Abstract: Chloride-induced corrosion of the reinforcement is considered as one of the major mechanisms resulting in the reduction of structural resistance of reinforced concrete structural elements located in marine and other aggressive environments. A study of reinforced concrete structures located at the Fangcheng dock in the Beibu Gulf port, China, was present. The result from field survey indicates that the concrete cover depth and chloride diffusion coefficient fit best normal distribution and lognormal distribution, respectively. The service life of structure is about 55 a, while initiation time is 45 a. Sensitivity analysis indicates that the most influential factor of the structure service life prediction is concrete cover, followed by diffusion coefficient, diffusion decay index, critical chloride concentration, surface chloride concentration, current density and localized pitting corrosion. Finally, the effects of diffusion decay index and critical chloride concentration on structure service life prediction are discussed. Key words: chloride; existing concrete structure; service life; marine environment
1 Introduction
The durability and service life of concrete structures are widely recognized as one of the major components in the rational design of concrete structures. The necessity of time-variant reliability assessment of structural durability is becoming increasingly accepted by many researchers [1−2].
The durability of concrete structures is directly caused by steel corrosion [3]. The corrosion of the steel leads to concrete fracture, which exhibits in the form of steel cross-section reduction, loss of bond between concrete and steel, cracking, and degradation of concrete cover. As a result, the safety and serviceability of concrete structures are reduced, and their service life is shortened [4].
Tuutti’s model [5] is widely accepted as the conceptual model for the deterioration of structures (Fig. 1). The model clearly demonstrates an initiation time followed by a propagation time. During the initiation phase, chloride ions diffuse through concrete toward the reinforcements. The end of the first stage means the beginning of the corrosion of steel, once the chloride concentration reaches a threshold value. The propagation phase is defined as the time from the start of corrosion to a critical steel loss limitation. Therefore, the initiation and propagation time sum up as the service life of the structure [6].
Few researches have been conducted on investigating the existing concrete structures. LOUNIS and AMLEH [1] presented a probabilistic approach for predicting the chloride contamination of concrete and reinforcing steel corrosion of an aging reinforced concrete bridge deck exposed to chlorides from deicing salts for forty years. LIANG et al [6] proposed the basis for service life predictions of the existing reinforced concrete (RC) bridges in chloride-laden environments based on mathematical modeling. The Chung-shan Bridge, a 69 years old RC bridge in Taipei, was offered as a case study. STRAUSS et al [7] introduced a feasible approach to analyze the effects of chloride-induced deterioration on the overall safety level of a real highway bridge demolished after 38 years of service. ALIPOUR et al [8] developed an integrated computational methodology for the chloride intrusion simulation and the corrosion initiation time estimation. A comprehensive procedure for the structural performance evaluation and life-cycle cost analysis of reinforced concrete highway bridges located in extreme chloride-laden environments were also given. WANG et al [9] proposed a general method for probabilistic corrosion analysis of reinforcing bars in RC bridges. The uncertainties due to limited number of experimental data, incomplete inspection information, as well as the intrinsic randomness of variables affecting the prognostics of corrosion damage were also discussed.
The objective of this work is to take the random
Foundation item: Project(41274012) supported by the National Natural Science Foundation of China Received date: 2014−08−25; Accepted date: 2014−12−30 Corresponding author: ZHOU Yong-jun, Associate Professor; Tel: +86−13916680796; E-mail: [email protected]
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Fig. 1 Deterioration process of reinforced concrete structures
due to corrosion
nature of chloride induced corrosion of reinforcing steel into account, which includes the corrosion initiation and propagation phase, to predict the service life of existing harbor concrete structures subject to chloride induced corrosion using Monte Carlo simulations. Sensitivity analysis of the input variables of the model is also conducted. Finally, the influences of diffusion decay index and critical chloride concentration on structure service life prediction are discussed. 2 Corrosion model
Steel in concrete is usually in non-corroded passive conditions. However, being used in severe environments with sea water or deicing salts, it may lead to rusts and pits when exposing to chloride attacks [10].
Generally, steel reinforcement is covered by a white thin layer called as the passive layer, which provides protection against corrosion [11]. This passive layer will be disrupted once the chlorides penetrate into concrete and reach a threshold level. The corrosion initiation occurs when the protective layer is destroyed in the presence of moisture and oxygen. Then, concrete structures begin to damage in the propagation phase, owing to the corrosion of steels. 2.1 Corrosion initiation
Numerous studies indicate that the penetration of chlorides through concrete can be represented by a diffusion process by assuming that the concrete is relatively moist [12−13]. In this case, the penetration of chlorides is satisfied with the Fick’s second law of diffusion given by
2
2
( , ) ( , )
C x t C x t
Dt x
(1)
where C is the chloride concentration, and D is the diffusion coefficient.
The initial and boundary conditions of Eq. (1) are given as
0 ,) (0,
0 0,0) ,(
s tCtC
xxC (2)
Using the initial and boundary conditions, the
analytical solution of Eq. (1) becomes
s( , ) 1 erf2
xC x t C
t D (3)
where erf(·) is the error function.
When the chloride ion concentration reaches the threshold level at the reinforcement depth, the steel passive layer is destroyed and steel is depassivated. The time of corrosion initiation can be determined by solving Eq. (3) as follows:
221 cr
inis
erf 14
CdT
D C (4)
where d is the distance from clear concrete cover to the reinforcement, Cs is the surface chloride content, and Ccr is the critical chloride concentration.
However, the diffusion coefficient usually is treated as a time dependent random variable as
refref( )
mt
D t Dt
(5)
where D(t) is the diffusion coefficient at time t, Dref is the diffusion coefficient at reference time tref (usually 28 days), and m is the diffusion decay index. 2.2 Corrosion propagation
The propagation phase is the time required for corrosion to propagate to the extent at which the load capacity of the structural member becomes insufficient [11]. The estimation of the propagation phase depends on the definition of different levels of corrosion, in this work, on crack width. Models have been proposed by many researchers relating the level of corrosion to the formation of cracks [14−16]. From these literatures, we can find that most models do not take the loading effects on the corrosion-induced cracking into account. The model proposed by VIDAL et al [17] is based on the experimental investigation on reinforced concrete beams with loadings, so it is more reasonable in applications. The evolution of crack width (w(t)) with corrosion of reinforcement is modeled as follows:
00.0575 ( ) sw t A t A (6)
where ΔA(t) is the cross-section area loss of steel; ΔAs0 is the cross-section area loss of steel cross-section corresponding to the crack initiation due to corrosion of reinforcement.
2
3s0 s 1 1 7.53 9.32 10
0 0
R dA A
(7)
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where As is the initial cross-section area of steel; f(0) is the initial bar diameter; R is the factor that includes the effect of highly localized pitting normally associated with chloride contamination.
The reduction of bar diameter (f(t)) caused by chloride corrosion can be given as [18]
ini
ini ini ini
ini
0 ,
( ) 0 2 , 0 / 2
0, 0 / 2
t T
t t T T t T
t T
(8) where λ is the corrosion rate, λ=0.0116RJcorr (mm/a). The corrosion rate is most accurately measured from field/experimental studies as the current density Jcorr (normally expressed in μA/cm2).
Then, ΔA(t) can be expressed as
2 2π0
4 A t t (9)
3 Probabilistic lifetime evaluation
A general definition of structural reliability is introduced in ISO 1998. The verification of a structure with respect to its reliability (i.e., to a particular limit state), is carried out via estimation of the probability of the occurrence of failure, Pf, in a specified reference period. This probability is usually expressed as
f P P R S (10)
where S is effect of action and R is resistance, and both are random variables. The general limit conditions for serviceability limit states (e.g., cracking, and deflection) [19] are expressed as follows:
f dP P (11) where Pd is the design (acceptable or target) probability value.
In this work, owing to the ingression of chlorides, Eq. (11) may also be expressed as
f cr d P P w t w P (12) where wcr is the threshold crack width.
On the basis of the probability distributions of the structural and environmental variables, Monte-Carlo simulations are performed in order to provide the input parameters for the corrosion model. 4 Methods and materials 4.1 Field survey
The study area was the Fangcheng dock in the Beibu Gulf port, China. The dock consists of the first, the
second, and the third stage construction sites. The field tests only involved the second-stage construction site (13#) constructed in 2005. The concrete structure in 13# dock was tested in October 2012, about 80 months after the completion of construction. Figure 2 shows the field conditions of Fangcheng dock.
Fig. 2 Field condition of Fangcheng dock
4.2 Data
The field data include the concrete cover depth and the chloride contents on powdered samples extracted from the concrete walls. The data estimated from the literature include the surface chloride concentration and critical chloride concentration. 4.2.1 Chloride concentration and chloride diffusion
coefficient The device for measuring the concrete chloride
concentration was RCT. Based on the service life of the concrete wall, the thickness of the concrete cover, and the earlier pre-tests, the chloride penetration depth in 80-month-old concretes in the Beibu Gulf port area may reach about 60 mm. Therefore, the drilling depth was 56 mm, divided into 8 sections with a 7 mm depth gap between two sections.
The chloride diffusion coefficient was obtained by regression analysis of Eq. (3) from the chloride profiles obtained from field data. The chloride diffusion coefficient was found to have a lognormal distribution with an average of 8.85 mm2/a and a standard deviation of 0.97 mm2/a. 4.2.2 Concrete cover depth
The concrete cover depth for the concrete walls was
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examined in situ. The designed concrete cover depth to the steel embedment was 60 mm, and approximately 96 concrete cover depth measurements were taken by a Profometer5 cover depth meter. The concrete cover depth was found to be normally distributed with an average of 59.5 mm and a standard deviation of 3.93 mm. 4.2.3 Critical chloride concentration and surface chloride
concentration There is a considerable uncertainty associated with
the value of the critical chloride concentration (Ccr) obtained from laboratory and field studies where Ccr was found to vary between 0.06% and 2.2% in terms of free chlorides by the mass fraction of cement [20]. Based on empirical experiences from a wide range of concrete qualities and moisture conditions, an average value of 0.4% by the mass fraction of cement is often referred to in current concrete codes and recommendations and 0.2% for structures exposed to a more aggressive environment [21]. Considering the local condition of Fangcheng dock (tropical marine environment, under aggressive chloride attack) and large overall scatter of Ccr, in the present work, Ccr was treated as a lognormal random variable, with a mean value of 0.2% by cement mass fraction and coefficient of variation of 0.3.
For concrete walls at Fangcheng dock, the surface is subjected to a continually changing chloride exposure. The chloride concentration at the concrete surface varies with the seasons. Generally, the values of surface chloride concentration can be estimated from LNEC E465 [22]. With respect to the site conditions of Fangcheng dock, Cs=2.4% is chosen as the cement mass fraction. Most literatures [23] suggested that the surface chloride concentration is described by a normal distribution with coefficient of variation of 0.1.
A summary of the random variables for the corrosion models adopted in this work is given in Table 1. Table 1 Statistic of random variables
Parameter Distribution Mean Coefficient of variation
Reference
d/mm Normal 59.50 0.07
Dref/(mm2·a−1) Lognormal 8.85 0.11
f(0)/mm Determine 22
m Normal 0.40 0.08 [4]
Ccr/% Lognormal 0.20 0.30 [4]
Cs/% Normal 2.40 0.10 [22]
Jcorr/(μA·cm−2) Normal 1.0 0.20 [18]
R Normal 3.0 0.33 [18]
wcr/mm Uniform (0.3−0.6)
0.45 0.19 [18]
5 Results and discussion
The following results are expressed in terms of the reliability index instead of the probability of failure so that the outcomes can be easily compared to the minimum reliability index recommended in Design Codes for Serviceability Limit States. The relationship between reliability index and probability of failure is given by [24]
1f1 P (13)
5.1 Basic results
The reliability index is a function of time shown in Fig. 3. The concrete crack width reaches its limit states by using 10000 Monte Carlo simulations. Note that the threshold of reliability index (βSLS) recommended by ISO 2001 for the serviceability limit states (SLS) at 50 years is 1.5 [25]. Figure 3 indicates that the estimated corrosion initiation time is 45 years and the service life of structure is about 55 years. This clearly reveals that the total service life mainly depends on the corrosion initiation time. And this trend is also reported by other researchers [3, 26]. Hence, it is of vital importance to accurately predict the corrosion initiation time in evaluating the service life of RC structures under chloride attack.
Fig. 3 Time-variations of reliability index
In case of m=0, as shown in Fig. 3, the reliability
index declines rapidly with time, and the estimated service life is only 26 years. This means that ignorance of the time dependency of chloride transport in concrete will overestimate the risk of corrosion of the RC structures. 5.2 Sensitivity analysis of variables
In order to illustrate the contributions of each variable to the service life, a sensitivity analysis is conducted to show the changes of service life due to the
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variations of each random variable given in Table 1. The influence of uncertainty of individual random
variables on the service life can be illustrated by the use of the so-called sensitivity factors:
/
/
AS
A A
(14)
where SβA is the sensitivity factor of reliability index β on random variable A; ΔA/A is change of the random parameter (%); Δβ/β is the corresponding change of reliability index (%).
Taking the example of t=50 a, the sensitivity factors of each random parameter are shown in Table 2. Table 2 indicates that every 1% increment of d can lead to 3.43% increase of the reliability index accordingly. By comparison, we can find that the most influential variable to structure service life prediction is d, followed by Dref, m, Ccr, Cs, Jcorr and R. Moreover, the service life increases as the values of d, Ccr and m rise, while the other four parameters show the opposite tendency.
For all the random variables, d and D are based on field test; other five parameters are taken from empirical value. Among these five variables, uncertainty associated with Cs, Jcorr and R are of little importance for determination of the structure service life. So, in the next section, the effects of m and Ccr on the structure service life evaluations are discussed. 5.3 Influence of diffusion decay index m
Since the chloride diffusivity is a time-dependent property of the concrete, m is a very important durability parameter reflecting how the chloride diffusivity of a given concrete in a certain environment develops over time [3].
Figure 4 indicates a significant influence of m on the structural reliability. Reliability index increases as the diffusion decay index increases. For example, at a given time t=40 a, when m=0.1, 0.2, 0.3, 0.4 and 0.5, the reliability indexes are equal to 0.74, 1.19, 1.68, 2.22 and 2.76, respectively. Moreover, a strong dependency
between the reliability index and m is also verified in Fig. 4. The reliability index almost demonstrates a linear growth with the increasing of m. However, at t=20 a, when the value of m exceeds 0.3, the reliability index stays almost the same even with the increase of m. This is owing to the relatively small probability of structural failure at that time. The failure probability keeps at a small but steady value (about 0.1%). As shown in Fig. 4, given a target reliability index βSLS=1.5, the estimated service lives are 30, 35, 40, 55 and 80 a for m values of 0.1, 0.2, 0.3, 0.4 and 0.5, respectively.
DURACRETE advised to take 0.3 for the diffusion decay index for OPC concrete and 0.62–0.71 for blended concretes [27]. The Life365 model suggests that the diffusion decay index for OPC concrete should be about 0.2, and cannot exceed 0.6 for blended concretes. The CHLODIF model [28] advises a smaller value (0.1) for the diffusion decay index of OPC concrete. So, choosing an appropriate diffusion decay index for a more accurate prediction of service life of concrete structures is essential. 5.4 Influence of critical chloride concentration Ccr
For existing structures, it is hard to test the real Ccr, so empirical values from design codes and recommendations [29] are introduced. Figure 5 shows the time-dependent relationship between reliability index and Ccr.
It can be seen from Fig. 5 that Ccr has a significant influence in service life assessment. It indicates a considerable growth of the service life time as Ccr increases. At a given target reliability index βSLS=1.5, the estimated service lives for Ccr at 0.1, 0.2, 0.3, 0.4 and 0.5 are equal to 35, 55, 80, 120 and 160 a, respectively. For Ccr=0.5, when the expose time is less than 60 a, the reliability index stays almost the same, which may also attribute to the relatively small probability of structural failure at that time (the failure probability is about 0.1%).
The Ccr is influenced by those factors related to material characteristics, environments and steel−concrete
Table 2 Sensitivity factor of random variables
(ΔA/A)/% d Dref Cs Ccr m Jcorr R
−20 3.36 −1.92 −0.40 1.01 1.30 −0.17 −0.07
−15 3.40 −1.88 −0.38 0.99 1.38 −0.15 −0.07
−10 3.44 −1.82 −0.37 1.00 1.33 −0.15 −0.09
−5 3.46 −1.75 −0.42 0.95 1.31 −0.05 −0.10
5 3.58 −1.63 −0.35 0.94 1.41 −0.14 −0.18
10 3.54 −1.54 −0.30 0.95 1.39 −0.16 −0.14
15 3.44 −1.52 −0.31 0.96 1.41 −0.14 −0.15
20 3.21 −1.46 −0.31 0.93 1.39 −0.12 −0.12
Mean 3.43 −1.69 −0.35 0.97 1.36 −0.14 −0.11
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Fig. 4 Variations of reliability index with diffusion decay index
Fig. 5 Variations of reliability index with critical chloride
concentration
interfaces [30]. So, it will vary even for similar structures, and choosing a suitable value for service life assessment of existing concrete structure is very important. 6 Conclusions
1) The concrete cover depth fits normal distribution well, with mean value of 59.5 mm and a standard deviation of 3.93 mm; the chloride diffusion coefficient is found to have a lognormal distribution with an average of 8.85 mm2/a and a standard deviation of 0.97 mm2/a.
2) The service life of the structure is about 55 a, where the corrosion initiation time is 45 a. Compared with corrosion initiation period, corrosion propagation period is relatively short.
3) Sensitivity analysis indicates that the most influential parameter to structure service life prediction is concrete cover, followed by diffusion coefficient, diffusion decay index, critical chloride concentration, surface chloride concentration, current density and localized pitting corrosion factor.
4) The estimated service lives of structure diffusion decay index at 0.1, 0.2, 0.3, 0.4 and 0.5 are 30, 35, 40, 55 and 80 a, respectively; for critical chloride concentration
at 0.1, 0.2, 0.3, 0.4 and 0.5, they are 35, 55, 80, 120 and 160 a, respectively. Choosing an appropriate value is very important for a more accurate prediction of service life of existing concrete structures.
References [1] LOUNIS Z, AMLEH L. Reliability-based prediction of chloride
ingress and reinforcement corrosion of aging concrete bridge decks
[C]// Life-Cycle Performance of Deteriorating Structures. Lausanne:
IABMAS, 2003: 113− 122.
[2] VOŘECHOVSKÁ D, TEPLÝ B, CHROMÁ M. Probabilistic
assessment of concrete structure durability under reinforcement
corrosion attack [J]. Journal of Performance of Constructed Facilities,
2010, 24(6): 571−579.
[3] NOGUEIRA C G, LEONEL E D. Probabilistic models applied to
safety assessment of reinforced concrete structures subjected to
