. The state of steel corrosion of each steel bar was sketched and the corroded area on thesurface 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 eachvertical-jointed specimen per unit surface area. Fig. 6 similarly shows the corrosion loss of the steel bars ineach horizontal-jointed specimen per unit surface area. Fig. 7 shows macro-cell corrosion losses calculatedfrom macro-cell current in the horizontal-jointed specimens. As can be seen from Fig. 6, uneven chloride iondistribution caused the formation of macro-cell corrosion circuit in the horizontal-jointed specimens. Theresults 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
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correlation exists between corrosion loss and the polarisation resistance of the steel bars:
GM
FI dt K
M
F Rdt
acorr
a p
= = × ×∫ ∫2 2
1Eq. (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 unitsurface area of steel bar if the Stern-Geary constant K is known. However, in order to obtain the polarisationresistance of steel bars embedded in concrete, the polarised area must be determined appropriately, taking intoconsideration the uneven flow of the polarising current into the steel bars. In order to determine the polarisedarea, the distributions of electric potential and current flow were simulated using a two-dimensional finitedifferential method under the following conditions with respect to both longitudinal and cross sections of thespecimen being polarised.
a. For the sake of simplicity, it was supposed that the concrete was evenly dense and that the distributionsof electric potential u(x,y) in the model specimen satisfied the following Laplace equation:
∂∂
∂∂
2
2
2
2 0u
x
u
y+ = Eq. (2)
b. The analysing models had the same dimensions as the vertical-jointed specimen, and one reinforcingsteel bar 10mm in diameter and 700mm in length was embedded in the model with 20mm of concretecover.
c. Polarisations were made with both types of counter electrode mentioned above: one was a rectangularcopper sheet covering the entire cover surface of the model, and the other was a double structure 40mmand 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 thehalf-cell potential of the steel bar, E0mV, and that the steel bar was polarised to (E0-10) mV, assuming
Fig. 6 Corrosion loss of steel bars(horizontal-jointed specimens)
Fig. 7 Calculated macro-cell corrosion loss ofsteel bars (horizontal-jointed specimens)
0
0.01
0.02
0.03C
orro
sion
loss
of
stee
l bar
(g/
cm2 )
Repaired Not repaired
B part
T part
T part B part
NN N30N30 -SH
N30 -SL
N30 -NN
0
0.0010.008
0.009
0.010
Cal
cula
ted
mac
ro-c
ell c
orro
sion
los
s of
ste
el b
ar (
g/cm
2 ) T part B part
Repaired Not repaired
B part
T partNN N30N30
-SHN30 -SL
N30 -NN
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(a) (b) (c)
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
that each of them bore uniform electric potential in themselves respectively, with the potential differencebetween 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 wascalculated from the electric potential difference between adjacent nodal points, taking account theseresistor values.
f. It was supposed that the electric potential of the nodal points at the end of the analysing model that werenot in contact with the counter electrode was equal to the electric potential of adjacent nodal pointsinside the specimen.
g. Calculation of the electric potential was repeated until the electric potential of all the nodal pointsreached 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 at1mm. The actual electrical resistivity of the cover concrete between the steel bar and the rectangular counterelectrode, as obtained in measurements of polarisation resistance in vertical-jointed specimens at the age of160 days, ranged approximately from 20 to 60Ω. To calculate simply the resistivity between nodal points inthe analysing model, it was assumed that a 100mm wide counter electrode lay beneath the bottom of the coverconcrete 100mm in width and 20mm in height, while reinforcing steel plate 100mm in width was in contactwith 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 was40Ω based on the actual results mentioned above, the resistivity R between each pair of nodal points was takento be 200Ω (= 40Ω x (100mm / 1mm) ÷ (20mm / 1mm), where 100mm and 20mm respectively are the widthand 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 at2.5mm. As above, it was supposed that a 700mm wide reinforcing steel plate and a 700mm wide counterelectrode 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 twonodal points was calculated as 1,400Ω (= 40Ω x (700mm / 2.5mm) ÷ (20mm / 2.5mm), where 700mm and20mm respectively are the width and height of the cover concrete, and 2.5mm is the distance between nodalpoints).
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
Counter electrode
100m
m
100m
m
100mm 100mm 100mm
-2
-4
-6
-8
-2 -2-2
-6
-8
-2
-4 -4-4
-6 -6
-8 -8
-2 -4
-6-8
-2 -4
-6-8
Counter electrodeGuard counter electrode
Counter electrode
100m
m
- 110 -
(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, asused in the double-pulse method measurement. Fig. 8 (b) illustrates the case where the counter electrode hasa double structure, as used in the AC impedance method (see Fig. 4). Fig. 8 (c) is a cross sectional illustrationof another analysing model in which only the main counter electrode of the double-disk counter electrode isused 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 eacharrow represent the amount and direction of the current.
As these diagrams make clear, the distribution of electric potential in the analysing model with the rectangularcounter electrode is very similar to that of the model with the double structure counter electrode. The currentflow distributions in the three analysing models are also similar to each other, with current flowing into thesteel bar not only from the cover concrete side but also from the upper side. The ratio of current flowing intothe steel bar from the upper side of the cross section to the entire current flow is as high as 40% in all cases (seeFig. 9).
With respect to the model specimen with the double structure electrode, the current flowing from the mainelectrode accounts for 59.6% of all current from the counter electrode, including the guard electrode, almostmatching the 59.5% (see Fig. 9 (b)) of current flowing into the steel bar from the cover concrete side relativeto the entire current flow. Consequently, it is assumed that all current from the main counter electrode flowsinto 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 thepolarised 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 ofthe 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 thesteel bar.
With respect to the analysing model with only the main counter electrode of the double-disk, the ratio of thecurrent flowing into the steel bar from the upper part of the specimen is 38.5%, as shown in Fig. 9 (c), almostthe same as in the other two cases, although the width of the counter electrode is less. This implies that theguard 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 800mmlong rectangular counter electrode while Fig. 10 (b) shows the model with the double structure counter electrodeat the center of the model. As can be seen, the potential distributions in these two specimens differ from eachother. Fig. 11 shows the intensity and direction of current in the vicinity of the double-disk electrode. Currentfrom the main counter electrode flows up vertically into the steel bar, while the current from the guard electrodetends to diverge.
52.7µA (59.9%)
35.2µA (40.1%)
51.3µA (59.5%)
35.0µA (40.5%)
45.0µA (61.5%)
28.1µA (38.5%)
- 111 -
(a) (b)
Fig. 10 Electric potential distribution in longitudinal section; (a) with large rectangular counter electrode,(b) with double-disk counter electrode
Fig. 11 Electric potential and current distribution inlongitudinal section around double-disk counterelectrode
Fig. 12 Current flows out from the counter electrodesand into the steel bar in the longitudinal section
Fig. 12 shows the intensity of current flowing from orinto the nodal points which represent the counterelectrode or steel bar. In the case of the double-disccounter electrode, 33.3% of all current originates fromthe main counter electrode. Meanwhile, the current flowing into the steel bar just above the main counterelectrode including the center hole accounts for 31.7% of the current flowing into the whole surface area of thesteel bar. Thus the intensity of current flowing out from the main counter electrode almost matches theintensity of current flowing into the steel bar just over the main counter electrode. Therefore, in conjunctionwith the assumption mentioned above with respect to the analysis of the lateral section, it can be consideredthat the polarised area of the steel bar is equal to half the surface area of the steel bar over the main counterelectrode. In this study, the polarised area of the steel bar is calculated as 4cm x 3cm / 2 = 6cm2, where 4cm isthe diameter of the main counter electrode, and 3cm is the nominal circumference of the steel bar. It should benoted, however, that this result may lack precision, because it is obtained from two- dimensional analysiswhile 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 isdistributed almost evenly along the steel bar, except for areas at its ends, as shown in Fig. 12. The ratio ofcurrent flowing into the steel bar from upper side of analysing model is only a few percent in the analysis ofthe longitudinal section. However, it was ascertained from analysis of the lateral section that a considerableamount of current does flow into the steel bar from the upper side of analysing model, and therefore it must betaken into consideration. Thus the polarized area of the steel bar in the specimen with the rectangular counter
800mm
Counter electrode
100m
mCL
800mm
CL
Counter electrodeGuard counter electrode
0
1.0
2.0
0.5
1.5
02468
Dis
tanc
e fr
om to
p su
rfac
e of
spe
cim
en (
cm)
Distance from centre of specimen (cm)CL
Counter electrodeGuard counter electrode
Steel bar
0
0.5
1.0
1.5
2.0
0102040 30
Location of steel bar
Current into steel barDouble-diskType of counter electrode
Rectangular
Current from counter electrode
CL
33.3%
31.7%
33.3%
31.7%
Location of double-diskelectrode
Location of rectangular electrode
Distance from centre of specimen (cm)
Cur
rent
into
ste
el b
ar o
r fr
om c
ount
er e
lect
rode
(µA
)
- 112 -
electrode was considered to be 70cm x 3cm = 210cm2, where 70cm is the length of the steel bar, and 3cm is thenominal 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 calculatedin accordance with Eq. (1). In this study, the reciprocal of the polarisation resistance, 1/Rp (1/Ω/cm2), isdefined as the corrosion rate index, because it is proportional to the corrosion current density (which correspondsto the corrosion rate).
With the AC impedance method, it was difficult to determine the exact polarisation resistance from theincomplete circle obtained in the complex-plane presentation when the corrosion rate was very low. Sincehardly any corrosion has occurred in a steel bar with a corrosion rate index under 0.01 (1/Ω/cm2), it is safe toregard 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 inFig. 13. As can be seen, they differ greatly from each other. The reason for these large differences is thatalthough the polarisation resistance distribution in the vertical-joint specimens is non-uniform because of theuneven chloride concentration, this was not taken into account in the analysis of polarisation area in theprevious section.
In this section, the effects of polarisation resistance will also be taken into account so as to obtain more precisedistributions 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 chloridecontaminated 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 currentdistributions in a longitudinal section of the analysing model under polarisation. The distance between nodalpoints representing concrete and the steel bar was set at 2.5mm. The electrical resistivity of the cover concretebetween the steel bar and the large rectangular counter electrode of vertical- jointed specimen N30 was measuredas 40Ω by the double-pulse method. Based on this value, the resistance between nodal points in the left andright parts of the model, consisting of mixture N30, was calculated as R1=1,400Ω as in the analysis in the
Fig. 13 Relationships between corrosion rate indexes by the two methods
0.01
0.1
1
0.01 0.1 1
0.01 0.1 1
0.01 0.1 1
**-SL-**SL
**-SH-**SH
**-NN-**,NN, N15, N30
(Vertical joint) (Vertical joint) (Vertical joint)
Corrosion rate index of steel bar by rectangular pulse method (1/kΩ/cm2)Cor
rosi
on r
ate
inde
x of
ste
el b
ar
by A
C im
peda
nce
met
hod
(1/
kΩ/c
m2 )
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Fig. 14 Distributions of current flows out from thecounter electrodes and into the steel barconsidering the effect of polarization resistance
previous section. As for the resistance between nodal pointsrepresenting concrete in the central part of the model, this wascalculated as R2=1.5R1 because the electrical resistivity of thecover concrete in vertical-jointed specimen SH was 60Ω.
Furthermore, additional nodal points were allotted to theinterface between the concrete and the steel bar, and the electricalresistivity between these points and points in the neighboringconcrete was treated as the polarisation resistance.The polarisation resistance of the steel bar in theleft and right parts of specimen N30-SH-N30obtained by actual measurements using the ACimpedance method was about 2,000Ωcm2. Basedon this value, the resistivity between nodal pointsrepresenting polarisation resistance and nodalpoints in the neighboring concrete was calculatedas Rp1=5,333Ω (=2,000Ωcm2 x (1cm ÷ 2.5mm) ÷1.5cm (= one-half of the nominal circumferenceof the steel bar)) ≈ 4R1. As for the central part ofthe model, the resistivity was calculated as Rp2 ≈13R1, based on the measured value, 7,000Ωcm2,of polarisation resistance in the central part ofspecimen N30-SH-30.
5.3 Polarisation behaviour of steel bar
It was supposed that the steel bar uniformlypolarises to (E0-10)mV when polarised by anexternal voltage source, because the potential ofthe steel bar evens out although the half-cellpotential is distributed unevenly along thereinforcing steel. The concrete resistivity andpolarisation resistance used for calculation by afinite differential method are as shown in Table 5.
Fig. 14 shows the calculated current distributions flowing from the counter electrode and into the steel bar forthree cases: one using the large rectangular counter electrode, and two using the double-disk electrode locatedto the left or in the centre.
In the case with the rectangular counter electrode, less current flowed into the steel bar in the central higherresistivity and polarisation resistance section than in the left part, where the chloride-contaminated concretewas. 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 valueof electric resistivity for chloride-contaminated concrete. This difference is attributable to the effect of thepolarisation resistance, which was larger than the concrete resistivity. The effect of polarisation resistance isconsidered to be even more significant in the part consisting of sound concrete, where the polarisation resistanceof the steel bar was relatively larger. Accordingly, it is assumed that the polarisation resistance should betaken into consideration in order to obtain more precise determinations of the electric potential distribution ina specimen.
With the 800mm long counter electrode, current flowing from the upper side of the specimen into the steel barwas negligible in the analysis of longitudinal section. Thus, the entire model specimen can be treated as anelectrical circuit consisting of a resistor R' representing the concrete resistivity and a polarisation resistanceRp' 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
Table 5 Resistivity between nodal points
nemicepS 03N-HS-03N
traP R&L C
lacirtcelE(ytivitsiser Ω)
R1
5.1 R1
noitaziraloP(ecnatsiser Ω)
4R1
31 R1
36.2%
27.8%
36.2%
33.4%
CL
40 30 20 10 0
0
0.4
0.8
1.2
1.6
soundwith Cl-
31.8%
31.1%
Location of steel bar
Current into steel barDouble-diskType of counter electrode
Rectangular
Current from counter electrode
Location of double-diskelectrode
Distance from centre of specimen (cm)Distance from centre of specimen (cm)Cur
rent
into
ste
el b
ar o
r fr
om c
ount
er e
lect
rode
(µA
)
Location of rectangular electrode
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0
0.5
0 0.5 1
-iZ
" (k
Ω)
Z' (k Ω)
N30-SH-N30
100mm 400mm 700mm
0.1Hz
100mHz0.1Hz
10Hz
0.01Hz
0.01Hz
Fig. 15 Examples of complex-planepresentation of electrochemicalproprieties of steel bars obtained in thisstudy
Fig. 16 Relationship between corrosion loss andcorrosion rate index by double-pulse method
0
0.005
0.010
0.015
0.020
0.025
0 0.2 0.4 0.6 0.8 1.0
(g/V/cm2)
with two or three concrete mixtures with one concrete
mixture
Cor
rosi
on lo
ss o
f st
eel b
ar (
g/cm
2 )
M
F Rdt
a p2
1× ∫
between the nodal points was calculated as follows: Rp=106Ω(or 86Ω) x (steel surface area on the cover concrete side52.5cm2) ≈5,600Ωcm2 (or 4,500Ωcm2). These values aresmaller than 7,000Ωcm2, which is the assumed polarisationresistance of the sound concrete part, and are 2.5 to 2.8 timeslarger than 2,000Ωcm2, which is the polarisation resistanceof the chloride-contaminated part.
This leads to a conclusion that, when evaluating thedeterioration of an RC member subjected to macro-cellcorrosion where a corroded area and a sound area coexist,the polarisation resistance cannot be determined precisely ifa large rectangular counter electrode is used.
It should be noted, however, that this study is based on theassumption that the electric potential distribution when thebar is in a polarised state is uniform in the longitudinaldirection 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 referenceelectrode on the sound part differed from the results when the reference electrode was on the chloride-contaminated part. Furthermore, it has been reported that the polarisation resistance of the cathode region ina macro-cell corrosion circuit is small even in the absence of corrosion [10]. Thus, further investigation willbe necessary to clarify the electrochemical behaviour of reinforcing steel bars in concrete suffering macro-cell corrosion.
In the case in which the double structure counter electrode was placed at the centre of the specimen, thecurrent flowing out from the main counter electrode accounted for 31.8% of the total current from the entirecounter 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 thecounter 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 counterelectrode flows into the part of the steel bar just above it.
Furthermore, as is obvious from the examples of steel bar electrochemical properties in complex-planepresentation as shown in Fig. 15, the polarisation resistance obtained by the double-pulse method at twofrequencies (0.1 and 800Hz in this study) differs considerably from the result obtained by the AC impedancemethod, particularly when the polarisation resistance is large.
In summary, polarisation resistance can be measuredmore precisely by the AC impedance method using adouble-disk counter electrode.
6. STUDY OF CONSTANT K
As mentioned in Section 4, in order to calculate theamount of corrosion loss from the polarisation resistance,constant K must be given.
The measured polarisation resistance of the anode regionis affected not only by the anode reaction of the macro-cell circuit but also by both the anode and cathodereactions of micro-cell corrosion. Moreover, thepolarisation resistance obtained with the use of therectangular counter electrode is influenced by the macro-cell cathode reaction. However, it is impossible in
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nemicepS oitaR
03N-LS-** )51.2(74.6
03N-HS-** )67.1(13.5
03N-NN-** )19.1(57.5
03N-03N-03N,03N )00.1(10.3
Table 6 Ratios of corrosion rate index in vertical-jointed specimens (Results by ACimpedance method/those by double-pulsemethod; Values in brackets are normalizedratios divided by the ratio for specimens N30and N30-N30-N30)
** =NN, N15,N30
practice to precisely isolate these component effectsfrom the measured polarisation resistance so as toobtain the micro-cell corrosion loss and macro-cellcorrosion loss independently. Further investigationneeds to be carried out to clarify the implications ofthe physical and electrochemical properties of steel bars in macro-cell corrosion circuits. As for the possibilityof estimating corrosion loss by the AC impedance method using a double-disk counter electrode, this is notpractical, 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 thepolarisation resistance measured by the simple double-pulse method with the use of the large rectangularcounter electrode. Fig. 16 shows the relationship between corrosion loss and integrated corrosion rate indexup to the age of 160 days. This index is the reciprocal of polarisation resistance obtained by the double-pulsemethod using the large rectangular counter electrode multiplied by M/2Fa. The corrosion loss per unit surfacearea was obtained by dividing the total corrosion loss caused by both macro-cell corrosion and micro-cellcorrosion 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 thisgradient between specimens of different types. Specifically, constant K was 0.0566(V) in the case of jointedspecimens with uneven chloride distribution, whereas it was 0.0252(V) in the case of specimens with anuniform chloride distribution. This difference is attributable to the use of a counter electrode covering theentire surface of the cover concrete, which results in both anode and cathode regions of the macro-cell beingpolarised together.
Table 6, derived from Fig. 13, shows the ratios of corrosion rate index according to the AC impedance methodto that according to the double-pulse method for specimens that include an N30 part at 160 days. As thisshows, the results obtained by the two methods differed greatly, even in the case of specimens consisting onlyof 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 likelyto corrode because of the formation of a water membrane caused by bleeding. Further, the lower part of thespecimens was kept wet by water spraying in the experiments, leading to the formation of an anode on thelower 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 valueof corrosion of the entire circumference of the steel bar, because of use of the double-disk counter electrodewith which only the lower half of the steel bar is polarised. The large difference between the two methods isalso 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 counterelectrode was used, the ratios shown in Table 6 can be normalised, as shown in brackets, by dividing by 3.01
Fig. 17 Relationship between corrosion loss andcorrosion rate index by double-pulse methodmodified by considering the results obtainedby AC impedance method
0
0.005
0.010
0.015
0.020
0.025
0 0.2 0.4 0.6 0.8 1.0 (g/V/cm2)
Cor
rosi
on lo
ss o
f st
eel b
ar (
g/cm
2 )
y = 0.0296x R =0.8776
M
F Rdt
a p2
1× ′∫
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(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 measuredwith the large rectangular counter electrode was calculated to be 2.5 to 2.8 times larger than the polarisationresistance of the corroded area alone. The normalised ratios in Table 6 for the jointed specimens are abouttwice as large for the specimens consisting of N30 alone. This confirms, therefore, that in addition to thedifference in frequency used for polarisation resistance measurements and the circumferentially unevendistribution of corrosion rate around the steel bar, the large difference between polarisation resistance valuesobtained by the two methods with the two different counter electrodes contributes to the uneven distributionof 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 themwith the normalised ratios shown in brackets in Table 6, and the results are re-plotted in Fig. 17. This figureshows only the results for specimens using mixture N30. As can be seen, the variations were reduced to aninsignificant level, with the constant K being 0.0296(V). It is thus demonstrated that the "apparent" polarisationresistance obtained using the double-pulse method with the large rectangular counter electrode can be correctedto a more realistic value by integrating the results obtained using the AC impedance method with the double-disk counter electrode. This means it is possible to predict corrosion loss more accurately from the polarisationresistance. The constant K obtained in this study also falls within the range 0.017 to 0.050(V), which haspreviously 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 notfacing the counter electrode, irrespective of the type of electrode.
Fig. 18 Flow chart representing this study
defining polarisation area
defining polarisation area
effect of circumferentialdistribution of
corrosion
Rp' (I corr')
AC impedance method(double-disk electrode)
double-pulse method(rectangular electrode)
Rp2 (Icorr)Rp1 (Icorr1) ratio
nomalisedratio
effect of macro-cell and
applied frequency
corrosion loss
constantK
- 117 -
(2) Where a double-disk counter electrode is used, the amount of current flowing out from the main counterelectrode 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 combiningthe measurements obtained using the double-pulse method with a large counter electrode and those obtainedusing 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-diskcounter electrode, which restricts diffusion of the polarisation current, gives results that accurately reflect thepolarisation resistance of the steel bar. On the other hand, it entails time-consuming measurements at a largenumber 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 double-pulse method. For example, it can be used to add corrections to the results obtained by the double-pulsemethod 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 thetwo methods varies depending on the corrosion distribution, half cell potential, age of the concrete, and variousother factors. Therefore, the electrochemical properties of a reinforcing steel bar suffering macro-cell corrosionshould 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 ofSteel Bar with Polarisation Resistance Method", Proceedings of the JCI, Vol. 5, pp. 249-252, 1983 (inJapanese)
[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 (inJapanese)
[4] Matsumura, T., Kanazu, T., and Nishiuchi, T., "Corrosion Detection Using AC Impedance Method forReinforcing 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 Non-Destructive Inspection Method of Reinforcements Embedded in Concrete", Journal of Materials, ConcreteStructures 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 Barsin 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, KyotoUniversity, 1985
[8] JCI Technical Committee on Steel Corrosion and Corrosion Protection, "Test Methods and Standards forSteel 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 Chloride-contaminated 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 ImpedanceMethod", 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 theart and future trends related to steel corrosion, corrosion protection and repair", Concrete EngineeringSeries, 1997 (in Japanese)
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