Reinforcement Corrosion Concrete 2008

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ACI Materials Journal/January-February 2008 3

ACI MATERIALS JOURNAL TECHNICAL PAPER

ACI Materials Journal, V. 105, No. 1, January-February 2008.MS No. M-2005-335.R3 received February 2, 2007, and reviewed under Institute

publication policies. Copyright © 2008, American Concrete Institute. All rights reserved,including the making of copies unless permission is obtained from the copyright proprietors.Pertinent discussion including authors’ closure, if any, will be published in the November-December 2008 ACI Materials Journal if the discussion is received by August 1, 2008.

Based on extensive research on reinforcing steel corrosion inconcrete in the past decades, it is now possible to estimate theeffect of the progression of reinforcement corrosion in concreteinfrastructure on its structural performance. There are still areasof considerable uncertainty in the models and in the data available,however. This paper uses a recently developed model for reinforcementcorrosion in concrete to improve the estimation process and toindicate the practical implications. In particular, stochastic modelsare used to estimate the time likely to elapse for each phase of thewhole corrosion process: initiation, corrosion-induced concretecracking, and structural strength reduction. It was found that, for

practical flexural structures subject to chloride attacks, corrosion

initiation may start quite early in their service life. It was also foundthat, once the structure is considered to be unserviceable due tocorrosion-induced cracking, there is considerable remaining servicelife before the structure can be considered to have become unsafe.The procedure proposed in the paper has the potential to serve as arational tool for practitioners, operators, and asset managers tomake decisions about the optimal timing of repairs, strengthening,and/or rehabilitation of corrosion-affected concrete infrastructure.Timely intervention has the potential to prolong the service lifeof infrastructure.

Keywords: cracking; serviceability; steel corrosion; strength.

INTRODUCTIONThe corrosion of reinforcing steel in concrete is recognized as

a significant problem for concrete infrastructure subjected tochloride environments (Bentur et al. 1997). Corrosion-induced structural deterioration is a gradual process with acommencement time not always obvious from externalexamination. Once reinforcement corrosion becomes active,however, it almost invariably causes concrete cracking;excessive deflection, and, eventually, the loss of structuralultimate strength, with potentially catastrophic consequences.There has been extensive research on steel corrosion inconcrete in the past decades (ACI Committee 365 2000;Andrade et al. 1993; Castel et al. 2000; Hong and Hooton1999; Melchers and Li 2006; Pantazopoulou and Papoulia2001; Roberts et al. 2000; Weyers et al. 1994); and it is nowpossible to provide a reasonable estimate of the wholeprocess of reinforcement corrosion in concrete infrastructure. Itis important to note that this also allows its effects on structuralperformance to be estimated and enables the service life ofcorrosion-affected concrete infrastructure to be predictedusing various theoretical frameworks developed in the pastfew years (Frangopol et al. 1997).

Despite these significant advances, there are still areas ofconsiderable uncertainty in the various models and in thedata available. In an effort to provide some improvement,Melchers and Li (2006) recently developed a phenomeno-logical model for the corrosion of reinforcing steel bars inconcrete as a function of time (Fig. 1). The model has a

number of features in common with earlier models butdiffers from them in important ways (Tuutti 1982; Weyers etal. 1994; Bentur et al. 1997; Francois and Arliguie 1999). Inprinciple, the model applies to the steel bar at a generic crosssection of a reinforced concrete member. The model dividesthe corrosion process into two stages with six detailedphases. The two stages of corrosion initiation and propagationare similar to those of Tuutti (1982), but the detailed phasescomprising them are derived from the mechanics of corrosion

(Melchers 2003). As shown in Fig. 1, Phase D1 is the diffusionof chlorides into the concrete and the commencement ofleaching of hydroxyl ions out of the concrete. When there arecracks present in the member (for example, flexuralmembers), the local time to initiation t ic is governed by thetime of occurrence of the local crack(s) (Li 2002). When nocracks occur in the member, t ic tends to be the initiation timet i, which is governed by the rate of diffusion and thereforethe permeability of the concrete (Melchers and Li 2006). Att i, the chlorides will have reached the steel but the balancebetween the concentrations of the Cl– and (OH)– ions and thepH may not be such that active corrosion will actuallycommence (which is denoted as t ac).

During Phase C0, the rate of corrosion tends to increase

because the pH will typically reduce due to the leaching ofhydroxyl ions out of the concrete. In Phase C1, the propagationof corrosion is governed by the rate of oxygen and watersupplies and the conditions at the steel corroding surface.Because of microcracking (for example, caused by stress)and the resulting loss of influence from Cl– and (OH)– ionsand the greater permeability, the environment external to the

Title no. 105-M01

Prediction of Reinforcement Corrosion in Concrete and Its

Effects on Concrete Cracking and Strength Reduction

by Chun-Qing Li, Yang Yang, and Robert E. Melchers

Fig. 1—Phenomenological model for steel corrosion inconcrete. (Note: diameter loss in mm.)



4 ACI Materials Journal/January-February 2008

concrete will increasingly control the corrosion rate. As

corrosion progresses, there will be an increasing build-up of

corrosion products and associated increased radial stresses,

causing longitudinal cracking and, eventually, concrete spalling.

Moreover, the increasing build-up of corrosion products on

the corroding surfaces will contribute to an increasing resistance

to oxygen diffusion (that is, the rate of oxygen supply to the

corroding surfaces). Phase C2 denotes the period when this

controls the rate of corrosion. Eventually, the rate of oxygen

diffusion to the corroding bars through the rust layer will

become so low that anaerobic corrosion activity will set in

(Melchers 2003). This is shown as Phase C3 in Fig. 1.

This paper explores the implications of the corrosion

model in Fig. 1 for practical applications. Moreover, it

investigates the effects of the whole corrosion process on

structural performance over time, using criteria relevant to

practical applications and expressed in conventional ultimate

and serviceability limit states. To allow for the fact that there

are still considerable degrees of uncertainty in data and in

some of the models, stochastic methods are applied. This

recognizes that both the corrosion process and its effects on

structural performance are not only random but also time

variant. The procedure proposed in the paper can serve as arational tool for practitioners, operators, and asset managers

to make decisions about the optimal timing of repairs and

strengthening and/or rehabilitating corrosion-affected

concrete infrastructure.

RESEARCH SIGNIFICANCEAlthough research on steel corrosion in concrete has been

both extensive and intensive for the past three decades or so

(see the previous references), it has focused largely on the

initiation of corrosion and, to a lesser extent, its propagation,

rather than on its effect on structural performance. The

whole process of corrosion in concrete infrastructure and, in

particular, its effects on structural deterioration over timehave been accorded little attention (Val and Melchers 1997;

Iwanami et al. 2002). In practice, corrosion tends to be a

visual problem for concrete infrastructure (for example,

stains and concrete cracking), but its effect on structural

performance (that is, the downgrading of safety and

serviceability) is of greater concern to practitioners, operators,

and asset managers. This paper addresses both issues by

attempting to provide a means for estimating the onset of

each phase of the corrosion process, thereby facilitating timely

maintenance for corrosion-affected concrete infrastructure, with

the potential to prolong its service life.

CORROSION INITIATIONIt is well known that even when the chloride content at the

surface of reinforcing steel bars exceeds a threshold value,the corrosion of the steel does not necessarily start in theconcrete (Li 2002). For this reason alone it is appropriate torepresent the corrosion of reinforcing steel in concrete as arandom phenomenon. The time to corrosion initiation can beestimated in a stochastic manner as follows

pi(t ) = P[ A ∩ B] (1)

where pi(t ) is the probability of corrosion initiation at time t , Pis the probability of an event, and ∩ denotes the intersectionof events, and B is the event of corrosion onset. In Eq. (1), A isthe event that the chloride content C Cl at the surface of steelbars exceeds a threshold value δCl, which is denoted as

(2)

Using conditional probability and substituting Eq. (2) intoEq. (1) yields

(3)

where P[ξ] = P[ B| A] is the probability of corrosion onset fora given threshold value δCl. Thus, for a given acceptableprobability pi,a, whenever

pi(t i) ≥ pi,a (4)

the initiation time of steel corrosion in concrete is determined,that is, t i. Clearly, pi,a represents the reliability (or confidence) ofthe prediction.

Model for chloride content CCl(t)—Various attempts havebeen made to model the chloride ingress in concrete,including analytical models based on such theories as diffusion,absorption and electrostatic fields (for example, Bažant1979; Roberts et al. 2000), and empirical models based onresults from laboratory experiments (Hong and Hooton1999) and/or collected from sites (Bamforth 1999). Of allmodels available, it appears that the model based on thetheory of diffusion can best represent the chloride ingress inconcrete (Bamforth 1999). According to the diffusiontheory, the chloride content (concentration) in concreteC Cl( x ,t ), at a distance from the concrete surface x and at agiven time t , can be estimated by Fick’s second law asfollows (Roberts et al. 2000)

(5)

where Dc is the apparent (or effective) diffusion coefficientfor concrete. Taking x as the concrete cover, the chloridecontent C cl (t ) at the surface of steel bars at time t can be obtainedas follows (Bamforth 1999; Li et al. 2003)

(6)

A C Cl t ( ) δCl≥[ ]=

pi t ( ) P C Cl t ( ) δCl≥[ ] P ξ[ ]×=

∂C Cl x t ,( )∂t

------------------------ Dc∂2C Cl x t ,( )

∂ x 2

--------------------------=

C Cl t ( ) C s 1 er f x

Dct 2

------------

–=

Chun-Qing Li is a Professor of civil engineering at Zhejiang University of Technology,

Hangzhou, China, and at the University of Greenwich, London, UK. His research

interests include risk and reliability analysis of civil works, effects of steel corrosion on

structural behavior, methodology of whole life designs and assessment of infrastructure,

stochastic modeling of loads (for example, winds) and structural resistance deterioration,

and general risk assessment.

Yang Yang is a Professor of civil engineering at Zhejiang University of Technology.

His research interests include durability of concrete and concrete structures, chloride

ingress in concrete, behaviors of concrete at early age, creep and volume change of

concrete, and properties of materials in concrete structures.

Robert E. Melchers is the Chair of Civil Engineering and Director of the Centre for

Infrast ructure Performance and Reliabi lity at the Univers ity of Newcastle,Callaghan, Australia. His research interests include structural engineering risk andreliability analyses, risk-based decision-making and life-cycle management, and

deterioration modeling (including corrosion and fiber composites).




where C s is the equilibrium chloride content on thesurface of the concrete and erf is the error function. Ascan be seen, both Dc and C s are assumed constant,although in practice they are generally not constant(Bamforth 1999 and Li et al 2003).

In applying Fick’s second law to predicting chlorideingress in concrete, an important assumption has been madein deriving the solution to Eq. (6). That is, the bulk concreteis assumed to be a homogeneous material, thereby essentiallyeliminating the possible influence of internal cracking. Most

concrete design codes and standards allow concrete to crackto certain limits of crack width, for example, ACI 318-99(ACI Committee 318 1999) and British Standard BS 8110(1997). Hence, it is desirable that solutions to Fick’s secondlaw can accommodate this. A solution based on fluidmechanics, whereby the diffusion of chloride into thecracked concrete is modeled as a combined Knudsen flowand viscous flow, has been proposed (Li et al. 2003), with thediffusion coefficient for cracked concrete determined from

(7)

where µ is the coefficient of viscosity of the chloride ions(in Pa·s); λc is the mean free path of chloride ions (in µm); wis the crack width at concrete surface (in mm); and β is aconstant for the chloride to be in a steady state. Obviously,the parameters of Eq. (7) are environment-dependent andhence need to be calibrated in each application. Based onexperimental results on cracked concrete with crack widthsin the range of 0.05 to 0.3 mm (0.002 to 0.012 in.) and underthe simulated marine environment (tidal and splash zones) (Li etal. 2003), it can be shown that Dc

cr = 43.89w2 in mm2 /day,where w is the crack width on the surface of the concrete(in mm).

Model for corrosion onset P[ξ ]—In the real world ofconcrete structures, the corrosion onset on the steel bar is

also random. Most research in this area (Bamforth 1999;Roberts et al. 2000) focuses on determining a critical valueof chloride concentration, that is, the threshold above whichthe corrosion is initiated. Unfortunately, there is no generalagreement as to the threshold level of chloride content.According to Dhir (1999), the threshold value for corrosioninitiation varies from 0.15 to 1.5 (in percent of cementweight) based on the results of various researchers andvalues used in the standards. This dispersion of thresholdvalues highlights the need to develop a probabilistic model forcorrosion onset with respect to chloride content because thethreshold itself is a random variable.

Li (2002) carried out comprehensive experiments on theonset of steel corrosion in concrete under marine tidal andsplash conditions that were simulated in an environmentalchamber with controlled saltwater spray for intermittentwetting and drying. In the experiment, the corrosion onsetwas verified by visual inspection after breaking open theconcrete and taking out the reinforcing bars. Due to the spacelimit, details of the experiment cannot be described herein(refer to Li 2002). Test results shown in Fig. 2 represent 39 testspecimens of normal portland cement concrete with a water-cement ratio (w / c) of 0.45. As can be seen, the range of chloridecontent from 0.04 to 0.07 (in percent of concrete weight, whichis approximately 0.334 to 0.585 in percent of cement weight forgiven mixture proportions) is the most sensitive concentration to

Dc

cr βλc

6µ---------w

2=

corrosion onset. These values are consistent with the thresholdvalues noted previously for a range of w / c (Dhir 1999). Inprinciple, Fig. 2 can be represented by a normal distribution.

With models for both C Cl(t ) and P[ξ] now available, using

Eq. (3), it is possible for a given threshold value of chloridecontent to estimate the probability of corrosion initiation asa function of time. Standard reliability methods are employedin the computation, such as the first-order reliability (FOR)method and the Monte Carlo simulation, both of which arewell known and described in Melchers (1999). With thestatistical values of basic variables in Table 1, such resultsare shown in Fig. 3 and 4 for both cracked and uncrackedconcrete (where the corresponding coefficients of diffusionare used in estimating C Cl(t )). As can be seen, the effects ofchloride ingress and threshold values of chloride content onthe probability of corrosion initiation are interrelated. Asexpected, the threshold value determines the final probability ofcorrosion initiation. Thus, for a given acceptable probability

of corrosion initiation pi,a, the initiation time t i can bedetermined using Eq. (4). To be consistent with ASTMC876 (1991), which uses 90% confidence level to predictcorrosion initiation, let

pi(t i) = 0.9 (8)

from which t i ≈ 16 years (189 months) with the threshold δCl =0.06 for concrete without cracks. This result is consistentwith many of published results (Bamforth 1999; Roberts et al.2000). For cracked concrete with a crack width of 0.1 mm(0.0004 in.), Eq. (8) gives t ic = 0.57 years (208 days) for the

Fig. 2—Probability distribution of corrosion onset in termsof chloride content.

Fig. 3—Probability of corrosion initiation with time (crackedconcrete).




same δCl = 0.06. Observations from practical concretestructures (with flexural cracks) located in a marine environment(Francois and Castel 2001; Mohammed and Hamada 2003)correspond well to this result.

CORROSION-INDUCED CONCRETE CRACKINGBecause in practice the time to active corrosion t ac cannot

be observed, it is conventional to use a substitute t nom (referto Fig. 1), which is the time determined by Eq. (4) and is thetime at which corrosion is assumed to occur at a significantrate. In this paper t nom is taken to be either t i or t ic (only oneof which occurs).

For the same reasons as for the initiation time, the time tocorrosion-induced concrete cracking should be determinedin a probabilistic manner. According to design codes andstandards (ACI Committee 318 1999; British Standard BS8110 1997), the practical criterion related to concrete crackingof concrete structures is to limit the crack width to aprescribed level rather than attempt to eliminate crackingcompletely. The probability that the corrosion-induced crackwidth w(t ) on a concrete surface is greater than a prescribed

limit wcr can be determined from

pc(t ) = P[w(t ) ≥ wcr ] (9)

where t is the time from corrosion initiation. In analogy tocorrosion initiation, for a given acceptable probability pc,a,whenever

pc(t c) ≥ pc,a (10)

the time t c to corrosion-induced cracking is determined. Toperform this analysis, models are required for crack widthand for a crack width limit. These are now considered.

Model for crack width w(t)—Concrete with embeddedreinforcing steel bars can be modeled as a thick-wallcylinder (Bažant 1979; Pantazopoulou and Papoulia 2001).This is shown schematically in Fig. 5(a), where D is thediameter of steel bar, d 0 is the thickness of the annular layerof concrete pores (that is, a pore band) at the interfacebetween the steel bar and concrete, and C is the concretecover. The inner and outer radii of the thick-wall cylinder area = ( D + 2d 0)/2 and b = C + ( D + 2d 0)/2. When the steel barcorrodes in concrete, its products (that is, rust, mainlyferrous and ferric hydroxides, Fe(OH)2 and Fe(OH)3) fill thepore band completely and a ring of corrosion products forms,

the thickness of which, d s(t ) (Fig. 5(b)), can be determined

from (Liu and Weyers 1998)

(11)

where αrust is a coefficient related to the type of corrosionproducts, ρrust is the density of corrosion products, ρst is thedensity of steel, and W rust (t ) is the mass of corrosion products.Obviously, W rust (t ) increases with time and can be determinedfrom (Liu and Weyers 1998)

(12)

where icorr (t ) is the corrosion current density (in µA/cm2),which is a measure of the corrosion rate r 0 (in mm/year)(Fig. 1). Based on Faraday’s law (Bentur et al. 1997), r 0 =0.0116icorr ,where r 0 is measured as the metal loss of steelbars in a radial direction.

The growth of the ring of corrosion products (known as arust band) exerts an outward pressure on the concrete at theinterface between the rust band and concrete. Under thisexpansive pressure, the concrete cylinder undergoes threephases in the cracking process: 1) not cracked; 2) partially

cracked; and 3) completely cracked. In the Phase 1 (nocracking), the concrete can be considered to be elasticallyisotropic so that the theory of elasticity can be used to determinethe stress and strain distribution in the cylinder (Timoshenkoand Goodier 1970). For a partially cracked concrete cylinder,cracks are considered to be smeared and the concrete to be aquasi-brittle material, so that the stress and strain distributionin the cylinder can be determined based on fracture mechanics(Bažant and Planas 1998; Pantazopoulou and Papoulia 2001).When the crack penetrates to the concrete surface, theconcrete cylinder fractures completely. With known distribu-tion of stress and strain, the crack width at the surface of theconcrete cylinder can be determined simply by the difference

(13)

where εθ(b) is the tangential strain at the surface, that is,at r = b (Fig. 5) and equal to (Li et al. 2006)

(14)

where νc is Poisson’s ratio of concrete and α (<1) is thetangential stiffness reduction factor, which is to account for

d s t ( )W rust t ( )

π D 2d 0+( )---------------------------

1

ρrust

----------- αrust

ρst

-----------– =

W rust t ( ) 2 0.1050

t

∫ 1 αrust ⁄ ( )π D icorr × t ( )dt

1 2 ⁄

=

wc 2πb εθ b( ) εθe m, b( )–[ ]=

εθ b( )2d s b ⁄

1 νc–( ) a b ⁄ ( ) α1 νc+( ) b a ⁄ ( ) α

+

---------------------------------------------------------------------------------------=

Fig. 4—Probability of corrosion initiation with time(uncracked concrete).

Fig. 5—Schematic representation of cracking process.




residual tangential stiffness of the cracked concrete andrelated to the average tangential strain at the cracked surfaceand concrete properties (Bažant and Planas 1998; Li et al.2006). In Eq. (13), εe,m

φ (b) is the maximum elastic strain atr = b and equal to (Timoshenko and Goodier 1970)

(15)

where E ef is the effective elastic modulus of concrete. Thus,the crack width can be expressed as

(16)

In Eq. (16), the key variables are the thickness of corrosionproducts d s, which is directly related to the corrosion rate r 0(or icorr ), and the stiffness reduction factor α, which is relatedto stress conditions and concrete property and geometry.

Equation (16) has been verified by both numerical andexperimental results (Li et al. 2006).

It needs to be noted that Eq. (16) represents a single crack.Due to the random nature of crack occurrence, there may bemore than one crack occurring either simultaneously orwithin a short period of time. In this case, the assumption thatthe crack width of all cracks is equal could be made (Li et al.2006). Thus, Eq. (16) is still applicable but wc should bedivided equally by the number of cracks. In any event,Eq. (16) represents the maximum crack width on the surfaceof concrete.

Limit for crack widthwcr — To determine the probability ofcorrosion-induced cracking, a critical limit for the crackwidth needs to be established. In general, the acceptablelimit for crack width wcr is in the range of 0.1 to 0.5 mm(0.004 to 0.02 in.), depending on exposure conditions(Andrade et al. 1993; Vu and Stewart 2002). Most designcodes and standards, such as ACI 318-99 (ACI Committee318 1999) and British Standard BS 8110 (1997), however,prescribe the maximum permissible crack width to be 0.3 mm(0.012 in.) for concrete structures. With wcr = 0.03 mm(0.0012 in.) and the values of other variables given in Table 1,the probability of corrosion-induced concrete cracking canbe computed using Eq. (9) and a Monte Carlo simulationmethod. The results are shown in Fig. 6 with differentacceptable limits for crack width.

εe m,θ b( )

f t

E ef

-------=

wc

4πd s

1 νc–( ) a b ⁄ ( ) α1 νc+( ) b a ⁄ ( ) α

+

---------------------------------------------------------------------------------------2πbf t

E ef

-------------–=

The time to corrosion-induced concrete cracking can be

determined for a given acceptable risk pc,a using Eq. (10).

For example, Fig. 6 shows that t c = 5.37 years for pc,a = 0.1.

Although a large number of variables can affect the corrosion

process and hence the resulting concrete cracking, the

corrosion rate (r 0 or icorr ) is usually the most significant

factor (refer to the sensitivity analysis in Li et al. [2006]).Figure 7 shows the effects of corrosion rate (taken as a

constant in the computation) on the probability of concrete

cracking. For example, an increase of icorr from 1 to 10 µA/cm2

can lead to the reduction of cracking time from approximately

8 years to 1year, given the same acceptance criterion, that

is pc,a = 0.1. Interestingly, these results are consistent with

practical experience and laboratory observations (Andrade

et al. 1993; Liu and Weyers 1998). As may be appreciated, in

real structural assessment icorr can only be obtained from site-

specific measurement on the structure to be assessed and is

known to be subject to considerable uncertainty. The accuracy

Fig. 6—Probability of corrosion-induced cracking fordifferent acceptable limit wcr.

Table 1—Values of basic variables usedin computation

Basic variable Symbol MeanCoefficientof variation Source

Steel content Ast 226 mm2 0.1Li (2003),

Mirza et al. (1979)

Width of beamsection

B 120 mm 0.1Li (2003),

Mirza et al. (1979)

Concrete cover C 31 mm 0.2Li (2003),

Mirza et al. (1979)

Equilibrium

surfacechloride content

C s

0.306

(percent ofconcrete weight)

0.2 Bamforth (1999),Li (2002)

Diameter ofsteel bar

D 12 mm 0.15Li (2003),

Mirza et al. (1979)

Diffusioncoefficient(uncrackedconcrete)

Dc

1.55 ×

10–11 m2 /s

(1.34 mm2 /day)

0.2Bamforth (1999),

Li (2002)

Diffusioncoefficient(crackedconcrete)

D ccr

43.89w2 0.2 Li (2003)

Thickness ofpore band

d 0 12.5 µm —Liu and Weyers

(1998)

Compressivestrength of concrete

f c 57 MPa 0.14Li (2003),

Mirza et al. (1979)

Tensile strengthof concrete

f t 5.725 MPa 0.2Li (2003),

Mirza et al. (1979)

Yield strengthof steel

f y 400 MPa 0.1Li (2003),

Mirza et al. (1979)

Height of beamsection

H 200 mm 0.1Li (2003),

Mirza et al. (1979)

Corrosioncurrent density

icorr 0.3686ln(t ) +

1.1305 µA/cm2 0.2Li (2003),

Vu and Stewart(2002)

Effectiveelastic modulus

of concrete E ef 18.82 GPa 0.12

Li (2003),Mirza et al. (1979)

Coefficientrelated to type

of rustαrust 0.57 —

Liu and Weyers(1998)

Density of rust ρrust 3600 kg/m3 — Liu and Weyers(1998)

Density of steel ρst 7850 kg/m3 —Liu and Weyers

(1998)

Poisson’s ratioof concrete

νc 0.18 — Li (2003)

Note: Random variables are assumed of normal distribution.




with which it can be measured is therefore directly reflected inthe accuracy with which the serviceability and safety ofcorrosion-affected concrete structures can be predicted. Thismay vindicate the significance of developing a corrosionmodel as proposed in Fig. 1.

CORROSION-INDUCED STRENGTH REDUCTIONEventually, the steel corrosion in concrete will reduce the

cross-sectional area of the steel bar. As a result, the strengthof the cross section of the structural member is reduced,perhaps leading to the final rupture of the structural member.An estimate of the probability ps of corrosion-induced loss ofstrength is as follows

(17)

where Rs(t ) is the residual strength at a cross section of the

structural member at time t and Ra is a minimum acceptablestrength. Again, t is the time from corrosion initiation. For agiven acceptable probability for loss of strength ps,a, whenever

ps(t s) ≥ ps,a (18)

it is the time the structure loses its strength due to corrosion.This is usually the end of service life for the structure basedon the criterion of safety or major strengthening is required.

Model for Rs(t)—The residual sectional strength Rs(t ) of aconcrete structural member can be expressed in terms of thenet area of the cross section of the reinforcing bar Anet (t ), as

ps t ( ) P Rs t ( ) Ra≤[ ]=

(19)

where the function f [ ] is provided in standard references forreinforced concrete structures (Park and Paulay 1975) ordesign codes (ACI Committee 318 1999). In Eq. (19), ψ isa coefficient to be determined from calibration against dataproduced from direct loading tests (Li 2003), which will takeinto account those aspects that have not been explicitlyconsidered in the model, such as debonding due to corrosion;and E is a vector of factors affecting the cross-sectional areareduction of the reinforcing bar, including concrete mixtures(for example, w / c) and the environment (for example,marine). The most significant overall factor is the corrosioncurrent density icorr (that is, corrosion rate r 0).

Based on Faraday’s law and from the corrosion model ofFig. 1, the net area of the reinforcing bar Anet (t ) can beexpressed as

(20)

Obviously, the coefficient ψ is application dependent andshould be calibrated using data obtained from the structure tobe assessed. Herein, it is estimated that ψ ≈ 0.85 from testresults produced on concrete beams (flexural failure) ofstructurally significant size under simulated marine environment(tidal and splash zones) (Li 2003). Other failure modes canbe incorporated once data are available.

Acceptable strength Ra — It is very difficult to decide anacceptable limit for loss of strength because the safety is ofparamount importance. It is not just a technical issue andthere is not much practical experience in this area either.Gonzalez et al. (1996) observed that a damage level of 25%in terms of the cross-sectional area reduction of steel barsseemed to be prominent in corrosion-affected concretestructures. This observation is based on the data from theEuro-International Committee of Concrete (CEB) thatclassifies structural deterioration according to the externalsigns, such as rust spots, concrete cracks, cover delamination,as well as cross section area reduction of steel bars. Gonzalezet al. (1996) indicated that the acceptable limit depends onthe type of structure and its use. Amey et al. (1998) predictedthe service life of corrosion-affected concrete structures usinga more simplistic 30% of reinforcing bar area reduction as thefailure criterion. In this paper, Amey et al.’s criterion will beused as the strength limit, that is, for Ra = 0.7 R0, where R0 isthe original strength of the intact structure and can be obtainedfor a given cross section (width B and height H ) and materialproperties (for example, steel content Ast and yield strength f yand concrete compressive strength f c).

With values of basic variables in Table 1, Fig. 8 shows theprobability of corrosion-induced loss of strength (measured

Rs t ( ) ψ f Ane t E t ,( )[ ]×=

Ane t t ( )

π D 2 0.0116 icorr ×

0

t

∫ t ( )dt –

2

4-------------------------------------------------------------------------=Fig. 8—Probability of corrosion-induced loss of strength for

different acceptable limit Ra (as a percentage of R0).

Table 2—Summary of each phaseof corrosion process

PhaseTime period with 90%

confidence, years Relative to t s , %

Corrosion initiation (0, t i ) (0, 0.57) 4.76

Concrete cracking (t i , t c) (0.57, 5.94) 49.58

Loss of strength (t c , t s) (5.94, 11.98) 100

Fig. 7—Effect of corrosion rate (icorr) on concrete cracking.




by flexural capacity) with different acceptable limits forstrength. As can be seen, the probability of loss of strength isvery sensitive to the acceptable limit. It is therefore essentialto determine an optimal acceptable limit based on a risk-costoptimization for the structure (Thoft-Christensen andSorensen 1987), coupled with comprehensive field surveyon conditions of structural deterioration during its wholeservice life (Amey et al. 1998; Gonzalez et al. 1996). Finally, thetime that a concrete structure becomes unsafe due to corrosion-induced loss of strength can be determined for a given

acceptable risk. Again, different acceptance criteria willresult in different times for the structure to be unsafe. This isthe risk involved in decision making. To be consistent withpredictions for corrosion initiation and corrosion-inducedcracking, in which a 90% confidence level is used, the timefor the structure to be unsafe t s can be determined as follows

ps(t s) = 0.1 (21)

which results in t s = 11.41 years.In summary, each phase of the corrosion process as

determined based on structural performance is shown inTable 2. Because the values of those environment-dependentparameters used in computation were taken from the data

produced from the tests carried out on flexural members (Li2003), the results in Table 2 are, strictly speaking, onlyapplicable to concrete structures with (flexural) cracks.The significance of the results, however, lies in the provisionof a complete picture for service life performance of corrosion-affected concrete infrastructure. With this picture, each phaseof the service life of the structure can be determined in relativeterms. For example, for a given reliability of 90%, structuraldeterioration as marked by corrosion initiation starts as earlyas approximately 5% of the service life of concrete flexuralmembers in marine environments (without prior preventionmeasures). After the structure deteriorates to such an extentto become unserviceable due to concrete cracking (withoutany interventions), there is some 50% of the service life

remaining before the structure finally becomes unsafe (lossof strength) according to the criteria used herein.

The information in Table 2 could be of practical interest tostructural engineers, operators, and asset mangers ofconcrete infrastructure concerned with decisions aboutwhen, where, and what interventions (repairs, strengthening,and/or rehabilitation) might be required and, more importantly,how much longer can a deteriorated structure can lastwithout intervention at a certain stage.

The results in Table 2 may suggest that the serviceabilityof corrosion-affected concrete structures (as measured bycracking) deteriorates much faster than their strength. Thismay explain why many concrete structures are seen as badlydeteriorated (for example, mass concrete spalling) but maystill be structurally adequate (Roberts et al. 2000).

CONCLUSIONThe whole process of corrosion of steel reinforcement in

concrete structures and its effects on structural performanceover time can be estimated using the principles outlined inthis paper. The approach is based on practical criteriaincluding safety and serviceability as functions of time foreach phase of the corrosion process. Because of unresolveduncertainties in the models and the data currently available,the procedure relies on using stochastic methods. The resultsfor a typical example structure show that with 90% confidence

structural deterioration as marked by corrosion initiationstarts as early as approximately 5% of the service life ofconcrete infrastructure with cracks and located in marineenvironments. Also, for the example considered, once aconcrete structure becomes unserviceable due to corrosion-induced concrete cracking, there is still some 50% of theservice life remaining before it becomes structurallyunsafe. The methods presented have the potential to serveas a rational guide for practitioners, operators, and assetmanagers to make decisions with regard to repairs,

strengthening, and/or rehabilitation of corrosion-affectedconcrete infrastructure.

ACKNOWLEDGMENTSFinancial support from the Engineering and Physical Sciences Research

Council (Grant No. EP/E00444X/01) and the Royal Academy of Engineering(Award No. 10177/93), and the Australian Research Council (GrantNo. LX0559653) is gratefully acknowledged.

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