# Seismic Behavior of Corroded RC Bridges: Review and Research Gaps

Authors: Kaveh Andisheh; Allan Scott; Alessandro Palermo
Journal: International Journal of Corrosion
 (2016)

---

## Abstract

Chloride-induced corrosion and its effect on structural and seismic performance of reinforced concrete (RC) structures have been the topic of several research projects in past decades. This literature review summarizes the state of the art by presenting a brief description of chloride-induced corrosion, its main characteristics and influencing factors, a summary of experimental published data, and existing corrosion-induced deterioration models together with numerical and experimental methods used to evaluate corroded RC bridge pier. This literature review highlights the need for reliable deterioration models for RC structures and appropriate analysis methods are needed for design of new structures or assessment of existing civil engineering structures especially in seismic areas.


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## Body

## 1. Introduction

In recent years, growing attention has been given to the effects of corrosion on the structural performance of reinforced concrete (RC) structures. According to National Association of Corrosion Engineers (NACE), the direct annual cost of corrosion of infrastructure was more than $22 billion in the USA in 2002. American Society of Civil Engineers (ASCE) has reported that the USA should invest $2.2 trillion over the next five years to repair and upgrade more than 300,000 bridges in the USA that are approaching the end of their design life [1]. While RC structures in pristine condition can be expected to satisfy the code requirements of a given era, corrosion of reinforcing steel affects the seismic performance of the structure over time. Therefore, old corroded RC structures become vulnerable to probable future earthquakes. It should be noted that there are two well-known forms of corrosion: carbonation-induced and chloride-induced corrosion. Carbonation-induced corrosion is defined as a chemical reaction between atmospheric carbon dioxide and the product of cement hydration, mainly calcium hydroxide [2]. Chloride-induced corrosion is defined as an electrochemical reaction between chloride product (such as iron(II)-chloride) and water. In this paper, chloride-induced corrosion has been studied. The vast majority of deterioration in RC structures is a result of corrosion of reinforcing steel due to ingress of chloride ions from either deicing salts or marine environment. Corrosion changes effective characteristics and mechanical properties of materials, leading to possible degraded seismic performance of corroded RC structures. This problem is very critical for bridges and more importantly for bridge piers since they dissipate earthquake energy through the formation of plastic hinges. Corrosion is a time-dependent process. Therefore, lifetime analysis is needed to evaluate seismic and structural performance of corroded structures. Long-term seismic performance of RC structures subject to corrosion includes three main parts that are shown in Figure 1: (1) chloride-induced corrosion, (2) deterioration of RC structures or elements due to corrosion, and (3) lifetime (time-dependent) seismic analysis and performance of corroded RC bridge pier.Figure 1
Outline of long-term seismic performance of corroded structures.Figure2 shows an overview of the aforementioned three main parts. Two critical phenomena are the reduction in cross section area of reinforcing steel and the formation of corrosion by-product, leading to cracking and spalling of concrete in RC structures. Hence, corrosion-induced deterioration of RC structures can be classified into four groups as follows:(1)
Reduction in mechanical properties of steel reinforcements.
(2)
Deterioration of bond between steel and concrete.
(3)
Degradation of confinement (decreasing shear strength).
(4)
Damage to concrete material.Figure 2
Overview of main parts of long-term seismic performance of corroded RC bridge pier.Traditional seismic analysis cannot be used for RC structures subjected to corrosion hazard for the following reasons. The first reason is that corrosion depends on time, so mechanical properties of structural elements are a function of time. The second reason is lack of robust analytical/numerical cyclic models to predict behavior of corroded RC structures subjected to earthquakes. Hence, lifetime analysis of corroded RC structures is needed, taking into consideration the corresponding deterioration models for corroded RC structures, amount of corrosion, and important factors influencing corrosion process such as corrosion initiation time. Figure3 illustrated force-displacement response of a corroded bridge pier over time. The outcomes of lifetime seismic analysis of corroded RC structures can be represented in terms of reduction in structural capacity or increase in probability of failure over time.Figure 3
Force-displacement response of a corroded bridge pier over time.This paper summarizes the state of the art by presenting a brief description of chloride-induced corrosion, its main characteristics and influencing factors, a summary of experimental published data, and existing corrosion-induced deterioration models together with numerical and experimental methods used to evaluate corroded RC bridge pier. The main objective of this paper is highlighting research gaps and critical need to further studies in this field.


## 2. Chloride-Induced Corrosion

Corrosion of reinforcing steel embedded in concrete is an electrochemical process. The process is initiated as soon as aggressive ions such as chloride penetrate the concrete cover and reach the steel reinforcement. Once the corrosion process commences, not only does the cross-sectional area of the corroding reinforcing steel decrease but also corrosion by-products such as rust are formed. The irregular loss of cross section leads to alterations in mechanical properties of reinforcing steels. The average volume of rust is approximately 2–4 times greater than that of the steel resulting in the development of tensile stresses in concrete, which ultimately lead to cracking and spalling of the cover concrete [3, 4]. Moreover, bond between steel and concrete decreases. It should be noted that a low level of corrosion can result in a slight increase in bond strength, but increasing corrosion level leads to reduction in bond between concrete and steel reinforcement [5–10].


### 2.1. Chloride Content in Reinforced Concrete Structures: Initial Stage and Threshold Value

Chloride content is the amount of chloride ion at the surface of steel reinforcement. To initiate corrosion, it should reach a certain level called critical chloride content (C
c
r
i
t). C
c
r
i
t is a threshold value needed to propagate chloride ion. However, there is difference between the scientific and practical definitions of C
c
r
i
t. In scientific definition, C
c
r
i
t is the threshold required to propagate on the surface of the steel, while in practical definition it is associated with the acceptable deterioration of reinforcing steel.Angst et al. [11] have summarized the values of C
c
r
i
t experimentally measured from steel embedded in cement based material in laboratory condition, from real structures and from steel directly immersed in solution, reported by 32 published articles. The maximum and minimum values of C
c
r
i
t based on the review of aforementioned experimental results together with maximum allowable total C
l
-% cement weight proposed by various ACI documents are presented in Table 1.Table 1
Maximum and minimum critical chloride content based on 32 experimental works reviewed by [11] compared with C
c
r
i
t proposed by ACI codes.
Maximum-minimum
C
c
r
i
t from steel embedded in cement based material
C
c
r
i
t real structures
⁢C
c
r
i
t from the steel directly immersed in solution
TotalC
l
-% binder weight
C
l
-
/
O
H
- ratio
FreeC
l
- (mol/L); % bw
TotalC
l
- (% bw)
C
l
-
/
O
H
- ratio
FreeC
l
- (mol/L)
0.04–8.34
0.09–45
0.045–4; 0.07–1.16
0.1–1.96
0.01–4.9
0.0056–0.42
C
c
r
i
t expressed as total chloride content relative to cement weight proposed by various ACI documents for prestressed RC structures in service
ACI documents
ACI 357
ACI 222
ACI 201
C
c
r
i
t expressed as C
l
-% binder weight
0.06
0.08
Not stated
0.1
0.2
0.1Moreover, Hussain et al. [12] estimated critical chloride of steel embedded in cement based material and showed that threshold of free C
l
-, independent from C
3
A content, varies from 0.22 to 0.29% cw (cement weight), while threshold of total chloride, dependent on C
3
A content, varies from 0.48 to 1.2% cw for various amounts of C
3
A content. The results agree with the associated range represented in Table 1. Ann and Song [13] stated that measurement accuracy of C
c
r
i
t in terms of free C
l
- and C
l
-
/
O
H
- ratio is relatively low. Expressing C
c
r
i
t in terms of total C
l
- (% cement weight) takes into consideration inhibiting effect of cement and the aggressive nature of chloride. Angst et al. [11] also have reported important factors influencing C
c
r
i
t based on reviewing 24 articles. The important factors influencing C
c
r
i
t have been categorized into three groups: steel type and condition, concrete and binder properties, and external factors. In addition to this, Alonso et al. [14] concluded that the type of steel does not significantly affect the critical chloride value, but after depassivation, the average rate of corrosion is slightly higher in ribbed bar. Glass and Buenfeld [15] showed that chloride binding reduced free chloride due to the removal of chloride ions from the pore solution of concrete. It also reduced total chloride content at depth. Maruya et al. [16] concluded that, because of condensation and ion absorption due to pore wall in wetting and drying cycles, increasing the cycle raises total chloride in RC structures. Polder [17] stated that, from a theoretical point of view, the effect of concrete resistivity on critical chloride value still remains unclear. Based on information above, the table presented by Angst et al. [11] has been updated. The update also includes additional new factors marked as “∗”. Finally, Table 2 presents important factors influencing critical chloride content in terms of total C
l
-, C
l
-
/
O
H
- ratio, and free C
l
-.Table 2
Important factors and their effects on critical chloride content.
Factor
Effect on critical chloride content
TotalC
l
-% cement weight
C
l
-
/
O
H
- ratio
FreeC
l
-
Steel type and condition
Defect at steel-concrete interface
↓
↓
↓
Polishing and sandblasting
↑
↑
↑
Steel potential (>−200 mV SCE)
O
O
O
Steel potential (<−200 mV SCE)
↓
↓
↓
Steel type
∗
O
O
O
Concrete and binder properties
w/c ratio
↓
↓
↓
Chloride binding
∗
↓
↑
O
↓  O
pH
↑
↑
↑
Electrical resistivity
∗
↑  NC
↑
↑
Silica fume
↓
↓
↓
Fly ash
↓↑O
b
↓O
b
↓O
b
GGBS (ground granulated blast furnace slag)
↓↑O
b
O
O
SRPC (lowC
3
A
+
C
4
A
F content)
↓
NS
NS
External factors
Moisture in rather dry concrete
↓
↓
↓
Moisture in nearly saturated concrete
↑
↑
↑
Moisture variation
↓
↓
↓
Oxygen availability
↓
↓
↓
Temperature
↓
↓
↓
Condensation in wet and drying cycle
∗
↑
NS
NS
↓
↑  indicates decreasing and increasing critical value with an increase of concerning factor; NS: result not stated; NC: the effect of the concerning factor is unclear; O: the concerning factor has no effect; b: contradicting results reported in the literature. SRPC: sulphate resistant Portland cement.
∗ indicates additional new factors if compared with the table presented by Angst et al. [11].It is worth noting that Angst et al. [18] have developed a probabilistic model to investigate the effect of specimen size on C
c
r
i
t measured in laboratories. They have concluded that increasing sample’s geometrical dimension decreases C
c
r
i
t, but to apply this result to steel embedded in concrete it has to be verified through experimental studies.A number of methods for determining the total chloride content and the free chloride content are applied in practical applications. For measuring the total chloride content, drilled cores from hardened concrete are analyzed. The total chloride content in concrete powder-nitric acid solution can be measured by a number of methods such as titration, use of ion selective electrodes, or spectrophotometric methods. However, a more expensive but very accurate method is to determine the total chloride content in concrete powder using X-ray fluorescence spectrometry (XRF). To determine the free chloride content, pore solution expression, leaching techniques, and ion selective electrodes are used in the literature [11]. Further information can be found in [11] and its corresponding references.


### 2.2. Pitting Corrosion: Limit Step to Start Pitting Corrosion

It has been shown that the formation of macrocell, that is, small anodic area in comparison with large cathodic area, is observed in pitting (localized) corrosion [19–23]. It has been confirmed that three transitions occur in pitting corrosion: the first is transition from initiation stage to propagation stage, called depassivation [24]; the second is transition from depassivation to repassivation (the repassivation phase called metastable); and the third is transition from metastable to pit growth. As mentioned before, the first transition is related to existing critical chloride content. In metastable, nucleation occurs, also called repassivation, depending on chemistry or metallurgy condition. Then in case of maintaining aggressive chemical composition in pit cavity, the transition from nucleation to stable pit growth occurs. This transition is due to the simultaneous ingress of H
+ and C
l
- and other anions into pit cavity [25–27]. Bertolini et al. [28] stated that pitting corrosion for reinforcement of steel in concrete is due to the acidification of pit cavity and ingress of C
l
- into the pit. Broomfield [29] found that steel reinforcement corrosion starts with the formation of a number of pits. Increasing the number of pits causes them to join up and form a general corrosion. Angst et al. [30] concluded that a transition from anodic to cathodic control occurs in pitting corrosion. However, it is not clear in which chloride content this transition takes place, so further investigation in this area should be carried out. It is clear that pitting corrosion occurs due to existence of high amount of chloride ion in a certain location. This means that corrosion potential is greater than pitting potential in that location [11]. Since pitting corrosion causes significant cross section loss in reinforcing steels, in structural analysis the amount of cross section loss due to pitting corrosion is a very important parameter. Therefore, researchers estimated a factor called “pitting factor” that is used to calculate pit depth and related loss of steel cross section. Pitting factor is the ratio of maximum pit depth on average corrosion penetration. Pitting factors reported in the literature have been collected from 8 experimental investigations and are summarized in Table 3.Table 3
Pitting factors obtained from literature.
Authors and date
D
(
m
m
)
L
(
m
m
)
Time (day)
Number of samples
i
c
o
r
r (μA/cm2)
Pitting factor: (R) Mean; COV
González et al. [73]
8
500
6 years
NS
0.1–7.0
4.4–5.9; NS
16
400
30
10–100
5.9–16.1; NS
Rodriguez et al. [74]
6
650
100–200
18
100
4–11.7; 0.05–0.22
Rodriguez et al. [75]
12
2300
100–200
16
100
4.0; 0.15
Torres-Acosta and Martínez-Madrid [31]
13
310
700
35
NS
5.5; 0.59
Stewart [76]
8
800
50 years
1
7.00; 0.18
16
7.68; 0.16
24
8.08; 0.16
28
8.23; 0.15
32
8.36; 0.15
36
8.48; 0.15
10
100
1.65; 0.22
Cairns et al. [77]
16
NS
100–400
25
10–50
23.8; 0.56
Torres-Acosta et al. [78]
10
1500
40, 80, 200
8
80
11.7; NS
Stewart and Al-Harthy [79]
16
100
78
32
160–185
6.20; 0.18
27
125–150
7.10; 0.17Figure4 shows the relationship between diameter size of reinforcing steel and pitting factor regressed from the results represented in Table 5. According to this figure, pitting factor increases with the growth of diameter sizes of reinforcing steels.Figure 4
Pitting factor for different diameter sizes of bars regresses from results represented in Table5.Average corrosion penetration can be calculated based on mass loss due to corrosion and estimation of associated equivalent diameter of corroded bar [31]. It has been stated that pitting factor rises with increase of reinforcing steel bars diameter [32].Using Faraday’s law, assuming hemispherical form for pits, the maximum pit depth is as follows [33]:(1)
p
t
=
0.0116
×
R
×
i
c
o
r
r
l
×
t
,where p
t is the maximum pit depth (mm), R is pitting factor, i
c
o
r
r
(
l
) is corrosion current density (μ
A
/
c
m
2), and t is time (year).


### 2.3. Predicting the Rate of Corrosion

Rate of corrosion and time of the commencement of corrosion are very important factors influencing the deterioration of RC structures as they are related to residual capacity of corroded structures. Many factors affect the corrosion rate which are classified into three groups: named steel condition, concrete and binder properties, and external factors. Based on the empirical and mathematical models developed by past studies, Table4 shows important factors affecting corrosion rate and initiation time of corrosion [34–52]. Among all factors, one may notice that increasing total chloride raises corrosion rate. This means that all factors affecting total chloride (see Table 2) influence corrosion rate. Increasing saturation degree of pore in empirical model causes both reduction and rising of corrosion rate. On the other hand, the mathematical model showed that increasing the degree of saturation pore from 30% to 50% causes increasing corrosion rate, while further increase from 60% to 100% causes reduction in corrosion rate [36].Table 4
Important factors and their effects on corrosion rate and start time of corrosion.
Factor
Empirical corrosion rate (r
c
o
r
r) model
⁢Mathematical corrosion rate
Start time
r
c
o
r
r
Steel condition
Temperature at steel level
↑
Galvanic coupling
↑
Corroding area to exposure area
↓
Anodic and cathodic resistivity
↑
Concrete and binder properties
w/c ratio
↑
↑
TotalC
l
-%
↑
pH
↓
Electrical resistivity
↓
↓
Permeability
↑
Cracks
↓
NC
Size distribution of aggregates
↓
Initiation crack width
↓
Degree saturation of pore
↓
↑
(30%–50)↑; (60%–100%) ↓
External factors
Slag concentration
↓
Chloride conductivity
RH
↑
Time
↓
Oxygen availability
↑
Aging of oxides in dry concrete
↓
Aging of oxides in wet concrete
O
Cover
↓
↓
↓
↑  indicates decreasing and increasing corrosion rate value with an increase of concerning factor; NC: the effect of the concerning factor is unclear; NS: not stated; O: the concerning factor has no effect.Table 5
Simple method to evaluate grade of corrosion.
Corrosion grade
Noncorroded
Slight corrosion
Moderate corrosion
Severe corrosion
Corrosion current density [µA/cm2]/corrosion duration [year]
<0.0066
0.0066–0.05
0.05–2.5
>2.5
Corrosion duration [year]
>15
10 to 15
2 to 10
<2While measuring corrosion accurately is difficult, there are some simple methods based on corrosion potential and corrosion rate that can be used by researchers and practical engineers to estimate active corrosion in RC structures. For example, according to ASTM C-876-91, if corrosion potential,V, is less than −0.35, probability of active corrosion is more than 95% [53]. Elsener et al. [54] have stated that corrosion potential ranging from -
0.4 to -
0.6 means that steel is corroding. Liang et al. [55] have reported that using corrosion current density to corrosion duration ratio the grade of corrosion can be evaluated according to Table 5.


### 2.4. Corrosion By-Products and Corrosion-Induced Cracking

As discussed earlier, when corrosion initiates, corrosion by-products are formed. The volume of corrosion by-products is greater than that of steel. Therefore, volumetric expansion causes tensile stress leading to propagation of cracks into concrete cover. Zhao et al. [56] have suggested the expansion coefficient of 2.64, 2.85, and 3.02 for samples corroded in NaCl solution, near or on the coast and in splash zone, respectively. Table 6 presents the volume expansion of different components of corrosion by-product found by past studies.Table 6
Volume expansion of corrosion by-product components.
References
Volume expansion coefficient of different components of corrosion by-product
F
e
O
F
e
3
O
4
F
e
2
O
3
α
F
e
O
H
γ
F
e
O
H
F
e
2
O
3 ⋅H
2
O
β
F
e
O
H
F
e
(
O
H
)
2
F
e
(
O
H
)
3
F
e
(
O
H
)
3 ⋅3
H
2
O
F
e
2
O
3 ⋅3
H
2
O
[62]
1.82
2.08
2.17
—
—
—
—
3.76
4.24
6.46
—
[80]
1.74
2.1
2.11, 2.26
2.9
3.12
—
3.5
3.7
4
6.24
[65]
1.8
2
2.2
—
—
—
—
3.75
4.2
6.4
—
[57]
—
2.08
2.12
2.91
3.03
—
3.48
—
—
—
—
[81]
1.77
2.1
2.14
2.92
3.06
3.12
—
3.71
4.82
—
6.5
[56]
—
2.1
—
2.95
3.07
—
3.53
—
—
—
—Predicting the expansion volume of rusts is very important to improve the knowledge of service life of reinforced concrete structures. The variation in expansion coefficient reported by past studies clearly indicates that the need for further studies on rust compositions is demanded.With respect to mechanical properties and characteristics of corrosion by-products, Caré et al. [57] have stated that Young’s modulus of rust layers depends on the diameter of uncorroded steel bar and thickness of the rust layers. Zhao et al. [56] have shown that environmental parameters such as amount of humidity and oxygen availability vary the volume expansion coefficient. Increasing the amount of humidity and oxygen raises the expansion coefficient.Past studies investigated corrosion-induced cracking and shared the influencing factors and measured crack width based on experimental data. A summary of 18 reviewed works has been presented in Table7 showing crack width measured in addition to some details such as amount, current density, and/or type of corrosion and time of exposure. Table 7 can give an overall view on corrosion-induced cracking. It is worth noting that the maximum crack width reported in the literature so far has been 6 mm [31]. Few models have been developed for predicting width of crack in the literature. Andrade et al. [58], for example, presented a simple formula to predict average width of crack in elements exposed to natural corrosion [59]:(2)
w
=
k
P
x
C
/
ϕ
,where w is the crack width (mm), k is a nondimensional factor, C
/
ϕ is concrete cover/diameter of the bar ratio, and P
x is penetration of the corrosion in time t (year) and equal to(3)
P
x
=
0.0115
r
c
o
r
r
t
,where r
c
o
r
r (mm/year) is the corrosion rate.Table 7
Relationship between crack widths with corrosion obtained from literature.
References
Type of specimen
Time (day)
i
c
o
r
r (μA/cm2)
A
c
o
r
r (%)
Crack width (mm)
[82]
Beam
NS
2000
<4.5
1.3
[83]
Beam
3–15
0.5
2.5–12
0.1–0.75
Bond-pull
500
NS
NS
[58]
Prism
1–100
10, 100
0.5–2.5
0.05–0.5
[84]
Beam
28
0.8–9.2
NS
Bond-pull
1–28
3.6–19.2
0.06–0.46
[74]
Column
106–204
100
9.1–17.8
0.8–4.0
[75]
Beam
100–200
100
10.1–26.3
0.2–0.6
[85]
Slabs
1–2.5
3
1–75
NS
[86]
Beam
126 hours
5
×
10
8
<1
NS
[43]
Prism
68–221
10, 100
NS
0.06–1
[87]
Prism
NS
5 V current
0, 12
0.35, 0.8
[88]
Beam
15–18
1–4
2.5–10
NS
[89]
Beam
16–64 h
3
1.25–5
NS
[31]
Prism
700
Up to 51
0–6
[90]
Prism
815, 766, 380, 306
100, 200, 350, 500
4.38, 7.3, 6.5, 7.26
0.25–1
[91]
Beam
17 years
Saline Environment
26
1.6
Beam
14 years
12
1.8
[92]
Slab
2–9 months
100
NS
0.05–1.5
[93]
T-beam
2–15 years
Average: 0.128
NS
0.31–3.94
Column
2–15 years
NS
0.2–0.51
[94]
Wall spec.
20–56 weeks
R
p = ±20 mV
Up to 6.5%
0.01–1Andrade et al. [59] validated their formula with 15-year-old RC specimens. They proposed k
=
9.5 for their formula. Du et al. [60] showed that both decrease of w/c (water to cement) ratio and increase of cover are important factors to resist cracking due to ingress of chloride. It is clear that rate of corrosion is always an important factor affecting crack-induced corrosion.The relationship between corrosion current density,i
c
o
r
r (mA/m2), and corrosion rate, r
c
o
r
r (μm/year), can be expressed in the following equation [61]:(4)
r
c
o
r
r
=
0.327
M
i
c
o
r
r
n
ρ
,where M (g/mol) is the atomic weight, n is the ion valence, and ρ is the density (g/cm3).Predicting time of corrosion cracking is another important factor in corrosion-induced cracking topic and is used for predicting the service life of corroded RC structures. Predicting the time of corrosion cracking has been addressed by a number of researchers including [55]. In this regard, a few mathematical models have been developed by [62–67]. Figure 5 shows the relationship between percentage of cross section loss in steel bars and crack width (mm) based on the results represented in Table 8. Figure 5 shows increasing percentage loss of cross section due to corrosion raising crack width.Table 8
Corrosion-induced reduction factors of mechanical properties of steel reinforcing.
References
Sample (D); test
Corrosion method and condition
A
c
o
r
r
%
α
y
α
u
α
E
α
ε
u
[95]
Ribbed (8–32);t
Open air (environment)
0–0.5
0.0
0.0
Plain (8–32);t
[96]
Ribbed (12);t
Acc. 0.5–2.0m
A
/
c
m
2
0–11
0.45
0.33
[97]
Bare;t
Open air (environment); Arabian coast
0-1
0.0
0.0
[98]
Ribbed (8); tensile
Acc. 0.5m
A
/
c
m
2
0–28
0.16
0.44
Plain (8); tensile
0.28
0.68
[99]
RC-ribbed (10–25);t
Open air (environment); carbonation
0–67
0.04
0.05
RC-plain (8–14);t
[100]
RC
Open air (environment); chloride
0–25
0.6
0.63
[101]
Ribbed (10); tensile
Acc. 13.0m
A
/
c
m
2
0–25
0.21
NS
[102]
RC beam (6, 12);B
Chlorides; saline environment
0–20∗
NS
NS
3.5
[103]
Rib-RC (8, 16, 32);t
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; tensile
0–25
0.12
0.15
Plain-RC (8, 16);t
0–25
0.49
0.65
[104]
6 mm
Acc. 2.0m
A
/
c
m
2
0–75
1.98∗
∗
NS
4.6
12 mm
0–80
0.74∗
∗
NS
NS
[105]
NS
Open air (Environment); chloride
0–>30
0.00
0.00
[60]
Ribbed (8, 16, 32) and RC; tensile
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; yield force
0–25
1.14–1.28∗
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; ultimate force
0–25
1.22–1.39∗
∗
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; yield strength
0–25
0.16–0.36
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; ultimate strength
0–25
0.26–0.48
Plain (8,16) and RC; tensile
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; yield force
0–25
1.60, 1.48∗
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; ultimate force
0–25
1.71, 1.26∗
∗
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; yield strength
0–25
0.79, 0.58
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; ultimate strength
0–25
0.94, 0.44
[77]
RC cube; tensile
Acc. 0.01–0.05m
A
/
c
m
2; cyclic wet-dry
0–3
1.2
1.1
NS
3
RC cylinders;t
Acc. (electric); 5% NaCl
[69]
S400, 10 mm
Salt spray corrosion
1.5–8.5
1.47
1.31
NS
6.97
[68]
RC ribbed (10, 13);t
Accelerated uniform (electric); 3% NaCl
0–35
1.24
1.07
1.75
1.95
RC ribbed (10, 13);t
Acc. pitting (chloride induced); cyclic wet-dry
0–35
1.98
1.57
1.15
2.95
[106]
RC beam; bending
Open air (environment); 1–12 years
0–50
NS
1.97∗
NS
NS
RC beam; bending
Accelerated (electric); 3% NaCl
0–50
NS
1.59∗
NS
NS
Ribbed; tensile
Open air (environment); 1–12 years
0–50
NS
1.41
NS
NS
Ribbed; tensile
Accelerated (electric); 3% NaCl
0–50
NS
1.34
NS
NS
[71]
BS B500B; 10 mm;t
NS
9.5–19.6
1.21
1.38
NS
1.91
[72]
RC plain (6.5 mm);t
Naturally carbonation-induced corroded
14–38
1.12
1.36
NS
NS
RC ribbed (12);t
Acc. 0.1m
A
/
c
m
2; 5% NaCl
4–28
1.1
1.22
NS
NS
∗ indicates factor associated with yield force.
∗
∗ indicates reduction factor associated with ultimate force.Figure 5
Crack width versus percentage loss of cross section regresses from results represented in Table8.The reason for rising crack width with corrosion percentage is that more corrosion by-products in higher level of corrosion lead to increase of crack width.


### 2.5. Research Gaps

The main research gaps in chloride-induced corrosion can be summarized as follows:(i)
More accurate value of critical content of chloride concentration for real RC structures.
(ii)
Factors and their effects on the critical content of chloride.
(iii)
Robust pitting factors for real corroded structures.
(iv)
Factors and their effects on corrosion rate and time of initiation.
(v)
Robust corrosion rate and time of initiation prediction.
(vi)
More accurate values volume expansion for corrosion by-product and rust components, especially for real corroded RC structures.Research studies aiming to fill the above research gaps will lead to decrease of uncertainties in estimation of chloride-induced corrosion.


## 2.1. Chloride Content in Reinforced Concrete Structures: Initial Stage and Threshold Value

Chloride content is the amount of chloride ion at the surface of steel reinforcement. To initiate corrosion, it should reach a certain level called critical chloride content (C
c
r
i
t). C
c
r
i
t is a threshold value needed to propagate chloride ion. However, there is difference between the scientific and practical definitions of C
c
r
i
t. In scientific definition, C
c
r
i
t is the threshold required to propagate on the surface of the steel, while in practical definition it is associated with the acceptable deterioration of reinforcing steel.Angst et al. [11] have summarized the values of C
c
r
i
t experimentally measured from steel embedded in cement based material in laboratory condition, from real structures and from steel directly immersed in solution, reported by 32 published articles. The maximum and minimum values of C
c
r
i
t based on the review of aforementioned experimental results together with maximum allowable total C
l
-% cement weight proposed by various ACI documents are presented in Table 1.Table 1
Maximum and minimum critical chloride content based on 32 experimental works reviewed by [11] compared with C
c
r
i
t proposed by ACI codes.
Maximum-minimum
C
c
r
i
t from steel embedded in cement based material
C
c
r
i
t real structures
⁢C
c
r
i
t from the steel directly immersed in solution
TotalC
l
-% binder weight
C
l
-
/
O
H
- ratio
FreeC
l
- (mol/L); % bw
TotalC
l
- (% bw)
C
l
-
/
O
H
- ratio
FreeC
l
- (mol/L)
0.04–8.34
0.09–45
0.045–4; 0.07–1.16
0.1–1.96
0.01–4.9
0.0056–0.42
C
c
r
i
t expressed as total chloride content relative to cement weight proposed by various ACI documents for prestressed RC structures in service
ACI documents
ACI 357
ACI 222
ACI 201
C
c
r
i
t expressed as C
l
-% binder weight
0.06
0.08
Not stated
0.1
0.2
0.1Moreover, Hussain et al. [12] estimated critical chloride of steel embedded in cement based material and showed that threshold of free C
l
-, independent from C
3
A content, varies from 0.22 to 0.29% cw (cement weight), while threshold of total chloride, dependent on C
3
A content, varies from 0.48 to 1.2% cw for various amounts of C
3
A content. The results agree with the associated range represented in Table 1. Ann and Song [13] stated that measurement accuracy of C
c
r
i
t in terms of free C
l
- and C
l
-
/
O
H
- ratio is relatively low. Expressing C
c
r
i
t in terms of total C
l
- (% cement weight) takes into consideration inhibiting effect of cement and the aggressive nature of chloride. Angst et al. [11] also have reported important factors influencing C
c
r
i
t based on reviewing 24 articles. The important factors influencing C
c
r
i
t have been categorized into three groups: steel type and condition, concrete and binder properties, and external factors. In addition to this, Alonso et al. [14] concluded that the type of steel does not significantly affect the critical chloride value, but after depassivation, the average rate of corrosion is slightly higher in ribbed bar. Glass and Buenfeld [15] showed that chloride binding reduced free chloride due to the removal of chloride ions from the pore solution of concrete. It also reduced total chloride content at depth. Maruya et al. [16] concluded that, because of condensation and ion absorption due to pore wall in wetting and drying cycles, increasing the cycle raises total chloride in RC structures. Polder [17] stated that, from a theoretical point of view, the effect of concrete resistivity on critical chloride value still remains unclear. Based on information above, the table presented by Angst et al. [11] has been updated. The update also includes additional new factors marked as “∗”. Finally, Table 2 presents important factors influencing critical chloride content in terms of total C
l
-, C
l
-
/
O
H
- ratio, and free C
l
-.Table 2
Important factors and their effects on critical chloride content.
Factor
Effect on critical chloride content
TotalC
l
-% cement weight
C
l
-
/
O
H
- ratio
FreeC
l
-
Steel type and condition
Defect at steel-concrete interface
↓
↓
↓
Polishing and sandblasting
↑
↑
↑
Steel potential (>−200 mV SCE)
O
O
O
Steel potential (<−200 mV SCE)
↓
↓
↓
Steel type
∗
O
O
O
Concrete and binder properties
w/c ratio
↓
↓
↓
Chloride binding
∗
↓
↑
O
↓  O
pH
↑
↑
↑
Electrical resistivity
∗
↑  NC
↑
↑
Silica fume
↓
↓
↓
Fly ash
↓↑O
b
↓O
b
↓O
b
GGBS (ground granulated blast furnace slag)
↓↑O
b
O
O
SRPC (lowC
3
A
+
C
4
A
F content)
↓
NS
NS
External factors
Moisture in rather dry concrete
↓
↓
↓
Moisture in nearly saturated concrete
↑
↑
↑
Moisture variation
↓
↓
↓
Oxygen availability
↓
↓
↓
Temperature
↓
↓
↓
Condensation in wet and drying cycle
∗
↑
NS
NS
↓
↑  indicates decreasing and increasing critical value with an increase of concerning factor; NS: result not stated; NC: the effect of the concerning factor is unclear; O: the concerning factor has no effect; b: contradicting results reported in the literature. SRPC: sulphate resistant Portland cement.
∗ indicates additional new factors if compared with the table presented by Angst et al. [11].It is worth noting that Angst et al. [18] have developed a probabilistic model to investigate the effect of specimen size on C
c
r
i
t measured in laboratories. They have concluded that increasing sample’s geometrical dimension decreases C
c
r
i
t, but to apply this result to steel embedded in concrete it has to be verified through experimental studies.A number of methods for determining the total chloride content and the free chloride content are applied in practical applications. For measuring the total chloride content, drilled cores from hardened concrete are analyzed. The total chloride content in concrete powder-nitric acid solution can be measured by a number of methods such as titration, use of ion selective electrodes, or spectrophotometric methods. However, a more expensive but very accurate method is to determine the total chloride content in concrete powder using X-ray fluorescence spectrometry (XRF). To determine the free chloride content, pore solution expression, leaching techniques, and ion selective electrodes are used in the literature [11]. Further information can be found in [11] and its corresponding references.


## 2.2. Pitting Corrosion: Limit Step to Start Pitting Corrosion

It has been shown that the formation of macrocell, that is, small anodic area in comparison with large cathodic area, is observed in pitting (localized) corrosion [19–23]. It has been confirmed that three transitions occur in pitting corrosion: the first is transition from initiation stage to propagation stage, called depassivation [24]; the second is transition from depassivation to repassivation (the repassivation phase called metastable); and the third is transition from metastable to pit growth. As mentioned before, the first transition is related to existing critical chloride content. In metastable, nucleation occurs, also called repassivation, depending on chemistry or metallurgy condition. Then in case of maintaining aggressive chemical composition in pit cavity, the transition from nucleation to stable pit growth occurs. This transition is due to the simultaneous ingress of H
+ and C
l
- and other anions into pit cavity [25–27]. Bertolini et al. [28] stated that pitting corrosion for reinforcement of steel in concrete is due to the acidification of pit cavity and ingress of C
l
- into the pit. Broomfield [29] found that steel reinforcement corrosion starts with the formation of a number of pits. Increasing the number of pits causes them to join up and form a general corrosion. Angst et al. [30] concluded that a transition from anodic to cathodic control occurs in pitting corrosion. However, it is not clear in which chloride content this transition takes place, so further investigation in this area should be carried out. It is clear that pitting corrosion occurs due to existence of high amount of chloride ion in a certain location. This means that corrosion potential is greater than pitting potential in that location [11]. Since pitting corrosion causes significant cross section loss in reinforcing steels, in structural analysis the amount of cross section loss due to pitting corrosion is a very important parameter. Therefore, researchers estimated a factor called “pitting factor” that is used to calculate pit depth and related loss of steel cross section. Pitting factor is the ratio of maximum pit depth on average corrosion penetration. Pitting factors reported in the literature have been collected from 8 experimental investigations and are summarized in Table 3.Table 3
Pitting factors obtained from literature.
Authors and date
D
(
m
m
)
L
(
m
m
)
Time (day)
Number of samples
i
c
o
r
r (μA/cm2)
Pitting factor: (R) Mean; COV
González et al. [73]
8
500
6 years
NS
0.1–7.0
4.4–5.9; NS
16
400
30
10–100
5.9–16.1; NS
Rodriguez et al. [74]
6
650
100–200
18
100
4–11.7; 0.05–0.22
Rodriguez et al. [75]
12
2300
100–200
16
100
4.0; 0.15
Torres-Acosta and Martínez-Madrid [31]
13
310
700
35
NS
5.5; 0.59
Stewart [76]
8
800
50 years
1
7.00; 0.18
16
7.68; 0.16
24
8.08; 0.16
28
8.23; 0.15
32
8.36; 0.15
36
8.48; 0.15
10
100
1.65; 0.22
Cairns et al. [77]
16
NS
100–400
25
10–50
23.8; 0.56
Torres-Acosta et al. [78]
10
1500
40, 80, 200
8
80
11.7; NS
Stewart and Al-Harthy [79]
16
100
78
32
160–185
6.20; 0.18
27
125–150
7.10; 0.17Figure4 shows the relationship between diameter size of reinforcing steel and pitting factor regressed from the results represented in Table 5. According to this figure, pitting factor increases with the growth of diameter sizes of reinforcing steels.Figure 4
Pitting factor for different diameter sizes of bars regresses from results represented in Table5.Average corrosion penetration can be calculated based on mass loss due to corrosion and estimation of associated equivalent diameter of corroded bar [31]. It has been stated that pitting factor rises with increase of reinforcing steel bars diameter [32].Using Faraday’s law, assuming hemispherical form for pits, the maximum pit depth is as follows [33]:(1)
p
t
=
0.0116
×
R
×
i
c
o
r
r
l
×
t
,where p
t is the maximum pit depth (mm), R is pitting factor, i
c
o
r
r
(
l
) is corrosion current density (μ
A
/
c
m
2), and t is time (year).


## 2.3. Predicting the Rate of Corrosion

Rate of corrosion and time of the commencement of corrosion are very important factors influencing the deterioration of RC structures as they are related to residual capacity of corroded structures. Many factors affect the corrosion rate which are classified into three groups: named steel condition, concrete and binder properties, and external factors. Based on the empirical and mathematical models developed by past studies, Table4 shows important factors affecting corrosion rate and initiation time of corrosion [34–52]. Among all factors, one may notice that increasing total chloride raises corrosion rate. This means that all factors affecting total chloride (see Table 2) influence corrosion rate. Increasing saturation degree of pore in empirical model causes both reduction and rising of corrosion rate. On the other hand, the mathematical model showed that increasing the degree of saturation pore from 30% to 50% causes increasing corrosion rate, while further increase from 60% to 100% causes reduction in corrosion rate [36].Table 4
Important factors and their effects on corrosion rate and start time of corrosion.
Factor
Empirical corrosion rate (r
c
o
r
r) model
⁢Mathematical corrosion rate
Start time
r
c
o
r
r
Steel condition
Temperature at steel level
↑
Galvanic coupling
↑
Corroding area to exposure area
↓
Anodic and cathodic resistivity
↑
Concrete and binder properties
w/c ratio
↑
↑
TotalC
l
-%
↑
pH
↓
Electrical resistivity
↓
↓
Permeability
↑
Cracks
↓
NC
Size distribution of aggregates
↓
Initiation crack width
↓
Degree saturation of pore
↓
↑
(30%–50)↑; (60%–100%) ↓
External factors
Slag concentration
↓
Chloride conductivity
RH
↑
Time
↓
Oxygen availability
↑
Aging of oxides in dry concrete
↓
Aging of oxides in wet concrete
O
Cover
↓
↓
↓
↑  indicates decreasing and increasing corrosion rate value with an increase of concerning factor; NC: the effect of the concerning factor is unclear; NS: not stated; O: the concerning factor has no effect.Table 5
Simple method to evaluate grade of corrosion.
Corrosion grade
Noncorroded
Slight corrosion
Moderate corrosion
Severe corrosion
Corrosion current density [µA/cm2]/corrosion duration [year]
<0.0066
0.0066–0.05
0.05–2.5
>2.5
Corrosion duration [year]
>15
10 to 15
2 to 10
<2While measuring corrosion accurately is difficult, there are some simple methods based on corrosion potential and corrosion rate that can be used by researchers and practical engineers to estimate active corrosion in RC structures. For example, according to ASTM C-876-91, if corrosion potential,V, is less than −0.35, probability of active corrosion is more than 95% [53]. Elsener et al. [54] have stated that corrosion potential ranging from -
0.4 to -
0.6 means that steel is corroding. Liang et al. [55] have reported that using corrosion current density to corrosion duration ratio the grade of corrosion can be evaluated according to Table 5.


## 2.4. Corrosion By-Products and Corrosion-Induced Cracking

As discussed earlier, when corrosion initiates, corrosion by-products are formed. The volume of corrosion by-products is greater than that of steel. Therefore, volumetric expansion causes tensile stress leading to propagation of cracks into concrete cover. Zhao et al. [56] have suggested the expansion coefficient of 2.64, 2.85, and 3.02 for samples corroded in NaCl solution, near or on the coast and in splash zone, respectively. Table 6 presents the volume expansion of different components of corrosion by-product found by past studies.Table 6
Volume expansion of corrosion by-product components.
References
Volume expansion coefficient of different components of corrosion by-product
F
e
O
F
e
3
O
4
F
e
2
O
3
α
F
e
O
H
γ
F
e
O
H
F
e
2
O
3 ⋅H
2
O
β
F
e
O
H
F
e
(
O
H
)
2
F
e
(
O
H
)
3
F
e
(
O
H
)
3 ⋅3
H
2
O
F
e
2
O
3 ⋅3
H
2
O
[62]
1.82
2.08
2.17
—
—
—
—
3.76
4.24
6.46
—
[80]
1.74
2.1
2.11, 2.26
2.9
3.12
—
3.5
3.7
4
6.24
[65]
1.8
2
2.2
—
—
—
—
3.75
4.2
6.4
—
[57]
—
2.08
2.12
2.91
3.03
—
3.48
—
—
—
—
[81]
1.77
2.1
2.14
2.92
3.06
3.12
—
3.71
4.82
—
6.5
[56]
—
2.1
—
2.95
3.07
—
3.53
—
—
—
—Predicting the expansion volume of rusts is very important to improve the knowledge of service life of reinforced concrete structures. The variation in expansion coefficient reported by past studies clearly indicates that the need for further studies on rust compositions is demanded.With respect to mechanical properties and characteristics of corrosion by-products, Caré et al. [57] have stated that Young’s modulus of rust layers depends on the diameter of uncorroded steel bar and thickness of the rust layers. Zhao et al. [56] have shown that environmental parameters such as amount of humidity and oxygen availability vary the volume expansion coefficient. Increasing the amount of humidity and oxygen raises the expansion coefficient.Past studies investigated corrosion-induced cracking and shared the influencing factors and measured crack width based on experimental data. A summary of 18 reviewed works has been presented in Table7 showing crack width measured in addition to some details such as amount, current density, and/or type of corrosion and time of exposure. Table 7 can give an overall view on corrosion-induced cracking. It is worth noting that the maximum crack width reported in the literature so far has been 6 mm [31]. Few models have been developed for predicting width of crack in the literature. Andrade et al. [58], for example, presented a simple formula to predict average width of crack in elements exposed to natural corrosion [59]:(2)
w
=
k
P
x
C
/
ϕ
,where w is the crack width (mm), k is a nondimensional factor, C
/
ϕ is concrete cover/diameter of the bar ratio, and P
x is penetration of the corrosion in time t (year) and equal to(3)
P
x
=
0.0115
r
c
o
r
r
t
,where r
c
o
r
r (mm/year) is the corrosion rate.Table 7
Relationship between crack widths with corrosion obtained from literature.
References
Type of specimen
Time (day)
i
c
o
r
r (μA/cm2)
A
c
o
r
r (%)
Crack width (mm)
[82]
Beam
NS
2000
<4.5
1.3
[83]
Beam
3–15
0.5
2.5–12
0.1–0.75
Bond-pull
500
NS
NS
[58]
Prism
1–100
10, 100
0.5–2.5
0.05–0.5
[84]
Beam
28
0.8–9.2
NS
Bond-pull
1–28
3.6–19.2
0.06–0.46
[74]
Column
106–204
100
9.1–17.8
0.8–4.0
[75]
Beam
100–200
100
10.1–26.3
0.2–0.6
[85]
Slabs
1–2.5
3
1–75
NS
[86]
Beam
126 hours
5
×
10
8
<1
NS
[43]
Prism
68–221
10, 100
NS
0.06–1
[87]
Prism
NS
5 V current
0, 12
0.35, 0.8
[88]
Beam
15–18
1–4
2.5–10
NS
[89]
Beam
16–64 h
3
1.25–5
NS
[31]
Prism
700
Up to 51
0–6
[90]
Prism
815, 766, 380, 306
100, 200, 350, 500
4.38, 7.3, 6.5, 7.26
0.25–1
[91]
Beam
17 years
Saline Environment
26
1.6
Beam
14 years
12
1.8
[92]
Slab
2–9 months
100
NS
0.05–1.5
[93]
T-beam
2–15 years
Average: 0.128
NS
0.31–3.94
Column
2–15 years
NS
0.2–0.51
[94]
Wall spec.
20–56 weeks
R
p = ±20 mV
Up to 6.5%
0.01–1Andrade et al. [59] validated their formula with 15-year-old RC specimens. They proposed k
=
9.5 for their formula. Du et al. [60] showed that both decrease of w/c (water to cement) ratio and increase of cover are important factors to resist cracking due to ingress of chloride. It is clear that rate of corrosion is always an important factor affecting crack-induced corrosion.The relationship between corrosion current density,i
c
o
r
r (mA/m2), and corrosion rate, r
c
o
r
r (μm/year), can be expressed in the following equation [61]:(4)
r
c
o
r
r
=
0.327
M
i
c
o
r
r
n
ρ
,where M (g/mol) is the atomic weight, n is the ion valence, and ρ is the density (g/cm3).Predicting time of corrosion cracking is another important factor in corrosion-induced cracking topic and is used for predicting the service life of corroded RC structures. Predicting the time of corrosion cracking has been addressed by a number of researchers including [55]. In this regard, a few mathematical models have been developed by [62–67]. Figure 5 shows the relationship between percentage of cross section loss in steel bars and crack width (mm) based on the results represented in Table 8. Figure 5 shows increasing percentage loss of cross section due to corrosion raising crack width.Table 8
Corrosion-induced reduction factors of mechanical properties of steel reinforcing.
References
Sample (D); test
Corrosion method and condition
A
c
o
r
r
%
α
y
α
u
α
E
α
ε
u
[95]
Ribbed (8–32);t
Open air (environment)
0–0.5
0.0
0.0
Plain (8–32);t
[96]
Ribbed (12);t
Acc. 0.5–2.0m
A
/
c
m
2
0–11
0.45
0.33
[97]
Bare;t
Open air (environment); Arabian coast
0-1
0.0
0.0
[98]
Ribbed (8); tensile
Acc. 0.5m
A
/
c
m
2
0–28
0.16
0.44
Plain (8); tensile
0.28
0.68
[99]
RC-ribbed (10–25);t
Open air (environment); carbonation
0–67
0.04
0.05
RC-plain (8–14);t
[100]
RC
Open air (environment); chloride
0–25
0.6
0.63
[101]
Ribbed (10); tensile
Acc. 13.0m
A
/
c
m
2
0–25
0.21
NS
[102]
RC beam (6, 12);B
Chlorides; saline environment
0–20∗
NS
NS
3.5
[103]
Rib-RC (8, 16, 32);t
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; tensile
0–25
0.12
0.15
Plain-RC (8, 16);t
0–25
0.49
0.65
[104]
6 mm
Acc. 2.0m
A
/
c
m
2
0–75
1.98∗
∗
NS
4.6
12 mm
0–80
0.74∗
∗
NS
NS
[105]
NS
Open air (Environment); chloride
0–>30
0.00
0.00
[60]
Ribbed (8, 16, 32) and RC; tensile
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; yield force
0–25
1.14–1.28∗
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; ultimate force
0–25
1.22–1.39∗
∗
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; yield strength
0–25
0.16–0.36
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; ultimate strength
0–25
0.26–0.48
Plain (8,16) and RC; tensile
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; yield force
0–25
1.60, 1.48∗
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; ultimate force
0–25
1.71, 1.26∗
∗
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; yield strength
0–25
0.79, 0.58
Acc. 0.5–2.0m
A
/
c
m
2; 3.5% NaCl; ultimate strength
0–25
0.94, 0.44
[77]
RC cube; tensile
Acc. 0.01–0.05m
A
/
c
m
2; cyclic wet-dry
0–3
1.2
1.1
NS
3
RC cylinders;t
Acc. (electric); 5% NaCl
[69]
S400, 10 mm
Salt spray corrosion
1.5–8.5
1.47
1.31
NS
6.97
[68]
RC ribbed (10, 13);t
Accelerated uniform (electric); 3% NaCl
0–35
1.24
1.07
1.75
1.95
RC ribbed (10, 13);t
Acc. pitting (chloride induced); cyclic wet-dry
0–35
1.98
1.57
1.15
2.95
[106]
RC beam; bending
Open air (environment); 1–12 years
0–50
NS
1.97∗
NS
NS
RC beam; bending
Accelerated (electric); 3% NaCl
0–50
NS
1.59∗
NS
NS
Ribbed; tensile
Open air (environment); 1–12 years
0–50
NS
1.41
NS
NS
Ribbed; tensile
Accelerated (electric); 3% NaCl
0–50
NS
1.34
NS
NS
[71]
BS B500B; 10 mm;t
NS
9.5–19.6
1.21
1.38
NS
1.91
[72]
RC plain (6.5 mm);t
Naturally carbonation-induced corroded
14–38
1.12
1.36
NS
NS
RC ribbed (12);t
Acc. 0.1m
A
/
c
m
2; 5% NaCl
4–28
1.1
1.22
NS
NS
∗ indicates factor associated with yield force.
∗
∗ indicates reduction factor associated with ultimate force.Figure 5
Crack width versus percentage loss of cross section regresses from results represented in Table8.The reason for rising crack width with corrosion percentage is that more corrosion by-products in higher level of corrosion lead to increase of crack width.


## 2.5. Research Gaps

The main research gaps in chloride-induced corrosion can be summarized as follows:(i)
More accurate value of critical content of chloride concentration for real RC structures.
(ii)
Factors and their effects on the critical content of chloride.
(iii)
Robust pitting factors for real corroded structures.
(iv)
Factors and their effects on corrosion rate and time of initiation.
(v)
Robust corrosion rate and time of initiation prediction.
(vi)
More accurate values volume expansion for corrosion by-product and rust components, especially for real corroded RC structures.Research studies aiming to fill the above research gaps will lead to decrease of uncertainties in estimation of chloride-induced corrosion.


## 3. Corrosion-Induced Deterioration of RC Structures

As discussed earlier, the two main outcomes of corrosion are decreasing cross section area of steel reinforcement and volumetric expansion caused by corrosion by-products. As a result, mechanical properties of steel reinforcement such as modules of elasticity, force, stress and strain at yield, and ultimate points alter with corrosion. Regarding cyclic behavior of steel reinforcement, in particular, corrosion changes energy dissipating characteristic and number of cycles needed for failure. Bond between concrete and steel varies in corroded reinforced concrete members. The stress-strain model of confined concrete in compression region is affected by corrosion and maximum compression stress of concrete decreases because of cracks propagated into concrete cover due to corrosion. Up to date, there is no experimental study showing the effects of corrosion on stress-strain relationship on RC columns. It is worth noting that the similar experimental study is in progress by authors. Therefore, materials characteristics of corroded reinforced concrete members have to be applied for analyses and simulations of corroded structures.


### 3.1. Effect of Corrosion on Mechanical Properties of Steel Reinforcing

Irregular decreases in cross-sectional area of steel reinforcing cause changes in mechanical properties of reinforcements. A number of monotonic tensile tests on bare bars and RC elements and bending tests on RC beams and slabs have been carried out to estimate the reduction factors corresponding to the mechanical properties. Reduction factors indicate the percentage of reductions in mechanical properties that will happen for 1% reduction in cross section, and they have been estimated from experimental results and reported by past studies. In this paper, a survey on 18 experimental works has been done and the results and references have been presented in Table8. The following investigated mechanical properties were included: yield and ultimate (stress or force) strength, elongation, and module of elasticity. Equations (5)–(10) are typical models regressed from experimental data used by past studies that can be used to calculate mechanical properties of corroded steel reinforcements: (5)
σ
y
c
=
100
-
α
y
×
A
c
o
r
r
%
σ
y
,
(6)
σ
u
c
=
100
-
α
u
×
A
c
o
r
r
%
σ
u
,
(7)
E
s
c
=
100
-
α
E
×
A
c
o
r
r
%
E
s
,
(8)
δ
s
c
=
100
-
α
ε
u
×
A
c
o
r
r
%
δ
s
,
(9)
F
y
c
=
100
-
α
y
∗
×
A
c
o
r
r
%
F
y
,
(10)
F
u
c
=
100
-
α
u
∗
∗
×
A
c
o
r
r
%
F
u
,where σ
y
c, σ
u
c, E
s
c, δ
s
c, F
y
c, and F
u
c are yield stress, ultimate stress, module of elasticity, elongation, yield force, and ultimate force of corroded bars, respectively, α
y, α
u, α
E, α
ε
u, α
y
∗, and α
u
∗
∗ are their associated reduction factors, A
c
o
r
r
% is the percentage loss of cross section, and σ
y, σ
u, E
s, δ
s, F
y, and F
u are yield stress, ultimate stress, module of elasticity, elongation, yield force, and ultimate force of noncorroded bars.While the results presented in the literature have a wide variation, some conclusions reported by the above reviewed references are as follows:(i)
Very low corrosion may not affect the mechanical properties of the steel reinforcing.
(ii)
Usually, reduction factors for environment corrosion and plain steel reinforcement are higher than accelerated corrosion and deformed steel reinforcement.
(iii)
The greatest reduction factor is related to elongation. This is very important for seismic behavior of RC structures.
(iv)
Usually, pitting corrosion and irregularities in corrosion increase the reduction factors. On the other hand, reduction factors for pitting corrosion are greater than those for general corrosion [68].
(v)
The reduction factors for corroded bare steel reinforcement and those corroded while embedded in concrete are similar [60].
(vi)
The effects of the type (plain or deformed type) and diameter of reinforcing steels on reduction factors can be neglected [60].To illustrate the variation of the published reduction factors, the minimum and maximum reduction factors of four mechanical properties of steel reinforcement based on the data represented in Table8 are shown in Figure 6. The mechanical properties include elongation, modulus of elasticity (E), yield stress, and ultimate stress. Since linear regression has been employed by all past studies to estimate reduction factors, the minimum and maximum reduction factors shown in Figure 6 are represented based on linear regression.Figure 6
Maximum and minimum reduction factors for elongation, modulus of elasticity, yield stress, and ultimate stress.Figure6 shows that corrosion deteriorates the mechanical properties of reinforcing steel. However, there are big variations in results published in the literature based on monotonic tests. The results also show that the maximum reduction factors and the greatest difference between minimum and maximum reduction factors have been reported for elongation.A few number of studies identified cyclic behavior of corroded steel reinforcements. Apostolopoulos and Papadopoulos [69] have shown that a mass loss less than 2% and 3% causes 22% and 47% reduction to the number of maximum cycles required for rupture, respectively. Apostolopoulos and Pasialis [70] have studied the low cycle fatigue behavior of smooth and ribbed steel reinforcement for different degrees of corrosion. They have reported that smooth bars showed a better cyclic behavior than that of ribbed bars for low strain amplitude and up to 8% loss of mass due to corrosion. On the other hand, smooth bars can dissipate more energy and need higher number of cycles to fail in low strain magnitude (±
1
%) than those of ribbed bars. These advantages disappear as strain amplitude increases. Hawileh et al. [71] studied the effect of corrosion on cyclic behavior of BS B500B bars. They have demonstrated that corrosion decreases low cycle fatigue life of the bars. They have pointed out that lower strain amplitude (±
4
%) causes more reduction in dissipating energy and more cycles are needed for failure than those of higher strain amplitude (±
6
%). Zhang et al. [72] have found that increasing the degree of corrosion causes reduction in fatigue life of corroded bars. They also have claimed that the impact of corrosion on fatigue behavior and naturally corroded steel bar is more than that on monotonic behavior and artificially corroded steel bar, respectively.


### 3.2. The Effects of Corrosion on Bond Strength between Steel and Concrete

Table9 shows the effect of the percentage of corrosion on bond strength based on 16 experimental works reviewed by the authors. As an overall trend, low corrosion percentage increases the bond strength, while high percentage of corrosion always decreases the bond strength. Type of steel bars and confinement are the important factors that influence the change of bond strength due to corrosion. In spite of the above general trends, the variation is very high indicating the significance of further investigation in this area. Since chloride-induced corrosion is a function of concrete cover and stirrups always have less cover than longitudinal bars, further research should be performed to consider this problem that to the best of the authors’ knowledge there is no report on in the literature. Moreover, high level of corrosion causes a critical reduction in bond under cyclic loading, while corrosion under 5% increases bond capacity [114]. It has been reported that confinement efficiently decreases bond degradation under cyclic loading [114].Table 9
Effect of corrosion on bond strength between concrete and steel reinforcement.
Authors and date
Sample (D); test
Corrosion method
Time exposure
A
c
o
r
r
%
Bond strength; % of change
[82]
14 mm bending
2000μ
A
/
c
m
2
NS
0.55
↑; 40
10 mm pullout
0.55
↑; 42
10 mm pullout
3.5–7.4
↓; 0–66
14 mm pullout
0.65
↑; 28
14 mm pullout
2.6–5.7
↓; 0–65
20 mm pullout
0.43
↑; 25
20 mm pullout
1.6–4
↓; 0–47
[107]
12 mm, pullout
0.4 A current electric
NS
<4
↑; 17
5–7
↓; 30–69
8–12
↓; 70–78
12–80
↓; 78–86
[84]
12 mm, pullout
2–64 A current electric
<28 days
0.7
↑; 18
2.42, 12
↓; 5, 60
[108]
19 mm, pullout
Saturated in Ca(OH)2
<5 weeks
NS
↑; NS
>5 weeks
NS
↓; NS
[5]
10 mm, bending
0.1 A current electric
21–63 days
20
↓; 74
[6]
19 mm, pullout
12 A current electric
>3 days
0–5.2
↓; 78
[7]
13 mm, pullout
1 A current electric
NS
3
↓; 35
NS
16.8
↓; 77
NS
13∗
↓; 13
NS
24∗
↓; 38
[109]
10 mm, pullout, 15 mm cover specimen
140μ
A
/
c
m
2
NS
5
↑; ≅15
10
↓; ≅35
[110]
10 mm, bending
12 A current electric
NS
2
↑; 30
2.8, 15
↓; 0, 77
[111]
Deformed pullout
0–2 A current electric
10–12 days
4, 9
↓; 45, 68
Deformed pullout
3.8∗, 6∗
↓; 4, 12
Smooth, pullout
3.3
↑; 21
[8]
20 mm, pullout
0–2 A current electric
NS
4
↓; 45
3.8∗
↓; 5
[112]
20 mm, pullout
500μ
A
/
c
m
2
8–48 h
0.2, 0.36
↑; 50, 20
56–96 h
0.4, 0.76
↓; 20, 84
Berto et al. [9]
10 mm, pullout
NS
NS
4.27
↓; 12
7.8
↓; 75
Chung et al. [113]
13 mm, pullout
12 A current electric
>3 days
<3
↑; 40
3–7
↓; 27
Kivell [10]
Deformed, 20 mm pullout
0.1 A current electric
10–50 days
0.6∗, 11∗
↓; 6, 50
20∗
↓; 76
Def. 20 mm cyclic
18.6∗
↓; 59
↓
↑ indicates decreasing and increasing bond strength of corroded bar in comparison with sound bar; ∗ indicates confined reinforced concrete. It should be noted that increasing cycles also cause a reduction in bond strength.The information collected in Table9 has been graphically presented in Figure 7. Figure 7, therefore, shows bond strength of corroded to noncorroded steel reinforcement ratio over corrosion percentage based on past published experimental studies. The data have been classified into two groups including confined and unconfined RC samples.Figure 7
The relationship between bond strength of corroded to noncorroded reinforcing steels and corrosion for confined and unconfined RC samples based on collected experimental results.


### 3.3. The Effects of Corrosion on Stress-Strain Model of Confined Concrete

As far as confinement is concerned, corrosion of lateral steel bars alters confinement properties of reinforced concrete members. However, there is no evidence indicating how the stress-strain model of a confined concrete changes due to corrosion. Mander et al. [115] stated that “confinement is defined as sufficient lateral reinforcement in the form of the circular or rectangular arrangement of steel.” They also stated that “the aim is to confine reinforced concrete members under compression to avoid the buckling of longitudinal bars, and to prevent shear failure.” Confinement is a critical factor in plastic hinge region, because it ensures the ductility capacity demanded in seismic events. Transversal steel reinforcements are the closest steel bars to the surface of RC members. Therefore, they are corroded more severely than longitudinal bars. The effect of corrosion on confinement is very rare and only one report [116] was found on this subject in the literature. Ou et al. [116] analytically calculated confining strength ratio based on corroded steel reinforcing and ultimate strain of confined concrete based on reduction in mechanical properties of reinforcing steels. It is clear that further investigation is needed in this area. A study in this area is in progress by authors at the University of Canterbury.


### 3.4. The Effects of Corrosion on Concrete Strength of Reinforced Concrete Structures

As discussed earlier, corrosion causes propagating cracks into concrete core, influencing compression and tensile strength of concrete material. A few studies have identified the effects of cracks on tensile and compression strength of concrete materials. Vecchio and Collins [117], for example, presented the following equation that addresses the effect of cracks on the compressive strength of concrete:(11)
f
c
∗
=
f
c
0.8
-
0.34
ε
1
/
ε
c
,where f
c
∗ is compression stress of cracked concrete, f
c is maximum compression stress of noncracked concrete, and ε
1
/
ε
c is the ratio of principle tensile strain to maximum strain corresponding to maximum compression stress (f
c). It is clear that ε
1
/
ε
c is negative.The above equation has been improved by the following research studies [118, 119].Further investigation is critically needed to identify the effects of corrosion on concrete cracks and consequent concrete strength.


### 3.5. Time-Dependent Deterioration Models for Reinforced Concrete Members

Corrosion and consequent degradation are time-dependent. Therefore, deterioration models are time variant mathematical equations showing relationships between the deteriorated mechanical properties and time. For example, with replacement ofA
c
o
r
r with an equation showing relationship between A
c
o
r
r and time, (4) to (9) will be time-dependent deterioration models for mechanical properties of reinforcing steels.There are two different types of deterioration models for RC structures called macro model and micro model. The macro deterioration model has been developed based on growing micro cracks. Growing micro cracks lead to macro cracks and also to accelerated ingress of aggressive ions [120, 121].The micro deterioration model frequently used in the literature has been developed based on three models including transport model of aggressive ions, electrochemical model of corrosion, and structural model. The structural model can be developed corresponding to decrease of dimension, reduction in strength, or increase of cracks [121]. Fick’s second law of diffusion is used for ion transport model [24]. There are a few studies that have been developed on the degradation of reinforced concrete structures due to corrosion [3, 122–124].


### 3.6. Main Research Gaps

The main research gaps in corrosion-induced deterioration of RC structures can be summarized as follows:(i)
Robust deterioration model for corroded steel reinforcement considering cyclic behavior of steel reinforcement in seismic events.
(ii)
Robust deterioration model to predict bond between steel and concrete in corroded RC structures.
(iii)
Corrosion-induced stress-strain model of confined concrete.
(iv)
Corrosion influencing compression strength of concrete.


## 3.1. Effect of Corrosion on Mechanical Properties of Steel Reinforcing

Irregular decreases in cross-sectional area of steel reinforcing cause changes in mechanical properties of reinforcements. A number of monotonic tensile tests on bare bars and RC elements and bending tests on RC beams and slabs have been carried out to estimate the reduction factors corresponding to the mechanical properties. Reduction factors indicate the percentage of reductions in mechanical properties that will happen for 1% reduction in cross section, and they have been estimated from experimental results and reported by past studies. In this paper, a survey on 18 experimental works has been done and the results and references have been presented in Table8. The following investigated mechanical properties were included: yield and ultimate (stress or force) strength, elongation, and module of elasticity. Equations (5)–(10) are typical models regressed from experimental data used by past studies that can be used to calculate mechanical properties of corroded steel reinforcements: (5)
σ
y
c
=
100
-
α
y
×
A
c
o
r
r
%
σ
y
,
(6)
σ
u
c
=
100
-
α
u
×
A
c
o
r
r
%
σ
u
,
(7)
E
s
c
=
100
-
α
E
×
A
c
o
r
r
%
E
s
,
(8)
δ
s
c
=
100
-
α
ε
u
×
A
c
o
r
r
%
δ
s
,
(9)
F
y
c
=
100
-
α
y
∗
×
A
c
o
r
r
%
F
y
,
(10)
F
u
c
=
100
-
α
u
∗
∗
×
A
c
o
r
r
%
F
u
,where σ
y
c, σ
u
c, E
s
c, δ
s
c, F
y
c, and F
u
c are yield stress, ultimate stress, module of elasticity, elongation, yield force, and ultimate force of corroded bars, respectively, α
y, α
u, α
E, α
ε
u, α
y
∗, and α
u
∗
∗ are their associated reduction factors, A
c
o
r
r
% is the percentage loss of cross section, and σ
y, σ
u, E
s, δ
s, F
y, and F
u are yield stress, ultimate stress, module of elasticity, elongation, yield force, and ultimate force of noncorroded bars.While the results presented in the literature have a wide variation, some conclusions reported by the above reviewed references are as follows:(i)
Very low corrosion may not affect the mechanical properties of the steel reinforcing.
(ii)
Usually, reduction factors for environment corrosion and plain steel reinforcement are higher than accelerated corrosion and deformed steel reinforcement.
(iii)
The greatest reduction factor is related to elongation. This is very important for seismic behavior of RC structures.
(iv)
Usually, pitting corrosion and irregularities in corrosion increase the reduction factors. On the other hand, reduction factors for pitting corrosion are greater than those for general corrosion [68].
(v)
The reduction factors for corroded bare steel reinforcement and those corroded while embedded in concrete are similar [60].
(vi)
The effects of the type (plain or deformed type) and diameter of reinforcing steels on reduction factors can be neglected [60].To illustrate the variation of the published reduction factors, the minimum and maximum reduction factors of four mechanical properties of steel reinforcement based on the data represented in Table8 are shown in Figure 6. The mechanical properties include elongation, modulus of elasticity (E), yield stress, and ultimate stress. Since linear regression has been employed by all past studies to estimate reduction factors, the minimum and maximum reduction factors shown in Figure 6 are represented based on linear regression.Figure 6
Maximum and minimum reduction factors for elongation, modulus of elasticity, yield stress, and ultimate stress.Figure6 shows that corrosion deteriorates the mechanical properties of reinforcing steel. However, there are big variations in results published in the literature based on monotonic tests. The results also show that the maximum reduction factors and the greatest difference between minimum and maximum reduction factors have been reported for elongation.A few number of studies identified cyclic behavior of corroded steel reinforcements. Apostolopoulos and Papadopoulos [69] have shown that a mass loss less than 2% and 3% causes 22% and 47% reduction to the number of maximum cycles required for rupture, respectively. Apostolopoulos and Pasialis [70] have studied the low cycle fatigue behavior of smooth and ribbed steel reinforcement for different degrees of corrosion. They have reported that smooth bars showed a better cyclic behavior than that of ribbed bars for low strain amplitude and up to 8% loss of mass due to corrosion. On the other hand, smooth bars can dissipate more energy and need higher number of cycles to fail in low strain magnitude (±
1
%) than those of ribbed bars. These advantages disappear as strain amplitude increases. Hawileh et al. [71] studied the effect of corrosion on cyclic behavior of BS B500B bars. They have demonstrated that corrosion decreases low cycle fatigue life of the bars. They have pointed out that lower strain amplitude (±
4
%) causes more reduction in dissipating energy and more cycles are needed for failure than those of higher strain amplitude (±
6
%). Zhang et al. [72] have found that increasing the degree of corrosion causes reduction in fatigue life of corroded bars. They also have claimed that the impact of corrosion on fatigue behavior and naturally corroded steel bar is more than that on monotonic behavior and artificially corroded steel bar, respectively.


## 3.2. The Effects of Corrosion on Bond Strength between Steel and Concrete

Table9 shows the effect of the percentage of corrosion on bond strength based on 16 experimental works reviewed by the authors. As an overall trend, low corrosion percentage increases the bond strength, while high percentage of corrosion always decreases the bond strength. Type of steel bars and confinement are the important factors that influence the change of bond strength due to corrosion. In spite of the above general trends, the variation is very high indicating the significance of further investigation in this area. Since chloride-induced corrosion is a function of concrete cover and stirrups always have less cover than longitudinal bars, further research should be performed to consider this problem that to the best of the authors’ knowledge there is no report on in the literature. Moreover, high level of corrosion causes a critical reduction in bond under cyclic loading, while corrosion under 5% increases bond capacity [114]. It has been reported that confinement efficiently decreases bond degradation under cyclic loading [114].Table 9
Effect of corrosion on bond strength between concrete and steel reinforcement.
Authors and date
Sample (D); test
Corrosion method
Time exposure
A
c
o
r
r
%
Bond strength; % of change
[82]
14 mm bending
2000μ
A
/
c
m
2
NS
0.55
↑; 40
10 mm pullout
0.55
↑; 42
10 mm pullout
3.5–7.4
↓; 0–66
14 mm pullout
0.65
↑; 28
14 mm pullout
2.6–5.7
↓; 0–65
20 mm pullout
0.43
↑; 25
20 mm pullout
1.6–4
↓; 0–47
[107]
12 mm, pullout
0.4 A current electric
NS
<4
↑; 17
5–7
↓; 30–69
8–12
↓; 70–78
12–80
↓; 78–86
[84]
12 mm, pullout
2–64 A current electric
<28 days
0.7
↑; 18
2.42, 12
↓; 5, 60
[108]
19 mm, pullout
Saturated in Ca(OH)2
<5 weeks
NS
↑; NS
>5 weeks
NS
↓; NS
[5]
10 mm, bending
0.1 A current electric
21–63 days
20
↓; 74
[6]
19 mm, pullout
12 A current electric
>3 days
0–5.2
↓; 78
[7]
13 mm, pullout
1 A current electric
NS
3
↓; 35
NS
16.8
↓; 77
NS
13∗
↓; 13
NS
24∗
↓; 38
[109]
10 mm, pullout, 15 mm cover specimen
140μ
A
/
c
m
2
NS
5
↑; ≅15
10
↓; ≅35
[110]
10 mm, bending
12 A current electric
NS
2
↑; 30
2.8, 15
↓; 0, 77
[111]
Deformed pullout
0–2 A current electric
10–12 days
4, 9
↓; 45, 68
Deformed pullout
3.8∗, 6∗
↓; 4, 12
Smooth, pullout
3.3
↑; 21
[8]
20 mm, pullout
0–2 A current electric
NS
4
↓; 45
3.8∗
↓; 5
[112]
20 mm, pullout
500μ
A
/
c
m
2
8–48 h
0.2, 0.36
↑; 50, 20
56–96 h
0.4, 0.76
↓; 20, 84
Berto et al. [9]
10 mm, pullout
NS
NS
4.27
↓; 12
7.8
↓; 75
Chung et al. [113]
13 mm, pullout
12 A current electric
>3 days
<3
↑; 40
3–7
↓; 27
Kivell [10]
Deformed, 20 mm pullout
0.1 A current electric
10–50 days
0.6∗, 11∗
↓; 6, 50
20∗
↓; 76
Def. 20 mm cyclic
18.6∗
↓; 59
↓
↑ indicates decreasing and increasing bond strength of corroded bar in comparison with sound bar; ∗ indicates confined reinforced concrete. It should be noted that increasing cycles also cause a reduction in bond strength.The information collected in Table9 has been graphically presented in Figure 7. Figure 7, therefore, shows bond strength of corroded to noncorroded steel reinforcement ratio over corrosion percentage based on past published experimental studies. The data have been classified into two groups including confined and unconfined RC samples.Figure 7
The relationship between bond strength of corroded to noncorroded reinforcing steels and corrosion for confined and unconfined RC samples based on collected experimental results.


## 3.3. The Effects of Corrosion on Stress-Strain Model of Confined Concrete

As far as confinement is concerned, corrosion of lateral steel bars alters confinement properties of reinforced concrete members. However, there is no evidence indicating how the stress-strain model of a confined concrete changes due to corrosion. Mander et al. [115] stated that “confinement is defined as sufficient lateral reinforcement in the form of the circular or rectangular arrangement of steel.” They also stated that “the aim is to confine reinforced concrete members under compression to avoid the buckling of longitudinal bars, and to prevent shear failure.” Confinement is a critical factor in plastic hinge region, because it ensures the ductility capacity demanded in seismic events. Transversal steel reinforcements are the closest steel bars to the surface of RC members. Therefore, they are corroded more severely than longitudinal bars. The effect of corrosion on confinement is very rare and only one report [116] was found on this subject in the literature. Ou et al. [116] analytically calculated confining strength ratio based on corroded steel reinforcing and ultimate strain of confined concrete based on reduction in mechanical properties of reinforcing steels. It is clear that further investigation is needed in this area. A study in this area is in progress by authors at the University of Canterbury.


## 3.4. The Effects of Corrosion on Concrete Strength of Reinforced Concrete Structures

As discussed earlier, corrosion causes propagating cracks into concrete core, influencing compression and tensile strength of concrete material. A few studies have identified the effects of cracks on tensile and compression strength of concrete materials. Vecchio and Collins [117], for example, presented the following equation that addresses the effect of cracks on the compressive strength of concrete:(11)
f
c
∗
=
f
c
0.8
-
0.34
ε
1
/
ε
c
,where f
c
∗ is compression stress of cracked concrete, f
c is maximum compression stress of noncracked concrete, and ε
1
/
ε
c is the ratio of principle tensile strain to maximum strain corresponding to maximum compression stress (f
c). It is clear that ε
1
/
ε
c is negative.The above equation has been improved by the following research studies [118, 119].Further investigation is critically needed to identify the effects of corrosion on concrete cracks and consequent concrete strength.


## 3.5. Time-Dependent Deterioration Models for Reinforced Concrete Members

Corrosion and consequent degradation are time-dependent. Therefore, deterioration models are time variant mathematical equations showing relationships between the deteriorated mechanical properties and time. For example, with replacement ofA
c
o
r
r with an equation showing relationship between A
c
o
r
r and time, (4) to (9) will be time-dependent deterioration models for mechanical properties of reinforcing steels.There are two different types of deterioration models for RC structures called macro model and micro model. The macro deterioration model has been developed based on growing micro cracks. Growing micro cracks lead to macro cracks and also to accelerated ingress of aggressive ions [120, 121].The micro deterioration model frequently used in the literature has been developed based on three models including transport model of aggressive ions, electrochemical model of corrosion, and structural model. The structural model can be developed corresponding to decrease of dimension, reduction in strength, or increase of cracks [121]. Fick’s second law of diffusion is used for ion transport model [24]. There are a few studies that have been developed on the degradation of reinforced concrete structures due to corrosion [3, 122–124].


## 3.6. Main Research Gaps

The main research gaps in corrosion-induced deterioration of RC structures can be summarized as follows:(i)
Robust deterioration model for corroded steel reinforcement considering cyclic behavior of steel reinforcement in seismic events.
(ii)
Robust deterioration model to predict bond between steel and concrete in corroded RC structures.
(iii)
Corrosion-induced stress-strain model of confined concrete.
(iv)
Corrosion influencing compression strength of concrete.


## 4. Evaluation of Seismic Performance of Corroded Reinforced Concrete Bridge Piers

According to what has been discussed so far, corrosion degrades mechanical and structural characteristics leading to negative impact on seismic performance of RC structures. Bridge piers are earthquake-resistant elements of bridges. Therefore, assessing seismic performance of bridge piers exposed to corrosion is very important. Numerical simulation of corroded bridge piers is very complicated, and a number of uncertainties have limited utilizing the numerical simulation. On the other hand, both numerical and experimental investigations are needed for a comprehensive study on long-term seismic performance of corroded bridge piers. A number of studies have developed methods and formulations to predict initiation and propagation time of corrosion, corrosion cracking time, time of breaking of bond between steel and concrete, minimum load carry capacity, maximum deformation, maximum permeability, or failure probability [55, 125–130]. Then, developing methodologies for performance-based earthquake engineering and developing seismic fragility of bridges made a basis to evaluate seismic performance of RC bridges and other structures using fragility curves based on probability of failure [131–137]. The seismic performance assessment using fragility function can be applied for either a member or the whole bridge structure. Recently, Akiyama and Frangopol [138] have presented a procedure to estimate life-cycle seismic reliability of corroded bridge piers based on integration of probabilistic assessment of seismic and airborne chloride hazard. Ou et al. [116] have developed a simple seismic evaluation of corroded RC bridges based on nonlinear static pushover analysis. They have presented seismic capacity and demand of the RC bridges in terms of peak ground acceleration (PGA). Actually, the number of years that the seismic demand (collapse PGA) becomes greater than the seismic capacity (design PGA) has been calculated for real RC bridges.However, as mentioned earlier, difficulties and uncertainties in numerical simulation of RC bridge piers subjected to corrosion and seismic hazards indicate critical needs for further investigation, and advanced numerical methods are needed in this content. The next generations of numerical methods to evaluate seismic performance of corroded RC bridge piers are possibly as follows:(i)
Developing a new formulation of finite element methods based on fiber element or fiber beam method [139].
(ii)
Real-time signal processing and finite element model updating of existing bridges based on vibration and corrosion potential measurements.
(iii)
Artificial intelligence methods such as genetic algorithm [140].


### 4.1. Numerical Methods to Simulate Degradation of Reinforced Concrete Bridge Piers Exposed to Corrosion

Numerical methods to simulate seismic behavior of RC bridge piers exposed to corrosion can be classified into three groups including cross section, member, and system level analysis. This classification is similar to the one applied for noncorroded RC bridge piers. The integration of nonlinear analysis and finite element method is a popular numerical method that has been used for corroded and noncorroded RC bridge piers [140–143]. According to the literature, remarkable results obtained from numerical simulations of seismic behavior of bridges with corroded RC piers can be summarized as follows:(i)
Corrosion alters mechanism of collapse [143].
(ii)
Corrosion decreases load carrying capacity due to increasing seismic demand and decreasing seismic capacity leading to increase of probability of failure [144–146].
(iii)
Corrosion increases uncertainty in probabilistic model-based analysis models [147].Cross section level analysis is probably the oldest numerical method among the three methods used to simulate deterioration of RC bridge piers. Corrosion causes damage to concrete material and bond between steel and concrete leading to loss in section ductility. The loss of section ductility can be calculated using moment-curvature analysis [148, 149]. There are some studies where degradation of RC bridge piers caused by corrosion has been investigated using moment-curvature analysis of cross section. Seismic capacity of corroded cross section can also be achieved using the cross section level analysis [143, 145, 150, 151].Member level analysis is a numerical method providing an opportunity to evaluate the seismic performance of whole corroded bridge piers. Finite element formulation is used to simulate seismic behavior of a corroded bridge pier. To this aim, a relationship, for example, between lateral force and displacement is developed [152]. The simulation should take into consideration deterioration models to simulate degradation due to corrosion. Failure modes and seismic response of corroded RC bridge piers can be obtained from the member level analysis.System level analysis is aiming to assess dynamic response of a corroded bridge exposed to ground motions. There are a number of studies in the literature where the system level analysis of corroded bridges has been done using fragility estimation [124, 144–146, 153]. However, Lv et al. [142], for example, have evaluated the effects of corrosion on seismic performance of curved beam with height piers using time-history analysis of the bridge finite element model. They found that corrosion deteriorates the seismic performance of the bridge, and two main factors including pier-height and pier-corrosion are responsible for increasing plastic strain.


### 4.2. Large Scale Experimental Tests to Evaluate Seismic Performance of Corroded Bridge Piers

As mentioned earlier, numerical simulations of corroded bridge piers are very complicated and they probably cannot capture all the effects of corrosion on seismic performance of bridge piers. Therefore, large scale experimental tests need to assess seismic performance of corroded bridge piers. Some studies have been reported on the effects of corrosion on cyclic behavior of RC columns [154, 155]. However, according to the best knowledge of the authors, large scale seismic experimental test on corroded bridge piers is rare and only one case [139] was found in the literature. Dietz et al. [139] designed a reinforced concrete bridge pier to EC2. They corroded the bridge pier using accelerated corrosion technique by ponding a part of the pier in NaCl solution for 6 months. The corroded bridge pier was then subjected to lateral cyclic loading up to 50 KN using a hydraulic actuator. They measured deflection at the top, rotation at the base, strains in the concrete and steel bars, and width of cracks. From a structural point of view, the bridge pier rigidly connected to the foundation is high damage system because formation of plastic hinge at the end(s) of the pier is the mechanism of dissipating energy in seismic events. The high damage system is the traditional seismic resistant system that has been criticized by past studies because of high repair time and cost and problems arising from traffic interruption [156].


### 4.3. Seismic, Structural, and Durability Behavior of Repaired Bridge Piers Exposed to Corrosion-Induced Damage

The need for retrofit of corroded bridge piers has been addressed by past studies. There is a traditional method to rehabilitate corroded bridge pier that includes two stages: first, all critically corroded areas should be removed; then, an overlay of materials with low-permeability has been used [157, 158]. Gergely et al. [159] rehabilitated corroded bridge pier samples using fiber-reinforced plastic composites. They compared seismic performance of the piers through numerical and large scale experimental tests and found that shear capacity and ductility have been improved significantly. However, to simulate the effect of corrosion on steel reinforcement, they cut three stirrup loops of column and three stirrup loops of each side of the cap-beam near the joint. They noted that an advantage of using FRP composite is that it does not increase weight of column. Toutanji [160] has found that the confinement provided by FRP warps improves compression strength and ductility of RC columns. However, durability is affected by the type of epoxy used. Demers and Neale [161] have showed that the type of FRP influences ductility and strength of RC columns. Pantazopoulou et al. [162] compared alternative methods to assess seismic performance of repaired corroded bridge piers using external fiber-reinforced polymer (FRP) wraps. They stated that the best repair strategy in terms of postrepair corrosion, strength recovery, and ductility was cleaning the damaged surface (without removal of materials) and then jacketing using layers of FRP. However, further experiments are needed to confirm the efficiency of the proposed strategy in practice. Baiyasi and Harichandran [163] have concluded that a greater amount of glass fiber than carbon fiber was needed to achieve the equivalent structural performance of postcorrosion repair. Teng et al. [164] have reported that while FRP increases durability characteristics of RC columns, it possibly has some negative impacts on mechanical properties of the RC columns. A number of studies have revealed that FRP does not fully stop chloride-induced corrosion but decreases the rate of corrosion [162, 163, 165–173]. To answer an important question of what the best strategy is to repair corroded bridge pier using FRP, Sen [169] stated that the best strategy to protect concrete columns against chloride-induced corrosion is applying FRP jackets and filling gaps between the column and jackets using epoxy so that the following conditions are satisfied:(i)
Applying FRP jacket over the full length when no visible corrosion-induced sign can be found.
(ii)
Utilizing appropriate epoxy as a surface corrosion barrier and filling gap between the column and jacket.
(iii)
Utilizing at least two layers of FRP.Sen [169] has argued that confined concrete by FRP warps changes corrosion diffusion. He also has recommended not using FRP warps before visible corrosion sign to minimize repair cost. Wootton et al. [170] have concluded that FRP warps protect the RC columns better than epoxy alone. It has been shown that low amount of corrosion (up to 4.2%) does not influence eccentric load carrying capacity of RC columns, and the strength of damaged columns fully warped with carbon FRP was higher than undamaged columns. The performance of full length covered by CFRP was better than that partially covered by CFRP [174]. Li et al. [175] have analyzed seismic performance of corroded RC columns confined by FRP and steel jacket. They showed that FRP and steel jacket enhance the seismic performance of RC columns, and applying both jackets improves seismic performance better than applying one alone. A recent survey carried out on corroded RC bridges in New York State emphasized the demand for retrofitting corroded RC bridge columns, in particular, corroded lap-splice, to decrease possible damage in future seismic events [176].


### 4.4. Development in Time-Dependent Seismic Evaluation of Corroded RC Bridge Piers Reported in the Literature

Traditional structural analysis is not able to analyze systems and structures under multiple time-invariant hazards. A time-dependent analysis during lifetime, therefore, is needed to take into consideration all hazards. In case of RC structures (in particular RC bridge pier) subjected to corrosion and earthquake, two hazards are corrosion-induced deterioration and seismic events. There are some studies in the literature, mainly published in recent years, showing that corrosion influences the seismic performance of bridge piers over time. However, different criteria have been used by past studies. Biondini et al. [151], for example, have presented time-dependent bending moment resistance of a bridge pier exposed to corrosion. They have shown that the bending moment resistance of the corroded bridge pier decreased over time. Time-dependent deformation capacity, drift ratio demand, shear capacity, and demand of a corroded bridge pier have been studied [93, 124, 144]. Time-dependent probability of failure (time-dependent fragility analysis) of corroded bridge piers has been developed by past studies that can be directly used for seismic analysis purposes [93, 124, 144, 145, 177, 178]. Moreover, a fragility increment function has been developed that is a function of time and given deformation or shear demand and can be used to predict fragility of corroded bridge piers in life-cycle analysis and risk assessment [147, 178].


### 4.5. Research Gaps

The main research gaps in evaluation of seismic performance of corroded reinforced concrete bridge piers can be summarized as follows:(i)
Robust numerical modelling of corroded bridge piers.
(ii)
Large scale experimental tests on seismic behavior of corroded bridge piers and bridge structures (half scale and full scale tests).
(iii)
Experimental tests on efficiency of repair methods used for corroded bridge piers.
(iv)
Robust numerical model to evaluate time-dependent seismic performance of RC bridges exposed to corrosion.


## 4.1. Numerical Methods to Simulate Degradation of Reinforced Concrete Bridge Piers Exposed to Corrosion

Numerical methods to simulate seismic behavior of RC bridge piers exposed to corrosion can be classified into three groups including cross section, member, and system level analysis. This classification is similar to the one applied for noncorroded RC bridge piers. The integration of nonlinear analysis and finite element method is a popular numerical method that has been used for corroded and noncorroded RC bridge piers [140–143]. According to the literature, remarkable results obtained from numerical simulations of seismic behavior of bridges with corroded RC piers can be summarized as follows:(i)
Corrosion alters mechanism of collapse [143].
(ii)
Corrosion decreases load carrying capacity due to increasing seismic demand and decreasing seismic capacity leading to increase of probability of failure [144–146].
(iii)
Corrosion increases uncertainty in probabilistic model-based analysis models [147].Cross section level analysis is probably the oldest numerical method among the three methods used to simulate deterioration of RC bridge piers. Corrosion causes damage to concrete material and bond between steel and concrete leading to loss in section ductility. The loss of section ductility can be calculated using moment-curvature analysis [148, 149]. There are some studies where degradation of RC bridge piers caused by corrosion has been investigated using moment-curvature analysis of cross section. Seismic capacity of corroded cross section can also be achieved using the cross section level analysis [143, 145, 150, 151].Member level analysis is a numerical method providing an opportunity to evaluate the seismic performance of whole corroded bridge piers. Finite element formulation is used to simulate seismic behavior of a corroded bridge pier. To this aim, a relationship, for example, between lateral force and displacement is developed [152]. The simulation should take into consideration deterioration models to simulate degradation due to corrosion. Failure modes and seismic response of corroded RC bridge piers can be obtained from the member level analysis.System level analysis is aiming to assess dynamic response of a corroded bridge exposed to ground motions. There are a number of studies in the literature where the system level analysis of corroded bridges has been done using fragility estimation [124, 144–146, 153]. However, Lv et al. [142], for example, have evaluated the effects of corrosion on seismic performance of curved beam with height piers using time-history analysis of the bridge finite element model. They found that corrosion deteriorates the seismic performance of the bridge, and two main factors including pier-height and pier-corrosion are responsible for increasing plastic strain.


## 4.2. Large Scale Experimental Tests to Evaluate Seismic Performance of Corroded Bridge Piers

As mentioned earlier, numerical simulations of corroded bridge piers are very complicated and they probably cannot capture all the effects of corrosion on seismic performance of bridge piers. Therefore, large scale experimental tests need to assess seismic performance of corroded bridge piers. Some studies have been reported on the effects of corrosion on cyclic behavior of RC columns [154, 155]. However, according to the best knowledge of the authors, large scale seismic experimental test on corroded bridge piers is rare and only one case [139] was found in the literature. Dietz et al. [139] designed a reinforced concrete bridge pier to EC2. They corroded the bridge pier using accelerated corrosion technique by ponding a part of the pier in NaCl solution for 6 months. The corroded bridge pier was then subjected to lateral cyclic loading up to 50 KN using a hydraulic actuator. They measured deflection at the top, rotation at the base, strains in the concrete and steel bars, and width of cracks. From a structural point of view, the bridge pier rigidly connected to the foundation is high damage system because formation of plastic hinge at the end(s) of the pier is the mechanism of dissipating energy in seismic events. The high damage system is the traditional seismic resistant system that has been criticized by past studies because of high repair time and cost and problems arising from traffic interruption [156].


## 4.3. Seismic, Structural, and Durability Behavior of Repaired Bridge Piers Exposed to Corrosion-Induced Damage

The need for retrofit of corroded bridge piers has been addressed by past studies. There is a traditional method to rehabilitate corroded bridge pier that includes two stages: first, all critically corroded areas should be removed; then, an overlay of materials with low-permeability has been used [157, 158]. Gergely et al. [159] rehabilitated corroded bridge pier samples using fiber-reinforced plastic composites. They compared seismic performance of the piers through numerical and large scale experimental tests and found that shear capacity and ductility have been improved significantly. However, to simulate the effect of corrosion on steel reinforcement, they cut three stirrup loops of column and three stirrup loops of each side of the cap-beam near the joint. They noted that an advantage of using FRP composite is that it does not increase weight of column. Toutanji [160] has found that the confinement provided by FRP warps improves compression strength and ductility of RC columns. However, durability is affected by the type of epoxy used. Demers and Neale [161] have showed that the type of FRP influences ductility and strength of RC columns. Pantazopoulou et al. [162] compared alternative methods to assess seismic performance of repaired corroded bridge piers using external fiber-reinforced polymer (FRP) wraps. They stated that the best repair strategy in terms of postrepair corrosion, strength recovery, and ductility was cleaning the damaged surface (without removal of materials) and then jacketing using layers of FRP. However, further experiments are needed to confirm the efficiency of the proposed strategy in practice. Baiyasi and Harichandran [163] have concluded that a greater amount of glass fiber than carbon fiber was needed to achieve the equivalent structural performance of postcorrosion repair. Teng et al. [164] have reported that while FRP increases durability characteristics of RC columns, it possibly has some negative impacts on mechanical properties of the RC columns. A number of studies have revealed that FRP does not fully stop chloride-induced corrosion but decreases the rate of corrosion [162, 163, 165–173]. To answer an important question of what the best strategy is to repair corroded bridge pier using FRP, Sen [169] stated that the best strategy to protect concrete columns against chloride-induced corrosion is applying FRP jackets and filling gaps between the column and jackets using epoxy so that the following conditions are satisfied:(i)
Applying FRP jacket over the full length when no visible corrosion-induced sign can be found.
(ii)
Utilizing appropriate epoxy as a surface corrosion barrier and filling gap between the column and jacket.
(iii)
Utilizing at least two layers of FRP.Sen [169] has argued that confined concrete by FRP warps changes corrosion diffusion. He also has recommended not using FRP warps before visible corrosion sign to minimize repair cost. Wootton et al. [170] have concluded that FRP warps protect the RC columns better than epoxy alone. It has been shown that low amount of corrosion (up to 4.2%) does not influence eccentric load carrying capacity of RC columns, and the strength of damaged columns fully warped with carbon FRP was higher than undamaged columns. The performance of full length covered by CFRP was better than that partially covered by CFRP [174]. Li et al. [175] have analyzed seismic performance of corroded RC columns confined by FRP and steel jacket. They showed that FRP and steel jacket enhance the seismic performance of RC columns, and applying both jackets improves seismic performance better than applying one alone. A recent survey carried out on corroded RC bridges in New York State emphasized the demand for retrofitting corroded RC bridge columns, in particular, corroded lap-splice, to decrease possible damage in future seismic events [176].


## 4.4. Development in Time-Dependent Seismic Evaluation of Corroded RC Bridge Piers Reported in the Literature

Traditional structural analysis is not able to analyze systems and structures under multiple time-invariant hazards. A time-dependent analysis during lifetime, therefore, is needed to take into consideration all hazards. In case of RC structures (in particular RC bridge pier) subjected to corrosion and earthquake, two hazards are corrosion-induced deterioration and seismic events. There are some studies in the literature, mainly published in recent years, showing that corrosion influences the seismic performance of bridge piers over time. However, different criteria have been used by past studies. Biondini et al. [151], for example, have presented time-dependent bending moment resistance of a bridge pier exposed to corrosion. They have shown that the bending moment resistance of the corroded bridge pier decreased over time. Time-dependent deformation capacity, drift ratio demand, shear capacity, and demand of a corroded bridge pier have been studied [93, 124, 144]. Time-dependent probability of failure (time-dependent fragility analysis) of corroded bridge piers has been developed by past studies that can be directly used for seismic analysis purposes [93, 124, 144, 145, 177, 178]. Moreover, a fragility increment function has been developed that is a function of time and given deformation or shear demand and can be used to predict fragility of corroded bridge piers in life-cycle analysis and risk assessment [147, 178].


## 4.5. Research Gaps

The main research gaps in evaluation of seismic performance of corroded reinforced concrete bridge piers can be summarized as follows:(i)
Robust numerical modelling of corroded bridge piers.
(ii)
Large scale experimental tests on seismic behavior of corroded bridge piers and bridge structures (half scale and full scale tests).
(iii)
Experimental tests on efficiency of repair methods used for corroded bridge piers.
(iv)
Robust numerical model to evaluate time-dependent seismic performance of RC bridges exposed to corrosion.


## 5. Conclusions

In this paper, chloride-induced corrosion, the effects of corrosion on structural and mechanical properties of RC structures or elements, and seismic performance of corroded RC bridge pier have been reviewed. To meet this aim, a large number of published papers with all their experimental and numerical details have been collected and reviewed. From the present literature review, the following main conclusions are drawn:(1)
The results of published papers represented in this review paper have been obtained from samples or structures mainly utilizing ordinary Portland cement material, and the behavior of upcoming and more recent cement materials need further investigations.
(2)
Damage prediction of RC structures due to chloride-induced corrosion significantly depends on estimation of important input parameters such as corrosion rate, critical content, limit step to start pitting corrosion, and corrosion-induced cracking. However, results reported by past studies exhibit critical problems including contradictory results and uncertainty in experimental techniques and reported results. Moreover, the obtained results cannot be transferred to real structures. Therefore, further investigations are needed in these areas.
(3)
More reliable deterioration models are highly demanded for seismic evaluation and analysis of corroded RC structures. On the other side, the deterioration models have been mainly developed for artificial corroded samples, while the relationship between natural and artificial corrosion in many aspects is unknown. Hence, this area is an important direction of research.
(4)
Seismic analysis of corroded RC structures (in particular bridge piers) is very complicated, and many uncertainties limit utilizing of numerical methods. Hence, developing more recent numerical methods and large scale experimental tests is needed for the analysis of RC structures under multiple hazards (corrosion and earthquake).
(5)
While few researchers based on their modelling have already started to build fragility functions to be integrated in a lifetime seismic performance framework, still many gaps need to be covered in testing and modelling.
(6)
Long-term seismic performance of RC bridge pier exposed to chloride incorporates the three main subareas reviewed in Sections2 to 4 in this paper aiming to develop the following steps that are in common with LCA of corroded RC bridge piers:
(7)
Time-dependent deterioration models.
(8)
Time-dependent seismic performance of corroded structure.



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*Source: 3075184-2016-05-19.xml*