E-Journal of Advanced Maintenance Vol.5-1 (2013) 77-84
Japan Society of Maintenology

Durability Evaluation Method on Rebar Corrosion of Reinforced Concrete
Yoshinori KITSUTAKA 1*
1

Department of Architecture and Building Engineering, Tokyo Metropolitan University, 1-1 Minamiohsawa,
Hachiohji, Tokyo 192-0397, Japan

ABSTRACTIn this paper, method on the durability evaluation in nuclear power plant concrete structures was investigated. In
view of the importance of evaluating the degree of deterioration of reinforced concrete structures, relationships
should be formulated among the number of years elapsed, t, the amount of action of a deteriorative factor, F, thedegree of material deterioration, D, and the performance of the structure, P. Evaluation by PDFt diagrams
combining these relationships may be effective. A detailed procedure of durability evaluation for a reinforced
concrete structure using PDFt concept is presented for the deterioration of rebar corrosion caused byneutralization and penetration of salinity by referring to the recent papers.
KEYWORDS
concrete, rebar, corrosion, durability, aging management

1. Introduction

ARTICLE INFORMATION￣￣￣￣￣￣￣￣￣￣￣￣.Article
history:
Received 20 November 2012
Accepted 19 February 2013

Important reinforced concrete structures in nuclear power plant require aging management andevaluation. There has been an enormous accumulation of study results regarding the durability
evaluation and deterioration prediction of reinforced concrete structures. However, durability
evaluation of reinforced concrete structures generally involves the problems of a wide variety of
external factors and a combination of reinforcing steel and concrete. Evaluation on the aging of
nuclear power plants, "Review Manual for Age-Related Technical Assessment in Japan " [2] isgenerally used, but more accurate evaluation will be needed. The problems involved in these studies
or evaluations are the relations between time changes, deteriorative factors, material deteriorations
and performances of structure are not clearly indicated. If these relations are cleared and combined,
the evaluation method can be more accurate. In view of the importance of evaluating not only eachmaterial but also the composite body for evaluating the degree of deterioration of reinforced concrete
structures, relationships should be formulated among the number of years elapsed, t, the amount ofaction of a deteriorative factor, F, the degree of material deterioration, D, and the performance of thestructure, P. Evaluation by PDFt diagrams combining these relationships may be effective [1].
In this paper, a detailed procedure of durability evaluation for a reinforced concrete structureusing PDFt concept is presented for the deterioration of rebar corrosion caused by neutralization andpenetration of salinity by referring to the recent papers.

2. Deterioration evaluation based on PDFt diagrams [1]2.1. Concept
In this method, problems on the durability evaluation of reinforced concrete structures wereconsidered. Durability evaluation of reinforced concrete structures generally involves the following
problems:(1) A wide variety of external factors: Reinforced concrete structures are placed in naturalenvironments involving external factors that vary from one place to another and over a long time*

Corresponding author, E-mail: kitsu@tmu.ac.jp

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

77

Y. Kitsutaka./Durability Evaluation Method on Rebar Corrosion of Reinforced Concrete

span.
(2) Combined materials: In order to evaluate the performance of reinforced concrete structural
bodies, which are a combination of reinforcing steel and concrete, not only the acting factors anddeterioration degrees of individual materials but also the combined action of factors on the combinedmaterial should be considered.
One solution to problem (1) above is the assumption of the uniformity of deteriorative action.
Despite the wide variety of deteriorative factors acting on a structure, uniformity may be assumed fortheir action when considering long-term changes on one year-unit basis at a certain place, as eachstructure is fixed to a location for a long time. In other words, evaluation may be carried out by
continuous deterioration functions based on changes on a scale of a minimum unit of one year. Also,
since physical changes can be regarded as increasing functions generally having a cumulative property,
the following estimation method may be considered simpler and more accurate than deductive
evaluation using a number of parameters: Determine a basic form of the deterioration function using
only time or a deteriorative factor as the parameter, and extrapolate actual measurement data ofdeterioration degrees into the function to determine the coefficient in an inductive manner. Thiscoefficient allows the evaluation of properties related to the durability of various structures on auniversal scale.
As to the combined action stated in item (2) above, it is necessary to clarify the relationships
among the time, the effect of deteriorative factors, the degree of material deterioration, and theperformance degradation of the structure.

2.2. Integrity evaluation method by PDFt curve
A deterioration evaluation diagram, V(t), expressing time-related changes in an evaluation value,V, is assumed as follows,
V(t) = αv(t)(1)

where  is the coefficient, t is time (years), and v(t) is a basic evaluation equation having noparameters other than t. “v(t)” is determined beforehand based on past experiment data and analysis
results. Evaluation values, Vobs, at certain points of time, tobs, are determined by actual measurement
and plotted. The coefficient, , is then determined by extrapolating v(t). This method provides
evaluation values approximated to actual situations even when various deteriorative factors are
involved. Also,  serves as an evaluation index characteristic of the structure. While a larger amountof Vobs data are preferable.
Evaluation is carried out by determining the evaluation value, Veva, at a desired year, teva, using
the established deterioration evaluation diagram, V(t), and comparing the result with thepredetermined specification values (Vrg: regulation value, Vcr: critical value, etc.). When Veva exceeds
Vrg, a necessary step may be taken, such as to proceed to the secondary evaluation.
In order to obtain a rational evaluation, the relationships of the deterioration factor and year (F-tdiagram), the material deterioration and deterioration factor (D-F diagram) and the structural
performance and material deterioration (P-D diagram) should be cleared. Examples of parameters are
given in Table 1. A diagram of the evaluation of the deterioration degree of reinforced concrete
structures (hereafter referred to as a PDFt diagram) is obtained by integrating the above-mentioned
evaluation diagrams as shown in Fig. 1. The diagram in the right lower quadrant (level IV), which isdetermined by plotting several values of t and P in the right upper (level I) and left lower (level III)
quadrants, respectively, forms a P-t diagram for assessing the time-related changes in the structural
performance. This diagram also clarifies the relationships among the physical quantities. Thorough78

E-Journal of Advanced Maintenance Vol.5-1 (2013) 77-84
Japan Society of Maintenology

preliminary investigation of the basic evaluation equation for each diagram is necessary as to whether
it can be expressed by coefficients given in Fig. 1 as  and  regarding its adequacy and accuracy.
There are many factors rerating F-t relation and D-F relation, but these relations can be easily
evaluated by fitting the actual measured data to the basic equations and deciding the  and  values
by extrapolation technique.

Table 1 Example of parameters

Fig. 1. Integrity evaluation diagram of reinforced concrete structures (PDFt diagram)[1]79Y. Kitsutaka./Durability Evaluation Method on Rebar Corrosion of Reinforced Concrete

2.3. Current evaluation method of aging management for NPP concrete structures
In the current evaluation method on the neutralization and penetration of salinity contained in the"Review Manual for Age-Related Technical Assessment in Japan " [2] is as follows.
Neutralization: The degradation of concrete is evaluated according to whether or not the depth of
concrete neutralization over the life span of the structure is less than reference levels, and whether or
not neutralization reached to rebar.
Penetration of salinity: The deterioration of reinforced concrete due to penetration of salinity isevaluated according to whether or not the chloride concentration over the life span of the structure isless than reference levels, and whether or not cracks occur in the concrete.

3. Evaluation formula for integrity evaluation of reinforced concrete structures
3.1.

Neutralization

3.1.1. F-t diagram, relation between a deteriorative factor and the number of years elapsed
The amount of action of Oxygen as it affects the corrosion of reinforcing steel. However, it isdifficult to measure this value, so the neutralization depth is used as an alternate value. The
neutralization depth is represented as F1, (subscript “1” represents the neutralization of concrete)
which is the evaluation physical property. Generically, the neutralization depth can be expressed by
the square root t theory as follows [3, 4] ,
1

1√

(2)

where, F1 is neutralization depth (mm),  1 is neutralization rate coefficient (mm/√year) and t is time(year).
3.1.2. D-F diagram, relation between the material deterioration and the deteriorative factor
The rate of loss of steel reinforcing bars, D3 (subscript “3” represents the corrosion of steel
reinforcing bars), is the amount of corrosion of steel reinforcing bars as compared to their condition at
the time of construction. Based on the corrosion experiments of Tomosawa et al. the Eq. (3) is
proposed [5].
1
1.35
38.1

2.76

1.800 2163 ∙ √

(3)

where, WC is rate of loss of steel reinforcing bars by corrosion (10-4g/cm2), T is temperature (°C), H isrelative humidity (%), O2 is concentration of oxygen (%) and t is elapsed time after neutralization
reaches the steel reinforcing bars (day). The corrosion loss of steel reinforcing bars, Wc, and thesquare root t show a linear relationship. So the rate of corrosion loss of steel reinforcing bars, D3,
could be expressed by simple basic equation and extrapolating coefficient 3 as Eq. (4).
3

3∙

1

2

0

2

(4)

where, D3 is rate of corrosion loss of steel reinforcing bars (-),3 is environmental condition(temperature, relative humidity, concentration of oxygen et al.) and material (steel reinforcing bars,
concrete) constant, F0 is concrete cover depth (mm). Real phenomena on rebar corrosion will be socomplicated and be including many factors, but we may evaluate the rebar corrosion by using thebasic equation Eq.(4) according to the obtained some actual data of the rebar corrosion on the site anddeciding the 3 by using extrapolation technique.
3.2. Penetration of salinity80

E-Journal of Advanced Maintenance Vol.5-1 (2013) 77-84
Japan Society of Maintenology

3.2.1. F-t diagram, relation between the deteriorative factor and the number of years elapsed
For the action of the chloride ion F2 (subscript “2” represents the penetration of salinity) , wepropose the value of chloride concentration as show in Fig. 2. This evaluation uses the integrated
value per annum in practice.
,

2

(5)

0

where, F2 is amount of action of chloride ion (kg/m3 year), Ct is chloride concentration (kg/m3), t is
time (year), tn is evaluation period (year) and Ccr is critical chloride concentration of stainless steel
corrosion (=1.2kg/m3).

Fig. 2. The conceptual diagram of integrated value of chloride concentration F2
The normally used equation for the prediction of the distribution of chloride concentration in
concrete is Eq. (6), which is based on the diffusion equation [6, 7].

0

1

(6)

2√ ∙

where, C0 is chloride concentration at surface of concrete (kg/m3), x is thickness of concrete cover(mm) and D is apparent diffusion coefficient (mm2/year). In Eq. (7) an approximation formula [8] isapplied in place of the error function “erf” found in Eq. (6).

0

1

2∙

1

2

,

1
2

(7)

where, 2 is constant of the amount of action of degradation factor as related to the material properties.
C0 and 2 are calculated using the distribution of chloride concentration values as measured at thedetermined evaluation periods.
3.2.2. D-F diagram, relation between the material deterioration and the deteriorative factor
The amount of action of degradation factor, F2, which represents the integrated value of chloride81

Y. Kitsutaka./Durability Evaluation Method on Rebar Corrosion of Reinforced Concrete

concentration around steel reinforcing bars, is expressed as Eq. (8),
2

(8)

∆
0

0

where, F2 is amount of action of chloride ion around steel reinforcing bars, Ct is amount of chloride
ion around steel reinforcing bars at evaluation time t (kg/m3), t is time (year) and t is unit time
(1year).
The rate of deterioration of material is D3 (subscript “3” represents the corrosion loss of steel
reinforcing bars) and is assumed to be the rate of corrosion loss of carbon steel reinforcing bars. D3 isthe amount of corrosion of steel reinforcing bars as compared to their condition at the time of
construction. D3 can represent as follows,
(9)

3

0

where, D3 is the corrosion loss of steel reinforcing bars (mg/cm2), Vt is corrosion rate (mg/cm2/year),Vt can be represented as Eq. (10).
1

(10)

√

where, a and b is constants. By substituting the Eq. (10) into the Eq. (9), the Eq. (11) is obtained,
which is the relational expression of D-F. An example of the determination of the value of theconstants a, b is as follows [9],
1
3

√

6.0,

2

0.4 /

31.7

(11)

where, W/C is water to cement ratio (%). If the diagram is to be determined by the measurement value,then the corrosion loss of steel reinforcing bars should use a multi-year measurement.
3.3.

Concrete surface cracking by rebar corrosion

3.3.1. P-D diagram, relation of the material deterioration and the performance of structure
By the evaluation of salinity indicated in "Review Manual for Age-Related Technical Assessment
in Japan " [2], the deterioration of reinforced concrete is evaluated according to whether or not thechloride concentration over the life span of the structure is less than reference levels, and whether or
not cracks occur in the concrete. So in this study, the performance of the structure, P is set to thewidth of cracks in the concrete surface.
The relation between when cracks will occur in the concrete and the corrosion loss of steel
reinforcing bars which diameter is used as stirrup or tye is shown as follows [10] ,
0.19

0.06

2.0 ∙

0.1

47

(12)

where Du is critical corrosion loss of steel reinforcing bars to affect a crack in the concrete at a widthof 0.1mm by FEM analysis (mg/cm2), d : diameter of steel reinforcing bars (mm) which size isassuming the use of stirrup or hoop, x : thickness of concrete cover (mm), Fc : compressive strength of
concrete (N/mm2) which represents the crack resistance of concrete. There exists a linear relationshipbetween the corrosion loss of steel reinforcing bars and width of cracks in the concrete [11]. The
relation between the corrosion loss of steel reinforcing bars, D3, and width of cracks in the concrete,
P8 (subscript “8” represents the crack of concrete) is expressed as follows:82

E-Journal of Advanced Maintenance Vol.5-1 (2013) 77-84
Japan Society of Maintenology

8

0.1

3

(13)

3.3.2. PDFt diagram, relation of the number of years elapsed, the deteriorative factor, thematerial deterioration and the performance of structure
An example of the integrity evaluation diagram (PDFt diagram) in the case of time changes (t)and concrete surface cracking (P) caused by the penetration of salinity (F) and rebar corrosion (D) byusing formulas mentioned above is shown in Fig. 3.

※ On the assumption of a sever
The amount of action of a deteriorative factor,Ｆ
environmental salinity (sea) of
Ｆ2 The amount of action of chloride ion (kg/m3・year) : C0=6.9(kg/m3)

F - t Diagram※1

40, 5060, 30400

50, 30

Ct：Cl- concentration (kg/m3) , t ：Year (year)
C0： Cl- concentration at surface (kg/m3),
α2： Const. x： Thickness of concrete cover (mm)
D: Diffusion coefficient (mm2/year)※2

60, 50300

40, 3050, 50a = 6.0, b = 0.4 W/C - 31.7
x： Thickness of concrete cover (mm), a,b : Const.
tn： Evaluation period (year), W/C：Water cement ratio（%)

200

40, 3050, 5040, 50(1year)50, 3060, 5060, 3040, 1050, 10
W/C=60, x=1040

tn： Evaluation period (year)
Ccr： Critical Cl - =1.2kg/m3
Ct： Cl- concentration(kg/m3) ⊿t : Unit time

100

20
30

20

40

60

80

10
0.05
Crack occurrence
baseline

W/C=50, x=10
40, 3050, 3060, 3050, 50

d=10
10 13
16
10 13
16 19
10 13
19
13 16
10
16 19
13
19
16

x=10 (mm)x=30 (mm)x=50 (mm)

0.15

0.2

Du = - (0.19d + 0.06x + 2) ・ ln (Fc) + (0.1d + 47) ※3

0.25

※4

19

Ｐ – Ｄ Diagram

0.1

W/C=40 (%) , Fc=70(N/mm2)
W/C=50 (%) , Fc=50(N/mm2)
W/C=60 (%) , Fc=35(N/mm2)

Du : Critical corrosion loss of reinforcing bars to affecta crack in the concrete (0.1mm) (mg/cm2)
d : Diameter of reinforcing bars (mm), x： Thickness ofconcrete cover (mm), Fc : Compressive strength (N/mm2)

0.3

The number of years elapsed t (year)

Relation the degree of material deterioration Ｄ
Ｄ3 The corrosion loss of steel reinforcing bars (mg/cm2)

Ｄ - Ｆ Diagram

d=19 1613 10 19 1613 10 19 16 13 10
W/C=50, x=10 60, 30
50, 3019 16 13 10 19 16 13 10
50, 50 40, 30

Ｐ8 The width of cracks in the concrete surface (mm)The relation between the performance of the structureＰＰ – ｔ Diagram
7

Fig.3 PDFt diagram – time changes, chloride ion, rebar corrosion and concrete surface cracking

4. CONCLUSIONS
Conclusions obtaind from this study is summarized as follows:
1. A method of inductively determining a deterioration index and evaluation diagram is
proposed for evaluating the integrity of reinforced concrete structures subjected to multiple
deteriorative external factors.
2. Relationships are formulated among the number of years elapsed t, the amount of action of adeteriorative factor F, the degree of material deterioration D, and the performance of thestructure P and these relationships are conbined as a PDFt diagram.

83

Y. Kitsutaka./Durability Evaluation Method on Rebar Corrosion of Reinforced Concrete

3.

Detailed procedure of durability evaluation for a reinforced concrete structure using PDFt
concept is proposed by referring to the recent papers for the deterioration of rebar corrosion
caused by neutralization and penetration of salinity.

Acknowledgement
A part of this study was supported by a grant from the Japanese Ministry of Economy, Trade andIndustry.

References[1]

Y. Kitsutaka: Methodology on the Integrity Evaluation in the Aging Management and
Evaluation of Reinforced Concrete Structures, AIJ Journal of Technology, NO.32, pp.27-30,
2010.2[2] Japan Nuclear Energy Safety Organization (JNES)., “Review Manual for Age-related Technicalassessment Reduction in Strength and Reduction in Radiation Shielding Capability ofConcrete”, JNES-SS-0512-04, 2009.4[3] Hamada, M., “Neutralization (carbonation) of concrete and corrosion of reinforcing steel”,
Cement & concrete (272), 1969.10, pp.2-18.
[4] Kishitani, K., “Durability of reinforced concrete”, Kajima Publishing Co. Ltd., 1963.
[5] Tomosawa, F., Fukushi, I., Morinaga, S., “A Preliminary Study on the Prediction of Service
Life of Reinforced Concrete Based on Carbonation and Corrosion of Reinforcement”,
Summaries of technical papers of Annual Meeting, AIJ (60), pp.101-102, 1985.9[6] Maruya, T., Uji, K., “Prediction of diffusive salt penetration into concrete”, JCI Annual
Convention Proceedings, Vol.1, No.1, 1989, pp.597-602.
[7] Kawakami, H., Waki, K., “Chloride Permeation into Concrete and Estimation of Saline
Environment”, Journal of structural and construction engineering. AIJ (453), 1993.11, pp.9-14.
[8] Murakami, Y., Suda, K., Nagata, S., “The Square Root Theory on Chloride Ingress”,
Proceedings of the 58th Annual Conference of the Japan Society of Civil Engineers V-5, 2003.9,
pp.9-10.
[9] Japan Concrete Institute., “Commission's Report, Symposium of Development of Simulation
Model for Detecting Long-term Performance of Concrete Structure, Equation of Tottori”,
2004.10, pp.204.
[10] Kitsutaka, Y., Nguyen, L. P., Tsukagoshi, M., Matsuzawa, K., “Study of Initial Cracking inConcrete and the Corrosion Loss of Steel Reinforcing Bars”, JCI Annual Convention
Proceedings, CD-ROM, 2011.7, pp.1145-1150.
[11] Kitsutaka, Y., “Fracture-mechanical interpretation of Prediction of Corrosion Rate of Steel Bar
by Crack Width in the Concrete”, Japan Concrete Institute, Symposium of Rehabilitation
System of Concrete Structures, 1998, pp.21-28.

84