on

lavraal U

" Carbonation model calibrated with long term results.initiation stage.e Carlo simulations.or service life design semi-probabilistic approach.

vice Life Design. 2012 Elsevier Ltd. All rights reserved.

Reinforcing steel corrosion is the most common deteriorationmechanism in reinforced concrete structures [13,19,29]. Steel cor-rodes when in contact with humidity and oxygen but when it is in-side concrete an oxide lm builds up that makes steel passive andprotects it against corrosion. This lm is stable in an alkaline envi-

tion [24].The service life of a structural component is the period after

construction when all the properties exceed the minimum accept-able values when routinely maintained [1]. Predicting service liferequires a model that simulates the behaviour of the structure un-der environmental actions. The model must take into account therelevant physical and chemical mechanisms and its performancewhen simulating real behaviour must be assessed [14].

Tuutti [40] presented a model where the service life for con-crete structures with regard to reinforcement corrosion is brokendown into an initial and a propagation stage. This division is

Corresponding author at: Department of Civil Engineering and Architecture,Section of Construction, IST, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal. Tel.: +351 21 8419709; fax: +351 21 8497650.

E-mail addresses: rui.neves@estbarreiro.ips.pt (R. Neves), fbranco@civil.ist.utl.pt

Construction and Building Materials 36 (2012) 585591

Contents lists available at

Construction and B

ev(F.A. Branco), jb@civil.ist.utl.pt (J. de Brito).CorrosionService lifePerformance-based design

1. Introduction

The service life design of reinforced concrete structures is animportant subject that has led to extensive research worldwide.That research has given us the performance-based design methodsin use today [16,26,14]. These methods are founded on predictionmodels and reliability concepts and, unlike the deemed-to-satisfyapproach, allow lifecycle cost analyses [31,37]. To encourage thewidespread use of the performance-based design its methods mustbe as simple (user-friendly) and accurate as possible.

ronment such as young concrete. But it can be destroyed if the pHfalls or if the chloride content reaches a critical threshold. The pHcan decrease because of concrete carbonation, and so CO2 and chlo-ride action are the most relevant processes in this context.Although chloride-induced corrosion is considered to be worsethan carbonation-induced corrosion, Parrott [35] apud Jones et al.[22] states that 2/3 of all structural concrete is exposed to environ-mental conditions that favour carbonation-induced corrosion. InTaipei, signicant carbonation-induced corrosion of existing con-crete bridges has been observed within 1015 years of construc-Carbonation

Concrete

full probabilistic approachthe b Model Code for Ser" Deterioration model considering only" Safety factors determined using Mont" Comparative study with model code f

a r t i c l e i n f o

Article history:Received 20 March 2012Received in revised form 22 May 2012Accepted 4 June 2012Available online 10 July 2012

Keywords:0950-0618/$ - see front matter 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.conbuildmat.2012.06.028a b s t r a c t

This work aims to provide a simple semi-probabilistic approach to the service life design of reinforcedconcrete structures with respect to reinforcement corrosion induced by concrete carbonation.This paper presents an analytical model for the initiation period, calibrated with long-term carbonation

results, which uses the accelerated carbonation resistance and the environmental class as input param-eters. The issue of dening a limit for deterioration is discussed and a maximum accepted level of dete-rioration and reliability indexes are dened. The corresponding partial safety factors are derived from a

. The performance of the proposed method is compared with that proposed onA method for the use of accelerated carb

R. Neves b, F.A. Branco a,c, J. de Brito a,c,aDECivil-IST, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugab ESTBarreiro, Polytechnic Institute of Setbal, R. Amrico da Silva Marinho, 2839-001 LcDepartment of Civil Engineering and Architecture, Section of Construction, IST, Technic

h i g h l i g h t s

journal homepage: www.elsll rights reserved.ation tests in durability design

dio, Portugalniversity of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal

SciVerse ScienceDirect

uilding Materials

ier .com/locate /conbui ldmat

needed because the primary ruling factors in these sub-processesdiffer.

For the specic deterioration mechanism of carbonation-in-duced corrosion, the initial stage is the period from the beginningof a structures life until the carbonation depth is the same as thatof the reinforcement cover, when corrosion is considered possible.

The propagation stage is the period from the end of the initialstage until the reinforcement reaches an unacceptable level of cor-rosion degradation.

2. Limit states and reliability

Dening a level of unacceptable corrosion degradation, i.e. alimit state, is not a simple matter. If the maximum acceptable dete-rioration level is associated with a service requirement, a service-

the cost of concrete, or indirectly, by reducing the reinforcementsexural strength efciency.

The verication of a certain limit state is performed using amodel which numerically expresses that limit state through afunction known as the reliability function, commonly expressed as:

Z R S 1where R is a function that quanties a response; S is a function thatquanties the effect of an action.

According to Eq. (1), Z 6 0 represents failure [21]. Functions Rand S have input parameters that are stochastic variables. More-over, the functions (models) themselves exhibit uncertainty.Hence, a probabilistic approach to service life design is recom-mended [8,25,23].

In probability-based design, the probability of reaching a givenlimit state is computed. That probability is designated as probabil-

te

586 R. Neves et al. / Construction and Building Materials 36 (2012) 585591De

Service lifeability limit state (SLS) is dened, while if the maximumacceptable deterioration level is associated with collapse or similarforms of structural failure, an ultimate limit state (ULS) is dened.

Criteria such as corrosion onset, cracking and spalling dene SLSs[18,25], while spalling with apparent risk from falling pieces, loss ofbond between concrete and reinforcement and loss of cross-sectionleading to fracture of structural component dene ULSs [23].

The criterion for service life design, especially for prestressedstructures or those affected by chloride ion penetration, is oftencorrosion onset [2,5,15,36], which can be designated as a depassiva-tion limit state. The advantages of this option are: ease of predictionand less expensive pro-active protection measures. In addition, asthe rate of steel corrosion in chloride-induced corrosion is fast,the impact on the initial costs of disregarding the propagation stagewill be small. But if the propagation stage of carbonation-inducedcorrosion in dry exposure conditions is disregarded, this willsignicantly raise production costs.

In a scenario of cracking limit state, for carbonation-inducedcorrosion, the ratio of initial and propagation stages in service lifeis variable since, contrary to what happens with chloride-inducedcorrosion, the conditions most favourable to depassivation are gen-erally not ideal for the development of corrosion [34,38]. Therefore,it is possible that identical elements, when exposed to differentenvironments, have the same lifetime but with different contribu-tions from the initial and propagation stages, as illustrated in Fig. 1.

Thus, for a certain required service life, adopting a depassiva-tion limit state instead of a cracking limit state implies extendingthe initial stage. The relevance of this extension may range fromnegligible (RHc > 85%) to overriding (45% < RHc < 65%). The mostdirect ways to achieve such an extension are to increase rebar cov-er thickness and to improve concretes resistance to carbonation.Any of these actions will raise costs, either directly by increasing

riora

tion

CrackingFig. 1. Concrete relative humiditys (RHc) inity of failure, pf, and may be expressed as the probability of re-sponse falling below the action:

pf pR 6 S 2Based on probability of failure, a reliability index, b, may be

dened:

b U1pf 3where U1(.) is the inverse standardised normal distributionfunction.

In general, the R and S functions, and therefore also the Z func-tion, are time-dependant. Their expected values, and even scatter,may vary with time. Therefore, the probability of failure should notbe determined as an absolute value, but relative to a certain periodof time, usually the service life. Two approaches are possible: limitstate format and service life format [27]. Although they have differ-ent formats, they use the same basic theoretical concepts and de-liver exactly the same results [8].

In the limit state format, the probability of failure is determinedby considering the relevant time interval: intended service life (Eq.(4)).

pf ;T pZ 6 0 4where pf,T is the probability of failure during the period 0 T; T isthe target service life.

In the service life format, a lifetime function must be denedwhose result is a given service life, to be compared with the targetservice life:

pf ;T pL 6 T 5where L is a lifetime function.

Time

45%

Fig. 2 shows the differences between these approaches for areinforcement depassivation process, and highlights the use ofthe same information. In Fig. 2, R stands for reinforcement cover,S stands for chloride threshold or carbonation depth, fL(t) standsfor probability density function of service life and T stands for tar-get service life.

According to Maes et al. [27], the service life format approach isof particular interest when the majority of uncertainties lie on thedeterioration model, when the deterioration model has severalstages, e.g. initiation and propagation stages, or when the elementis subjected to more than one deterioration mechanism.

The numerical quantication of reliability is important as it en-ables target values to be dened according to the causes and pro-cesses evolved in the attainment of a limit state, the correspondingconsequences, and the cost of the construction works [10]. Further-more, the possibilities of detecting damage and taking correctivemeasures in the event of failure must be also considered whendening target reliabilities [23].

The consequences associated with the attainment of a limitstate depend on the maximum level of deterioration accepted.

bonation can be organised into two major groups: environmentalfactors and factors intrinsic to concrete. The environmental factorsinclude: the occurrence of drywet cycles [4], relative humidity[41] and CO2 concentration [41]. Intrinsic factors are mainly re-lated to concrete porous structure and the amount of matter thatcan be transformed into carbonates.

The main transport mechanism in concrete carbonation is CO2diffusion through its porous system, which can be described usingFicks rst law. Assuming that the CO2 concentration, the amountof CO2 required to carbonate a unit volume of concrete and the dif-fusion coefcient for CO2 through carbonated concrete are all con-stant, and also that a complete reaction takes place beforecarbonation proceeds, and integrating the diffusion equation, thefollowing formula is obtained:

x Kt

p6

where x is the carbonation depth (mm); K the carbonation coef-cient (mm/year1/2); and t is the exposure time to CO2 (year).

In Eq. (6), K is a parameter that takes into account all factorsaffecting carbonation. Separating those factors into environmental

R. Neves et al. / Construction and Building Materials 36 (2012) 585591 587Nevertheless, attaining a limit state always entails economic costs,which is why setting a reliability index must be supported by aneconomic analysis aimed at cost optimisation. In this analysis,the production cost needed to guarantee extra protection and thecost of the consequences must be balanced to pursue the optimumreliability index from an economic point of view.

This approach is of particular interest for limit states related toreinforcement corrosion. Actually, the cost of repairs (consequences)increases as higher levels of deterioration, i.e. depassivation, crackingand spalling, are allowed. Higher reliability indexes will therefore berequired. Thus, if a limit state of spalling is considered, which in-creases the service life when compared to a depassivation limit state,the required reliability index will also be higher than for depassiva-tion limit state. Consequently, the requirements for reinforcementcover and concrete durability-related properties will be similar ifeither a depassivation or spalling limit state is considered.

3. Carbonation rate model

Adequate modelling of carbonation is a delicate issue since sev-eral factors must be taken into account and users expect researchto deliver simple and user-friendly models. Factors affecting car-

R,S

S(t)

R

L(t)

T

Mean service life

pf,Tf

Fig. 2. Reliability analyses byand concrete intrinsic factors, K may be dened as:

K kake

7

where ka is the parameter related to concrete intrinsic factors; andke is parameter related to environmental factors.

Under the same environmental conditions, including CO2 con-centration, the coefcient K is a relative indicator of concrete car-bonation resistance and the most straightforward and reliableparameter for characterising the inuence of concrete intrinsic fac-tors on carbonation. To evaluate carbonation resistance withtimely delivery of results, accelerated tests have to be used inwhich concrete is exposed to mediums with relatively high CO2concentration.

Neves et al. [33] investigated the relationship between carbon-ation resistance in accelerated and natural conditions, using coresdrilled from 96 spots in real structures, using different structuralelements, exposed to environmental class XC3 or XC4 [12] whoseage ranged from 4 to 32 years. Based on their conclusions and usingEq. (6), which has exhibited an ability to simulate carbonationdepth evolution over time in natural conditions [32,7,28,17,30,39], the following model is proposed:

Time

Limit state format

Service life formattwo different approaches.

588 R. Neves et al. / Construction and Buildx kake

t

p8

where x is the carbonation depth (mm); ka the resistance to accel-erated carbonation (mm/year1/2); ke the environmental parameter,being 9.9 for environmental class XC3 and 15.0 for environmentalclass XC4; and t is the exposure time to CO2 (year).

Resistance to carbonation in accelerated conditions (ka) is quan-tied by means of K in Eq. (1), i.e. an accelerated carbonation coef-cient, which has proven to be suitable for simulating carbonationin accelerated conditions [20,32,3,6], using the following testconditions:

Preconditioning: 3 weeks at 20 3 C and 65 5% RH. Testing age: from 5 weeks. Accelerated carbonation conditions: 20 3 C, 65 5% RH and5 0.1% CO2 concentration.

The performance of the model is illustrated in Figs. 3 and 4, forenvironmental classes XC3 and XC4, respectively, using the resultsfrom Neves et al. [33]. According to these authors, when usingdifferent CO2 concentrations in accelerated testing for carbonation

Fig. 3. Measured vs. predicted carbonation depths for environmental class XC3.resistance, a correction factor, ka, given by the square root of theaccelerated testing concentrations ratio may be used if CO2 con-centrations are still near 5%.

Fig. 4. Measured vs. predicted carbonation depths for environmental class XC4.4. Design criteria

The maximum accepted level of deterioration is corrosion onset,thus it corresponds to an SLS: depassivation limit state. Corrosionmodels are not as developed and reliable as initiation stage mod-els; hence it is considered preferable to limit the deterioration levelto the end of the initiation stage. However, as stated, disregardingthe propagation stage in certain conditions of carbonation-inducedcorrosion may lead to a signicant increase of the initial cost. Butin these conditions the propagation stage can be seen as an addi-tional safety margin, which can be balanced against allowing a lar-ger failure probability [23].

A semi-probabilistic approach (safety factors) is commonly usedin structural design. The semi-probabilistic approach provides arelatively simple reliability analysis of sufcient accuracy. Unlikethe full-probabilistic approach, the intended values are achieved di-rectly, i.e. without iterations.

According to EN 1990 [10], a reliability index b = 1.50 must beconsidered for SLSs. This reliability index is related to a failureprobability pf = 0.066. The failure probability is the probability thatresistance R may fall below the action S. In a semi-probabilisticprocedure the restriction of failure probability can be expressed as:

RccR

cSSc > 0 9

where Rc is the resistance based on characteristic values; cR, cS thesafety factors; and Sc is the action based on characteristic values.

Within the aim of a carbonation-induced corrosions reliabilityanalysis, R is the thickness of reinforcement cover and S is carbon-ation depth. The safety factor related to reinforcement cover is of-ten replaced by a safety margin. The reinforcement cover designvalue is thus given by:

cd cnom Dc 10

where cd is the reinforcement cover design value; cnom the nominal(specied) reinforcement cover; and Dc is the reinforcement coversafety margin, usually 10 mm [16,9].

To quantify the safety factors related to carbonation depth, life-time simulations using the Monte Carlo technique were performed.In the process, the reinforcement cover was considered a deter-ministic variable (cd) and parameters ka and ke, from the carbon-ation model (Eq. (8)) were assumed to be stochastic variables.

For environmental class XC4, ke was considered as a normal dis-tributed variable with a mean value of 15 and a standard deviationof 0.88 [33]. The resistance to accelerated carbonation (ka) was alsoconsidered as a normal distributed variable, with a coefcient ofvariation of 13% [32].

The analysis of simulations results led to a safety factor cS = 1.25for a reliability index b = 1.50.

A different analysis was performed for environmental class XC3since it was intended to express the safety margin (propagationstage) in terms of a reliability index. The propagation stage wasconsidered as the period between depassivation and crack forma-tion due to corrosion. A lowest estimation of 45 years was consid-ered for this period [26].

The design service life for the depassivation limit state was as-sessed by performing simulations using a Monte Carlo technique,where ke was considered as a normal distributed variable with amean value of 9.9 and a standard deviation of 0.61 [33]. The resis-tance to accelerated carbonation (ka) was again considered as anormal distributed variable, with a coefcient of variation of 13%.Adding the propagation period to the design service life for the

ing Materials 36 (2012) 585591depassivation limit state, considering at the worst a specied ser-vice life of 200 years and a failure criterion of concrete crackingdue to corrosion, a safety factor cS = 1.00 is computed. In terms

of the depassivation limit state, this value for the safety factormeans a failure probability of 0.50. This failure probability corre-sponds to a reliability index b = 0, which is within the range ofreliability indexes for XC3 class quoted by Lay and Schiessl [23].

5. Proposed method

As a consequence of the discussion and analysis in the previoussections a simple method for service life design with respect to car-bonation induced corrosion is proposed.

First, a nominal reinforcement cover, according to EN 1992 [11],must be dened. Next, the resistance to accelerated carbonation, tobe assessed in the test conditions set out in Section 2, must be fore-seen using the following equation:

with the model codes partial safety factor approach. The corre-sponding limit state equation, in its most simplied form, withpartial safety factors already included, is:

cdP1:133:05 1011 RH5c 2:5kc;d3:08 103R1ACC0:52tSL

q0:0767tSL

0:5psrToW0:446

12where cd is the reinforcement cover design value (mm), accordingto Eq. (10); RHc the relative humidity of concrete (%); kc,d the exe-cution transfer parameter; R1ACC the inverse effective carbonationresistance ((mm2/year)/(kg/m3)); tSL the specied service life(year); psr the probability of driving rain; and ToW is the time ofwetness.

Solving Eq. (12), an upper bound for inverse effective carbon-ation resistance is found. The parameters used in Eq. (12) for the

R. Neves et al. / Construction and Building Materials 36 (2012) 585591 589ka cd kecStSL

p 11

where ka is the resistance to accelerated carbonation (mm/year1/2);cd the reinforcement cover design value (mm), according to Eq.(10); ke is the environmental parameter, being 9.9 for environmen-tal class XC3 and 15.0 for environmental class XC4; cS is the safetyfactor, being 1.0 for environmental class XC3 and 1.25 for environ-mental class XC4; and tSL is the specied service life (year).

The required accelerated carbonation resistances obtained byapplying the method for nominal reinforcement cover rangingfrom 15 mm to 40 mm and service life between 10 and 120 yearsare presented in Figs. 5 and 6, for environmental classes XC3 andXC4, respectively. In fact, ka represents the inverse of resistanceto accelerated carbonation as higher values of ka correspond to lesscarbonation resistant concrete.

6. Comparative analysis

The proposed method is compared with a reference methodestablished in the Model Code for Service Life Design [16]. Thecomparison is made in terms of required accelerated carbonationresistance using four scenarios, which vary in: reinforcement cov-er, service life and environmental class (Table 1). Two indicativeservice life times are considered: 50 years for building structuresand 100 years for bridges [10]. The environmental classes consid-ered are those covered by the method proposed in this paper andthe reinforcement covers are selected according to EN 1992 table4.4N [11], taking structural class S4.

The Model Code for Service Life Design considers the depassiva-tion limit state and three different levels for its verication: a fullprobabilistic approach, a partial safety factor approach and adeemed-to-satisfy approach. The proposed method is comparedFig. 5. Required ka for envvarious scenarios taken from the literature on the subject [23,26]are presented in Table 2. The resulting inverse effective carbon-ation resistance is to be assessed by accelerated carbonation test-ing. The value of inverse effective carbonation resistance isdetermined using Eq. (13).

R1ACC x2

Cs t13

where x is the carbonation depth (mm); CS the CO2 concentration(kg/m3); and t is the exposure time to CO2 (year).

For the purpose of comparing the requirements of both meth-ods, R1ACC values resulting from Eq. (13) are converted to ka, usingthe following expression:

ka 2 Cs R1ACC

q14

where ka is the resistance to accelerated carbonation (mm/year1/2);CS the CO2 concentration = 0.09 kg/m3; and R

1ACC is the inverse effec-

tive carbonation resistance ((mm2/year)/(kg/m3)).The required accelerated carbonation resistances for the consid-

ered scenarios, taken from the Model Code for Service Life Designand the new (previous section) methods, are presented in Table 3.

For environmental class XC3 (scenarios A and B) the referencemethod leads to more restrictive accelerated carbonation resis-tances. For environmental class XC4 (scenarios C and D) similaraccelerated carbonation resistances are required from bothmethods.

The difference between the required values for scenarios A andB is mainly due to the adoption of different reliability indexes:b = 1.3 in Model Code for Service Life Design and b = 1.0 in the pro-posed method. This distinction relies on taking into account themargin of safety provided by the slow corrosion development forXC3 exposure conditions.ironmental class XC3.

uild590 R. Neves et al. / Construction and B7. Conclusions

One of the processes responsible for the reinforcement corro-sion problems in reinforced concrete structures is the natural car-bonation of concrete, which depends on both the materialscharacteristics and the surrounding environment.

Although a structures durability can generally be assured bymeans of a deemed-to-satisfy approach, performance-based designis preferable as it allows a more rational use of the available re-sources and a lifecycle cost analysis.

The aim of this study was to provide a simple performance-based design method to prevent carbonation-induced corrosion.

The issue of acceptable degradation level was discussed, and adepassivation limit state which requires only one prediction modelwas adopted.

A model to predict carbonation depth based on Ficks rst lawand that was calibrated with long term natural exposure condi-tions carbonation assessments was considered.

Fig. 6. Required ka for env

Table 1Scenarios for the comparative analysis.

Scenario Cover (cd) (mm) Service life (tSL) (year) Environmental class

A 25 50 XC3B 25 100 XC3C 30 50 XC4D 30 100 XC4

Table 2Parameters for Eq. (12).

Scenario cd (mm) RHc (%) kc,d tSL (year) psr ToW

A 25 70 1 50 0 B 25 70 1 100 0 C 30 80 1 50 0.05 0.21D 30 80 1 100 0.05 0.21

Table 3Required accelerated carbonation resistances (ka in mm/year1/2).

Scenario Model code New method

A 24 35B 16 24C 47 50D 35 36A semi-probabilistic approach that uses a safety factor in asso-ciation with a reliability index was adopted.

The impact of not considering an acceptable level of deteriora-tion where corrosion is allowed was analysed. For situations wherethe relative weight of the propagation stage was high (environ-mental class XC3), the period was considered as an additionalsafety margin, as reected in the allowance of a lower reliabilityindex.

A practical method was proposed, whose main features are:

Use of only one analytical model. Analytical model calibrated with long term results. Analytical model requiring just two parameters. Use of a single safety factor.

Moreover, a comparative analysis with a reference method hasshown that the new proposed method is suitable to establish car-bonation performance requirements.

Acknowledgments

The authors acknowledge Brisa Auto-Estradas de Portugal, SAfor the possibility of using structures from its concessions for thedevelopment of this work and are grateful for the support of theICIST Research Institute, ESTBarreiro, Polytechnic Institute of Set-

ironmental class XC4.

ing Materials 36 (2012) 585591bal, IST, Technical University of Lisbon and FCT (Foundation forScience and Technology).

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A method for the use of accelerated carbonation tests in durability design1 Introduction2 Limit states and reliability3 Carbonation rate model4 Design criteria5 Proposed method6 Comparative analysis7 ConclusionsAcknowledgmentsReferences