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Experimental and Numerical Investigation ofCorrosion-Induced Cover Cracking in ReinforcedConcrete StructuresDimitri V. Val1; Leonid Chernin2; and Mark G. Stewart3Abstract: In the paper corrosion-induced crack initiation and propagation are investigated experimentally and numerically, with particu-lar emphasis on quantifying the proportion of corrosion products that are dissipated within the concrete pores and cracks, thus reducingthe pressure exerted by corrosion products on the surrounding concrete. Initially, experimental data on crack initiation and propagationobtained from accelerated corrosion tests of reinforced concrete slabs are presented. A comparison of finite-element model results andexperimental data is used to estimate the amount of corrosion products penetrating into concrete pores and cracks, which is an essentialparameter for prediction of corrosion initiation and propagation. It was found that the amount of corrosion products penetrating into theconcrete pores before crack initiation is larger than that obtained by other researchers. The paper also showed that corrosion products donot fully fill corrosion-induced cracks in concrete immediately after their initiation as the cracks are being filled gradually over time andthe thicker the concrete cover the longer it will take to fully fill a crack.DOI: 10.1061/?ASCE?0733-9445?2009?135:4?376?CE Database subject headings: Corrosions; Reinforced concrete; Cracking; Serviceability; Concrete structures.IntroductionCorrosion of embedded reinforcing steel is the main cause ofdeterioration of reinforced concrete ?RC? structures. Corrosioncan be caused by carbonation or by chloride ions penetrating intoconcrete ?Bentur et al. 1997?. Its effects on RC structures includecracking of the concrete cover, reduction and eventually loss ofbond between concrete and corroding reinforcement, and reduc-tion of cross-sectional area of reinforcing steel. Therefore, corro-sion affects both strength and serviceability of RC structures.Usually, excessive cracking caused by corrosion, which affectsthe normal performance of a structure, appears before corrosionhas any significant influence on the strength of the structure ?ElMaaddawy et al. 2005; Val 2005?. As a result, the time for struc-tural repair/replacement due to corrosion is usually controlled byserviceability limit states.Often, the initiation of corrosion has been treated as a service-ability failure ?Maage et al. 1996?. It is based on the assumptionthat the initiation period ?i.e., the time from the initial exposure ofa RC structure to an aggressive environment until corrosion ini-tiation? is much longer than the time from corrosion initiationto cracking. An alternative approach is to define serviceabilityfailure due to corrosion as the formation of a first crack in theconcrete cover ?Liu and Weyers 1998; Torres-Acosta andMartinez-Madrid 2003?. However, as has been shown by experi-mental studies, the time between corrosion initiation and firstcracking is usually short ?Andrade et al. 1993? and, therefore,differences between the two definitions of serviceability failureare insignificant. Moreover, cracks immediately after their initia-tion are very small ?hairline cracks of width less than 0.05 mm?and generally do not represent any danger or serviceability con-cern for a structure.Experimental studies carried out by Andrade et al. ?1993?showed that the time required for the formation of cracks of0.3 mm width ?which is the crack width usually associated withserviceability limit state? is about ten times longer than the timebetween corrosion initiation and first cracking. The result wascorroborated by other studies ?Stewart 2001?. This indicated thattreating corrosion initiation as a serviceability failure may be tooconservative. Thus, analyzing the behavior of RC structures aftercorrosion initiation ?i.e., predicting the time of first cracking,crack growth, the time when cracks become unacceptable due toserviceability requirements? is important for selecting efficientmaintenance and repair strategies. Of course, when it concernsserviceability it is usually within the jurisdiction of the owner ofa deteriorating structure to choose the time and type of action?e.g., inspection, repair, retrofit, replacement?. However, in orderto make rational decisions there is a need for sufficiently accurateand reliable predictive models. Moreover, in order to assess thecondition of an existing RC structure, knowledge of the amountof reinforcing steel lost due to corrosion is essential. While thisamount cannot be measured directly without removing the rein-forcing steel from the structure, it can be estimated indirectlyusing a model that relates the width of corrosion-induced crackswith the loss of cross-sectional area of reinforcement ?Maruyama1Reader, School of the Built Environment, Heriot-Watt Univ., Edin-burgh EH14 4AS, U.K. ?corresponding author?. E-mail: d.valhw.ac.uk2Ph.D. Student, Dept. of Structural Engineering and ConstructionManagement,FacultyofCivilandEnvironmentalEngineering,Technion-Israel Institute of Technology, Haifa 32000, Israel. E-mail:chernintx.technion.ac.il3Professor and Director, Centre for Infrastructure Performance andReliability, School of Engineering, The Univ. of Newcastle, Callaghan,NSW 2308, Australia. E-mail: mark.stewart.auNote. Associate Editor: Yahya C. Kurama. Discussion open untilSeptember 1, 2009. Separate discussions must be submitted for individualpapers. The manuscript for this paper was submitted for review and pos-sible publication on May 16, 2007; approved on November 11, 2008.This paper is part of the Journal of Structural Engineering, Vol. 135,No. 4, April 1, 2009. ASCE, ISSN 0733-9445/2009/4-376385/$25.00.376 / JOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2009Downloaded 16 Mar 2009 to 04. Redistribution subject to ASCE license or copyright; see /copyrightet al. 1989; Vidal et al. 2004; Thoft-Christensen 2005?.Some crack initiation models ?Liu and Weyers 1998; Panta-zopoulou and Papoulia 2001; Wang and Li 2004; Bhargava et al.2006? consider the effect of the penetration of corrosion productsinto a porous zone around a reinforcing bar, so that corrosionproducts only exert tensile stresses on the surrounding concreteafter this porous zone is filled. For crack propagation it has beenconveniently assumed that corrosion products fully fill a crackimmediately after its formation ?Molina et al. 1993; Berra et al.2003; Thoft-Christensen 2005?. This paper will investigate thethickness of the porous zone and extent of corrosion products thatpenetrate into cracks as this information is needed for crack ini-tiation and propagation modeling, respectively. In fact, the diffu-sion of corrosion products into concrete pores and cracks andassociated reduction of the pressure applied by the corrosionproducts to the surrounding concrete represent one of the mainfactors controlling crack initiation and propagation.Initially, a critical review of existing models for corrosion-induced crack initiation and propagation is presented. Results oncrack initiation and propagation obtained from accelerated corro-sion tests of RC slabs ?Vu et al. 2005? are then presented. Afinite-element ?FE? model is developed to numerically simulatethe cracking behavior of concrete. For the purpose of model veri-fication, comparison of FE results with experiments involving ac-tual corrosion of reinforcing steel is complicated since corrosionproducts diffuse through concrete pores and cracks so that inter-nal pressure acting on the surrounding concrete cannot be esti-mated accurately. In the case of crack initiation the model isverified quantitatively against a specific set of experimental data,in which cracking of the concrete cover is initiated by directapplication of pressure within holes made in concrete specimens?Williamson and Clark 2000?. Unfortunately, for crack propaga-tion similar experimental data ?i.e., when pressure is known? arenot available so in this case quantitative verification of the modelis not possible. In order to check the model capability to predictcrack propagation qualitative comparison with results of the ac-celerated corrosion tests ?Vu et al. 2005? is carried out. Since inboth cases a good agreement between the tests and FE results isobserved it is assumed that differences between FE analyses andexperimental data are mainly due to a certain amount of corrosionproducts penetrating into concrete pores and cracks and, there-fore, this amount can be estimated by assessing these differences.These preliminary results indicate that currently accepted ap-proaches to modeling the phenomena of corrosion products pen-etrating into concrete pores and cracks may be inconsistent andfurther research, in particular experimental, is needed.Overview of Existing Models for Corrosion-InducedCrack Initiation and PropagationOne of the first analytical models predicting the time of covercracking caused by the corrosion of the embedded reinforcingsteel was proposed by Bazant ?1979?. The model considers con-crete around a corroding reinforcing bar as a thick-walled cylin-der, which is subjected to internal pressure due to the formation ofcorrosion products having larger volume than that of the originalsteel. Stresses in the cylinder wall are calculated using the solu-tion provided by isotropic linear elasticity theory and it is as-sumed that cracking occurs when the stresses reach the tensilestrength of concrete. However, experiments and field observationshave showed that the model significantly underestimates the timeof first cracking ?Liu and Weyers 1998?. This has been mainlyattributed to the following limitations of the model: it did not takeinto account diffusion of corrosion products into concrete poresand microcracks, and the corrosion rate was assumed constant. Anumber of modifications of the Bazant model, which tried to ac-count for these factors ?often by introducing empirical coeffi-cients which adjusted model predictions to experimental results?,have been proposed ?Liu and Weyers 1998; Pantazopoulou andPapoulia 2001; Wang and Liu 2004; Bhargava et al. 2006?. Themain modification of the Bazant model initially proposed by Liuand Weyers ?1998? consists of the introduction of a porous zonearound a reinforcing bar. The zone should be completely filledwith corrosion products before they start to exert pressure on thesurrounding concrete. Thus, the thickness of the porous zone be-comes one of the main parameters controlling the time of firstcracking. Liu and Weyers ?1998? also suggested that a corrosionrate was inversely proportional to the amount of corrosion prod-ucts formed and, therefore, decreased with time. However, thesolution, which they presented, was inconsistent and violatedFaradays law of electrolysis ?Chernin and Val 2008?.A number of experimental studies have been undertaken todetermine the critical amount of corrosion needed for concretecover cracking, to establish parameters having major influence onthis amount, and to derive simple empirical models for its evalu-ation ?Rasheeduzzafar et al. 1992; Andrade et al. 1993; William-son and Clark 2000?. The critical amount ?in terms of the weightof corrosion products or the depth of corrosion penetration? wasexpressed as a function of either only geometric parameterstheconcrete cover and the diameter of a reinforcing bar ?Alonso et al.1998?, or in addition also concrete propertiesthe compressivestrength ?Aligizaki 1999? or the splitting tensile strength ?Rod-riguez et al. 1996?. The last model was later adopted in DuraCrete?2000?.Crack propagation ?i.e., crack opening? due to corrosion hasbeen investigated in a number of studies, most of which involvedaccelerated corrosion tests ?with impressed current? that provideddata on the crack growth depending on the amount of corrosion?Maruyama et al. 1989; Andrade et al. 1993; Cabrera 1996; Ro-driguez et al. 1996; Alonso et al. 1998; Mangat and Elgarf 1999;Vu et al. 2005?. Vidal et al. ?2004? reported results linking theamount of corrosion with the width of cover cracks, which wereobtained from two beams naturally corroded in a saline environ-ment. In most of the experiments a linear relationship between theamount of corrosion and the crack width has been observed.Based on this observation a number of formulas relating the crackwidth with the amount of corrosion have been proposed. Some ofthe formulas were based on simple analytical considerations likethe assumptions of rigid body movements of cracked concrete?Maruyama et al. 1989; Cabrera 1996? or that an increase in thecrack volume was equal to the volume of corrosion products ?Mo-lina et al. 1993; Thoft-Christensen 2005?, while others were ob-tained by regression analysis of experimental data ?Rodriguez etal. 1996; Alonso et al. 1998; Vidal et al. 2004?. Vu et al. ?2005?proposed a nonlinear relationship between crack propagation and“concrete quality” defined as the ratio between the cover and thewater-cement ratio; the relationship includes a number of empiri-cal coefficients estimated by regression analysis of experimentaldata. Vu et al. ?2005? also developed a rate of loading correctionfactor to extrapolate crack propagation times obtained from accel-erated corrosion test results to crack propagation times for realis-tic ?lower? levels of corrosion.A number of numerical studies on corrosion-induced crackingof concrete using FE ?Dagher and Kulendran 1992; Molina et al.1993; Padovan and Jae 1997; Hansen and Saouma 1999; Thoft-JOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2009 / 377Downloaded 16 Mar 2009 to 04. Redistribution subject to ASCE license or copyright; see /copyrightChristensen 2005; Toongoenthong and Maekawa 2005; Du et al.2006; Ahmed et al. 2007? and boundary-element ?BE? ?Ohtsu andYosimura 1997; Farid Uddin et al. 2004? analysis have been un-dertaken. The studies used different two-dimensional ?2D? consti-tutive models ?plane strain formulation? to describe nonlinearbehavior and cracking of concrete. Several factors such as thediffusion of corrosion products into concrete and changes of thecorrosion rate with time were not taken into account. No com-parison with test results was provided ?Dagher and Kulendran1992; Ohtsu and Yosimura 1997; Hansen and Saouma 1999;Thoft-Christensen 2005?, or the comparison was just qualitative?Padovan and Jae 1997?, or when the comparison was quantitativepoor agreement was observed ?Molina et al. 1993?. The mainreason for the poor agreement between FE analysis and experi-mental results is that diffusion of corrosion products into concretepores and cracks has not been taken into account. Much betteragreement with test results was reported by Toongoenthong andMaekawa ?2005?, who explicitly considered the penetration ofcorrosion products into cracks forming in the surrounding con-crete ?possible diffusion of corrosion products into concrete poreswas ignored?. However, they did not validate their model againsttests results, in which corrosion-induced load acting on concrete?or the one simulating it?, was actually known. They also did nothave experimental data to examine the penetration of corrosionproducts into cracks after cracking of the concrete cover ?i.e.,during the crack propagation stage?. Moreover, friction betweencorroding reinforcing bars and concrete was neglected, whilecrack opening at the reinforcing bar/concrete interface and, sub-sequently, crack initiation and propagation, would depend on it?Leung 2001?.Experimental Data for Crack Initiation andPropagationThe numerical modeling to be developed herein relies on calibra-tion with experimental data when evaluating the corrosion prod-ucts ?rust? that dissipate into the concrete pores and cracks whichin turn reduces the concrete tensile stresses due to the expansivenature of the corrosion products.Eight RC 700 mm?1,000 mm?250 mm rectangular slabswere subject to accelerated rates of corrosion to study the relativeinfluence of concrete cover and water-cement ?w/c? ratio on thetime to crack initiation and crack propagation. The top mat of theslab contained four 16 mm diameter round steel reinforcing barsspaced 150 mm apart. The impressed current method was used toaccelerate the corrosion process ?see Fig. 1?. To generate crackswithin a reasonable time period, an accelerated corrosion rate of100 ?A/cm2was induced in all reinforcing bars. Three percent ofcalcium chloride ?CaCl2? by weight of cement was added to themix to induce corrosion along the length of the reinforcing bars.The following variables were used in this study: concrete cover?25, 50 mm? and w/c ratio ?0.45, 0.5, 0.58?. See Table 1 for adescription of the test variables for all specimens. The cementused for all specimens was ordinary Portland cement. Immedi-ately after crack initiation, 10 mm linear potentiometer displace-ment transducers ?POTs? were glued on both sides of the cracks tomonitor crack propagation. At the completion of the tests, rein-forcing bars were removed, cleaned, and the weight loss of barswas measured according to the gravimetric weight loss method asspecified in ASTM G1-90. The ability of such a test to realisti-cally simulate realistic corrosion conditions is yet to be fully con-firmed, however, an X-ray diffraction analysis of rust productsfound that corrosion products from this accelerated corrosion testproduced a similar morphology of rust products taken from aspecimen exposed to a marine environment for 5 years.Crack initiation is defined to occur when the crack is firstvisiblethis occurs when the width is approximately 0.05 mm?the same value for the initial crack width is also suggested inDuraCrete 2000?. After crack initiation, cracks then propagatewith their width and length increasing in an inhomogeneous man-ner, which then extend and join together to create continuouslongitudinal cracking when the crack width is approximately0.250.4 mm. In addition to the main cracks that propagated ver-tically above the reinforcing bars, there were two other radialcracks with lengths between 80 and 150 mm. These cracks wereinclined either 45 or 90 to the main crack.Experimental results showed that the measured corrosion ratesbased on weight loss data were not the same as the nominal?intended? corrosion rate of 100 ?A/cm2. Therefore, to give ameaningful comparison between specimen results, times to crackinitiation and crack propagation were corrected to a nominal cor-rosion rate of 100 ?A/cm2?e.g., if measured corrosion rate is120 ?A/cm2then the measured times to crack initiation andpropagation are increased by a factor 120/100? ?see Table 1 andFig. 2?. See Vu et al. ?2005? for further details of the experimentaldesign, results, and empirical model for crack propagation.Finite-Element Model DescriptionCrack initiation and propagation due to pressure caused by expan-sive corrosion products is initially modeled assuming that no cor-rosion products penetrate into the concrete pores and cracks. Theconcrete behavior is dominated by tensile cracking at a low levelof compressive stresses and in this case the constitutive behaviorof concrete can be modeled using an elastic cracking model. TheNaClsolutionRC specimenStainlessSteel plateCurrentregulatorReinforcing bar+Fig. 1. Impressed current experimental methodTable 1. Test Variables and Experimental Data for Time to Crack Initia-tion ?Adapted from Vu et al. 2005?Specimenw/cfc?MPa?ft?MPa?Cover?mm?Corrosion rate?A/cm2?Time to crackinitiationtcr,exp?h?SII?40.4552.74.5525100223.1SII?350100490.7SI?10.5203.0625100134.0SI?250100194.7SI?30.5434.1625100116.0SI?450100155.7SII?20.5842.253.9425100136.1SII?150100402.8378 / JOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2009Downloaded 16 Mar 2009 to 04. Redistribution subject to ASCE license or copyright; see /copyrightmodel accounts for cracking of concrete in tension, while con-crete between cracks is treated as an isotropic linear elastic con-tinuum. The crack initiation is defined based on the Rankinecriterion, according to which a crack forms in the direction nor-mal to the maximum principle tensile stress when this stress ex-ceeds the tensile strength of the concrete. Once a crack is formedat a point, its orientation is stored for subsequent calculations; anew crack at the same point can form only in a direction orthogo-nal to the direction of an existing crack ?the so-called fixed or-thogonal crack model?. The tension softening in the directionnormal to a crack is described based on the Hillerborg cohesivecrack model ?Hillerborg et al. 1976?, in which a stress-displacement curve is adopted from CEB-FIP model code 1990?CEB 1993?. Friction between a reinforcing bar and surroundingconcrete is described using the Coulomb friction model with thecoefficient of friction of 0.4 ?the lower limit for the coefficient offriction between concrete and corroded steel as suggested byLundgren 2002?. Deformability of corrosion products is ne-glected, which is a reasonable simplification since in the problemsconsidered in this study compressive stresses on the contact be-tween the corroded reinforcing bar and the concrete do not exceed30 MPa ?checked in the analyses? so that a relative decrease inthe thickness of the rust layer should be less than 10%. The latterestimate can be obtained by using experimental data on the de-formability of corrosion products reported by Ouglova et al.?2006?.In this study crack initiation and propagation are considered asa 2D problemplain strain formulation. Since this study concen-trates on the analysis of RC slabs subject to accelerated corrosiontests, in which uniformity of corrosion along the slab length isensured, the 2D simplification is suitable. For modeling naturalcorrosion, which may be strongly nonuniform along the length ofRC elements, the use of a 3D formulation can be more appropri-ate. The model is implemented in ABAQUSa commercial soft-ware package for nonlinear FE analysis. Four-node bilinear planestrain quadrilateral finite-elements with reduced integration andhourglass control are used to represent concrete, while steel of areinforcing bar is described by three-node linear plane strain tri-angle elements. The penalty contact algorithm is employed tomodel interaction ?including previously described friction? be-tween a corroded reinforcing bar and concrete. A nonlinear solu-tion is obtained using the explicit solution scheme. The meshsensitivity of results of the FE analyses has been checked. For thispurpose a concrete section with an embedded reinforcing bar wasanalyzed using two different FE mesheswith 700 elements ?seeFig. 5; the FE mesh inside the reinforcing bar is not shown? and1,600 elements. The difference between results of the analyseswas negligible ?less than 1%?. Thus, for further analyses thecruder and less time-consuming mesh ?700 elements? has beenselected.The free increase in the radius of a reinforcing bar due tocorrosion, ?, can be estimated as ?Lundgren 2002? =?r2+ ?v 1?2rpcorr pcorr2? r?1?where r=d/2=radius of the reinforcing bar; pcorr=corrosion pen-etration; and ?v=volumetric expansion ratio of corrosion prod-ucts. If pcorr?r, then instead of using Eq. ?1? it is sufficientlyaccurate to estimate ? as? = ?v 1?pcorr?2?If the corrosion rate is constant, the corrosion penetration ?mm? attime t ?years? after corrosion initiation can be found using Fara-days law of electrolysis as ?DuraCrete 2000?pcorr= 0.0116icorrt?3?where icorr=corrosion current density ?A/cm2?. Substitution ofEq. ?3? into Eq. ?1? ?or Eq. ?2? allows us to estimate the freeincrease in the radius of a corroding reinforcing bar at time t. Theexpansion of corrosion products around a corroding reinforcingbar is modeled using thermal analogy, i.e., by increasing the tem-perature of the reinforcing bar that leads to its thermal expansion? = ?T?Tr?4?where ?T=coefficient of thermal expansion; and ?T=increase intemperature. Since the material model is rate independent anycombination of values of ?Tand ?T providing a necessary valueof ? can be used.In order to validate the model it is necessary to compare it withexperimental results. However, a quantitative comparison withactual corrosion tests is difficult. Corrosion-induced cracking oc-curs because corrosion products have a larger volume than theoriginal steel of a corroding reinforcing bar. Thus, as corrosionprogresses the volume occupied by the reinforcing bar and thecorrosion products accumulating around it increases. This createsever increasing pressure on the surrounding concrete, which even-tually leads to the concrete cracking. Since part of forming cor-rosion products penetrates into concrete pores and cracks ?i.e.,does not accumulate around a corroding reinforcing bar? the ac-tual corrosion-induced expansion ?which has to be defined inorder to carry out a numerical analysis? cannot be estimated un-less the amount of corrosion products penetrated into concrete isknown. Up until now, this amount has never been measured di-rectly in experiments; its estimates have been obtained only indi-rectly ?by fitting the times to crack initiation calculated byanalytical/numerical models to those observed in tests? and assuch cannot be used for model validation, especially since theircorrectness is doubtful ?as will be shown further in the paper?.In order to resolve this problem, the model is validated againstresults of the tests carried out by Williamson and Clark ?2000?,which investigated cracking of the concrete cover due to pressureapplied within holes made in concrete specimens. Parameters var-ied in the tests included the diameter of the holes, d, the thicknessof the concrete cover, c, and the tensile strength of concrete.01.6010002000300000.4Crack width (mm)Time from start of test (hours)SI_3SII_2SI_4SII_3SII_4SII_1SI_1SI_2Corrosion penetration pcorr,exp(mm)Fig.2.Testresultsforrackpropagation?nominalicorr=100 ?A/cm2? ?adapted from Vu et al. 2005?JOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2009 / 379Downloaded 16 Mar 2009 to 04. Redistribution subject to ASCE license or copyright; see /copyrightResults of the comparison of pressure needed to cause crack ini-tiation are shown in Fig. 3, for bar diameters of 8 and 16 mm andvarious concrete tensile strengths. As can be seen, there is a goodagreement between the test and analytical results for d=8 mm?Fig. 3?a?, i.e., for the same tensile strength of concrete values ofthe failure pressure yielded by the FE analysis are within therange of those observed in the tests. For d=16 mm the agreementis worse, especially when the tensile strength of concrete is4.1 MPain this case the finite-element analysis leads to muchhigher values of the failure pressure compared with the tests ?seeFig. 3?b?. It is necessary to note that Williamson and Clark?2000? used the cylinder-splitting test to determine the tensilestrength of concrete ?Fig. 3 shows values of the failure pressureversus the splitting tensile strength?.The values of the splitting tensile strength have also been em-ployed in the FE analysis, which is not exactly correct since con-crete tensile strength depends on the test method and with theRankine criterion the axial tensile strength should be used. How-ever, there is still no general agreement concerning the relation-ship between the splitting and axial strengths of concrete. Whilein most of the publications addressing the topic it is stated that thesplitting of tensile strength of concrete is about 10% higher thanthat of the axial ?Neville 1977; CEB 1993?, other work has con-cluded that the splitting tensile strength actually underestimatesthat of the axial by about 1520% ?Lin and Wood 2003?. More-over, even a 10% decrese in the value of the concrete tensilestrength in the FE analysis would not significantly reduce thedifference between the numerical and experimental results for d=16 mm and the splitting tensile strength of 4.1 MPa. As can beseen, in this case failure pressures obtained in the tests decreasewith increasing tensile strength, while the calculated results showthe opposite tendency ?Fig. 3?b?. Williamson and Clark ?2000?tried to explain this by implying that fracture energy rather thanthe splitting tensile strength controlled failure of the concretecover. Since in the FE analysis crack propagation is described bythe cohesive crack model, which is based on fracture energy, thisexplanation does not look plausible. In fact, it is difficult to findany credible explanation for these particular test results.In the case of crack propagation, quantitative comparison withaccelerated corrosion test results is not possible due to the reasonexplained previouslypart of the corrosion products penetratesinto cracks and, thus, the actual expansion around a corrodingreinforcing bar corresponding to a certain level of corrosion can-not be defined. Tests on crack propagation similar to those byWilliamson and Clark ?2000?, when pressure acting on concrete isknown, have not been performed. Therefore, in the case of crackpropagation the model can be validated only qualitatively. Forthis purpose results of the accelerated corrosion tests described inthe previous section have been used.Fig. 4 shows a photo of a RC slab from the tests with cracksformed around corroded reinforcing bars. Corrosion-inducedcracking around the corner bar ?Fig. 4, left? and the middle bar oftheslabwassimulatedusingthesameFEmodel?150?150 mm concrete section of the upper part of the slab with anembedded 16 mm diameter reinforcing bar and 25 mm concretecover, see Fig. 5? but with different boundary conditions. For thecorner bar horizontal constraints were introduced along the rightedge of the section, while for the middle baralong both rightand left edges ?see Fig. 5?. All the degrees of freedom were re-stricted at the bottom edge of the section for both reinforcingbars. Similar FE models have been used further in the study toinvestigate crack initiation and propagation.Results of the nonlinear FE analysis are shown in Fig. 5 fordifferent stages of expansion around the reinforcing bars ?num-bers 13 indicate the order of increase in the expansion?. As canbe seen, initially vertical cracks appear in the concrete cover,followed by the formation of a horizontal crack between the re-inforcing bars and delamination of the concrete cover. There is agood agreement between the crack formation and propagation0246810123.6c/d=0.5, testc/d=0.5, FEAc/d=1, testc/d=1, FEAFailure pressure (MPa)Concrete tensile strength (MPa)(a)024681012c/d=0.5, testc/d=0.5, FEAc/d=1, testc/d=1, FEAFailure pressure (MPa)Concrete tensile strength (MPa)(b)Fig. 3. Comparison of results of finite-element analysis with testresults from Williamson and Clark ?2000?: ?a? d=8 mm; ?b? d=16 mmFig. 4. Crack pattern observed from accelerated corrosion test380 / JOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2009Downloaded 16 Mar 2009 to 04. Redistribution subject to ASCE license or copyright; see /copyrightobtained by the analysis ?Fig. 5? and those observed in the realslab ?Fig. 4?. It should be noted that closing of the vertical cracksat the last stage of the analysis ?Stage 3 in Fig. 5? is due to a sharpdrop after delamination ?i.e., formation of a horizontal crack? intensile stresses in the direction normal to the cracks. However, inthe model cracks are irrecoverable, i.e., the vertical cracks afterbeing formed ?Stage 1 in Fig. 5? remain there throughout the restof the analysis.Results of AnalysisEstimation of Amount ofCorrosion Products Penetrating into ConcretePores and CracksCrack InitiationThere is sufficient experimental evidence that part of the rustforming in the process of corrosion of reinforcing steel in con-crete penetrates into the concrete pores and ?micro?cracks ?Liuand Weyers 1998; Vu et al. 2005?. This part of the corrosionproducts does not contribute to pressure buildup between corrod-ing reinforcement and concrete and, therefore, should be excludedfrom analysis of cracking of the concrete cover. It seems that thepenetration of corrosion products into the concrete pores and mi-crocracks is the main reason for discrepancy between analyticalpredictions of the time to crack initiation and the correspondingtest results. Liu and Weyers ?1998? suggested modeling this phe-nomenon by assuming that there was a porous zone around areinforcing bar and corrosion products would not apply any pres-sure to the surrounding concrete until they fully filled this zone.The thickness of the porous zone, ?0, is a governing parameter ofthis model. By adjusting their own model ?a thick-cylinder model,in which the corrosion rate was considered as decreasing withtime? to their test results Liu and Weyers ?1998? estimated that?0=12.5 ?m.In this study ?0has been estimated based on the crack initia-tion test results presented in Table 1?0= ?cr,exp ?cr,FEA= 0.0116icorrtcr,exp?v 1? ?T?Tcrr?5?where ?cr,expand ?cr,FEA=increases in the reinforcing bar radiuscorresponding to the crack initiation from a test result and FEanalysis, respectively; tcr,exp=time of crack initiation from the test?Table 1?; and ?Tcr=increase in temperature needed in the FEanalysis to cause crack initiation. Note that ?cr,expis estimated byEq. ?2? since at the time of the first cracking the corrosion pen-etration is still very small. The analysis is based on icorr=100 ?A/cm2and ?v=2.94 ?Vu et al. 2005?.Values of ?0versus compressive strength of concrete are pre-sented in Fig. 6?a?. As can be seen, the values of ?0obtained inthe analysis are much higher than ?0=12.5 ?m proposed by Liuand Weyers ?1998?. Moreover, it is expected that ?0should de-pend on the concrete porosity and, subsequently, on the water-cement ratio and the concrete compressive strength. Fig. 6?a? doesnot provide clear evidence of such dependence, although the ten-dency of an increase in ?0with increasing concrete strength canbe observed. The latter is unexpected since the concrete porosityshould normally decrease with an increase in the concretestrength. Fig. 6?b? presenting ?0versus the time to crack initiationFig. 5. Sequence of crack propagation from FE analysis0204060801001200102030405060Thickness of porous zone, 0(m)Concrete compressive strength (MPa)Liu and Weyers (1998)(a)(b)0204060801001201400100200300400500Thickness of porous zone, 0(m)Time to crack initiation (hours)Liu and Weyers (1998)Fig. 6. Thickness of porous zone versus: ?a? compressive strength ofconcrete; ?b? time to crack initiationJOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2009 / 381Downloaded 16 Mar 2009 to 04. Redistribution subject to ASCE license or copyright; see /copyrighthelps to explain this result. As can be seen, there is a clear linearrelationship between ?0and the time to crack initiation. Thismeans that corrosion products penetrate into concrete pores andmicrocracks constantly over time before full cracking of the con-crete cover and not only until they fully fill the porous zone ?i.e.,the longer the time to crack initiation the larger the amount ofcorrosion products penetrated?.It should be noted that the effective modulus of elasticity ofconcrete Ec,eff=Ec/?1+?t?, where Ec?tangent modulus of elastic-ity of concrete at 28 days and ?tthe creep coefficient, is used inthe FE analysis for the calculation of crack initiation. Usually, insuch calculations values of ?tare taken for time t=?, e.g., ?t=2 ?Bazant 1979, Bharghava et al. 2006? or ?t=2.35 ?El Maadd-awy and Soudki 2007?. However, in the accelerated corrosiontests considered herein the first cracks appeared within 20 days orless after corrosion initiation. Values of the creep coefficient cor-responding to the times of first cracking given in Table 1 havebeen estimated in accordance with CEB ?1993? and varied be-tween 0.22 and 0.36. Their influence on the values of ?0is insig-nificant ?the difference between the values of ?0calculated usingEcand Ec,effis less than 10%?.Crack PropagationThe explicit solution scheme used with the elastic cracking modelof concrete ?described in the previous section and employed toinvestigate crack initiation? requires extensive computationaltime. Compared with crack initiation analysis, the computationaltime for studying crack propagation increases dramatically due toa significant increase in a number of steps in an explicit solutionsince in this case the analysis has to proceed far beyond the pointof crack initiation. In order to reduce the computational time twoalternate models have been employed to describe the behavior ofconcrete. One of them is the “concrete smeared cracking model”provided by ABAQUS, which can be used with an implicit solu-tion scheme. The other is a linear elastic model with a verticalcrack introduced in the concrete cover above a corroding reinforc-ing bar ?i.e., linear elastic analysis?. A comparison of results ob-tained from these three models for a reinforcing bar at the side ofa RC slab is shown in Fig. 7. As can be seen, values of the crackwidth obtained using these three models are quite close ?note thatonly values of the crack width above 0.05 mm are of interestsince this value is defined as crack initiation in the acceleratedcorrosion tests?. This means that crack propagation can be accu-rately estimated by using the computationally efficient linear elas-tic model with an initially introduced crack.The results in Fig. 7 also indicate that the estimation of crackpropagation ?i.e., opening of the crack width as corrosionprogresses? using FE analysis almost does not depend on the con-stitutive model of concrete employed in the analysis so that themain cause of the discrepancy between results of FE analysis andtests is the penetration of corrosion products into cracks. Thus, inorder to correctly predict crack propagation it is essential to knowthe amount of corrosion products penetrating into cracks, Vr,cr,which will be expressed in terms of the volume of the corrosionproducts. A value of Vr,cris estimated as the difference betweenthe volume of corrosion products in a test, Vr,exp, corresponding toa crack width on the concrete surface of ws?shown in Fig. 2? andthat obtained from FE analysis, Vr,FEA?see Fig. 8?, i.e.Vr,cr= Vr,exp Vr,FEA?6?The FE analysis is also used to predict the volume of cracking Vcr,defined as the product of the area of the main crack measuredfrom the surface of a corroding reinforcing bar to the concretesurface ?Acrsee Fig. 9? and the crack length along the length ofthe bar, lcr. The contribution of other cracks which may formaround the reinforcing bar is neglected. It is assumed that thecross-sectional area of a crack Acrhas a form of trapezium ?Fig.9?, which remains constant over length lcr, so thatVcr= Acrlcr=c2?wb+ ws?lcr?7?where wb=crack width near the surface of a reinforcing bar. Sinceonly crack widths on the concrete surface were measured in thetests, wbwas obtained from FE analysis as a value of the crackwidth near the reinforcing bar surface corresponding to a consid-ered value of ws. Values of Vr,expand Vr,FEAcan be estimated asVr,exp= ?lcr?r + ?exp?2 ?r pcorr,exp?2?8?Vr,FEA= ?lcr?r + ?FEA?2 ?r pcorr,FEA?2?9?where ?exp, pcorr,exp, and ?FEAare calculated using Eqs. ?1?, ?3?,and ?4?, respectively, while pcorr,FEAis found from Eq.?1? when?=?FEA. Since in this study crack propagation is investigatedusing 2D ?plain strain formulation? in the following lcris treatedas a unit length.Results of the analysis for slab specimens from the tests arepresented separately for 25 and 50 mm covers in Figs. 10 and 11,respectively. Note that the curves shown in Figs. 10 and 11 have00.050.10.15020406080100explicitimplicitelasticCrack width (mm)Time since corrosion initiation (hours)Fig. 7. Crack widthcomparison of results obtained with differentFE modelsVr,expVr,FEAVr,crExperimentalFEAwsCrack widthVolume of corrosion productsFig. 8. Evaluation of amount of corrosion products inside cracks382 / JOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2009Downloaded 16 Mar 2009 to 04. Redistribution subject to ASCE license or copyright; see /copyrightbeen estimated at discrete points based on the test results ?asfollows from Eqs. ?6?9? values of Vr,cr, Vcrdepend directly onthe experimentally measured crack widths given in Fig. 2? andsince these results are not smooth ?Fig. 2? the curves in Figs. 10and 11 are not smooth as well ?actually, this nonsmoothness iseven amplified at the small values of Vcrwhen the ratio ?Vr,crVr,0?/Vcris estimated, see Figs. 10?c? and 11?c?.The curves in Figs. 10 and 11 start from the point correspond-ing to crack initiation, i.e., from a value of the corrosion penetra-tion corresponding to the appearance on the slab surface of acrack with width ws=0.05 mm ?this was defined in the tests ascrack initiation?. The value of Vr,crgiven by Eq. ?6?, which cor-responds to this point, is denoted as Vr,0and represents the vol-ume of corrosion products penetrated into concrete pores andcracks at the time of crack initiation, i.e., the volume of the po-rous zone around a reinforcing bar. Immediately after crack ini-tiation, Figs. 10?b? and 11?b? show that the crack volume, Vcr, issmaller than Vr,0?see Figs. 10?a? and 11?a?. Thus, if at this mo-ment the corrosion products exceed the crack volume then somecorrosion products should appear on the concrete surface aroundthe crack ?they cannot be contained within the crack since theirvolume is greater than that of the crack?. However, rust stains onthe concrete surface were not observed by Vu et al. ?2005? in theirexperiments immediately after crack initiation. Therefore, it canbe assumed that the corrosion products at the time of crack ini-tiation ?Vr,0? penetrate mainly into the pores and microcracksaround the corroding reinforcing bar and not into the newlyformed crack. This means that it would be more correct to esti-mate the volume of corrosion products penetrating into cracks as?Vr,crVr,0?.The ratio of the volume of corrosion products penetrating intocracksaftercrackinitiationtothevolumeofcracks,?Vr,crVr,0?/Vcr, is shown in Figs. 10?c? and 11?c?. As can be seen,corrosion products fill cracks gradually over time. As the ratio?Vr,crVr,0?/Vcrexceeds unity rust stains should appear on theslab surface, which was observed in the tests of RC slabs with25 mm concrete cover. According to the results in Figs. 10?c? and11?c? this ratio exceeds unity only for the specimens SI?1 andSII?4; in other cases the cracks have not been fully filled bycorrosion products. Moreover, since the area of a crack increaseswith an increase in the thickness of the concrete cover ?compareFigs. 10?b? and 11?b?, the fraction of cracks filled by corrosionproducts in the slabs with 50 mm concrete cover is approximately50% smaller than in the slabs with 25 mm cover ?see Figs. 10?c?and 11?c?.As has been noted previously, up until now it has been as-wscwbCrack areaAcrReinforcing barConcrete surfaceFig. 9. Crack area definition(a)(b)(c)0102030405000.40.5SI_1SI_3SII_2SII_4Volume of rust in cracks, Vr,cr(mm3)Corrosion penetration, pcorr,exp(mm)0102030405000.40.5SI_1SI_3SII_2SII_4Volume of cracks, Vcr(mm3)Corrosion penetration, pcorr,exp(mm)00.800.40.5SI_1SI_3SII_2SII_4Ratio (Vr,cr- Vr,0)/VcrCorrosion penetration, pcorr,exp(mm)Fig. 10. Results on penetration of corrosion products into cracks forRC slabs with 25 mm concrete cover(a)(b)0102030405000.40.5SI_2SI_4SII_1SII_3Volume of rust in cracks, Vr,cr(mm3)Corrosion penetration, pcorr,exp(mm)0102030405000.40.5SI_2SI_4SII_1SII_3Volume of cracks, Vcr(mm3)Corrosion penetration, pcorr,exp(mm)(c)00.800.40.5SI_2SI_4SII_1SII_3Ratio (Vr,cr- Vr,0)/VcrCorrosion penetration, pcorr,exp(mm)Fig. 11. Results on penetration of corrosion products into cracks forRC slabs with 50 mm concrete coverJOURNAL OF STRUCTURAL ENGINEERING ASCE / APRIL 2009 / 383Downloaded 16 Mar 2009 to 04. Redistribution subject to ASCE license or copyright; see /copyrightsumed that corrosion products fully fill a crack immediately afterits initiation ?Molina et al. 1993; Berra et al. 2003; Thoft-Christensen 2005?. The results obtained in this study ?Figs. 10and 11? indicate that this assumption may be incorrect and resultin overestimation of the amount of corrosion products penetratinginto corrosion-induced cracks. This, in turn, may lead to underes-timation of the predicted crack width. The error will increase withan increase in the thickness of the concrete cover.ConclusionsIn the paper crack initiation and propagation in RC structures dueto corrosion of reinforcing steel have been investigated using non-linear FE analysis. Initially, the FE model has been briefly de-scribed and then verified against available experimental data. Themodel has been employed to estimate the amount of corrosionproducts penetrating into concrete pores and cracks and, there-fore, not contributing to crack initiation and propagation. Accord-ing to the results of this research, the amount of corrosionproducts penetrating into the concrete pores before crack initia-tion is larger than that obtained by other researchers. Moreover, itis expected that this amount should depend on the concrete po-rosity and, subsequently, on the water-cement ratio and the con-crete compressive strength, which has not been confirmed by theresults obtained. It has also been shown that corrosion-productsdo not fully fill corrosion-induced cracks in concrete immediatelyafter their initiation. The cracks are being filled gradually overtime and the thicker the concrete cover the longer it will take tofully fill a crack. These preliminary results indicate that furtherresearch, and especially experimental research, is needed.AcknowledgmentsThis research was supported by the Fund for the Promotion ofResearch at the Technion. The support of the Australian ResearchCouncil is also gratefully acknowledged.NotationThe following symbols are used in this paper:Acr? cross-sectional area of corrosion-inducedcrack;c ? thickness of concrete cover;d ? diameter of reinforcing bar;Ec? modulus of elasticity of concrete at 28 days;Ec,ef? effective modulus of elasticity of concrete;icorr? corrosion current density;lcr? crack length along length of reinforcing bar;pcorr? corrosion penetration;pcorr,exp? corrosion penetration corresponding to givencrack width from test;pcorr,FEA? corrosion penetration corresponding to givencrack width from FE analysis;r ? radius of reinforcing bar;t ? time since corrosion initiation;tcr,exp? time of crack initiation from test;Vcr? volume of corrosion-induced crack;Vr,cr? volume of corrosion products penetrated intocracks;Vr,exp? volume of corrosion products correspondingto given crack width from test;Vr,FEA? volume of corrosion products correspondingto given crack width from FE analysis;Vr,0? volume of corrosion products in concretepores at crack initiation;wb? crack width near surface of reinforcing bar;ws? crack width on concrete surface;?T? coefficient of thermal expansion;?v? volumetric expansion ratio of corrosionproducts;?T ? change of temperature;? ? free corrosion-induced increase in radius ofreinforcing bar;?cr,exp? increase in reinforcing bar radius at crackinitiation from test;?cr,FEA? increase in reinforcing bar radius at crackinitiation from FE analysis;?exp? increase in reinforcing bar radiuscorresponding to given crack width from test;?FEA? increase in reinforcing bar radiuscorresponding to given crack width from FEanalysis;?0? thickness of porous zone; and?t? creep coefficient for concrete.ReferencesAhmed, S. 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